[1] The problems of identifying the most appropriate model structure for a given problem and quantifying the uncertainty in model structure remain outstanding research challenges for the discipline of hydrology. Progress on these problems requires understanding of the nature of differences between models. This paper presents a methodology to diagnose differences in hydrological model structures: the Framework for Understanding Structural Errors (FUSE). FUSE was used to construct 79 unique model structures by combining components of 4 existing hydrological models. These new models were used to simulate streamflow in two of the basins used in the Model Parameter Estimation Experiment (MOPEX): the Guadalupe River (Texas) and the French Broad River (North Carolina). Results show that the new models produced simulations of streamflow that were at least as good as the simulations produced by the models that participated in the MOPEX experiment. Our initial application of the FUSE method for the Guadalupe River exposed relationships between model structure and model performance, suggesting that the choice of model structure is just as important as the choice of model parameters. However, further work is needed to evaluate model simulations using multiple criteria to diagnose the relative importance of model structural differences in various climate regimes and to assess the amount of independent information in each of the models. This work will be crucial to both identifying the most appropriate model structure for a given problem and quantifying the uncertainty in model structure. To facilitate research on these problems, the FORTRAN-90 source code for FUSE is available upon request from the lead author.

No abstract

This work advances a unified approach to process-based hydrologic modeling to enable controlled and systematic evaluation of multiple model representations (hypotheses) of hydrologic processes and scaling behavior. Our approach, which we term the Structure for Unifying Multiple Modeling Alternatives (SUMMA), formulates a general set of conservation equations, providing the flexibility to experiment with different spatial representations, different flux parameterizations, different model parameter values, and different time stepping schemes. In this paper, we introduce the general approach used in SUMMA, detailing the spatial organization and model simplifications, and how different representations of multiple physical processes can be combined within a single modeling framework. We discuss how SUMMA can be used to systematically pursue the method of multiple working hypotheses in hydrology. In particular, we discuss how SUMMA can help tackle major hydrologic modeling challenges, including defining the appropriate complexity of a model, selecting among competing flux parameterizations, representing spatial variability across a hierarchy of scales, identifying potential improvements in computational efficiency and numerical accuracy as part of the numerical solver, and improving understanding of the various sources of model uncertainty.

[1] Monthly temperature and precipitation data from 41 global climate models (GCMs) of the Coupled Model Intercomparison Project Phase 5 (CMIP5) were compared to observations for the 20 th century, with a focus on the United States Pacific Northwest (PNW) and surrounding region. A suite of statistics, or metrics, was calculated, that included correlation and variance of mean seasonal spatial patterns, amplitude of seasonal cycle, diurnal temperature range, annual-to decadal-scale variance, long-term persistence, and regional teleconnections to El Niño Southern Oscillation (ENSO). Performance, or credibility, was assessed based on the GCMs' abilities to reproduce the observed metrics. GCMs were ranked in their credibility using two methods. The first simply treated all metrics equally. The second method considered two properties of the metrics: (1) redundancy of information (dependence) among metrics, and (2) confidence in the reliability of an individual metric for accurately ranking models. Confidence was related to how robust the estimate of the metric was to ensemble size, given that for most of the models only a small number of ensemble members (i.e., realizations of the 20 th century) were available. A cursory comparison with 24 CMIP3 models revealed few differences between the two generations of models with respect to the statistics analyzed.

Abstract:The purpose of this paper is to identify simple connections between observations of hydrological processes at the hillslope scale and observations of the response of watersheds following rainfall, with a view to building a parsimonious model of catchment processes. The focus is on the well-studied Panola Mountain Research Watershed (PMRW), Georgia, USA. Recession analysis of discharge Q shows that while the relationship between dQ/dt and Q is approximately consistent with a linear reservoir for the hillslope, there is a deviation from linearity that becomes progressively larger with increasing spatial scale. To account for these scale differences conceptual models of streamflow recession are defined at both the hillslope scale and the watershed scale, and an assessment made as to whether models at the hillslope scale can be aggregated to be consistent with models at the watershed scale.Results from this study show that a model with parallel linear reservoirs provides the most plausible explanation (of those tested) for both the linear hillslope response to rainfall and non-linear recession behaviour observed at the watershed outlet. In this model each linear reservoir is associated with a landscape type. The parallel reservoir model is consistent with both geochemical analyses of hydrological flow paths and water balance estimates of bedrock recharge. Overall, this study demonstrates that standard approaches of using recession analysis to identify the functional form of storage-discharge relationships identify model structures that are inconsistent with field evidence, and that recession analysis at multiple spatial scales can provide useful insights into catchment behaviour.

[1] The method of recession analysis proposed by Brutsaert and Nieber (1977) remains one of the few analytical tools for estimating aquifer hydraulic parameters at the field scale and beyond. In the method, the recession hydrograph is examined as ÀdQ/dt = f(Q), where Q is aquifer discharge and f is an arbitrary function. The observed function f is parameterized through analytical solutions to the one-dimensional Boussinesq equation for unconfined flow in a homogeneous and horizontal aquifer. While attractive in its simplicity, as originally presented it is not applicable to settings where slope is an important driver of flow, or where hydraulic parameters vary greatly with depth. We compare analytical solutions to the linearized one-dimensional Boussinesq equation for a sloping aquifer to numerical solutions of the full nonlinear equation. The behavior of the nonlinear Boussinesq equation is also assessed when the aquifer is heterogeneous wherein the lateral saturated hydraulic conductivity k varies as a power law with height z above the impermeable layer (k $ z n , n constant ! 0). All of the analytical solutions differ in key aspects from the nonlinear solution when plotted as ÀdQ/dt = f(Q) and thus are inappropriate for a Brutsaert and Nieber-type analysis. However, new analytical solutions for a sloping aquifer are derived ''empirically'' from the numerical simulations that are applicable during the late period of recession when the recession curve converges to ÀdQ/dt = aQ b , where b = (2n + 1)/(n + 1) and a is a function of the dimensions and hydraulic properties of the aquifer.

This work advances a unified approach to process-based hydrologic modeling, which we term the ''Structure for Unifying Multiple Modeling Alternatives (SUMMA).'' The modeling framework, introduced in the companion paper, uses a general set of conservation equations with flexibility in the choice of process parameterizations (closure relationships) and spatial architecture. This second paper specifies the model equations and their spatial approximations, describes the hydrologic and biophysical process parameterizations currently supported within the framework, and illustrates how the framework can be used in conjunction with multivariate observations to identify model improvements and future research and data needs. The case studies illustrate the use of SUMMA to select among competing modeling approaches based on both observed data and theoretical considerations. Specific examples of preferable modeling approaches include the use of physiological methods to estimate stomatal resistance, careful specification of the shape of the within-canopy and below-canopy wind profile, explicitly accounting for dust concentrations within the snowpack, and explicitly representing distributed lateral flow processes. Results also demonstrate that changes in parameter values can make as much or more difference to the model predictions than changes in the process representation. This emphasizes that improvements in model fidelity require a sagacious choice of both process parameterizations and model parameters. In conclusion, we envisage that SUMMA can facilitate ongoing model development efforts, the diagnosis and correction of model structural errors, and improved characterization of model uncertainty.

No abstract