Applying Fourier and Wavelet Transforms to Extract Instantaneous Unit Hydrograph

Document Type : Original Article

Abstract

This paper applies the discrete wavelet transform to decompose the instantaneous unit hydrograph (IUH) into low and high frequency bands. The fast Fourier transform exploits to extract IUH from observed rainfall – runoff data. It is estimated the oscillations of IUH by wavelet coefficients and coefficients that are close to zero are set to zero. The obtained result is a hydrograph with the information of low frequency that approximates the real IUH. Calibration criteria between observed and calculated hydrographs are used to select the best filter length in wavelet. In this research, it is demonstrated that wavelets introduced by Daubechies (1992) with filter length 6 is the best alternative in this study. The results have shown that the methodology is acceptable for the system identification of rainfall – runoff for small catchments.
 

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References

Chou, C., and Wang, R. (2002), "On-Line estimation of unit hydrograph using the wavelet-based LMS algorithm," Hydrological Science J, 47(5), pp. 721-737.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988), Applied Hydrology, McGraw-Hill Series in Water Resources and Environmental Engineering.
Daubechies, I. (1992), Ten Lectures on wavelets, SIAM.
Donoho, D. L., and Johnstone, I. M. (1998), “Attempting to unknown smoothness via wavelet shrinkage,” Annual Statistic, 90, pp. 1200–1224.
Huthmann, G. (1975) "Short-term forecasting of streamflow with the aid of multiple frequency response functions," IAHS.
Kharate, G. K., Patil, V. H., and Bhale, N. L. (2007), "Selection of mother wavelet for image compression on basis of nature of image," J Multimedia, 2, pp. 44-51.
Levi, E., and Valdes, R. (1964), "A method for direct analysis of hydrographs," J.of Hydrology, 2, pp. 182-190.
O' Flynn, M., and Moriarty, E. (1987), Linear systems: Time Domain and Transform Analysis, Wiley.
Rao, A., and Delleur, J. W. (1971), The Instantaneous Unit Hydrograph: It's Calculation by the Transform Method and Noise Control by Digital Filtering, Indian Water Resources Research Centre, TR/20.
Rao, R. A., and Delleur, J. W. (1974), "Instantaneous unit hydrographs, peak discharges and time lags in urban basins," hydrological Sciences Bulletin, 6, pp. 185-198.
Satish, L., and Nazneen, B. (2003), "Wavelet-based denoising of partial discharge signals buried in excessive noise and interference," IEEE Transactions on Dielectrics and Electrical Insulation, 10, pp. 354-367.
Sherman, L. K. (1932), "Streamflow from rainfall by the Unit-Graph method," Engineering New Record, 108, pp. 501-505.
Soman, K. P., and Ramachandran, K. I. (2005), Insight into Wavelets: From Theory to Practice, Prentice Hall of India.
SWRC (SouthwestWatershedResearchCenter) – ARS (Agricultural Research Service) – USDA (United States Department of Agriculture), (2007), Southwest Watershed Research Center & WALNUT GULCH Experimental Watershed, ww.ars.usda.gov.
 
Iran-Water Resources Research
Volume 6, Issue 1
July 2010
Pages 27-35

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History

  • Receive Date: 04 February 2009
  • Accept Date: 30 December 2009

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