Reservoir routing in ephemeral streams in arid regions

Abstract

This paper presents a methodology for reservoir routing in general and for arid region in particular. The proposed methodology combines the mass conservation equation of the dam reservoir, the discharge equation of the dam outlet devices, and a dimensionless depth–volume equation to calculate the outflow hydrograph downstream of the dam for a given inflow hydrograph. The proposed model is solved numerically using first- and second-order Euler finite difference schemes and shows pretty good agreement when compared with analytical solution of a specific example in the published literature and with the traditional (modified puls) method (RMSE is 0.668, 0.673, and 0.94 m³/s respectively for the time step of 300 s). The results show that there is no significant difference between first- and second-order schemes which have been supported by published literature even with higher order methods. The results also show that the RMSE decreases with decreasing the value of the time step. The key parameter of the proposed model is the so-called reservoir coefficient, N, which is estimated from fitting depth–volume data with the dimensionless depth–volume equation. Best estimation of the reservoir coefficient provides reliable reservoir routing outflow hydrograph. The implementation of the methodology and the parameters selection has been illustrated on a real case study (AL-Ulb dam in Riyadh). The effect of reservoir condition wether it is full or empty is considered. The estimated reservoir coefficient N is 0.381, and the corresponding relative RMSE is 0.073. The estimated RMSE of the outflow hydrograph is 12.75 and 12.90 m³/s in case the reservoir is full and empty respectively when considering modified puls method as a reference case. The attenuation ratio on average is 65% in case the reservoir is full. However, in case of empty reservoir, an attenuation of 50% is reached for return periods more than 10 years. These results suggest that the design of reservoir in arid region should consider an empty reservoir routing, which leads to an economic design of the downstream flood channel. While in perennial rivers, a full reservoir routing is recommended. For further application of the proposed methodology, a priori analysis of eight proposed dam locations in different provinces in the Kingdom of Saudi Arabia is performed. The values of the reservoir coefficient N range between 0.39 and 0.68. The smallest value of the reservoir coefficient (N = 0.39) corresponds to the highest value of the reservoir shape factor (M = 3.06) which indicates reservoir of type II (Hill), while the rest of the reservoirs are of type III (Flood Plain Foothill). The values can be used as a prior design of these dams, and a detailed analysis using the proposed methodology is needed in the final stage.