final docs fixes

docs/src/IceNucleationParcel0D.md

@@ -375,15 +375,14 @@ We can calculate the variance ``\bf{V}`` as,
 \end{equation}
 ```
 
-We use this process to model the logarithm of INPC (``x=\log(\text{INPC})``),
-which tends toward the mean ``\mu(T)``.
+We use this process to model ``x=\log(\text{INPC})``,
+  which tends toward the mean ``\mu(T)``.
 If we denote ``\tau = 1 / \gamma`` as the process timescale and
-``\sigma = g / \sqrt(2 \gamma)`` as the process uncertainty,
-then the tendency
-
+  ``\sigma = g / \sqrt{2 / \gamma}`` as the process uncertainty,
+  then
 ```math
 \begin{equation}
-  d\log(\text{INPC}) = - \frac{\log(\text{INPC}) - μ}{\tau} + \sigma \sqrt(\frac{2}{\tau dt}) \; {\bf{N}}(0, 1))
+  d\log(\text{INPC}) = - \frac{\log(\text{INPC}) - μ}{\tau} + \sigma \sqrt{\frac{2}{\tau \; dt}} \; {\bf{N}}(0, 1))
 \end{equation}
 ```
 

parcel/Example_Frostenberg_Immersion_Freezing.jl

@@ -106,9 +106,9 @@ for (const_dt, n_dt_range) in zip(const_dt_range, n_dt_range_12)
     end
 end
 
-results_stochastic = []
-labels_stochastic = []
-time_stochastic = []
+results_stoch = []
+labels_stoch = []
+time_stoch = []
 for const_dt in const_dt_range
     # Frostenberg_stochastic with different timescales γ
     for τ in τ_range
@@ -130,17 +130,14 @@ for const_dt in const_dt_range
             push!(solutions_st, sol_st)
         end
         mean_sol = sum(solutions_st) / length(solutions_st)
-        push!(time_stochastic, solutions_st[1].t)
-        push!(results_stochastic, mean_sol)
-        push!(
-            labels_stochastic,
-            "dt = " * string(const_dt) * " τ = " * string(τ),
-        )
+        push!(time_stoch, solutions_st[1].t)
+        push!(results_stoch, mean_sol)
+        push!(labels_stoch, "dt = " * string(const_dt) * " τ = " * string(τ))
     end
 end
 
 # Plotting
-fig = MK.Figure(size = (900, 700))
+fig = MK.Figure(size = (1200, 900))
 ax1 = MK.Axis(fig[1, 1], ylabel = "Ice Supersaturation [-]")
 ax2 = MK.Axis(fig[1, 2], ylabel = "T [K]")
 ax3 = MK.Axis(fig[2, 1], ylabel = "q_ice [g/kg]")
@@ -178,12 +175,7 @@ function plot_results(sol, t, ll, cl, ls)
         label = ll,
     )
 end
-for (sol, t, ll, cl) in zip(
-    results_stochastic,
-    time_stochastic,
-    labels_stochastic,
-    colors_stochastic,
-)
+for (sol, t, ll, cl) in zip(results_stoch, time_stoch, labels_stoch, colors)
     ls = :solid
     plot_results(sol, t, ll, cl, ls)
     MK.lines!(ax7, sol[3, :], exp.(sol[11, :]), linestyle = ls, color = cl)

parcel/Example_Liquid_only.jl

@@ -26,6 +26,7 @@ r₀ = FT(8e-6)
 p₀ = FT(800 * 1e2)
 T₀ = FT(273.15 + 7.0)
 x_sulph = FT(0)
+ln_INPC = FT(0)
 e = TD.saturation_vapor_pressure(tps, T₀, TD.Liquid())
 Sₗ = FT(1)
 md_v = (p₀ - e) / R_d / T₀
@@ -34,7 +35,7 @@ ml_v = Nₗ * 4 / 3 * FT(π) * ρₗ * r₀^3
 qᵥ = mv_v / (md_v + mv_v + ml_v)
 qₗ = ml_v / (md_v + mv_v + ml_v)
 qᵢ = FT(0)
-IC = [Sₗ, p₀, T₀, qᵥ, qₗ, qᵢ, Nₐ, Nₗ, Nᵢ, x_sulph]
+IC = [Sₗ, p₀, T₀, qᵥ, qₗ, qᵢ, Nₐ, Nₗ, Nᵢ, x_sulph, ln_INPC]
 
 # Simulation parameters passed into ODE solver
 w = FT(10)                                 # updraft speed

parcel/Example_Tully_et_al_2023.jl

@@ -29,8 +29,7 @@ function get_initial_condition(
     R_v = TD.Parameters.R_v(tps)
     e_sl = TD.saturation_vapor_pressure(tps, T, TD.Liquid())
     e = eᵥ(qᵥ, p_air, R_a, R_v)
-    S_liq = e / e_sl
-    ln_INPC = FT(0)
+    Sₗ = e / e_sl
 
     return [Sₗ, p_air, T, qᵥ, qₗ, qᵢ, Nₐ, Nₗ, Nᵢ, x_sulph, ln_INPC]
 end