1 |
jmc |
1.1 |
\section{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 |
|
|
This package provides a simple land model |
8 |
|
|
based on Rong Zhang [e-mail:roz@gfdl.noaa.gov] 2 layers model |
9 |
|
|
(see documentation below). |
10 |
|
|
|
11 |
|
|
It is primarily implemented for AIM (\_v23) atmospheric physics |
12 |
|
|
but could be adapted to work with a different atmospheric physics. |
13 |
|
|
Two subroutines ({\it aim\_aim2land.F} {\it aim\_land2aim.F} |
14 |
|
|
in {\it pkg/aim\_v23}) are used as interface with AIM physics. |
15 |
|
|
|
16 |
|
|
Number of layers is a parameter ({\it land\_nLev} in {\it LAND\_SIZE.h}) |
17 |
|
|
and can be changed. |
18 |
|
|
|
19 |
|
|
%--------------------------------------------------------------------- |
20 |
|
|
|
21 |
|
|
% \documentclass[12pt,thmsa]{article} |
22 |
|
|
|
23 |
|
|
% \begin{document} |
24 |
|
|
|
25 |
|
|
\begin{center} |
26 |
|
|
{\bf Note on Land Model}\\ |
27 |
|
|
date: June 1999\\ |
28 |
|
|
author: Rong Zhang\\ |
29 |
|
|
\end{center} |
30 |
|
|
|
31 |
|
|
% \baselineskip19pt |
32 |
|
|
|
33 |
|
|
This is a simple 2-layer land model. The top layer depth $z1=0.1m$, the |
34 |
|
|
second layer depth $z2=4m$. |
35 |
|
|
|
36 |
|
|
Let $T_{g1},T_{g2}$ be the temperature of each layer, $W_{1,}W_{2}$ be the |
37 |
|
|
soil moisture of each layer. The field capacity $f_{1,}$ $f_{2}$ are the |
38 |
|
|
maximum water amount in each layer, so $W_{i}$ is the ratio of available |
39 |
|
|
water to field capacity. $f_{i}=\gamma z_{i},\gamma =0.24$ is the field |
40 |
|
|
capapcity per meter soil$,$ so $f_{1}=0.024m,$ $f_{2}=0.96m.$ |
41 |
|
|
|
42 |
|
|
The land temperature is determined by total surface downward heat flux $F,$ |
43 |
|
|
|
44 |
|
|
\begin{equation} |
45 |
|
|
z_{1}C_{1}\frac{dT_{g1}}{dt}=F-\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2} |
46 |
|
|
\end{equation} |
47 |
|
|
|
48 |
|
|
\begin{center} |
49 |
|
|
\begin{equation} |
50 |
|
|
z_{2}C_{2}\frac{dT_{g2}}{dt}=\lambda \frac{T_{g1}-T_{g2}}{(z_{1}+z_{2})/2} |
51 |
|
|
\end{equation} |
52 |
|
|
\end{center} |
53 |
|
|
|
54 |
|
|
here $C_{1},C_{2}$ are the heat capacity of each layer , $\lambda $ is the |
55 |
|
|
thermal conductivity, $\lambda =0.42Wm^{-1}K^{-1}.$ |
56 |
|
|
|
57 |
|
|
\begin{center} |
58 |
|
|
\bigskip |
59 |
|
|
\begin{equation} |
60 |
|
|
C_{1}=C_{w}W_{1}\gamma +C_{s} |
61 |
|
|
\end{equation} |
62 |
|
|
|
63 |
|
|
\begin{equation} |
64 |
|
|
C_{2}=C_{w}W_{2}\gamma +C_{s} |
65 |
|
|
\end{equation} |
66 |
|
|
\end{center} |
67 |
|
|
|
68 |
|
|
$C_{w},C_{s}$ are the heat capacity of water and dry soil respectively. $% |
69 |
|
|
C_{w}=4.2\times 10^{6}Jm^{-3}K^{-1},C_{s}=1.13\times 10^{6}Jm^{-3}K^{-1}.$ |
70 |
|
|
|
71 |
|
|
\bigskip |
72 |
|
|
|
73 |
|
|
The soil moisture is determined by precipitation $P(m/s)$,surface |
74 |
|
|
evaporation $E(m/s)$ and runoff $R(m/s).$ |
75 |
|
|
|
76 |
|
|
\begin{equation} |
77 |
|
|
\frac{dW_{1}}{dt}=\frac{P-E-R}{f_{1}}+\frac{W_{2}-W_{1}}{\tau } |
78 |
|
|
\end{equation} |
79 |
|
|
|
80 |
|
|
$\tau =2$ $days$ is the time constant for diffusion of moisture between |
81 |
|
|
layers. |
82 |
|
|
|
83 |
|
|
\begin{equation} |
84 |
|
|
\frac{dW_{2}}{dt}=\frac{f_{1}}{f_{2}}\frac{W_{1}-W_{2}}{\tau } |
85 |
|
|
\end{equation} |
86 |
|
|
|
87 |
|
|
In the code, $R=0$ gives better result, $W_{1},W_{2}$ are set to be within |
88 |
|
|
[0, 1]. If $W_{1}$ is greater than 1, then let $\delta W_{1}=W_{1}-1,W_{1}=1$ |
89 |
|
|
and $W_{2}=W_{2}+p\delta W_{1}\frac{f_{1}}{f_{2}}$, i.e. the runoff of top |
90 |
|
|
layer is put into second layer. $p=0.5$ is the fraction of top layer runoff |
91 |
|
|
that is put into second layer. |
92 |
|
|
|
93 |
|
|
The time step is 1 hour, it takes several years to reach equalibrium offline. |
94 |
|
|
|
95 |
|
|
\begin{center} |
96 |
|
|
\bigskip |
97 |
|
|
\end{center} |
98 |
|
|
|
99 |
|
|
\textbf{References} |
100 |
|
|
|
101 |
|
|
Hansen J. et al. Efficient three-dimensional global models for climate |
102 |
|
|
studies: models I and II. \emph{Monthly Weather Review}, vol.111, no.4, pp. |
103 |
|
|
609-62, 1983 |
104 |
|
|
|
105 |
|
|
% \end{document} |