Skillful forecasts of daily streamflow on river networks are crucial for flood mitigation, especially in rainfall-driven river basins. This is of acute importance on the Narmada River Basin in Central India, which is driven by the summer monsoon rainfall, and floods lead to heavy loss of life and infrastructure. Physical hydrologic models based on the land surface model – Variable Infiltration Capacity (VIC), have been developed in an experimental mode to model and forecast the hydrologic system, which includes – storage, soil moisture and runoff – by incorporating rainfall data from the India Meteorological Department (IMD). To enhance the forecast skill by model-combination, we propose a coupled physical-statistical modeling framework. In this, we couple the VIC model with a novel Bayesian Hierarchical Network Model (BHNM) for daily streamflow forecasts that uses the network topology to capture the spatial dependence. The daily streamflow at each station is modelled as Gamma distribution with time-varying parameters. The distribution parameters for each day are modeled as a linear function of covariates, which include antecedent streamflow from upstream gauges and, daily 2-day, or 3-day precipitation from the upstream contributing areas - that reflect the antecedent land conditions. The posterior distribution of the model parameters and, consequently, the predictive posterior distribution of the daily streamflow at each station and for each day are obtained. To the BHNM model, we will couple the VIC model by including the hydrologic forecasts – especially soil moisture and storage – as additional covariates. The coupled model will be demonstrated by its application to daily summer (July-August) streamflow at 4 gauges in the Narmada basin network for the period 1978 – 2014. The skill of the probabilistic forecast will be assessed using rank histograms and skill scores such as CRPS and RPS. The model skill will also be tested on five high flooding events on both the timing and magnitude. These model combinations will enable to combine the strengths of the individual models in capturing the hydrologic processes, biases and nonstationary relationships, to provide skillful daily streamflow forecasts. This will be of immense help in flood mitigation.

A novel Bayesian Hierarchical Network Model (BHNM) for ensemble forecasts of daily streamflow that uses the spatial dependence induced by the river network topology and hydrometeorological variables from the upstream contributing area between station gauges is presented. Model parameters are allowed to vary with time as functions of selected covariates for each day. Using the network structure to incorporate flow information from upstream gauges and precipitation from the immediate contributing area as covariates allows one to model the spatial correlation of flows simultaneously and parsimoniously. An application to daily monsoon period (July-August) streamflow at four gauges in the Narmada basin in central India for the period 1978 – 2014 is presented. The covariates include daily streamflow from upstream gauges or from the gauge above of the upstream gauges depending on travel times and daily, 2-day, or 3-day precipitation from the area between two stations. The model validation indicates that the model is highly skillful relative to climatology and relative to a null-model of linear regression. We applied the BHNM out of sample to two high flooding years. High skill in both the timing and magnitude of the events is demonstrated.

We developed a novel Bayesian Hierarchical Network Model (BHNM) for daily streamflow, which uses the spatial dependence induced by the river network topology, and average daily precipitation from the upstream contributing area between station gauges. In this, daily streamflow at each station is assumed to be distributed as Gamma distribution with temporal non-stationary parameters. The mean and standard deviation of the Gamma distribution for each day are modeled as a linear function of suitable covariates. The covariates include daily streamflow from upstream gauges or from the gauge above of the upstream gauges depending on the travel times, and daily, 2-day, or 3-day precipitation from the area between two stations that attempts to reflect the antecedent land conditions. Intercepts and slopes of the mean and standard deviation parameters are modeled as a Multivariate Normal distribution (MVN) to capture their dependence structure. To ensure that the covariance matrix of MVN is positive definite, it is model as an Inverse Wishart distribution. Non-informative priors for each parameter were considered. Using the network structure in incorporating flow information from upstream gauges and precipitation from the immediate contributing area as covariates, enables to capture the spatial correlation of flows simultaneously and parsimoniously. The posterior distribution of the model parameters and, consequently, the predictive posterior Gamma distribution of the daily streamflow at each station and for each day are obtained. The model is demonstrated by its application to daily summer (July-August) streamflow at 4 gauges in the Narmada basin network in central India for the period 1978 – 2014. The skill of the probabilistic forecast is carried out by rank histograms and the Continuous Ranked Probability Score (CRPS). The model validation indicates that the model is highly skillful relative to climatology and relative to a null-model of linear regression. The forecasts present an adequate spread of uncertainty and non-bias. Since flooding is of major concern in this basin, we applied the BHNM in a cross-validated mode on two high flooding years – in that, the model was fitted on other years, and forecasts were made for the dropped-out high flooding year. The skill of the model in forecasting the high flood events was very good across the network – in both the timing and magnitude of the events. The model will be of immense help to policy makers in risk-based flood mitigation. The BHNM framework is general in nature and can be applied to any river network with other covariates as appropriate.

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.

Hydroclimate extreme events, especially precipitation and streamflow, pose serious threats to life, livelihoods, and infrastructure. However, the extremes exhibit significant space-time variability and in conjunction with societal vulnerability and resiliency, resulting in varying levels of damage. Regardless, robust understanding and modeling of these extremes is crucial for effective hazard mitigation strategies. For this study, we focus on the Krishna River Basin in south India, which experiences flooding each year due to monsoon rains and impacts urban and rural communities along its network covering three States. We implement a Bayesian hierarchical model to capture the spatio-temporal variability of streamflow extremes on this river network. In this model, the extremes (3-day maximum seasonal flow) at each station are assumed to follow a Generalized Extreme Value (GEV) distribution with non-stationary parameters. The parameters are modeled as a linear function of suitable covariates. In addition, the spatial dependence of the streamflow extremes is modeled via a Gaussian copula. With suitable priors on the parameters, posterior distribution of the parameters and the predictive posterior distribution of streamflow (i.e., ensembles) at each location. Consequently, various return levels can also be obtained from these ensembles. We developed and tested the model on the monsoon seasonal 3-day max flow at 10-gauge stations for the period 1973 -2015. To find the covariates, we perform analysis to identify relationships between large-scale climate variables such as Sea Surface Temperatures, 850 mb winds, Sea Level Pressure, etc. Statistical learning methods will be employed for this analysis and as a result, obtain potential covariates that best relate to streamflow extremes in the basin. This modeling approach can be adapted to the seasonal and multidecadal projection of extremes, which will greatly help disaster mitigation planning efforts.

Hydroclimate extreme events, especially precipitation and streamflow extremes during wet seasons, pose severe threats to life, livelihoods, and infrastructure. Therefore, timely and skillful projections of attributes of seasonal streamflow extremes are imperative to plan mitigation strategies. In particular, the number of ‘events’ – i.e., exceedances of flow thresholds that result in flooding and the magnitude of such extremes during the season, will be of immense use to policymakers for early planning and implementation of flood risk mitigation and adaptation strategies. However, predicting seasonal extremes is challenging, particularly under spatial and temporal non-stationarity. To address this need, we develop a space-time model to project seasonal flow risk attributes using a Bayesian hierarchical modeling (BHM) framework in this study. In this model, the number of events exceeding a threshold during a season at a suite of gauge locations on a river network are modeled as Poisson margins. The seasonal daily maximum flows are modeled as a generalized extreme value (GEV). The rate parameters of the Poisson distribution and scale and shape parameters of the GEV are modeled as a linear function of suitable covariates. Gaussian Elliptical Copulas are applied to capture the spatial dependence. The best set of covariates is selected using the leave-one-out cross-validation information criteria (LOOIC). The modeling framework results in the posterior distribution of the risk attributes for each season and, thus, the uncertainties. We demonstrate the utility of this modeling framework to project the flood risk attributes during the summer peak monsoon season (July-August) at five gauges in the Narmada River basin of West-Central India. As potential covariates, we consider climate indices such as El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Pacific Warm Pool Region (PWPR) from the precedent season, which have shown strong teleconnections with the Indian monsoon. This spatiotemporal modeling framework helps in the planning of seasonal adaptation and preparedness measures as predictions of monsoon high flow risk occurrence become available up to 3 months before actual flood occurrence.

River basin floods due to summer monsoon (June-September) rainfall are the major causes of infrastructure damage and loss of human lives in India. Thus, skillful forecasts of daily streamflows are crucial for flood mitigation. We develop an experimental forecasting system that combines a deterministic physical model forecast in a Bayesian Hierarchical Framework to generate an ensemble daily streamflow forecast. The physical hydrologic model based on the land surface model – Variable Infiltration Capacity (VIC) - developed in an experimental mode to model and forecast hydrologic systems over India is used. Rainfall forecast from the Indian Meteorological Department (IMD) at several lead times (1-day, 2-day, 3-day, 4-day, and 5-day) is used to drive the VIC model to provide a single deterministic forecast trace. A Bayesian Hierarchical Model (BHM) framework is developed to post-process the VIC model forecast and generate skillful daily ensemble streamflow forecast. We demonstrate the BHM framework to daily summer (July-August) streamflow forecast at five stations in the Narmada River Basin in Central India for the period 2003-2014 and, provide preliminary assessment for the period 2015-2018. In this framework, the daily streamflow at each station is modeled as Gamma distribution with time varying parameters, which are modeled as a linear function of potential covariates that include VIC model deterministic streamflow forecast and observed spatially-averaged precipitation from the previous days. With suitable priors on the parameters, posterior distributions of the parameters and predictive posterior distributions of the daily streamflows – and thus ensembles –are obtained. The skill of the probabilistic forecast is assessed a suite of metrics (correlation coefficient, and BIAS), rank histograms, and skill scores such as CRPSS. The model skills are also assessed for various flow thresholds. The BHM framework provides a novel, flexible and powerful approach to combine forecasts from multiple models (including qualitative) and provide a combined skill ensemble forecast. This will be of immense help to enable effective disaster management and 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.