3.3 THE WEAP MODEL
3.3.1 The Rainfall–Runoff Soil Moisture Method
While there are several options within the WEAP model for simulating streamflow, this study used the ‘rainfall-runoff soil moisture’ method. This method uses a two compartment soil moisture accounting structure that is designed to account for inputs of rainfall, losses through evapotranspiration and runoff generated as surface runoff, interflow (from the upper soil storage) and groundwater (from the lower storage). The model is therefore simpler than the Pitman model but also simulates the main water balance components of natural hydrological systems (Figure 3.7).
57 Figure 3.7 Conceptual diagram of the rainfall–runoff soil moisture model (Adopted
from SEI, 2013).
Some of the default functionalities of the different components of the WEAP model have been modified by including some expressions in the parameter definitions to achieve simulations matching those of the Pitman model. The following sub-sections present a brief overview of the WEAP model components and compare them to the Pitman model.
3.3.1.1 Evapotranspiration
There is no interception function within the WEAP model and therefore all atmospheric losses are dealt with in a single non-linear equation (3.1) that relates the relative soil moisture store and the proportion of potential evaporation that contributes to actual evaporation losses:
ET = PET * Kc* (5Z1-2Z12) / 3 … Equation 3.1 Where:
PET = Potential evapotranspiration (seasonally variable)
58 Kc = Crop coefficient (seasonally variable)
Z1 = Current upper storage level (relative to maximum storage)
Figure 3.8 compares the estimations of actual evapotranspiration of the WEAP and Pitman models for PET values of 120 and 60 mm, assuming the Kc-value of 1 and the Pitman parameter R of 0. While the Pitman evapotranspiration increases proportionately with moisture content, the non-linearity relationship in the WEAP function implies that higher values of evapotranspiration will be generated for the same demand value (PE * Kc) and this will have the largest impact at moderate relative moisture storages.
Kc, the crop coefficient parameter, is a property of plants which can be used to predict evapotranspiration for a particular type of vegetation. It therefore varies with the type and stage of growth of a crop. The Z value in WEAP is similar to S/ST of the Pitman model.
Figure 3.8 WEAP model actual evapotranspiration from soil moisture function.
3.3.1.2 Surface Runoff
The default surface runoff (SQ) equation for WEAP is given by Equation 3.2, where P and Z are monthly rainfall and relative soil moisture content of the upper zone, respectively and RRF is the surface runoff parameter.
SQ = P*Z1RRF … Equation 3.2
59 This implies that surface runoff is dependent not only on rainfall (as in the Pitman model) but also on storage level of the upper soil zone. This default equation also implies that surface runoff will occur at all rainfall depths, unlike in the Pitman model where rainfall has to exceed ZMIN. To better align the surface runoff calculations of the two models, an expression was developed for RRF rather than using a fixed value. This expression (Equation 3.3) was developed after various approaches were explored within an Excel spreadsheet.
If P-Pmin<0.5, 20, N + Pmax/(P-Pmin)(Ln(P)/5) ; … Equation 3.3 Where:
P = monthly rainfall depth (mm)
Pmin = monthly rainfall (mm) below which surface runoff is not expected N = nominal RRF
Pmax = rainfall scale factor
Figure 3.9 compares the simulated surface runoff for the WEAP and Pitman models using various combinations of ZMIN, ZAVE and ZMAX (for Pitman) and Pmax, Pmin and N for different relative moisture contents in the WEAP model. Figure 3.9 suggests that the general shape of the surface runoff relationship for WEAP can be made similar to that of the Pitman model.
60 Figure 3.9 Differences in simulation of surface runoff between the two models. For WEAP the numbers refer to the rainfall scale factor, minimum rainfall, relative moisture content and nominal RRF; for Pitman the number refers to ZMIM, ZAVE and ZMAX.
3.3.1.3 Interflow Function
The WEAP interflow function is used to determine both interflow and percolation to the lower storage zone and is based on two parameters; Ks1 (root zone conductivity in mm month-1) and f (dimensionless fraction), the preferred flow direction (Equations 3.4 and 3.5).
Interflow = Ks1 * f * Z12 … Equation 3.4 Percolation = Ks1 * (1-f) * Z12 … Equation 3.5
This is a similar function to that used in the Pitman model with Ks*f being equivalent to FT and POW is fixed at a value of 2. The percolation component is roughly equivalent to groundwater recharge in the Pitman model but is clearly less flexible in the WEAP model.
0 20 40 60 80 100 120 140 160 180 200
0 50 100 150 200 250 300
Simula te d Surf ace Runoff (mm )
Monthly Rainfall (mm)
WEAP 250, 50, 0.5, 1.3 WEAP 280, 50, 0.5, 1.2 WEAP 250, 50, 0.6, 1.2 Pitman 20,300,600 Pitman 50,200,400 Pitman 50,400,600 WEAP fixed
61 3.3.1.4 Groundwater or Baseflow
The WEAP model baseflow function is based on a simple non-linear function (Equation 3.6) of the relative storage level of the lower zone (Z2) storage using a single deep conductivity parameter (Ks2):
Baseflow = Ks2*Z22 … Equation 3.6
This is clearly much simpler than the approach used in the Pitman model and therefore less flexible. One of the problems with the use of the WEAP model in semi-arid areas is that the default function does not allow for zero flows. The function was therefore modified using a conditional expression (Equation 3.7) for Ks1 and Ks2 based on either the upper (Ks1) or deep (Ks2) zone storage levels at the end of the previous time step (prevTSValue(Z%) and a threshold parameter (Zthresh).
If (prevTSValue(Z%) < Zthresh, 0, Ks1 * (prevTSValue(Z%) – Zthresh)/ prevTSValue(Z%))
…Equation 3.7
In ephemeral river systems Equation 3.7 would be used for the upper zone and Ks1, while the preferred flow direction parameter (f), and the deep storage zone capacity values would be set to 0. The Zthresh value could then be calibrated to ensure the correct duration and patterns of zero flow.
Within the Pitman model it is possible to have groundwater recharge as well as zero flow periods because of the riparian evapotranspiration function which can intercept the movement of groundwater towards the river channel system.
3.3.1.5 Summary on Functionalities of the Models
There are substantial differences in the conceptual structures, assumptions and functionalities of the WEAP and the Pitman models. Some of the differences include surface runoff and drainage from storage functions. There are also a number of similarities in the processes the two models simulate and therefore some of the parameters (individually or combined) can be compared. Table 3.2 shows the processes and the related parameters of the two models.
While some of the WEAP parameter values can yield similar results to the Pitman model outputs (given the same climate inputs), some WEAP expressions have to be used achieve comparable outputs from parts of the WEAP model. The WEAP model was ‘forced’ to produce similar outputs to Pitman mainly because the latter has been extensively used in the region
62 and hence gained a lot of confidence, while the former is yet to be applied as much. Another reason is that the Pitman simulations are bound on constraints based on observed records.
Table 3.2 List of comparable parameters controlling similar hydrological processes of the WEAP and Pitman models.