A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering of the Asian Institute of Technology, Bangkok, Thailand

Thesis (M.Eng.) - Asian Institute of Technology, 1979

The study focusses its attention on system analysis approach to quotative modelling of rainfall - runoff relationship. Beginning with the conventional instantaneous unit hydrograph theory a brief mathematical review of the functional series model and the various methods that are currently in practice to evaluate it's kernels is presented. An elaborate mathematical analysis of a stationary, non-anticipating initially relaxed ·quadratic functional series model along the lines of Diskin and Boneh, but using total rainfall and total runoff instead of effective rainfall and direct runoff as used by Diskin and Boneh, is performed to identify and sum up the properties of the first and the second order kernels. Hence a Laguerre-exponential function is introduced to model the second order kernel and a special least square method is device to calibrate it. A feedback control model (FCM) with a constant feedback factor is postulated anticipating the fact that the feedback component may model the losses such as infiltration, etc. and thus allows the use of total rainfall as input. Z-transformation and matrix inversion (pseudoinverse) techniques are explored to calibrate this model. Extended 0-Delay Filter method (E0-DFM) based on the assumption that the rainfall is white noise is reviewed. FCM and Eo-DFM were· used to simulate two smaller catchments (drainage area < 500 sq.km) in North-Eastern part of Thailand. It was found that FCM predicts well for the case (a wet year) where the prediction is reasonable without a feedback. For a medium year the system seems to accept only a little feedback thus stipulating a time varying feedback function. The overall prediction of Eo-DFM was found to be unsatisfactory. In this case, the prediction of FCM is found to be better than that of Eo-DFM. H9wever, this is not a universal statement unless we have thoroughly identify some conditions under which each of them is applicable in relation to catchment and rainfall properties. The failure of the use of runoff coefficient reflects the fact that those definitions of runoff coefficient are not universal unless some constraints are identified in relation to catchment and rainfall characteristics to select the suitable definition for a catchment.