Hybrid, Markov Chain-Based Model for Daily Streamflow Generation at Multiple Catchment Sites

Abstract

A hybrid, seasonal, Markov chain-based model is formulated for daily streamflow generation at multiple sites of a watershed. Diurnal increments of the rising limb of the main channel hydrograph were stochastically generated using fitted, seasonally varying distributions in combination with an additive noise term, the standard deviation of which depended linearly on the actual value of the generated increment. Increments of the ascension hydrograph values at the tributary sites were related by third- or second-order polynomials to the main channel ones, together with an additive noise term, the standard deviation of which depended nonlinearly on the main channel’s actual increment value. The recession flow rates of the tributaries, as well as of the main channel, were allowed to decay deterministically in a nonlinear way. The model-generated daily values retain the short-term characteristics of the original measured time series (i.e., the general shape of the hydrograph) as well as the probability distributions and basic long-term statistics (mean, variance, skewness, autocorrelation structure, and zero-lag cross correlations) of the measured values. Probability distributions of the annual maxima, means, and minima of the measured daily values were also well replicated.