Another Look at Z-transform Technique for Deriving Unit Impulse Response Function

Springer Science and Business Media LLC - Tập 21 - Trang 1829-1848 - 2007
R. K. Rai1, M. K. Jain1, S. K. Mishra2, C. S. P. Ojha3, V. P. Singh4
1Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee, India
2Department of WRDM, Indian Institute of Technology Roorkee, Roorkee, India
3Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, India
4Department of Biological and Agricultural Engineering, Texas A&M University, College Station, USA

Tóm tắt

This paper presents a technique to derive the unit impulse response functions (UIRF) used for determination of unit hydrograph by employing the Z-transform technique to the response function derived from the Auto Regressive Moving Average (ARMA) process of order (p, q). The proposed approach was applied to reproduce direct surface runoff for single storm event data registered over four watersheds of area ranging from 0.42 to 295 km2. It is observed that the UIRF based on ARMA (1, 2) and ARMA (2, 2) provides a better representation of the watershed response. Further, to test the superiority of the developed impulse response function form ARMA process, the direct runoff hydrographs were computed using the simple ARMA process and optimized Nash’s two parameter model and compared with the results obtained from UIRF’s of ARMA model. The performance of the models based on the graphical presentation as well as from the test statistics viz. RMSE and MAPE indicates that UIRF-ARMA (p, q) performs better than optimized Nash Model and mostly similar to simple ARMA (p,q) model. Further more, the ARMA process of order p ≤ 2 and q ≤ 2 is generally sufficient and less cumbersome than the Argand diagram based approach for UIRF derivation.

Tài liệu tham khảo

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