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Stochastic hydrology produces ensembles of time series that represent plausible future streamflow to simulate and test the operation of water resource systems. A premise of stochastic hydrology is that ensembles should be statistically representative of what may occur in the future. In the past, the application of this premise has involved producing ensembles that are statistically equivalent to the observed or historical streamflow sequence. This requires a number of metrics or statistics that can be used to test statistical similarity. However, with climate change, the past may no longer be representative of the future. Ensembles to test future systems operations should recognize non‐stationarity and include time series representing expected changes. This poses challenges for their testing and validation. In this paper, we suggest an evidence‐based analysis in which streamflow ensembles, whether statistically similar to and representative of the past or a changing future, should be characterized and assessed using an extensive set of statistical metrics. We have assembled a broad set of metrics and applied them to annual streamflow in the Colorado River at Lees Ferry to illustrate the approach. We have also developed a tree‐based classification approach to categorize both ensembles and metrics. This approach provides a way to visualize and interpret differences between streamflow ensembles. The metrics presented, along with the classification, provide an analytical framework for characterizing and assessing the suitability of future streamflow ensembles, recognizing the presence of non‐stationarity. This contributes to better planning in large river basins, such as the Colorado, facing water supply shortages. Plain Language Summary: Long‐range water supply planning in many river basins requires an assessment of ensembles of plausible future streamflow time series used to simulate and test the operation of water resource systems. With climate change, and growing recognition that hydrologic processes are changing over time, the past may no longer be representative of the future. This poses challenges when using statistical metrics to test future streamflow ensembles. In this paper, we suggest an evidence‐based approach in which streamflow ensembles, whether statistically similar to and representative of the past or a changing future, should be characterized using an extensive set of statistical metrics. We have assembled a broad set of metrics and applied them to annual streamflow in the Colorado River at Lees Ferry to illustrate the approach. We have also developed an approach to categorize both ensembles and metrics. The metrics presented and the classification provide an analytical framework for characterizing and assessing the suitability of future streamflow ensembles for water resources system planning. The metrics and classification developed advance and contribute to better planning in large river basins facing water supply shortages. Key Points: Many ensembles representing plausible future streamflow are available for the Colorado River BasinMetrics are presented to provide an evidence‐based framework for evaluating these streamflow ensemblesA classification approach was developed to group similar ensembles and assess their suitability for planning in different future scenarios [ABSTRACT FROM AUTHOR]

In this Reply, we address the concerns of Knoben and Clark (2023, https://doi.org/10.1029/2022WR034294) or KC23 that "the assumptions needed to effectively use difference‐based variance estimation methods are not always met by hourly streamflow records." There should be little doubt that the assumptions of our difference‐based estimator will sometimes be violated in hourly streamflow records but the results from de Oliveira and Vrugt (2022, https://doi.org/10.1029/2022wr032263) and confirmed by the findings in our Reply show that such violations are sporadic enough not to affect much the error variance estimates. Snowmelt as pointed out by KC23 (https://doi.org/10.1029/2022WR034294) may not have received sufficient attention in our paper, yet their 365‐day record is simply not long enough to demonstrate bias of our discharge error variance estimates (and their dependence on flow level). This would require analysis of a much longer, multi‐year, streamflow record of a snowmelt‐driven watershed. The snowmelt catchment analyzed in dOV22 (https://doi.org/10.1029/2022wr032263) did not demonstrate bias in the discharge error variance estimates. We also provide additional clarification on the interpretation of the variance estimates obtained with the nonparametric estimator, and discuss the main issues in the test case presented in Knoben and Clark (2023, https://doi.org/10.1029/2022WR034294)). Key Points: We address the concerns of Knoben and Clark (2023) on the use of the nonparametric estimator with hourly discharge dataWe provide further clarification on the interpretation of the variance estimates obtained with the nonparametric estimator [ABSTRACT FROM AUTHOR]

Stochastic methods have been typically used for the design and operations of hydraulic infrastructure. They allow decision makers to evaluate existing or new infrastructure under different possible scenarios, giving them the flexibility and tools needed in decision making. In this paper, we present a novel stochastic streamflow simulation approach able to replicate both temporal and spatial dependencies from the original data in a multi‐site basin context. The proposed model is a multi‐site extension of the modified Fractional Gaussian Noise (mFGN) model which is well‐known to be efficient to maintain periodic correlation for several time lags, but presents shortcomings in preserving the spatial correlation. Our method, called Weighted‐mFGN (WmFGN), incorporates spatial dependency into streamflows simulated with mFGN by relying on the Cholesky decomposition of the spatial correlation matrix of the historical streamflow records. As the order in which the decomposition steps are performed (temporal then spatial, or vice‐versa) affects the performance in terms of preserving the temporal and spatial correlation, our method searches for an optimal convex combination of the resulting correlation matrices. The result is a Pareto‐curve that indicates the optimal weights of the convex combination depending on the importance given by the user to spatial and temporal correlations. The model is applied to a number of river basins in Chile, where the results show that the WmFGN approach maintains the qualities of the single‐site mFGN, while significantly improving spatial correlation. Key Points: Weighted modified Fractional Gaussian Noise model improves spatial correlations without significantly sacrificing temporal correlationThe method searches for an optimal convex combination of the spatial and temporal correlation matrices according on the user's priorityOur results in several Chilean basins demonstrate that Weighted‐modified Fractional Gaussian Noise (WmFGN) represents a significant improvement over the mFGN in preserving correlations [ABSTRACT FROM AUTHOR]

Optimization of spatially consistent parameter fields is believed to increase the robustness of parameter estimation and its transferability to ungauged basins. The current paper extends previous multi‐objective and transferability studies by exploring the value of both multi‐basin and spatial pattern calibration of distributed hydrologic models as compared to single‐basin and single‐objective model calibrations, with respect to tradeoffs, performance and transferability. The mesoscale Hydrological Model (mHM) is used across six large central European basins. Model simulations are evaluated against streamflow observations at the basin outlets and remotely sensed evapotranspiration patterns. Several model validation experiments are performed through combinations of single‐ (temporal evaluation through discharge) and multi‐objective (temporal and spatial evaluation through discharge and spatial evapotranspiration patterns) calibrations with holdout experiments saving alternating basins for model evaluation. The study shows that there are very minimal tradeoffs between spatial and temporal performance objectives and that a joint calibration of multiple basins using multiple objective functions provides the most robust estimations of parameter fields that perform better when transferred to ungauged basins. The study indicates that particularly the multi‐basin calibration approach is key for robust parametrizations, and that the addition of an objective function tailored for matching spatial patterns of ET fields alters the spatial parameter fields while significantly improving the spatial pattern performance without any tradeoffs with discharge performance. In light of model equifinality, the minimal tradeoff between spatial and temporal performance shows that adding spatial pattern evaluation to the traditional temporal evaluation of hydrological models can assist in identifying optimal parameter sets. Plain Language Summary: Hydrological models typically require local observations of river flow to calibrate the models and test their predictive capability. This limits the possibility for predictions in ungauged basins. This study used holdout tests to investigate the robustness of hydrological predictions for ungauged basins. Particularly we investigate how adding more basins and observed spatial patterns of evapotranspiration in the calibration of these models impact this robustness and transferability of model parameters to basins not used for calibration. Results show that transferability and spatial consistency of parameters increase when adding more basins and spatial pattern observations. Key Points: Clear improvements in simulated spatial patterns can be achieved with very limited tradeoff with discharge performanceMulti‐basin and spatial pattern‐based calibration improve parameter realism and transferability to ungauged basins [ABSTRACT FROM AUTHOR]

River networks are not steady blue lines drawn in a map, since they continuously change their shape and extent in response to climatic drivers. Therefore, the flowing length of rivers (L) and the corresponding catchment‐scale streamflow (Qsur) co‐evolve dynamically. This paper analyzes the relationship between the wet channel length and the streamflow of a river basin, formulating a general analytical model that includes the case of temporarily dry outlets. In particular, the framework relaxes the common assumption that when the discharge at the outlet tends to zero the upstream flowing length approaches zero. Different analytical expressions for the L(Qsur) law are derived for the cases of (a) a perennial outlet; (b) a non‐perennial outlet that dries out only when the whole network is dry; and (c) a temporarily dry outlet, that experiences surface flow for less time than other network nodes. In all cases, the shape of the L(Qsur) relationship is controlled by the distribution of the specific subsurface discharge capacity along the network. For temporarily dry outlets, however, the relation between L and Qsur might depend on an unknown shifting factor. Three real‐world examples are presented to demonstrate the flexibility and the robustness of the theory. Our results indicate that the whole shape of the L(Qsur) relation might not be empirically observable if a significant fraction of the network is perennial or some reaches in the network experience surface flow for longer than the discharge gauging station. The study provides a basis for integrating empirical L(Qsur) data gathered in diverse sites. Key Points: Active network length (L) versus catchment discharge (Qsur) relations are extended to temporarily dry outletsAll the L(Qsur) relations represent translations/truncations of the spatial cumulative distribution of the specific subsurface capacityThe L(Qsur) law is not fully visible if the outlet is less persistent than other network nodes (as in a spring‐fed stream drying upward) [ABSTRACT FROM AUTHOR]