Derivation of instantaneous unit hydrographs using linear reservoir models

Abstract

In this research, a new conceptual model for producing instantaneous unit hydrographs (IUHs) is introduced by a linear combination of the Nash model, which assumes that the discharge from a reservoir is a linear function of its storage, and a model called inter-connected linear reservoir model (ICLRM), which assumes that the discharge from a reservoir is a linear function of the difference of its storage and its adjacent downstream reservoir. By employing these assumptions, a system of first-order linear differential equations with three degrees of freedom (storage coefficient, number of reservoirs, and weighting coefficient) is obtained as the governing equation for the proposed model. This model may be considered as the general form of the two models and is therefore capable of simulating IUHs laying between these two models. To show the capabilities of the model, linear and curvilinear soil conservation service (SCS) hydrographs are simulated using dimensionless hydrographs obtained by this model. Moreover, several real hydrographs were simulated by the proposed model and compared with hydrographs obtained by Nash, ICLRM, and SCS models. The results show that the model yields more accurate results compared to other studied models and may be considered as a new model for simulating IUHs. HIGHLIGHTS Nash model and inter-connected linear reservoir model (ICLRM), being two extremes of linear reservoir models, are unified.; The general model is a linear combination of the Nash and ICLRM models.; The weighting coefficient gives the proposed model an extra degree of freedom.; This model yields more accurate results for the simulation of SCS hydrographs.;

Keywords

• instantaneous unit hydrograph
• linear reservoir model
• nash model
• system of linear first-order differential equations