A study of drainage basin linearity and non-linearity

Abstract

Standardized peak discharge distribution is defined as the log of peak discharge regressed on log runoff volume. The first-order (FSPDD) and the second-order (SSPDD) standardized peak discharge distributions are obtained by replacing the dependent variable of the original distribution with the log of peak discharge divided by runoff volume and by runoff volume squared respectively. The distributions were developed in the U.S.A. and the slope of the SSPDD was proposed as a criterion indicating drainage basin hydrologic non-linearity. For testing the distributions' applicability to other localities, investigating some rainfall-runoff linearity and non-linearity characteristics and implications in relation to distributions' characteristics and studying the latter's predictability, the three peak discharge distributions are estimated for eight drainage basins between 200 and 6000 km 2 in northern and western Greece. They are found to be similar to the ones obtained in the U.S.A. The distributions' slopes have no geographic, climatic or basin morphological influence and their coefficients of determination are linearly related to the degree of hydrologic non-linearity. It is shown that only the original peak discharge distribution is necessary and quite sufficient by itself for checking basin hydrologic linearity and accurately predicting peak discharges. Its slope, equal to 1.0 for linear and less than 1.0 for non-linear basins, is a criterion indicating with its magnitude the degree of basin hydrologic non-linearity. Hydrologic design requires identification of the degree of basin hydrologic non-linearity prior to applying linear design methods. The latter's application to non-linear basins can result in serious design errors. The variation in the peak discharge distribution's intercept is significantly explained by the log of any of the two basin morphological indices AS L and A L , with A the drainage area, and L and S the main course length and average bedslope of the river, respectively. The prediction of the intercept facilitates the distribution estimation in the region.