Merge #217

217: untangling water activity from abifm docs r=amylu00 a=amylu00



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

docs/src/IceNucleation.md

@@ -50,47 +50,28 @@ Water Activity-Based Immersion Freezing Model (ABFIM)
   classical nucleation theory (CNT). More on CNT can be found in [Karthika2016](@cite).
   The nucleation rate coefficient, ``J``, describes the number of ice nuclei formed per unit area
   per unit time and can be determined by the water activity, ``a_w``. This parameterization follows
-  [KnopfAlpert2013](@cite), [Koop2002](@cite), [MurphyKoop2005](@cite), and [Luo1995](@cite). In this model,
-  aerosols are assumed to contain an insoluble and soluble material. When immersed in water,
-  the soluble material diffuses into the liquid water to create a sulphuric acid solution.
+  [KnopfAlpert2013](@cite). In this model, aerosols are assumed to contain an insoluble and
+  soluble material. When immersed in water, the soluble material diffuses into the liquid water
+  to create a sulphuric acid solution.
 
 Using empirical coefficients, ``m`` and ``c``, from [KnopfAlpert2013](@cite),
-  the heterogeneous nucleation rate coefficient in units of ``cm^{-2}s^{-1}`` can be determined by the linear equation
+  the heterogeneous nucleation rate coefficient in units of ``cm^{-2}s^{-1}``
+  can be determined by the linear equation
 ```math
 \begin{equation}
   log_{10}J_{ABIFM} = m \Delta a_w + c
 \end{equation}
 ```
+A parameterization for ``\Delta a_w`` can be found in `Common.jl`. More information on
+  it can be found in the `Water Activity` section.
+
 !!! note
 
     Our source code for the nucleation rate coefficient returns
     ``J`` in base SI units.
 
-``\Delta a_w``is the difference between the water activity of the droplet, ``a_w``, and the water activity of ice at the same temperature, ``a_{w,ice}(T)``. From [Koop2002](@cite),
-```math
-\begin{equation}
-  a_w = \frac{p_{sol}}{p_{sat}}
-\end{equation}
-```
-```math
-\begin{equation}
-  a_{w,ice} = \frac{p_{i,sat}}{p_{sat}}
-\end{equation}
-```
-where ``p_{sol}`` is saturated vapor pressure of water above solution, ``p_{sat}``
-  is saturated vapor pressure above pure liquid water, and ``p_{i,sat}`` is saturated
-  vapor pressure above ice. ``p_{sol}`` is determined in mbar using a parameterization
-  for supercooled, binary ``H_2SO_4/H_2O`` solution from [Luo1995](@cite) which is valid for ``185K < T < 235K``:
-```math
-\begin{equation}
-  ln(p_{sol}) = 23.306 - 5.3465x + 12xw_h - 8.19xw_h^2 + \frac{1}{T}(-5814 + 928.9x - 1876.7xw_h)
-\end{equation}
-```
-where ``x`` is the weight fraction of sulphuric acid in the droplets
-  (i.e. if droplets are 10% sulphuric acid by mass, ``x = 0.1``), ``w_h = 1.4408x``,
-  and temperature is in Kelvins.
-
-Once ``J_{ABIFM}`` is calculated, it can be used to determine the ice production rate, ``P_{ice}``, per second via immersion freezing.
+Once ``J_{ABIFM}`` is calculated, it can be used to determine the ice production rate, ``P_{ice}``,
+per second via immersion freezing.
 ```math
 \begin{equation}
   P_{ice} = J_{ABIFM}A(N_{tot} - N_{ice})

docs/src/WaterActivity.md

@@ -1,10 +1,12 @@
 # Water Activity
+
 The `Common.jl` module includes
   a parameterization for difference in water activity between a H2SO4
   solution droplet and ice. This can be used in immersion and homogeneous
   freezing parameterizations of nucleation rate coefficient, ``J``.
+  The parameterization is based on [Baumgartner2022](@cite), [Koop2000](@cite),
+  and [Luo1995](@cite).
 
-``\Delta a_w``is the difference between the water activity of the droplet, ``a_w``,
   and the water activity of ice at the same temperature, ``a_{w,ice}(T)``. When the
   droplet is in equilibrium with its surroundings, ``a_w`` is equivalent to relative
   humidity. Otherwise, a parameterization can be found in the `Common.jl` file and
@@ -22,7 +24,8 @@ The `Common.jl` module includes
 where ``p_{sol}`` is saturated vapor pressure of water above solution, ``p_{sat}``
   is saturated vapor pressure above pure liquid water, and ``p_{i,sat}`` is saturated
   vapor pressure above ice. ``p_{sol}`` is determined in mbar using a parameterization
-  for supercooled, binary ``H_2SO_4/H_2O`` solution from [Luo1995](@cite) which is only valid for ``185K < T < 235K``:
+  for supercooled, binary ``H_2SO_4/H_2O`` solution from [Luo1995](@cite) which is only
+  valid for ``185K < T < 235K``:
 ```math
 \begin{equation}
   ln(p_{sol}) = 23.306 - 5.3465x + 12xw_h - 8.19xw_h^2 + \frac{1}{T}(-5814 + 928.9x - 1876.7xw_h)
@@ -38,7 +41,8 @@ where ``x`` is the weight fraction of sulphuric acid in the droplets
     There is a need to find a parameterization for p_{sol}
     at temperatures warmer than 235K for mixed phase clouds.
 
-For now, the equation used to find water activity of a droplet at equilibrium at temperatures warmer than 235K is taken from [Baumgartner2022](@cite) equation 4:
+For now, the equation used to find water activity of a droplet at equilibrium at
+  temperatures warmer than 235K is taken from [Baumgartner2022](@cite) equation 4:
 ```math
 \begin{equation}
   a_w = S_i \frac{p_{i,sat}(T)}{p_{sat}(T)}
@@ -86,11 +90,23 @@ To verify that our parameterizations for water activty using `Thermodynamics.jl`
 include("water_activity_plots/Baumgartner2022_fig5.jl")
 ```
 ![](Baumgartner2022_fig5.svg)
-Shown in red is the water activity over ice using our parameterization. With these two lines plotted (critical water activity of the droplet and ice water activity), we create a phase diagram. Under the red line is liquid, above the critical water activity is ice, and between the two curves is supercooled liquid.
+Shown in red is the water activity over ice using our parameterization. With these two lines
+  plotted (critical water activity of the droplet and ice water activity), we create a phase
+  diagram. Under the red line is liquid, above the critical water activity is ice, and between
+  the two curves is supercooled liquid.
 
-Another plot to test if our parameterization is reasonable is plotting against other parameterizations of water activity (as opposed to critical water activity) as a function of temperature. Plotted in green are various ways to compute water activity over ice. ``using p(0,T)`` refers to how the denominator, ``a_w``, is calculated. By default, this is parameterized assuming a pure liquid droplet with `Thermodynamics.jl`. ``using p(0,T)`` implies that the parameterization of vapor pressure of a solution droplet is used but setting concentration of H2SO4 to zero. ``using \mu`` refers to the parameterization used in [Koop2000](@cite) where water activity is dependent on chemical potential.
+Another plot to test if our parameterization is reasonable is plotting against other parameterizations
+  of water activity (as opposed to critical water activity) as a function of temperature. Plotted in
+  green are various ways to compute water activity over ice. ``using p(0,T)`` refers to how the denominator,
+  ``a_w``, is calculated. By default, this is parameterized assuming a pure liquid droplet with
+  `Thermodynamics.jl`. ``using p(0,T)`` implies that the parameterization of vapor pressure of a solution
+  droplet is used but setting concentration of H2SO4 to zero. ``using \mu`` refers to the parameterization
+  used in [Koop2000](@cite) where water activity is dependent on chemical potential.
 ```@example
 include("water_activity_plots/T_vs_wateractivity.jl")
 ```
 ![](T_vs_wateractivity.svg)
-Taking the difference between any pair of blue and green lines will give a ``\Delta a_w(T)``. Since all the blue lines are similar and all the green lines are similar, we can assume that our parameterization of pure liquid and ice water activities are reasonable.
+Taking the difference between any pair of blue and green lines will give a ``\Delta a_w(T)``.
+  Since all the blue lines are similar and all the green lines are similar, we can
+  assume that our parameterization of pure liquid and ice water activities are reasonable.
+