Changes between Version 6 and Version 7 of doc/tec/lsm

Timestamp:

Apr 4, 2016 2:54:19 PM (9 years ago)

Author:

maronga

Comment:

--

doc/tec/lsm

@@ -10 +10 @@
 {{{
 #!Latex
-\begin{equation}
+\begin{equation*}
    C_0 \dfrac{dT_0}{dt} = R_\mathrm{n} - H - LE - G
-\end{equation}
+\end{equation*}
 }}}
 where ''C'',,0,, and ''T'',,0,, are the heat capacity and radiative temperature of the surface skin layer, respectively. ''R'',,n,,, ''H'', ''LE'', and ''G'' are the net radiation, sensible heat flux, latent heat flux, and ground (soil) heat flux at the surface, respectively. ''H'' is calculated as
 {{{
 #!Latex
-\begin{equation}
+\begin{equation*}
   H = - \rho\ c_\mathrm{p}\ \dfrac{1}{r_\mathrm{a}} ( \theta_1 - \theta_0 )
-\end{equation}
+\end{equation*}
 }}}
 where ''ρ'' is the density of the air, ''c'',,p,, = 1005 J kg^-1^ K^-1^$ is the specific heat at constant pressure, ''r'',,a,, is the aerodynamic resistance, and ''θ'',,0,, and ''θ'',,1,, are the potential temperature at the surface and at the first grid level above the surface, respectively. ''r'',,a,, is calculated via Monin-Obukhov similarity theory, based on roughness lengths for heat and momentum and the assumption of a constant flux layer between the surface and the first grid level.
+
+''G'' is parametrized as (Duynkerke 1999)
+{{{
+#!Latex
+\begin{equation*}
+  G = \Lambda ( T_0 - T_{\mathrm{soil},1} )
+\end{equation*}
+}}}
+with ''Λ'' being the heat conductivity between skin layer and the soil, and ''T'',,soil,1,, being the temperature of the uppermost soil layer. The latent heat flux is calculated as 
+{{{
+#!Latex
+\begin{equation*}
+  LE = - \rho\ l_\mathrm{v}\ \dfrac{1}{r_\mathrm{a} + r_\mathrm{s}} ( q_{\mathrm{v},1} - q_{\mathrm{v,sat}}(T_0) )\;.
+\end{equation*}
+}}}
+Here, ''l'',,v,, = 2.5 * 10^6^ J kg^-1^ is the latent heat of vaporisation, ''r'',,s,, is the surface resistance, ''q'',,v,1,, is the specific humidity at first grid level, and ''q'',,v,sat,, is the saturation specific humidity at temperature ''T'',,0,,. 
+
+All equations above are solved locally for each surface element of the LES grid. Each element can consist of both patches of bare soil, vegetation, and a liquid water reservoir, which is the interception water stored on plants and soil from precipitation. Therefore, an additional equation is solved for the liquid water reservoir. ''LE'' is then calculated for each of the three components (bare soil, vegetation, liquid water). The resistances are calculated following Jarvis (1976).
+
+''C'',,0,, is set to zero, the energy balance is solved implicitly by linearising ''q'',,v,sat,,.
 
 == Soil model ==