Changes between Version 23 and Version 24 of doc/tec/lsm

Timestamp:

Apr 5, 2016 8:32:53 AM (9 years ago)

Author:

maronga

Comment:

--

doc/tec/lsm

@@ -70 +70 @@
 $e_\mathrm{def}$: Water-vapor pressure deficit
 }}}
+The correction functions read
+{{{
+#!Latex
+\begin{equation*}
+\dfrac{1}{f_1(R_\mathrm{sw,in})} = min\left(1, \dfrac{0.004\ R_\mathrm{sw,in}}{0.81(0.004\ R_\mathrm{sw,in} + 1)}\right)
+\end{equation*}
+}}}
+which accounts for the reaction of plants to shortwave radiation (opening/closing stomata),
+{{{
+#!Latex
+\begin{equation*}
+\dfrac{1}{f_3(e_\mathrm{def})} = exp(g_\mathrm{D}\ e_\mathrm{def})
+\end{equation*}
+}}}
+where ''g'',,D,, is a correction factor (for high vegetation only, otherwise zero). Moreover, the reaction of plants to water availability in the soil is considered:
+{{{
+#!Latex
+\begin{equation*}
+\dfrac{1}{f_2(\tilde m)} = 
+\begin{cases}
+0 & \tilde m < m_\mathrm{wilt}\\
+\dfrac{\tilde m - m_\mathrm{wilt}}{m_\mathrm{fc} - m_\mathrm{wilt}} & m_\mathrm{wilt} \leq \tilde m \leq m_\mathrm{fc}\\
+1 & \tilde m > m_\mathrm{fc}
+\end{cases}
+\end{equation*}
+}}}
+where
+{{{
+#!Latex
+$m_\mathrm{wilt}$: Permanent wilting point\\
+$m_\mathrm{fc}$: Field capacity
+}}}
+and
+{{{
+#!Latex
+\begin{equation*}
+ \tilde m = \sum\limits_{k = 1}^4 R_k\ max(m_\mathrm{soil,k}, m_\mathrm{wilt})
+\end{equation*}
+}}}
+where
+{{{
+#!Latex
+$R_k$: Root fraction in layer $k$
+}}}
+
 The bare soil resistance is given by
 {{{
@@ -225 +270 @@
 #!Latex
 \begin{equation*}
-m_\mathrm{total} = \sum \limits_{k = 0}^3 R_\mathrm{fr}(k)\ m_\mathrm{soil}(k)
+m_\mathrm{total} = \sum \limits_{k = 1}^4 R_\mathrm{fr}(k)\ m_\mathrm{soil}(k)
 \end{equation*}
 }}}
@@ -231 +276 @@
 #!Latex
 \begin{equation*}
-\sum \limits_{k = 0}^3 R_\mathrm{fr}(k) = 1
+\sum \limits_{k = 1}^4 R_\mathrm{fr}(k) = 1
 \end{equation*}
 }}}