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.