Homogeneous freezing (as a new option in Freezing dynamic, disabled by default + new physics formulae for hom. nucl. rate); new example: Spichtinger_et_al_2023 (#1488)

Co-authored-by: Sylwester Arabas <sylwester.arabas@agh.edu.pl>

Author: tluettm

PySDM/backends/impl_common/freezing_attributes.py

@@ -25,3 +25,14 @@ class TimeDependentAttributes(
     """groups attributes required in time-dependent regime"""
 
     __slots__ = ()
+
+
+class TimeDependentHomogeneousAttributes(
+    namedtuple(
+        typename="TimeDependentHomogeneousAttributes",
+        field_names=("volume", "signed_water_mass"),
+    )
+):
+    """groups attributes required in time-dependent regime for homogeneous freezing"""
+
+    __slots__ = ()

PySDM/backends/impl_numba/methods/freezing_methods.py

@@ -1,5 +1,6 @@
 """
-CPU implementation of backend methods for freezing (singular and time-dependent immersion freezing)
+CPU implementation of backend methods for homogeneous freezing and
+heterogeneous freezing (singular and time-dependent immersion freezing)
 """
 
 from functools import cached_property
@@ -12,31 +13,40 @@
 from ...impl_common.freezing_attributes import (
     SingularAttributes,
     TimeDependentAttributes,
+    TimeDependentHomogeneousAttributes,
 )
 
 
 class FreezingMethods(BackendMethods):
-    def __init__(self):
-        BackendMethods.__init__(self)
-        unfrozen_and_saturated = self.formulae.trivia.unfrozen_and_saturated
-        frozen_and_above_freezing_point = (
-            self.formulae.trivia.frozen_and_above_freezing_point
-        )
-
-        @numba.njit(**{**self.default_jit_flags, "parallel": False})
-        def _freeze(water_mass, i):
-            water_mass[i] = -1 * water_mass[i]
+    @cached_property
+    def _freeze(self):
+        @numba.njit(**{**self.default_jit_flags, **{"parallel": False}})
+        def body(signed_water_mass, i):
+            signed_water_mass[i] = -1 * signed_water_mass[i]
             # TODO #599: change thd (latent heat)!
 
-        @numba.njit(**{**self.default_jit_flags, "parallel": False})
-        def _thaw(water_mass, i):
-            water_mass[i] = -1 * water_mass[i]
+        return body
+
+    @cached_property
+    def _thaw(self):
+        @numba.njit(**{**self.default_jit_flags, **{"parallel": False}})
+        def body(signed_water_mass, i):
+            signed_water_mass[i] = -1 * signed_water_mass[i]
             # TODO #599: change thd (latent heat)!
 
+        return body
+
+    @cached_property
+    def _freeze_singular_body(self):
+        _thaw = self._thaw
+        _freeze = self._freeze
+        frozen_and_above_freezing_point = (
+            self.formulae.trivia.frozen_and_above_freezing_point
+        )
+        unfrozen_and_saturated = self.formulae.trivia.unfrozen_and_saturated
+
         @numba.njit(**self.default_jit_flags)
-        def freeze_singular_body(
-            attributes, temperature, relative_humidity, cell, thaw
-        ):
+        def body(attributes, temperature, relative_humidity, cell, thaw):
             n_sd = len(attributes.freezing_temperature)
             for i in numba.prange(n_sd):  # pylint: disable=not-an-iterable
                 if attributes.freezing_temperature[i] == 0:
@@ -53,13 +63,21 @@ def freeze_singular_body(
                 ):
                     _freeze(attributes.signed_water_mass, i)
 
-        self.freeze_singular_body = freeze_singular_body
+        return body
 
+    @cached_property
+    def _freeze_time_dependent_body(self):
+        _thaw = self._thaw
+        _freeze = self._freeze
+        frozen_and_above_freezing_point = (
+            self.formulae.trivia.frozen_and_above_freezing_point
+        )
+        unfrozen_and_saturated = self.formulae.trivia.unfrozen_and_saturated
         j_het = self.formulae.heterogeneous_ice_nucleation_rate.j_het
         prob_zero_events = self.formulae.trivia.poissonian_avoidance_function
 
         @numba.njit(**self.default_jit_flags)
-        def freeze_time_dependent_body(  # pylint: disable=too-many-arguments
+        def body(  # pylint: disable=too-many-arguments
             rand,
             attributes,
             timestep,
@@ -90,12 +108,69 @@ def freeze_time_dependent_body(  # pylint: disable=too-many-arguments
                     if rand[i] < prob:
                         _freeze(attributes.signed_water_mass, i)
 
-        self.freeze_time_dependent_body = freeze_time_dependent_body
+        return body
+
+    @cached_property
+    def _freeze_time_dependent_homogeneous_body(self):
+        _thaw = self._thaw
+        _freeze = self._freeze
+        frozen_and_above_freezing_point = (
+            self.formulae.trivia.frozen_and_above_freezing_point
+        )
+        unfrozen_and_ice_saturated = self.formulae.trivia.unfrozen_and_ice_saturated
+        j_hom = self.formulae.homogeneous_ice_nucleation_rate.j_hom
+        prob_zero_events = self.formulae.trivia.poissonian_avoidance_function
+        d_a_w_ice_within_range = (
+            self.formulae.homogeneous_ice_nucleation_rate.d_a_w_ice_within_range
+        )
+        d_a_w_ice_maximum = (
+            self.formulae.homogeneous_ice_nucleation_rate.d_a_w_ice_maximum
+        )
+
+        @numba.njit(**self.default_jit_flags)
+        def body(  # pylint: disable=unused-argument,too-many-arguments
+            rand,
+            attributes,
+            timestep,
+            cell,
+            a_w_ice,
+            temperature,
+            relative_humidity_ice,
+            thaw,
+        ):
+
+            n_sd = len(attributes.signed_water_mass)
+            for i in numba.prange(n_sd):  # pylint: disable=not-an-iterable
+                cell_id = cell[i]
+                if thaw and frozen_and_above_freezing_point(
+                    attributes.signed_water_mass[i], temperature[cell_id]
+                ):
+                    _thaw(attributes.signed_water_mass, i)
+                elif unfrozen_and_ice_saturated(
+                    attributes.signed_water_mass[i], relative_humidity_ice[cell_id]
+                ):
+                    d_a_w_ice = (relative_humidity_ice[cell_id] - 1.0) * a_w_ice[
+                        cell_id
+                    ]
+
+                    if d_a_w_ice_within_range(d_a_w_ice):
+                        d_a_w_ice = d_a_w_ice_maximum(d_a_w_ice)
+                        rate_assuming_constant_temperature_within_dt = (
+                            j_hom(temperature[cell_id], d_a_w_ice)
+                            * attributes.volume[i]
+                        )
+                        prob = 1 - prob_zero_events(
+                            r=rate_assuming_constant_temperature_within_dt, dt=timestep
+                        )
+                        if rand[i] < prob:
+                            _freeze(attributes.signed_water_mass, i)
+
+        return body
 
     def freeze_singular(
         self, *, attributes, temperature, relative_humidity, cell, thaw: bool
     ):
-        self.freeze_singular_body(
+        self._freeze_singular_body(
             SingularAttributes(
                 freezing_temperature=attributes.freezing_temperature.data,
                 signed_water_mass=attributes.signed_water_mass.data,
@@ -118,7 +193,7 @@ def freeze_time_dependent(
         relative_humidity,
         thaw: bool,
     ):
-        self.freeze_time_dependent_body(
+        self._freeze_time_dependent_body(
             rand.data,
             TimeDependentAttributes(
                 immersed_surface_area=attributes.immersed_surface_area.data,
@@ -132,6 +207,32 @@ def freeze_time_dependent(
             thaw=thaw,
         )
 
+    def freeze_time_dependent_homogeneous(
+        self,
+        *,
+        rand,
+        attributes,
+        timestep,
+        cell,
+        a_w_ice,
+        temperature,
+        relative_humidity_ice,
+        thaw: bool,
+    ):
+        self._freeze_time_dependent_homogeneous_body(
+            rand.data,
+            TimeDependentHomogeneousAttributes(
+                volume=attributes.volume.data,
+                signed_water_mass=attributes.signed_water_mass.data,
+            ),
+            timestep,
+            cell.data,
+            a_w_ice.data,
+            temperature.data,
+            relative_humidity_ice.data,
+            thaw=thaw,
+        )
+
     @cached_property
     def _record_freezing_temperatures_body(self):
         ff = self.formulae_flattened

PySDM/dynamics/freezing.py

@@ -1,14 +1,25 @@
 """
-immersion freezing using either singular or time-dependent formulation
+droplet freezing using either singular or
+time-dependent formulation for immersion freezing
+and homogeneous freezing and thaw
 """
 
 from PySDM.dynamics.impl import register_dynamic
 
 
 @register_dynamic()
-class Freezing:
-    def __init__(self, *, singular=True, thaw=False):
+class Freezing:  # pylint: disable=too-many-instance-attributes
+    def __init__(
+        self,
+        *,
+        singular=True,
+        homogeneous_freezing=False,
+        immersion_freezing=True,
+        thaw=False,
+    ):
         self.singular = singular
+        self.homogeneous_freezing = homogeneous_freezing
+        self.immersion_freezing = immersion_freezing
         self.thaw = thaw
         self.enable = True
         self.rand = None
@@ -26,12 +37,21 @@ def register(self, builder):
         if self.singular:
             builder.request_attribute("freezing temperature")
 
-        if not self.singular:
+        if not self.singular and self.immersion_freezing:
             assert (
                 self.particulator.formulae.heterogeneous_ice_nucleation_rate.__name__
                 != "Null"
             )
             builder.request_attribute("immersed surface area")
+
+        if self.homogeneous_freezing:
+            assert (
+                self.particulator.formulae.homogeneous_ice_nucleation_rate.__name__
+                != "Null"
+            )
+            builder.request_attribute("volume")
+
+        if self.homogeneous_freezing or not self.singular:
             self.rand = self.particulator.Storage.empty(
                 self.particulator.n_sd, dtype=float
             )
@@ -49,11 +69,19 @@ def __call__(self):
         if not self.enable:
             return
 
-        if self.singular:
-            self.particulator.immersion_freezing_singular(thaw=self.thaw)
-        else:
+        if self.immersion_freezing:
+            if self.singular:
+                self.particulator.immersion_freezing_singular(thaw=self.thaw)
+            else:
+                self.rand.urand(self.rng)
+                self.particulator.immersion_freezing_time_dependent(
+                    rand=self.rand,
+                    thaw=self.thaw,
+                )
+
+        if self.homogeneous_freezing:
             self.rand.urand(self.rng)
-            self.particulator.immersion_freezing_time_dependent(
+            self.particulator.homogeneous_freezing_time_dependent(
                 rand=self.rand,
                 thaw=self.thaw,
             )

PySDM/formulae.py

@@ -47,6 +47,7 @@ def __init__(  # pylint: disable=too-many-locals
         hydrostatics: str = "ConstantGVapourMixingRatioAndThetaStd",
         freezing_temperature_spectrum: str = "Null",
         heterogeneous_ice_nucleation_rate: str = "Null",
+        homogeneous_ice_nucleation_rate: str = "Null",
         fragmentation_function: str = "AlwaysN",
         isotope_equilibrium_fractionation_factors: str = "Null",
         isotope_kinetic_fractionation_factors: str = "Null",
@@ -86,6 +87,7 @@ def __init__(  # pylint: disable=too-many-locals
         self.hydrostatics = hydrostatics
         self.freezing_temperature_spectrum = freezing_temperature_spectrum
         self.heterogeneous_ice_nucleation_rate = heterogeneous_ice_nucleation_rate
+        self.homogeneous_ice_nucleation_rate = homogeneous_ice_nucleation_rate
         self.fragmentation_function = fragmentation_function
         self.isotope_equilibrium_fractionation_factors = (
             isotope_equilibrium_fractionation_factors

PySDM/particulator.py

@@ -8,6 +8,7 @@
 from PySDM.backends.impl_common.freezing_attributes import (
     SingularAttributes,
     TimeDependentAttributes,
+    TimeDependentHomogeneousAttributes,
 )
 from PySDM.backends.impl_common.index import make_Index
 from PySDM.backends.impl_common.indexed_storage import make_IndexedStorage
@@ -537,3 +538,18 @@ def immersion_freezing_singular(self, *, thaw: bool):
             thaw=thaw,
         )
         self.attributes.mark_updated("signed water mass")
+
+    def homogeneous_freezing_time_dependent(self, *, thaw: bool, rand: Storage):
+        self.backend.freeze_time_dependent_homogeneous(
+            rand=rand,
+            attributes=TimeDependentHomogeneousAttributes(
+                volume=self.attributes["volume"],
+                signed_water_mass=self.attributes["signed water mass"],
+            ),
+            timestep=self.dt,
+            cell=self.attributes["cell id"],
+            a_w_ice=self.environment["a_w_ice"],
+            temperature=self.environment["T"],
+            relative_humidity_ice=self.environment["RH_ice"],
+            thaw=thaw,
+        )

PySDM/physics/__init__.py

@@ -27,6 +27,7 @@
     fragmentation_function,
     freezing_temperature_spectrum,
     heterogeneous_ice_nucleation_rate,
+    homogeneous_ice_nucleation_rate,
     hydrostatics,
     hygroscopicity,
     impl,