Temporal Hierarchical Reconciliation for Consistent Water Resources Forecasting Across Multiple Timescales: An Application to Precipitation Forecasting

Obtaining consistent forecasts at different timescales is important for reliable decision-making. This study introduces and evaluates the benefits of utilizing temporal hierarchical reconciliation methods for water resources forecasting, with an application to precipitation. Original (precipitation) Forecasts (ORFs) were produced using automatic Exponential Time-Series Smoothing (ETS), Artificial Neural Network (ANN), and Seasonal Auto-Regressive Integrated Moving Average (SARIMA) models at six timescales, namely, monthly, 2-monthly, quarterly, 4-monthly, bi-annual, and annual, for 84 basins extracted from the Canadian model parameter experiment. Temporal hierarchical reconciliation methods, including structural scaling-based Weighted Least Squares (WLS), series variance scaling-based WLS, and Ordinary Least Squares, along with the simple Bottom-Up (BU) method, were applied to reconcile the forecasts. In general, ETS (direct forecasting) demonstrated better performance compared to ANN and SARIMA (recursive forecasting). The results confirmed that improvements in accuracy due to reconciliation is dependent on the basin, timescale, and the ORFs' accuracy. For different forecast models, the reconciliation methods showed different levels of performance. For ETS, BU was able to improve forecast accuracy to a greater extent than the temporal hierarchical reconciliation methods, while for ANN and SARIMA, forecast accuracy was improved through all temporal hierarchical reconciliation methods but not BU. The reconciled forecasts' accuracy was affected more by the ORFs' accuracy than by the reconciliation method. Different timescales showed dissimilar sensitivity to reconciliation. The presented results are anticipated to serve as a valuable benchmark for evaluating future developments in the promising area of temporal hierarchical reconciliation for water resources forecasting.

Automated summary

This study introduces and evaluates the benefits of utilizing temporal hierarchical reconciliation methods for water resources forecasting, with an application to precipitation. The results show that improvements in accuracy due to reconciliation is dependent on various factors and different forecast models show different levels of performance with the reconciliation methods.