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

Author

Listed:
  • R. Rai
  • M. Jain
  • S. Mishra
  • C. Ojha
  • V. Singh

Abstract

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 km 2 . 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. Copyright Springer Science+Business Media, Inc. 2007

Suggested Citation

  • R. Rai & M. Jain & S. Mishra & C. Ojha & V. Singh, 2007. "Another Look at Z-transform Technique for Deriving Unit Impulse Response Function," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 21(11), pages 1829-1848, November.
    • Handle: RePEc:spr:waterr:v:21:y:2007:i:11:p:1829-1848
    DOI: 10.1007/s11269-006-9132-1
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    References listed on IDEAS

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    1. Dooge, James C. I., 1973. "Linear Theory of Hydrologic Systems," Technical Bulletins 160041, United States Department of Agriculture, Economic Research Service.
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    1. R. Rai & S. Sarkar & V. Singh, 2009. "Evaluation of the Adequacy of Statistical Distribution Functions for Deriving Unit Hydrograph," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(5), pages 899-929, March.
    2. R. Rai & S. Sarkar & Alka Upadhyay & V. Singh, 2010. "Efficacy of Nakagami-m Distribution Function for Deriving Unit Hydrograph," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(3), pages 563-575, February.

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