A Multivariate Approach to Generate Synthetic Short‐To‐Medium Range Hydro‐Meteorological Forecasts Across Locations, Variables, and Lead Times

Abstract

The use of hydro-meteorological forecasts in water resources management holds great promise as a soft pathway to improve system performance. Methods for generating synthetic forecasts of hydro-meteorological variables are crucial for robust validation of forecast use, as numerical weather prediction hindcasts are only available for a relatively short period (10-40 years) that is insufficient for assessing risk related to forecast-informed decision-making during extreme events. We develop a generalized error model for synthetic forecast generation that is applicable to a range of forecasted variables used in water resources management. The approach samples from the distribution of forecast errors over the available hindcast period and adds them to long records of observed data to generate synthetic forecasts. The approach utilizes the Skew Generalized Error Distribution (SGED) to model marginal distributions of forecast errors that can exhibit heteroskedastic, auto-correlated, and non-Gaussian behavior. An empirical copula is used to capture covariance between variables, forecast lead times, and across space. We demonstrate the method for medium-range forecasts across Northern California in two case studies for (1) streamflow and (2) temperature and precipitation, which are based on hindcasts from the NOAA/NWS Hydrologic Ensemble Forecast System (HEFS) and the NCEP GEFS/R V2 climate model, respectively. The case studies highlight the flexibility of the model and its ability to emulate space-time structures in forecasts at scales critical for water resources management. The proposed method is generalizable to other locations and computationally efficient, enabling fast generation of long synthetic forecast ensembles that are appropriate for risk analysis.

Forecast Families: A New Method to Systematically Evaluate the Benefits of Improving the Skill of an Existing Forecast

“…It focuses on a single degree of freedom -error magnitude -and relates it to skill analytically. For more versatile applications, it is best to envision this method as complementary to traditional synthetic forecast generation techniques that are designed to replicate the error structure of an existing hindcast, and in particular error magnitude (e.g., Brodeur and Steinschneider, 2021). This combination would enable these traditional generators to extend the range of "what if" questions they are designed to answer..…”

“…F can be either deterministic -a single prediction for each point X t -or an ensemble -N predictions for each point. Forecasts are commonly characterised by the error ε with respect to the quantity they are trying to predict, defined ∀t as: (Lamontagne and Stedinger, 2018;Brodeur and Steinschneider, 2021):…”

“…While relating to actual forecasts only indirectly, this work shows the value of simple but well-conceived numerical experiments in exploring the skill-value relationship. Another noteworthy effort is a direct statistical generation approach using the empirical error correlation structure of multivariate forecasts with multiple lead times (Brodeur and Steinschneider, 2021). This approach generates synthetic forecasts that are statistically difficult to distinguish from an existing hindcast, but does not enable in itself to explore the relationship between skill and value.…”

Synthetic Forecast Ensembles for Evaluating Forecast Informed Reservoir Operations

“…The central section of Figure 3 shows the primary components of the synthetic forecast procedure in Brodeur and Steinschneider (2021) that operate on the forecast errors e t , k , with some minor modifications from that original study. To produce a set of independent, random deviates for each of the K forecast time series, the first three steps of the procedure are: (a) standardize the errors to remove heteroscedasticity; (b) remove auto‐ and cross‐correlation both within and between time series; and (c) fit suitable distributions to enable sampling of new random deviates.…”

“…To date, there are no synthetic forecast approaches that can (a) emulate the nuanced behavior of modern daily medium-range hydrologic ensemble forecast systems (HEFSs), while also being able to (b) generate novel forecasting sequences with different timing of events compared to the hindcast, and (c) generate synthetic forecasts for extreme events outside of the hindcast period. The work in Brodeur and Steinschneider (2021) can achieve the latter two points, but not the former (i.e., not for ensemble forecasts). This work builds upon Brodeur and Steinschneider (2021) to develop a novel multivariate procedure to generate synthetic hydrologic ensemble forecasts.…”