Abstract

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.