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

Abstract

Accurate forecasts of key water resources variables (e.g., precipitation, streamflow, evaporation) across multiple timescales (e.g., daily, monthly, yearly) are integral for the successful planning, management, and operation of water resources systems (van Den Hurk et al., 2016). However, in water resources, it is often the case that different models are applied for forecasting different timescales of a particular variable (Peters-Lidard et al., 2019), without ensuring that the forecasts are consistent across timescales (e.g., that monthly forecasts aggregate to seasonal or yearly forecasts), providing decision-makers with disparate information that may lead to sub-optimal planning, management, and operation of water resources systems. Further, "Bottom-Up" (BU) forecasts, which aggregate finer scale forecasts to a coarser scale (see, e.g., E. Wang et al., 2011), miss an opportunity to exploit low-and high-frequency characteristics of the data that may prove helpful in improving forecast quality (Spiliotis et al., 2020). To overcome these significant issues, that have been mostly ignored in the water resources forecasting literature, this paper explores the use of temporal hierarchical reconciliation (Athanasopoulos et al., 2017), a development in the time-series forecasting community, for generating consistent forecasts of water resources variables across multiple timescales. Briefly, temporal hierarchical reconciliation is a statistical procedure used to ensure that forecasts produced from different models, each at a specific timescale, are consistent with the forecasts at all other timescales (see Section 2 for more details). The approach explored here applies to any variable that can be aggregated across timescales (e.g., precipitation, evaporation, streamflow volumes) and thus, should prove useful in numerous water resources applications (reservoir operation, irrigation scheduling, water supply, etc.).Since temporal hierarchical reconciliation has yet to be explored within the water resources domain, a brief explanation is given on the differences between two common reconciliation methods and two broader approaches, more commonly adopted in the hydrology and water resources domains, when working with time-series at multiple