Merge #145

145: Plotting HOM J r=amylu00 a=amylu00



Co-authored-by: amylu00 <alu3@caltech.edu>

docs/bibliography.bib

@@ -260,6 +260,19 @@ @article{Kirkby2016
   year = {2016}
 }
 
+@Article{KnopfAlpert2013,
+  author = "Knopf, Daniel A. and Alpert, Peter A.",
+  title  = "A water activity based model of heterogeneous ice nucleation kinetics for freezing of water and aqueous solution droplets",
+  journal = "Faraday Discuss.",
+  year = "2013",
+  volume = "165",
+  issue = "0",
+  pages = "513-534",
+  publisher = "The Royal Society of Chemistry",
+  doi = "10.1039/C3FD00035D",
+  url = "http://dx.doi.org/10.1039/C3FD00035D",
+}
+
 @article{Koop2000,
 author = {Koop, Thomas and al, et},
 title = {Water activity as the determinant for homogeneous ice nucleation in aqueous solutions},
@@ -516,6 +529,18 @@ @article{SeifertBeheng2006
   publisher = {Springer}
 }
 
+@article{Spichtinger2023,
+  AUTHOR = {Spichtinger, P. and Marschalik, P. and Baumgartner, M.},
+  TITLE = {Impact of formulations of the homogeneous nucleation rate on ice nucleation events in cirrus},
+  JOURNAL = {Atmospheric Chemistry and Physics},
+  VOLUME = {23},
+  YEAR = {2023},
+  NUMBER = {3},
+  PAGES = {2035--2060},
+  URL = {https://acp.copernicus.org/articles/23/2035/2023/},
+  DOI = {10.5194/acp-23-2035-2023}
+}
+
 @article{TripoliCotton1980,
   title = {A Numerical Investigation of Several Factors Contributing to the Observed Variable Intensity of Deep Convection over South Florida},
   author = {Tripoli, G.J. and Cotton, W.R.},
@@ -569,17 +594,3 @@ @article{Wood2005
   doi = {10.1175/JAS3530.1},
   year = {2005}
 }
-
-@article{SeifertBeheng2006,
-  title={A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description},
-  author={Seifert, Axel and Beheng, Klaus Dieter},
-  journal={Meteorology and atmospheric physics},
-  volume={92},
-  number={1-2},
-  pages={45--66},
-  doi = {https://doi.org/10.1007/s00703-005-0112-4},
-  year={2006},
-  publisher={Springer}
-}
-
-

docs/src/IceNucleation.md

@@ -80,23 +80,7 @@ per second via immersion freezing.
 where ``A`` is surface area of an individual ice nuclei, ``N_{tot}`` is total number
   of ice nuclei, and ``N_{ice}`` is number of ice crystals already in the system.
 
-## Homogeneous Freezing for Sulphuric Acid Containing Droplets
-Homogeneous freezing occurs when supercooled liquid droplets freeze on their own.
-  Closly based off [Koop2000](@cite), this parameterization determines a homoegneous nucleation
-  rate coefficient, ``J_{hom}``, using water activity. The change in water activity,
-  ``\Delta a_w(c,T,P)``, can be found in the same fashion that it is determined under the ABIFM
-  section above. It is then used to empirically calculate ``J_{hom}(\Delta a_w)`` with units of
-  ``cm^{-3}s^{-1}``.
-
-The nucleation rate coefficient is determined with the cubic function from [Koop2000](@cite)
-```math
-\begin{equation}
-  logJ_{hom} = -906.7 + 8502 \Delta a_w - 26924(\Delta a_w)^2 + 29180(\Delta a_w)^3
-\end{equation}
-```
-This parameterization is valid only when ``0.26 < \Delta a_w < 0.36`` and ``185K < T < 235K``.
-
-## ABIFM Example Figures
+### ABIFM Example Figures
 The following plot shows ``J`` as a function of ``\Delta a_w`` as compared to
   figure 1 in Knopf & Alpert 2013. Solution droplets were assumed to contain
   a constant 10% wt. sulphuric acid. Changing the concentration will simply
@@ -133,3 +117,46 @@ where `T_dew` is the dewpoint (in this example, it is constant at -45C).
 It is also important to note that this plot is reflective of cirrus clouds
   and shows only a very small temperature range. The two curves are slightly
   off because of small differences in parameterizations for vapor pressures.
+
+## Homogeneous Freezing for Sulphuric Acid Containing Droplets
+Homogeneous freezing occurs when supercooled liquid droplets freeze on their own.
+  Closly based off [Koop2000](@cite), this parameterization determines a homoegneous nucleation
+  rate coefficient, ``J_{hom}``, using water activity. The change in water activity,
+  ``\Delta a_w(c,T,P)``, can be found in `Common.jl` and is described in the
+  `Water Activity section`. It is then used to empirically calculate ``J_{hom}(\Delta a_w)``
+  with units of ``cm^{-3}s^{-1}``.
+
+The nucleation rate coefficient is determined with the cubic function from [Koop2000](@cite)
+```math
+\begin{equation}
+  logJ_{hom} = -906.7 + 8502 \Delta a_w - 26924(\Delta a_w)^2 + 29180(\Delta a_w)^3
+\end{equation}
+```
+This parameterization is valid only when ``0.26 < \Delta a_w < 0.36`` and ``185K < T < 235K``.
+
+### Homogeneous Ice Nucleation Rate Coefficient
+Here is a comparison of our parameterization of ``J_{hom}`` compared to Koop 2000 as
+  plotted in figure 1 of [Spichtinger2023](@cite). Our parameterization differs in the calculation
+  of ``\Delta a_w``. We define water activity to be a ratio of saturated vapor pressures whereas
+  Koop 2000 uses the difference in chemical potential. 
+
+```@example
+include("ice_nucleation_plots/HomFreezingPlots.jl")
+```
+![](HomFreezingPlots.svg)
+
+It should be noted that the Koop 2000
+  parameterization is only valid for temperatures up to 240K and a temperature-dependent max
+  pressure. The max valid pressure becomes negative around 237K, so the Koop 2000 parameterizaiton
+  should not be valid beyond 237K. For this reason, we limit the curve from [Spichtinger2023](@cite)
+  to 237K.
+
+Multiple sulphuric acid concentrations, ``x``,
+  are plotted since the actual concentration used in literature values is unspecified. 
+
+!!! note
+
+    Spichtinger plot may be under the condition that x = 0 (pure liquid droplets).
+    The current parameterization in CloudMicrophysics.jl is not valid for \Delta a_w
+    values that are obtained from pure water droplets. Though CliMA lines look far
+    from the Spichtinger 2023 line, the lines seem to move closer as x approaches 0.

docs/src/ice_nucleation_plots/HomFreezingPlots.jl

@@ -0,0 +1,90 @@
+import CairoMakie as MK
+
+import Thermodynamics as TD
+import CloudMicrophysics as CM
+import CLIMAParameters as CP
+
+const CMO = CM.Common
+const CMI = CM.HomIceNucleation
+const CMP = CM.Parameters
+
+include(joinpath(pkgdir(CM), "test", "create_parameters.jl"))
+FT = Float64
+toml_dict = CP.create_toml_dict(FT; dict_type = "alias")
+const prs = cloud_microphysics_parameters(toml_dict)
+thermo_params = CMP.thermodynamics_params(prs)
+
+# Initializing
+T_range = range(229.0, stop = 234.5, length = 50)  # air temperature
+x_sulph = Vector{FT}([0.03, 0.04, 0.06])           # wt% sulphuric acid in droplets
+
+# Solving for Δa and J values
+Δa1 = [CMO.Delta_a_w(prs, x_sulph[1], T) for T in T_range]
+Δa2 = [CMO.Delta_a_w(prs, x_sulph[2], T) for T in T_range]
+Δa3 = [CMO.Delta_a_w(prs, x_sulph[3], T) for T in T_range]
+
+J1 = @. CMI.homogeneous_J(prs, Δa1)
+J2 = @. CMI.homogeneous_J(prs, Δa2)
+J3 = @. CMI.homogeneous_J(prs, Δa3)
+
+log10J_1 = @. log10(J1)
+log10J_2 = @. log10(J2)
+log10J_3 = @. log10(J3)
+
+Δa_range = range(0.27, stop = 0.32, length = 50)
+J_given_Δa = @. CMI.homogeneous_J(prs, Δa_range)
+
+#! format: off
+# Spichtinger et al 2023
+# https://acp.copernicus.org/articles/23/2035/2023/acp-23-2035-2023.pdf
+# Values are from Koop et al. (2000) line in Figure 1
+Spichtinger2023_temp = [
+    230.0139, 231.0179, 231.9860, 233.00797, 234.01195, 235.01594, 236.00199, 237.16733,
+]
+Spichtinger2023_log10J = [
+    24.33735, 22.6506, 21.0843, 19.5181, 18.072289, 16.626506, 15.24096, 13.493975,
+]
+
+# Baumgartner et al 2022
+# https://acp.copernicus.org/articles/22/65/2022/acp-22-65-2022.pdf
+# Figure 2a
+Baum_Delta_a = [0.26, 0.27, 0.28, 0.29, 0.3, 0.32, 0.33, 0.339]
+Baum_J = [4.25e-5, 0.306, 454.09, 2.06e5, 6.31e7, 1.8e12, 4.45e14, 1.69e17]
+
+# Plotting
+fig = MK.Figure(resolution = (800, 500))
+ax1 = MK.Axis(
+    fig[1, 1],
+    ylabel = "log10(J) with J in SI units",
+    xlabel = "Temperature [K]",
+    title = "CliMA vs Spichtinger2023",
+    xticklabelsize = 14.0f0,
+    xlabelsize = 14,
+    ylabelsize = 14,
+    limits = ((228.0, 240.0), nothing),
+)
+ax2 = MK.Axis(
+    fig[1, 2],
+    xlabel = "Δa_w [-]",
+    ylabel = "J [cm^-3 s^-1]",
+    title = "CliMA vs Baumgartner2022",
+    yscale = log10,
+    xticklabelsize = 14.0f0,
+    xlabelsize = 14,
+    ylabelsize = 14,
+)
+
+MK.lines!(ax1, Spichtinger2023_temp, Spichtinger2023_log10J, label = "Spichtinger 2023 x = ?")
+MK.lines!(ax1, T_range, log10J_1, label = "CliMA x = 0.03")
+MK.lines!(ax1, T_range, log10J_2, label = "CliMA x = 0.04")
+MK.lines!(ax1, T_range, log10J_3, label = "CliMA x = 0.06")
+
+MK.lines!(ax2, Baum_Delta_a, Baum_J, label = "Baumgartner 2022")
+MK.lines!(ax2, Δa_range, J_given_Δa .* 1e-6, label = "CliMA")
+#! format: on
+
+MK.axislegend(ax1, position = :rt, labelsize = 13.0f0)
+MK.axislegend(ax2, position = :rb, labelsize = 14.0f0)
+
+MK.save("HomFreezingPlots.svg", fig)
+fig