s_phys_pkgs/text/land.tex

\subsection{Land package}
\label{sec:pkg:land}
\begin{rawhtml}
<!-- CMIREDIR:package_land: -->
\end{rawhtml}

\subsubsection{Introduction}
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

\subsubsection{Equations and Key Parameters}
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.

\subsubsection{Land diagnostics}
\label{sec:pkg:land:diagnostics}

{\footnotesize
\begin{verbatim}

------------------------------------------------------------------------
<-Name->|Levs|<-parsing code->|<--  Units   -->|<- Tile (max=80c) 
------------------------------------------------------------------------
GrdSurfT|  1 |SM      Lg      |degC            |Surface Temperature over land
GrdTemp |  2 |SM      MG      |degC            |Ground Temperature at each level
GrdEnth |  2 |SM      MG      |J/m3            |Ground Enthalpy at each level
GrdWater|  2 |SM P    MG      |0-1             |Ground Water (vs Field Capacity) Fraction at each level
LdSnowH |  1 |SM P    Lg      |m               |Snow Thickness over land
LdSnwAge|  1 |SM P    Lg      |s               |Snow Age over land
RUNOFF  |  1 |SM      L1      |m/s             |Run-Off per surface unit
EnRunOff|  1 |SM      L1      |W/m^2           |Energy flux associated with run-Off
landHFlx|  1 |SM      Lg      |W/m^2           |net surface downward Heat flux over land
landPmE |  1 |SM      Lg      |kg/m^2/s        |Precipitation minus Evaporation over land
ldEnFxPr|  1 |SM      Lg      |W/m^2           |Energy flux (over land) associated with Precip (snow,rain)
\end{verbatim}
}

\subsubsection{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	molod	1.3	\subsection{Land package}
2	edhill	1.2	\label{sec:pkg:land}
3			\begin{rawhtml}
4			<!-- CMIREDIR:package_land: -->
5			\end{rawhtml}
6	jmc	1.1
7	molod	1.4	\subsubsection{Introduction}
8	jmc	1.1	This package provides a simple land model
9			based on Rong Zhang [e-mail:roz@gfdl.noaa.gov] 2 layers model
10			(see documentation below).
11
12			It is primarily implemented for AIM (\_v23) atmospheric physics
13			but could be adapted to work with a different atmospheric physics.
14			Two subroutines ({\it aim\_aim2land.F} {\it aim\_land2aim.F}
15			in {\it pkg/aim\_v23}) are used as interface with AIM physics.
16
17			Number of layers is a parameter ({\it land\_nLev} in {\it LAND\_SIZE.h})
18			and can be changed.
19
20			%---------------------------------------------------------------------
21
22			% \documentclass[12pt,thmsa]{article}
23
24			% \begin{document}
25
26			\begin{center}
27			{\bf Note on Land Model}\\
28			date: June 1999\\
29			author: Rong Zhang\\
30			\end{center}
31
32			% \baselineskip19pt
33
34	molod	1.4	\subsubsection{Equations and Key Parameters}
35	jmc	1.1	This is a simple 2-layer land model. The top layer depth $z1=0.1m$, the
36			second layer depth $z2=4m$.
37
38			Let $T_{g1},T_{g2}$ be the temperature of each layer, $W_{1,}W_{2}$ be the
39			soil moisture of each layer. The field capacity $f_{1,}$ $f_{2}$ are the
40			maximum water amount in each layer, so $W_{i}$ is the ratio of available
41			water to field capacity. $f_{i}=\gamma z_{i},\gamma =0.24$ is the field
42			capapcity per meter soil$,$ so $f_{1}=0.024m,$ $f_{2}=0.96m.$
43
44			The land temperature is determined by total surface downward heat flux $F,$
45
46			\begin{equation}
47			z_{1}C_{1}\frac{dT_{g1}}{dt}=F-\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2}
48			\end{equation}
49
50			\begin{center}
51			\begin{equation}
52			z_{2}C_{2}\frac{dT_{g2}}{dt}=\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2}
53			\end{equation}
54			\end{center}
55
56			here $C_{1},C_{2}$ are the heat capacity of each layer , $\lambda $ is the
57			thermal conductivity, $\lambda =0.42Wm^{-1}K^{-1}.$
58
59			\begin{center}
60			\bigskip
61			\begin{equation}
62			C_{1}=C_{w}W_{1}\gamma +C_{s}
63			\end{equation}
64
65			\begin{equation}
66			C_{2}=C_{w}W_{2}\gamma +C_{s}
67			\end{equation}
68			\end{center}
69
70			$C_{w},C_{s}$ are the heat capacity of water and dry soil respectively. $%
71			C_{w}=4.2\times 10^{6}Jm^{-3}K^{-1},C_{s}=1.13\times 10^{6}Jm^{-3}K^{-1}.$
72
73			\bigskip
74
75			The soil moisture is determined by precipitation $P(m/s)$,surface
76			evaporation $E(m/s)$ and runoff $R(m/s).$
77
78			\begin{equation}
79			\frac{dW_{1}}{dt}=\frac{P-E-R}{f_{1}}+\frac{W_{2}-W_{1}}{\tau }
80			\end{equation}
81
82			$\tau =2$ $days$ is the time constant for diffusion of moisture between
83			layers.
84
85			\begin{equation}
86			\frac{dW_{2}}{dt}=\frac{f_{1}}{f_{2}}\frac{W_{1}-W_{2}}{\tau }
87			\end{equation}
88
89			In the code, $R=0$ gives better result, $W_{1},W_{2}$ are set to be within
90			[0, 1]. If $W_{1}$ is greater than 1, then let $\delta W_{1}=W_{1}-1,W_{1}=1$
91			and $W_{2}=W_{2}+p\delta W_{1}\frac{f_{1}}{f_{2}}$, i.e. the runoff of top
92			layer is put into second layer. $p=0.5$ is the fraction of top layer runoff
93			that is put into second layer.
94
95			The time step is 1 hour, it takes several years to reach equalibrium offline.
96
97	molod	1.4	\subsubsection{Land diagnostics}
98			\label{sec:pkg:land:diagnostics}
99
100	edhill	1.5	{\footnotesize
101	molod	1.4	\begin{verbatim}
102
103			------------------------------------------------------------------------
104			<-Name->\|Levs\|<-parsing code->\|<-- Units -->\|<- Tile (max=80c)
105			------------------------------------------------------------------------
106			GrdSurfT\| 1 \|SM Lg \|degC \|Surface Temperature over land
107			GrdTemp \| 2 \|SM MG \|degC \|Ground Temperature at each level
108			GrdEnth \| 2 \|SM MG \|J/m3 \|Ground Enthalpy at each level
109			GrdWater\| 2 \|SM P MG \|0-1 \|Ground Water (vs Field Capacity) Fraction at each level
110			LdSnowH \| 1 \|SM P Lg \|m \|Snow Thickness over land
111			LdSnwAge\| 1 \|SM P Lg \|s \|Snow Age over land
112			RUNOFF \| 1 \|SM L1 \|m/s \|Run-Off per surface unit
113			EnRunOff\| 1 \|SM L1 \|W/m^2 \|Energy flux associated with run-Off
114			landHFlx\| 1 \|SM Lg \|W/m^2 \|net surface downward Heat flux over land
115			landPmE \| 1 \|SM Lg \|kg/m^2/s \|Precipitation minus Evaporation over land
116			ldEnFxPr\| 1 \|SM Lg \|W/m^2 \|Energy flux (over land) associated with Precip (snow,rain)
117			\end{verbatim}
118	edhill	1.5	}
119	jmc	1.1
120	molod	1.4	\subsubsection{References}
121	jmc	1.1
122			Hansen J. et al. Efficient three-dimensional global models for climate
123			studies: models I and II. \emph{Monthly Weather Review}, vol.111, no.4, pp.
124			609-62, 1983
125
126			% \end{document}