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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}

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