Eqn. 1This one dimensional, 2-compartment (or "bucket") soil moisture accounting scheme is based on empirical functions that describe evapotranspiration, surface runoff, sub-surface runoff (i.e., interflow), and deep percolation for a watershed unit (see Figure 1). This method allows for the characterization of land use and/or soil type impacts to these processes. The deep percolation within the watershed unit can be transmitted to a surface water body as baseflow or directly to groundwater storage if the appropriate link is made between the watershed unit node and a groundwater node.
A watershed unit can be divided into N fractional areas representing different land uses/soil types, and a water balance is computed for each fractional area, j of N. Climate is assumed uniform over each sub-catchment, and the water balance is given as,
Eqn. 1
where z1,j = [1,0] is the
relative storage given as a fraction of the total effective storage of
the root zone, 
(mm) for land cover fraction, j. The effective
precipitation, Pe , includes
snowmelt from accumulated snowpack in the sub-catchment, where mc is the melt coefficient given as,
Eqn. 2
where Ti is the observed temperature for month i, and Tl and Ts are the melting and freezing temperature thresholds. Snow accumulation, Aci, is a function of mc and the observed monthly total precipitation, Pi, by the following relation,
Eqn. 3
with the melt rate, mr, defined as,
Eqn. 4
The effective precipitation, Pe, is then computed as
Eqn. 5
In Eqn. 1, PET is the Penman-Monteith reference crop potential evapotranspiration, where kc,j is the crop/plant coefficient for each fractional land cover. The third term represents surface runoff, where RRFj is the Runoff Resistance Factor of the land cover. Higher values of RRFj lead to less surface runoff. The fourth and fifth terms are the interflow and deep percolation terms, respectively, where the parameter ks,j is an estimate of the root zone saturated conductivity (mm/time) and fj is a partitioning coefficient related to soil, land cover type, and topography that fractionally partitions water both horizontally and vertically. Thus total surface and interflow runoff, RT, from each sub-catchment at time t is,
Eqn. 6
For applications where no return flow link is created from a catchment to a groundwater node, baseflow emanating from the second bucket will be computed as:
Eqn. 7
where the inflow to this storage, Smax is the deep percolation from the upper storage given in Eqn. 1, and Ks2 is the saturated conductivity of the lower storage (mm/time), which is given as a single value for the catchment and therefore does not include a subscript, j. Equations 1 and 7 are solved using a predictor-corrector algorithm.
When an alluvial aquifer is introduced into the model and a runoff/infiltration link is established between the watershed unit and the groundwater node, the second storage term in Eqn. 7 is ignored, and recharge R (volume/time) to the aquifer is
Eqn.
8
where A is the watershed unit's contributing area. The stylized aquifer characterizes the height of the water table relative to the stream, where individual river segments can either gain or lose water to the aquifer (see Groundwater-Surface water Interactions).
Figure 1. Conceptual diagram and equations incorporated in the Soil Moisture model
Irrigation runoff can be included in total runoff emanating from a catchment. WEAP calculates this irrigation runoff by first assuming no irrigation exists and calculating flows accordingly. WEAP then performs the calculations incorporating irrigation, assuming all requested irrigation is supplied. Knowing how much more runoff would flow due solely to irrigation, WEAP calculates an "average" irrigation runoff fraction (that goes to a river and/or groundwater). This fraction is then applied to the quantity of irrigation that was actually supplied, and essentially becomes the runoff fraction. Note: this irrigation runoff fraction is specified as data by the user when simulating a catchment with the Rainfall Runoff method.