Bayesian networks and network science applied to water resources: streamflow analysis and forecast incorporating the non-stationarity

Abstract

The violation of the stationarity assumption in streamflow timeseries requires the development of methodologies to (1) identify the existence of changes in the series and its location, (2) incorporate this aspect in the streamflow modelling and forecasting framework and (3) analyze the full extension regarding its impact. Naturalized streamflow of the Brazilian electricity sector was used as a case study to analyze these aspects. The problem of detecting changes in the statistical properties of streamflow series is currently an open question with concerns regarding the reliability of the results of the different methodologies available. Three methodologies were used to detect changes in the mean value and the change point reliability was assessed evaluating the convergence among them. This approach showed great potential since the different methodologies presented a high convergence rate for the correct change point and a lower convergence rate for the incorrect points. The changes detected coincided to phase shift of low frequency oscillations of the Atlantic and Pacific oceans and its impact in the South Atlantic Convergence Zone. A first attempt to incorporate this non-stationarity was made using Gaussian Bayesian Networks (GBN). Discrete variables representing the different phases of low frequency oscillations were included in the networks, allowing different network parameters according to the phases. The focus on Bayesian Networks relies in recent articles that indicated Bayesian Networks as a promising tool in hydroclimate studies, simultaneously providing good modelling results and allowing causal discovery through the analysis of the network structure. The results demonstrated a great potential of the GBN to forecast streamflow with lead times from one to eight months. The results also unveiled a good streamflow forecasting potential via Bayesian Inference based on Likelihood Weighting simulations. The use of the phases resulted in the performance improvement for some stations, however, it did not improve the results of the stations that presented changes in the timeseries, suggesting significant changes between the network structures of each homogeneous periods. Network structures were obtained through different methodologies for each homogeneous period to analyze this aspect. The results confirmed the initial hypothesis, showing significant differences between the network structures of each homogeneous periods, with alterations in the relationship between the variables and in its autocorrelation function. Therefore, the use of the same set of parents for the complete series may not comprise the extension of the changes observed. Finally, an analysis was made to evaluate the non-stationarity impact in the relationship between the streamflow series, this aspect is important in the generation of spatially coherent streamflow forecasts. A framework was proposed to obtain weighted complex networks between the stations, using network science theory to detect and analyze changes in the clustering results. The results showed significant changes in the clustering results across time, demonstrating the necessity of a more complex approach to correct correlate the streamflow forecasts. The use of a correlation matrix for each homogeneous phase could be a viable solution since similarities were found between the changes in the mean value and in the relationship between the stations.