Understanding the Impact of Observation Data Uncertainty on Probabilistic Streamflow Forecasts Using a Dynamic Hierarchical Model

Earlier researches have proposed algorithms to quantify the measurement uncertainty in rating curves and found that the magnitude of the uncertainty can be significant enough to impact hydrologic modeling. Therefore, they suggested frameworks to include measurement uncertainty in the rating curve to make it robust. Despite their efforts, a robust rating curve is often ignored in traditional practices, considering the investment of time and money as well as the resulting benefit from it. In the current research, we are interested in understanding the role of the measurement error variance in real-time streamflow forecasting. Our objectives are (i) to employ a state-of-the-art statistical forecasting model that can handle measurement uncertainty in daily streamflow and (ii) to understand the trade-off in forecasting performance when substantial knowledge regarding the measurement uncertainty is provided to the modeler. We apply the Bayesian dynamic hierarchical model (BDHM) on four gauging sites in the United States. Results show that the BDHM performs better than the daily climatology and local linear regression model. Also, the forecast variance changes proportionally with the change in the error variance as an input in the observation equation. Following this, we design a simulation-based study, which assigns the measurement error in the reported streamflow to obtain multiple realizations of the true streamflow. The inclusion of substantial knowledge about the true error improves the BDHM's performance by lowering the CRPS (continuous rank probability score) values. However, the inclusion increases the forecast variance to bring the true streamflow within the sampling variability of the forecasted streamflow. Overall, an improved trade-off between the success rate of forecasts and the forecast variance can be achieved by including the measurement error in the BDHM for rivers that witness less dispersed streamflow data. Plain Language Summary Rating curve uncertainty is one of the major sources of measurement uncertainty in reported streamflow. It occurs when a precalibrated stage-discharge relationship curve is used to indirectly measure the streamflow volume based on river stage measurement. Considering the cost and time involved to include the uncertainty in reported streamflow, rating curve uncertainty is often ignored in traditional streamflow modeling practices. The current study adopts a state-of-the-art statistical model that can include rating curve uncertainty while issuing daily streamflow forecasts 1 to 3 days in advance. The study found that a proper knowledge of rating curve uncertainty at a gauge site significantly improves the forecasting of true streamflow. Key Points Bayesian dynamic hierarchical model (BDHM) can include the measurement uncertainty that has a substantial impact on real-time forecasting BDHM efficiently predicts the reported streamflow 1 to 3 days in advance while compared with the daily climatology and a semiparametric forecasting model Knowledge of the measurement uncertainty improves the overall performance of BDHM in predicting the true streamflows