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

Abstract

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.

Improved National-Scale Flood Prediction for Gauged and Ungauged Basins using a Spatio-temporal Hierarchical Model

“…However, fitting the STHM purely for at-site would limit its ability to predict in ungauged predictions. In a traditional hierarchical modeling approach, this would be considered as an "unpooled regression" model (Das Bhowmik et al, 2020;Devineni et al, 2013) as such a model will result with no regional modeling terms. It can be easily understood that post-processing a model's flow would naturally result in improved model performance as regression is expected to reduce the model bias.…”

“…However, most of these two-step approaches have focused primarily on design flood as opposed to predicting daily flood flows, which are critically important for issuing early warnings. Further, these two-step regression modeling can be effectively integrated into a single step using a hierarchical model (Das Bhowmik et al, 2020;Devineni et al, 2013). To our knowledge, limited/no application of hierarchical model has been performed for estimating daily flows at ungauged locations over the CONUS.…”

An overview of approaches for reducing uncertainties in hydrological forecasting: progress, and challenges

“…This can be possible with the help of an understanding of measurement errors and pre-processing techniques employed. The estimation of measurement errors within the modeling framework will help to reduce these uncertainties (Das Bhowmik et al, 2020). The accuracy level of the measurement error does matter in in uencing the outcomes according to the employed modeling framework and type of measurement inputs.…”

“…A degradation in accuracy and availability can occur in modern sensory systems such as remote observation or complex IoT sensor networks and the usage of sensors. In such cases, any prior knowledge about measurement accuracy can be integrated into a qualitative /quantitative estimation of errors (Das Bhowmik et al, 2020). This knowledge of measurement error can help reduce measurement uncertainty, thereby, increasing the forecasts' reliability.…”

Quantifying the contribution of uncertainty sources of artificial neural network models using ANOVA for reservoir power generation

“…This observed data was considered as the exact value and directly used in this paper. However, some researchers reported that the measurement errors of observation exist due to accidental factors (Bhowmik et al 2020). Therefore, the uncertainty from measurement errors in the reservoir operation may need to be considered in future studies.…”