From 2ab077a9a95b1c87a45c11d12241158e260ec9f7 Mon Sep 17 00:00:00 2001 From: amylu00 Date: Wed, 6 Sep 2023 13:15:27 -0700 Subject: [PATCH] untangling water activity from abifm docs --- docs/src/IceNucleation.md | 39 ++++++++++----------------------------- docs/src/WaterActivity.md | 28 ++++++++++++++++++++++------ 2 files changed, 32 insertions(+), 35 deletions(-) diff --git a/docs/src/IceNucleation.md b/docs/src/IceNucleation.md index 9a0fda68d..55fe6594b 100644 --- a/docs/src/IceNucleation.md +++ b/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}) diff --git a/docs/src/WaterActivity.md b/docs/src/WaterActivity.md index 53fd49def..d3cf7091c 100644 --- a/docs/src/WaterActivity.md +++ b/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. \ No newline at end of file +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. + \ No newline at end of file