Changes between Version 7 and Version 8 of doc/tec/lsm


Ignore:
Timestamp:
Apr 4, 2016 3:31:17 PM (9 years ago)
Author:
maronga
Comment:

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  • doc/tec/lsm

    v7 v8  
    4545== Soil model ==
    4646
     47== Technical details ==
     48The discretized and linearized energy budget equation in PALM reads
     49{{{
     50#!Latex
     51\begin{equation*}
     52T_\mathrm{0,p} = \dfrac{A \Delta t + C_\mathrm{sk} T_0}{C_\mathrm{sk} + B \Delta t}
     53\end{equation*}
     54}}}
     55with
     56{{{
     57#!Latex
     58\begin{equation*}
     59A = R_\mathrm{n} + 3 \sigma T_0^4 + \dfrac{f_H}{\Pi} T_1 + f_{LE} \left( q_1 - q_s + \dfrac{d q_s}{d T} T_0 \right) + \Lambda T_\mathrm{soil}
     60\end{equation*}
     61}}}
     62and
     63{{{
     64#!Latex
     65\begin{equation*}
     66B = \Lambda + f_{LE} \dfrac{d q_s}{d T} + \dfrac{f_H}{\Pi} + 4 \sigma T_0^3
     67\end{equation*}
     68}}}
     69with (in order of occurence):
     70{{{
     71#!Latex
     72$T_\mathrm{0,p}$:  prognostic skin temperature\\
     73$\Delta t$: time step\\
     74$C_\mathrm{sk}$: skin heat capacity\\
     75$T_\mathrm{0}$: skin temperature before time step\\
     76$R_\mathrm{n}$: net radiation at the surface\\
     77$\sigma$: Stefan-Boltzmann constant\\
     78$f_{H} = \dfrac{\rho c_\mathrm{p}}{r_\mathrm{a}}$\\
     79$\Pi$: conversion factor from actual temperature to potential temperature\\
     80$T_1$: temperature at first grid level\\
     81$f_{LE} = \dfrac{\rho l_\mathrm{v}}{r_\mathrm{a} + r_\mathrm{s}}$\\
     82$q_1$: specific humidity at first grid level\\
     83$q_s$: saturation specific humidity at the surface\\
     84$\Lambda$: heat conductivity of the skin layer\\
     85$T_\mathrm{soil}$: temperature of the uppermost soil layer
     86}}}
     87
     88
     89
     90
     91
    4792== Usage ==
    4893