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 hydrograph͒ as well as the probability distributions and basic long-term statistics ͑mean, variance, skewness, autocorrelation structure, and zero-lag cross correlations͒ of the measured values. Probability distributions of the annual maxima, means, and minima of the measured daily values were also well replicated.

A nonparametric stochastic method for generating daily climate-adjusted streamflows

“…This general model formulation has since been used to generate synthetic daily streamflows in a wide range of hydrologic scenarios [Kottegoda, 1980] including intermittent streams [Aksoy and Bayazit, 2000;Aksoy, 2003] and multiple sites [Szilagyi et al, 2006].…”

“…The two-parameter gamma distribution used in Aksoy [2003] was also tested but was found to provide a poor fit to the data ( Figure 2). Selection of the Weibull distribution is reasonable, given its success in similar studies [Szilagyi et al, 2006] and its use in many other hydrologic applications as an extreme value distribution with a relatively flexible shape parameter. Randomly generated increment values are then ranked in increasing order from smallest to largest increment, which occurs at the hydrograph peak.…”

Copula-based method for multisite monthly and daily streamflow simulation

“…It may help prepare for events that have not yet been observed in the past but nonetheless can be expected in the future (Szilagyi et al, 2006). Since multiple reservoirs and stream sections are often considered in a system's operation plan and more information is needed accompanying the rapidly increasing construction of reservoirs, there is a need to generate concurrent multisite stream flow series.…”

Operational Prediction of Groundwater Fluctuation in South Florida using Sequence Based Markovian Stochastic Model

“…This study hypothesized that a state sequence representation of groundwater fluctuation could be used to predict groundwater fluctuation over shallow water table areas. Several authors introduced application of Markovian stochastic models for synthetic generation of stream flow, power and wind speed (Aksoy 2004(Aksoy , 2003Szilagyi et al 2006;Zahabiyoun 2005;Shamshad et al 2005). The analogy of groundwater fluctuation patterns with stream flow pattern would be intuitive in view of the similarities of flow patterns that show increasing, decreasing or constant flow (Aksoy 2004) versus the rising, falling and constant head of groundwater levels.…”