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Land surface model

This page is part of the Land Surface Model (LSM) documentation.
It describes the physical and numerical realization of the LSM.
Please also see the namelist parameters.

Overview

Since r1551 a full land surface model (LSM) is available in PALM (see land_surface_model_mod.f90 ). It consists of a multi layer soil model, predicting soil temperature and moisture content, and a solver for the energy balance, predicting the temperature of the surface or the skin layer (depending on land use classification). Moreover, a liquid water reservoir accounts for the presence of liquid water on plants, pavement, and bare soil due to precipitation. The implementation is based on the ECMWF-IFS land surface parametrization (H-TESSEL) and its adaptation in the DALES model (Heus et al. 2010).

Note that the use of the LSM requires using some kind of radiation model to provide radiative fluxes at the surface.

Energy balance solver

The energy balance of the Earth's surface reads

$\begin{equation*} C_0 \dfrac{dT_0}{dt} = R_\mathrm{n} - H - LE - G \end{equation*}$

where C₀ and T₀ are the heat capacity and radiative temperature of the surface skin layer, respectively. Note that C₀ is usually zero as it is assumed that the skin layer does not have a heat capacity (see also below). R_n, H, LE, and G are the net radiation, sensible heat flux, latent heat flux, and ground (soil) heat flux at the surface, respectively.

Parameterization of H

H is calculated as

$\begin{equation*} H = - \rho\ c_\mathrm{p}\ \dfrac{1}{r_\mathrm{a}} ( \theta_1 - \theta_0 ) \end{equation*}$

where ρ is the density of the air, c_p = 1005 J kg^-1 K^-1 is the specific heat at constant pressure, r_a is the aerodynamic resistance, and θ₀ and θ₁ are the potential temperature at the surface and at the first grid level above the surface, respectively. r_a is calculated via Monin-Obukhov similarity theory, based on roughness lengths for heat and momentum and the assumption of a constant flux layer between the surface and the first grid level:

$\begin{equation*} r_\mathrm{a} = \dfrac{\theta_1 - \theta_0}{u_*\ \theta_*} \end{equation*}$

where u_* and θ_* are the friction velocity and the characteristic temperature scale according to Monin-Obukhov similarity scaling (these are calculated in surface_layer_fluxes_mod.f90 ).

Parameterization of G

G is parametrized as (see Duynkerke 1999)

$\begin{equation*} G = \Lambda ( T_0 - T_{\mathrm{soil},1} ) \end{equation*}$

with Λ being the total thermal conductivity between skin layer and the uppermost soil layer, and T_soil,1 being the temperature of the uppermost soil layer. Λ is calculated as a combination of the conductivity between the canopy and the soil-top (constant value) and the conductivity of the top half of the uppermost soil layer:

$\begin{equation*} \Lambda = \dfrac{\Lambda_\mathrm{skin}\Lambda_\mathrm{soil}}{\Lambda_\mathrm{skin}+\Lambda_\mathrm{soil}} \end{equation*}$

When no skin layer is used (i.e. in case of bare soil and pavements), Λ reduces to the heat conductivity of the uppermost soil layer (divided by the layer depth). In that case, it is assumed that the soil temperature is constant within the uppermost 1/4 of the top soil layer and equals the radiative temperature. C₀ is then set to a non-zero value according to the material properties.

Parameterization of LE

The latent heat flux is calculated as

$\begin{equation*} LE = - \rho\ l_\mathrm{v}\ \dfrac{1}{r_\mathrm{a} + r_\mathrm{s}} ( q_{\mathrm{v},1} - q_{\mathrm{v,sat}}(T_0) )\;. \end{equation*}$

Here, l_v = 2.5 * 10⁶ J kg^-1 is the latent heat of vaporisation, r_s is the surface resistance, q_v,1 is the water vapor mixing ratio at first grid level, and q_v,sat is the water vapor mixing ratio at temperature T₀.

All equations above are solved locally for each surface element of the LES grid. Each element for the surface type 'vegetation' can consist of patches of bare soil, vegetation, and a liquid water reservoir, which is the interception water stored on plants and soil from precipitation. Therefore, an additional equation is solved for the liquid water reservoir. A liquid water reservoir is also available when the surface type is set to 'pavement'. LE is then calculated for each of the three components (bare soil, vegetation, liquid water). The resistances are calculated separately for bare soil and vegetation following Jarvis (1976). The canopy resistance is calculated as

$\begin{equation*} r_\mathrm{c} = \dfrac{r_\mathrm{c,min}}{LAI}\ f_1(R_\mathrm{sw,in})\ f_2(\widetilde m)\ f_3(e_\mathrm{def}) \end{equation*}$

with

$$r_\mathrm{c,min}$: Minimum stomatal resistance\\ $LAI$: Leaf area index\\ $f_i$: Correction functions ($f_i \geq 1$)\\ $R_\mathrm{sw,in}$: Incoming shortwave radiation\\ $\widetilde m$: Layer-averaged soil moisture\\ $e_\mathrm{def}$: Water-vapor pressure deficit$

The correction functions read

$\begin{equation*} \dfrac{1}{f_1(R_\mathrm{sw,in})} = min\left(1, \dfrac{0.004\ R_\mathrm{sw,in}}{0.81(0.004\ R_\mathrm{sw,in} + 1)}\right) \end{equation*}$

which accounts for the reaction of plants to shortwave radiation (opening/closing stomata),

$\begin{equation*} \dfrac{1}{f_3(e_\mathrm{def})} = exp(g_\mathrm{D}\ e_\mathrm{def}) \end{equation*}$

where g_D is a correction factor (for high vegetation only, otherwise zero). Moreover, the reaction of plants to water availability in the soil is considered:

$\begin{equation*} \dfrac{1}{f_2(\tilde m)} = \begin{cases} 0 & \tilde m < m_\mathrm{wilt}\\ \dfrac{\tilde m - m_\mathrm{wilt}}{m_\mathrm{fc} - m_\mathrm{wilt}} & m_\mathrm{wilt} \leq \tilde m \leq m_\mathrm{fc}\\ 1 & \tilde m > m_\mathrm{fc} \end{cases} \end{equation*}$

where

$$m_\mathrm{wilt}$: Permanent wilting point\\ $m_\mathrm{fc}$: Field capacity$

and

$\begin{equation*} \tilde m = \sum\limits_{k = 1}^N R_k\ max(m_\mathrm{soil,k}, m_\mathrm{wilt}) \end{equation*}$

where

$R_k$: Root fraction in layer $k$

and N is the number of soil layers.

The bare soil resistance is given by

$\begin{equation*} r_\mathrm{soil} = r_\mathrm{soil,min}\ f_{2b}(m_\mathrm{soil,1}) \end{equation*}$

with

$$r_\mathrm{soil,min}$: Minimum soil resistance\\ $f_{2b}$: Correction function ($f_i \geq 1$)\\ $m_\mathrm{soil,1}$: Soil moisture of the uppermost layer)$

The total evapotranspiration is then calculated as

$\begin{equation*} LE = c_\mathrm{veg} (1 - c_\mathrm{liq})\ LE_\mathrm{veg} + c_\mathrm{liq}\ LE_\mathrm{liq} + (1 - c_\mathrm{liq}) (1 - c_\mathrm{veg}) \ LE_\mathrm{soil} \end{equation*}$

where c_veg, and c_liq is the surface fraction covered with vegetation and liquid water, respectively.

Prognostic equation for the liquid water reservoir

The prognostic equation for the liquid water stored on plants and bare soil m_liq reads

$\begin{equation*} \dfrac{d m_\mathrm{liq}}{dt} = \dfrac{LE_\mathrm{liq}}{\rho_\mathrm{l}\ l_\mathrm{v}} \end{equation*}$

The maximum amount of water that can be stored on plants is calculated via

$\begin{equation*} m_\mathrm{liq,max} = \min\left(1, m_\mathrm{liq,ref}\ c_\mathrm{veg}\ LAI + (1 - c_\mathrm{veg})\right)\;, \end{equation*}$

where m_,liq,ref, = 0.2 mm is the reference liquid water column on a single leaf or bare soil. Exceeding liquid water is directly removed from the surface and infiltrated in the underlying soil. For positive values of LE_liq, liquid water is evaporating from the surface, while negative values indicate precipitation (rain, dew). The values of c_,liq, are calculated either as the ratio

$\begin{equation*} m_\mathrm{liq} / m_\mathrm{liq,max} \end{equation*}$

for vegetation (following the HTESSEL scheme, Viterbo & Beljaars, 1995) and

$\begin{equation*} m_\mathrm{liq} / m_\mathrm{liq,max})^{0.67} \end{equation*}$

following Masson (2000).

Soil model

The soil model consists of prognostic equations for the soil temperature and the volumetric soil moisture which are solved for multiple layers. The soil model only takes into account vertical transport within the soil and no ice phase is considered. By default, the soil model consists of eight layers (see Fig. 12 below), in which the vertical heat and water transport is modelled using the Fourier law of diffusion and Richards' equation, respectively. Also, root fractions can be assigned to each soil layer to account for the explicit water withdrawal of plants used for transpiration from the respective soil layer.

Figure 12: Default layer distribution in the soil model.

Soil heat transport

The prognostic equation for soil temperature reads

$\begin{equation*} (\rho C)_\mathrm{soil} \dfrac{\partial T_\mathrm{soil}}{\partial t} = \dfrac{\partial}{\partial z} \left( \lambda_T \dfrac{\partial T_\mathrm{soil}}{\partial z}\right) \end{equation*}$

with

$$(\rho C)_\mathrm{soil}$: Volumetric heat capacity of the soil layer\\ $\lambda_T$: Heat conductivity of the soil layer$

The heat conductivity is calculated as

$\begin{equation*} \lambda_T = Ke\ (\lambda_{T,\mathrm{sat}} - \lambda_{T,\mathrm{dry}}) + \lambda_{T,\mathrm{dry}} \end{equation*}$

with

$$\lambda_{T,\mathrm{sat}}$: Heat conductivity of saturated soil\\ $\lambda_{T,\mathrm{dry}}$: Heat conductivity of dry soil $Ke$: Kersten number$

The heat conductivity of saturated soil is given by

$\begin{equation*} \lambda_{T,\mathrm{sat}} = \lambda_{T,\mathrm{sm}}^{1-m_\mathrm{soil,sat}}\ \lambda_\mathrm{m} \end{equation*}$

with

$$\lambda_{T,\mathrm{sm}}$: Heat conductivity of the soil matrix\\ $\lambda_\mathrm{m}$: Heat conductivity of water\\$

The Kersten number is calculated as

$\begin{equation*} Ke = \log_{10} \left[max\left(0.1, \dfrac{m_\mathrm{soil}}{m_\mathrm{sat}}\right) \right] + 1 \end{equation*}$

Soil moisture transport

The prognostic equation for volumetric soil moisture reads

$\begin{equation*} \dfrac{\partial m_\mathrm{soil}}{\partial t} = \dfrac{\partial}{\partial z} \left( \lambda_m \dfrac{\partial m_\mathrm{soil}}{\partial z} - \gamma\right) + S_m \end{equation*}$

with

$$\lambda_m$: Hydraulic diffusion coefficient\\ $\gamma$: Hydraulic conductivity\\ $S_m$: Sink term due to root extraction$

The hydraulic diffusion coefficient is calculated after Clapp and Hornberger (1978) as

$\begin{equation*} \lambda_m = \dfrac{b \gamma_\mathrm{sat}(-\Psi_\mathrm{sat})}{m_\mathrm{sat}}\left(\dfrac{m_\mathrm{soil}}{m_\mathrm{sat}}\right)^{b+2} \end{equation*}$

with

$$b = 6.04$: exponent\\ $\gamma_\mathrm{sat}$: Hydraulic conductivity at saturation\\ $\Psi_\mathrm{sat} = -338 m$: Matrix potential at saturation$

The hydraulic conductivity is calculated either after Van Genuchten (1980) (as in H-TESSEL):

$\begin{equation*} \gamma = \gamma_\mathrm{sat} \dfrac{\left[(1 + (\alpha h)^n)^{1 - 1/n} - (\alpha h)^{n-1}\right]^2}{(1+ (\alpha h)^n)^{(1 - 1/n)(l + 2)}} \end{equation*}$

where

$$\alpha$: Van Genuchten coefficient\\ $h$: Pressure head\\ $n$: Van Genuchten coefficient\\ $l$: Van Genuchten coefficient$

and

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You can't use `macro parameter character #' in horizontal mode.\nl.141 ...d via the parameter [wiki:doc/app/radpar#\n                                                  albedo_type albedo_type].\n! Missing $ inserted.\n<inserted text> \n                $\nl.141 ...he parameter [wiki:doc/app/radpar#albedo_\n                                                  type albedo_type].\n! Missing $ inserted.\n<inserted text> \n                $\nl.142 \n      \n! You can't use `macro parameter character #' in horizontal mode.\nl.146 * [=#\n           beljaars]'''Beljaars, ACM''' 1994. The parametrization of surface...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.148 * [=#\n           balsamo]'''Balsamo G, Vitebo P, Beljaars A, van den Hurk B, Hirsc...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.150 * [=#\n           clapp]'''Clapp RB, Hornberger GM.''' 1978. Empirical Equations fo...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.152 * [=#\n           duynkerke]'''Duynkerke PG.''' 1999. Turbulence, radiation and fog...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.154 * [=#\n           heus]'''Heus T, Van Heerwaarden CC, Jonker HJJ, Siebesma AP, Axel...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.156 * [=#\n           jarvis]'''Jarvis PG.''' 1976. The interpretation of the variation...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.158 * [=#\n           vangenuchten]'''van Genuchten M.''' 1980. A closed form equation ...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.160 * [=#\n           viterbo]'''Viterbo P, Beljaars ACM.''' 1995. An Improved Land Sur...\n\n! You can't use `macro parameter character #' in horizontal mode.\nl.162 * [=#\n           masson]'''Masson, V.''' 2000. A physically-based scheme for the u...\n\n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \n! Missing } inserted.\n<inserted text> \n                }\nl.163 \\end{preview}\n                   \nPreview: Tightpage -32891 -32891 32891 32891\n[1{/localdata/software/texlive/2013/texmf-var/fonts/map/pdftex/updmap/pdftex.ma\np}] (./eed2247ad78d615fafec8b6990e4937296f32fff.aux) )\n(see the transcript file for additional information){/localdata/software/texliv\ne/2013/texmf-dist/fonts/enc/dvips/cm-super/cm-super-t1.enc}</localdata/software\n/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb></localdata/\nsoftware/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></lo\ncaldata/software/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.p\nfb></localdata/software/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/\ncmr10.pfb></localdata/software/texlive/2013/texmf-dist/fonts/type1/public/amsfo\nnts/cm/cmr7.pfb></localdata/software/texlive/2013/texmf-dist/fonts/type1/public\n/amsfonts/cm/cmsy10.pfb></localdata/software/texlive/2013/texmf-dist/fonts/type\n1/public/amsfonts/cm/cmsy7.pfb></localdata/software/texlive/2013/texmf-dist/fon\nts/type1/public/cm-super/sfrm1000.pfb>\nOutput written on eed2247ad78d615fafec8b6990e4937296f32fff.pdf (1 page, 113057 \nbytes).\nTranscript written on eed2247ad78d615fafec8b6990e4937296f32fff.log.\n"

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2015_LSM.pdf (2.8 MB) - added by maronga 10 years ago. LSM introduction
wall_concept_type1.png (34.1 KB) - added by maronga 8 years ago. soil model (vegetation)

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