diff --git a/PySDM/backends/impl_numba/test_helpers/scipy_ode_condensation_solver.py b/PySDM/backends/impl_numba/test_helpers/scipy_ode_condensation_solver.py
index 1ea2a43d0..1ac2740af 100644
--- a/PySDM/backends/impl_numba/test_helpers/scipy_ode_condensation_solver.py
+++ b/PySDM/backends/impl_numba/test_helpers/scipy_ode_condensation_solver.py
@@ -83,7 +83,7 @@ def _condensation(
         RH_max=RH_max.data,
         success=success.data,
     )
-    particulator.attributes.mark_updated("water mass")
+    particulator.attributes.mark_updated("signed water mass")
 
 
 @lru_cache()
diff --git a/PySDM/particulator.py b/PySDM/particulator.py
index 5919feb80..7c0824fe0 100644
--- a/PySDM/particulator.py
+++ b/PySDM/particulator.py
@@ -546,6 +546,7 @@ def homogeneous_freezing_time_dependent(self, *, rand: Storage):
             temperature=self.environment["T"],
             relative_humidity_ice=self.environment["RH_ice"],
         )
+        self.attributes.mark_updated("signed water mass")
 
     def homogeneous_freezing_threshold(self):
         self.backend.homogeneous_freezing_threshold(
@@ -556,6 +557,7 @@ def homogeneous_freezing_threshold(self):
             temperature=self.environment["T"],
             relative_humidity_ice=self.environment["RH_ice"],
         )
+        self.attributes.mark_updated("signed water mass")
 
     def thaw_instantaneous(self):
         self.backend.thaw_instantaneous(
@@ -565,3 +567,4 @@ def thaw_instantaneous(self):
             cell=self.attributes["cell id"],
             temperature=self.environment["T"],
         )
+        self.attributes.mark_updated("signed water mass")
diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/__init__.py b/examples/PySDM_examples/Luettmer_homogeneous_freezing/__init__.py
new file mode 100644
index 000000000..d7b9c920c
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/__init__.py
@@ -0,0 +1,15 @@
+"""
+Homogeneous freezing example
+
+hom_freezing.ipynb:
+.. include:: ./hom_freezing.ipynb
+"""
+
+from .settings import Settings
+from .simulation import Simulation
+from .plot import (
+    plot_thermodynamics_and_bulk,
+    plot_freezing_temperatures_histogram,
+    plot_freezing_temperatures_2d_histogram,
+    plot_freezing_temperatures_2d_histogram_seaborn,
+)
diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/commons.py b/examples/PySDM_examples/Luettmer_homogeneous_freezing/commons.py
new file mode 100644
index 000000000..156a0a3bf
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/commons.py
@@ -0,0 +1,85 @@
+# import numpy as np
+from PySDM import Formulae
+from PySDM.physics.constants import si
+from PySDM.backends import CPU
+import time
+
+from PySDM_examples.Luettmer_homogeneous_freezing.settings import Settings
+from PySDM_examples.Luettmer_homogeneous_freezing.simulation import Simulation
+
+
+formulae = Formulae(
+    particle_shape_and_density="MixedPhaseSpheres",
+)
+
+
+def run_simulations(setting):
+
+    simulation = {
+        "settings": setting,
+        "ensemble_member_outputs": [],
+    }
+    for n in range(setting["number_of_ensemble_runs"]):
+        model_setup = Settings(**simulation["settings"])
+        model_setup.formulae.seed += 1
+        model = Simulation(model_setup)
+        simulation["ensemble_member_outputs"].append(model.run())
+
+    return simulation
+
+
+def hom_pure_droplet_freezing_backend():
+    backends = {
+        "threshold": CPU(
+            formulae=Formulae(
+                particle_shape_and_density="MixedPhaseSpheres",
+                homogeneous_ice_nucleation_rate="Null",
+                saturation_vapour_pressure="MurphyKoop2005",
+                seed=time.time_ns(),
+            )
+        ),
+        "KoopMurray2016": CPU(
+            formulae=Formulae(
+                particle_shape_and_density="MixedPhaseSpheres",
+                homogeneous_ice_nucleation_rate="KoopMurray2016",
+                saturation_vapour_pressure="MurphyKoop2005",
+                seed=time.time_ns(),
+            )
+        ),
+        "Spichtinger2023": CPU(
+            formulae=Formulae(
+                particle_shape_and_density="MixedPhaseSpheres",
+                homogeneous_ice_nucleation_rate="Koop_Correction",
+                saturation_vapour_pressure="MurphyKoop2005",
+                seed=time.time_ns(),
+            )
+        ),
+        "Koop2000": CPU(
+            formulae=Formulae(
+                particle_shape_and_density="MixedPhaseSpheres",
+                homogeneous_ice_nucleation_rate="Koop2000",
+                saturation_vapour_pressure="MurphyKoop2005",
+                seed=time.time_ns(),
+            )
+        ),
+    }
+    return backends
+
+
+def hom_pure_droplet_freezing_standard_setup():
+    standard = {
+        "n_sd": int(1e3),
+        "w_updraft": 1.0 * si.meter / si.second,
+        "T0": formulae.trivia.C2K(-25),
+        "dz": 0.1 * si.meter,
+        "N_dv_droplet_distribution": 750 / si.cm**3,
+        "r_mean_droplet_distribution": 15 * si.nanometer,
+        "type_droplet_distribution": "monodisperse",
+        "RH_0": 0.995,
+        "p0": 500 * si.hectopascals,
+        "condensation_enable": True,
+        "deposition_enable": True,
+        "deposition_adaptive": True,
+        "number_of_ensemble_runs": 1,
+    }
+    return standard
diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing.ipynb b/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing.ipynb
new file mode 100644
index 000000000..20ed870c7
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing.ipynb
@@ -0,0 +1,923 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "id": "initial_id",
+   "metadata": {
+    "collapsed": true,
+    "ExecuteTime": {
+     "end_time": "2025-09-29T01:46:26.621707Z",
+     "start_time": "2025-09-29T01:46:16.313525Z"
+    }
+   },
+   "source": [
+    "import numpy as np\n",
+    "from PySDM.physics.constants import si\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.commons import run_simulations, hom_pure_droplet_freezing_backend, hom_pure_droplet_freezing_standard_setup\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.simulation import Simulation\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.settings import Settings\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing import plot\n",
+    "from importlib import reload\n",
+    "from matplotlib import pyplot\n",
+    "from open_atmos_jupyter_utils import show_plot"
+   ],
+   "outputs": [],
+   "execution_count": 1
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-25T07:45:50.718554Z",
+     "start_time": "2025-09-25T07:45:50.104588Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" General settings \"\"\"\n",
+    "hom_freezing_types     = [  \"KoopMurray2016\", \"Spichtinger2023\" ]\n",
+    "hom_freezing_types_all = [  \"KoopMurray2016\", \"Spichtinger2023\", \"Koop2000\"  ]\n",
+    "vertical_updrafts = np.geomspace(0.2,10,num=9) * si.meter / si.second\n",
+    "number_concentrations = np.geomspace(100, 20000, num=10) / si.cm ** 3\n",
+    "\n",
+    "backends = hom_pure_droplet_freezing_backend()\n",
+    "standard = hom_pure_droplet_freezing_standard_setup()"
+   ],
+   "id": "4d6a0d9ca45d5029",
+   "outputs": [],
+   "execution_count": 2
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-25T08:22:15.004972Z",
+     "start_time": "2025-09-25T08:13:48.244449Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\n",
+    "\"\"\" High output step reference simulations \"\"\"\n",
+    "setting_dict = {\n",
+    "            **standard,\n",
+    "            \"backend\": backends[\"KoopMurray2016\"],\n",
+    "            \"hom_freezing\": \"KoopMurray2016\",\n",
+    "            \"w_updraft\": 2.5,\n",
+    "            \"deposition_enable\": False,\n",
+    "            \"n_output\": 1\n",
+    "            }\n",
+    "KoopMurray2016_reference_high_w_simulation = run_simulations(setting_dict)\n",
+    "setting_dict = {\n",
+    "            **standard,\n",
+    "            \"backend\": backends[\"Spichtinger2023\"],\n",
+    "            \"hom_freezing\": \"Spichtinger2023\",\n",
+    "            \"w_updraft\": 2.5,\n",
+    "            \"deposition_enable\": False,\n",
+    "            \"n_output\": 1,\n",
+    "            \"dz\": 0.1,\n",
+    "            }\n",
+    "Spichtinger2023_reference_high_w_simulation = run_simulations(setting_dict)\n",
+    "setting_dict = {\n",
+    "            **standard,\n",
+    "            \"backend\": backends[\"KoopMurray2016\"],\n",
+    "            \"hom_freezing\": \"KoopMurray2016\",\n",
+    "            \"w_updraft\": 0.2,\n",
+    "            \"deposition_enable\": False,\n",
+    "            \"n_output\": 1,\n",
+    "            \"dz\": 0.1,\n",
+    "            }\n",
+    "KoopMurray2016_reference_low_w_simulation = run_simulations(setting_dict)"
+   ],
+   "id": "9f42826e52927bdf",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=2.5 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=2.5 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.2 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 7
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-25T08:35:02.292843Z",
+     "start_time": "2025-09-25T08:34:30.039503Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "reload(plot)\n",
+    "plot.plot_thermodynamics_and_bulk(KoopMurray2016_reference_high_w_simulation, \" without vapor deposition\")\n",
+    "show_plot(\"fig_KM16_high_w_no_dep\")\n",
+    "plot.plot_thermodynamics_and_bulk(Spichtinger2023_reference_high_w_simulation, \" without vapor deposition\")\n",
+    "show_plot(\"fig_SP23_high_w_no_dep\")\n",
+    "plot.plot_thermodynamics_and_bulk(KoopMurray2016_reference_low_w_simulation, \" without vapor deposition\")\n",
+    "show_plot(\"fig_KM16_low_w_no_dep\")"
+   ],
+   "id": "69e81c6c0f755b5b",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 1000x1000 with 6 Axes>"
+      ],
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+     },
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+     "output_type": "display_data",
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+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./fig_KM16_low_w_no_dep.pdf' target='_blank'>./fig_KM16_low_w_no_dep.pdf</…"
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+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "1f27da42a3914487bec688de7a1c1d53"
+      }
+     },
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+     "output_type": "display_data",
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+    }
+   ],
+   "execution_count": 11
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-25T14:39:13.993608Z",
+     "start_time": "2025-09-25T14:23:08.505732Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Simulations for n_sd ensemble without deposition \"\"\"\n",
+    "nsd_ensemble_simulations =[]\n",
+    "number_of_nsd = (1e1, 1e2, 1e3)\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for n_sd in number_of_nsd:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"n_sd\": int(n_sd),\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "            \"number_of_ensemble_runs\": 5,\n",
+    "            \"deposition_enable\": False,\n",
+    "            }\n",
+    "        nsd_ensemble_simulations.append( run_simulations(setting_dict) )"
+   ],
+   "id": "3e2e1854ea79f7b",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 12
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T06:40:31.975151Z",
+     "start_time": "2025-09-24T06:40:24.630199Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Plots for n_sd ensemble without deposition \"\"\"\n",
+    "reload(plot)\n",
+    "for n_sd in number_of_nsd:\n",
+    "    fig, axs = pyplot.subplots(1, 2, figsize=(12, 4), constrained_layout=True)\n",
+    "    fig.suptitle(r\"$N_{sd}$: \"+\"{}\".format(int(n_sd))+\"     w: \"+str(standard[\"w_updraft\"])+r\" $\\mathrm{m \\, s^{-1}}$\"+r\"     $n_{ccn}$: \"+str(750)+r\" $\\mathrm{kg \\, kg^{-1}}$\",fontsize=20)\n",
+    "    axs = axs.ravel()\n",
+    "    i = 0\n",
+    "    for simulation in nsd_ensemble_simulations:\n",
+    "        if simulation[\"settings\"][\"n_sd\"] == n_sd and simulation[\"settings\"][\"w_updraft\"] == standard[\"w_updraft\"]:\n",
+    "            axs[i] = plot.plot_freezing_temperatures_histogram(axs[i], simulation)\n",
+    "            i += 1\n",
+    "    show_plot(\"n_sd_\"+str(n_sd)+\"_ensemble_without_deposition\")"
+   ],
+   "id": "4583396062c65a6",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 1200x400 with 2 Axes>"
+      ],
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+   "source": [
+    "\"\"\" Updraft ensemble simulations without deposition  \"\"\"\n",
+    "simulations_ensemble_no_deposition = []\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for updraft in vertical_updrafts:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"w_updraft\": updraft  * si.meter / si.second,\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "            \"deposition_enable\": False,\n",
+    "            }\n",
+    "        simulations_ensemble_no_deposition.append( run_simulations(setting_dict) )"
+   ],
+   "id": "c6b2cb90d6533376",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.2 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.32613788179066194 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.5318295896944989 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.8672488792828036 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.4142135623730951 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=2.306143078159937 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=3.760603093086394 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=6.132375635173039 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=10.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.2 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.32613788179066194 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.5318295896944989 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.8672488792828036 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.4142135623730951 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=2.306143078159937 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=3.760603093086394 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=6.132375635173039 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=10.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 9
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T07:04:15.501592Z",
+     "start_time": "2025-09-24T07:04:10.605370Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Plot ensemble simulations without deposition  \"\"\"\n",
+    "reload(plot)\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "\n",
+    "    histogram_data_dict = {}\n",
+    "\n",
+    "    histogram_data_dict[\"hom_freezing_type\"] = hom_freezing_type\n",
+    "    histogram_data_dict[\"T_frz_histogram_list\"] = []\n",
+    "    histogram_data_dict[\"w_updraft_histogram_list\"] = []\n",
+    "\n",
+    "    for i, updraft in enumerate(vertical_updrafts):\n",
+    "        for simulation in simulations_ensemble_no_deposition:\n",
+    "            if (simulation[\"settings\"][\"w_updraft\"] == updraft\n",
+    "                    and simulation[\"settings\"][\"hom_freezing\"] == hom_freezing_type):\n",
+    "                output = simulation[\"ensemble_member_outputs\"][0]\n",
+    "                T_frz = output[\"T_frz\"]\n",
+    "                histogram_data_dict[\"T_frz_histogram_list\"].extend( T_frz )\n",
+    "                histogram_data_dict[\"w_updraft_histogram_list\"].extend( np.full_like(T_frz, updraft) )\n",
+    "\n",
+    "    plot.plot_freezing_temperatures_2d_histogram_seaborn(histogram_data_dict, title_add = \" without vapor deposition\")\n",
+    "    show_plot(hom_freezing_type+\"_updraft_ensemble_no_deposition\")"
+   ],
+   "id": "bed0dd6290f2a8ec",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./Spichtinger2023_updraft_ensemble_no_deposition.pdf' target='_blank'>./Sp…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "3dbdd068dc79410486d1ddbc9df2584a"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 10
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T07:28:52.645062Z",
+     "start_time": "2025-09-24T07:04:15.603620Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Simulations for CCN concentration histogram  \"\"\"\n",
+    "simulations_ccn_concentration_ensemble = []\n",
+    "\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for n_dv in number_concentrations:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"N_dv_droplet_distribution\": n_dv,\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "            \"deposition_enable\": False,\n",
+    "        }\n",
+    "        simulations_ccn_concentration_ensemble.append(run_simulations(setting_dict))"
+   ],
+   "id": "5ad7e4f68543fae0",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=99999999.99999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=180164823.06544116\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=324593634.7020169\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=584803547.6425728\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=1053610276.8906642\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=1898235091.1593704\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=3419951893.3533926\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=6161550277.583339\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=11100946155.696224\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=19999999999.999996\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=99999999.99999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=180164823.06544116\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=324593634.7020169\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=584803547.6425728\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=1053610276.8906642\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=1898235091.1593704\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=3419951893.3533926\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=6161550277.583339\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=11100946155.696224\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=19999999999.999996\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 11
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T07:29:04.320244Z",
+     "start_time": "2025-09-24T07:28:53.154955Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "\n",
+    "    histogram_data_ccn_concentration_ensemble = {}\n",
+    "    histogram_data_ccn_concentration_ensemble[\"hom_freezing_type\"] = hom_freezing_type\n",
+    "\n",
+    "    histogram_data_ccn_concentration_ensemble[\"T_frz_histogram_list\"] = []\n",
+    "    histogram_data_ccn_concentration_ensemble[\"n_ccn_histogram_list\"] = []\n",
+    "    histogram_data_ccn_concentration_ensemble[\"rc_max_histogram_list\"] = []\n",
+    "\n",
+    "    for n_ccn in number_concentrations:\n",
+    "        for simulation in simulations_ccn_concentration_ensemble:\n",
+    "            if (simulation[\"settings\"][\"hom_freezing\"] == hom_freezing_type\n",
+    "                    and simulation[\"settings\"][\"N_dv_droplet_distribution\"] == n_ccn):\n",
+    "                output = simulation[\"ensemble_member_outputs\"][0]\n",
+    "                T_frz = np.asarray(output[\"T_frz\"])\n",
+    "                rc = np.asarray(output[\"rs\"])\n",
+    "                histogram_data_ccn_concentration_ensemble[\"T_frz_histogram_list\"].extend( T_frz )\n",
+    "                histogram_data_ccn_concentration_ensemble[\"n_ccn_histogram_list\"].extend( np.full_like(T_frz, n_ccn) )\n",
+    "                histogram_data_ccn_concentration_ensemble[\"rc_max_histogram_list\"].extend( np.full_like(T_frz, np.amax(rc)) )\n",
+    "\n",
+    "    plot.plot_freezing_temperatures_2d_histogram_seaborn(histogram_data_ccn_concentration_ensemble, title_add=\" without vapor deposition\")\n",
+    "    show_plot(hom_freezing_type+\"_ccn_ensemble_without_deposition\")\n",
+    "    del histogram_data_ccn_concentration_ensemble[\"n_ccn_histogram_list\"]\n",
+    "    plot.plot_freezing_temperatures_2d_histogram_seaborn(histogram_data_ccn_concentration_ensemble, title_add=\" without vapor deposition\")\n",
+    "    show_plot(hom_freezing_type+\"_radius_ensemble_without_deposition\")"
+   ],
+   "id": "cafadc301cb29d15",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 600x600 with 3 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./Spichtinger2023_radius_ensemble_without_deposition.pdf' target='_blank'>…"
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+   ],
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+  }
+ ],
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+ "nbformat": 4,
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+}
diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing_with_coalescence.ipynb b/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing_with_coalescence.ipynb
new file mode 100644
index 000000000..72e4b9099
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing_with_coalescence.ipynb
@@ -0,0 +1,486 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "id": "initial_id",
+   "metadata": {
+    "collapsed": true,
+    "ExecuteTime": {
+     "end_time": "2025-09-30T05:44:56.895488Z",
+     "start_time": "2025-09-30T05:44:47.897804Z"
+    }
+   },
+   "source": [
+    "import numpy as np\n",
+    "from PySDM.physics.constants import si\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.commons import run_simulations, hom_pure_droplet_freezing_backend, hom_pure_droplet_freezing_standard_setup\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.simulation import Simulation\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.settings import Settings\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing import plot\n",
+    "from importlib import reload\n",
+    "from matplotlib import pyplot\n",
+    "from open_atmos_jupyter_utils import show_plot"
+   ],
+   "outputs": [],
+   "execution_count": 1
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-30T05:44:57.356968Z",
+     "start_time": "2025-09-30T05:44:56.908912Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" General settings \"\"\"\n",
+    "hom_freezing_types     = [  \"KoopMurray2016\", \"Spichtinger2023\" ]\n",
+    "vertical_updrafts = np.geomspace(0.2,10,num=9) * si.meter / si.second\n",
+    "\n",
+    "backends = hom_pure_droplet_freezing_backend()\n",
+    "standard = hom_pure_droplet_freezing_standard_setup()"
+   ],
+   "id": "6733571921f473df",
+   "outputs": [],
+   "execution_count": 2
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-30T05:45:03.003239Z",
+     "start_time": "2025-09-30T05:44:57.382366Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "setting_dict = {\n",
+    "            **standard,\n",
+    "            \"backend\": backends[\"KoopMurray2016\"],\n",
+    "            \"hom_freezing\": \"KoopMurray2016\",\n",
+    "            \"w_updraft\": 1.,\n",
+    "            \"deposition_enable\": False,\n",
+    "            \"coalescence_enable\": True,\n",
+    "            \"n_output\": 1,\n",
+    "            \"dz\": 0.2 * si.meter,\n",
+    "            \"n_sd\": 10,\n",
+    "            }\n",
+    "test = Settings(**setting_dict)"
+   ],
+   "id": "a497f7abc7f90fda",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=749999999.9999999\n"
+     ]
+    }
+   ],
+   "execution_count": 3
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-30T05:49:27.849638Z",
+     "start_time": "2025-09-30T05:45:23.051127Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" High output step reference simulations \"\"\"\n",
+    "setting_dict = {\n",
+    "            **standard,\n",
+    "            \"backend\": backends[\"KoopMurray2016\"],\n",
+    "            \"hom_freezing\": \"KoopMurray2016\",\n",
+    "            \"w_updraft\": 1.,\n",
+    "            \"deposition_enable\": False,\n",
+    "            \"coalescence_enable\": True,\n",
+    "            \"n_output\": 1,\n",
+    "            \"dz\": 0.2 * si.meter,\n",
+    "            }\n",
+    "KoopMurray2016_reference_high_w_simulation_no_coal = run_simulations(setting_dict)\n",
+    "\n",
+    "setting_dict[\"coalescence_enable\"] = True\n",
+    "KoopMurray2016_reference_high_w_simulation_coal = run_simulations(setting_dict)\n",
+    "\n",
+    "setting_dict[\"deposition_enable\"] = True\n",
+    "KoopMurray2016_reference_high_w_simulation_coal_and_dep = run_simulations(setting_dict)"
+   ],
+   "id": "a03eb9d441925970",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 4
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-30T05:50:09.825402Z",
+     "start_time": "2025-09-30T05:49:39.530867Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "plot.plot_thermodynamics_and_bulk(KoopMurray2016_reference_high_w_simulation_no_coal, \" without coalescence\", show_conc = True)\n",
+    "show_plot(\"fig_KM16_low_w_no_coal\")\n",
+    "plot.plot_thermodynamics_and_bulk(KoopMurray2016_reference_high_w_simulation_coal, \" with coalescence\", show_conc = True)\n",
+    "show_plot(\"fig_KM16_low_w_coal\")\n",
+    "plot.plot_thermodynamics_and_bulk(KoopMurray2016_reference_high_w_simulation_coal_and_dep, \" with coalescence & deposition\", show_conc = True)\n",
+    "show_plot(\"fig_KM16_low_w_coal_dep\")"
+   ],
+   "id": "3fed46bd1729f946",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./fig_KM16_low_w_no_coal.pdf' target='_blank'>./fig_KM16_low_w_no_coal.pdf…"
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+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "20cb597ed3d647c4bda696451a905c19"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data",
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+   ],
+   "execution_count": 5
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-15T16:44:24.852687Z",
+     "start_time": "2025-09-15T16:35:22.458817Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Simulations for n_sd ensemble with coalescence \"\"\"\n",
+    "nsd_ensemble_simulations =[]\n",
+    "number_of_nsd = (1e1, 1e2, 1e3)\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for n_sd in number_of_nsd:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"n_sd\": int(n_sd),\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "            \"number_of_ensemble_runs\": 5,\n",
+    "            \"deposition_enable\": False,\n",
+    "            \"coalescence_enable\": True,\n",
+    "            }\n",
+    "        nsd_ensemble_simulations.append( run_simulations(setting_dict) )"
+   ],
+   "id": "73dc0631d7c8091a",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 5
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-15T16:44:27.982751Z",
+     "start_time": "2025-09-15T16:44:24.877458Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Plots for n_sd ensemble with coalescence \"\"\"\n",
+    "for n_sd in number_of_nsd:\n",
+    "    fig, axs = pyplot.subplots(1, 2, figsize=(12, 4), constrained_layout=True)\n",
+    "    fig.suptitle(\"Number of super droplets: {}\".format(int(n_sd)),fontsize=20)\n",
+    "    axs = axs.ravel()\n",
+    "    i = 0\n",
+    "    for simulation in nsd_ensemble_simulations:\n",
+    "        if simulation[\"settings\"][\"n_sd\"] == n_sd and simulation[\"settings\"][\"w_updraft\"] == standard[\"w_updraft\"]:\n",
+    "            axs[i] = plot.plot_freezing_temperatures_histogram(axs[i], simulation)\n",
+    "            i += 1\n",
+    "    show_plot(\"n_sd_\"+str(n_sd)+\"_ensemble_coalescence\")"
+   ],
+   "id": "fe27eedc073d8599",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 1200x400 with 2 Axes>"
+      ],
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+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./tmp7b38xu5y.pdf' target='_blank'>./tmp7b38xu5y.pdf</a><br>\"), HTML(value…"
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+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "829a3bcf6b474d53aebaf18f631f188b"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "execution_count": 6
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-29T07:48:13.836195Z",
+     "start_time": "2025-09-29T07:44:25.609327Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Updraft ensemble simulations with coalescence  \"\"\"\n",
+    "simulations_ensemble_no_deposition = []\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for updraft in vertical_updrafts:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"w_updraft\": updraft  * si.meter / si.second,\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "            \"deposition_enable\": False,\n",
+    "            \"coalescence_enable\": True,\n",
+    "            }\n",
+    "        simulations_ensemble_no_deposition.append( run_simulations(setting_dict) )"
+   ],
+   "id": "4574a44aa8f0bf8b",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.2 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "0.5\n",
+      "Starting simulation...\n"
+     ]
+    },
+    {
+     "ename": "KeyboardInterrupt",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001B[31m---------------------------------------------------------------------------\u001B[39m",
+      "\u001B[31mKeyboardInterrupt\u001B[39m                         Traceback (most recent call last)",
+      "\u001B[36mCell\u001B[39m\u001B[36m \u001B[39m\u001B[32mIn[3]\u001B[39m\u001B[32m, line 13\u001B[39m\n\u001B[32m      4\u001B[39m \u001B[38;5;28;01mfor\u001B[39;00m updraft \u001B[38;5;129;01min\u001B[39;00m vertical_updrafts:\n\u001B[32m      5\u001B[39m     setting_dict = {\n\u001B[32m      6\u001B[39m         **standard,\n\u001B[32m      7\u001B[39m         \u001B[33m\"\u001B[39m\u001B[33mw_updraft\u001B[39m\u001B[33m\"\u001B[39m: updraft  * si.meter / si.second,\n\u001B[32m   (...)\u001B[39m\u001B[32m     11\u001B[39m         \u001B[33m\"\u001B[39m\u001B[33mcoalescence_enable\u001B[39m\u001B[33m\"\u001B[39m: \u001B[38;5;28;01mTrue\u001B[39;00m,\n\u001B[32m     12\u001B[39m         }\n\u001B[32m---> \u001B[39m\u001B[32m13\u001B[39m     simulations_ensemble_no_deposition.append( \u001B[43mrun_simulations\u001B[49m\u001B[43m(\u001B[49m\u001B[43msetting_dict\u001B[49m\u001B[43m)\u001B[49m )\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/examples/PySDM_examples/Luettmer_homogeneous_freezing/commons.py:26\u001B[39m, in \u001B[36mrun_simulations\u001B[39m\u001B[34m(setting)\u001B[39m\n\u001B[32m     24\u001B[39m     model_setup.formulae.seed += \u001B[32m1\u001B[39m\n\u001B[32m     25\u001B[39m     model = Simulation(model_setup)\n\u001B[32m---> \u001B[39m\u001B[32m26\u001B[39m     simulation[\u001B[33m\"\u001B[39m\u001B[33mensemble_member_outputs\u001B[39m\u001B[33m\"\u001B[39m].append(\u001B[43mmodel\u001B[49m\u001B[43m.\u001B[49m\u001B[43mrun\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m)\n\u001B[32m     28\u001B[39m \u001B[38;5;28;01mreturn\u001B[39;00m simulation\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/examples/PySDM_examples/Luettmer_homogeneous_freezing/simulation.py:173\u001B[39m, in \u001B[36mSimulation.run\u001B[39m\u001B[34m(self)\u001B[39m\n\u001B[32m    170\u001B[39m \u001B[38;5;28;01mwhile\u001B[39;00m \u001B[38;5;28;01mTrue\u001B[39;00m:\n\u001B[32m    172\u001B[39m     \u001B[38;5;28;01mfor\u001B[39;00m i \u001B[38;5;129;01min\u001B[39;00m \u001B[38;5;28mrange\u001B[39m(\u001B[38;5;28mself\u001B[39m.n_substeps):\n\u001B[32m--> \u001B[39m\u001B[32m173\u001B[39m         \u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mparticulator\u001B[49m\u001B[43m.\u001B[49m\u001B[43mrun\u001B[49m\u001B[43m(\u001B[49m\u001B[32;43m1\u001B[39;49m\u001B[43m)\u001B[49m\n\u001B[32m    174\u001B[39m     \u001B[38;5;66;03m#     do_sedimenation_function:\u001B[39;00m\n\u001B[32m    175\u001B[39m     \u001B[38;5;66;03m#          for j in n_sd:\u001B[39;00m\n\u001B[32m    176\u001B[39m     \u001B[38;5;66;03m#                íf vt(j) > updraft: remove particle\u001B[39;00m\n\u001B[32m    177\u001B[39m     \u001B[38;5;28mself\u001B[39m.save(output)\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/particulator.py:55\u001B[39m, in \u001B[36mParticulator.run\u001B[39m\u001B[34m(self, steps)\u001B[39m\n\u001B[32m     53\u001B[39m \u001B[38;5;28;01mfor\u001B[39;00m key, dynamic \u001B[38;5;129;01min\u001B[39;00m \u001B[38;5;28mself\u001B[39m.dynamics.items():\n\u001B[32m     54\u001B[39m     \u001B[38;5;28;01mwith\u001B[39;00m \u001B[38;5;28mself\u001B[39m.timers[key]:\n\u001B[32m---> \u001B[39m\u001B[32m55\u001B[39m         \u001B[43mdynamic\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[32m     56\u001B[39m \u001B[38;5;28mself\u001B[39m.n_steps += \u001B[32m1\u001B[39m\n\u001B[32m     57\u001B[39m \u001B[38;5;28mself\u001B[39m._notify_observers()\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/dynamics/freezing.py:99\u001B[39m, in \u001B[36mFreezing.__call__\u001B[39m\u001B[34m(self)\u001B[39m\n\u001B[32m     97\u001B[39m \u001B[38;5;28;01melif\u001B[39;00m \u001B[38;5;28mself\u001B[39m.homogeneous_freezing == \u001B[33m\"\u001B[39m\u001B[33mtime-dependent\u001B[39m\u001B[33m\"\u001B[39m:\n\u001B[32m     98\u001B[39m     \u001B[38;5;28mself\u001B[39m.rand.urand(\u001B[38;5;28mself\u001B[39m.rng)\n\u001B[32m---> \u001B[39m\u001B[32m99\u001B[39m     \u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mparticulator\u001B[49m\u001B[43m.\u001B[49m\u001B[43mhomogeneous_freezing_time_dependent\u001B[49m\u001B[43m(\u001B[49m\n\u001B[32m    100\u001B[39m \u001B[43m        \u001B[49m\u001B[43mrand\u001B[49m\u001B[43m=\u001B[49m\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mrand\u001B[49m\u001B[43m,\u001B[49m\n\u001B[32m    101\u001B[39m \u001B[43m    \u001B[49m\u001B[43m)\u001B[49m\n\u001B[32m    103\u001B[39m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mself\u001B[39m.thaw == \u001B[33m\"\u001B[39m\u001B[33minstantaneous\u001B[39m\u001B[33m\"\u001B[39m:\n\u001B[32m    104\u001B[39m     \u001B[38;5;28mself\u001B[39m.particulator.thaw_instantaneous()\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/particulator.py:540\u001B[39m, in \u001B[36mParticulator.homogeneous_freezing_time_dependent\u001B[39m\u001B[34m(self, rand)\u001B[39m\n\u001B[32m    536\u001B[39m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[34mhomogeneous_freezing_time_dependent\u001B[39m(\u001B[38;5;28mself\u001B[39m, *, rand: Storage):\n\u001B[32m    537\u001B[39m     \u001B[38;5;28mself\u001B[39m.backend.homogeneous_freezing_time_dependent(\n\u001B[32m    538\u001B[39m         rand=rand,\n\u001B[32m    539\u001B[39m         attributes=TimeDependentHomogeneousAttributes(\n\u001B[32m--> \u001B[39m\u001B[32m540\u001B[39m             volume=\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mattributes\u001B[49m\u001B[43m[\u001B[49m\u001B[33;43m\"\u001B[39;49m\u001B[33;43mvolume\u001B[39;49m\u001B[33;43m\"\u001B[39;49m\u001B[43m]\u001B[49m,\n\u001B[32m    541\u001B[39m             signed_water_mass=\u001B[38;5;28mself\u001B[39m.attributes[\u001B[33m\"\u001B[39m\u001B[33msigned water mass\u001B[39m\u001B[33m\"\u001B[39m],\n\u001B[32m    542\u001B[39m         ),\n\u001B[32m    543\u001B[39m         timestep=\u001B[38;5;28mself\u001B[39m.dt,\n\u001B[32m    544\u001B[39m         cell=\u001B[38;5;28mself\u001B[39m.attributes[\u001B[33m\"\u001B[39m\u001B[33mcell id\u001B[39m\u001B[33m\"\u001B[39m],\n\u001B[32m    545\u001B[39m         a_w_ice=\u001B[38;5;28mself\u001B[39m.environment[\u001B[33m\"\u001B[39m\u001B[33ma_w_ice\u001B[39m\u001B[33m\"\u001B[39m],\n\u001B[32m    546\u001B[39m         temperature=\u001B[38;5;28mself\u001B[39m.environment[\u001B[33m\"\u001B[39m\u001B[33mT\u001B[39m\u001B[33m\"\u001B[39m],\n\u001B[32m    547\u001B[39m         relative_humidity_ice=\u001B[38;5;28mself\u001B[39m.environment[\u001B[33m\"\u001B[39m\u001B[33mRH_ice\u001B[39m\u001B[33m\"\u001B[39m],\n\u001B[32m    548\u001B[39m     )\n\u001B[32m    549\u001B[39m     \u001B[38;5;28mself\u001B[39m.attributes.mark_updated(\u001B[33m\"\u001B[39m\u001B[33msigned water mass\u001B[39m\u001B[33m\"\u001B[39m)\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/impl/particle_attributes.py:93\u001B[39m, in \u001B[36mParticleAttributes.__getitem__\u001B[39m\u001B[34m(self, item)\u001B[39m\n\u001B[32m     92\u001B[39m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[34m__getitem__\u001B[39m(\u001B[38;5;28mself\u001B[39m, item):\n\u001B[32m---> \u001B[39m\u001B[32m93\u001B[39m     \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43m__attributes\u001B[49m\u001B[43m[\u001B[49m\u001B[43mitem\u001B[49m\u001B[43m]\u001B[49m\u001B[43m.\u001B[49m\u001B[43mget\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/attributes/impl/attribute.py:32\u001B[39m, in \u001B[36mAttribute.get\u001B[39m\u001B[34m(self)\u001B[39m\n\u001B[32m     31\u001B[39m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[34mget\u001B[39m(\u001B[38;5;28mself\u001B[39m):\n\u001B[32m---> \u001B[39m\u001B[32m32\u001B[39m     \u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mupdate\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n\u001B[32m     33\u001B[39m     \u001B[38;5;28;01mreturn\u001B[39;00m \u001B[38;5;28mself\u001B[39m.data\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/attributes/impl/derived_attribute.py:23\u001B[39m, in \u001B[36mDerivedAttribute.update\u001B[39m\u001B[34m(self)\u001B[39m\n\u001B[32m     21\u001B[39m \u001B[38;5;28;01mif\u001B[39;00m \u001B[38;5;28mself\u001B[39m.timestamp < dependencies_timestamp:\n\u001B[32m     22\u001B[39m     \u001B[38;5;28mself\u001B[39m.timestamp = dependencies_timestamp\n\u001B[32m---> \u001B[39m\u001B[32m23\u001B[39m     \u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mrecalculate\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/attributes/physics/volume.py:17\u001B[39m, in \u001B[36mVolume.recalculate\u001B[39m\u001B[34m(self)\u001B[39m\n\u001B[32m     16\u001B[39m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[34mrecalculate\u001B[39m(\u001B[38;5;28mself\u001B[39m):\n\u001B[32m---> \u001B[39m\u001B[32m17\u001B[39m     \u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mparticulator\u001B[49m\u001B[43m.\u001B[49m\u001B[43mbackend\u001B[49m\u001B[43m.\u001B[49m\u001B[43mvolume_of_water_mass\u001B[49m\u001B[43m(\u001B[49m\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mdata\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43mwater_mass\u001B[49m\u001B[43m.\u001B[49m\u001B[43mget\u001B[49m\u001B[43m(\u001B[49m\u001B[43m)\u001B[49m\u001B[43m)\u001B[49m\n",
+      "\u001B[36mFile \u001B[39m\u001B[32m~/python/PySDM/PySDM/backends/impl_numba/methods/physics_methods.py:119\u001B[39m, in \u001B[36mPhysicsMethods.volume_of_water_mass\u001B[39m\u001B[34m(self, volume, mass)\u001B[39m\n\u001B[32m    118\u001B[39m \u001B[38;5;28;01mdef\u001B[39;00m\u001B[38;5;250m \u001B[39m\u001B[34mvolume_of_water_mass\u001B[39m(\u001B[38;5;28mself\u001B[39m, volume, mass):\n\u001B[32m--> \u001B[39m\u001B[32m119\u001B[39m     \u001B[38;5;28;43mself\u001B[39;49m\u001B[43m.\u001B[49m\u001B[43m_volume_of_mass_body\u001B[49m\u001B[43m(\u001B[49m\u001B[43mvolume\u001B[49m\u001B[43m.\u001B[49m\u001B[43mdata\u001B[49m\u001B[43m,\u001B[49m\u001B[43m \u001B[49m\u001B[43mmass\u001B[49m\u001B[43m.\u001B[49m\u001B[43mdata\u001B[49m\u001B[43m)\u001B[49m\n",
+      "\u001B[31mKeyboardInterrupt\u001B[39m: "
+     ]
+    }
+   ],
+   "execution_count": 3
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "outputs": [],
+   "execution_count": null,
+   "source": "",
+   "id": "ca3dff61011a9506"
+  }
+ ],
+ "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",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing_with_deposition.ipynb b/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing_with_deposition.ipynb
new file mode 100644
index 000000000..05051bce5
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/hom_freezing_with_deposition.ipynb
@@ -0,0 +1,1032 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "id": "initial_id",
+   "metadata": {
+    "collapsed": true,
+    "ExecuteTime": {
+     "end_time": "2025-09-29T02:31:22.166432Z",
+     "start_time": "2025-09-29T02:30:58.759493Z"
+    }
+   },
+   "source": [
+    "import numpy as np\n",
+    "from PySDM.physics.constants import si\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.commons import run_simulations, hom_pure_droplet_freezing_backend, hom_pure_droplet_freezing_standard_setup\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.simulation import Simulation\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing.settings import Settings\n",
+    "from PySDM_examples.Luettmer_homogeneous_freezing import plot\n",
+    "from importlib import reload\n",
+    "from matplotlib import pyplot\n",
+    "from open_atmos_jupyter_utils import show_plot"
+   ],
+   "outputs": [],
+   "execution_count": 1
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T13:39:44.732670Z",
+     "start_time": "2025-09-24T13:39:44.048662Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" General settings \"\"\"\n",
+    "hom_freezing_types     = [  \"KoopMurray2016\", \"Spichtinger2023\" ]\n",
+    "hom_freezing_types_all = [  \"KoopMurray2016\", \"Spichtinger2023\", \"Koop2000\"  ]\n",
+    "vertical_updrafts = np.geomspace(0.2,10,num=9) * si.meter / si.second\n",
+    "\n",
+    "backends = hom_pure_droplet_freezing_backend()\n",
+    "standard = hom_pure_droplet_freezing_standard_setup()"
+   ],
+   "id": "e567ea5dc9abaf7d",
+   "outputs": [],
+   "execution_count": 2
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T13:36:09.312612098Z",
+     "start_time": "2025-09-17T11:59:13.164154Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "setting_dict = {\n",
+    "            **standard,\n",
+    "            \"backend\": backends[\"KoopMurray2016\"],\n",
+    "            \"hom_freezing\": \"KoopMurray2016\",\n",
+    "            \"w_updraft\": 10.,\n",
+    "            \"deposition_enable\": True,\n",
+    "            \"n_output\": 1,\n",
+    "             \"n_sd\": int(1e4),\n",
+    "            }\n",
+    "reference_high_dep_KoopMurray2016_simulation = run_simulations(setting_dict)\n",
+    "setting_dict = {\n",
+    "            **standard,\n",
+    "            \"backend\": backends[\"Spichtinger2023\"],\n",
+    "            \"hom_freezing\": \"Spichtinger2023\",\n",
+    "            \"w_updraft\": 10.,\n",
+    "            \"deposition_enable\": True,\n",
+    "            \"n_output\": 1,\n",
+    "             \"n_sd\": int(1e4),\n",
+    "            }\n",
+    "reference_high_dep_Spichtinger2023_simulation = run_simulations(setting_dict)"
+   ],
+   "id": "a7fedd700b66e5f",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=10.0 and n_sd=10000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=10.0 and n_sd=10000 and n_dv=4999999999.999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 4
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T13:38:06.344883884Z",
+     "start_time": "2025-09-17T12:12:40.964422Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "plot.plot_thermodynamics_and_bulk(reference_high_dep_KoopMurray2016_simulation, \" with vapor deposition\")\n",
+    "show_plot(\"fig_KM16_high_w_dep\")\n",
+    "plot.plot_thermodynamics_and_bulk(reference_high_dep_Spichtinger2023_simulation, \" with vapor deposition\")\n",
+    "show_plot(\"fig_SP23_high_w_dep\")"
+   ],
+   "id": "c661ea3f9edfa2e7",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 1000x1000 with 6 Axes>"
+      ],
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+     },
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+     "output_type": "display_data",
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+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./fig_SP23_high_w_dep.pdf' target='_blank'>./fig_SP23_high_w_dep.pdf</a><b…"
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+       "version_major": 2,
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+   ],
+   "execution_count": 6
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T15:01:54.420538Z",
+     "start_time": "2025-09-24T13:39:51.537949Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Simulations for n_sd ensemble with deposition \"\"\"\n",
+    "nsd_ensemble_deposition_simulations =[]\n",
+    "number_of_nsd = (1e2, 1e3, 1e4)\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for n_sd in number_of_nsd:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"n_sd\": int(n_sd),\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "            \"number_of_ensemble_runs\": 5,\n",
+    "            \"deposition_enable\": True,\n",
+    "            }\n",
+    "        nsd_ensemble_deposition_simulations.append( run_simulations(setting_dict) )"
+   ],
+   "id": "cd4e4bc0ab5abdbd",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=100 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=1000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 3
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T23:17:52.836703Z",
+     "start_time": "2025-09-24T23:17:42.188648Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "reload(plot)\n",
+    "for n_sd in number_of_nsd:\n",
+    "    fig, axs = pyplot.subplots(1, 2, figsize=(12, 4), constrained_layout=True)\n",
+    "    fig.suptitle(r\"$N_{sd}$: \"+\"{}\".format(int(n_sd))+\"   $w$: \"+str(standard[\"w_updraft\"])+r\" $\\mathrm{m \\, s^{-1}}$\"+r\"   $n_{ccn}$: \"+str(750)+r\" $\\mathrm{cm^{-3}}$\"+\" with vapor deposition\",fontsize=20)\n",
+    "    axs = axs.ravel()\n",
+    "    i = 0\n",
+    "    for simulation in nsd_ensemble_deposition_simulations:\n",
+    "        if simulation[\"settings\"][\"n_sd\"] == n_sd and simulation[\"settings\"][\"w_updraft\"] == standard[\"w_updraft\"]:\n",
+    "            axs[i] = plot.plot_freezing_temperatures_histogram(axs[i], simulation)\n",
+    "            i += 1\n",
+    "    show_plot(\"n_sd_\"+str(n_sd)+\"_ensemble_deposition\")"
+   ],
+   "id": "c22014e092d352b8",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 1200x400 with 2 Axes>"
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+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./n_sd_10000.0_ensemble_deposition.pdf' target='_blank'>./n_sd_10000.0_ens…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "30ece0a8acca4f33b1cf32f64cefb7ae"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
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+     }
+    }
+   ],
+   "execution_count": 15
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T17:19:10.141356Z",
+     "start_time": "2025-09-24T15:02:02.998734Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Simulations for updraft histogram with deposition \"\"\"\n",
+    "simulations_updraft_ensemble = []\n",
+    "\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for updraft in vertical_updrafts:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"w_updraft\": updraft  * si.meter / si.second,\n",
+    "            \"n_sd\": int(1e4),\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "            \"number_of_ensemble_runs\": 1,\n",
+    "            }\n",
+    "\n",
+    "        simulations_updraft_ensemble.append( run_simulations(setting_dict) )"
+   ],
+   "id": "93d3f3f886290b",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.2 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.32613788179066194 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.5318295896944989 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=0.8672488792828036 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.4142135623730951 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=2.306143078159937 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=3.760603093086394 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=6.132375635173039 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=10.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.2 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.32613788179066194 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.5318295896944989 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=0.8672488792828036 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.4142135623730951 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=2.306143078159937 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=3.760603093086394 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=6.132375635173039 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=10.0 and n_sd=10000 and n_dv=749999999.9999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 5
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T17:19:16.908008Z",
+     "start_time": "2025-09-24T17:19:10.439950Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "\n",
+    "    histogram_data_dict = {}\n",
+    "\n",
+    "    histogram_data_dict[\"hom_freezing_type\"] = hom_freezing_type\n",
+    "    histogram_data_dict[\"T_frz_histogram_list\"] = []\n",
+    "    histogram_data_dict[\"w_updraft_histogram_list\"] = []\n",
+    "\n",
+    "    for i, updraft in enumerate(vertical_updrafts):\n",
+    "        for simulation in simulations_updraft_ensemble:\n",
+    "            if (simulation[\"settings\"][\"w_updraft\"] == updraft\n",
+    "                    and simulation[\"settings\"][\"hom_freezing\"] == hom_freezing_type):\n",
+    "                output = simulation[\"ensemble_member_outputs\"][0]\n",
+    "                T_frz = output[\"T_frz\"]\n",
+    "                histogram_data_dict[\"T_frz_histogram_list\"].extend( T_frz )\n",
+    "                histogram_data_dict[\"w_updraft_histogram_list\"].extend( np.full_like(T_frz, updraft) )\n",
+    "\n",
+    "    plot.plot_freezing_temperatures_2d_histogram_seaborn(histogram_data_dict, title_add=\" with vapor deposition\")\n",
+    "    show_plot(hom_freezing_type+\"_updraft_ensemble_deposition\")"
+   ],
+   "id": "93a76944f19bfcb1",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 600x600 with 3 Axes>"
+      ],
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+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./Spichtinger2023_updraft_ensemble_deposition.pdf' target='_blank'>./Spich…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "de5ea028bb9b43c0b52330a7665bde77"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 6
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T23:23:34.350554Z",
+     "start_time": "2025-09-24T23:23:28.921260Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "for var_name in [\"ni\",\"freezing_fraction\"]:\n",
+    "    plot.plot_ensemble_bulk(simulations_updraft_ensemble, var_name, (vertical_updrafts, \"w_updraft\"), hom_freezing_types, title_add=\" with vapor deposition\")\n",
+    "    show_plot(\"w_ensemble_with_deposition_\"+var_name)"
+   ],
+   "id": "dffa5cba9fb189e6",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+      ],
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+       "HBox(children=(HTML(value=\"<a href='./w_ensemble_with_deposition_freezing_fraction.pdf' target='_blank'>./w_en…"
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+   "execution_count": 16
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T19:37:53.558927Z",
+     "start_time": "2025-09-24T17:19:21.621075Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "\"\"\" Simulations for CCN concentration histogram  \"\"\"\n",
+    "simulations_ccn_concentration_ensemble = []\n",
+    "number_concentrations = np.geomspace(100, 20000, num=10) / si.cm ** 3\n",
+    "\n",
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "    for n_dv in number_concentrations:\n",
+    "        setting_dict = {\n",
+    "            **standard,\n",
+    "            \"n_sd\": int(1e4),\n",
+    "            \"N_dv_droplet_distribution\": n_dv,\n",
+    "            \"backend\": backends[hom_freezing_type],\n",
+    "            \"hom_freezing\": hom_freezing_type,\n",
+    "        }\n",
+    "        simulations_ccn_concentration_ensemble.append(run_simulations(setting_dict))"
+   ],
+   "id": "a2ece44e2e802c0c",
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=99999999.99999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=180164823.06544116\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=324593634.7020169\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=584803547.6425728\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=1053610276.8906642\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=1898235091.1593704\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=3419951893.3533926\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=6161550277.583339\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=11100946155.696224\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for KoopMurray2016 with wpdraft=1.0 and n_sd=10000 and n_dv=19999999999.999996\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=99999999.99999999\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=180164823.06544116\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=324593634.7020169\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=584803547.6425728\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=1053610276.8906642\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=1898235091.1593704\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=3419951893.3533926\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=6161550277.583339\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=11100946155.696224\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n",
+      "Setting up simulation for Spichtinger2023 with wpdraft=1.0 and n_sd=10000 and n_dv=19999999999.999996\n",
+      "Starting simulation...\n",
+      "all particles frozen or evaporated\n"
+     ]
+    }
+   ],
+   "execution_count": 8
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T19:38:02.225019Z",
+     "start_time": "2025-09-24T19:37:53.807715Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "for hom_freezing_type in hom_freezing_types:\n",
+    "\n",
+    "    histogram_data_ccn_concentration_ensemble = {}\n",
+    "    histogram_data_ccn_concentration_ensemble[\"hom_freezing_type\"] = hom_freezing_type\n",
+    "\n",
+    "    histogram_data_ccn_concentration_ensemble[\"T_frz_histogram_list\"] = []\n",
+    "    histogram_data_ccn_concentration_ensemble[\"n_ccn_histogram_list\"] = []\n",
+    "    histogram_data_ccn_concentration_ensemble[\"rc_max_histogram_list\"] = []\n",
+    "\n",
+    "    for n_ccn in number_concentrations:\n",
+    "        for simulation in simulations_ccn_concentration_ensemble:\n",
+    "            if (simulation[\"settings\"][\"hom_freezing\"] == hom_freezing_type\n",
+    "                    and simulation[\"settings\"][\"N_dv_droplet_distribution\"] == n_ccn):\n",
+    "                output = simulation[\"ensemble_member_outputs\"][0]\n",
+    "                T_frz = np.asarray(output[\"T_frz\"])\n",
+    "                rc = np.asarray(output[\"rs\"])\n",
+    "                histogram_data_ccn_concentration_ensemble[\"T_frz_histogram_list\"].extend( T_frz )\n",
+    "                histogram_data_ccn_concentration_ensemble[\"n_ccn_histogram_list\"].extend( np.full_like(T_frz, n_ccn) )\n",
+    "                histogram_data_ccn_concentration_ensemble[\"rc_max_histogram_list\"].extend( np.full_like(T_frz, np.amax(rc)) )\n",
+    "\n",
+    "    plot.plot_freezing_temperatures_2d_histogram_seaborn(histogram_data_ccn_concentration_ensemble, title_add=\" with vapor deposition\")\n",
+    "    show_plot(hom_freezing_type+\"_ccn_ensemble_deposition\")\n",
+    "    del histogram_data_ccn_concentration_ensemble[\"n_ccn_histogram_list\"]\n",
+    "    plot.plot_freezing_temperatures_2d_histogram_seaborn(histogram_data_ccn_concentration_ensemble, title_add=\" with vapor deposition\")\n",
+    "    show_plot(hom_freezing_type+\"_radius_ensemble_deposition\")"
+   ],
+   "id": "332bd1dcfbdd531f",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Figure size 600x600 with 3 Axes>"
+      ],
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+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    },
+    {
+     "data": {
+      "text/plain": [
+       "HBox(children=(HTML(value=\"<a href='./Spichtinger2023_radius_ensemble_deposition.pdf' target='_blank'>./Spicht…"
+      ],
+      "application/vnd.jupyter.widget-view+json": {
+       "version_major": 2,
+       "version_minor": 0,
+       "model_id": "5fef68b1062c4d7da4f3af093ff94da4"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data",
+     "jetTransient": {
+      "display_id": null
+     }
+    }
+   ],
+   "execution_count": 9
+  },
+  {
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2025-09-24T23:27:02.147968Z",
+     "start_time": "2025-09-24T23:26:56.630617Z"
+    }
+   },
+   "cell_type": "code",
+   "source": [
+    "for var_name in [\"ni\",\"freezing_fraction\"]:\n",
+    "    plot.plot_ensemble_bulk(simulations_ccn_concentration_ensemble, var_name, (number_concentrations, \"N_dv_droplet_distribution\"), hom_freezing_types)\n",
+    "    show_plot(\"ccn_ensemble_with_deposition_\"+var_name)"
+   ],
+   "id": "1655c74e1492ff5",
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+      ],
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diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/plot.py b/examples/PySDM_examples/Luettmer_homogeneous_freezing/plot.py
new file mode 100644
index 000000000..5bfcba3e0
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/plot.py
@@ -0,0 +1,351 @@
+import matplotlib.pyplot as plt
+from matplotlib import pyplot
+import numpy as np
+from scipy.ndimage import histogram
+import seaborn as sns
+
+from PySDM import Formulae
+
+formulae = Formulae(
+    particle_shape_and_density="MixedPhaseSpheres",
+)
+
+# general plot settings
+ax_lab_fsize = 15
+tick_fsize = 15
+# title_fsize = 15
+# line_width = 2.5
+T_frz_bins = np.linspace(-40, -34, num=60, endpoint=True)
+T_frz_bins_kelvin = np.linspace(230, 240, num=100, endpoint=True)
+
+
+def plot_thermodynamics_and_bulk(simulation, title_add="", show_conc=False):
+
+    output = simulation["ensemble_member_outputs"][0]
+    time = output["t"]
+    T = np.asarray(output["T"])
+    RH = np.asarray(output["RH"])
+    RHi = np.asarray(output["RHi"])
+    qc = np.asarray(output["LWC"])
+    qi = np.asarray(output["IWC"])
+    qv = np.asarray(output["qv"])
+    qt = qc + qv + qi
+    rc = np.asarray(output["rs"])
+    ri = np.asarray(output["ri"])
+    if show_conc:
+        nc = np.asarray(output["ns"])
+        ni = np.asarray(output["ni"])
+
+    svp = Formulae(
+        saturation_vapour_pressure="FlatauWalkoCotton"
+    ).saturation_vapour_pressure
+    a_w_ice = svp.pvs_ice(T) / svp.pvs_water(T)
+    d_a_w_ice = (RHi / 100 - 1) * a_w_ice
+
+    j_hom_rate = Formulae(
+        homogeneous_ice_nucleation_rate="Koop2000"
+    ).homogeneous_ice_nucleation_rate
+    koop_2000 = j_hom_rate.j_hom(T, d_a_w_ice)
+    j_hom_rate = Formulae(
+        homogeneous_ice_nucleation_rate="KoopMurray2016"
+    ).homogeneous_ice_nucleation_rate
+    koop_murray_2016 = j_hom_rate.j_hom(T, d_a_w_ice)
+    j_hom_rate = Formulae(
+        homogeneous_ice_nucleation_rate="Koop_Correction"
+    ).homogeneous_ice_nucleation_rate
+    spichtinger_2023 = j_hom_rate.j_hom(T, d_a_w_ice)
+
+    fig, axs = pyplot.subplots(
+        2, 2, figsize=(10, 10), sharex=False, constrained_layout=True
+    )
+
+    title = (
+        "Freezing: "
+        + simulation["settings"]["hom_freezing"]
+        + "  n_sd: "
+        + str(simulation["settings"]["n_sd"])
+        + "  w: "
+        + str(simulation["settings"]["w_updraft"])
+        + r" $\mathrm{m \, s^{-1}}$"
+        + title_add
+    )
+    fig.suptitle(title, fontsize=16)
+
+    """ Temperture profile """
+    ax = axs[0, 0]
+    ax.plot(time, formulae.trivia.K2C(T), color="black", linestyle="-", label="T")
+    ax.set_xlabel("time [s]", fontsize=ax_lab_fsize)
+    ax.set_ylabel("temperature [°C]", fontsize=ax_lab_fsize)
+    ax.legend(loc="upper left", fontsize=ax_lab_fsize)
+    ax.tick_params(labelsize=tick_fsize)
+
+    twin = ax.twinx()
+    twin.plot(time, RH, color="red", linestyle="-", label=r"$S_{w}$")
+    twin.plot(time, RHi, color="blue", linestyle="-", label=r"$S_{i}$")
+    twin.set_ylabel("relative humidity [%]", fontsize=ax_lab_fsize)
+    twin.legend(loc="center right", fontsize=ax_lab_fsize)
+    twin.tick_params(labelsize=tick_fsize)
+    twin.grid(visible=True)
+
+    """ Water activity difference profile """
+    lin_s_SP2023 = "--"
+    lin_s_KM2016 = "-"
+    if simulation["settings"]["hom_freezing"] == "Spichtinger2023":
+        lin_s_SP2023 = "-"
+        lin_s_KM2016 = "--"
+    ax = axs[0, 1]
+    # ax.plot(time, koop_2000, color="black", linestyle="-", label="Koop2000")
+    ax.plot(
+        time,
+        koop_murray_2016,
+        color="blue",
+        linestyle=lin_s_KM2016,
+        label="KoopMurray2016",
+    )
+    ax.plot(
+        time,
+        spichtinger_2023,
+        color="red",
+        linestyle=lin_s_SP2023,
+        label="Spichtinger2023",
+    )
+    ax.set_xlabel("time [s]", fontsize=ax_lab_fsize)
+    ax.set_ylabel(
+        r"nucleation rate [$\mathrm{m^{-3} \, s^{-1}}$]", fontsize=ax_lab_fsize
+    )
+    ax.legend(loc="upper left", fontsize=ax_lab_fsize)
+    ax.set_ylim(1e-30, 1e30)
+    ax.set_yscale("log")
+    ax.tick_params(labelsize=tick_fsize)
+    ax.grid(visible=True)
+    twin = ax.twinx()
+    twin.plot(time, d_a_w_ice, color="gray", linestyle="-", label=r"$\Delta a_{w}$")
+    twin.set_ylim(0.2, 0.35)
+    twin.set_ylabel("water activity difference", fontsize=ax_lab_fsize)
+    twin.tick_params(labelsize=tick_fsize)
+    twin.legend(loc="lower right", fontsize=ax_lab_fsize)
+
+    """ Mass content and number concentration"""
+    ax = axs[1, 0]
+    ax.plot(time, qc, color="red", linestyle="-", label="water")
+    ax.plot(time, qi, color="blue", linestyle="-", label="ice")
+    ax.plot(time, qv, color="black", linestyle="-", label="vapor")
+    ax.plot(time, qt, color="black", linestyle="dotted", label="total")
+    ax.set_yscale("log")
+    ax.set_ylim(1e-5, 1e-2)
+    ax.set_xlabel("time [s]", fontsize=ax_lab_fsize)
+    ax.set_ylabel(r"mass content [$\mathrm{kg \, kg^{-1}}$]", fontsize=ax_lab_fsize)
+    ax.legend(fontsize=ax_lab_fsize)
+    ax.tick_params(labelsize=tick_fsize)
+    ax.grid(visible=True)
+
+    if show_conc:
+        twin = ax.twinx()
+        twin.plot(time, nc, color="red", linestyle="--", label="water")
+        twin.plot(time, ni, color="blue", linestyle="--", label="ice")
+        twin.set_yscale("log")
+        twin.set_xlabel("time [s]", fontsize=ax_lab_fsize)
+        twin.set_ylabel(
+            r"number concentration [$\mathrm{kg^{-1}}$]", fontsize=ax_lab_fsize
+        )
+        twin.tick_params(labelsize=tick_fsize)
+
+    """ Mean radius """
+    ax = axs[1, 1]
+    ax.plot(time, rc * 1e6, color="red", linestyle="-", label="water")
+    ax.plot(time, ri * 1e6, color="blue", linestyle="-", label="ice")
+    ax.set_yscale("log")
+    ax.set_ylim(1e-2, 1e2)
+    ax.set_xlabel("time [s]", fontsize=ax_lab_fsize)
+    ax.set_ylabel("mean radius [µm]", fontsize=ax_lab_fsize)
+    ax.legend(fontsize=ax_lab_fsize)
+    ax.tick_params(labelsize=tick_fsize)
+    ax.grid(visible=True)
+
+
+def plot_freezing_temperatures_histogram(ax, simulation):
+
+    number_of_ensemble_runs = simulation["settings"]["number_of_ensemble_runs"]
+
+    for i in range(number_of_ensemble_runs):
+        output = simulation["ensemble_member_outputs"][i]
+        T_frz = np.asarray(output["T_frz"])
+
+        title = "Nucleation rate=" + simulation["settings"]["hom_freezing"]
+
+        """ Freezing temperatures """
+        hist = ax.hist(
+            # formulae.trivia.K2C(T_frz),
+            T_frz,
+            # bins=T_frz_bins,
+            bins=T_frz_bins_kelvin,
+            density=True,
+            cumulative=-1,
+            alpha=1.0,
+            histtype="step",
+            linewidth=1.5,
+        )
+
+    ax.set_xlim(left=234, right=239)
+    ax.axvline(x=235, color="k", linestyle="--")
+    ax.set_title(title, fontsize=ax_lab_fsize)
+    ax.set_xlabel("freezing temperature [K]", fontsize=ax_lab_fsize)
+    ax.set_ylabel("frequency", fontsize=ax_lab_fsize)
+    ax.tick_params(labelsize=tick_fsize)
+
+    return ax
+
+
+def plot_freezing_temperatures_2d_histogram(histogram_data_dict):
+
+    vertical_updrafts_bins = np.geomspace(0.05, 15, num=6, endpoint=True)
+
+    hom_freezing_types = histogram_data_dict.keys()
+
+    fig, axs = pyplot.subplots(2, 2, figsize=(10, 10), constrained_layout=True)
+    axs = axs.ravel()
+    i = 0
+    for hom_freezing_type in hom_freezing_types:
+
+        title = "Freezing method=" + hom_freezing_type
+
+        ax = axs[i]
+        T_frz = formulae.trivia.K2C(
+            np.asarray(histogram_data_dict[hom_freezing_type]["T_frz_histogram_list"])
+        )
+
+        hist, x, y = np.histogram2d(
+            T_frz,
+            histogram_data_dict[hom_freezing_type]["w_updraft_histogram_list"],
+            bins=(T_frz_bins, vertical_updrafts_bins),
+        )
+        y = np.log10(y)
+        X, Y = np.meshgrid(x, y)
+
+        hist = hist.T / sum(hist.flatten())
+
+        c = ax.pcolor(X, Y, hist)
+        fig.colorbar(c, ax=ax)
+
+        ax.set_title(title, fontsize=ax_lab_fsize)
+        ax.set_xlabel("freezing temperature [°C]", fontsize=ax_lab_fsize)
+        ax.set_ylabel("vertical updraft [m/s]", fontsize=ax_lab_fsize)
+
+        i += 1
+
+
+def plot_freezing_temperatures_2d_histogram_seaborn(histogram_data_dict, title_add=""):
+
+    # hom_freezing_types = ["KoopMurray2016", "Koop_Correction", "Koop2000"]
+    sns.set_theme(style="ticks")
+
+    hom_freezing_type = histogram_data_dict["hom_freezing_type"]
+    # for i, hom_freezing_type in enumerate(hom_freezing_types):
+
+    # T_frz = formulae.trivia.K2C(
+    #     (np.asarray(histogram_data_dict["T_frz_histogram_list"]))
+    # )
+    T_frz = np.asarray(histogram_data_dict["T_frz_histogram_list"])
+
+    if "w_updraft_histogram_list" in histogram_data_dict:
+        w = histogram_data_dict["w_updraft_histogram_list"]
+        y_label = r"vertical updraft [$\mathrm{m \, s^{-1}}$]"
+    elif "n_ccn_histogram_list" in histogram_data_dict:
+        w = histogram_data_dict["n_ccn_histogram_list"]
+        y_label = r"ccn concentration [$\mathrm{m^{-3}}$]"
+    elif "rc_max_histogram_list" in histogram_data_dict:
+        w = np.asarray(histogram_data_dict["rc_max_histogram_list"]) * 1e6
+        y_label = "(maximum) radius [µm]"
+
+    # xlim = (-39.5, -34)
+    xlim = (233, 241)
+    h = sns.JointGrid(
+        x=T_frz,
+        y=w,
+        xlim=xlim,
+    )
+    h.ax_joint.set(yscale="log")
+    # if hom_freezing_type == "KoopMurray2016":
+    #     x_pos_cbar = 0.75
+    # else:
+    x_pos_cbar = 0.75
+    cax = h.figure.add_axes([x_pos_cbar, 0.55, 0.02, 0.2])
+    h.plot_joint(
+        sns.histplot,
+        stat="density",
+        binwidth=0.25,
+        discrete=(False, False),
+        pmax=0.8,
+        cbar=True,
+        cbar_ax=cax,
+    )
+
+    h.plot_marginals(
+        sns.histplot,
+        element="step",
+    )
+    h.set_axis_labels("freezing temperature [K]", y_label, fontsize=ax_lab_fsize)
+    h.ax_joint.set_title(
+        "Freezing: " + hom_freezing_type + title_add,
+        pad=70,
+        fontsize=ax_lab_fsize,
+    )
+    h.ax_marg_y.remove()
+
+    return h
+
+
+def plot_ensemble_bulk(
+    simulations, var_name, ensemble_var, freezing_types, title_add=""
+):
+
+    ens_var, ens_var_name = ensemble_var
+    len_ens_var = len(ens_var)
+
+    for hom_freezing_type in freezing_types:
+        var = np.zeros(len_ens_var)
+        for i in range(len_ens_var):
+            for simulation in simulations:
+                if (
+                    simulation["settings"]["hom_freezing"] == hom_freezing_type
+                    and simulation["settings"][ens_var_name] == ens_var[i]
+                ):
+                    output = simulation["ensemble_member_outputs"][0]
+                    if var_name == "freezing_fraction":
+                        ni = np.asarray(output["ni"])[-1]
+                        nc = np.asarray(output["ns"])[0]
+                        var[i] = (1 - (nc - ni) / nc) * 100
+                        # print("{:.2E}".format(nc),"{:.2E}".format(ni), var[i])
+                        # quit()
+                    else:
+                        var[i] = np.asarray(output[var_name])[-1]
+
+        pyplot.scatter(var, ens_var, label=hom_freezing_type)
+
+    if var_name == "ni":
+        pyplot.xscale("log")
+        x_label = r"$n_{i} \, [\mathrm{kg^{-1}}$]"
+        title = "Ice number concentrations"
+        pyplot.xlim(1e6, 1e10)
+
+    if var_name == "IWC":
+        pyplot.xscale("log")
+        x_label = r"mass content [$\mathrm{kg \, kg^{-1}}$]"
+        title = "Ice mass content"
+
+    if var_name == "freezing_fraction":
+        title = "frozen fraction of real droplets "
+        x_label = r"$n_{frz} \, [\mathrm{\%}$]"
+
+    if ens_var_name == "N_dv_droplet_distribution":
+        pyplot.yscale("log")
+        y_label = r"$n_{ccn} \, [\mathrm{m^{-3}}$]"
+
+    if ens_var_name == "w_updraft":
+        pyplot.yscale("log")
+        y_label = r"w [$\mathrm{m \, s^{-1}}$]"
+
+    pyplot.title(title + title_add, fontsize=ax_lab_fsize)
+    pyplot.xlabel(x_label, fontsize=ax_lab_fsize)
+    pyplot.ylabel(y_label, fontsize=ax_lab_fsize)
+    pyplot.legend(fontsize=ax_lab_fsize)
diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/settings.py b/examples/PySDM_examples/Luettmer_homogeneous_freezing/settings.py
new file mode 100644
index 000000000..d41cebda7
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/settings.py
@@ -0,0 +1,122 @@
+import time
+
+import numpy as np
+from pystrict import strict
+
+from PySDM import Formulae
+from PySDM.physics.constants import si
+from PySDM.initialisation.spectra import Lognormal
+from PySDM.initialisation.sampling import spectral_sampling
+from tests.unit_tests.backends.test_oxidation import formulae
+from PySDM.dynamics.collisions.collision_kernels import Golovin, Geometric
+
+
+class Settings:
+    def __init__(
+        self,
+        *,
+        hom_freezing: str,
+        n_sd: int,
+        w_updraft: float,
+        T0: float,
+        dz: float,
+        N_dv_droplet_distribution: float,
+        r_mean_droplet_distribution: float,
+        sigma_droplet_distribution: float = None,
+        type_droplet_distribution: str,
+        p0: float = 200 * si.hectopascals,
+        RH_0: float = 1.0,
+        kappa: float = 0.64,
+        condensation_enable: bool = True,
+        deposition_enable: bool = True,
+        coalescence_enable: bool = False,
+        deposition_adaptive: bool = True,
+        n_output: int = 30,
+        backend=None,
+        scipy_solver=False,
+        number_of_ensemble_runs: None,
+    ):
+        self.backend = backend
+        print(
+            "Setting up simulation for "
+            + hom_freezing
+            + " with wpdraft="
+            + str(w_updraft)
+            + " and n_sd="
+            + str(n_sd)
+            + " and n_dv="
+            + str(N_dv_droplet_distribution)
+        )
+        self.n_sd = n_sd
+        self.w_updraft = w_updraft
+        self.N_dv_droplet_distribution = N_dv_droplet_distribution
+        self.r_mean_droplet_distribution = r_mean_droplet_distribution
+        self.sigma_droplet_distribution = sigma_droplet_distribution
+        self.type_droplet_distribution = type_droplet_distribution
+
+        self.mass_of_dry_air = 1000 * si.kilogram
+        self.initial_pressure = p0
+        self.initial_water_supersaturation = RH_0
+        # self.initial_ice_supersaturation = RHi_0
+        self.kappa = kappa
+        self.initial_temperature = T0
+
+        self.condensation_enable = condensation_enable
+        self.coalescence_enable = coalescence_enable
+        self.deposition_enable = deposition_enable
+        self.deposition_adaptive = deposition_adaptive
+        self.scipy_solver = scipy_solver
+        self.collision_kernel = Geometric()
+
+        if hom_freezing == "threshold":
+            self.hom_freezing_type = "threshold"
+        else:
+            self.hom_freezing_type = "time-dependent"
+
+        self.formulae = backend.formulae
+
+        const = self.formulae.constants
+        pvs_w = self.formulae.saturation_vapour_pressure.pvs_water(
+            self.initial_temperature
+        )
+        self.initial_water_vapour_mixing_ratio = const.eps / (
+            self.initial_pressure / self.initial_water_supersaturation / pvs_w - 1
+        )
+
+        dry_air_density = (
+            self.formulae.trivia.p_d(
+                self.initial_pressure, self.initial_water_vapour_mixing_ratio
+            )
+            / self.initial_temperature
+            / const.Rd
+        )
+
+        if self.type_droplet_distribution == ("monodisperse"):
+            self.r_wet = np.ones(self.n_sd) * r_mean_droplet_distribution
+            self.specific_concentration = (
+                np.ones(self.n_sd)
+                * N_dv_droplet_distribution
+                / self.n_sd
+                / dry_air_density
+            )
+            if coalescence_enable:  # do lucky droplet method
+                v_small = self.formulae.trivia.volume(
+                    radius=r_mean_droplet_distribution
+                )
+                self.r_wet[0 : int(self.n_sd * 0.1)] = self.formulae.trivia.radius(
+                    volume=2 * v_small
+                )
+        elif self.type_droplet_distribution == ("lognormal"):
+            spectrum = Lognormal(
+                norm_factor=N_dv_droplet_distribution / dry_air_density,
+                m_mode=r_mean_droplet_distribution,
+                s_geom=sigma_droplet_distribution,
+            )
+            self.r_wet, self.specific_concentration = spectral_sampling.Linear(
+                spectrum
+            ).sample(n_sd)
+
+        self.dz = dz
+        self.t_max_duration = 10000
+        self.dt = dz / self.w_updraft
+        self.n_output = n_output
diff --git a/examples/PySDM_examples/Luettmer_homogeneous_freezing/simulation.py b/examples/PySDM_examples/Luettmer_homogeneous_freezing/simulation.py
new file mode 100644
index 000000000..7785e57b3
--- /dev/null
+++ b/examples/PySDM_examples/Luettmer_homogeneous_freezing/simulation.py
@@ -0,0 +1,201 @@
+import numpy as np
+import warnings
+import PySDM.products as PySDM_products
+from PySDM.backends import CPU
+from PySDM.builder import Builder
+from PySDM.dynamics import (
+    AmbientThermodynamics,
+    Condensation,
+    Freezing,
+    VapourDepositionOnIce,
+    Coalescence,
+)
+from PySDM.environments import Parcel
+from PySDM.initialisation import discretise_multiplicities
+from PySDM.initialisation.hygroscopic_equilibrium import equilibrate_dry_radii
+from PySDM.backends.impl_numba.test_helpers import scipy_ode_condensation_solver
+
+
+class Simulation:
+    def __init__(self, settings, backend=CPU):
+
+        dt = settings.dt
+
+        formulae = settings.formulae
+
+        env = Parcel(
+            mixed_phase=True,
+            dt=dt,
+            mass_of_dry_air=settings.mass_of_dry_air,
+            p0=settings.initial_pressure,
+            initial_water_vapour_mixing_ratio=settings.initial_water_vapour_mixing_ratio,
+            T0=settings.initial_temperature,
+            w=settings.w_updraft,
+        )
+
+        builder = Builder(
+            backend=settings.backend,
+            n_sd=settings.n_sd,
+            environment=env,
+        )
+
+        builder.add_dynamic(AmbientThermodynamics())
+        if settings.condensation_enable:
+            builder.add_dynamic(Condensation(adaptive=True))
+        if settings.coalescence_enable:
+            builder.add_dynamic(
+                Coalescence(collision_kernel=settings.collision_kernel, adaptive=False)
+            )
+        if settings.deposition_enable:
+            builder.add_dynamic(
+                VapourDepositionOnIce(adaptive=settings.deposition_adaptive)
+            )
+        builder.add_dynamic(
+            Freezing(
+                homogeneous_freezing=settings.hom_freezing_type, immersion_freezing=None
+            )
+        )
+
+        self.n_sd = settings.n_sd
+        self.multiplicities = discretise_multiplicities(
+            settings.specific_concentration * env.mass_of_dry_air
+        )
+        # self.r_dry = settings.r_dry
+        self.r_wet = settings.r_wet
+
+        kappa = np.full_like(settings.r_wet, settings.kappa)
+
+        self.r_dry = equilibrate_dry_radii(
+            r_wet=self.r_wet,
+            environment=builder.particulator.environment,
+            kappa=kappa,
+        )
+        v_dry = settings.formulae.trivia.volume(radius=self.r_dry)
+        self.initial_mass = formulae.particle_shape_and_density.radius_to_mass(
+            self.r_wet
+        )
+
+        attributes = {
+            "multiplicity": self.multiplicities,
+            "dry volume": v_dry,
+            "kappa times dry volume": kappa * v_dry,
+            "signed water mass": self.initial_mass,
+        }
+        builder.request_attribute("temperature of last freezing")
+        builder.request_attribute("radius")
+
+        products = [
+            PySDM_products.ParcelDisplacement(name="z"),
+            PySDM_products.Time(name="t"),
+            PySDM_products.AmbientRelativeHumidity(name="RH", unit="%"),
+            PySDM_products.AmbientRelativeHumidity(name="RH_ice", unit="%"),
+            PySDM_products.AmbientTemperature(name="T"),
+            PySDM_products.AmbientPressure(name="p", unit="hPa"),
+            PySDM_products.WaterMixingRatio(name="water", radius_range=(0, np.inf)),
+            PySDM_products.WaterMixingRatio(name="ice", radius_range=(-np.inf, 0)),
+            PySDM_products.WaterMixingRatio(
+                name="total", radius_range=(-np.inf, np.inf)
+            ),
+            PySDM_products.AmbientWaterVapourMixingRatio(
+                name="vapour", var="water_vapour_mixing_ratio"
+            ),
+            PySDM_products.ParticleSpecificConcentration(
+                name="n_s", radius_range=(0, np.inf), unit="kg^-1"
+            ),
+            PySDM_products.ParticleSpecificConcentration(
+                name="n_i", radius_range=(-np.inf, 0), unit="kg^-1"
+            ),
+            PySDM_products.MeanRadius(name="r_s", radius_range=(0, np.inf)),
+            PySDM_products.MeanRadius(name="r_i", radius_range=(-np.inf, 0)),
+        ]
+
+        self.particulator = builder.build(attributes, products)
+        if settings.scipy_solver:
+            scipy_ode_condensation_solver.patch_particulator(self.particulator)
+
+        self.n_output = settings.n_output
+        if settings.n_output == 1:
+            self.n_substeps = 1
+        else:
+            self.n_substeps = int(self.n_output / dt)
+        self.t_max_duration = settings.t_max_duration
+
+    def save(self, output):
+        cell_id = 0
+
+        output["z"].append(self.particulator.products["z"].get()[cell_id])
+        output["t"].append(self.particulator.products["t"].get())
+        output["RH"].append(self.particulator.products["RH"].get()[cell_id])
+        output["RHi"].append(self.particulator.products["RH_ice"].get()[cell_id])
+        output["T"].append(self.particulator.products["T"].get()[cell_id])
+        output["P"].append(self.particulator.products["p"].get()[cell_id])
+        output["LWC"].append(self.particulator.products["water"].get()[cell_id])
+        output["IWC"].append(self.particulator.products["ice"].get()[cell_id])
+        output["qv"].append(self.particulator.products["vapour"].get()[cell_id])
+        output["ns"].append(self.particulator.products["n_s"].get()[cell_id])
+        output["ni"].append(self.particulator.products["n_i"].get()[cell_id])
+        output["rs"].append(self.particulator.products["r_s"].get()[cell_id])
+        output["ri"].append(self.particulator.products["r_i"].get()[cell_id])
+        # output["water_mass"].append(
+        #     self.particulator.attributes["signed water mass"].data.tolist()
+        # )
+        # output["T_frz"].append(
+        #     self.particulator.attributes["temperature of last freezing"].data.tolist()
+        # )
+        output["T_frz"] = self.particulator.attributes[
+            "temperature of last freezing"
+        ].data.tolist()
+
+    def run(self):
+
+        print("Starting simulation...")
+
+        output = {
+            "t": [],
+            "z": [],
+            "RH": [],
+            "RHi": [],
+            "T": [],
+            "P": [],
+            "LWC": [],
+            "IWC": [],
+            "qv": [],
+            "ns": [],
+            "ni": [],
+            "rs": [],
+            "ri": [],
+            # "water_mass": [],
+            "T_frz": [],
+        }
+
+        self.save(output)
+
+        while True:
+
+            self.particulator.run(self.n_substeps)
+            self.save(output)
+
+            # print( output["t"][-1], output["T"][-1], output["RH"][-1], output["LWC"][-1], output["IWC"][-1] )
+
+            if output["LWC"][-1] < output["LWC"][0]:
+                print("all particles frozen or evaporated")
+                # Assert for water saturation
+                test_water_saturation = np.asarray(output["RH"])
+                # Sort out times before CCN activation & after first occurence of ice
+                test_water_saturation = np.where(
+                    np.asarray(output["rs"]) < 1e-6, 100.0, test_water_saturation
+                )
+                test_water_saturation = np.where(
+                    np.asarray(output["IWC"]) > 0.0, 100.0, test_water_saturation
+                )
+                if np.allclose(test_water_saturation, 100.0, rtol=5e-2) == False:
+                    print(
+                        "Warning: water saturation is too high outside of activation and mixed-phase environment"
+                    )
+
+                break
+            if output["t"][-1] >= self.t_max_duration:
+                print("time exceeded")
+                break
+
+        return output
diff --git a/tests/smoke_tests/box/luettmer_homogeneous_freezing/__init__.py b/tests/smoke_tests/box/luettmer_homogeneous_freezing/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/smoke_tests/box/luettmer_homogeneous_freezing/test_notebook.py b/tests/smoke_tests/box/luettmer_homogeneous_freezing/test_notebook.py
new file mode 100644
index 000000000..cc2713895
--- /dev/null
+++ b/tests/smoke_tests/box/luettmer_homogeneous_freezing/test_notebook.py
@@ -0,0 +1,29 @@
+"""basic tests for threshold freezing temperatures"""
+
+from pathlib import Path
+
+import pytest
+
+from open_atmos_jupyter_utils import notebook_vars
+from PySDM_examples import Luettmer_homogeneous_freezing
+
+PLOT = False
+
+
+@pytest.fixture(scope="session", name="variables")
+def variables_fixture():
+    return notebook_vars(
+        file=Path(Luettmer_homogeneous_freezing.__file__).parent
+        / "hom_freezing_cloud_droplets.ipynb",
+        plot=PLOT,
+    )
+
+
+class TestNotebook:
+    @staticmethod
+    def test_1(variables):
+        assert variables["n_sd"] == 100
+
+    @staticmethod
+    def test_2(variables):
+        print(len(variables["simulations"]))
diff --git a/tests/unit_tests/dynamics/condensation/test_ventilation.py b/tests/unit_tests/dynamics/condensation/test_ventilation.py
index 04978bcd4..e30ad3694 100644
--- a/tests/unit_tests/dynamics/condensation/test_ventilation.py
+++ b/tests/unit_tests/dynamics/condensation/test_ventilation.py
@@ -33,7 +33,7 @@ def _make_particulator(backend):
     return builder.build(
         attributes={
             "multiplicity": np.ones(1),
-            "water mass": np.asarray([INITIAL_DROPLET_MASS]),
+            "signed water mass": np.asarray([INITIAL_DROPLET_MASS]),
             "dry volume": np.asarray([DRY_VOLUME]),
             "kappa times dry volume": 0.5 * np.asarray([DRY_VOLUME]),
         },
@@ -75,7 +75,8 @@ def test_ventilation(backend_class, var_ventilation, var_drop_growth, scipy_solv
 
     # assert
     mass_ratios = {
-        key: particulator.attributes["water mass"].to_ndarray() / INITIAL_DROPLET_MASS
+        key: particulator.attributes["signed water mass"].to_ndarray()
+        / INITIAL_DROPLET_MASS
         for key, particulator in particulators.items()
     }
     assert 0.93 < mass_ratios[var_ventilation] < mass_ratios["Neglect"] < 1
diff --git a/tests/unit_tests/dynamics/test_freezing.py b/tests/unit_tests/dynamics/test_freezing.py
index ddf81fede..d1fde7b47 100644
--- a/tests/unit_tests/dynamics/test_freezing.py
+++ b/tests/unit_tests/dynamics/test_freezing.py
@@ -13,7 +13,7 @@
 )
 from PySDM.backends import ThrustRTC
 
-VERY_BIG_J_HET = 1e20
+VERY_BIG_RATE = 1e20
 EPSILON_RH = 1e-3
 
 
@@ -23,8 +23,16 @@ class TestDropletFreezing:
         "record_freezing_temperature",
         (pytest.param(True, id="recording"), pytest.param(False, id="not recording")),
     )
+    @pytest.mark.parametrize(
+        "freezing_mode",
+        (
+            {"immersion_freezing": "time-dependent", "homogeneous_freezing": None},
+            {"immersion_freezing": None, "homogeneous_freezing": "threshold"},
+            {"immersion_freezing": None, "homogeneous_freezing": "time-dependent"},
+        ),
+    )
     def test_record_freezing_temperature_on_time_dependent_freeze(
-        backend_class, record_freezing_temperature
+        backend_class, record_freezing_temperature, freezing_mode
     ):
         if backend_class is ThrustRTC and record_freezing_temperature:
             pytest.skip("TODO #1495")
@@ -33,7 +41,11 @@ def test_record_freezing_temperature_on_time_dependent_freeze(
         formulae = Formulae(
             particle_shape_and_density="MixedPhaseSpheres",
             heterogeneous_ice_nucleation_rate="Constant",
-            constants={"J_HET": VERY_BIG_J_HET},
+            homogeneous_ice_nucleation_rate="Constant",
+            constants={
+                "J_HET": VERY_BIG_RATE,
+                "J_HOM": VERY_BIG_RATE,
+            },
         )
         builder = Builder(
             n_sd=1,
@@ -41,7 +53,12 @@ def test_record_freezing_temperature_on_time_dependent_freeze(
             environment=Box(dt=1 * si.s, dv=1 * si.m**3),
         )
         builder.add_dynamic(
-            Freezing(immersion_freezing="time-dependent", thaw="instantaneous")
+            # Freezing(immersion_freezing="time-dependent", thaw="instantaneous")
+            Freezing(
+                immersion_freezing=freezing_mode["immersion_freezing"],
+                homogeneous_freezing=freezing_mode["homogeneous_freezing"],
+                thaw="instantaneous",
+            )
         )
         if record_freezing_temperature:
             builder.request_attribute("temperature of last freezing")
@@ -55,8 +72,9 @@ def test_record_freezing_temperature_on_time_dependent_freeze(
 
         temp_1 = 200 * si.K
         temp_2 = 250 * si.K
+        temp_3 = 220 * si.K
         particulator.environment["a_w_ice"] = np.nan
-        particulator.environment["T"] = temp_1
+        particulator.environment["T"] = temp_2
 
         # act & assert
         attr_name = "temperature of last freezing"
@@ -68,23 +86,30 @@ def test_record_freezing_temperature_on_time_dependent_freeze(
 
             # still not frozen since RH not greater than 100%
             particulator.environment["RH"] = 1.0
+            particulator.environment["RH_ice"] = 1.0
             particulator.run(steps=1)
             np.isnan(particulator.attributes[attr_name].to_ndarray()).all()
+            assert all(particulator.attributes["signed water mass"].to_ndarray() > 0)
 
             # should freeze and record T1
             particulator.environment["RH"] += EPSILON_RH
+            particulator.environment["RH_ice"] += EPSILON_RH
+            particulator.environment["T"] = temp_1
             particulator.run(steps=1)
+            assert all(particulator.attributes["signed water mass"].to_ndarray() < 0)
             assert all(particulator.attributes[attr_name].to_ndarray() == temp_1)
 
             # should thaw
             particulator.environment["T"] = 300 * si.K
             particulator.run(steps=1)
+            assert all(particulator.attributes["signed water mass"].to_ndarray() > 0)
             np.isnan(particulator.attributes[attr_name].to_ndarray()).all()
 
             # should re-freeze and record T2
-            particulator.environment["T"] = temp_2
+            particulator.environment["T"] = temp_3
             particulator.run(steps=1)
-            assert all(particulator.attributes[attr_name].to_ndarray() == temp_2)
+            assert all(particulator.attributes["signed water mass"].to_ndarray() < 0)
+            assert all(particulator.attributes[attr_name].to_ndarray() == temp_3)
 
     # TODO #599
     def test_no_subsaturated_freezing(self):
diff --git a/tests/unit_tests/physics/test_homogeneous_nucleation_rates.py b/tests/unit_tests/physics/test_homogeneous_nucleation_rates.py
index f3b51a01e..876ea8a57 100644
--- a/tests/unit_tests/physics/test_homogeneous_nucleation_rates.py
+++ b/tests/unit_tests/physics/test_homogeneous_nucleation_rates.py
@@ -51,6 +51,7 @@ def test_fig_2_in_spichtinger_et_al_2023(
         # arrange
         formulae = Formulae(
             homogeneous_ice_nucleation_rate=parametrisation,
+            saturation_vapour_pressure="MurphyKoop2005",
         )
 
         # act
@@ -93,6 +94,112 @@ def test_fig_2_in_spichtinger_et_al_2023(
                 significant=2,
             )
 
+    @staticmethod
+    @pytest.mark.parametrize(
+        "pvs_parametrisation, context",
+        (
+            (
+                "FlatauWalkoCotton",
+                pytest.raises(
+                    AssertionError, match="Not equal to tolerance rtol=0.05, atol=0"
+                ),
+            ),
+            ("MurphyKoop2005", nullcontext()),
+        ),
+    )
+    def test_fig_1_in_spichtinger_et_al_2023(
+        pvs_parametrisation, context, plot=False
+    ):  # pylint disable=too-many-locals
+        # arrange
+        si = physics.si
+        formulae = Formulae(
+            homogeneous_ice_nucleation_rate="KoopMurray2016",
+            saturation_vapour_pressure=pvs_parametrisation,
+        )
+        formulae_koop2000 = Formulae(
+            homogeneous_ice_nucleation_rate="Koop2000",
+        )
+        formulae_Koop_Correction = Formulae(
+            homogeneous_ice_nucleation_rate="Koop_Correction",
+        )
+        temperature = np.linspace(230, 245, num=16) * si.K
+
+        with context:
+            # act
+            pv_sat_water = (
+                formulae.saturation_vapour_pressure.pvs_water(temperature) * si.Pa
+            )
+            pv_sat_ice = (
+                formulae.saturation_vapour_pressure.pvs_ice(temperature) * si.Pa
+            )
+
+            d_aw_ice = (pv_sat_water * 1.0 / pv_sat_ice - 1) * pv_sat_ice / pv_sat_water
+
+            J_hom_parametrisations = {
+                "KoopMurray2016": np.log10(
+                    formulae.homogeneous_ice_nucleation_rate.j_hom(
+                        temperature, d_aw_ice
+                    )
+                ),
+                "Koop2000": np.log10(
+                    formulae_koop2000.homogeneous_ice_nucleation_rate.j_hom(
+                        temperature, d_aw_ice
+                    )
+                ),
+                "Koop_Correction": np.log10(
+                    formulae_Koop_Correction.homogeneous_ice_nucleation_rate.j_hom(
+                        temperature, d_aw_ice
+                    )
+                ),
+            }
+
+            # plot
+            J_hom_range = (-10, 25)
+            for parametrisation, data in J_hom_parametrisations.items():
+                pyplot.plot(
+                    temperature,
+                    data,
+                    label=parametrisation,
+                )
+            pyplot.grid()
+            pyplot.gca().set(
+                xlabel=r"temperature (K)",
+                ylabel="log$_{10}(J)$",
+                title="saturation_vapour_pressure: " + pvs_parametrisation,
+                xlim=(np.amin(temperature), np.amax(temperature)),
+                ylim=J_hom_range,
+            )
+            pyplot.xticks(ticks=temperature, minor=True)
+            pyplot.xticks(ticks=np.arange(230, 250, 5), minor=False)
+            pyplot.yticks(
+                ticks=np.arange(J_hom_range[0], J_hom_range[1] + 1, 1), minor=True
+            )
+            pyplot.legend()
+
+            if plot:
+                pyplot.show()
+            else:
+                pyplot.clf()
+
+            # Assert
+            assert all(
+                J_hom_parametrisations["Koop2000"]
+                >= J_hom_parametrisations["KoopMurray2016"]
+            )
+            assert all(
+                J_hom_parametrisations["Koop2000"]
+                >= J_hom_parametrisations["Koop_Correction"]
+            )
+            index = range(
+                np.where(temperature == 235)[0][0],
+                np.where(temperature == 240)[0][0] + 1,
+            )
+            np.testing.assert_allclose(
+                J_hom_parametrisations["Koop_Correction"][index],
+                J_hom_parametrisations["KoopMurray2016"][index],
+                rtol=0.05,
+            )
+
     @staticmethod
     @pytest.mark.parametrize("variant", _choices(homogeneous_ice_nucleation_rate))
     def test_units(variant):