Abstract
Present study emphasizes the applicability of linear theory concept onto hilly watersheds. For this purpose, Z-transform technique was used to derive the instantaneous unit hydrograph (IUH) from the transfer function of autoregressive and moving average (ARMA) type linear difference equation. Parameters of the ARMA type rainfall-runoff process were estimated by least-squares method. The derived IUH from Z-transform (i.e. ARMA-IUH) has been used to compute the hydrologic response i.e. direct runoff hydrograph (DRH). Fur-ther, the superiority of the proposed approach has been tested by comparing the results through the results obtained from the Nash-IUH. Analyzing the results obtained from ARMA-IUH and Nash-IUH for the two hilly watersheds of North Western Himalayas shows the applicability of the linear theory concept even in turbulent flow conditions which are frequently encountered in hilly terrains under similar conditions of flow.
Highlights
The rainfall-runoff process is nonlinear and dynamic with spatially distributed inputs and outputs
Analyzing the results obtained from Auto Regressive Moving Average (ARMA)-instantaneous unit hydrograph (IUH) and Nash-IUH for the two hilly watersheds of North Western Himalayas shows the applicability of the linear theory concept even in turbulent flow conditions which are frequently encountered in hilly terrains under similar conditions of flow
Transfer function derived from the ARMA type difference equation has been used for the derivation of IUH applying the Z-transform technique
Summary
The rainfall-runoff process is nonlinear and dynamic with spatially distributed inputs and outputs. Watershed response is inherently spatial, non-linear and time-variant. Linear models are frequently used for analysis of watershed response to rainfall, as they are mathematically more convenient to handle than non-linear models. The input-output mathematical models based on linear theory of hydrologic systems attempt to establish a link between two or more observed phenomena without detailed description of physical process under investigation. A discrete linear cascade model was developed for hydrology using the cascade concept of the Auto Regressive Moving Average (ARMA)-type difference equation and derived the unit impulse response function as a discrete time function for a family of discrete-parametric models [3,4]. Wang et al [6] developed a rainfall-runoff model for small watersheds and an applied discrete excess rainfall-runoff model to calculate the hydrograph of a watershed from the excess rainfall under the concept of linear system
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