From 428e796788e113383df508d3659ea62c25790baa Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Mon, 19 May 2025 23:17:43 +0200
Subject: [PATCH 01/26] add Bolot 2013 formula for kinetic fract. factor

---
 .../__init__.py                               |  1 +
 .../bolot_et_al_2013.py                       | 46 +++++++++++++++++++
 docs/bibliography.json                        |  3 +-
 3 files changed, 49 insertions(+), 1 deletion(-)
 create mode 100644 PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py b/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py
index cc26e74a89..c91897f53b 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py
@@ -5,3 +5,4 @@
 from PySDM.impl.null_physics_class import Null
 from .jouzel_and_merlivat_1984 import JouzelAndMerlivat1984
 from .craig_gordon import CraigGordon
+from .bolot_et_al_2013 import BolotEtAl2013
diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py b/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py
new file mode 100644
index 0000000000..49e78baf17
--- /dev/null
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py
@@ -0,0 +1,46 @@
+"""
+kinetic fractionation factor from [Bolot et al. 2013](https://doi.org/10.5194/acp-13-7903-2013)
+eq. (1) with subsequent variable definitions on pages 7906 and 7907 and in Appendix (A6, A6).
+In the paper, alpha_kinetic is probably actually alpha_effective
+(contains alpha_equilibrium in numerator).
+q_sat_inf in Bolot eq (A7) is substituted with equivalent form of (1/S * rho_v_inf/rho_[l,i]_inf).
+"""
+
+from .jouzel_and_merlivat_1984 import JouzelAndMerlivat1984
+
+
+class BolotEtAl2013(JouzelAndMerlivat1984):
+    def __init__(self, _):
+        pass
+
+    @staticmethod
+    def transfer_coefficient_liq_to_ice(
+        const,
+        diffusion_ventilation_coefficient,
+        condensed_water_density,
+        # mass_ventilation_coefficient,
+        # heat_ventilation_coefficient,
+        pvs,
+        molar_mass,
+        temperature,
+        relative_humidity,
+        r_dr_dt_assuming_RHeq0,
+    ):  # pylint: disable=too-many-arguments
+        """
+        Temperature is in 'infinity' T_inf;
+        For exact formula from Bolot et al. 2013 use `r_dr_dt` from Mason 1971
+            assuming `RH_eq` equal to zero and putting
+            `K * heat_ventilation_coefficient / mass_ventilation_coefficient`
+            instead of `K`.
+        """
+        return 1 / (
+            r_dr_dt_assuming_RHeq0
+            * condensed_water_density
+            / relative_humidity
+            / diffusion_ventilation_coefficient
+            * (const.R_str * temperature / molar_mass / pvs)
+        )
+
+    @staticmethod
+    def effective_supersaturation(transfer_coefficient_liq_to_ice, relative_humidity):
+        return 1 / (1 - transfer_coefficient_liq_to_ice * (1 - 1 / relative_humidity))
diff --git a/docs/bibliography.json b/docs/bibliography.json
index 505e225906..9c2f246ab3 100644
--- a/docs/bibliography.json
+++ b/docs/bibliography.json
@@ -526,7 +526,8 @@
   "https://doi.org/10.5194/acp-13-7903-2013": {
     "usages": [
       "examples/PySDM_examples/Bolot_et_al_2013/__init__.py",
-      "tests/unit_tests/physics/test_isotope_equilibrium_fractionation_factors.py"
+      "tests/unit_tests/physics/test_isotope_equilibrium_fractionation_factors.py",
+      "PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py"
     ],
     "label": "Bolot et al. 2013 (Atmos. Chem. Phys. 13)",
     "title": "Modelling and interpreting the isotopic composition of water vapour in convective updrafts "

From 41e3acf332691771a582f5241eb28137cdfb7fac Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 4 Jun 2025 15:27:47 +0200
Subject: [PATCH 02/26] clean up functions; add test checking n

---
 PySDM/physics/drop_growth/howell_1949.py      | 12 +++-
 .../bolot_et_al_2013.py                       | 40 +++++--------
 ...t_isotope_kinetic_fractionation_factors.py | 58 +++++++++++++++++++
 3 files changed, 84 insertions(+), 26 deletions(-)

diff --git a/PySDM/physics/drop_growth/howell_1949.py b/PySDM/physics/drop_growth/howell_1949.py
index 617398ff7b..63a29a952d 100644
--- a/PySDM/physics/drop_growth/howell_1949.py
+++ b/PySDM/physics/drop_growth/howell_1949.py
@@ -14,7 +14,17 @@ class Howell1949(Fick):  # pylint: disable=too-few-public-methods
 
     @staticmethod
     def Fk(const, T, K, lv):
-        """thermodynamic term associated with heat conduction"""
+        """Thermodynamic term associated with heat conduction.
+
+        Parameters
+        ----------
+        T
+            Temperature in Kelvins.
+        K
+            Thermal diffusivity with heat ventilation factor.
+        lv
+            Latent heat of evaporation or sublimation.
+        """
         return const.rho_w * lv / T / K * (lv / T / const.Rv)
 
     @staticmethod
diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py b/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py
index 49e78baf17..9f43882272 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py
@@ -14,32 +14,22 @@ def __init__(self, _):
         pass
 
     @staticmethod
-    def transfer_coefficient_liq_to_ice(
-        const,
-        diffusion_ventilation_coefficient,
-        condensed_water_density,
-        # mass_ventilation_coefficient,
-        # heat_ventilation_coefficient,
-        pvs,
-        molar_mass,
-        temperature,
-        relative_humidity,
-        r_dr_dt_assuming_RHeq0,
-    ):  # pylint: disable=too-many-arguments
-        """
-        Temperature is in 'infinity' T_inf;
-        For exact formula from Bolot et al. 2013 use `r_dr_dt` from Mason 1971
-            assuming `RH_eq` equal to zero and putting
-            `K * heat_ventilation_coefficient / mass_ventilation_coefficient`
-            instead of `K`.
+    def transfer_coefficient_liq_to_ice(D, Fk):
+        """eq. (A6) in Bolot.
+
+        Parameters
+        ----------
+        D
+            light isotope diffusion coefficient
+        Fk
+            term associated with heat transfer
+
+        Returns
+        ----------
+        A_li
+            liquid to ice transfer coefficient
         """
-        return 1 / (
-            r_dr_dt_assuming_RHeq0
-            * condensed_water_density
-            / relative_humidity
-            / diffusion_ventilation_coefficient
-            * (const.R_str * temperature / molar_mass / pvs)
-        )
+        return 1 / (1 + D * Fk)
 
     @staticmethod
     def effective_supersaturation(transfer_coefficient_liq_to_ice, relative_humidity):
diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index fa8f0caf61..95386c27d8 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -5,12 +5,15 @@
 import numpy as np
 import pytest
 from matplotlib import pyplot
+from open_atmos_jupyter_utils import show_plot
 
 from PySDM import Formulae
 from PySDM import physics
 from PySDM.physics.dimensional_analysis import DimensionalAnalysis
 from PySDM.physics.isotope_kinetic_fractionation_factors import JouzelAndMerlivat1984
 
+PLOT = False
+
 
 class TestIsotopeKineticFractionationFactors:
     @staticmethod
@@ -114,3 +117,58 @@ def test_fig9_values(temperature_C, saturation, alpha):
 
         # assert
         np.testing.assert_approx_equal(actual=sut, desired=alpha, significant=3)
+
+    @staticmethod
+    @pytest.mark.parametrize("isotope", ("2H", "18O", "17O"))
+    def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(isotope, plot=PLOT):
+        # arrange
+        T = 273
+        RH = np.linspace(0.3, 1)
+        formulae = Formulae(
+            isotope_equilibrium_fractionation_factors="VanHook1968",
+            isotope_diffusivity_ratios="HellmannAndHarvey2020",
+            isotope_kinetic_fractionation_factors="JouzelAndMerlivat1984",
+        )
+        Si = formulae.saturation_vapour_pressure.pvs_ice(T)
+        alpha_eq = getattr(
+            formulae.isotope_equilibrium_fractionation_factors, f"alpha_l_{isotope}"
+        )(T)
+        D_heavy_to_light = getattr(
+            formulae.isotope_diffusivity_ratios, f"ratio_{isotope}_heavy_to_light"
+        )(T)
+        alpha_kin_jm = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(
+            alpha_equilibrium=alpha_eq,
+            saturation_over_ice=Si,
+            diffusivity_ratio_heavy_to_light=D_heavy_to_light,
+        )
+        formulae = Formulae(
+            isotope_equilibrium_fractionation_factors="VanHook1968",
+            isotope_diffusivity_ratios="HellmannAndHarvey2020",
+            isotope_kinetic_fractionation_factors="CraigGordon",
+        )
+        alpha_kin_cg = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(
+            relative_humidity=RH,
+            turbulence_parameter_n=1,
+            delta_diff=alpha_eq - 1,
+            theta=1,
+        )
+
+        # act
+        n = (alpha_kin_jm + 1) / (alpha_kin_cg + 1)
+
+        # plot
+        pyplot.plot(1 - RH, n)
+        pyplot.gca().set(
+            xlabel="1-RH",
+            ylabel="turbulence parameter n",
+        )
+        pyplot.grid()
+
+        if plot:
+            show_plot()
+        else:
+            pyplot.clf()
+
+        # assert
+        np.testing.assert_equal(n > 0.5, True)
+        np.testing.assert_equal(n < 1, True)

From f81c961b8648cc290a0e45b1a7bfdfeaff02ad11 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 4 Jun 2025 16:38:41 +0200
Subject: [PATCH 03/26] remove Bolot formula as it is defined in Jouzel &
 Merlivat

---
 .../__init__.py                               |  1 -
 .../bolot_et_al_2013.py                       | 36 ----------
 .../jouzel_and_merlivat_1984.py               | 69 ++++++++++++++++---
 3 files changed, 58 insertions(+), 48 deletions(-)
 delete mode 100644 PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py b/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py
index 989573ee5c..b3f96b4aa7 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/__init__.py
@@ -4,5 +4,4 @@
 
 from PySDM.impl.null_physics_class import Null
 from .craig_gordon import CraigGordon
-from .bolot_et_al_2013 import BolotEtAl2013
 from .jouzel_and_merlivat_1984 import JouzelAndMerlivat1984
diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py b/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py
deleted file mode 100644
index 9f43882272..0000000000
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py
+++ /dev/null
@@ -1,36 +0,0 @@
-"""
-kinetic fractionation factor from [Bolot et al. 2013](https://doi.org/10.5194/acp-13-7903-2013)
-eq. (1) with subsequent variable definitions on pages 7906 and 7907 and in Appendix (A6, A6).
-In the paper, alpha_kinetic is probably actually alpha_effective
-(contains alpha_equilibrium in numerator).
-q_sat_inf in Bolot eq (A7) is substituted with equivalent form of (1/S * rho_v_inf/rho_[l,i]_inf).
-"""
-
-from .jouzel_and_merlivat_1984 import JouzelAndMerlivat1984
-
-
-class BolotEtAl2013(JouzelAndMerlivat1984):
-    def __init__(self, _):
-        pass
-
-    @staticmethod
-    def transfer_coefficient_liq_to_ice(D, Fk):
-        """eq. (A6) in Bolot.
-
-        Parameters
-        ----------
-        D
-            light isotope diffusion coefficient
-        Fk
-            term associated with heat transfer
-
-        Returns
-        ----------
-        A_li
-            liquid to ice transfer coefficient
-        """
-        return 1 / (1 + D * Fk)
-
-    @staticmethod
-    def effective_supersaturation(transfer_coefficient_liq_to_ice, relative_humidity):
-        return 1 / (1 - transfer_coefficient_liq_to_ice * (1 - 1 / relative_humidity))
diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index 5dd9f9e1bd..a49579247c 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -1,6 +1,8 @@
 """
-kinetic fractionation factor from [Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749)
-(as eq. 3e for n=1 in [Stewart 1975](https://doi.org/10.1029/JC080i009p01133))
+kinetic fractionation factor  for liquid and ice from [Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749),
+as eq. 3e for n=1 in [Stewart 1975](https://doi.org/10.1029/JC080i009p01133)
+and eq. 1 in [Bolot 2013](https://doi.org/10.5194/acp-13-7903-2013),
+where alpha_kinetic is multiplied by alpha equilibrium (eq. 1 defines effective alpha).
 """
 
 
@@ -9,13 +11,58 @@ def __init__(self, _):
         pass
 
     @staticmethod
-    def alpha_kinetic(
-        alpha_equilibrium, saturation_over_ice, diffusivity_ratio_heavy_to_light
-    ):
-        """eq. (11)"""
-        return saturation_over_ice / (
-            alpha_equilibrium
-            / diffusivity_ratio_heavy_to_light
-            * (saturation_over_ice - 1)
-            + 1
+    def alpha_kinetic(alpha_equilibrium, saturation, D_ratio_heavy_to_light):
+        """eq. (11)
+
+        Parameters
+        ----------
+        alpha_equilibrium
+            Equilibrium fractionation factor.
+        saturation
+            Over liquid water or ice.
+        D_ratio_heavy_to_light
+            Diffusivity ratio for heavy to light isotope.
+
+        Returns
+        ----------
+        alpha_kinetic
+            Kinetic fractionation factor for liquid water or ice."""
+        return saturation / (
+            alpha_equilibrium / D_ratio_heavy_to_light * (saturation - 1) + 1
         )
+
+    @staticmethod
+    def transfer_coefficient(D, Fk):
+        """
+        eq. (A4) in Jouzel & Merlivat 1984,
+        eq. (A6) in Bolot 2013.
+
+        Parameters
+        ----------
+        D
+            Diffusion coefficient for light isotope.
+        Fk
+            Term associated with heat transfer.
+
+        Returns
+        ----------
+        Thermal transfer coefficient between water vapour and condensate.
+        """
+        return 1 / (1 + D * Fk)
+
+    @staticmethod
+    def effective_saturation(transfer_coefficient, RH):
+        """
+
+        Parameters
+        ----------
+        transfer_coefficient
+            Thermal transfer coefficient between water vapour and condensate (liquid water or ice).
+        RH
+            Relative humidity.
+
+        Returns
+        ----------
+        Effective vapour saturation over liquid water or ice.
+        """
+        return 1 / (1 - transfer_coefficient * (1 - 1 / RH))

From b0590ca6dadd48f60c2549475e72a5ba8c51b31e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 4 Jun 2025 16:44:33 +0200
Subject: [PATCH 04/26] update signatures

---
 .../jouzel_and_merlivat_1984.py                |  3 ++-
 docs/bibliography.json                         |  4 ++--
 ...st_isotope_kinetic_fractionation_factors.py | 18 ++++++++----------
 3 files changed, 12 insertions(+), 13 deletions(-)

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index a49579247c..8b2a9dbc12 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -1,5 +1,6 @@
 """
-kinetic fractionation factor  for liquid and ice from [Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749),
+kinetic fractionation factor  for liquid and ice from
+[Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749),
 as eq. 3e for n=1 in [Stewart 1975](https://doi.org/10.1029/JC080i009p01133)
 and eq. 1 in [Bolot 2013](https://doi.org/10.5194/acp-13-7903-2013),
 where alpha_kinetic is multiplied by alpha equilibrium (eq. 1 defines effective alpha).
diff --git a/docs/bibliography.json b/docs/bibliography.json
index 5706be1b5c..b757bd31ab 100644
--- a/docs/bibliography.json
+++ b/docs/bibliography.json
@@ -528,8 +528,8 @@
   "https://doi.org/10.5194/acp-13-7903-2013": {
     "usages": [
       "examples/PySDM_examples/Bolot_et_al_2013/__init__.py",
-      "tests/unit_tests/physics/test_isotope_equilibrium_fractionation_factors.py",
-      "PySDM/physics/isotope_kinetic_fractionation_factors/bolot_et_al_2013.py"
+      "PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py",
+      "tests/unit_tests/physics/test_isotope_equilibrium_fractionation_factors.py"
     ],
     "label": "Bolot et al. 2013 (Atmos. Chem. Phys. 13)",
     "title": "Modelling and interpreting the isotopic composition of water vapour in convective updrafts "
diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 95386c27d8..80b419885b 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -28,8 +28,8 @@ def test_units():
             # act
             sut = JouzelAndMerlivat1984.alpha_kinetic(
                 alpha_equilibrium=alpha_eq,
-                diffusivity_ratio_heavy_to_light=D_ratio,
-                saturation_over_ice=saturation_over_ice,
+                D_ratio_heavy_to_light=D_ratio,
+                saturation=saturation_over_ice,
             )
 
             # assert
@@ -57,10 +57,8 @@ def test_fig_9_from_jouzel_and_merlivat_1984(plot=False):
         alpha_k = {
             temperature: sut(
                 alpha_equilibrium=alpha_s[temperature],
-                saturation_over_ice=saturation,
-                diffusivity_ratio_heavy_to_light=diffusivity_ratio_heavy_to_light(
-                    temperature
-                ),
+                saturation=saturation,
+                D_ratio_heavy_to_light=diffusivity_ratio_heavy_to_light(temperature),
             )
             for temperature in temperatures
         }
@@ -108,8 +106,8 @@ def test_fig9_values(temperature_C, saturation, alpha):
         alpha_s = formulae.isotope_equilibrium_fractionation_factors.alpha_i_18O(T)
         alpha_k = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(
             alpha_equilibrium=alpha_s,
-            saturation_over_ice=saturation,
-            diffusivity_ratio_heavy_to_light=diffusivity_ratio_18O(T),
+            saturation=saturation,
+            D_ratio_heavy_to_light=diffusivity_ratio_18O(T),
         )
 
         # act
@@ -138,8 +136,8 @@ def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(isotope, plot=PLOT):
         )(T)
         alpha_kin_jm = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(
             alpha_equilibrium=alpha_eq,
-            saturation_over_ice=Si,
-            diffusivity_ratio_heavy_to_light=D_heavy_to_light,
+            saturation=Si,
+            D_ratio_heavy_to_light=D_heavy_to_light,
         )
         formulae = Formulae(
             isotope_equilibrium_fractionation_factors="VanHook1968",

From f66f3cf22e69740d18b6e6c07bcd3b56c326890c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 4 Jun 2025 17:10:55 +0200
Subject: [PATCH 05/26] add units tests

---
 ...t_isotope_kinetic_fractionation_factors.py | 39 ++++++++++++++++---
 1 file changed, 34 insertions(+), 5 deletions(-)

diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 80b419885b..f2cb0e4541 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -17,7 +17,7 @@
 
 class TestIsotopeKineticFractionationFactors:
     @staticmethod
-    def test_units():
+    def test_units_alpha_kinetic():
         """checks that alphas are dimensionless"""
         with DimensionalAnalysis():
             # arrange
@@ -35,6 +35,34 @@ def test_units():
             # assert
             assert sut.check("[]")
 
+    @staticmethod
+    def test_units_transfer_coefficient():
+        with DimensionalAnalysis():
+            # arrange
+            D = 1 * physics.si.m**2 / physics.si.s
+            Fk = 1 * physics.si.s / physics.si.m**2
+
+            # act
+            sut = JouzelAndMerlivat1984.transfer_coefficient(D=D, Fk=Fk)
+
+            # assert
+            assert sut.check("[]")
+
+    @staticmethod
+    def test_units_eff_saturation():
+        with DimensionalAnalysis():
+            # arrange
+            transfer_coeff = 1 * physics.si.dimensionless
+            relative_humidity = 1 * physics.si.dimensionless
+
+            # act
+            sut = JouzelAndMerlivat1984.effective_saturation(
+                transfer_coefficient=transfer_coeff, RH=relative_humidity
+            )
+
+            # assert
+            assert sut.check("[]")
+
     @staticmethod
     def test_fig_9_from_jouzel_and_merlivat_1984(plot=False):
         """[Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749)"""
@@ -118,9 +146,12 @@ def test_fig9_values(temperature_C, saturation, alpha):
 
     @staticmethod
     @pytest.mark.parametrize("isotope", ("2H", "18O", "17O"))
-    def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(isotope, plot=PLOT):
+    @pytest.mark.parametrize("temperature_C", (-30, -20, -1))
+    def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(
+        isotope, temperature_C, plot=PLOT
+    ):
         # arrange
-        T = 273
+        T = Formulae().trivia.C2K(temperature_C)
         RH = np.linspace(0.3, 1)
         formulae = Formulae(
             isotope_equilibrium_fractionation_factors="VanHook1968",
@@ -140,8 +171,6 @@ def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(isotope, plot=PLOT):
             D_ratio_heavy_to_light=D_heavy_to_light,
         )
         formulae = Formulae(
-            isotope_equilibrium_fractionation_factors="VanHook1968",
-            isotope_diffusivity_ratios="HellmannAndHarvey2020",
             isotope_kinetic_fractionation_factors="CraigGordon",
         )
         alpha_kin_cg = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(

From 1bf0b8cf31a069fcb8d9d15a6c226d13a9f5d657 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 4 Jun 2025 23:51:14 +0200
Subject: [PATCH 06/26] after @slayoo review :)

---
 PySDM/physics/drop_growth/howell_1949.py                       | 2 +-
 .../jouzel_and_merlivat_1984.py                                | 3 +--
 examples/PySDM_examples/Fisher_1991/fig_2.ipynb                | 2 +-
 examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb | 2 +-
 .../physics/test_isotope_kinetic_fractionation_factors.py      | 3 +--
 5 files changed, 5 insertions(+), 7 deletions(-)

diff --git a/PySDM/physics/drop_growth/howell_1949.py b/PySDM/physics/drop_growth/howell_1949.py
index 63a29a952d..fb3a1b06a3 100644
--- a/PySDM/physics/drop_growth/howell_1949.py
+++ b/PySDM/physics/drop_growth/howell_1949.py
@@ -19,7 +19,7 @@ def Fk(const, T, K, lv):
         Parameters
         ----------
         T
-            Temperature in Kelvins.
+            Temperature.
         K
             Thermal diffusivity with heat ventilation factor.
         lv
diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index 8b2a9dbc12..ebe731051c 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -1,6 +1,5 @@
 """
-kinetic fractionation factor  for liquid and ice from
-[Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749),
+kinetic fractionation factor [Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749),
 as eq. 3e for n=1 in [Stewart 1975](https://doi.org/10.1029/JC080i009p01133)
 and eq. 1 in [Bolot 2013](https://doi.org/10.5194/acp-13-7903-2013),
 where alpha_kinetic is multiplied by alpha equilibrium (eq. 1 defines effective alpha).
diff --git a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
index 73bb810339..7abe0fae9c 100644
--- a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
+++ b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
@@ -108,7 +108,7 @@
     "    return formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium = alpha_eq[iso](T),\n",
     "        diffusivity_ratio_heavy_to_light=diffusivity_ratio[iso](T),\n",
-    "        saturation_over_ice = ice_saturation_curve_4(const=const, T=T)\n",
+    "        saturation = ice_saturation_curve_4(const=const, T=T)\n",
     "    )"
    ],
    "id": "754af83e4ab216bc",
diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
index 6b30aeef25..94543cf90c 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
@@ -158,7 +158,7 @@
     "    alpha_s = formulae.isotope_equilibrium_fractionation_factors.alpha_i_18O(T)\n",
     "    alpha_k = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium=alpha_s,\n",
-    "        saturation_over_ice=Si,\n",
+    "        saturation=Si,\n",
     "        diffusivity_ratio_heavy_to_light=formulae.isotope_diffusivity_ratios.ratio_18O_heavy_to_light(T)\n",
     "    )\n",
     "    alphas_eff[:, i] = alpha_k * alpha_s"
diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index f2cb0e4541..8125a4404d 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -5,7 +5,6 @@
 import numpy as np
 import pytest
 from matplotlib import pyplot
-from open_atmos_jupyter_utils import show_plot
 
 from PySDM import Formulae
 from PySDM import physics
@@ -192,7 +191,7 @@ def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(
         pyplot.grid()
 
         if plot:
-            show_plot()
+            pyplot.show()
         else:
             pyplot.clf()
 

From ec889b8f799a53321d8fb8f08562a3643c4a3b08 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Fri, 6 Jun 2025 13:09:17 +0200
Subject: [PATCH 07/26] refactor

---
 .../PySDM_examples/Fisher_1991/fig_2.ipynb    | 77 +++++++++++++------
 1 file changed, 53 insertions(+), 24 deletions(-)

diff --git a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
index 7abe0fae9c..070698c227 100644
--- a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
+++ b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
@@ -22,8 +22,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:02.863998Z",
-     "start_time": "2025-05-16T15:57:02.859648Z"
+     "end_time": "2025-06-06T05:46:08.614401Z",
+     "start_time": "2025-06-06T05:46:08.610816Z"
     }
    },
    "cell_type": "code",
@@ -43,8 +43,8 @@
    "id": "c36c2f5c-17c1-422e-9ab9-f7d612064199",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:04.803260Z",
-     "start_time": "2025-05-16T15:57:02.868238Z"
+     "end_time": "2025-06-06T05:46:10.345865Z",
+     "start_time": "2025-06-06T05:46:08.619814Z"
     }
    },
    "source": [
@@ -68,8 +68,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:04.920566Z",
-     "start_time": "2025-05-16T15:57:04.898066Z"
+     "end_time": "2025-06-06T05:46:10.431716Z",
+     "start_time": "2025-06-06T05:46:10.411970Z"
     }
    },
    "cell_type": "code",
@@ -98,17 +98,20 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:04.927752Z",
-     "start_time": "2025-05-16T15:57:04.925715Z"
+     "end_time": "2025-06-06T05:46:10.437845Z",
+     "start_time": "2025-06-06T05:46:10.435829Z"
     }
    },
    "cell_type": "code",
    "source": [
     "def alpha_kin(iso, T):\n",
+    "    D = const.D0\n",
+    "    Fk = formulae.drop_growth.Fk(T, const.K0, formulae.latent_heat_vapourisation.lv(T))\n",
+    "    transfer_coefficient = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D, Fk)\n",
     "    return formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium = alpha_eq[iso](T),\n",
-    "        diffusivity_ratio_heavy_to_light=diffusivity_ratio[iso](T),\n",
-    "        saturation = ice_saturation_curve_4(const=const, T=T)\n",
+    "        D_ratio_heavy_to_light=diffusivity_ratio[iso](T),\n",
+    "        saturation = ice_saturation_curve_4(const=const, T=T) #formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient, formulae.saturation_vapour_pressure.pvs_ice(T)) #ice_saturation_curve_4(const=const, T=T)\n",
     "    )"
    ],
    "id": "754af83e4ab216bc",
@@ -118,8 +121,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:04.937527Z",
-     "start_time": "2025-05-16T15:57:04.934227Z"
+     "end_time": "2025-06-06T05:46:10.446894Z",
+     "start_time": "2025-06-06T05:46:10.444780Z"
     }
    },
    "cell_type": "code",
@@ -147,8 +150,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:04.944946Z",
-     "start_time": "2025-05-16T15:57:04.942980Z"
+     "end_time": "2025-06-06T05:46:10.452542Z",
+     "start_time": "2025-06-06T05:46:10.450693Z"
     }
    },
    "cell_type": "code",
@@ -167,8 +170,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:07.414569Z",
-     "start_time": "2025-05-16T15:57:04.949635Z"
+     "end_time": "2025-06-06T05:46:13.268671Z",
+     "start_time": "2025-06-06T05:46:10.456287Z"
     }
    },
    "cell_type": "code",
@@ -193,8 +196,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-16T15:57:07.885751Z",
-     "start_time": "2025-05-16T15:57:07.422220Z"
+     "end_time": "2025-06-06T05:46:13.639419Z",
+     "start_time": "2025-06-06T05:46:13.274832Z"
     }
    },
    "cell_type": "code",
@@ -232,7 +235,7 @@
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ],
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@@ -301,7 +304,7 @@
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        "version_major": 2,
        "version_minor": 0,
-       "model_id": "49d222ee4a414698aacdd4979e00c4f3"
+       "model_id": "507e8628a5284dc195fed85eee0b929d"
       }
      },
      "metadata": {},
@@ -309,6 +312,32 @@
     }
    ],
    "execution_count": 9
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-06T05:46:13.818266Z",
+     "start_time": "2025-06-06T05:46:13.798626Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "",
+   "id": "34e05ba4f6fb8e89",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-06T05:46:13.829695Z",
+     "start_time": "2025-06-06T05:46:13.827998Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "",
+   "id": "ed8d36417a5336d0",
+   "outputs": [],
+   "execution_count": null
   }
  ],
  "metadata": {

From 2ec24269ceff775fb1f39eaf2857c6cafcdadb8c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 25 Jun 2025 14:42:09 +0200
Subject: [PATCH 08/26] rerun notebook

---
 .../PySDM_examples/Fisher_1991/fig_2.ipynb    | 52 +++++++++----------
 1 file changed, 26 insertions(+), 26 deletions(-)

diff --git a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
index 070698c227..be9c6149a8 100644
--- a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
+++ b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
@@ -22,8 +22,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-06T05:46:08.614401Z",
-     "start_time": "2025-06-06T05:46:08.610816Z"
+     "end_time": "2025-06-25T12:41:17.048483Z",
+     "start_time": "2025-06-25T12:41:17.041726Z"
     }
    },
    "cell_type": "code",
@@ -43,8 +43,8 @@
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-     "end_time": "2025-06-06T05:46:10.345865Z",
-     "start_time": "2025-06-06T05:46:08.619814Z"
+     "end_time": "2025-06-25T12:41:21.768860Z",
+     "start_time": "2025-06-25T12:41:17.056517Z"
     }
    },
    "source": [
@@ -68,8 +68,8 @@
   {
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     "ExecuteTime": {
-     "end_time": "2025-06-06T05:46:10.431716Z",
-     "start_time": "2025-06-06T05:46:10.411970Z"
+     "end_time": "2025-06-25T12:41:21.875872Z",
+     "start_time": "2025-06-25T12:41:21.845639Z"
     }
    },
    "cell_type": "code",
@@ -98,8 +98,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-06T05:46:10.437845Z",
-     "start_time": "2025-06-06T05:46:10.435829Z"
+     "end_time": "2025-06-25T12:41:21.884154Z",
+     "start_time": "2025-06-25T12:41:21.881306Z"
     }
    },
    "cell_type": "code",
@@ -121,8 +121,8 @@
   {
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-     "end_time": "2025-06-06T05:46:10.446894Z",
-     "start_time": "2025-06-06T05:46:10.444780Z"
+     "end_time": "2025-06-25T12:41:21.894710Z",
+     "start_time": "2025-06-25T12:41:21.891746Z"
     }
    },
    "cell_type": "code",
@@ -150,8 +150,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-06T05:46:10.452542Z",
-     "start_time": "2025-06-06T05:46:10.450693Z"
+     "end_time": "2025-06-25T12:41:21.901806Z",
+     "start_time": "2025-06-25T12:41:21.899568Z"
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@@ -170,8 +170,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-06T05:46:13.268671Z",
-     "start_time": "2025-06-06T05:46:10.456287Z"
+     "end_time": "2025-06-25T12:41:25.203838Z",
+     "start_time": "2025-06-25T12:41:21.907105Z"
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    },
    "cell_type": "code",
@@ -196,8 +196,8 @@
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-     "end_time": "2025-06-06T05:46:13.639419Z",
-     "start_time": "2025-06-06T05:46:13.274832Z"
+     "end_time": "2025-06-25T12:41:25.731698Z",
+     "start_time": "2025-06-25T12:41:25.217926Z"
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@@ -235,7 +235,7 @@
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@@ -304,7 +304,7 @@
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        "version_major": 2,
        "version_minor": 0,
-       "model_id": "507e8628a5284dc195fed85eee0b929d"
+       "model_id": "dea4782dea4b4c10ac692d809bdbe1c1"
       }
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      "metadata": {},
@@ -316,8 +316,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-06T05:46:13.818266Z",
-     "start_time": "2025-06-06T05:46:13.798626Z"
+     "end_time": "2025-06-25T12:41:25.933336Z",
+     "start_time": "2025-06-25T12:41:25.931149Z"
     }
    },
    "cell_type": "code",
@@ -329,8 +329,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-06T05:46:13.829695Z",
-     "start_time": "2025-06-06T05:46:13.827998Z"
+     "end_time": "2025-06-25T12:41:25.943651Z",
+     "start_time": "2025-06-25T12:41:25.941809Z"
     }
    },
    "cell_type": "code",

From 106f8db855a6cacf806f379a3335f4bcf998c7ef Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 25 Jun 2025 14:55:15 +0200
Subject: [PATCH 09/26] revert adding effective saturation as not used here

---
 .../jouzel_and_merlivat_1984.py                 | 17 -----------------
 examples/PySDM_examples/Fisher_1991/fig_2.ipynb |  3 +--
 ...est_isotope_kinetic_fractionation_factors.py | 15 ---------------
 3 files changed, 1 insertion(+), 34 deletions(-)

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index ebe731051c..5cd2e6ae1f 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -49,20 +49,3 @@ def transfer_coefficient(D, Fk):
         Thermal transfer coefficient between water vapour and condensate.
         """
         return 1 / (1 + D * Fk)
-
-    @staticmethod
-    def effective_saturation(transfer_coefficient, RH):
-        """
-
-        Parameters
-        ----------
-        transfer_coefficient
-            Thermal transfer coefficient between water vapour and condensate (liquid water or ice).
-        RH
-            Relative humidity.
-
-        Returns
-        ----------
-        Effective vapour saturation over liquid water or ice.
-        """
-        return 1 / (1 - transfer_coefficient * (1 - 1 / RH))
diff --git a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
index be9c6149a8..ac7206dd82 100644
--- a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
+++ b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
@@ -107,11 +107,10 @@
     "def alpha_kin(iso, T):\n",
     "    D = const.D0\n",
     "    Fk = formulae.drop_growth.Fk(T, const.K0, formulae.latent_heat_vapourisation.lv(T))\n",
-    "    transfer_coefficient = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D, Fk)\n",
     "    return formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium = alpha_eq[iso](T),\n",
     "        D_ratio_heavy_to_light=diffusivity_ratio[iso](T),\n",
-    "        saturation = ice_saturation_curve_4(const=const, T=T) #formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient, formulae.saturation_vapour_pressure.pvs_ice(T)) #ice_saturation_curve_4(const=const, T=T)\n",
+    "        saturation = ice_saturation_curve_4(const=const, T=T)\n",
     "    )"
    ],
    "id": "754af83e4ab216bc",
diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 8125a4404d..0596c876fc 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -47,21 +47,6 @@ def test_units_transfer_coefficient():
             # assert
             assert sut.check("[]")
 
-    @staticmethod
-    def test_units_eff_saturation():
-        with DimensionalAnalysis():
-            # arrange
-            transfer_coeff = 1 * physics.si.dimensionless
-            relative_humidity = 1 * physics.si.dimensionless
-
-            # act
-            sut = JouzelAndMerlivat1984.effective_saturation(
-                transfer_coefficient=transfer_coeff, RH=relative_humidity
-            )
-
-            # assert
-            assert sut.check("[]")
-
     @staticmethod
     def test_fig_9_from_jouzel_and_merlivat_1984(plot=False):
         """[Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749)"""

From b50b61865b783116b27d43d7be1a48bf76633076 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 25 Jun 2025 21:36:42 +0200
Subject: [PATCH 10/26] remove unused variables

---
 examples/PySDM_examples/Fisher_1991/fig_2.ipynb | 2 --
 1 file changed, 2 deletions(-)

diff --git a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
index ac7206dd82..6ebee29c8b 100644
--- a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
+++ b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
@@ -105,8 +105,6 @@
    "cell_type": "code",
    "source": [
     "def alpha_kin(iso, T):\n",
-    "    D = const.D0\n",
-    "    Fk = formulae.drop_growth.Fk(T, const.K0, formulae.latent_heat_vapourisation.lv(T))\n",
     "    return formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium = alpha_eq[iso](T),\n",
     "        D_ratio_heavy_to_light=diffusivity_ratio[iso](T),\n",

From b98187da7f8ce972adc79a1f50ba2910995a26f6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 26 Jun 2025 01:26:00 +0200
Subject: [PATCH 11/26] refactor variable name

---
 .../Jouzel_and_Merlivat_1984/fig_8_9.ipynb    | 42 +++++++++----------
 1 file changed, 21 insertions(+), 21 deletions(-)

diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
index 94543cf90c..7baee37250 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
@@ -22,8 +22,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-15T17:06:23.997785Z",
-     "start_time": "2025-05-15T17:06:23.992595Z"
+     "end_time": "2025-06-25T23:25:40.862379Z",
+     "start_time": "2025-06-25T23:25:40.859115Z"
     }
    },
    "cell_type": "code",
@@ -44,8 +44,8 @@
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2025-05-15T17:06:26.070690Z",
-     "start_time": "2025-05-15T17:06:24.024797Z"
+     "end_time": "2025-06-25T23:25:42.736860Z",
+     "start_time": "2025-06-25T23:25:40.951437Z"
     }
    },
    "source": [
@@ -62,8 +62,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-15T17:06:26.537352Z",
-     "start_time": "2025-05-15T17:06:26.155905Z"
+     "end_time": "2025-06-25T23:25:43.030796Z",
+     "start_time": "2025-06-25T23:25:42.742196Z"
     }
    },
    "cell_type": "code",
@@ -88,8 +88,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-15T17:06:28.504366Z",
-     "start_time": "2025-05-15T17:06:26.549958Z"
+     "end_time": "2025-06-25T23:25:44.982409Z",
+     "start_time": "2025-06-25T23:25:43.041753Z"
     }
    },
    "cell_type": "code",
@@ -120,7 +120,7 @@
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ],
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@@ -133,7 +133,7 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "ba46c750ca244844a1be1b2659613866"
+       "model_id": "8c15bde98c9c4698979a4cb47ad75d48"
       }
      },
      "metadata": {},
@@ -145,8 +145,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-15T17:06:29.307012Z",
-     "start_time": "2025-05-15T17:06:28.519678Z"
+     "end_time": "2025-06-25T23:25:45.731460Z",
+     "start_time": "2025-06-25T23:25:44.995396Z"
     }
    },
    "cell_type": "code",
@@ -159,19 +159,19 @@
     "    alpha_k = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium=alpha_s,\n",
     "        saturation=Si,\n",
-    "        diffusivity_ratio_heavy_to_light=formulae.isotope_diffusivity_ratios.ratio_18O_heavy_to_light(T)\n",
+    "        D_ratio_heavy_to_light=formulae.isotope_diffusivity_ratios.ratio_18O_heavy_to_light(T)\n",
     "    )\n",
     "    alphas_eff[:, i] = alpha_k * alpha_s"
    ],
-   "id": "bfc8afbd66b88f32",
+   "id": "1a7e5ae0c7093428",
    "outputs": [],
    "execution_count": 5
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-15T17:06:29.540790Z",
-     "start_time": "2025-05-15T17:06:29.320601Z"
+     "end_time": "2025-06-25T23:25:45.959914Z",
+     "start_time": "2025-06-25T23:25:45.739364Z"
     }
    },
    "cell_type": "code",
@@ -193,14 +193,14 @@
     "pyplot.legend()\n",
     "show_plot('fig_9')"
    ],
-   "id": "c13c409d4d6f6360",
+   "id": "8b1287b4696c7dda",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
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@@ -213,7 +213,7 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "b58a64bd5bb740b8a1a80b60dc0f27a0"
+       "model_id": "a478d96b93d34ed2936063de54732783"
       }
      },
      "metadata": {},
@@ -225,8 +225,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-05-15T17:06:29.554379Z",
-     "start_time": "2025-05-15T17:06:29.551542Z"
+     "end_time": "2025-06-25T23:25:45.972541Z",
+     "start_time": "2025-06-25T23:25:45.970842Z"
     }
    },
    "cell_type": "code",

From 40267200320e752f20246a03102fd0c5eb3be4e1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 26 Jun 2025 01:28:26 +0200
Subject: [PATCH 12/26] remove unused function as will be addressed in new PR

---
 .../jouzel_and_merlivat_1984.py               | 19 -------------------
 ...t_isotope_kinetic_fractionation_factors.py | 13 -------------
 2 files changed, 32 deletions(-)

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index 5cd2e6ae1f..f17186751d 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -30,22 +30,3 @@ def alpha_kinetic(alpha_equilibrium, saturation, D_ratio_heavy_to_light):
         return saturation / (
             alpha_equilibrium / D_ratio_heavy_to_light * (saturation - 1) + 1
         )
-
-    @staticmethod
-    def transfer_coefficient(D, Fk):
-        """
-        eq. (A4) in Jouzel & Merlivat 1984,
-        eq. (A6) in Bolot 2013.
-
-        Parameters
-        ----------
-        D
-            Diffusion coefficient for light isotope.
-        Fk
-            Term associated with heat transfer.
-
-        Returns
-        ----------
-        Thermal transfer coefficient between water vapour and condensate.
-        """
-        return 1 / (1 + D * Fk)
diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 0596c876fc..84feeb7ed4 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -34,19 +34,6 @@ def test_units_alpha_kinetic():
             # assert
             assert sut.check("[]")
 
-    @staticmethod
-    def test_units_transfer_coefficient():
-        with DimensionalAnalysis():
-            # arrange
-            D = 1 * physics.si.m**2 / physics.si.s
-            Fk = 1 * physics.si.s / physics.si.m**2
-
-            # act
-            sut = JouzelAndMerlivat1984.transfer_coefficient(D=D, Fk=Fk)
-
-            # assert
-            assert sut.check("[]")
-
     @staticmethod
     def test_fig_9_from_jouzel_and_merlivat_1984(plot=False):
         """[Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749)"""

From b443915482bc42f1f150e8b998877e054ca42ddf Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 26 Jun 2025 09:21:19 +0200
Subject: [PATCH 13/26] add effective saturation

---
 .../jouzel_and_merlivat_1984.py               |  36 +++++
 .../PySDM_examples/Fisher_1991/fig_2.ipynb    | 125 +++++++++---------
 ...t_isotope_kinetic_fractionation_factors.py |  13 ++
 3 files changed, 112 insertions(+), 62 deletions(-)

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index f17186751d..ebe731051c 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -30,3 +30,39 @@ def alpha_kinetic(alpha_equilibrium, saturation, D_ratio_heavy_to_light):
         return saturation / (
             alpha_equilibrium / D_ratio_heavy_to_light * (saturation - 1) + 1
         )
+
+    @staticmethod
+    def transfer_coefficient(D, Fk):
+        """
+        eq. (A4) in Jouzel & Merlivat 1984,
+        eq. (A6) in Bolot 2013.
+
+        Parameters
+        ----------
+        D
+            Diffusion coefficient for light isotope.
+        Fk
+            Term associated with heat transfer.
+
+        Returns
+        ----------
+        Thermal transfer coefficient between water vapour and condensate.
+        """
+        return 1 / (1 + D * Fk)
+
+    @staticmethod
+    def effective_saturation(transfer_coefficient, RH):
+        """
+
+        Parameters
+        ----------
+        transfer_coefficient
+            Thermal transfer coefficient between water vapour and condensate (liquid water or ice).
+        RH
+            Relative humidity.
+
+        Returns
+        ----------
+        Effective vapour saturation over liquid water or ice.
+        """
+        return 1 / (1 - transfer_coefficient * (1 - 1 / RH))
diff --git a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
index 6ebee29c8b..6327574c20 100644
--- a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
+++ b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
@@ -22,8 +22,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:17.048483Z",
-     "start_time": "2025-06-25T12:41:17.041726Z"
+     "end_time": "2025-06-26T00:01:47.406303Z",
+     "start_time": "2025-06-26T00:01:47.403017Z"
     }
    },
    "cell_type": "code",
@@ -36,15 +36,15 @@
    ],
    "id": "31481014375c7d36",
    "outputs": [],
-   "execution_count": 1
+   "execution_count": 21
   },
   {
    "cell_type": "code",
    "id": "c36c2f5c-17c1-422e-9ab9-f7d612064199",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:21.768860Z",
-     "start_time": "2025-06-25T12:41:17.056517Z"
+     "end_time": "2025-06-26T00:01:47.416649Z",
+     "start_time": "2025-06-26T00:01:47.414494Z"
     }
    },
    "source": [
@@ -63,13 +63,13 @@
     ")"
    ],
    "outputs": [],
-   "execution_count": 2
+   "execution_count": 22
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:21.875872Z",
-     "start_time": "2025-06-25T12:41:21.845639Z"
+     "end_time": "2025-06-26T00:07:51.434963Z",
+     "start_time": "2025-06-26T00:07:51.358744Z"
     }
    },
    "cell_type": "code",
@@ -91,18 +91,27 @@
     "    alpha_eq[isotope] = getattr(formulae.isotope_equilibrium_fractionation_factors, f'alpha_i_{isotope}')\n",
     "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
    ],
-   "id": "91bb290498429f53",
-   "outputs": [],
-   "execution_count": 3
+   "id": "92e11666a7b83d4d",
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'Formulae' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
+      "\u001B[0;31mNameError\u001B[0m                                 Traceback (most recent call last)",
+      "Cell \u001B[0;32mIn[1], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m formulae\u001B[38;5;241m=\u001B[39m \u001B[43mFormulae\u001B[49m(\n\u001B[1;32m      2\u001B[0m     isotope_meteoric_water_line\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mDansgaard1964\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      3\u001B[0m     isotope_diffusivity_ratios\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mStewart1975\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      4\u001B[0m     isotope_kinetic_fractionation_factors\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mJouzelAndMerlivat1984\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      5\u001B[0m     isotope_equilibrium_fractionation_factors\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mMerlivatAndNief1967+Majoube1970\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      6\u001B[0m )\n\u001B[1;32m      7\u001B[0m const \u001B[38;5;241m=\u001B[39m formulae\u001B[38;5;241m.\u001B[39mconstants\n\u001B[1;32m      8\u001B[0m K2C \u001B[38;5;241m=\u001B[39m formulae\u001B[38;5;241m.\u001B[39mtrivia\u001B[38;5;241m.\u001B[39mK2C\n",
+      "\u001B[0;31mNameError\u001B[0m: name 'Formulae' is not defined"
+     ]
+    }
+   ],
+   "execution_count": 1
   },
   {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:21.884154Z",
-     "start_time": "2025-06-25T12:41:21.881306Z"
-    }
-   },
+   "metadata": {},
    "cell_type": "code",
+   "outputs": [],
+   "execution_count": null,
    "source": [
     "def alpha_kin(iso, T):\n",
     "    return formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
@@ -111,15 +120,13 @@
     "        saturation = ice_saturation_curve_4(const=const, T=T)\n",
     "    )"
    ],
-   "id": "754af83e4ab216bc",
-   "outputs": [],
-   "execution_count": 4
+   "id": "cd4693f604f74961"
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:21.894710Z",
-     "start_time": "2025-06-25T12:41:21.891746Z"
+     "end_time": "2025-06-26T00:06:26.448958Z",
+     "start_time": "2025-06-26T00:06:26.443863Z"
     }
    },
    "cell_type": "code",
@@ -142,13 +149,13 @@
    ],
    "id": "9ca4e3256065274b",
    "outputs": [],
-   "execution_count": 5
+   "execution_count": 37
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:21.901806Z",
-     "start_time": "2025-06-25T12:41:21.899568Z"
+     "end_time": "2025-06-26T00:06:26.830205Z",
+     "start_time": "2025-06-26T00:06:26.825441Z"
     }
    },
    "cell_type": "code",
@@ -160,15 +167,15 @@
     "y_e = 0\n",
     "yf = partial(vapour_mixing_ratio, formulae)\n"
    ],
-   "id": "71979cfe7348344d",
+   "id": "7bce3bc5674ae8cb",
    "outputs": [],
-   "execution_count": 6
+   "execution_count": 38
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:25.203838Z",
-     "start_time": "2025-06-25T12:41:21.907105Z"
+     "end_time": "2025-06-26T00:06:27.188718Z",
+     "start_time": "2025-06-26T00:06:27.181208Z"
     }
    },
    "cell_type": "code",
@@ -180,21 +187,17 @@
     "    t_eval=temperature\n",
     ")\n",
     "assert result.success, result.message\n",
-    "delta_2H, delta_18O = result.y\n",
-    "d_excess = formulae.isotope_meteoric_water_line.excess_d(\n",
-    "    delta_2H=delta_2H,\n",
-    "    delta_18O=delta_18O\n",
-    ")"
+    "delta_2H, delta_18O = result.y\n"
    ],
-   "id": "4e112378083e50f5",
+   "id": "200252902b10ccb6",
    "outputs": [],
-   "execution_count": 7
+   "execution_count": 39
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:25.731698Z",
-     "start_time": "2025-06-25T12:41:25.217926Z"
+     "end_time": "2025-06-26T00:06:27.846799Z",
+     "start_time": "2025-06-26T00:06:27.548756Z"
     }
    },
    "cell_type": "code",
@@ -225,14 +228,14 @@
     "pyplot.legend()\n",
     "show_plot(\"fig_1\")"
    ],
-   "id": "153a6e26bc2be38a",
+   "id": "262ff6a72a6d27ec",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ],
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      "metadata": {},
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@@ -245,27 +248,30 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "d85508aab73e4fbc91cf47f982b6d8a7"
+       "model_id": "c198c7cc9c674242806e574bcdb7f519"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 8
+   "execution_count": 40
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:25.918505Z",
-     "start_time": "2025-06-25T12:41:25.743022Z"
+     "end_time": "2025-06-26T00:06:28.750924Z",
+     "start_time": "2025-06-26T00:06:28.600727Z"
     }
    },
    "cell_type": "code",
    "source": [
     "d_excess_from_fig2 = np.array((10, 8, 7, 6.8, 6, 5.3, 4, 2.5, 0)) * PER_MILLE\n",
     "T_from_fig2 = np.linspace(-50, -10, n_points)\n",
-    "\n",
+    "d_excess = formulae.isotope_meteoric_water_line.excess_d(\n",
+    "    delta_2H=delta_2H,\n",
+    "    delta_18O=delta_18O\n",
+    ")\n",
     "\n",
     "pyplot.plot(\n",
     "    K2C(temperature[::-1]),\n",
@@ -281,14 +287,14 @@
     "pyplot.legend()\n",
     "show_plot(\"fig_2\")"
    ],
-   "id": "571d258dc7dea96f",
+   "id": "2cf7385894279338",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
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@@ -301,40 +307,35 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "dea4782dea4b4c10ac692d809bdbe1c1"
+       "model_id": "e15f8309dda943039c51bdf321ca7e1d"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 9
+   "execution_count": 41
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:25.933336Z",
-     "start_time": "2025-06-25T12:41:25.931149Z"
+     "end_time": "2025-06-26T00:01:47.815828Z",
+     "start_time": "2025-06-26T00:01:47.813196Z"
     }
    },
    "cell_type": "code",
-   "source": "",
-   "id": "34e05ba4f6fb8e89",
    "outputs": [],
+   "source": "",
+   "id": "56c93f096262f1bd",
    "execution_count": null
   },
   {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-25T12:41:25.943651Z",
-     "start_time": "2025-06-25T12:41:25.941809Z"
-    }
-   },
+   "metadata": {},
    "cell_type": "code",
-   "source": "",
-   "id": "ed8d36417a5336d0",
    "outputs": [],
-   "execution_count": null
+   "execution_count": null,
+   "source": "",
+   "id": "e77f759f327ff7ac"
   }
  ],
  "metadata": {
diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 84feeb7ed4..0596c876fc 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -34,6 +34,19 @@ def test_units_alpha_kinetic():
             # assert
             assert sut.check("[]")
 
+    @staticmethod
+    def test_units_transfer_coefficient():
+        with DimensionalAnalysis():
+            # arrange
+            D = 1 * physics.si.m**2 / physics.si.s
+            Fk = 1 * physics.si.s / physics.si.m**2
+
+            # act
+            sut = JouzelAndMerlivat1984.transfer_coefficient(D=D, Fk=Fk)
+
+            # assert
+            assert sut.check("[]")
+
     @staticmethod
     def test_fig_9_from_jouzel_and_merlivat_1984(plot=False):
         """[Jouzel & Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749)"""

From 0620222f6fbd1eea5b7d8f22e99dbfc64b2141f6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 26 Jun 2025 16:25:44 +0200
Subject: [PATCH 14/26] create alphas comparison and temperatures

---
 .../jouzel_and_merlivat_1984.py               |   2 +-
 .../PySDM_examples/Fisher_1991/fig_2.ipynb    | 104 ++++---
 .../alpha_kin_comparison.ipynb                | 270 ++++++++++++++++++
 3 files changed, 322 insertions(+), 54 deletions(-)
 create mode 100644 examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index ebe731051c..0e4ae30502 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -34,7 +34,7 @@ def alpha_kinetic(alpha_equilibrium, saturation, D_ratio_heavy_to_light):
     @staticmethod
     def transfer_coefficient(D, Fk):
         """
-        eq. (A4) in Jouzel & Merlivat 1984,
+        eq. (A4) in Jouzel & Merlivat 1975,
         eq. (A6) in Bolot 2013.
 
         Parameters
diff --git a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
index 6327574c20..b822819267 100644
--- a/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
+++ b/examples/PySDM_examples/Fisher_1991/fig_2.ipynb
@@ -22,8 +22,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:01:47.406303Z",
-     "start_time": "2025-06-26T00:01:47.403017Z"
+     "end_time": "2025-06-26T12:52:06.895292Z",
+     "start_time": "2025-06-26T12:52:06.870075Z"
     }
    },
    "cell_type": "code",
@@ -36,15 +36,15 @@
    ],
    "id": "31481014375c7d36",
    "outputs": [],
-   "execution_count": 21
+   "execution_count": 75
   },
   {
    "cell_type": "code",
    "id": "c36c2f5c-17c1-422e-9ab9-f7d612064199",
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:01:47.416649Z",
-     "start_time": "2025-06-26T00:01:47.414494Z"
+     "end_time": "2025-06-26T12:52:06.933264Z",
+     "start_time": "2025-06-26T12:52:06.920052Z"
     }
    },
    "source": [
@@ -63,13 +63,13 @@
     ")"
    ],
    "outputs": [],
-   "execution_count": 22
+   "execution_count": 76
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:07:51.434963Z",
-     "start_time": "2025-06-26T00:07:51.358744Z"
+     "end_time": "2025-06-26T12:52:06.969470Z",
+     "start_time": "2025-06-26T12:52:06.943624Z"
     }
    },
    "cell_type": "code",
@@ -92,26 +92,17 @@
     "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
    ],
    "id": "92e11666a7b83d4d",
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'Formulae' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
-      "\u001B[0;31mNameError\u001B[0m                                 Traceback (most recent call last)",
-      "Cell \u001B[0;32mIn[1], line 1\u001B[0m\n\u001B[0;32m----> 1\u001B[0m formulae\u001B[38;5;241m=\u001B[39m \u001B[43mFormulae\u001B[49m(\n\u001B[1;32m      2\u001B[0m     isotope_meteoric_water_line\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mDansgaard1964\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      3\u001B[0m     isotope_diffusivity_ratios\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mStewart1975\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      4\u001B[0m     isotope_kinetic_fractionation_factors\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mJouzelAndMerlivat1984\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      5\u001B[0m     isotope_equilibrium_fractionation_factors\u001B[38;5;241m=\u001B[39m\u001B[38;5;124m\"\u001B[39m\u001B[38;5;124mMerlivatAndNief1967+Majoube1970\u001B[39m\u001B[38;5;124m\"\u001B[39m,\n\u001B[1;32m      6\u001B[0m )\n\u001B[1;32m      7\u001B[0m const \u001B[38;5;241m=\u001B[39m formulae\u001B[38;5;241m.\u001B[39mconstants\n\u001B[1;32m      8\u001B[0m K2C \u001B[38;5;241m=\u001B[39m formulae\u001B[38;5;241m.\u001B[39mtrivia\u001B[38;5;241m.\u001B[39mK2C\n",
-      "\u001B[0;31mNameError\u001B[0m: name 'Formulae' is not defined"
-     ]
-    }
-   ],
-   "execution_count": 1
+   "outputs": [],
+   "execution_count": 77
   },
   {
-   "metadata": {},
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T12:52:06.995059Z",
+     "start_time": "2025-06-26T12:52:06.991365Z"
+    }
+   },
    "cell_type": "code",
-   "outputs": [],
-   "execution_count": null,
    "source": [
     "def alpha_kin(iso, T):\n",
     "    return formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
@@ -120,13 +111,15 @@
     "        saturation = ice_saturation_curve_4(const=const, T=T)\n",
     "    )"
    ],
-   "id": "cd4693f604f74961"
+   "id": "cd4693f604f74961",
+   "outputs": [],
+   "execution_count": 78
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:06:26.448958Z",
-     "start_time": "2025-06-26T00:06:26.443863Z"
+     "end_time": "2025-06-26T12:52:07.012903Z",
+     "start_time": "2025-06-26T12:52:07.009364Z"
     }
    },
    "cell_type": "code",
@@ -149,13 +142,13 @@
    ],
    "id": "9ca4e3256065274b",
    "outputs": [],
-   "execution_count": 37
+   "execution_count": 79
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:06:26.830205Z",
-     "start_time": "2025-06-26T00:06:26.825441Z"
+     "end_time": "2025-06-26T12:52:07.035034Z",
+     "start_time": "2025-06-26T12:52:07.029001Z"
     }
    },
    "cell_type": "code",
@@ -169,13 +162,13 @@
    ],
    "id": "7bce3bc5674ae8cb",
    "outputs": [],
-   "execution_count": 38
+   "execution_count": 80
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:06:27.188718Z",
-     "start_time": "2025-06-26T00:06:27.181208Z"
+     "end_time": "2025-06-26T12:52:07.060065Z",
+     "start_time": "2025-06-26T12:52:07.051207Z"
     }
    },
    "cell_type": "code",
@@ -191,13 +184,13 @@
    ],
    "id": "200252902b10ccb6",
    "outputs": [],
-   "execution_count": 39
+   "execution_count": 81
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:06:27.846799Z",
-     "start_time": "2025-06-26T00:06:27.548756Z"
+     "end_time": "2025-06-26T12:52:07.270301Z",
+     "start_time": "2025-06-26T12:52:07.071166Z"
     }
    },
    "cell_type": "code",
@@ -235,7 +228,7 @@
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@@ -248,20 +241,20 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "c198c7cc9c674242806e574bcdb7f519"
+       "model_id": "30c9f38a49434a6c8ee0dc089a86776f"
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      "metadata": {},
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    ],
-   "execution_count": 40
+   "execution_count": 82
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T00:06:28.750924Z",
-     "start_time": "2025-06-26T00:06:28.600727Z"
+     "end_time": "2025-06-26T12:53:44.714805Z",
+     "start_time": "2025-06-26T12:53:44.491727Z"
     }
    },
    "cell_type": "code",
@@ -274,7 +267,7 @@
     ")\n",
     "\n",
     "pyplot.plot(\n",
-    "    K2C(temperature[::-1]),\n",
+    "    K2C(temperature)[::-1],\n",
     "    in_unit(d_excess, PER_MILLE)[::-1],\n",
     "    label=\"d-excess, TODO #1601 (WORK IN PROGRESS - NO MATCH WITH THE PAPER YET)\",\n",
     ")\n",
@@ -294,7 +287,7 @@
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+   "execution_count": 87
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-   "outputs": [],
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diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb
new file mode 100644
index 0000000000..fafc9eba8d
--- /dev/null
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb
@@ -0,0 +1,270 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "id": "initial_id",
+   "metadata": {
+    "collapsed": true,
+    "ExecuteTime": {
+     "end_time": "2025-06-26T13:21:35.322671Z",
+     "start_time": "2025-06-26T13:21:33.674043Z"
+    }
+   },
+   "source": [
+    "from matplotlib import pyplot\n",
+    "import numpy as np\n",
+    "from open_atmos_jupyter_utils import show_plot\n",
+    "\n",
+    "from PySDM import Formulae\n",
+    "from PySDM.physics import si\n",
+    "from PySDM.physics.constants import PER_MILLE, in_unit\n",
+    "from PySDM_examples.Jouzel_and_Merlivat_1984.thermodynamic_profiles import (\n",
+    "    vapour_mixing_ratio,\n",
+    "    ice_saturation_curve_4\n",
+    ")"
+   ],
+   "outputs": [],
+   "execution_count": 1
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T14:09:26.955516Z",
+     "start_time": "2025-06-26T14:09:26.872107Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "formulae= Formulae(\n",
+    "    latent_heat_vapourisation=\"Lowe2019\",\n",
+    "    latent_heat_sublimation=\"MurphyKoop2005\",\n",
+    "    saturation_vapour_pressure=\"Lowe1977\",\n",
+    "    isotope_meteoric_water_line=\"Dansgaard1964\",\n",
+    "    isotope_diffusivity_ratios=\"Stewart1975\",\n",
+    "    isotope_kinetic_fractionation_factors=\"JouzelAndMerlivat1984\",\n",
+    "    isotope_equilibrium_fractionation_factors=\"MerlivatAndNief1967+Majoube1970\",\n",
+    ")\n",
+    "const = formulae.constants\n",
+    "K2C = formulae.trivia.K2C\n",
+    "\n",
+    "diffusivity_ratio = {}\n",
+    "alpha_eq = {}\n",
+    "alpha_kinetic = {}\n",
+    "isotopes = (\"2H\", \"18O\")\n",
+    "for isotope in isotopes:\n",
+    "    alpha_eq[isotope] = getattr(formulae.isotope_equilibrium_fractionation_factors, f'alpha_i_{isotope}')\n",
+    "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
+   ],
+   "id": "bcad8d46c3f5e984",
+   "outputs": [],
+   "execution_count": 47
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T14:09:51.737325Z",
+     "start_time": "2025-06-26T14:09:51.034917Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "iso = '2H'\n",
+    "temperature = np.linspace(260, 225, 10) * si.K\n",
+    "saturation = ice_saturation_curve_4(const=const, T=temperature)\n",
+    "D_ratio = diffusivity_ratio[iso](temperature)\n",
+    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
+    "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation = saturation\n",
+    "    )\n",
+    "K = const.K0\n",
+    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
+    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
+    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
+    "D_light = const.D0\n",
+    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
+    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
+    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation)\n",
+    "alpha_kinetic_eff = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation =  eff_saturation\n",
+    "    )"
+   ],
+   "id": "e1141ca04de296b9",
+   "outputs": [],
+   "execution_count": 48
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T14:09:51.932853Z",
+     "start_time": "2025-06-26T14:09:51.930293Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "print(A)",
+   "id": "5bb968b5fb3bcadf",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[0.72500524 0.78282009 0.8327799  0.87434292 0.90772033 0.93366521\n",
+      " 0.95324779 0.9676606  0.97805234 0.9853561 ]\n"
+     ]
+    }
+   ],
+   "execution_count": 49
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T14:09:53.219247Z",
+     "start_time": "2025-06-26T14:09:53.062662Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(saturation, alpha_kinetic, label=\"with Si\")\n",
+    "pyplot.plot(saturation, alpha_kinetic_eff, label=\"with S_eff\")\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    xlabel=\"S\",\n",
+    "    ylabel=\"$\\\\alpha$\",\n",
+    ")\n",
+    "show_plot('alpha_kinetic')"
+   ],
+   "id": "ce09807c50d4242d",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "9f1585c97ed24293a55d3218540f4510"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 50
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T14:18:49.634381Z",
+     "start_time": "2025-06-26T14:18:49.627140Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "cp = 1885 * si.joule / si.kilogram / si.K\n",
+    "q_s = 1\n",
+    "drop_temperature = temperature - ls / cp * (1 - saturation) * D_light / K * q_s / A"
+   ],
+   "id": "d2b5ece731ef507d",
+   "outputs": [],
+   "execution_count": 55
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T14:20:06.536451Z",
+     "start_time": "2025-06-26T14:20:06.478027Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(temperature, drop_temperature)\n",
+    "pyplot.plot(temperature, temperature, '--')\n",
+    "pyplot.grid()"
+   ],
+   "id": "6bc3f1e45bcc2cfc",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 61
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T14:20:51.127353Z",
+     "start_time": "2025-06-26T14:20:51.049864Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(temperature, drop_temperature-temperature)\n",
+    "pyplot.grid()"
+   ],
+   "id": "7663dc1bca8593d",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+   "id": "de3209afcdf0f90c"
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+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

From c4ea180db33a5af3627ad71202b9700dfc9b26cc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Fri, 27 Jun 2025 10:56:32 +0200
Subject: [PATCH 15/26] work with Elise

---
 .../alpha_kin_comparison.ipynb                | 476 ++++++++++++++++--
 1 file changed, 434 insertions(+), 42 deletions(-)

diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb
index fafc9eba8d..ce8183174c 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb
@@ -6,8 +6,8 @@
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2025-06-26T13:21:35.322671Z",
-     "start_time": "2025-06-26T13:21:33.674043Z"
+     "end_time": "2025-06-26T18:19:05.478936Z",
+     "start_time": "2025-06-26T18:19:05.420687Z"
     }
    },
    "source": [
@@ -24,13 +24,13 @@
     ")"
    ],
    "outputs": [],
-   "execution_count": 1
+   "execution_count": 121
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T14:09:26.955516Z",
-     "start_time": "2025-06-26T14:09:26.872107Z"
+     "end_time": "2025-06-26T18:19:05.600952Z",
+     "start_time": "2025-06-26T18:19:05.527167Z"
     }
    },
    "cell_type": "code",
@@ -38,7 +38,7 @@
     "formulae= Formulae(\n",
     "    latent_heat_vapourisation=\"Lowe2019\",\n",
     "    latent_heat_sublimation=\"MurphyKoop2005\",\n",
-    "    saturation_vapour_pressure=\"Lowe1977\",\n",
+    "    saturation_vapour_pressure=\"MurphyKoop2005\",\n",
     "    isotope_meteoric_water_line=\"Dansgaard1964\",\n",
     "    isotope_diffusivity_ratios=\"Stewart1975\",\n",
     "    isotope_kinetic_fractionation_factors=\"JouzelAndMerlivat1984\",\n",
@@ -57,20 +57,161 @@
    ],
    "id": "bcad8d46c3f5e984",
    "outputs": [],
-   "execution_count": 47
+   "execution_count": 122
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T14:09:51.737325Z",
-     "start_time": "2025-06-26T14:09:51.034917Z"
+     "end_time": "2025-06-26T18:19:05.612304Z",
+     "start_time": "2025-06-26T18:19:05.609170Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "def curve_6(temperature):\n",
+    "    return 0.05 + 0.906 * np.exp(-0.008 * (temperature - 273.15))"
+   ],
+   "id": "47d40031c9347bb1",
+   "outputs": [],
+   "execution_count": 123
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:19:05.630204Z",
+     "start_time": "2025-06-26T18:19:05.618929Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "iso = '2H'\n",
+    "temperature = np.linspace(300, 225, 10) * si.K\n",
+    "saturation_4 = ice_saturation_curve_4(const=const, T=temperature)\n",
+    "D_ratio = diffusivity_ratio[iso](temperature)\n",
+    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
+    "alpha_kinetic_4 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation = saturation_4\n",
+    "    )\n",
+    "K = const.K0\n",
+    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
+    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
+    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
+    "D_light = const.D0\n",
+    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
+    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
+    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation_4)\n",
+    "alpha_kinetic_eff_4 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation =  eff_saturation\n",
+    "    )"
+   ],
+   "id": "e1141ca04de296b9",
+   "outputs": [],
+   "execution_count": 124
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:19:05.640846Z",
+     "start_time": "2025-06-26T18:19:05.637112Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "iso = '2H'\n",
+    "temperature = np.linspace(300, 225, 10) * si.K\n",
+    "saturation_6 = curve_6(temperature)\n",
+    "D_ratio = diffusivity_ratio[iso](temperature)\n",
+    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
+    "alpha_kinetic_6 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation = saturation_6\n",
+    "    )\n",
+    "K = const.K0\n",
+    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
+    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
+    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
+    "D_light = const.D0\n",
+    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
+    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
+    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation_6)\n",
+    "alpha_kinetic_eff_6 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation =  eff_saturation\n",
+    "    )"
+   ],
+   "id": "5bb968b5fb3bcadf",
+   "outputs": [],
+   "execution_count": 125
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:26:31.720957Z",
+     "start_time": "2025-06-26T18:26:31.535609Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(temperature, alpha_kinetic_6, 'k', label=\"with Si (6)\")\n",
+    "pyplot.plot(temperature, alpha_kinetic_eff_6, '--k', label=\"with S_eff (6)\")\n",
+    "pyplot.plot(temperature, alpha_kinetic_4, 'r', label=\"with Si (4)\")\n",
+    "pyplot.plot(temperature, alpha_kinetic_eff_4, '--r', label=\"with S_eff (4)\")\n",
+    "\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    xlabel=\"temperature\",\n",
+    "    ylabel=\"$\\\\alpha$\",\n",
+    ")\n",
+    "pyplot.grid()\n",
+    "show_plot('alpha_kinetic')"
+   ],
+   "id": "48a9b80209b0890",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "e6b2b91e3fca40a78e12f9279e44dcec"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 140
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:21:42.885690Z",
+     "start_time": "2025-06-26T18:21:42.873547Z"
     }
    },
    "cell_type": "code",
    "source": [
     "iso = '2H'\n",
-    "temperature = np.linspace(260, 225, 10) * si.K\n",
-    "saturation = ice_saturation_curve_4(const=const, T=temperature)\n",
+    "temperature = np.linspace(300, 225, 10) * si.K\n",
+    "saturation= ice_saturation_curve_4(const=const, T=temperature)\n",
     "D_ratio = diffusivity_ratio[iso](temperature)\n",
     "alpha_equilibrium = alpha_eq[iso](temperature)\n",
     "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
@@ -92,37 +233,63 @@
     "        saturation =  eff_saturation\n",
     "    )"
    ],
-   "id": "e1141ca04de296b9",
+   "id": "89c8cff2d2b25160",
    "outputs": [],
-   "execution_count": 48
+   "execution_count": 131
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T14:09:51.932853Z",
-     "start_time": "2025-06-26T14:09:51.930293Z"
+     "end_time": "2025-06-26T18:21:43.635172Z",
+     "start_time": "2025-06-26T18:21:43.460528Z"
     }
    },
    "cell_type": "code",
-   "source": "print(A)",
-   "id": "5bb968b5fb3bcadf",
+   "source": [
+    "pyplot.plot(temperature, alpha_kinetic, label=\"with Si\")\n",
+    "pyplot.plot(temperature, alpha_kinetic_eff, label=\"with S_eff\")\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    xlabel=\"temperature\",\n",
+    "    ylabel=\"$\\\\alpha$\",\n",
+    ")\n",
+    "pyplot.grid()\n",
+    "show_plot('alpha_kinetic')"
+   ],
+   "id": "ce09807c50d4242d",
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[0.72500524 0.78282009 0.8327799  0.87434292 0.90772033 0.93366521\n",
-      " 0.95324779 0.9676606  0.97805234 0.9853561 ]\n"
-     ]
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "8b5754396baa488483374e0487e16fc2"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
-   "execution_count": 49
+   "execution_count": 132
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T14:09:53.219247Z",
-     "start_time": "2025-06-26T14:09:53.062662Z"
+     "end_time": "2025-06-26T18:21:52.036310Z",
+     "start_time": "2025-06-26T18:21:51.884225Z"
     }
    },
    "cell_type": "code",
@@ -134,16 +301,17 @@
     "    xlabel=\"S\",\n",
     "    ylabel=\"$\\\\alpha$\",\n",
     ")\n",
+    "pyplot.grid()\n",
     "show_plot('alpha_kinetic')"
    ],
-   "id": "ce09807c50d4242d",
+   "id": "7e55c2745ba63c49",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ],
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+   "execution_count": 133
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    "metadata": {
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-     "end_time": "2025-06-26T14:18:49.634381Z",
-     "start_time": "2025-06-26T14:18:49.627140Z"
+     "end_time": "2025-06-26T18:21:59.437794Z",
+     "start_time": "2025-06-26T18:21:59.432790Z"
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    },
    "cell_type": "code",
@@ -180,13 +348,13 @@
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    "id": "d2b5ece731ef507d",
    "outputs": [],
-   "execution_count": 55
+   "execution_count": 134
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-26T14:20:06.536451Z",
-     "start_time": "2025-06-26T14:20:06.478027Z"
+     "end_time": "2025-06-26T18:22:00.130776Z",
+     "start_time": "2025-06-26T18:22:00.063740Z"
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+   "execution_count": 135
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-     "start_time": "2025-06-26T14:20:51.049864Z"
+     "end_time": "2025-06-26T18:22:01.637627Z",
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 136
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:22:02.464586Z",
+     "start_time": "2025-06-26T18:22:02.459734Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "",
+   "id": "de3209afcdf0f90c",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:22:03.069180Z",
+     "start_time": "2025-06-26T18:22:03.057634Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\n",
+    "temperature = np.linspace(300, 225, 10) * si.K\n",
+    "saturation_wrt_ice = formulae.saturation_vapour_pressure.pvs_water(temperature)/formulae.saturation_vapour_pressure.pvs_ice(temperature)\n",
+    "print(formulae.saturation_vapour_pressure.pvs_water(temperature))\n",
+    "D_ratio = diffusivity_ratio[iso](temperature)\n",
+    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
+    "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation = saturation_wrt_ice\n",
+    "    )\n",
+    "K = const.K0\n",
+    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
+    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
+    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
+    "D_light = const.D0\n",
+    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
+    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
+    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation_wrt_ice)\n",
+    "alpha_kinetic_eff = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation =  eff_saturation\n",
+    "    )"
+   ],
+   "id": "ae040f63f5118298",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[3536.76441305 2132.90307391 1243.42896172  698.45958047  376.66801387\n",
+      "  194.22282511   95.30126979   44.23776275   19.27605025    7.80625087]\n"
+     ]
+    }
+   ],
+   "execution_count": 137
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:22:04.499054Z",
+     "start_time": "2025-06-26T18:22:04.345541Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(temperature, alpha_kinetic, label=\"with Si\")\n",
+    "pyplot.plot(temperature, alpha_kinetic_eff, label=\"with S_eff\")\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    xlabel=\"temperature\",\n",
+    "    ylabel=\"$\\\\alpha$\",\n",
+    ")\n",
+    "pyplot.grid()\n",
+    "show_plot('alpha_kinetic')"
+   ],
+   "id": "49fc37c3975214ab",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
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+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "590c2dfb2a634b8b9d105332bc1321de"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 138
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:22:07.452200Z",
+     "start_time": "2025-06-26T18:22:07.319946Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(temperature, saturation_wrt_ice, label=\"Si\")\n",
+    "pyplot.plot(temperature, eff_saturation, label=\"S_eff\")\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    xlabel=\"temperature\",\n",
+    "    ylabel=\"S\",\n",
+    ")\n",
+    "pyplot.grid()\n",
+    "show_plot('alpha_kinetic')"
+   ],
+   "id": "aed6a85080b0c92c",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
+      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"408.10125pt\" height=\"310.86825pt\" viewBox=\"0 0 408.10125 310.86825\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n <metadata>\n  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n   <cc:Work>\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n    <dc:date>2025-06-26T20:22:07.437913</dc:date>\n    <dc:format>image/svg+xml</dc:format>\n    <dc:creator>\n     <cc:Agent>\n      <dc:title>Matplotlib v3.10.0, https://matplotlib.org/</dc:title>\n     </cc:Agent>\n    </dc:creator>\n   </cc:Work>\n  </rdf:RDF>\n </metadata>\n <defs>\n  <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: 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+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
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+       "version_major": 2,
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+       "model_id": "df7f830b7f2c479695ca1d5e214565b0"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 139
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:19:06.207227Z",
+     "start_time": "2025-06-26T15:31:12.603552Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(K2C(temperature), saturation_wrt_ice - eff_saturation)\n",
+    "pyplot.grid()"
+   ],
+   "id": "50713009314f8a4d",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 116
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-06-26T18:19:06.207444Z",
+     "start_time": "2025-06-26T15:43:29.545239Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pvs_water = formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
+    "pvs_ice = formulae.saturation_vapour_pressure.pvs_ice(temperature)\n",
+    "pyplot.plot(temperature,pvs_water)\n",
+    "pyplot.plot(temperature, pvs_ice)\n",
+    "pyplot.plot(temperature, pvs_water-pvs_ice)\n",
+    "py"
+   ],
+   "id": "cab9b5d3df23f632",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x13f0870b0>]"
+      ]
+     },
+     "execution_count": 120,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
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      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 63
+   "execution_count": 120
   },
   {
    "metadata": {},
@@ -243,7 +635,7 @@
    "outputs": [],
    "execution_count": null,
    "source": "",
-   "id": "de3209afcdf0f90c"
+   "id": "eb3f1afea4b80f7a"
   }
  ],
  "metadata": {

From 5679ecbda123be87c10efc851e15028a5ce2c4ce Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 2 Jul 2025 15:39:07 +0200
Subject: [PATCH 16/26] add comparison notebook

---
 .../Si_vs_effective_Si.ipynb                  | 328 +++++++++
 .../alpha_kin_comparison.ipynb                | 662 ------------------
 2 files changed, 328 insertions(+), 662 deletions(-)
 create mode 100644 examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
 delete mode 100644 examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb

diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
new file mode 100644
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--- /dev/null
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
@@ -0,0 +1,328 @@
+{
+ "cells": [
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": [
+    "[![preview notebook](https://img.shields.io/static/v1?label=render%20on&logo=github&color=87ce3e&message=GitHub)](https://github.com/open-atmos/PySDM/blob/main/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb)\n",
+    "[![launch on mybinder.org](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/open-atmos/PySDM.git/main?urlpath=lab/tree/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb)\n",
+    "[![launch on Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/open-atmos/PySDM/blob/main/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb)"
+   ],
+   "id": "daf61c91cad1c865"
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": [
+    "# Comparison between saturation wrt. ice and effective saturation - based on [Jouzel and Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749) \"_Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation_\"\n",
+    "eq. (13)"
+   ],
+   "id": "9e0070d460275191"
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "start_time": "2025-07-02T13:39:03.791057Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "import sys\n",
+    "if 'google.colab' in sys.modules:\n",
+    "    !pip --quiet install open-atmos-jupyter-utils\n",
+    "    from open_atmos_jupyter_utils import pip_install_on_colab\n",
+    "    pip_install_on_colab('PySDM-examples')"
+   ],
+   "id": "d724e98702724300",
+   "outputs": [],
+   "execution_count": 1
+  },
+  {
+   "metadata": {
+    "collapsed": true,
+    "ExecuteTime": {
+     "end_time": "2025-07-02T13:38:10.894204Z",
+     "start_time": "2025-07-02T13:38:09.003268Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "from matplotlib import pyplot\n",
+    "import numpy as np\n",
+    "from open_atmos_jupyter_utils import show_plot\n",
+    "\n",
+    "from PySDM import Formulae\n",
+    "from PySDM.physics import si\n",
+    "from PySDM.physics.constants import PER_MILLE, in_unit"
+   ],
+   "id": "initial_id",
+   "outputs": [],
+   "execution_count": 2
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-02T13:38:10.976530Z",
+     "start_time": "2025-07-02T13:38:10.974834Z"
+    }
+   },
+   "cell_type": "code",
+   "source": "any_number = 44",
+   "id": "a5f9f81ce8a0ef42",
+   "outputs": [],
+   "execution_count": 3
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-02T13:38:11.008707Z",
+     "start_time": "2025-07-02T13:38:10.986082Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "formulae= Formulae(\n",
+    "    latent_heat_vapourisation=\"Lowe2019\",\n",
+    "    saturation_vapour_pressure=\"MurphyKoop2005\",\n",
+    "    isotope_diffusivity_ratios=\"Stewart1975\",\n",
+    "    isotope_kinetic_fractionation_factors=\"JouzelAndMerlivat1984\",\n",
+    "    isotope_equilibrium_fractionation_factors=\"MerlivatAndNief1967+Majoube1970\",\n",
+    "    diffusion_thermics=\"Neglect\",\n",
+    ")\n",
+    "const = formulae.constants\n",
+    "K2C = formulae.trivia.K2C\n",
+    "\n",
+    "diffusivity_ratio = {}\n",
+    "alpha_eq = {}\n",
+    "alpha_kinetic = {}\n",
+    "isotopes = (\"2H\", \"18O\")\n",
+    "for isotope in isotopes:\n",
+    "    alpha_eq[isotope] = getattr(formulae.isotope_equilibrium_fractionation_factors, f'alpha_i_{isotope}')\n",
+    "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
+   ],
+   "id": "bcad8d46c3f5e984",
+   "outputs": [],
+   "execution_count": 4
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-02T13:38:13.541102Z",
+     "start_time": "2025-07-02T13:38:11.018637Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "isotope_considered = '2H'\n",
+    "temperature = np.linspace(300, 225, 10) * si.K\n",
+    "\n",
+    "saturation_wrt_ice = (\n",
+    "        formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
+    "        / formulae.saturation_vapour_pressure.pvs_ice(temperature)\n",
+    ")\n",
+    "\n",
+    "D_ratio = diffusivity_ratio[isotope_considered](temperature)\n",
+    "alpha_equilibrium = alpha_eq[isotope_considered](temperature)\n",
+    "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation = saturation_wrt_ice\n",
+    "    )\n",
+    "\n",
+    "K = formulae.diffusion_thermics.K(T=temperature, p=any_number)\n",
+    "D_light = formulae.diffusion_thermics.D(T=temperature, p=any_number)\n",
+    "\n",
+    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
+    "Fk = formulae.drop_growth.Fk(\n",
+    "    T=temperature,\n",
+    "    K=K,\n",
+    "    lv=lv\n",
+    ")\n",
+    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
+    "\n",
+    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(\n",
+    "    D=D_light,\n",
+    "    Fk=Fk/const.rho_w * rho_s\n",
+    ")\n",
+    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
+    "    transfer_coefficient=A,\n",
+    "    RH=saturation_wrt_ice\n",
+    ")\n",
+    "eff_alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_equilibrium,\n",
+    "        D_ratio_heavy_to_light=D_ratio,\n",
+    "        saturation =  eff_saturation\n",
+    "    )"
+   ],
+   "id": "ae040f63f5118298",
+   "outputs": [],
+   "execution_count": 5
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-02T13:38:33.219511Z",
+     "start_time": "2025-07-02T13:38:32.809408Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(K2C(temperature), alpha_kinetic, label=\"with Si\")\n",
+    "pyplot.plot(K2C(temperature), eff_alpha_kinetic, label=\"with effective Si\")\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    title=\"Kinetic Fractionation Factors of Temperature\",\n",
+    "    xlabel=\"temperature [C]\",\n",
+    "    ylabel=\"$\\\\alpha_{{kinetic}}$ [ ]\",\n",
+    ")\n",
+    "pyplot.grid()\n",
+    "show_plot('alpha_kinetic_of_temperature')"
+   ],
+   "id": "49fc37c3975214ab",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+    "ExecuteTime": {
+     "end_time": "2025-07-02T13:38:36.803630Z",
+     "start_time": "2025-07-02T13:38:36.599032Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(K2C(temperature), saturation_wrt_ice, label=\"Saturation wrt. ice\")\n",
+    "pyplot.plot(K2C(temperature), eff_saturation, label=\"Effective saturation wrt ice\")\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    title=\"Saturation Fractionation Factors of Temperature\",\n",
+    "    xlabel=\"temperature [C]\",\n",
+    "    ylabel=\"saturation [ ]\",\n",
+    ")\n",
+    "pyplot.grid()\n",
+    "show_plot('saturation_of_temperature')"
+   ],
+   "id": "aed6a85080b0c92c",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./saturation_of_temperature.pdf' target='_blank'>./saturation_of_temperatu…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "2ca6bdbe9f8b45fd9cb7833b5f6a44a7"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 8
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-02T13:38:38.939105Z",
+     "start_time": "2025-07-02T13:38:38.762636Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(K2C(temperature), abs(saturation_wrt_ice - eff_saturation))\n",
+    "pyplot.grid()\n",
+    "pyplot.gca().set(\n",
+    "    title=\"Absolute difference between environment and effective saturation wrt ice\",\n",
+    "    xlabel=\"temperature [C]\",\n",
+    "    ylabel=\"$|Si - S_{{eff}}|$ [ ]\",\n",
+    ")\n",
+    "show_plot(\"Si_minus_effective_Si\")"
+   ],
+   "id": "50713009314f8a4d",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb
deleted file mode 100644
index ce8183174c..0000000000
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/alpha_kin_comparison.ipynb
+++ /dev/null
@@ -1,662 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "id": "initial_id",
-   "metadata": {
-    "collapsed": true,
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:19:05.478936Z",
-     "start_time": "2025-06-26T18:19:05.420687Z"
-    }
-   },
-   "source": [
-    "from matplotlib import pyplot\n",
-    "import numpy as np\n",
-    "from open_atmos_jupyter_utils import show_plot\n",
-    "\n",
-    "from PySDM import Formulae\n",
-    "from PySDM.physics import si\n",
-    "from PySDM.physics.constants import PER_MILLE, in_unit\n",
-    "from PySDM_examples.Jouzel_and_Merlivat_1984.thermodynamic_profiles import (\n",
-    "    vapour_mixing_ratio,\n",
-    "    ice_saturation_curve_4\n",
-    ")"
-   ],
-   "outputs": [],
-   "execution_count": 121
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:19:05.600952Z",
-     "start_time": "2025-06-26T18:19:05.527167Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "formulae= Formulae(\n",
-    "    latent_heat_vapourisation=\"Lowe2019\",\n",
-    "    latent_heat_sublimation=\"MurphyKoop2005\",\n",
-    "    saturation_vapour_pressure=\"MurphyKoop2005\",\n",
-    "    isotope_meteoric_water_line=\"Dansgaard1964\",\n",
-    "    isotope_diffusivity_ratios=\"Stewart1975\",\n",
-    "    isotope_kinetic_fractionation_factors=\"JouzelAndMerlivat1984\",\n",
-    "    isotope_equilibrium_fractionation_factors=\"MerlivatAndNief1967+Majoube1970\",\n",
-    ")\n",
-    "const = formulae.constants\n",
-    "K2C = formulae.trivia.K2C\n",
-    "\n",
-    "diffusivity_ratio = {}\n",
-    "alpha_eq = {}\n",
-    "alpha_kinetic = {}\n",
-    "isotopes = (\"2H\", \"18O\")\n",
-    "for isotope in isotopes:\n",
-    "    alpha_eq[isotope] = getattr(formulae.isotope_equilibrium_fractionation_factors, f'alpha_i_{isotope}')\n",
-    "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
-   ],
-   "id": "bcad8d46c3f5e984",
-   "outputs": [],
-   "execution_count": 122
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:19:05.612304Z",
-     "start_time": "2025-06-26T18:19:05.609170Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "def curve_6(temperature):\n",
-    "    return 0.05 + 0.906 * np.exp(-0.008 * (temperature - 273.15))"
-   ],
-   "id": "47d40031c9347bb1",
-   "outputs": [],
-   "execution_count": 123
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:19:05.630204Z",
-     "start_time": "2025-06-26T18:19:05.618929Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "iso = '2H'\n",
-    "temperature = np.linspace(300, 225, 10) * si.K\n",
-    "saturation_4 = ice_saturation_curve_4(const=const, T=temperature)\n",
-    "D_ratio = diffusivity_ratio[iso](temperature)\n",
-    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
-    "alpha_kinetic_4 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation = saturation_4\n",
-    "    )\n",
-    "K = const.K0\n",
-    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
-    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
-    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
-    "D_light = const.D0\n",
-    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
-    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
-    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation_4)\n",
-    "alpha_kinetic_eff_4 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation =  eff_saturation\n",
-    "    )"
-   ],
-   "id": "e1141ca04de296b9",
-   "outputs": [],
-   "execution_count": 124
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:19:05.640846Z",
-     "start_time": "2025-06-26T18:19:05.637112Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "iso = '2H'\n",
-    "temperature = np.linspace(300, 225, 10) * si.K\n",
-    "saturation_6 = curve_6(temperature)\n",
-    "D_ratio = diffusivity_ratio[iso](temperature)\n",
-    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
-    "alpha_kinetic_6 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation = saturation_6\n",
-    "    )\n",
-    "K = const.K0\n",
-    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
-    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
-    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
-    "D_light = const.D0\n",
-    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
-    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
-    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation_6)\n",
-    "alpha_kinetic_eff_6 = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation =  eff_saturation\n",
-    "    )"
-   ],
-   "id": "5bb968b5fb3bcadf",
-   "outputs": [],
-   "execution_count": 125
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:26:31.720957Z",
-     "start_time": "2025-06-26T18:26:31.535609Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(temperature, alpha_kinetic_6, 'k', label=\"with Si (6)\")\n",
-    "pyplot.plot(temperature, alpha_kinetic_eff_6, '--k', label=\"with S_eff (6)\")\n",
-    "pyplot.plot(temperature, alpha_kinetic_4, 'r', label=\"with Si (4)\")\n",
-    "pyplot.plot(temperature, alpha_kinetic_eff_4, '--r', label=\"with S_eff (4)\")\n",
-    "\n",
-    "pyplot.legend()\n",
-    "pyplot.gca().set(\n",
-    "    xlabel=\"temperature\",\n",
-    "    ylabel=\"$\\\\alpha$\",\n",
-    ")\n",
-    "pyplot.grid()\n",
-    "show_plot('alpha_kinetic')"
-   ],
-   "id": "48a9b80209b0890",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ],
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-     "data": {
-      "text/plain": [
-       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
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-      "application/vnd.jupyter.widget-view+json": {
-       "version_major": 2,
-       "version_minor": 0,
-       "model_id": "e6b2b91e3fca40a78e12f9279e44dcec"
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-     "metadata": {},
-     "output_type": "display_data"
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-   ],
-   "execution_count": 140
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:21:42.885690Z",
-     "start_time": "2025-06-26T18:21:42.873547Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "iso = '2H'\n",
-    "temperature = np.linspace(300, 225, 10) * si.K\n",
-    "saturation= ice_saturation_curve_4(const=const, T=temperature)\n",
-    "D_ratio = diffusivity_ratio[iso](temperature)\n",
-    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
-    "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation = saturation\n",
-    "    )\n",
-    "K = const.K0\n",
-    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
-    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
-    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
-    "D_light = const.D0\n",
-    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
-    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
-    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation)\n",
-    "alpha_kinetic_eff = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation =  eff_saturation\n",
-    "    )"
-   ],
-   "id": "89c8cff2d2b25160",
-   "outputs": [],
-   "execution_count": 131
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:21:43.635172Z",
-     "start_time": "2025-06-26T18:21:43.460528Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(temperature, alpha_kinetic, label=\"with Si\")\n",
-    "pyplot.plot(temperature, alpha_kinetic_eff, label=\"with S_eff\")\n",
-    "pyplot.legend()\n",
-    "pyplot.gca().set(\n",
-    "    xlabel=\"temperature\",\n",
-    "    ylabel=\"$\\\\alpha$\",\n",
-    ")\n",
-    "pyplot.grid()\n",
-    "show_plot('alpha_kinetic')"
-   ],
-   "id": "ce09807c50d4242d",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
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xlink:href=\"#DejaVuSans-74\" transform=\"translate(109.570312 0)\"/>\n      <use xlink:href=\"#DejaVuSans-68\" transform=\"translate(148.779297 0)\"/>\n      <use xlink:href=\"#DejaVuSans-20\" transform=\"translate(212.158203 0)\"/>\n      <use xlink:href=\"#DejaVuSans-53\" transform=\"translate(243.945312 0)\"/>\n      <use xlink:href=\"#DejaVuSans-69\" transform=\"translate(307.421875 0)\"/>\n     </g>\n    </g>\n    <g id=\"line2d_38\">\n     <path d=\"M 59.14375 34.976563 \nL 69.14375 34.976563 \nL 79.14375 34.976563 \n\" style=\"fill: none; stroke: #ff7f0e; stroke-width: 1.5; stroke-linecap: square\"/>\n    </g>\n    <g id=\"text_21\">\n     <!-- with S_eff -->\n     <g transform=\"translate(87.14375 38.476563) scale(0.1 -0.1)\">\n      <defs>\n       <path id=\"DejaVuSans-5f\" d=\"M 3263 -1063 \nL 3263 -1509 \nL -63 -1509 \nL -63 -1063 \nL 3263 -1063 \nz\n\" transform=\"scale(0.015625)\"/>\n       <path id=\"DejaVuSans-66\" d=\"M 2375 4863 \nL 2375 4384 \nL 1825 4384 \nQ 1516 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-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/plain": [
-       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
-      ],
-      "application/vnd.jupyter.widget-view+json": {
-       "version_major": 2,
-       "version_minor": 0,
-       "model_id": "8b5754396baa488483374e0487e16fc2"
-      }
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "execution_count": 132
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:21:52.036310Z",
-     "start_time": "2025-06-26T18:21:51.884225Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(saturation, alpha_kinetic, label=\"with Si\")\n",
-    "pyplot.plot(saturation, alpha_kinetic_eff, label=\"with S_eff\")\n",
-    "pyplot.legend()\n",
-    "pyplot.gca().set(\n",
-    "    xlabel=\"S\",\n",
-    "    ylabel=\"$\\\\alpha$\",\n",
-    ")\n",
-    "pyplot.grid()\n",
-    "show_plot('alpha_kinetic')"
-   ],
-   "id": "7e55c2745ba63c49",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
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-     "data": {
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-       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
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-       "version_major": 2,
-       "version_minor": 0,
-       "model_id": "c2e3e406b07244aeb9048b72127454ec"
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-   "execution_count": 133
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:21:59.437794Z",
-     "start_time": "2025-06-26T18:21:59.432790Z"
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-   },
-   "cell_type": "code",
-   "source": [
-    "cp = 1885 * si.joule / si.kilogram / si.K\n",
-    "q_s = 1\n",
-    "drop_temperature = temperature - ls / cp * (1 - saturation) * D_light / K * q_s / A"
-   ],
-   "id": "d2b5ece731ef507d",
-   "outputs": [],
-   "execution_count": 134
-  },
-  {
-   "metadata": {
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-     "end_time": "2025-06-26T18:22:00.130776Z",
-     "start_time": "2025-06-26T18:22:00.063740Z"
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-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(temperature, drop_temperature)\n",
-    "pyplot.plot(temperature, temperature, '--')\n",
-    "pyplot.grid()"
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-   "id": "6bc3f1e45bcc2cfc",
-   "outputs": [
-    {
-     "data": {
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-     "metadata": {},
-     "output_type": "display_data"
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-   ],
-   "execution_count": 135
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:22:01.637627Z",
-     "start_time": "2025-06-26T18:22:01.574159Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(temperature, drop_temperature-temperature)\n",
-    "pyplot.grid()"
-   ],
-   "id": "7663dc1bca8593d",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
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-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "execution_count": 136
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:22:02.464586Z",
-     "start_time": "2025-06-26T18:22:02.459734Z"
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-   "cell_type": "code",
-   "source": "",
-   "id": "de3209afcdf0f90c",
-   "outputs": [],
-   "execution_count": null
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:22:03.069180Z",
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-   "source": [
-    "\n",
-    "temperature = np.linspace(300, 225, 10) * si.K\n",
-    "saturation_wrt_ice = formulae.saturation_vapour_pressure.pvs_water(temperature)/formulae.saturation_vapour_pressure.pvs_ice(temperature)\n",
-    "print(formulae.saturation_vapour_pressure.pvs_water(temperature))\n",
-    "D_ratio = diffusivity_ratio[iso](temperature)\n",
-    "alpha_equilibrium = alpha_eq[iso](temperature)\n",
-    "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation = saturation_wrt_ice\n",
-    "    )\n",
-    "K = const.K0\n",
-    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
-    "ls = formulae.latent_heat_sublimation.ls(temperature)\n",
-    "Fk = formulae.drop_growth.Fk(T=temperature, K=K, lv=ls)\n",
-    "D_light = const.D0\n",
-    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
-    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(D=D_light, Fk=Fk/const.rho_w * rho_s)\n",
-    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(transfer_coefficient=A, RH=saturation_wrt_ice)\n",
-    "alpha_kinetic_eff = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation =  eff_saturation\n",
-    "    )"
-   ],
-   "id": "ae040f63f5118298",
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[3536.76441305 2132.90307391 1243.42896172  698.45958047  376.66801387\n",
-      "  194.22282511   95.30126979   44.23776275   19.27605025    7.80625087]\n"
-     ]
-    }
-   ],
-   "execution_count": 137
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:22:04.499054Z",
-     "start_time": "2025-06-26T18:22:04.345541Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(temperature, alpha_kinetic, label=\"with Si\")\n",
-    "pyplot.plot(temperature, alpha_kinetic_eff, label=\"with S_eff\")\n",
-    "pyplot.legend()\n",
-    "pyplot.gca().set(\n",
-    "    xlabel=\"temperature\",\n",
-    "    ylabel=\"$\\\\alpha$\",\n",
-    ")\n",
-    "pyplot.grid()\n",
-    "show_plot('alpha_kinetic')"
-   ],
-   "id": "49fc37c3975214ab",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
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-    {
-     "data": {
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-       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic.pdf' target='_blank'>./alpha_kinetic.pdf</a><br>\"), HTML(v…"
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-   "execution_count": 138
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:22:07.452200Z",
-     "start_time": "2025-06-26T18:22:07.319946Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(temperature, saturation_wrt_ice, label=\"Si\")\n",
-    "pyplot.plot(temperature, eff_saturation, label=\"S_eff\")\n",
-    "pyplot.legend()\n",
-    "pyplot.gca().set(\n",
-    "    xlabel=\"temperature\",\n",
-    "    ylabel=\"S\",\n",
-    ")\n",
-    "pyplot.grid()\n",
-    "show_plot('alpha_kinetic')"
-   ],
-   "id": "aed6a85080b0c92c",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
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-    "pyplot.plot(K2C(temperature), saturation_wrt_ice - eff_saturation)\n",
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-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "execution_count": 116
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-26T18:19:06.207444Z",
-     "start_time": "2025-06-26T15:43:29.545239Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pvs_water = formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
-    "pvs_ice = formulae.saturation_vapour_pressure.pvs_ice(temperature)\n",
-    "pyplot.plot(temperature,pvs_water)\n",
-    "pyplot.plot(temperature, pvs_ice)\n",
-    "pyplot.plot(temperature, pvs_water-pvs_ice)\n",
-    "py"
-   ],
-   "id": "cab9b5d3df23f632",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x13f0870b0>]"
-      ]
-     },
-     "execution_count": 120,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "text/plain": [
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From 9d9c443dfb7868f76439d3d5ed6e754d5cbc5d31 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Wed, 2 Jul 2025 16:30:53 +0200
Subject: [PATCH 17/26] add simple smoke test

---
 .../Si_vs_effective_Si.ipynb                  | 58 ++++++++++---------
 .../test_Si_vs_effective_Si.py                | 56 ++++++++++++++++++
 2 files changed, 86 insertions(+), 28 deletions(-)
 create mode 100644 tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py

diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
index a750226814..1414c89717 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
@@ -22,7 +22,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "start_time": "2025-07-02T13:39:03.791057Z"
+     "end_time": "2025-07-02T14:26:03.476998Z",
+     "start_time": "2025-07-02T14:26:03.439434Z"
     }
    },
    "cell_type": "code",
@@ -35,14 +36,14 @@
    ],
    "id": "d724e98702724300",
    "outputs": [],
-   "execution_count": 1
+   "execution_count": 2
   },
   {
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2025-07-02T13:38:10.894204Z",
-     "start_time": "2025-07-02T13:38:09.003268Z"
+     "end_time": "2025-07-02T14:26:05.419777Z",
+     "start_time": "2025-07-02T14:26:03.486767Z"
     }
    },
    "cell_type": "code",
@@ -57,26 +58,26 @@
    ],
    "id": "initial_id",
    "outputs": [],
-   "execution_count": 2
+   "execution_count": 3
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T13:38:10.976530Z",
-     "start_time": "2025-07-02T13:38:10.974834Z"
+     "end_time": "2025-07-02T14:26:05.433878Z",
+     "start_time": "2025-07-02T14:26:05.431720Z"
     }
    },
    "cell_type": "code",
    "source": "any_number = 44",
    "id": "a5f9f81ce8a0ef42",
    "outputs": [],
-   "execution_count": 3
+   "execution_count": 4
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T13:38:11.008707Z",
-     "start_time": "2025-07-02T13:38:10.986082Z"
+     "end_time": "2025-07-02T14:26:05.465713Z",
+     "start_time": "2025-07-02T14:26:05.443755Z"
     }
    },
    "cell_type": "code",
@@ -102,19 +103,19 @@
    ],
    "id": "bcad8d46c3f5e984",
    "outputs": [],
-   "execution_count": 4
+   "execution_count": 5
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T13:38:13.541102Z",
-     "start_time": "2025-07-02T13:38:11.018637Z"
+     "end_time": "2025-07-02T14:26:08.053416Z",
+     "start_time": "2025-07-02T14:26:05.472675Z"
     }
    },
    "cell_type": "code",
    "source": [
     "isotope_considered = '2H'\n",
-    "temperature = np.linspace(300, 225, 10) * si.K\n",
+    "temperature = np.linspace(225, 300, 10) * si.K\n",
     "\n",
     "saturation_wrt_ice = (\n",
     "        formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
@@ -156,13 +157,13 @@
    ],
    "id": "ae040f63f5118298",
    "outputs": [],
-   "execution_count": 5
+   "execution_count": 6
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T13:38:33.219511Z",
-     "start_time": "2025-07-02T13:38:32.809408Z"
+     "end_time": "2025-07-02T14:26:08.511063Z",
+     "start_time": "2025-07-02T14:26:08.066827Z"
     }
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    "cell_type": "code",
@@ -185,7 +186,7 @@
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@@ -247,7 +248,7 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "2ca6bdbe9f8b45fd9cb7833b5f6a44a7"
+       "model_id": "066046372e7a4aaab9581f46fd8848a4"
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@@ -259,13 +260,14 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T13:38:38.939105Z",
-     "start_time": "2025-07-02T13:38:38.762636Z"
+     "end_time": "2025-07-02T14:26:08.954558Z",
+     "start_time": "2025-07-02T14:26:08.781141Z"
     }
    },
    "cell_type": "code",
    "source": [
-    "pyplot.plot(K2C(temperature), abs(saturation_wrt_ice - eff_saturation))\n",
+    "diff = saturation_wrt_ice - eff_saturation\n",
+    "pyplot.plot(K2C(temperature), abs(diff))\n",
     "pyplot.grid()\n",
     "pyplot.gca().set(\n",
     "    title=\"Absolute difference between environment and effective saturation wrt ice\",\n",
@@ -281,7 +283,7 @@
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@@ -294,7 +296,7 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "5e928b1e95d445d69a9953bbfc7501fa"
+       "model_id": "bf955f00f69e4eec8d293e172915eb23"
       }
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      "metadata": {},
diff --git a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py
new file mode 100644
index 0000000000..03cfeafb4a
--- /dev/null
+++ b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py
@@ -0,0 +1,56 @@
+""" """
+
+from pathlib import Path
+import pytest
+import numpy as np
+from open_atmos_jupyter_utils import notebook_vars
+from PySDM_examples import Jouzel_and_Merlivat_1984
+
+PLOT = False
+
+
+@pytest.fixture(scope="session", name="notebook_variables")
+def notebook_variables_fixture():
+    return notebook_vars(
+        file=Path(Jouzel_and_Merlivat_1984.__file__).parent
+        / "Si_vs_effective_Si.ipynb",
+        plot=PLOT,
+    )
+
+
+class TestSiVsEffectiveSi:
+    @staticmethod
+    def test_alpha_kinetic_of_temperature_values(notebook_variables):
+        # arrange
+        temperature = notebook_variables["temperature"]
+        alpha_eff = notebook_variables["eff_alpha_kinetic"]
+        alpha = notebook_variables["alpha_kinetic"]
+        temp_below_0C = temperature <= 273.15
+
+        # act
+        sut = alpha_eff[temp_below_0C]
+
+        # assert
+        np.testing.assert_array_less(sut, 1)
+        np.testing.assert_array_less(alpha[temp_below_0C], alpha_eff[temp_below_0C])
+
+    @staticmethod
+    @pytest.mark.parametrize("temperature_C, expected", ((-20, 0.05),))
+    def test_max_difference(notebook_variables, temperature_C, expected):
+        # arrange
+        diff = notebook_variables["diff"]
+        temp = notebook_variables["temperature"]
+        temp_C = temp - 273.15
+        temp_C_tolerance = 1
+
+        # act
+        diff_max = np.max(diff)
+        temp_C_range_max = temp_C[np.isclose(diff, diff_max, rtol=0.1)]
+
+        # assert
+        assert diff_max <= expected
+        assert (
+            np.min(temp_C_range_max) - temp_C_tolerance
+            <= temperature_C
+            <= np.max(temp_C_range_max) + temp_C_tolerance
+        )

From b1682d3189e479f481bac766c4136acc7bf3867f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 3 Jul 2025 14:42:33 +0200
Subject: [PATCH 18/26] rename file to proper fig number from paper; add test
 for values on the plot

---
 docs/bibliography.json                        |  3 +-
 .../{Si_vs_effective_Si.ipynb => fig_8.ipynb} | 99 ++++++++++---------
 .../test_Si_vs_effective_Si.py                | 56 -----------
 .../jouzel_and_merlivat_1984/test_fig_8.py    | 97 ++++++++++++++++++
 4 files changed, 150 insertions(+), 105 deletions(-)
 rename examples/PySDM_examples/Jouzel_and_Merlivat_1984/{Si_vs_effective_Si.ipynb => fig_8.ipynb} (65%)
 delete mode 100644 tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py
 create mode 100644 tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py

diff --git a/docs/bibliography.json b/docs/bibliography.json
index 337dc2a2b6..39caa699ef 100644
--- a/docs/bibliography.json
+++ b/docs/bibliography.json
@@ -881,7 +881,8 @@
       "examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb",
       "examples/PySDM_examples/Jouzel_and_Merlivat_1984/thermodynamic_profiles.py",
       "tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py",
-      "examples/PySDM_examples/Fisher_1991/__init__.py"
+      "examples/PySDM_examples/Fisher_1991/__init__.py",
+      "tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py"
     ],
     "title": "Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation",
     "label": "Jouzel & Merlivat 1984 (J. Geophys. Res. Atmos. 89)"
diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8.ipynb
similarity index 65%
rename from examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
rename to examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8.ipynb
index 1414c89717..4914d869f5 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8.ipynb
@@ -22,8 +22,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:03.476998Z",
-     "start_time": "2025-07-02T14:26:03.439434Z"
+     "end_time": "2025-07-03T12:27:02.868763Z",
+     "start_time": "2025-07-03T12:27:02.861683Z"
     }
    },
    "cell_type": "code",
@@ -36,14 +36,14 @@
    ],
    "id": "d724e98702724300",
    "outputs": [],
-   "execution_count": 2
+   "execution_count": 6
   },
   {
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:05.419777Z",
-     "start_time": "2025-07-02T14:26:03.486767Z"
+     "end_time": "2025-07-03T12:27:02.882299Z",
+     "start_time": "2025-07-03T12:27:02.880178Z"
     }
    },
    "cell_type": "code",
@@ -58,26 +58,26 @@
    ],
    "id": "initial_id",
    "outputs": [],
-   "execution_count": 3
+   "execution_count": 7
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:05.433878Z",
-     "start_time": "2025-07-02T14:26:05.431720Z"
+     "end_time": "2025-07-03T12:27:02.896874Z",
+     "start_time": "2025-07-03T12:27:02.895381Z"
     }
    },
    "cell_type": "code",
    "source": "any_number = 44",
    "id": "a5f9f81ce8a0ef42",
    "outputs": [],
-   "execution_count": 4
+   "execution_count": 8
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:05.465713Z",
-     "start_time": "2025-07-02T14:26:05.443755Z"
+     "end_time": "2025-07-03T12:27:02.911786Z",
+     "start_time": "2025-07-03T12:27:02.906702Z"
     }
    },
    "cell_type": "code",
@@ -103,13 +103,13 @@
    ],
    "id": "bcad8d46c3f5e984",
    "outputs": [],
-   "execution_count": 5
+   "execution_count": 9
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:08.053416Z",
-     "start_time": "2025-07-02T14:26:05.472675Z"
+     "end_time": "2025-07-03T12:27:02.924456Z",
+     "start_time": "2025-07-03T12:27:02.920716Z"
     }
    },
    "cell_type": "code",
@@ -117,6 +117,7 @@
     "isotope_considered = '2H'\n",
     "temperature = np.linspace(225, 300, 10) * si.K\n",
     "\n",
+    "relative_humidity = 1/formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
     "saturation_wrt_ice = (\n",
     "        formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
     "        / formulae.saturation_vapour_pressure.pvs_ice(temperature)\n",
@@ -145,48 +146,50 @@
     "    D=D_light,\n",
     "    Fk=Fk/const.rho_w * rho_s\n",
     ")\n",
-    "eff_saturation = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
+    "eff_saturation_wrt_ice = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
     "    transfer_coefficient=A,\n",
     "    RH=saturation_wrt_ice\n",
     ")\n",
     "eff_alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium = alpha_equilibrium,\n",
     "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation =  eff_saturation\n",
+    "        saturation =  eff_saturation_wrt_ice\n",
     "    )"
    ],
    "id": "ae040f63f5118298",
    "outputs": [],
-   "execution_count": 6
+   "execution_count": 10
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:08.511063Z",
-     "start_time": "2025-07-02T14:26:08.066827Z"
+     "end_time": "2025-07-03T12:27:03.343721Z",
+     "start_time": "2025-07-03T12:27:02.958183Z"
     }
    },
    "cell_type": "code",
    "source": [
-    "pyplot.plot(K2C(temperature), alpha_kinetic, label=\"with Si\")\n",
-    "pyplot.plot(K2C(temperature), eff_alpha_kinetic, label=\"with effective Si\")\n",
+    "pyplot.plot(K2C(temperature), saturation_wrt_ice, 'k', label=\"Saturation wrt ice\")\n",
+    "pyplot.plot(K2C(temperature), eff_saturation_wrt_ice, 'k--',label=\"Effective saturation wrt ice\")\n",
     "pyplot.legend()\n",
     "pyplot.gca().set(\n",
-    "    title=\"Kinetic Fractionation Factors of Temperature\",\n",
+    "    title=\"Saturation wrt ice\",\n",
     "    xlabel=\"temperature [C]\",\n",
-    "    ylabel=\"$\\\\alpha_{{kinetic}}$ [ ]\",\n",
+    "    ylabel=\"Si [ ]\",\n",
+    "    xlim=(0, -50),\n",
+    "    ylim=(1, 1.7)\n",
     ")\n",
     "pyplot.grid()\n",
-    "show_plot('alpha_kinetic_of_temperature')"
+    "show_plot('fig_8')"
    ],
-   "id": "49fc37c3975214ab",
+   "id": "aed6a85080b0c92c",
    "outputs": [
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@@ -194,48 +197,48 @@
     {
      "data": {
       "text/plain": [
-       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic_of_temperature.pdf' target='_blank'>./alpha_kinetic_of_tem…"
+       "HBox(children=(HTML(value=\"<a href='./fig_8.pdf' target='_blank'>./fig_8.pdf</a><br>\"), HTML(value=\"<a href='.…"
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        "version_major": 2,
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-       "model_id": "019eba60fa8d4a2290831b28341d8d94"
+       "model_id": "295a22fb416047449e1dc10729e8dfbb"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 7
+   "execution_count": 11
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:08.770593Z",
-     "start_time": "2025-07-02T14:26:08.538127Z"
+     "end_time": "2025-07-03T12:27:03.597652Z",
+     "start_time": "2025-07-03T12:27:03.381769Z"
     }
    },
    "cell_type": "code",
    "source": [
-    "pyplot.plot(K2C(temperature), saturation_wrt_ice, label=\"Saturation wrt. ice\")\n",
-    "pyplot.plot(K2C(temperature), eff_saturation, label=\"Effective saturation wrt ice\")\n",
+    "pyplot.plot(K2C(temperature), alpha_kinetic, label=\"with Si\")\n",
+    "pyplot.plot(K2C(temperature), eff_alpha_kinetic, label=\"with effective Si\")\n",
     "pyplot.legend()\n",
     "pyplot.gca().set(\n",
-    "    title=\"Saturation Fractionation Factors of Temperature\",\n",
+    "    title=\"Kinetic Fractionation Factors of Temperature\",\n",
     "    xlabel=\"temperature [C]\",\n",
-    "    ylabel=\"saturation [ ]\",\n",
+    "    ylabel=\"$\\\\alpha_{{kinetic}}$ [ ]\",\n",
     ")\n",
     "pyplot.grid()\n",
-    "show_plot('saturation_of_temperature')"
+    "show_plot('alpha_kinetic_of_temperature')"
    ],
-   "id": "aed6a85080b0c92c",
+   "id": "49fc37c3975214ab",
    "outputs": [
     {
      "data": {
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+       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic_of_temperature.pdf' target='_blank'>./alpha_kinetic_of_tem…"
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+   "execution_count": 12
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    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-02T14:26:08.954558Z",
-     "start_time": "2025-07-02T14:26:08.781141Z"
+     "end_time": "2025-07-03T12:27:03.763835Z",
+     "start_time": "2025-07-03T12:27:03.616996Z"
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    "cell_type": "code",
    "source": [
-    "diff = saturation_wrt_ice - eff_saturation\n",
-    "pyplot.plot(K2C(temperature), abs(diff))\n",
+    "saturation_difference = saturation_wrt_ice - eff_saturation_wrt_ice\n",
+    "pyplot.plot(K2C(temperature), abs(saturation_difference))\n",
     "pyplot.grid()\n",
     "pyplot.gca().set(\n",
     "    title=\"Absolute difference between environment and effective saturation wrt ice\",\n",
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@@ -296,14 +299,14 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "bf955f00f69e4eec8d293e172915eb23"
+       "model_id": "7351a49ecf744e5b874809724b1fc5b3"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 9
+   "execution_count": 13
   }
  ],
  "metadata": {
diff --git a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py
deleted file mode 100644
index 03cfeafb4a..0000000000
--- a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py
+++ /dev/null
@@ -1,56 +0,0 @@
-""" """
-
-from pathlib import Path
-import pytest
-import numpy as np
-from open_atmos_jupyter_utils import notebook_vars
-from PySDM_examples import Jouzel_and_Merlivat_1984
-
-PLOT = False
-
-
-@pytest.fixture(scope="session", name="notebook_variables")
-def notebook_variables_fixture():
-    return notebook_vars(
-        file=Path(Jouzel_and_Merlivat_1984.__file__).parent
-        / "Si_vs_effective_Si.ipynb",
-        plot=PLOT,
-    )
-
-
-class TestSiVsEffectiveSi:
-    @staticmethod
-    def test_alpha_kinetic_of_temperature_values(notebook_variables):
-        # arrange
-        temperature = notebook_variables["temperature"]
-        alpha_eff = notebook_variables["eff_alpha_kinetic"]
-        alpha = notebook_variables["alpha_kinetic"]
-        temp_below_0C = temperature <= 273.15
-
-        # act
-        sut = alpha_eff[temp_below_0C]
-
-        # assert
-        np.testing.assert_array_less(sut, 1)
-        np.testing.assert_array_less(alpha[temp_below_0C], alpha_eff[temp_below_0C])
-
-    @staticmethod
-    @pytest.mark.parametrize("temperature_C, expected", ((-20, 0.05),))
-    def test_max_difference(notebook_variables, temperature_C, expected):
-        # arrange
-        diff = notebook_variables["diff"]
-        temp = notebook_variables["temperature"]
-        temp_C = temp - 273.15
-        temp_C_tolerance = 1
-
-        # act
-        diff_max = np.max(diff)
-        temp_C_range_max = temp_C[np.isclose(diff, diff_max, rtol=0.1)]
-
-        # assert
-        assert diff_max <= expected
-        assert (
-            np.min(temp_C_range_max) - temp_C_tolerance
-            <= temperature_C
-            <= np.max(temp_C_range_max) + temp_C_tolerance
-        )
diff --git a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
new file mode 100644
index 0000000000..33fc4ee32d
--- /dev/null
+++ b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
@@ -0,0 +1,97 @@
+"""
+tests for fig. 8 from [Jouzel & Merlivat 1984 (J. Geophys. Res. Atmos. 89)](https://doi.org/10.1029/JD089iD07p11749)
+"""  # pylint: disable=line-too-long
+
+from pathlib import Path
+import pytest
+import numpy as np
+from open_atmos_jupyter_utils import notebook_vars
+from PySDM.physics.constants import T0
+from PySDM_examples import Jouzel_and_Merlivat_1984
+
+PLOT = False
+
+
+@pytest.fixture(scope="session", name="notebook_variables")
+def notebook_variables_fixture():
+    return notebook_vars(
+        file=Path(Jouzel_and_Merlivat_1984.__file__).parent / "fig_8.ipynb",
+        plot=PLOT,
+    )
+
+
+class TestFig8:
+    @staticmethod
+    @pytest.mark.parametrize(
+        "if_effective, temp_C, value",
+        (
+            (False, 0, 1),
+            (False, -10, 1.1),
+            (False, -20, 1.22),
+            (False, -30, 1.34),
+            (False, -45, 1.54),
+            (True, 0, 1),
+            (True, -10, 1.08),
+            (True, -20, 1.18),
+            (True, -30, 1.30),
+            (True, -45, 1.52),
+        ),
+    )
+    def test_fig8_values_against_the_paper(
+        notebook_variables, if_effective, temp_C, value
+    ):
+        # arrange
+        temperature_C = notebook_variables["temperature"] - T0
+        if if_effective:
+            Si = notebook_variables["eff_saturation_wrt_ice"]
+        else:
+            Si = notebook_variables["saturation_wrt_ice"]
+
+        # act
+        sut = Si[np.argmin(np.abs(temperature_C - temp_C))]
+
+        # assert
+        np.testing.assert_approx_equal(sut, value, significant=1)
+
+    @staticmethod
+    @pytest.mark.parametrize("temperature_C, expected", ((-20, 0.05),))
+    def test_fig_8_max_difference(notebook_variables, temperature_C, expected):
+        """
+        Test maximum difference between saturation and effective saturation over ice.
+        Based on comment the on eq. (13)
+        in [Jouzel & Merlivat 1984 (J. Geophys. Res. Atmos. 89)](https://doi.org/10.1029/JD089iD07p11749)
+        """  # pylint: disable=line-too-long
+        # arrange
+        saturation_difference = notebook_variables["saturation_difference"]
+        temp = notebook_variables["temperature"]
+        temp_C = temp - T0
+        temp_C_tolerance = 0.01
+
+        # act
+        max_difference = np.max(saturation_difference)
+        temp_C_range_max = temp_C[
+            np.isclose(saturation_difference, max_difference, rtol=0.1)
+        ]
+
+        # assert
+        assert max_difference <= expected
+        assert (
+            np.min(temp_C_range_max) - temp_C_tolerance
+            <= temperature_C
+            <= np.max(temp_C_range_max) + temp_C_tolerance
+        )
+
+    @staticmethod
+    def test_alpha_kinetic_of_temperature_values(notebook_variables):
+        # arrange
+        temperature = notebook_variables["temperature"]
+        alpha_eff = notebook_variables["eff_alpha_kinetic"]
+        alpha = notebook_variables["alpha_kinetic"]
+        temp_below_0C = temperature <= T0
+
+        # act
+        sut = alpha_eff[temp_below_0C]
+
+        # assert
+        np.testing.assert_array_less(sut, 1)
+        np.testing.assert_array_less(alpha[temp_below_0C], alpha_eff[temp_below_0C])

From 2549a346d3eaeca3ce6852760161e0a327cb301a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 3 Jul 2025 15:19:45 +0200
Subject: [PATCH 19/26] compress fig8 with fig9

---
 docs/bibliography.json                        |   2 +-
 .../Jouzel_and_Merlivat_1984/fig_8.ipynb      | 333 ------------------
 .../Jouzel_and_Merlivat_1984/fig_8_9.ipynb    | 304 +++++++++++++---
 .../jouzel_and_merlivat_1984/test_fig_8.py    |  14 +-
 4 files changed, 262 insertions(+), 391 deletions(-)
 delete mode 100644 examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8.ipynb

diff --git a/docs/bibliography.json b/docs/bibliography.json
index 39caa699ef..fafca06568 100644
--- a/docs/bibliography.json
+++ b/docs/bibliography.json
@@ -882,7 +882,7 @@
       "examples/PySDM_examples/Jouzel_and_Merlivat_1984/thermodynamic_profiles.py",
       "tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py",
       "examples/PySDM_examples/Fisher_1991/__init__.py",
-      "tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_Si_vs_effective_Si.py"
+      "tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py"
     ],
     "title": "Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation",
     "label": "Jouzel & Merlivat 1984 (J. Geophys. Res. Atmos. 89)"
diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8.ipynb
deleted file mode 100644
index 4914d869f5..0000000000
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8.ipynb
+++ /dev/null
@@ -1,333 +0,0 @@
-{
- "cells": [
-  {
-   "metadata": {},
-   "cell_type": "markdown",
-   "source": [
-    "[![preview notebook](https://img.shields.io/static/v1?label=render%20on&logo=github&color=87ce3e&message=GitHub)](https://github.com/open-atmos/PySDM/blob/main/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb)\n",
-    "[![launch on mybinder.org](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/open-atmos/PySDM.git/main?urlpath=lab/tree/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb)\n",
-    "[![launch on Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/open-atmos/PySDM/blob/main/examples/PySDM_examples/Jouzel_and_Merlivat_1984/Si_vs_effective_Si.ipynb)"
-   ],
-   "id": "daf61c91cad1c865"
-  },
-  {
-   "metadata": {},
-   "cell_type": "markdown",
-   "source": [
-    "# Comparison between saturation wrt. ice and effective saturation - based on [Jouzel and Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749) \"_Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation_\"\n",
-    "eq. (13)"
-   ],
-   "id": "9e0070d460275191"
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-07-03T12:27:02.868763Z",
-     "start_time": "2025-07-03T12:27:02.861683Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "import sys\n",
-    "if 'google.colab' in sys.modules:\n",
-    "    !pip --quiet install open-atmos-jupyter-utils\n",
-    "    from open_atmos_jupyter_utils import pip_install_on_colab\n",
-    "    pip_install_on_colab('PySDM-examples')"
-   ],
-   "id": "d724e98702724300",
-   "outputs": [],
-   "execution_count": 6
-  },
-  {
-   "metadata": {
-    "collapsed": true,
-    "ExecuteTime": {
-     "end_time": "2025-07-03T12:27:02.882299Z",
-     "start_time": "2025-07-03T12:27:02.880178Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "from matplotlib import pyplot\n",
-    "import numpy as np\n",
-    "from open_atmos_jupyter_utils import show_plot\n",
-    "\n",
-    "from PySDM import Formulae\n",
-    "from PySDM.physics import si\n",
-    "from PySDM.physics.constants import PER_MILLE, in_unit"
-   ],
-   "id": "initial_id",
-   "outputs": [],
-   "execution_count": 7
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-07-03T12:27:02.896874Z",
-     "start_time": "2025-07-03T12:27:02.895381Z"
-    }
-   },
-   "cell_type": "code",
-   "source": "any_number = 44",
-   "id": "a5f9f81ce8a0ef42",
-   "outputs": [],
-   "execution_count": 8
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-07-03T12:27:02.911786Z",
-     "start_time": "2025-07-03T12:27:02.906702Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "formulae= Formulae(\n",
-    "    latent_heat_vapourisation=\"Lowe2019\",\n",
-    "    saturation_vapour_pressure=\"MurphyKoop2005\",\n",
-    "    isotope_diffusivity_ratios=\"Stewart1975\",\n",
-    "    isotope_kinetic_fractionation_factors=\"JouzelAndMerlivat1984\",\n",
-    "    isotope_equilibrium_fractionation_factors=\"MerlivatAndNief1967+Majoube1970\",\n",
-    "    diffusion_thermics=\"Neglect\",\n",
-    ")\n",
-    "const = formulae.constants\n",
-    "K2C = formulae.trivia.K2C\n",
-    "\n",
-    "diffusivity_ratio = {}\n",
-    "alpha_eq = {}\n",
-    "alpha_kinetic = {}\n",
-    "isotopes = (\"2H\", \"18O\")\n",
-    "for isotope in isotopes:\n",
-    "    alpha_eq[isotope] = getattr(formulae.isotope_equilibrium_fractionation_factors, f'alpha_i_{isotope}')\n",
-    "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
-   ],
-   "id": "bcad8d46c3f5e984",
-   "outputs": [],
-   "execution_count": 9
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-07-03T12:27:02.924456Z",
-     "start_time": "2025-07-03T12:27:02.920716Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "isotope_considered = '2H'\n",
-    "temperature = np.linspace(225, 300, 10) * si.K\n",
-    "\n",
-    "relative_humidity = 1/formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
-    "saturation_wrt_ice = (\n",
-    "        formulae.saturation_vapour_pressure.pvs_water(temperature)\n",
-    "        / formulae.saturation_vapour_pressure.pvs_ice(temperature)\n",
-    ")\n",
-    "\n",
-    "D_ratio = diffusivity_ratio[isotope_considered](temperature)\n",
-    "alpha_equilibrium = alpha_eq[isotope_considered](temperature)\n",
-    "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation = saturation_wrt_ice\n",
-    "    )\n",
-    "\n",
-    "K = formulae.diffusion_thermics.K(T=temperature, p=any_number)\n",
-    "D_light = formulae.diffusion_thermics.D(T=temperature, p=any_number)\n",
-    "\n",
-    "lv = formulae.latent_heat_vapourisation.lv(temperature)\n",
-    "Fk = formulae.drop_growth.Fk(\n",
-    "    T=temperature,\n",
-    "    K=K,\n",
-    "    lv=lv\n",
-    ")\n",
-    "rho_s = formulae.saturation_vapour_pressure.pvs_ice(temperature) / const.Rv / temperature\n",
-    "\n",
-    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(\n",
-    "    D=D_light,\n",
-    "    Fk=Fk/const.rho_w * rho_s\n",
-    ")\n",
-    "eff_saturation_wrt_ice = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
-    "    transfer_coefficient=A,\n",
-    "    RH=saturation_wrt_ice\n",
-    ")\n",
-    "eff_alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
-    "        alpha_equilibrium = alpha_equilibrium,\n",
-    "        D_ratio_heavy_to_light=D_ratio,\n",
-    "        saturation =  eff_saturation_wrt_ice\n",
-    "    )"
-   ],
-   "id": "ae040f63f5118298",
-   "outputs": [],
-   "execution_count": 10
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-07-03T12:27:03.343721Z",
-     "start_time": "2025-07-03T12:27:02.958183Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "pyplot.plot(K2C(temperature), saturation_wrt_ice, 'k', label=\"Saturation wrt ice\")\n",
-    "pyplot.plot(K2C(temperature), eff_saturation_wrt_ice, 'k--',label=\"Effective saturation wrt ice\")\n",
-    "pyplot.legend()\n",
-    "pyplot.gca().set(\n",
-    "    title=\"Saturation wrt ice\",\n",
-    "    xlabel=\"temperature [C]\",\n",
-    "    ylabel=\"Si [ ]\",\n",
-    "    xlim=(0, -50),\n",
-    "    ylim=(1, 1.7)\n",
-    ")\n",
-    "pyplot.grid()\n",
-    "show_plot('fig_8')"
-   ],
-   "id": "aed6a85080b0c92c",
-   "outputs": [
-    {
-     "data": {
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-     "end_time": "2025-07-03T12:27:03.597652Z",
-     "start_time": "2025-07-03T12:27:03.381769Z"
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-   "source": [
-    "pyplot.plot(K2C(temperature), alpha_kinetic, label=\"with Si\")\n",
-    "pyplot.plot(K2C(temperature), eff_alpha_kinetic, label=\"with effective Si\")\n",
-    "pyplot.legend()\n",
-    "pyplot.gca().set(\n",
-    "    title=\"Kinetic Fractionation Factors of Temperature\",\n",
-    "    xlabel=\"temperature [C]\",\n",
-    "    ylabel=\"$\\\\alpha_{{kinetic}}$ [ ]\",\n",
-    ")\n",
-    "pyplot.grid()\n",
-    "show_plot('alpha_kinetic_of_temperature')"
-   ],
-   "id": "49fc37c3975214ab",
-   "outputs": [
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-    "ExecuteTime": {
-     "end_time": "2025-07-03T12:27:03.763835Z",
-     "start_time": "2025-07-03T12:27:03.616996Z"
-    }
-   },
-   "cell_type": "code",
-   "source": [
-    "saturation_difference = saturation_wrt_ice - eff_saturation_wrt_ice\n",
-    "pyplot.plot(K2C(temperature), abs(saturation_difference))\n",
-    "pyplot.grid()\n",
-    "pyplot.gca().set(\n",
-    "    title=\"Absolute difference between environment and effective saturation wrt ice\",\n",
-    "    xlabel=\"temperature [C]\",\n",
-    "    ylabel=\"$|Si - S_{{eff}}|$ [ ]\",\n",
-    ")\n",
-    "show_plot(\"Si_minus_effective_Si\")"
-   ],
-   "id": "50713009314f8a4d",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
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-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/plain": [
-       "HBox(children=(HTML(value=\"<a href='./Si_minus_effective_Si.pdf' target='_blank'>./Si_minus_effective_Si.pdf</…"
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-      "application/vnd.jupyter.widget-view+json": {
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-   ],
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-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 2
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
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diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
index 446d44e577..1f8aef62fb 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
@@ -14,16 +14,17 @@
    "metadata": {},
    "cell_type": "markdown",
    "source": [
-    "# figs 8 and 9 from [Jouzel and Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749) \"_Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation_\"\n",
-    "\n"
+    "# Comparison between saturation wrt. ice and effective saturation - based on  [Jouzel and Merlivat 1984](https://doi.org/10.1029/JD089iD07p11749) \"_Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation_\"\n",
+    "\n",
+    "figs 8 and 9"
    ],
    "id": "841538e30be219a1"
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T23:25:40.862379Z",
-     "start_time": "2025-06-25T23:25:40.859115Z"
+     "end_time": "2025-07-03T13:12:31.948539Z",
+     "start_time": "2025-07-03T13:12:31.935402Z"
     }
    },
    "cell_type": "code",
@@ -36,7 +37,7 @@
    ],
    "id": "466d06cabb3174f3",
    "outputs": [],
-   "execution_count": 1
+   "execution_count": 12
   },
   {
    "cell_type": "code",
@@ -44,8 +45,8 @@
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2025-06-25T23:25:42.736860Z",
-     "start_time": "2025-06-25T23:25:40.951437Z"
+     "end_time": "2025-07-03T13:12:31.958842Z",
+     "start_time": "2025-07-03T13:12:31.953591Z"
     }
    },
    "source": [
@@ -57,21 +58,26 @@
     "from open_atmos_jupyter_utils import show_plot"
    ],
    "outputs": [],
-   "execution_count": 2
+   "execution_count": 13
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T23:25:43.030796Z",
-     "start_time": "2025-06-25T23:25:42.742196Z"
+     "end_time": "2025-07-03T13:12:31.994959Z",
+     "start_time": "2025-07-03T13:12:31.983552Z"
     }
    },
    "cell_type": "code",
    "source": [
-    "formulae = Formulae(\n",
+    "any_number = 44\n",
+    "\n",
+    "formulae= Formulae(\n",
+    "    latent_heat_vapourisation=\"Lowe2019\",\n",
+    "    saturation_vapour_pressure=\"MurphyKoop2005\",\n",
     "    isotope_diffusivity_ratios=\"Stewart1975\",\n",
-    "    isotope_equilibrium_fractionation_factors=\"Majoube1970\",\n",
-    "    isotope_kinetic_fractionation_factors=\"JouzelAndMerlivat1984\"\n",
+    "    isotope_kinetic_fractionation_factors=\"JouzelAndMerlivat1984\",\n",
+    "    isotope_equilibrium_fractionation_factors=\"MerlivatAndNief1967+Majoube1970\",\n",
+    "    diffusion_thermics=\"Neglect\",\n",
     ")\n",
     "const = formulae.constants\n",
     "svp = formulae.saturation_vapour_pressure\n",
@@ -83,31 +89,129 @@
    ],
    "id": "87e416d611926ad5",
    "outputs": [],
-   "execution_count": 3
+   "execution_count": 14
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-03T13:12:32.007354Z",
+     "start_time": "2025-07-03T13:12:32.005114Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "diffusivity_ratio = {}\n",
+    "alpha_eq = {}\n",
+    "alpha_kinetic = {}\n",
+    "isotopes = (\"2H\", \"18O\")\n",
+    "for isotope in isotopes:\n",
+    "    alpha_eq[isotope] = getattr(formulae.isotope_equilibrium_fractionation_factors, f'alpha_i_{isotope}')\n",
+    "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
+   ],
+   "id": "5249b42469926bfc",
+   "outputs": [],
+   "execution_count": 15
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "## Saturation wrt ice - comparison with effective saturation",
+   "id": "bbb54a367a947a49"
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-03T13:12:32.023183Z",
+     "start_time": "2025-07-03T13:12:32.020431Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "saturation_wrt_ice = (\n",
+    "        formulae.saturation_vapour_pressure.pvs_water(T_0_50)\n",
+    "        / formulae.saturation_vapour_pressure.pvs_ice(T_0_50)\n",
+    ")\n",
+    "\n",
+    "D_light = formulae.diffusion_thermics.D(T=T_0_50, p=any_number)\n",
+    "Fk = formulae.drop_growth.Fk(\n",
+    "    T=T_0_50,\n",
+    "    K=formulae.diffusion_thermics.K(T=T_0_50, p=any_number),\n",
+    "    lv=formulae.latent_heat_vapourisation.lv(T_0_50)\n",
+    ") / const.rho_w * formulae.saturation_vapour_pressure.pvs_ice(T_0_50) / const.Rv / T_0_50\n",
+    "\n",
+    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(\n",
+    "    D=D_light,\n",
+    "    Fk=Fk\n",
+    ")\n",
+    "eff_saturation_wrt_ice = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
+    "    transfer_coefficient=A,\n",
+    "    RH=saturation_wrt_ice\n",
+    ")"
+   ],
+   "id": "c915cc7a7b658abf",
+   "outputs": [],
+   "execution_count": 16
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-03T13:12:32.046762Z",
+     "start_time": "2025-07-03T13:12:32.043433Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "isotope_considered = '2H'\n",
+    "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_eq[isotope_considered](T_0_50),\n",
+    "        D_ratio_heavy_to_light=diffusivity_ratio[isotope_considered](T_0_50),\n",
+    "        saturation = saturation_wrt_ice\n",
+    "    )\n",
+    "\n",
+    "eff_alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
+    "        alpha_equilibrium = alpha_eq[isotope_considered](T_0_50),\n",
+    "        D_ratio_heavy_to_light=diffusivity_ratio[isotope_considered](T_0_50),\n",
+    "        saturation =  eff_saturation_wrt_ice\n",
+    "    )"
+   ],
+   "id": "2b2b7b44ca73464b",
+   "outputs": [],
+   "execution_count": 17
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T23:25:44.982409Z",
-     "start_time": "2025-06-25T23:25:43.041753Z"
+     "end_time": "2025-07-03T13:12:32.228180Z",
+     "start_time": "2025-07-03T13:12:32.067039Z"
     }
    },
    "cell_type": "code",
    "source": [
     "pyplot.plot(\n",
     "    K2C(T_0_50),\n",
-    "    svp.pvs_water(T_0_50) / svp.pvs_ice(T_0_50),\n",
-    "    label='saturation wrt liquid phase',\n",
+    "    saturation_wrt_ice,\n",
+    "    'g',\n",
+    "    label='saturation wrt ice',\n",
+    ")\n",
+    "pyplot.plot(\n",
+    "    K2C(T_0_50),\n",
+    "    eff_saturation_wrt_ice,\n",
+    "    'g--',\n",
+    "    label=\"effective saturation wrt ice\"\n",
     ")\n",
     "pyplot.plot(\n",
     "    K2C(T_0_50)[n_points//5:],\n",
     "    ice_saturation_curve_4(const,T_0_50[n_points//5:]),\n",
+    "    'k',\n",
     "    label='curve 4',\n",
     ")\n",
+    "pyplot.legend()\n",
     "pyplot.gca().set(\n",
-    "    ylabel='Si',\n",
-    "    xlabel='Temperature (C)',\n",
+    "    title=f\"Saturation wrt ice for {isotope_considered}\",\n",
+    "    xlabel=\"Temperature [°C]\",\n",
+    "    ylabel=\"Si [ ]\",\n",
     "    xlim=(K2C(T_0_50[0]), K2C(T_0_50[-1])),\n",
+    "    ylim=(1, 1.7)\n",
     ")\n",
     "pyplot.grid()\n",
     "pyplot.legend()\n",
@@ -120,7 +224,7 @@
       "text/plain": [
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@@ -133,45 +237,160 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "8c15bde98c9c4698979a4cb47ad75d48"
+       "model_id": "0eb6d20391bf4dacbf6c06a439ad7669"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 18
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-03T13:12:32.408909Z",
+     "start_time": "2025-07-03T13:12:32.248739Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "saturation_difference = saturation_wrt_ice - eff_saturation_wrt_ice\n",
+    "pyplot.plot(K2C(T_0_50), abs(saturation_difference), 'g')\n",
+    "pyplot.grid()\n",
+    "pyplot.gca().set(\n",
+    "    title=\"Absolute difference between environment and effective saturation wrt ice\",\n",
+    "    xlabel=\"temperature [C]\",\n",
+    "    ylabel=\"$|Si - S_{{eff}}|$ [ ]\",\n",
+    ")\n",
+    "show_plot(\"Si_minus_effective_Si\")"
+   ],
+   "id": "2e95a50c723d4181",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./Si_minus_effective_Si.pdf' target='_blank'>./Si_minus_effective_Si.pdf</…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "4aa2eb17a4214eb280239987e6e15ba7"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 19
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "## Kinetic fractionation factors",
+   "id": "c24f76eff2cd8537"
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-03T13:12:32.584004Z",
+     "start_time": "2025-07-03T13:12:32.426510Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "pyplot.plot(K2C(T_0_50), alpha_kinetic, 'g', label=\"with Si\")\n",
+    "pyplot.plot(K2C(T_0_50), eff_alpha_kinetic, 'g--', label=\"with effective Si\")\n",
+    "pyplot.legend()\n",
+    "pyplot.gca().set(\n",
+    "    title=\"Kinetic Fractionation Factors of Temperature\",\n",
+    "    xlabel=\"temperature [C]\",\n",
+    "    ylabel=\"$\\\\alpha_{{kinetic}}$ [ ]\",\n",
+    ")\n",
+    "pyplot.grid()\n",
+    "show_plot('alpha_kinetic_of_temperature')"
+   ],
+   "id": "15ec13a660cf954f",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic_of_temperature.pdf' target='_blank'>./alpha_kinetic_of_tem…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "a71b79fcdf3e4e39853ad8dbb0e67178"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 4
+   "execution_count": 20
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": [
+    "## Fig. 9: Effective fractionation factors\n",
+    "$\\alpha_{eff} = \\alpha_s\\alpha_k$\n",
+    "for $^{18}$O of saturation over ice"
+   ],
+   "id": "552c5304753132f5"
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T23:25:45.731460Z",
-     "start_time": "2025-06-25T23:25:44.995396Z"
+     "end_time": "2025-07-03T13:12:32.605388Z",
+     "start_time": "2025-07-03T13:12:32.602097Z"
     }
    },
    "cell_type": "code",
    "source": [
     "temperatures = C2K(np.array([-10., -20., -30.]))\n",
+    "isotope_considered = \"18O\"\n",
+    "\n",
     "alphas_eff = np.zeros((n_points, len(temperatures)))\n",
     "Si = np.linspace(1.0, 1.4, n_points)\n",
     "for i, T in enumerate(temperatures):\n",
-    "    alpha_s = formulae.isotope_equilibrium_fractionation_factors.alpha_i_18O(T)\n",
+    "    alpha_s = alpha_eq[isotope_considered](T)\n",
     "    alpha_k = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium=alpha_s,\n",
     "        saturation=Si,\n",
-    "        D_ratio_heavy_to_light=formulae.isotope_diffusivity_ratios.ratio_18O_heavy_to_light(T)\n",
+    "        D_ratio_heavy_to_light=diffusivity_ratio[isotope_considered](T),\n",
     "    )\n",
     "    alphas_eff[:, i] = alpha_k * alpha_s"
    ],
    "id": "1a7e5ae0c7093428",
    "outputs": [],
-   "execution_count": 5
+   "execution_count": 21
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-06-25T23:25:45.959914Z",
-     "start_time": "2025-06-25T23:25:45.739364Z"
+     "end_time": "2025-07-03T13:12:32.781402Z",
+     "start_time": "2025-07-03T13:12:32.621724Z"
     }
    },
    "cell_type": "code",
@@ -180,14 +399,14 @@
     "    pyplot.plot(\n",
     "        Si,\n",
     "        alphas_eff[:, i],\n",
-    "        label=f'{K2C(T):.5g} (C)',\n",
-    "        color='k',\n",
+    "        label=f'{K2C(T):.5g} [°C]',\n",
+    "        color='g',\n",
     "        linewidth = 1 + i/2\n",
     "    )\n",
     "pyplot.gca().set(\n",
     "    ylabel='$\\\\alpha_s\\\\alpha_k$',\n",
     "    xlabel='Si',\n",
-    "    title = \"$\\\\alpha_s\\\\alpha_k$ for $^{18}$O of saturation over ice\"\n",
+    "    title = f\"Effective fractionation factors for {isotope_considered}\"\n",
     ")\n",
     "pyplot.grid()\n",
     "pyplot.legend()\n",
@@ -200,7 +419,7 @@
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      },
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@@ -213,27 +432,14 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "a478d96b93d34ed2936063de54732783"
+       "model_id": "0501ac8ed30b49c49a0be9dbe35e4896"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 6
-  },
-  {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-06-25T23:25:45.972541Z",
-     "start_time": "2025-06-25T23:25:45.970842Z"
-    }
-   },
-   "cell_type": "code",
-   "source": "",
-   "id": "94ff2c9e78541ae",
-   "outputs": [],
-   "execution_count": null
+   "execution_count": 22
   }
  ],
  "metadata": {
diff --git a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
index 33fc4ee32d..2294d00c2f 100644
--- a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
+++ b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
@@ -15,7 +15,7 @@
 @pytest.fixture(scope="session", name="notebook_variables")
 def notebook_variables_fixture():
     return notebook_vars(
-        file=Path(Jouzel_and_Merlivat_1984.__file__).parent / "fig_8.ipynb",
+        file=Path(Jouzel_and_Merlivat_1984.__file__).parent / "fig_8_9.ipynb",
         plot=PLOT,
     )
 
@@ -41,7 +41,7 @@ def test_fig8_values_against_the_paper(
         notebook_variables, if_effective, temp_C, value
     ):
         # arrange
-        temperature_C = notebook_variables["temperature"] - T0
+        temperature_C = notebook_variables["T_0_50"] - T0
         if if_effective:
             Si = notebook_variables["eff_saturation_wrt_ice"]
         else:
@@ -63,7 +63,7 @@ def test_fig_8_max_difference(notebook_variables, temperature_C, expected):
         """  # pylint: disable=line-too-long
         # arrange
         saturation_difference = notebook_variables["saturation_difference"]
-        temp = notebook_variables["temperature"]
+        temp = notebook_variables["T_0_50"]
         temp_C = temp - T0
         temp_C_tolerance = 0.01
 
@@ -82,16 +82,14 @@ def test_fig_8_max_difference(notebook_variables, temperature_C, expected):
         )
 
     @staticmethod
-    def test_alpha_kinetic_of_temperature_values(notebook_variables):
+    def test_alpha_less_then_eff_alpha(notebook_variables):
         # arrange
-        temperature = notebook_variables["temperature"]
         alpha_eff = notebook_variables["eff_alpha_kinetic"]
         alpha = notebook_variables["alpha_kinetic"]
-        temp_below_0C = temperature <= T0
 
         # act
-        sut = alpha_eff[temp_below_0C]
+        sut = alpha_eff
 
         # assert
         np.testing.assert_array_less(sut, 1)
-        np.testing.assert_array_less(alpha[temp_below_0C], alpha_eff[temp_below_0C])
+        np.testing.assert_array_less(alpha, alpha_eff)

From c0653812da1a913a8823c28b69307d73d6661472 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 3 Jul 2025 23:07:59 +0200
Subject: [PATCH 20/26] change import order

---
 .../smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py  | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
index 2294d00c2f..af4a3679f8 100644
--- a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
+++ b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
@@ -6,8 +6,9 @@
 import pytest
 import numpy as np
 from open_atmos_jupyter_utils import notebook_vars
-from PySDM.physics.constants import T0
+
 from PySDM_examples import Jouzel_and_Merlivat_1984
+from PySDM.physics.constants import T0
 
 PLOT = False
 

From 1ba210e276421ef683f8928fd9159667de074280 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Sun, 6 Jul 2025 22:14:11 +0200
Subject: [PATCH 21/26] some changes to naming and plot styles

---
 .../Jouzel_and_Merlivat_1984/fig_8_9.ipynb    | 198 ++++++++----------
 1 file changed, 92 insertions(+), 106 deletions(-)

diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
index 1f8aef62fb..a59c28a76d 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
@@ -23,8 +23,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:31.948539Z",
-     "start_time": "2025-07-03T13:12:31.935402Z"
+     "end_time": "2025-07-06T20:04:14.905723Z",
+     "start_time": "2025-07-06T20:04:14.900796Z"
     }
    },
    "cell_type": "code",
@@ -37,7 +37,7 @@
    ],
    "id": "466d06cabb3174f3",
    "outputs": [],
-   "execution_count": 12
+   "execution_count": 9
   },
   {
    "cell_type": "code",
@@ -45,8 +45,8 @@
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:31.958842Z",
-     "start_time": "2025-07-03T13:12:31.953591Z"
+     "end_time": "2025-07-06T20:04:14.925137Z",
+     "start_time": "2025-07-06T20:04:14.922741Z"
     }
    },
    "source": [
@@ -58,18 +58,18 @@
     "from open_atmos_jupyter_utils import show_plot"
    ],
    "outputs": [],
-   "execution_count": 13
+   "execution_count": 10
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:31.994959Z",
-     "start_time": "2025-07-03T13:12:31.983552Z"
+     "end_time": "2025-07-06T20:04:14.947223Z",
+     "start_time": "2025-07-06T20:04:14.940365Z"
     }
    },
    "cell_type": "code",
    "source": [
-    "any_number = 44\n",
+    "ANY_NUMBER = 44\n",
     "\n",
     "formulae= Formulae(\n",
     "    latent_heat_vapourisation=\"Lowe2019\",\n",
@@ -87,15 +87,15 @@
     "n_points = 100\n",
     "T_0_50 = C2K(np.linspace(0.0, -50, n_points))"
    ],
-   "id": "87e416d611926ad5",
+   "id": "6f7078d9d56a0a7c",
    "outputs": [],
-   "execution_count": 14
+   "execution_count": 11
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.007354Z",
-     "start_time": "2025-07-03T13:12:32.005114Z"
+     "end_time": "2025-07-06T20:04:14.964248Z",
+     "start_time": "2025-07-06T20:04:14.957645Z"
     }
    },
    "cell_type": "code",
@@ -108,9 +108,9 @@
     "    alpha_eq[isotope] = getattr(formulae.isotope_equilibrium_fractionation_factors, f'alpha_i_{isotope}')\n",
     "    diffusivity_ratio[isotope] = getattr(formulae.isotope_diffusivity_ratios, f'ratio_{isotope}_heavy_to_light')"
    ],
-   "id": "5249b42469926bfc",
+   "id": "2c7e390144e7499",
    "outputs": [],
-   "execution_count": 15
+   "execution_count": 12
   },
   {
    "metadata": {},
@@ -121,42 +121,44 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.023183Z",
-     "start_time": "2025-07-03T13:12:32.020431Z"
+     "end_time": "2025-07-06T20:04:14.974512Z",
+     "start_time": "2025-07-06T20:04:14.971371Z"
     }
    },
    "cell_type": "code",
    "source": [
-    "saturation_wrt_ice = (\n",
-    "        formulae.saturation_vapour_pressure.pvs_water(T_0_50)\n",
-    "        / formulae.saturation_vapour_pressure.pvs_ice(T_0_50)\n",
-    ")\n",
+    "pvs_ice = formulae.saturation_vapour_pressure.pvs_ice\n",
+    "pvs_water = formulae.saturation_vapour_pressure.pvs_water\n",
+    "pressure = ANY_NUMBER\n",
     "\n",
-    "D_light = formulae.diffusion_thermics.D(T=T_0_50, p=any_number)\n",
+    "D_light = formulae.diffusion_thermics.D(T=T_0_50, p=pressure)\n",
     "Fk = formulae.drop_growth.Fk(\n",
     "    T=T_0_50,\n",
-    "    K=formulae.diffusion_thermics.K(T=T_0_50, p=any_number),\n",
+    "    K=formulae.diffusion_thermics.K(T=T_0_50, p=pressure),\n",
     "    lv=formulae.latent_heat_vapourisation.lv(T_0_50)\n",
-    ") / const.rho_w * formulae.saturation_vapour_pressure.pvs_ice(T_0_50) / const.Rv / T_0_50\n",
+    ") / const.rho_w * pvs_ice(T_0_50) / const.Rv / T_0_50 # TODO change A definition or call it differently\n",
+    "\n",
+    "\n",
+    "saturation_wrt_ice_at_RH100 = pvs_water(T_0_50) / pvs_ice(T_0_50)\n",
     "\n",
-    "A = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(\n",
+    "\n",
+    "eff_saturation_wrt_ice_at_RH100 = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
+    "    transfer_coefficient=formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(\n",
     "    D=D_light,\n",
     "    Fk=Fk\n",
-    ")\n",
-    "eff_saturation_wrt_ice = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
-    "    transfer_coefficient=A,\n",
-    "    RH=saturation_wrt_ice\n",
+    "),\n",
+    "    RH=saturation_wrt_ice_at_RH100\n",
     ")"
    ],
-   "id": "c915cc7a7b658abf",
+   "id": "47503ee93cc639b7",
    "outputs": [],
-   "execution_count": 16
+   "execution_count": 13
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.046762Z",
-     "start_time": "2025-07-03T13:12:32.043433Z"
+     "end_time": "2025-07-06T20:04:14.984673Z",
+     "start_time": "2025-07-06T20:04:14.982519Z"
     }
    },
    "cell_type": "code",
@@ -165,49 +167,55 @@
     "alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium = alpha_eq[isotope_considered](T_0_50),\n",
     "        D_ratio_heavy_to_light=diffusivity_ratio[isotope_considered](T_0_50),\n",
-    "        saturation = saturation_wrt_ice\n",
+    "        saturation = saturation_wrt_ice_at_RH100\n",
     "    )\n",
     "\n",
     "eff_alpha_kinetic = formulae.isotope_kinetic_fractionation_factors.alpha_kinetic(\n",
     "        alpha_equilibrium = alpha_eq[isotope_considered](T_0_50),\n",
     "        D_ratio_heavy_to_light=diffusivity_ratio[isotope_considered](T_0_50),\n",
-    "        saturation =  eff_saturation_wrt_ice\n",
+    "        saturation =  eff_saturation_wrt_ice_at_RH100\n",
     "    )"
    ],
-   "id": "2b2b7b44ca73464b",
+   "id": "ad049bb8d20fa39b",
    "outputs": [],
-   "execution_count": 17
+   "execution_count": 14
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.228180Z",
-     "start_time": "2025-07-03T13:12:32.067039Z"
+     "end_time": "2025-07-06T20:09:04.656624Z",
+     "start_time": "2025-07-06T20:09:04.456285Z"
     }
    },
    "cell_type": "code",
    "source": [
     "pyplot.plot(\n",
     "    K2C(T_0_50),\n",
-    "    saturation_wrt_ice,\n",
-    "    'g',\n",
-    "    label='saturation wrt ice',\n",
+    "    saturation_wrt_ice_at_RH100,\n",
+    "    'k',\n",
+    "    label='saturation wrt ice at RH100',\n",
     ")\n",
     "pyplot.plot(\n",
     "    K2C(T_0_50),\n",
-    "    eff_saturation_wrt_ice,\n",
-    "    'g--',\n",
-    "    label=\"effective saturation wrt ice\"\n",
+    "    pvs_ice(T_0_50),\n",
+    "    'b',\n",
+    "    label='',\n",
+    ")\n",
+    "pyplot.plot(\n",
+    "    K2C(T_0_50),\n",
+    "    eff_saturation_wrt_ice_at_RH100,\n",
+    "    'k--',\n",
+    "    label=\"effective saturation wrt ice at RH100\",\n",
     ")\n",
     "pyplot.plot(\n",
     "    K2C(T_0_50)[n_points//5:],\n",
     "    ice_saturation_curve_4(const,T_0_50[n_points//5:]),\n",
-    "    'k',\n",
+    "    'g',\n",
     "    label='curve 4',\n",
     ")\n",
     "pyplot.legend()\n",
     "pyplot.gca().set(\n",
-    "    title=f\"Saturation wrt ice for {isotope_considered}\",\n",
+    "    title=f\"Saturation wrt ice for {isotope_considered} at RH=100\",\n",
     "    xlabel=\"Temperature [°C]\",\n",
     "    ylabel=\"Si [ ]\",\n",
     "    xlim=(K2C(T_0_50[0]), K2C(T_0_50[-1])),\n",
@@ -217,14 +225,14 @@
     "pyplot.legend()\n",
     "show_plot('fig_8')"
    ],
-   "id": "3f97b336a478a65a",
+   "id": "fd51ae9370fec8d7",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ],
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@@ -237,26 +245,26 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "0eb6d20391bf4dacbf6c06a439ad7669"
+       "model_id": "cc95c25f87184e01a8cc0712442e21bd"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 18
+   "execution_count": 25
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.408909Z",
-     "start_time": "2025-07-03T13:12:32.248739Z"
+     "end_time": "2025-07-06T20:04:15.536558Z",
+     "start_time": "2025-07-06T20:04:15.173042Z"
     }
    },
    "cell_type": "code",
    "source": [
-    "saturation_difference = saturation_wrt_ice - eff_saturation_wrt_ice\n",
-    "pyplot.plot(K2C(T_0_50), abs(saturation_difference), 'g')\n",
+    "saturation_difference = saturation_wrt_ice_at_RH100 - eff_saturation_wrt_ice_at_RH100\n",
+    "pyplot.plot(K2C(T_0_50), abs(saturation_difference))\n",
     "pyplot.grid()\n",
     "pyplot.gca().set(\n",
     "    title=\"Absolute difference between environment and effective saturation wrt ice\",\n",
@@ -265,14 +273,14 @@
     ")\n",
     "show_plot(\"Si_minus_effective_Si\")"
    ],
-   "id": "2e95a50c723d4181",
+   "id": "2573a83fb26b7f0f",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ],
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@@ -285,14 +293,14 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "4aa2eb17a4214eb280239987e6e15ba7"
+       "model_id": "8e4839cdcd2b45a5a06471bc2243817c"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 19
+   "execution_count": 16
   },
   {
    "metadata": {},
@@ -301,16 +309,13 @@
    "id": "c24f76eff2cd8537"
   },
   {
-   "metadata": {
-    "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.584004Z",
-     "start_time": "2025-07-03T13:12:32.426510Z"
-    }
-   },
+   "metadata": {},
    "cell_type": "code",
+   "outputs": [],
+   "execution_count": null,
    "source": [
-    "pyplot.plot(K2C(T_0_50), alpha_kinetic, 'g', label=\"with Si\")\n",
-    "pyplot.plot(K2C(T_0_50), eff_alpha_kinetic, 'g--', label=\"with effective Si\")\n",
+    "pyplot.plot(K2C(T_0_50), alpha_kinetic, 'k', label=\"with Si\")\n",
+    "pyplot.plot(K2C(T_0_50), eff_alpha_kinetic, 'k--', label=\"with effective Si\")\n",
     "pyplot.legend()\n",
     "pyplot.gca().set(\n",
     "    title=\"Kinetic Fractionation Factors of Temperature\",\n",
@@ -320,34 +325,7 @@
     "pyplot.grid()\n",
     "show_plot('alpha_kinetic_of_temperature')"
    ],
-   "id": "15ec13a660cf954f",
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ],
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-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/plain": [
-       "HBox(children=(HTML(value=\"<a href='./alpha_kinetic_of_temperature.pdf' target='_blank'>./alpha_kinetic_of_tem…"
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-      "application/vnd.jupyter.widget-view+json": {
-       "version_major": 2,
-       "version_minor": 0,
-       "model_id": "a71b79fcdf3e4e39853ad8dbb0e67178"
-      }
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "execution_count": 20
+   "id": "a6f43368e6074e34"
   },
   {
    "metadata": {},
@@ -362,8 +340,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.605388Z",
-     "start_time": "2025-07-03T13:12:32.602097Z"
+     "end_time": "2025-07-06T20:04:16.545887Z",
+     "start_time": "2025-07-06T20:04:15.736925Z"
     }
    },
    "cell_type": "code",
@@ -384,13 +362,13 @@
    ],
    "id": "1a7e5ae0c7093428",
    "outputs": [],
-   "execution_count": 21
+   "execution_count": 18
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-03T13:12:32.781402Z",
-     "start_time": "2025-07-03T13:12:32.621724Z"
+     "end_time": "2025-07-06T20:07:07.248422Z",
+     "start_time": "2025-07-06T20:07:07.032942Z"
     }
    },
    "cell_type": "code",
@@ -399,8 +377,8 @@
     "    pyplot.plot(\n",
     "        Si,\n",
     "        alphas_eff[:, i],\n",
-    "        label=f'{K2C(T):.5g} [°C]',\n",
-    "        color='g',\n",
+    "        'g',\n",
+    "        label=f'${K2C(T):.5g}$ [°C]',\n",
     "        linewidth = 1 + i/2\n",
     "    )\n",
     "pyplot.gca().set(\n",
@@ -412,14 +390,14 @@
     "pyplot.legend()\n",
     "show_plot('fig_9')"
    ],
-   "id": "8b1287b4696c7dda",
+   "id": "7c07f76691edf597",
    "outputs": [
     {
      "data": {
       "text/plain": [
        "<Figure size 640x480 with 1 Axes>"
       ],
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        "version_major": 2,
        "version_minor": 0,
-       "model_id": "0501ac8ed30b49c49a0be9dbe35e4896"
+       "model_id": "aae7df482fc24947abeee8f5fde425fa"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 22
+   "execution_count": 23
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "outputs": [],
+   "execution_count": null,
+   "source": "",
+   "id": "d482baa7f1c16462"
   }
  ],
  "metadata": {

From 6efd7bf651d9eb94d600441a76965098a2ebfd7b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 10 Jul 2025 12:57:03 +0200
Subject: [PATCH 22/26] update formula for transfer coeff to match J&M 1984

---
 .../jouzel_and_merlivat_1984.py               |   4 +-
 .../Jouzel_and_Merlivat_1984/fig_8_9.ipynb    | 130 +++++++++++-------
 2 files changed, 84 insertions(+), 50 deletions(-)

diff --git a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
index 0e4ae30502..783388dc6a 100644
--- a/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
+++ b/PySDM/physics/isotope_kinetic_fractionation_factors/jouzel_and_merlivat_1984.py
@@ -32,7 +32,7 @@ def alpha_kinetic(alpha_equilibrium, saturation, D_ratio_heavy_to_light):
         )
 
     @staticmethod
-    def transfer_coefficient(D, Fk):
+    def transfer_coefficient(const, rho_s, D, Fk):
         """
         eq. (A4) in Jouzel & Merlivat 1975,
         eq. (A6) in Bolot 2013.
@@ -48,7 +48,7 @@ def transfer_coefficient(D, Fk):
         ----------
         Thermal transfer coefficient between water vapour and condensate.
         """
-        return 1 / (1 + D * Fk)
+        return 1 / (1 + D * rho_s / const.rho_w * Fk)
 
     @staticmethod
     def effective_saturation(transfer_coefficient, RH):
diff --git a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
index a59c28a76d..e38ee8b6fb 100644
--- a/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
+++ b/examples/PySDM_examples/Jouzel_and_Merlivat_1984/fig_8_9.ipynb
@@ -23,8 +23,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:04:14.905723Z",
-     "start_time": "2025-07-06T20:04:14.900796Z"
+     "end_time": "2025-07-10T10:48:11.678433Z",
+     "start_time": "2025-07-10T10:48:11.674981Z"
     }
    },
    "cell_type": "code",
@@ -37,7 +37,7 @@
    ],
    "id": "466d06cabb3174f3",
    "outputs": [],
-   "execution_count": 9
+   "execution_count": 1
   },
   {
    "cell_type": "code",
@@ -45,8 +45,8 @@
    "metadata": {
     "collapsed": true,
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:04:14.925137Z",
-     "start_time": "2025-07-06T20:04:14.922741Z"
+     "end_time": "2025-07-10T10:48:13.278425Z",
+     "start_time": "2025-07-10T10:48:11.743948Z"
     }
    },
    "source": [
@@ -58,13 +58,13 @@
     "from open_atmos_jupyter_utils import show_plot"
    ],
    "outputs": [],
-   "execution_count": 10
+   "execution_count": 2
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:04:14.947223Z",
-     "start_time": "2025-07-06T20:04:14.940365Z"
+     "end_time": "2025-07-10T10:48:13.549139Z",
+     "start_time": "2025-07-10T10:48:13.285324Z"
     }
    },
    "cell_type": "code",
@@ -89,13 +89,13 @@
    ],
    "id": "6f7078d9d56a0a7c",
    "outputs": [],
-   "execution_count": 11
+   "execution_count": 3
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:04:14.964248Z",
-     "start_time": "2025-07-06T20:04:14.957645Z"
+     "end_time": "2025-07-10T10:48:13.561668Z",
+     "start_time": "2025-07-10T10:48:13.559532Z"
     }
    },
    "cell_type": "code",
@@ -110,7 +110,7 @@
    ],
    "id": "2c7e390144e7499",
    "outputs": [],
-   "execution_count": 12
+   "execution_count": 4
   },
   {
    "metadata": {},
@@ -121,8 +121,8 @@
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:04:14.974512Z",
-     "start_time": "2025-07-06T20:04:14.971371Z"
+     "end_time": "2025-07-10T10:48:15.236361Z",
+     "start_time": "2025-07-10T10:48:13.569626Z"
     }
    },
    "cell_type": "code",
@@ -136,14 +136,13 @@
     "    T=T_0_50,\n",
     "    K=formulae.diffusion_thermics.K(T=T_0_50, p=pressure),\n",
     "    lv=formulae.latent_heat_vapourisation.lv(T_0_50)\n",
-    ") / const.rho_w * pvs_ice(T_0_50) / const.Rv / T_0_50 # TODO change A definition or call it differently\n",
-    "\n",
+    ")\n",
     "\n",
     "saturation_wrt_ice_at_RH100 = pvs_water(T_0_50) / pvs_ice(T_0_50)\n",
     "\n",
-    "\n",
     "eff_saturation_wrt_ice_at_RH100 = formulae.isotope_kinetic_fractionation_factors.effective_saturation(\n",
     "    transfer_coefficient=formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(\n",
+    "    rho_s = pvs_ice(T_0_50) / const.Rv / T_0_50,\n",
     "    D=D_light,\n",
     "    Fk=Fk\n",
     "),\n",
@@ -152,13 +151,13 @@
    ],
    "id": "47503ee93cc639b7",
    "outputs": [],
-   "execution_count": 13
+   "execution_count": 5
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:04:14.984673Z",
-     "start_time": "2025-07-06T20:04:14.982519Z"
+     "end_time": "2025-07-10T10:48:16.174530Z",
+     "start_time": "2025-07-10T10:48:15.248702Z"
     }
    },
    "cell_type": "code",
@@ -178,13 +177,13 @@
    ],
    "id": "ad049bb8d20fa39b",
    "outputs": [],
-   "execution_count": 14
+   "execution_count": 6
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:09:04.656624Z",
-     "start_time": "2025-07-06T20:09:04.456285Z"
+     "end_time": "2025-07-10T10:48:16.674907Z",
+     "start_time": "2025-07-10T10:48:16.184371Z"
     }
    },
    "cell_type": "code",
@@ -232,7 +231,7 @@
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        "<Figure size 640x480 with 1 Axes>"
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@@ -245,26 +244,26 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "cc95c25f87184e01a8cc0712442e21bd"
+       "model_id": "a1dfa4c3b72242c39e736397d22a942d"
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      "metadata": {},
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     }
    ],
-   "execution_count": 25
+   "execution_count": 7
   },
   {
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2025-07-06T20:04:15.536558Z",
-     "start_time": "2025-07-06T20:04:15.173042Z"
+     "end_time": "2025-07-10T10:48:16.991147Z",
+     "start_time": "2025-07-10T10:48:16.706807Z"
     }
    },
    "cell_type": "code",
    "source": [
     "saturation_difference = saturation_wrt_ice_at_RH100 - eff_saturation_wrt_ice_at_RH100\n",
-    "pyplot.plot(K2C(T_0_50), abs(saturation_difference))\n",
+    "pyplot.plot(K2C(T_0_50), abs(saturation_difference), 'k')\n",
     "pyplot.grid()\n",
     "pyplot.gca().set(\n",
     "    title=\"Absolute difference between environment and effective saturation wrt ice\",\n",
@@ -280,7 +279,7 @@
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@@ -293,14 +292,14 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "8e4839cdcd2b45a5a06471bc2243817c"
+       "model_id": "383f4d6a91a64d058af9e8e32b46fb5d"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 16
+   "execution_count": 8
   },
   {
    "metadata": {},
@@ -309,10 +308,13 @@
    "id": "c24f76eff2cd8537"
   },
   {
-   "metadata": {},
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-10T10:48:17.154165Z",
+     "start_time": "2025-07-10T10:48:17.008329Z"
+    }
+   },
    "cell_type": "code",
-   "outputs": [],
-   "execution_count": null,
    "source": [
     "pyplot.plot(K2C(T_0_50), alpha_kinetic, 'k', label=\"with Si\")\n",
     "pyplot.plot(K2C(T_0_50), eff_alpha_kinetic, 'k--', label=\"with effective Si\")\n",
@@ -325,7 +327,34 @@
     "pyplot.grid()\n",
     "show_plot('alpha_kinetic_of_temperature')"
    ],
-   "id": "a6f43368e6074e34"
+   "id": "a6f43368e6074e34",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ],
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      },
      "metadata": {},
      "output_type": "display_data"
@@ -410,22 +439,27 @@
       "application/vnd.jupyter.widget-view+json": {
        "version_major": 2,
        "version_minor": 0,
-       "model_id": "aae7df482fc24947abeee8f5fde425fa"
+       "model_id": "df8d0f3528124da78a006fd0b6c88e9c"
       }
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
-   "execution_count": 23
+   "execution_count": 11
   },
   {
-   "metadata": {},
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-07-10T10:48:18.272016Z",
+     "start_time": "2025-07-10T10:48:18.269850Z"
+    }
+   },
    "cell_type": "code",
-   "outputs": [],
-   "execution_count": null,
    "source": "",
-   "id": "d482baa7f1c16462"
+   "id": "d482baa7f1c16462",
+   "outputs": [],
+   "execution_count": null
   }
  ],
  "metadata": {

From dbe2f4b1feb96c7ab257ff5037d183cc4046824e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 10 Jul 2025 13:41:50 +0200
Subject: [PATCH 23/26] add test for effective saturation

---
 ...t_isotope_kinetic_fractionation_factors.py | 36 +++++++++++++++++++
 1 file changed, 36 insertions(+)

diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 0596c876fc..641e323ecb 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -4,6 +4,7 @@
 
 import numpy as np
 import pytest
+from _pytest import mark
 from matplotlib import pyplot
 
 from PySDM import Formulae
@@ -183,3 +184,38 @@ def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(
         # assert
         np.testing.assert_equal(n > 0.5, True)
         np.testing.assert_equal(n < 1, True)
+
+    @staticmethod
+    def test_effective_saturation():
+        # arrange
+        formulae = Formulae(
+            isotope_kinetic_fractionation_factors="JouzelAndMerlivat1984",
+            drop_growth="Mason1971",
+        )
+        const = formulae.constants
+        saturation = np.linspace(0.8, 1.2)
+        T = 263.15
+        rho_s = formulae.saturation_vapour_pressure.pvs_ice(T) / const.Rv / T
+        Fk = formulae.drop_growth.Fk(
+            T=T,
+            K=const.K0,
+            lv=formulae.latent_heat_vapourisation.lv(T),
+        )
+        A_li = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(
+            rho_s=rho_s, D=const.D0, Fk=Fk
+        )
+
+        # act
+        sut = formulae.isotope_kinetic_fractionation_factors.effective_saturation(
+            transfer_coefficient=A_li,
+            RH=saturation,
+        )
+        idx_subsaturation = np.where(saturation < 1)
+
+        # assert
+        np.testing.assert_array_less(
+            saturation[idx_subsaturation], sut[idx_subsaturation]
+        )
+        np.testing.assert_array_less(
+            sut[~idx_subsaturation[0]], saturation[~idx_subsaturation[0]]
+        )

From 06beac75d66df447657522ae9d1a7150902371d1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 10 Jul 2025 18:05:49 +0200
Subject: [PATCH 24/26] fix test after refactor

---
 .../test_isotope_kinetic_fractionation_factors.py   | 13 ++++++++-----
 1 file changed, 8 insertions(+), 5 deletions(-)

diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 641e323ecb..4aabeb3b5d 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -4,7 +4,6 @@
 
 import numpy as np
 import pytest
-from _pytest import mark
 from matplotlib import pyplot
 
 from PySDM import Formulae
@@ -39,11 +38,15 @@ def test_units_alpha_kinetic():
     def test_units_transfer_coefficient():
         with DimensionalAnalysis():
             # arrange
+            const = Formulae().constants
+            rho_s = 1 * physics.si.g / physics.si.m**3
             D = 1 * physics.si.m**2 / physics.si.s
             Fk = 1 * physics.si.s / physics.si.m**2
 
             # act
-            sut = JouzelAndMerlivat1984.transfer_coefficient(D=D, Fk=Fk)
+            sut = JouzelAndMerlivat1984.transfer_coefficient(
+                const=const, D=D, Fk=Fk, rho_s=rho_s
+            )
 
             # assert
             assert sut.check("[]")
@@ -186,15 +189,15 @@ def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(
         np.testing.assert_equal(n < 1, True)
 
     @staticmethod
-    def test_effective_saturation():
+    @pytest.mark.parametrize("T", np.linspace(240, 300, 11))
+    def test_effective_saturation(T):
         # arrange
         formulae = Formulae(
             isotope_kinetic_fractionation_factors="JouzelAndMerlivat1984",
             drop_growth="Mason1971",
         )
         const = formulae.constants
-        saturation = np.linspace(0.8, 1.2)
-        T = 263.15
+        saturation = np.linspace(0.8, 1.2, 21)
         rho_s = formulae.saturation_vapour_pressure.pvs_ice(T) / const.Rv / T
         Fk = formulae.drop_growth.Fk(
             T=T,

From 8bf5a4938b3a7c248353a4bbf778aed2a593aa80 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 10 Jul 2025 19:53:56 +0200
Subject: [PATCH 25/26] fix test after refactor vol2

---
 .../smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
index af4a3679f8..1064a89c5f 100644
--- a/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
+++ b/tests/smoke_tests/no_env/jouzel_and_merlivat_1984/test_fig_8.py
@@ -44,9 +44,9 @@ def test_fig8_values_against_the_paper(
         # arrange
         temperature_C = notebook_variables["T_0_50"] - T0
         if if_effective:
-            Si = notebook_variables["eff_saturation_wrt_ice"]
+            Si = notebook_variables["eff_saturation_wrt_ice_at_RH100"]
         else:
-            Si = notebook_variables["saturation_wrt_ice"]
+            Si = notebook_variables["saturation_wrt_ice_at_RH100"]
 
         # act
         sut = Si[np.argmin(np.abs(temperature_C - temp_C))]

From 7d555dfeec056e8dbfd41082fd0709c4c3bc0896 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Agnieszka=20=C5=BBaba?= <azaba@agh.edu.pl>
Date: Thu, 10 Jul 2025 20:32:46 +0200
Subject: [PATCH 26/26] use class in test instead Formulae

---
 .../test_isotope_kinetic_fractionation_factors.py     | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
index 4aabeb3b5d..1a1855c362 100644
--- a/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
+++ b/tests/unit_tests/physics/test_isotope_kinetic_fractionation_factors.py
@@ -192,10 +192,7 @@ def test_alpha_kinetic_jouzel_merlivat_vs_craig_gordon(
     @pytest.mark.parametrize("T", np.linspace(240, 300, 11))
     def test_effective_saturation(T):
         # arrange
-        formulae = Formulae(
-            isotope_kinetic_fractionation_factors="JouzelAndMerlivat1984",
-            drop_growth="Mason1971",
-        )
+        formulae = Formulae(drop_growth="Mason1971")
         const = formulae.constants
         saturation = np.linspace(0.8, 1.2, 21)
         rho_s = formulae.saturation_vapour_pressure.pvs_ice(T) / const.Rv / T
@@ -204,12 +201,12 @@ def test_effective_saturation(T):
             K=const.K0,
             lv=formulae.latent_heat_vapourisation.lv(T),
         )
-        A_li = formulae.isotope_kinetic_fractionation_factors.transfer_coefficient(
-            rho_s=rho_s, D=const.D0, Fk=Fk
+        A_li = JouzelAndMerlivat1984.transfer_coefficient(
+            const=const, rho_s=rho_s, D=const.D0, Fk=Fk
         )
 
         # act
-        sut = formulae.isotope_kinetic_fractionation_factors.effective_saturation(
+        sut = JouzelAndMerlivat1984.effective_saturation(
             transfer_coefficient=A_li,
             RH=saturation,
         )