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.

To aid California's water sector to better manage future climate extremes, we present a method for creating a regional ensemble of plausible daily future climate and streamflow scenarios that represent natural climate variability captured in a network of tree-ring chronologies, and then embed anthropogenic climate change trends within those scenarios. We use 600 years of paleo-reconstructed weather regimes to force a stochastic weather generator, which we develop for five subbasins in the San Joaquin River in the Central Valley region of California. To assess the compound effects of climate change, we create temperature series that reflect scenarios of warming and precipitation series that are scaled to reflect thermodynamically driven shifts in the daily precipitation distribution. We then use these weather scenarios to force hydrologic models for each of the San Joaquin subbasins. The paleo-forced streamflow scenarios highlight periods in the region's past that produce flood and drought extremes that surpass those in the modern record and exhibit large non-stationarity through the reconstruction. Variance decomposition is employed to characterize the contribution of natural variability and climate change to variability in decision-relevant metrics related to floods and drought. Our results show that a large portion of variability in individual subbasin and spatially compounding extreme events can be attributed to natural variability, but that anthropogenic climate changes become more influential at longer planning horizons. The joint importance of climate change and natural variability in shaping extreme floods and droughts is critical to resilient water systems planning and management in the Central Valley region.

Planning under deep uncertainty, when probabilistic characterizations of the future are unknown, is a major challenge in water resources management. Many planning frameworks advocate for “scenario-neutral” analyses in which alternative policies are evaluated over plausible future scenarios with no assessment of their likelihoods. Instead, these frameworks use sensitivity analysis to discover which uncertain factors have the greatest influence on performance. This knowledge can be used to design monitoring programs and adaptive policies that respond to changes in the critical uncertainties. However, scenario-neutral analyses make implicit assumptions about the range and independence of the uncertain factors that may not be consistent with the coupled human-hydrologic processes influencing the system. These assumptions could influence which factors are found to be most important and which policies most robust. Consequently, the assumptions of uniformity and independence could have decision-relevant implications. This study illustrates these implications using a multi-stakeholder planning problem within the Colorado River Basin, where hundreds of rights-holders vie for the river’s limited water under the law of prior appropriations. Variance-based sensitivity analyses are performed to assess users’ vulnerabilities to changing hydrologic conditions using four experimental designs: 1) scenario-neutral samples of hydrologic factors, centered on recent historical conditions, 2) scenarios informed by climate projections, 3) scenarios informed by paleo-hydrologic reconstructions, and 4) scenario-neutral samples of hydrologic factors spanning all previous experimental designs. Differences in sensitivities and user robustness rankings across the experiments illustrate the challenges of inferring the most consequential drivers of vulnerabilities to design effective monitoring programs and robust management policies.

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.

Climate vulnerability assessments rely on water infrastructure system models that imperfectly predict performance metrics under ensembles of future scenarios. There is a benefit to reduced complexity system representations to support these assessments, especially when large ensembles are used to better characterize future uncertainties. An important question is whether the total uncertainty in the output metrics is primarily attributable to the climate ensemble or to the systems model itself. Here we develop a method to address this question by combining time series error models of performance metrics with time-varying Sobol sensitivity analysis. The method is applied to a reduced complexity multi-reservoir systems model of the Sacramento-San Joaquin River Basin in California to demonstrate the decomposition of flood risk and water supply uncertainties under an ensemble of climate change scenarios. The results show that the contribution of systems model error to total uncertainty is small (~5-15%) relative to climate based uncertainties. This indicates that the reduced complexity systems model is sufficiently accurate for use in the context of the vulnerability assessment. We also observe that climate uncertainty is dominated by the choice of GCM and its interactive effects with the representative concentration pathway (RCP), rather than the RCP alone. This observation has implications for how climate vulnerabilities should be interpreted.