IDENTIFICATION OF LINEARITY AND NONLiNEARITY OF DRAINAGE BASINS

Abstract

Drainage basin hydrologic linearity is defined as the condition that exists on a drainage basin when runoff volume is directly proportional to precipitation volume. Hydrologic nonlinear exists when runoff volume is not directly proportional to precipitation volume. Original standardized peak discharge distribution (OPDD) is defined as the log of peak discharge regressed on log runoff volume. The OPDD and its variants were developed and tested by Rogers (1980, 1982) for basins in the U.S.A. The distributions have been tested for eight drainage basins in Greece (Mimikou, 1983). Singh and Aminian, (1986) proposed peak discharge distribution per unit area. The inherent assumption in OPDD is that time to peak (Tp) and ratio of time to peak (Ti,) and base period (Tb) are constant. In the present study, peak discharge, time and volume relationship (PDTVR) defined as relation between peak discharge (Qp), time to peak (Tp) and runoff volume (V) in logarithm space has also been investigated in addition to above mentioned distribution. Regression analysis in log space shows strong correlation between time to peak (Tp) and base period (Tb) and weak correlation between Qp & Tp and between V & Tp. Ratio Tb/Tp is not a fixed value 2.67 as assumed by Mockus. For linear basin, it is nearly 2.67 but for nonlinear basins, it is different and not necessarily constant. For testing the applicability of OPDD and its variants to other regions, various peak discharge distributions are developed and analyzed for six drainage basins ranging in size from 114 to 904 sq. km in India. From the analysis of 53 flood hydrographs, it is shown that only original peak discharge distribution (OPDD) is sufficient for identification of degree of nonlinearity and prediction of peak discharge. Out of six basins analyzed in the present study only one basin can be assumed to be linear (3fsub-zone of Godavari basin). Hydrologic design should be based on identification of the degree of basin hydrologic nonlinearity and selection of appropriate method Jr flood estimation. Use of linear method to nonlinear basins (such as Gola, Umar, Teriya etc) can result in serious design errors by over estimate or under estimate of design flood. The variation in the peak M Identification of Linearity and Nonlinearity of Drainage Basins discharge distribution's intercept b is significantly explained by the logarithm of any of the two basin morphological indices AS/L and A/L with A the drainage area in sq. km, L the length of main river in km and S the slope of river bed in % for the basins excluding Gola basin. Peak discharge distribution provides a more reliable method for estimation of flood in nonlinear drainage basins where application of unit hydrograph theory is not valid. Peak discharge, time and volume relationship (PDTVR) may be more useful in prediction peak discharge in highly nonlinear basins. Peak discharge distribution per unit area can be utilized for ungaged catchments in a variety of hydrologic analyses such as estimation of peak discharge in combination with SCS-CN method, estimation of flooding potential; identification of drainage basin similarity, estimation of sediment yields and derivation of unit hydrograph as illustrated in this study. The application of peak discharge distribution per unit area in combination with SCS-CN method is successfully validated for estimation of flood in 3f sub-zone of lower Godavari basin in India. This study does not confirm the finding of Singh and Aminian (1986) that basin area alone can be used to explain variance of intercept b. Basins with similar area but in different regions such as Himalayan region and central Indian region will produce significantly different magnitude of peak discharge per unit runoff volume (log inverse of b) as shown in the study. Therefore it is recommended that separate relationship between b and A/L or between b and AS/L should be evolved for different geomorphological regions. Further study for several basins in India is recommended particularly for establishing usefulness of peak discharge distribution in ungaged catchments, and for analyzing the influence ofpattern of rainfall on the peak discharge distributions.