Modified approaches to determine discharges indices using magnitude-frequency analysis

Abstract

Discharge indices such as effective discharge, fraction-load discharge, and functional-equivalent discharge are used to quantify the effectiveness of flow distribution in sediment transport through a river network. Effective discharge is a well-defined discharge index that is used to quantify the flow which carries the maximum amount of sediments over a long time. The fraction-load discharge is that discharge above which a fraction of the longterm sediment load is transported. The functional-equivalent discharge is that discharge that will reproduce the magnitude of the sediment load generated by the full hydrologic distribution assuming it occurred at all times. Magnitude-Frequency Analysis is generally used as a mathematical framework to determine these indices. In MFA, these indices are computed based on the transport effectiveness function which is constructed by using the product of assumed probability distribution (e.g., lognormal or Gamma) for discharge, and the power-law relationship between discharge and sediment transport rate. Mathematically, the effective discharge represents a magnitude of discharge for which the transport effectiveness function attains a maximum value. The other two discharge indices i.e., fraction-load discharge and functional-equivalent discharge are determined based on mean sediment load which is calculated by integrating the transport effectiveness function over the complete range of flows. Conventionally, the transport effectiveness function is constructed by assuming the discharges to be lognormally or Gamma distributed. However, the assumption of discharge distribution is location-specific, and hence lognormally or Gamma distributed discharges are not valid for all catchments. Thus, it is necessary to assess the uncertainty in the estimates of these indices when the discharge data do not follow either the lognormal or Gamma distribution. In this study, modified approaches are proposed to determine discharge indices for the general distribution of discharge datasets. The proposed approach utilizes a one-parameter BoxCox transformation to transform the discharge data. Analytical expressions for effective discharge and mean sediment load under the proposed framework are derived. The robustness of the proposed approach is established through a Monte Carlo simulation experiment by generating discharge data from various probability distributions such as lognormal, Gamma, and log Pearson type III distributions. Furthermore, the proposed approaches are applied to estimate discharge indices for catchments in South Indian Rivers (Mahanadi, Godavari, Krishna, and Cauvery). The influence of the hysteresis effect due to seasonal variation and stage tendency in the sediment rating curve is also studied. It was observed that grouping the rating-curve data according to seasonal variation and stage tendency resulted in reliable sediment rating relations. Subsequently, the estimates of discharge indices based on the proposed approach are computed considering various sediment rating relationships fitted for total, seasonal, stage, and season-stage based datasets. Finally, the dependence of discharge indices (and their return period) on various catchment descriptors such as average slope, basin relief, drainage area, maximum elevation, and mean elevation is explored.