Changes between Version 8 and Version 9 of doc/tec/microphysics

Timestamp:

Jun 9, 2016 7:50:49 PM (8 years ago)

Author:

Giersch

Comment:

--

doc/tec/microphysics

@@ -217 +217 @@
 == Evaporation of rainwater ==
 
+The evaporation of rain drops in subsaturated air (relative water supersaturation ''S < 0'') is parametrized following [#seifert2008 Seifert (2008)]:
+{{{
+#!Latex
+\begin{align*}
+  & \left.\frac{\partial q_\mathrm{r}}{\partial t}
+  \right|_{\text{evap}}= 2
+  \pi\,G\,S\,\frac{N_\mathrm{r}\,\lambda_\mathrm{r}^{\mu_\mathrm{r}+1}}{\Gamma(\mu_\mathrm{r}+1)}\,f_\mathrm{v}\,\rho,
+\end{align*}
+}}}
+where
+{{{
+#!Latex
+\begin{align*}
+  & G = \left[\frac{R_\mathrm{v}T}{K_\mathrm{v}p_\text{v, s}(T)} +
+    \left(\frac{L_\mathrm{V}}{R_\mathrm{v} T}-1\right)
+    \frac{L_\mathrm{V}}{\lambda_\mathrm{h}\,T}\right]^{-1},
+\end{align*}
+}}}
+with ''K'',,v,,'' = 2.3 x 10^-5^'' m^2^ s^-1^ being the molecular diffusivity water vapor in air and ''λ'',,h,,'' = 2.43 x 10^-2^'' W m^-1^ K^-1^ being the heat conductivity of air. Here, ''N'',,r,, ''λ'',,r,,^''μ'',,r,,''+1^ / Γ(μ'',,r,,+1) denotes the intercept parameter of the rain drop gamma distribution with ''Γ'' being the gamma-function. Following [#stevens2008 Stevens and Seifert (2008)], the slope parameter reads as
+{{{
+#!Latex
+\begin{align*}
+  & \lambda_\mathrm{r} = \frac{\left((\mu_\mathrm{r}+3)
+      (\mu_\mathrm{r}+2) (\mu_\mathrm{r}+1)\right)^{\frac{1}{3}}}{2
+    \cdot \widetilde{r_\mathrm{r}}},
+\end{align*}
+}}}
+with ''μ'',,r,, being the shape parameter, given by
+{{{
+#!Latex
+\begin{align*}
+  & \mu_\mathrm{r} = 10\,\cdot\,\left(1 +
+    \tanh{\left(1200\,\cdot\,\left(2 \cdot \widetilde{r_\mathrm{r}} -
+          0.0014 \right)\right)} \right).
+\end{align*}
+}}}
+In order to account for the increased evaporation of falling rain drops, the so-called ventilation effect, a ventilation factor ''f'',,v,, is calculated optionally by a series expansion considering the rain drop size distribution ([#seifert2008 Seifert, 2008, Appendix]).
+
+The complete evaporation of rain drops (i.e., their evaporation to a size smaller than the separation radius of 40 µm) is
+parametrized as
+{{{
+#!Latex
+\begin{align*}
+  & \left.\frac{\partial N_\mathrm{r}}{\partial t}
+  \right|_{\text{evap}}= \gamma\,\frac{N_\mathrm{r}}{\rho
+    q_\mathrm{r}}\,\left.\frac{\partial q_\mathrm{r}}{\partial t}
+  \right|_{\text{evap}},
+\end{align*}
+}}}
+with ''γ = 0.7'' (see also [#heus2010 Heus et al., 2010]).
+
 == Sedimentation of rainwater
 
@@ -245 +296 @@
 * [=#seifert2010]'''Seifert A, Nuijens L, Stevens B.''' 2010. Turbulence effects on warm-rain autoconversion in precipitating shallow convection. Q. J. Roy. Meteor. Soc. 136: 1753–1762.
 
+* [=#seifert2008]'''Seifert A.''' 2008. On the parameterization of evaporation of raindrops as simulated by a one-dimensional rainshaft model. J. Atmos. Sci. 65: 3608–3619. [http://dx.doi.org/10.1175/2008JAS2586.1 doi].
+
+