Advancing stochastic modeling and diagnostics of change for hydroclimatic processes and extremes

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We live in an era of unprecedented global hydroclimatic and environmental change that requires reliable tools to model and improve predictions in hydroclimatic extremes, quantify their uncertainty, and assess environmental changes under natural variability and human forcings.******The long-term goal of this research program is to advance stationary and non-stationary spatiotemporal stochastic modeling with extensions and applications into downscaling methods, infilling of missing values (MVs), and robust diagnostics of hydroclimatic change. ******The four short-term objectives of this research are to: (i) increase our understanding of the spatiotemporal structure of precipitation and temperature at multiple scales and provide novel stationary and non-stationary stochastic models; (ii) introduce novel infilling methods and advance current maxima extraction schemes from records with missing values through the use of stochastic approaches; (iii) develop novel spatiotemporal downscaling schemes for climate model projections and historical data; and, (iv) create accurate diagnostics to detect and assess the significance of observed changes and trends in hydroclimatic extremes. To fulfill the objectives, big-data analyses will be performed using thousands in situ stations, reanalysis grid products, and climate model outputs. The spatiotemporal structure of precipitation and temperature will be mathematically described by a set of parsimonious parametric spatial and temporal correlation structures. The properties of the marginal distribution at multiple scales will be explored using an extended set of entropy-derived distributions that are consistent with the nature of these processes. An advanced spatiotemporal stochastic modeling framework will be developed by extending the parent Gaussian scheme in order to include time varying marginals and incorporate important field features, including anisotropy and storm kinematics. These advances will be embodied in infilling methods for MVs, downscaling schemes, and diagnostics of hydroclimatic change by exploiting the precise representation and simulation of the spatiotemporal structure as well as the marginal distribution of precipitation and temperature.******The developed stochastic modeling tools and compiled databases will be freely available and benefit the scientific community through: (i) generating scientific knowledge as the developed methods are applicable beyond the field of hydroclimatology; (ii) improving hydrological modeling through precise stochastic modeling of complex processes such as precipitation; (iii) supporting informed decision making with robust diagnostics of hydroclimatic change and ready-to-use databases of reliable precipitation and temperature forcing data at multiple scales; and, (iv) improving the probabilistic prediction of risk and severity of extreme weather events.**