Optimal Determination of the T-Hour Unit Hydrograph by Using Goal Attainment Method

Abstract

T-hour Unit Hydrograph (TUH) is widely used in simulating surface runoff process in river basins. Traditional ways, like the Least Squared (LS) method, of deriving the TUHs are prone to produce a saw-tooth TUH, because of the mistaken data, or/and simplification of the hydrological process (to be linear) of the river basin. This paper applies a so-called Goal Attainment (GA) method to obtain an optimal TUH. The GA method is a multi-objective optimization method. In its implementation in this paper, it consists of three objectives and one constraint. The three objectives are: (1) minimizing the deviation between the observed and computed surface runoffs; (2)total water volume of the accumulated TUH coordinates being equal to that of the unit effective rainfall; (3) the total volume of the calculated surface runoffs being equal to that of the observed ones. The constraint is used to enable the recession limb of the TUH to be declining monotonically. The LS method is also applied for comparison. The data from the Wills Creek (in Maryland, the USA) are used for case study. The results show that the GA method has suppressed the saw-tooth phenomenon successfully in the recession limb of the TUH. And the goodness-of-fit of the calculated against observed surface runoff of the two methods are similar.