WWRC 94-24
Determination of Optimal Unit Hydrographs by
Linear Programming
Abstract
A unit hydrograph (UH) obtained from past storms can be used to predict a direct runoff
hydrograph (DRH) based on the effective rainfall hyetograph (ERH) of a new storm. The objective
functions in commonly used linear programming (LP) formulations for obtaining an optimal UH
are (1) minimizing the sum of absolute deviations (MSAD) and (2) minimizing the largest absolute
deviation (MLAD). This paper proposes two alternative LP formulations for obtaining an optimal
UH, namely, (1) minimizing the weighted sum of absolute deviations (MWSAD) and (2) minimizing
the range of deviations (MRNG). In this paper the predicted DRHs as well as the regenerated DRHs
by using the UHs obtained from different LP formulations were compared using a statistical cross-validation
technique. The golden section search method was used to determine the optimal weights
for the model of MWSAD. The numerical results show that the UH by MRNG is better than that
by MLAD in regenerating and predicting DRHs. It is also found that the model MWSAD with a
properly selected weighing function would produce a UH that is better in predicting the DRHs than
the commonly used MSAD.
Key words: unit hydrograph, linear programming, validation.
Water Resources Publications List
Water Resources Data System Library |
Water Resources Data System Homepage
