Non-linear optimization for parameter estimation for flood forecasting

Abstract

Floods are the response of a catchment area to severe rainfall events. Each catchment will have its unique response which is dependent on its own characteristics and the temporal and spatial distribution of the oncoming rainfall event. A non linear optimization technique has been applied to historical data for rainfall and river flows of the Kakanui catchment in North Otago, New Zealand, to estimate the parameters of a model based on the transfer function concept. The non linear optimization is based on Powell algorithm. Powell algorithm has been widely used in the literature, and it is more efficient and faster than the Simplex method (Press et al., 1989) Observed rainfall events at two locations in the Kakanui catchment, along with the corresponding observed flows of the river have been utilized to estimate the transfer function which represents the response of the Kakanui catchment to rainfall events. An adjusted form of Philip’s equation for infiltration was used to estimate the abstraction of the rainfall event and obtain the effective rainfall which will contribute to the river flow. Weighing factors were assigned to each of the rainfall sites to obtain the best fit between observed and forecasted flows. Nine flood events were used for the calibration process, while two events were utilized for the validation of the derived model. The model has 19 parameters for the transfer function, 2 parameters for the hydrologic abstractions model, and 2 parameters for the weighing factors of the rainfall sites. This results in a total of 23 parameters for the developed model. The ratio of observed cumulative rainfall at Clifton Falls to the corresponding rainfall at the Dasher for historical events is not consistent, and varies significantly from one event to another. This indicates the high variability of the spatial distribution of rainfall events over the Kakanui catchment. As these rainfall events were used in the model calibration, it was difficult to obtain the correct transfer function without proper accounting for the spatial distribution of rainfall over the whole watershed. However, the model, in general, performed satisfactory, given the difficulty in representing the spatial variability of the rainfall events. The model was capable of simulating the flood hydrographs of several events which were incorporated in its calibration, but did not perform well with others. The model was able to simulate well the flows of a flood event which was not included in its calibration. Moreover, in applying the derived model for a real case event which occurred most recently on 30 July 2007, the model was able to forecast very closely the peak flow, but the whole flow hydrograph was not forecasted as good.