s_phys_pkgs/text/land.tex

\section{Land package}

This package provides a simple land model
based on Rong Zhang [e-mail:roz@gfdl.noaa.gov] 2 layers model
(see documentation below).

It is primarily implemented for AIM (\_v23) atmospheric physics
but could be adapted to work with a different atmospheric physics.
Two subroutines ({\it aim\_aim2land.F} {\it aim\_land2aim.F}
in {\it pkg/aim\_v23}) are used as interface with AIM physics. 

Number of layers is a parameter ({\it land\_nLev} in {\it LAND\_SIZE.h})
and can be changed. 

%---------------------------------------------------------------------

% \documentclass[12pt,thmsa]{article}

% \begin{document}

\begin{center}
{\bf Note on Land Model}\\
date: June 1999\\
author: Rong Zhang\\
\end{center}

% \baselineskip19pt

This is a simple 2-layer land model. The top layer depth $z1=0.1m$, the
second layer depth $z2=4m$.

Let $T_{g1},T_{g2}$ be the temperature of each layer, $W_{1,}W_{2}$ be the
soil moisture of each layer. The field capacity $f_{1,}$ $f_{2}$ are the
maximum water amount in each layer, so $W_{i}$ is the ratio of available
water to field capacity. $f_{i}=\gamma z_{i},\gamma =0.24$ is the field
capapcity per meter soil$,$ so $f_{1}=0.024m,$ $f_{2}=0.96m.$

The land temperature is determined by total surface downward heat flux $F,$

\begin{equation}
z_{1}C_{1}\frac{dT_{g1}}{dt}=F-\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2}
\end{equation}

\begin{center}
\begin{equation}
z_{2}C_{2}\frac{dT_{g2}}{dt}=\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2}
\end{equation}
\end{center}

here $C_{1},C_{2}$ are the heat capacity of each layer , $\lambda $ is the
thermal conductivity, $\lambda =0.42Wm^{-1}K^{-1}.$

\begin{center}
\bigskip 
\begin{equation}
C_{1}=C_{w}W_{1}\gamma +C_{s}
\end{equation}

\begin{equation}
C_{2}=C_{w}W_{2}\gamma +C_{s}
\end{equation}
\end{center}

$C_{w},C_{s}$ are the heat capacity of water and dry soil respectively. $%
C_{w}=4.2\times 10^{6}Jm^{-3}K^{-1},C_{s}=1.13\times 10^{6}Jm^{-3}K^{-1}.$

\bigskip

The soil moisture is determined by precipitation $P(m/s)$,surface
evaporation $E(m/s)$ and runoff $R(m/s).$

\begin{equation}
\frac{dW_{1}}{dt}=\frac{P-E-R}{f_{1}}+\frac{W_{2}-W_{1}}{\tau }
\end{equation}

$\tau =2$ $days$ is the time constant for diffusion of moisture between
layers.

\begin{equation}
\frac{dW_{2}}{dt}=\frac{f_{1}}{f_{2}}\frac{W_{1}-W_{2}}{\tau }
\end{equation}

In the code, $R=0$ gives better result, $W_{1},W_{2}$ are set to be within
[0, 1]. If $W_{1}$ is greater than 1, then let $\delta W_{1}=W_{1}-1,W_{1}=1$
and $W_{2}=W_{2}+p\delta W_{1}\frac{f_{1}}{f_{2}}$, i.e. the runoff of top
layer is put into second layer. $p=0.5$ is the fraction of top layer runoff
that is put into second layer.

The time step is 1 hour, it takes several years to reach equalibrium offline.

\begin{center}
\bigskip
\end{center}

\textbf{References}

Hansen J. et al. Efficient three-dimensional global models for climate
studies: models I and II. \emph{Monthly Weather Review}, vol.111, no.4, pp.
609-62, 1983

% \end{document}
1	jmc	1.1	\section{Land package}
2
3			This package provides a simple land model
4			based on Rong Zhang [e-mail:roz@gfdl.noaa.gov] 2 layers model
5			(see documentation below).
6
7			It is primarily implemented for AIM (\_v23) atmospheric physics
8			but could be adapted to work with a different atmospheric physics.
9			Two subroutines ({\it aim\_aim2land.F} {\it aim\_land2aim.F}
10			in {\it pkg/aim\_v23}) are used as interface with AIM physics.
11
12			Number of layers is a parameter ({\it land\_nLev} in {\it LAND\_SIZE.h})
13			and can be changed.
14
15			%---------------------------------------------------------------------
16
17			% \documentclass[12pt,thmsa]{article}
18
19			% \begin{document}
20
21			\begin{center}
22			{\bf Note on Land Model}\\
23			date: June 1999\\
24			author: Rong Zhang\\
25			\end{center}
26
27			% \baselineskip19pt
28
29			This is a simple 2-layer land model. The top layer depth $z1=0.1m$, the
30			second layer depth $z2=4m$.
31
32			Let $T_{g1},T_{g2}$ be the temperature of each layer, $W_{1,}W_{2}$ be the
33			soil moisture of each layer. The field capacity $f_{1,}$ $f_{2}$ are the
34			maximum water amount in each layer, so $W_{i}$ is the ratio of available
35			water to field capacity. $f_{i}=\gamma z_{i},\gamma =0.24$ is the field
36			capapcity per meter soil$,$ so $f_{1}=0.024m,$ $f_{2}=0.96m.$
37
38			The land temperature is determined by total surface downward heat flux $F,$
39
40			\begin{equation}
41			z_{1}C_{1}\frac{dT_{g1}}{dt}=F-\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2}
42			\end{equation}
43
44			\begin{center}
45			\begin{equation}
46			z_{2}C_{2}\frac{dT_{g2}}{dt}=\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2}
47			\end{equation}
48			\end{center}
49
50			here $C_{1},C_{2}$ are the heat capacity of each layer , $\lambda $ is the
51			thermal conductivity, $\lambda =0.42Wm^{-1}K^{-1}.$
52
53			\begin{center}
54			\bigskip
55			\begin{equation}
56			C_{1}=C_{w}W_{1}\gamma +C_{s}
57			\end{equation}
58
59			\begin{equation}
60			C_{2}=C_{w}W_{2}\gamma +C_{s}
61			\end{equation}
62			\end{center}
63
64			$C_{w},C_{s}$ are the heat capacity of water and dry soil respectively. $%
65			C_{w}=4.2\times 10^{6}Jm^{-3}K^{-1},C_{s}=1.13\times 10^{6}Jm^{-3}K^{-1}.$
66
67			\bigskip
68
69			The soil moisture is determined by precipitation $P(m/s)$,surface
70			evaporation $E(m/s)$ and runoff $R(m/s).$
71
72			\begin{equation}
73			\frac{dW_{1}}{dt}=\frac{P-E-R}{f_{1}}+\frac{W_{2}-W_{1}}{\tau }
74			\end{equation}
75
76			$\tau =2$ $days$ is the time constant for diffusion of moisture between
77			layers.
78
79			\begin{equation}
80			\frac{dW_{2}}{dt}=\frac{f_{1}}{f_{2}}\frac{W_{1}-W_{2}}{\tau }
81			\end{equation}
82
83			In the code, $R=0$ gives better result, $W_{1},W_{2}$ are set to be within
84			[0, 1]. If $W_{1}$ is greater than 1, then let $\delta W_{1}=W_{1}-1,W_{1}=1$
85			and $W_{2}=W_{2}+p\delta W_{1}\frac{f_{1}}{f_{2}}$, i.e. the runoff of top
86			layer is put into second layer. $p=0.5$ is the fraction of top layer runoff
87			that is put into second layer.
88
89			The time step is 1 hour, it takes several years to reach equalibrium offline.
90
91			\begin{center}
92			\bigskip
93			\end{center}
94
95			\textbf{References}
96
97			Hansen J. et al. Efficient three-dimensional global models for climate
98			studies: models I and II. \emph{Monthly Weather Review}, vol.111, no.4, pp.
99			609-62, 1983
100
101			% \end{document}