An analytical procedure for multi-site, multi-season streamflow generation using maximum entropy bootstrapping

Abstract

Stochastic time series models are very useful in many environmental domains. In this paper, an analytical procedure for multi-site, multi-season streamflow generation using maximum entropy bootstrap stochastic model (M3EB) is developed that can implicitly preserve both the spatial and temporal dependence structure, in addition to the other statistical characteristics present in the historical time series. The proposed model is computationally less demanding and simple in terms of modeling complexity. The maximum entropy bootstrap (MEB) generates random samples from the empirical cumulative distribution function (ECDF) and rearranges the random series based on the rank ordering of the historical time series. The modeling structure of MEB implicitly satisfies the ergodic theorem (preservation of summary statistics) and guarantees the reproduction of the time dependent structure of an underlying process. The orthogonal transformation is used with M3EB to capture the spatial dependence present in the multi-site collinear data. The performance of M3EB is verified by comparing the statistical characteristics between the observed and synthetically generated streamflows. Three case studies from Colorado River Basin, USA; Red River Basin, USA and Canada; and Cauvery River Basin, India; are used to demonstrate the advantages of M3EB. The statistical measures adopted for evaluation of M3EB performance include monthly statistics (mean, standard deviation and skewness), temporal and spatial correlation, smoothing (flows other than present in historical data) and extrapolation (flows outside the range of historical data). The M3EB model shows (i) a high level of accuracy in preserving the statistics; and (ii) a high computational efficiency. Since M3EB can be used for multiple variable problems, the model can be easily extended to other environmental or hydroclimatic time series data.