The probability-distributed principle and runoff production at point and basin scales

ABSTRACT The probability-distributed principle in basin-scale hydrology considers the frequency of occurrence of hydrological variables (model inputs, parameters or elements) of certain magnitudes over the basin without regard to the location of a particular occurrence within the basin. The random assemblage of different parts is considered more important than the relation of the parts, one to another. Rainfall-runoff models based on probability-distributed infiltration capacity and storage capacity concepts, and which generate runoff according to Hortonian and saturation overland flow mechanisms respectively, are distinguished. Two types of probability-distributed storage capacity model are identified, one based on an assumption that storage elements at points in the basin respond independently of their neighbours, and the other where storage elements interact so as to equalize the depth of stored water over the basin. Allowing redistribution of water leads to simplification of the model equations. The probability-distributed principle is also used to represent the process of water translation through the basin. Interpretation of the instantaneous unit hydrograph as a probability density function of translation time is demonstrated and the inverse Gaussian density proposed as a suitable functional form on physical grounds.