# 8.5.2. Land package¶

## 8.5.2.1. 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 (aim_aim2land.F aim_land2aim.F in pkg/aim_v23) are used as interface with AIM physics.

Number of layers is a parameter (land_nLev in LAND_SIZE.h) and can be changed.

Note on Land Model date: June 1999 author: Rong Zhang

## 8.5.2.2. 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 $$F,$$

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

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

$C_{1}=C_{w}W_{1}\gamma +C_{s}$
$C_{2}=C_{w}W_{2}\gamma +C_{s}$

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

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

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

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

$\frac{dW_{2}}{dt}=\frac{f_{1}}{f_{2}}\frac{W_{1}-W_{2}}{\tau }$

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.

## 8.5.2.3. Land diagnostics¶

------------------------------------------------------------------------
<-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)
`

## 8.5.2.4. References¶

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

## 8.5.2.5. Experiments and tutorials that use land¶

• Global atmosphere experiment in aim.5l_cs verification directory.