Deficit and Constant

The Deficit and Constant model is a soil-moisture balance model also referred to a Soil-Moisture Deficit model (e.g. Andersson and Harding, 1991; Clark 2002). The soil is represented with a single homogeneous layer with a maximum soil moisture capacity and with the moisture distributed evenly throughout the soil layer. The soil moisture deficit, , is defined the soil moisture capacity minus the actual soil moisture. When the soil is saturated, is zero. The soil is not saturated when > 0. Therefore, the deficit is the amount of water needed to saturate the soil. The governing equation for the Deficit and Constant infiltration model is a simple water balance equation

where $//<![CDATA[ \begin{array}{l}E_v\end{array} //]]>$ is the soil evapotranspiration rate, $//<![CDATA[ \begin{array}{l}f\end{array} //]]>$ is the infiltration rate, $//<![CDATA[ \begin{array}{l}p\end{array} //]]>$ is the percolation (drainage) rate. When the soil is not saturated all of the rainfall will infiltrate until the soil is saturated. This assumption can lead to unreasonably high infiltration rates. Percolation only occurs was the soil is saturated. When the rainfall rate is larger than the percolation rate the difference becomes excess precipitation (i.e. $//<![CDATA[ \begin{array}{l}v=R-f\end{array} //]]>$ ).

In order to simplify the computation of the right-hand-side terms in the moisture deficit equation, the equation is solved using an explicit three step first order operator splitting method; one step for each rate on the right-hand-side of the equation. The order of the fractional steps is (1) infiltration, (2) evapotranspiration, and (3) percolation. The fractional steps allow limiting each rate easily.

Table 4-2. SCS Soil Groups and filtration rates (SCS, 1986; Skaggs and Khaleel 1982).