Stochastic Watershed Models (SWMs) are an important innovation in hydrologic modeling that propagate uncertainty into model predictions by adding samples of model error to deterministic simulations. A growing body of work shows that univariate SWMs effectively reduce bias in hydrologic simulations, especially at the upper and lower flow quantiles. This has important implications for short term forecasting and the estimation of design events for long term planning. However, the application of SWMs in a regional context across many sites is underexplored. Streamflow across nearby sites is highly correlated, and so too are hydrologic model errors. Further, in arid and semi-arid regions streamflow can be intermittent, but SWMs rarely model zero flows at one site, let alone correlated intermittency across sites. In this technical note, we contribute a multisite SWM that captures univariate attributes of model error (heteroscedasticity, autocorrelation, non-normality, conditional bias), as well as multisite attributes of model error (cross-correlated error magnitude and persistence). The SWM also incorporates a multisite, auto-logistic regression model to account for multisite persistence in streamflow intermittency. The model is applied and tested in a case study that spans 14 watersheds in the Sacramento, San Joaquin, and Tulare basins in California. We find that the multisite SWM is able to better reproduce regional low and high flow events and design statistics as compared to a single-site SWM applied independently to all locations.

Stochastic Watershed Models (SWMs) are emerging tools in hydrologic modeling used to propagate uncertainty into model predictions by adding samples of model error to deterministic simulations. One of the most promising uses of SWMs is uncertainty propagation for hydrologic simulations under climate change. However, a core challenge with this approach is that the predictive uncertainty inferred from hydrologic model errors in the historical record may not correctly characterize the error distribution under future climate. For example, the frequency of physical processes (e.g., snow accumulation and melt, droughts and hydrologic recessions) may change under climate change, and so too may the frequency of errors associated with those processes. In this work, we explore for the first time non-stationarity in hydrologic model errors under climate change in an idealized experimental design. We fit one hydrologic model to historical observations, and then fit a second model to the simulations of the first, treating the first model as the true hydrologic system. We then force both models with climate change impacted meteorology and investigate changes to the error distribution between the models in historical and future periods. We develop a hybrid machine learning method that maps model input and state variables to predictive errors, allowing for non-stationary error distributions based on changes in the frequency of internal state variables. We find that this procedure provides an internally consistent methodology to overcome stationarity assumptions in error modeling and offers an important path forward in developing stochastic hydrologic simulations under climate change.

Forecast informed reservoir operations holds great promise as a soft pathway to improve water resources system performance. Methods for generating synthetic forecasts of hydro-meteorological variables are crucial for robust validation of this approach, 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 operations 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 flexible 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 and 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 flood management. The proposed method is generalizable to other locations and computationally efficient, enabling fast generation of long synthetic forecast ensembles that are appropriate for water resources risk analysis.

Policy search methods provide a heuristic mapping between observations and decisions and have been widely used in reservoir control studies. However, recent studies have observed a tendency for policy search methods to overfit to the hydrologic data used in training, particularly the sequence of flood and drought events. This technical note develops an extension of bootstrap aggregation (bagging) and cross-validation techniques, inspired by the machine learning literature, to improve control policy performance on out-of-sample hydrology. We explore these methods using a case study of Folsom Reservoir, California using control policies structured as binary trees and daily streamflow resampling based on the paleo-inflow record. Results show that calibration-validation strategies for policy selection and certain ensemble aggregation methods can improve out-of-sample tradeoffs between water supply and flood risk objectives over baseline performance given fixed computational costs. These results highlight the potential to improve policy search methodologies by leveraging well-established model training strategies from machine learning.