[1] Surrogate modeling, also called metamodeling, has evolved and been extensively used over the past decades. A wide variety of methods and tools have been introduced for surrogate modeling aiming to develop and utilize computationally more efficient surrogates of high-fidelity models mostly in optimization frameworks. This paper reviews, analyzes, and categorizes research efforts on surrogate modeling and applications with an emphasis on the research accomplished in the water resources field. The review analyzes 48 references on surrogate modeling arising from water resources and also screens out more than 100 references from the broader research community. Two broad families of surrogates namely response surface surrogates, which are statistical or empirical data-driven models emulating the high-fidelity model responses, and lower-fidelity physically based surrogates, which are simplified models of the original system, are detailed in this paper. Taxonomies on surrogate modeling frameworks, practical details, advances, challenges, and limitations are outlined. Important observations and some guidance for surrogate modeling decisions are provided along with a list of important future research directions that would benefit the common sampling and search (optimization) analyses found in water resources.

Sensitivity analysis is an essential paradigm in Earth and Environmental Systems modeling.However, the term ''sensitivity'' has a clear definition, based in partial derivatives, only when specified locally around a particular point (e.g., optimal solution) in the problem space. Accordingly, no unique definition exists for ''global sensitivity'' across the problem space, when considering one or more model responses to different factors such as model parameters or forcings. A variety of approaches have been proposed for global sensitivity analysis, based on different philosophies and theories, and each of these formally characterizes a different ''intuitive'' understanding of sensitivity. These approaches focus on different properties of the model response at a fundamental level and may therefore lead to different (even conflicting) conclusions about the underlying sensitivities. Here we revisit the theoretical basis for sensitivity analysis, summarize and critically evaluate existing approaches in the literature, and demonstrate their flaws and shortcomings through conceptual examples. We also demonstrate the difficulty involved in interpreting ''global'' interaction effects, which may undermine the value of existing interpretive approaches. With this background, we identify several important properties of response surfaces that are associated with the understanding and interpretation of sensitivities in the context of Earth and Environmental System models. Finally, we highlight the need for a new, comprehensive framework for sensitivity analysis that effectively characterizes all of the important sensitivity-related properties of model response surfaces.

Computer simulation models are continually growing in complexity with increasingly more factors to be identified. Sensitivity Analysis (SA) provides an essential means for understanding the role and importance of these factors in producing model responses. However, conventional approaches to SA suffer from (1) an ambiguous characterization of sensitivity, and (2) poor computational efficiency, particularly as the problem dimension grows. Here, we present a new and general sensitivity analysis framework (called VARS), based on an analogy to ''variogram analysis,'' that provides an intuitive and comprehensive characterization of sensitivity across the full spectrum of scales in the factor space. We prove, theoretically, that Morris (derivative-based) and Sobol (variance-based) methods and their extensions are special cases of VARS, and that their SA indices can be computed as by-products of the VARS framework. Synthetic functions that resemble actual model response surfaces are used to illustrate the concepts, and show VARS to be as much as two orders of magnitude more computationally efficient than the state-of-the-art Sobol approach. In a companion paper, we propose a practical implementation strategy, and demonstrate the effectiveness, efficiency, and reliability (robustness) of the VARS framework on real-data case studies.

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Reservoirs significantly affect flow regimes in watershed systems by changing the magnitude and timing of streamflows. Failure to represent these effects limits the performance of hydrological and land-surface models (H-LSMs) in the many highly regulated basins across the globe and limits the applicability of such models to investigate the futures of watershed systems through scenario analysis (e.g., scenarios of climate, land use, or reservoir regulation changes). An adequate representation of reservoirs and their operation in an H-LSM is therefore essential for a realistic representation of the downstream flow regime. In this paper, we present a general parametric reservoir operation model based on piecewise-linear relationships between reservoir storage, inflow, and release to approximate actual reservoir operations. For the identification of the model parameters, we propose two strategies: (a) a "generalized" parameterization that requires a relatively limited amount of data and (b) direct calibration via multi-objective optimization when more data on historical storage and release are available. We use data from 37 reservoir case studies located in several regions across the globe for developing and testing the model. We further build this reservoir operation model into the MESH (Modélisation Environmentale-Surface et Hydrologie) modeling system, which is a large-scale H-LSM. Our results across the case studies show that the proposed reservoir model with both parameter-identification strategies leads to improved simulation accuracy compared with the other widely used approaches for reservoir operation simulation. We further show the significance of enabling MESH with this reservoir model and discuss the interdependent ef-fects of the simulation accuracy of natural processes and that of reservoir operations on the overall model performance. The reservoir operation model is generic and can be integrated into any H-LSM.

Based on the theoretical framework for sensitivity analysis called “Variogram Analysis of Response Surfaces” (VARS), developed in the companion paper, we develop and implement a practical “star‐based” sampling strategy (called STAR‐VARS), for the application of VARS to real‐world problems. We also develop a bootstrap approach to provide confidence level estimates for the VARS sensitivity metrics and to evaluate the reliability of inferred factor rankings. The effectiveness, efficiency, and robustness of STAR‐VARS are demonstrated via two real‐data hydrological case studies (a 5‐parameter conceptual rainfall‐runoff model and a 45‐parameter land surface scheme hydrology model), and a comparison with the “derivative‐based” Morris and “variance‐based” Sobol approaches are provided. Our results show that STAR‐VARS provides reliable and stable assessments of “global” sensitivity across the full range of scales in the factor space, while being 1–2 orders of magnitude more efficient than the Morris or Sobol approaches.

Abstract. A number of global and regional gridded climate products based on multiple data sources are available that can potentially provide reliable estimates of precipitation for climate and hydrological studies. However, research into the consistency of these products for various regions has been limited and in many cases non-existent. This study inter-compares several gridded precipitation products over 15 terrestrial ecozones in Canada for different seasons. The spatial and temporal variability of the errors (relative to station observations) was quantified over the period of 1979 to 2012 at a 0.5° and daily spatio-temporal resolution. These datasets were assessed in their ability to represent the daily variability of precipitation amounts by four performance measures: percentage of bias, root mean square error, correlation coefficient, and standard deviation ratio. Results showed that most of the datasets were relatively skilful in central Canada. However, they tended to overestimate precipitation amounts in the west and underestimate in the north and east, with the underestimation being particularly dominant in northern Canada (above 60° N). The global product by WATCH Forcing Data ERA-Interim (WFDEI) augmented by Global Precipitation Climatology Centre (GPCC) data (WFDEI [GPCC]) performed best with respect to different metrics. The Canadian Precipitation Analysis (CaPA) product performed comparably with WFDEI [GPCC]; however, it only provides data starting in 2002. All the datasets performed best in summer, followed by autumn, spring, and winter in order of decreasing quality. Findings from this study can provide guidance to potential users regarding the performance of different precipitation products for a range of geographical regions and time periods.

Environmental models are used extensively to evaluate the effectiveness of a range of design, planning, operational, management and policy options. However, the number of options that can be evaluated manually is generally limited, making it difficult to identify the most suitable options to consider in decision-making processes. By linking environmental models with evolutionary and other metaheuristic optimization algorithms, the decision options that make best use of scarce resources, achieve the best environmental outcomes for a given budget or provide the best tradeoffs between competing objectives can be identified. This Introductory Overview presents reasons for embedding formal optimization approaches in environmental decision-making processes, details how environmental problems are formulated as optimization problems and outlines how single-and multi-objective optimization approaches find good solutions to environmental problems. Practical guidance and potential challenges are also provided.