Ecological Archives M071-008-A7

P. R. Moorcroft, G. C. Hurtt, and S. W. Pacala. 2001. A method for scaling vegetation dynamics: the ecosystem demography model (ED). Ecological Monographs 71:557-585.

Appendix G. Soil Hydrology.

Local water availability $W(y,t)$ is calculated using a simple hydrology scheme describing vertical water fluxes in and out of a single soil layer with no horizontal coupling between adjacent areas

$\displaystyle {d W(y,t)\over dt}$ $\textstyle =$ $\displaystyle \underbrace{\quad P(t) \quad }_{\mbox{precipitation}} \quad - \quad \underbrace{\sum_{i=1}^{R_y} W_{up}^{(i)}}_{\mbox{plant uptake}}$  
    $\displaystyle - \underbrace{k \left[{W(y,t) \over d \theta_{max}} \right] ^{2\tau +2}}_{\mbox{percolation and runoff}}.$ (G.1)

where $W(y,t)$, is the local water availability per unit area in mm. While the precipitation rate $P_{}(t)$ is uniform across the grid cell, water availability $W(y,t)$, is spatially heterogeneous, since total water uptake by within a gap $y_{}$ is influenced by the number of individuals within the gap $R_y$ and their respective water uptake rates $W_{up}^{(i)}$, where the superscript $i =1 \dots R_y$ indicates the water uptake rate of the $ith_{}$ individual obtained from the growth sub-model (Equation (E.7), (E.11) or (E.15), depending on current state of the plant).

Water losses due to percolation and runoff are described using the Campbell (1974) empirical formulation for hydraulic conductivity as function of soil texture and soil moisture content. The conductivity of the soil depends on the saturated hydraulic conductivity, $k$, the degree of saturation, ${W(y,t) / d \theta_{max}}$, where $d$ is the soil depth and $\theta_{max}$ is the maximum soil moisture content; and $\tau$, an empirical parameter governing the rate at which conductivity decreases as saturation levels decrease. The soil characteristics of each grid cell used in the hydrology sub-model equation were specified from the ISLSCP I gridded data of soil depth and texture compiled by Sellers et al. (Sellers et al. 1995), and the suggested hydrologic parameters for each soil texture class (see Table G). The monthly precipitation values $P_{}(t)$ in Equation (G.1) were specified from the ISLSCP I $1_{}^{\circ} \mbox{x} 1_{}^{\circ}$ monthly precipitation dataset compiled by the Global Precipitation Climatology Centre (GPCC 1993).

In the SAS approximation, Equation (G.1) becomes

$\displaystyle {d W(a,t)\over dt}$ $\textstyle =$ $\displaystyle \underbrace{\quad P(t) \quad }_{\mbox{precipitation}} \quad - \qu... ...},{\bf x},a,t) n({\bf z},{\bf x},a,t) d {\bf x} d{\bf z}}_{\mbox{plant uptake}}$  
    $\displaystyle - \underbrace{k \left[{W(a,t) \over d \theta_{max}} \right] ^{2\tau +2}}_{\mbox{percolation and runoff}}.$ (G.2)

and $W(a,t)$ becomes the second element of the resource vector $\bar{r}({\bf z},{\bf x},a,t)$.

Table: ISLSCP Soil hydrology parameters.
Soil Type $\theta_{max}$ $K_{sat} (10^{-6} m s^{-1})$ $\tau$
       
coarse 0.0363 14.1 4.26
medium/coarse 0.1413 5.23 4.74
medium 0.3548 3.38 5.25
fine/medium 0.1349 4.45 6.77
fine 0.263 2.45 8.17
organic 0.354 3.38 5.25


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