Predicting Drought Durations and Magnitudes at Weekly Time Scale: Constant Flow as a Truncation Level

Abstract

At times hydrological droughts are defined using Q90 or Q95 (90% or 95% flow being equaled or exceeded) as truncation levels regardless of their seasonal variations. Truncation at a constant level of flow compared to a variable level (i.e. mean or median level for each season) postures unique statistical problems in modeling of drought durations and magnitudes (deficit volumes). This paper develops a procedure for predicting a T-week drought duration, E(LT ) for a weekly flow sequence based on the concept of standardized hydrological index (SHI). The SHI series were modeled using the first order Markov chain model (MC-1) while being truncated at a constant flow level such as Q90 or Q95. A T-week drought magnitude (standardized) was predicted using the relationship E(MT ) = α× I×E(LT ), where α is a scaling factor to account for the difference between averaged out (week-by-week) standard deviation and the overall standard deviation of the weekly flows, I is the drought intensity whose characteristics are assumed to resemble a truncated normal distribution of weekly deficits, and E(LT ) is based on the zero order Markov chain model (MC-0) of drought lengths. This analytical approach can be construed as distribution free, since simple and first order conditional probabilities of droughts are empirically estimated from the SHI series derived from weekly flow records irrespective of their underlying probability distribution function. Predictive ability of the proposed procedure has been found to be satisfactory for E(LT ) and E(MT ) at Q90 to Q95 truncation levels.