A Method Based on Taking the Average of Probabilities to Compute the Flow Duration Curve

In this study a method based on taking the average of the probabilities is presented to obtain flow duration curve. In this method the exceedance probability for each flow value is computed repeatedly for all time periods within a year. The final representing exceedance is just simply the average of all these probabilities. The applicability of the method to daily mean flows is tested assuming various marginal probability distributions like normal, Pearson type III, log-Pearson type III, 2-parameter lognormal and 3-parameter lognormal distributions. It is seen that the observed flow duration curves were quite well approximated by the 2-parameter lognormal average of probabilities curves. In that case the method requires the computation of the daily mean and standard deviation values of the observed flow data. The method curve enables extrapolation of the available data providing the exceedance probabilities for the flows higher than the observed maximum flow. The method is applied to the missing data and ungauged site problems and the results are quite satisfactory.

[1]  Denis A. Hughes,et al.  Regionalization of daily flow characteristics in part of the Eastern Cape, South Africa , 1997 .

[2]  H. Ogawa,et al.  Tradeoffs In Water Quality Management , 1984 .

[3]  Maria Mimikou,et al.  Regionalization of flow duration characteristics , 1985 .

[4]  Richard M. Vogel,et al.  ESTIMATION OF HARMONIC MEAN OF A LOGNORMAL VARIABLE , 2000 .

[5]  R. Vogel,et al.  L moment diagrams should replace product moment diagrams , 1993 .

[6]  K. Singh,et al.  Model Flow Duration and Streamflow Variability , 1971 .

[7]  L. R. Beard.  Statistical Analysis in Hydrology , 1943 .

[8]  Peter R. Waylen,et al.  A stochastic model of flow duration curves , 1993 .

[9]  J. R. Wallis,et al.  Regional Frequency Analysis: An Approach Based on L-Moments , 1997 .

[10]  S. Lawrence Dingman,et al.  SYNTHESIS OF FLOW‐DURATION CURVES FOR UNREGULATED STREAMS IN NEW HAMPSHIRE1 , 1978 .

[11]  Richard M. Vogel,et al.  Flow duration curves II : a review of applications in water resources planning , 1995 .

[12]  V. V. Srinivas,et al.  Application of Gamma Autoregressive Model to Analysis of Dry Periods , 2000 .

[13]  David R. Maidment,et al.  Handbook of Hydrology , 1993 .

[14]  W. Kirby,et al.  Computer‐oriented Wilson‐Hilferty transformation that preserves the first three moments and the lower bound of the Pearson type 3 distribution , 1972 .

[15]  Vladimir U. Smakhtin,et al.  Daily flow time series patching or extension: a spatial interpolation approach based on flow duration curves , 1996 .

[16]  J. Hosking.  L‐Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics , 1990 .

[17]  Richard M. Vogel,et al.  Flow‐Duration Curves. I: New Interpretation and Confidence Intervals , 1994 .

[18]  Pao-Shan Yu,et al.  Synthetic regional flow duration curve for southern Taiwan , 1996 .

[19]  H. Kerem Cigizoglu,et al.  A generalized seasonal model for flow duration curve , 2000 .