## Materials and Methods
### Computation of Available Discharges for Irrigation Supply  
HEC-RAS model, which is a computer program that models the hydraulics of water flow through natural rivers and other channels, was adopted in the present study. The HEC-RAS 5.0 with Geospatial Hydrologic Modeling extension (Arc-Hydro and HEC-GeoRAS) was used. The model is capable of performing one-dimensional (1-D) steady and unsteady-flow simulations. The unsteady, gradually varied flow simulation model is dependent on finite difference solutions of the Saint-Venant equations as presented in Equations (1) and (2) [41]:  
\[\frac{\partial A}{\partial t}+\frac{\partial Q}{\partial x}=0, \tag{11}\]  
\[\frac{\partial Q}{\partial t}+\frac{\partial\Big{(}\frac{Q^{2}}{A}\Big{)}}{ \partial x}+gA\frac{\partial H}{\partial x}+gA\Big{(}S_{o}-S_{f}\Big{)}=0, \tag{12}\]  
where: \(A\)--cross-sectional area normal to the flow; \(Q\)--discharge; \(g\)--acceleration due to gravity; \(H\)--elevation of the water surface above a specified datum, also called stage; \(S_{o}\)--bed slope; \(S_{f}\)--energy slope; \(t\)--temporal coordinate, and \(x\)--longitudinal coordinate.  
The data needed to perform the computations are categorized into two; geometric data and flow data. The basic geometric data in HEC-RAS comprise of establishment of the river system connectivity (river system schematic); cross section data; reach lengths; energy loss coefficients (friction losses, contraction and expansion losses); stream junction information; etc. Prior to using the HEC-RAS model, a DEM raster of the study area was downloaded from DIVA-GIS, converted to triangular irregular network (TIN) within Arc-GIS. The TIN was used to establish the river system connectivity; cross-section data, reach length, etc. using HEC-GeoRAS coupled with Arc-Hydro tool. After pre-processing stages using HEC-GeoRAS, the information that clarifies the shape, height and position and the overall cross section traits of channel were extracted and exported into the HEC-RAS model. Figure 5 summarized the HEC-RAS model setup for the study.  
The most sensitive calibration parameter required by the HEC-RAS model is channel resistance--specifically Manning's n. Its values can be extracted with the aid of land use map of the area using HEC-GeoRAS. However, due to insufficient land use data, covering all the river area, n values presented by another study [42] was used as a first estimate of the appropriate channel resistance and adjusted through calibration. The contraction coefficient was fixed to 0.1 and the coefficient of expansion was fixed to 0.3. The changes in cross sections is a common cause of energy losses within a reach (between two cross sections), which usually results in contraction or expansion of flow. The contraction or expansion coefficients used in the model were selected as reported by [41]. Unsteady flow data comprise of boundary conditions (external and internal) and initial conditions. The earlier simulated streamflow at the basin outlet by HEC-HMS model was used as input hydrograph to the HEC-RAS model for flow routing in the river. The downstream end of the river was modeled with the flow hydrograph at the intake of main canal (TRH). Moreover, the initial condition was established automatically by the software.  
Because of irregular and limited flow data at the downstream side, located at the inlet of the main canal, reliable data for four years (from 2001 to 2004) was used for model evaluation. The model was calibrated by comparing between the simulated and observed values using the 2001-2003 daily discharge records of the river. Finally, the calibrated model was validated using the 2004 daily discharge records.  
Figure 5: Hydroologic Engineering Centers River Analysis System (HEC-RAS) model setup for simulation of available canal flow.