Changes between Version 9 and Version 10 of doc/tec/microphysics

Timestamp:

Jun 9, 2016 8:19:37 PM (8 years ago)

Author:

Giersch

Comment:

--

doc/tec/microphysics

@@ -268 +268 @@
 with ''γ = 0.7'' (see also [#heus2010 Heus et al., 2010]).
 
-== Sedimentation of rainwater
+== Sedimentation of cloudwater ==
+
+As shown by [#ackerman Ackerman et al. (2009)], the sedimentation of cloud water has to be taken in account for the simulation of stratocumulus clouds. They suggest the cloud water sedimentation flux to be calculated as
+{{{
+#!Latex
+\begin{align*}
+  & F_{q_\mathrm{c}} = k \left(\frac{4}{3}
+    \pi\rho_\mathrm{l}N_\mathrm{c}\right)^{-2/3} \left(\rho
+    q_\mathrm{c}\right)^{\frac{5}{3}} \exp{\left(5
+      \ln^2{\sigma_\mathrm{g}}\right)},
+\end{align*}
+}}}
+based on a Stokes drag approximation of the terminal velocities of log-normal distributed cloud droplets.  Here, ''k = 1.2 x 10^8^'' m^-1^ s^-1^ is a parameter and ''σ'',,g,, ''= 1.3'' the geometric SD of the cloud droplet size distribution ([#geoffroy Geoffroy et al., 2010]). The tendency of ''q'' results from the sedimentation flux divergences and reads as
+{{{
+#!Latex
+\begin{align*}
+  & \left.\frac{\partial q}{\partial t} \right|_\text{sed, c}= -
+  \frac{\partial F_{q_\mathrm{c}}}{\partial z} \frac{1}{\rho}.
+\end{align*}
+}}}
+
+== Sedimentation of rainwater ==
 
 == Turbulence closure ==
@@ -298 +319 @@
 * [=#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].
 
-
+* [=#ackerman]'''Ackerman, AS, vanZanten MC, Stevens B, Savic-Jovcic V, Bretherton CS, Chlond A, Golaz J-C, Jiang H, Khairoutdinov M, Krueger SK, Lewellen DC, Lock A, Moeng C-H, Nakamura K, Petters MD, Snider JR, Weinbrecht S, Zuluaf M.''' 2009. Large-eddy simulations of a drizzling, stratocumulus-topped marine boundary layer, Mon. Weather Rev., 137: 1083–1110.
+
+* [=#geoffroy]'''Geoffroy O, Brenguier J-L, Burnet F.''' 2010. Parametric representation of the cloud droplet spectra for LES warm bulk microphysical schemes. Atmos. Chem. Phys. 10: 4835–4848. [http://dx.doi.org/10.5194/acp-10-4835-2010 doi].
+