Hierarchical Bayesian and machine learning models for multiscale hydroclimatic analysis and prediction for Brazil

Climate varies at multiple time and space scales, leading to like variations in hydrologic fluxes. Traditional stochastic hydrologic models do not directly incorporate such climatic variations. This dissertation considers several extensions to such models.;First, an extension to the traditional linear periodic autoregressive model used for monthly streamflow simulation and forecasting is considered by introducing exogenous climate predictors leading to a periodic autoregressive exogenous (PARX) model. Three regression frameworks for the PARX model are investigated: (i) ordinary linear regression with predictors selected by the Bayesian information criterion (BIC); (ii) Support Vector Machines (SVM) and (iii) Ridge regression. The models are tested using streamflow data from several hydropower reservoirs in Brazil. The results show an improvement in the forecasts over the classical periodic auto-regressive model up to 3 month lead times for most reservoirs. The SVM and Ridge regression PARX models provide more skillful forecasts than the BIC based PARX model.;Second, the potentially high dimensional, nonlinear dynamics of the climate system is considered, with a focus on modeling the dynamics of the El Nino Southern Oscillation, which is an important feature of interannual hydroclimatic variability. A nonlinear method of dimensionality reduction, namely maximum variance unfolding (MVU), is used to obtain the main modes of variation of the thermocline structure in the tropical Pacific in order to obtain predictors for long lead El Nino forecasts. The results obtained show skillful long term forecasts are possible for leads up to 22 months, significantly improving on current forecast models for El Nino and relative to a similar forecast model that uses the principal modes of the thermocline structure obtained from principal component analysis (PCA).;Since El Nino events directly affect rainfall and streamflow patterns across Brazil, a seasonal forecast model of hydroenergy inflow that uses the NINO3 index and the main MVU modes of the tropical Pacific thermocline structure identified in the previous step as climate predictors is considered. The networked hydropower reservoirs are first grouped into four clusters according to the streamflow seasonality. In three of the four clusters, which respond to roughly 50% of the electrical energy generated in Brazil, skillful forecasts are obtained up to 20 months in advance.;A particular challenge for hydrologic modeling is that many basins are un-gaged, and their statistics must be inferred from other stations. Much work has been done in the past to understand the scaling of flood flows as a function of drainage area. Here, a hierarchical Bayesian model is developed to explore the spatial scaling of streamflow with respect to drainage area for the (i) regionalization of Gumbel distribution parameters for annual maximum series and (ii) regionalization of monthly and annual maximum streamflow series. Cross-validated results using out-of-sample data show that the proposed models are able to reproduce statistics (e.g. 100 year flood) and series (annual maximum and monthly streamflow series) of streamflow stations not utilized for parameter estimates. Eventually, models that inform regional flood probabilities using climate predictors could be developed in this framework.;Finally, a hierarchical Bayesian model for the daily rainfall occurrence is proposed in order to identify the onset, duration and end of the main rainy season in Northeast Brazil. A first order Fourier series is used to fit the seasonally varying probabilities of rain for 504 rainfall stations. At site, time varying parameters are assumed to be drawn from a common distribution (the prior distribution) of hyperparameters, which in turn are modeled as linear spatial trends (the hyperprior distribution). Results show that the hierarchical Bayesian framework provides more robust estimates than those based on classical maximum likelihood estimates. The average rainy season timings and the three different regimes of rainfall season in Northeast are correctly identified by the model. Time trends in the peak date of the rainy season are observed in southern Northeast while time trends in the maximum probability of rain are identified in northern Northeast. Annual variability of rainy season timing is shown to be highly correlated with large scale climate variables. This provides an opportunity to forecast as well as to asses temporal trends under global climate changes in the onset, duration and end of the rainy season in Northeast Brazil.