We developed a space-time model to project seasonal streamflow extremes on a river network for at several lead times. In this, the extremes – 3-day maximum streamflow - at each gauge location on the network are assumed to be realized from a Generalized Extreme Value (GEV) distribution with temporal non-stationary parameters. The parameters are modeled as a linear function of suitable covariates. In addition, the spatial dependence of the extremes across the network is modeled via a Gaussian copula. The parameters of the non-stationary GEV at each location are estimated via maximum likelihood, whereas those of the Copula are estimated via maximum pseudo-likelihood. Best subset of covariates are selected using AIC. Ensembles of streamflow in time, which are based on the varying temporal covariates and from the Copula, are generated, consequently, capturing the spatial and temporal variability and the attendant uncertainty. We applied this framework to project spring (May-Jun) season 3-day maximum flow at seven gauges in the Upper Colorado River Basin (UCRB) network, at 0 ~ 3 months lead time. In this basin, almost all of the annual flow and extremes that cause severe flooding, arrives during the spring season as a result of melting of snow accumulated during the preceding winter season. As potential covariates, we used indices of large scale climate teleconnection – ENSO, AMO, and PDO, regional mean snow water equivalent and temperature from the preceding winter season. The skill of the probabilistic projections of flow extremes is assessed by rank histograms and skill scores such as CRPSS and ES for marginal and spatial performance. We also evaluate the utility of Gaussian Copula by computing spatial threshold exceedance probabilities compared to a model without the Copula – i.e. independent model at each gauge. The validation indicates that the model is able to capture the space-time variability of flow extremes very well, and the skills increase with decreasing lead time. Also the use of climate variables enhances skill relative to using just the snow information. The median projections and their uncertainties are highly consistent with the observations with a Gaussian copula than without it, indicating the role of spatial dependence. This framework will be of use in long leading planning of flood risk mitigation strategies.

India receives more than 80% of annual rainfall during the summer monsoon season of June – September. Extreme rainfall during summer monsoon season causes severe floods in many parts of India, annually. The floods in Kerala in 2019; Chennai during 2015 and Uttarakhand in 2013 are some of the major floods in recent years. With high population density and weaker infrastructure, even moderate precipitation extremes result in substantial loss to life and property. Thus, understanding and modeling the return levels of extreme precipitation in space and time is crucial for disaster mitigation efforts. To this end, we develop a Bayesian hierarchical model to capture the space-time variability of –summer season 3-day maximum precipitation over India. In this framework, the data layer, the precipitation extreme – i.e., seasonal maximum precipitation, at each station in each year is modeled using a generalized extreme value (GEV) distribution with temporally varying parameters, which are decomposed as linear functions of covariates. The coefficients of the covariates, in the process layer, are spatially modeled with a Gaussian multivariate process which enables capturing the spatial structure of the rainfall extremes and covariates. Suitable priors are used for the spatial model hyperparameters to complete the Bayesian formulation. With the posterior distribution of spatial fields of the GEV parameters for each year, posterior distribution of the nonstationary space–time return levels of the precipitation extremes are obtained. Climate diagnostics will be performed on the 3-day maximum precipitation field to obtain robust covariates. The model is demonstrated by application to extreme summer precipitation at 357 stations from this region. Preliminary model validation indicates that our model captures historical variability at the stations very well. Maps of return levels provide spatial and temporal variability of the risk of extreme precipitation over India that will be of great help in management and mitigation of hazards on natural resources and infrastructure.

The Southwest U.S. comprising of the four states-Arizona, New Mexico, Colorado, and Utah-is the hottest and driest region of the United States. Most of the precipitation arrives during the winter season, but the summer precipitation makes a significant contribution to the reliability of water resources and the health of ecology. However, summer precipitation and its extremes, over this region exhibit high degree of spatial and temporal variability. In this study we developed a novel spatial Bayesian hierarchical model to capture the space-time variability of –summer season 3-day maximum precipitation over the southwest U.S. In modeling framework, the data layer the extremes at each station are assumed to be distributed as Generalized Extreme Value (GEV) distribution with non-stationary parameters. In addition, the extremes across space is assumed to be related via a Gaussian Copula. In the process layer, the parameters are modeled as a linear function of large scale climate variables and regional mean precipitation covariates. This is akin to a Generalized Linear Model (GLM). The parameters of the covariates at each station are spatially modeled using spatial Gaussian processes to capture the spatial dependency and enable generating the spatial field of the hydroclimate extremes. The likelihood estimates of the GLM at each station form the initial priors. The posterior distribution of the model parameters and consequently the predictive posterior GEV distribution of the hydroclimate extremes at any arbitrary location, or grid and for any year are obtained. The model is demonstrated by application to extreme summer precipitation at 73 stations from this region. The model validation indicates that return levels and their associated uncertainty have a well-defined spatial structure and furthermore, they capture the historical variability very well. The posterior distribution of the GEV parameters were generated on a 1/8th degree grid, providing maps of various return levels for all the years. Maps of return levels provide information about the spatial and temporal variations of the risk of extreme precipitation in the Southwest U.S. that will be of immense help in management and planning of natural resources and infrastructure.