| 1 |
\subsection{Land package} |
| 2 |
\label{sec:pkg:land} |
| 3 |
\begin{rawhtml} |
| 4 |
<!-- CMIREDIR:package_land: --> |
| 5 |
\end{rawhtml} |
| 6 |
|
| 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} |
Parent Directory
| 
Revision Log
| 
Revision Graph