# 8.5.2. Land package¶

## 8.5.2.1. Introduction¶

This package provides a simple land model based on Rong Zhang [e-mail Rong.Zhang@noaa.gov] two 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 $$z1=0.1$$ m, the second layer depth $$z2=4$$ m.

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 $$f_{1}=0.024$$ m, $$f_{2}=0.96$$ m.

The land temperature is determined by total surface downward heat flux $$F$$,

\begin{split}\begin{aligned} z_1 C_1 \frac{dT_{g1}}{dt} & = F - \lambda \frac{T_{g1}-T_{g2}}{(z_1 + z_2)/2}, \nonumber\\ z_2 C_2 \frac{dT_{g2}}{dt} & = \lambda \frac{T_{g1}-T_{g2}}{(z_1 + z_2)/2}, \nonumber \end{aligned}\end{split}

here $$C_{1},C_{2}$$ are the heat capacity of each layer, $$\lambda$$ is the thermal conductivity, $$\lambda =0.42$$ W m–1 K–1.

\begin{split}\begin{aligned} C_{1} & = C_{w}W_{1}\gamma +C_{s}, \nonumber\\ C_{2} & = C_{w}W_{2}\gamma +C_{s}, \nonumber \end{aligned}\end{split}

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


## 8.5.2.5. Experiments and tutorials that use land¶

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