Error in Response of a Linear Reservoir in Comparison with That of a Nonlinear Reservoir

Abstract Linear and nonlinear reservoirs have been widely used in hydrology, especially in rainfall-runoff modeling, flow routing, and groundwater flow. Although hydrologic processes are nonlinear, it is often assumed that a linear reservoir is a good approximation of a nonlinear reservoir. That is why a linear reservoir forms the basis of the unit hydrograph theory. The question, however, is: How accurately the linear reservoir approximates the nonlinear reservoir. Normally, the approximation is measured by one metric for the entire hydrograph, such as root mean square error, efficiency criterion, and correlation coefficient. The objective of this study is to derive the graph of error for the entire hydrograph. This graph shows the error as a function of time, demonstrating that the error is not constant in time and may vary from one discharge value of the hydrograph to another.