[1] Meaningful quantification of data and structural uncertainties in conceptual rainfallrunoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes ill-posed unless sufficiently precise prior knowledge of data uncertainty is supplied; this ill-posedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfall-runoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.

[1] Ambiguities in the representation of environmental processes have manifested themselves in a plethora of hydrological models, differing in almost every aspect of their conceptualization and implementation. The current overabundance of models is symptomatic of an insufficient scientific understanding of environmental dynamics at the catchment scale, which can be attributed to difficulties in measuring and representing the heterogeneity encountered in natural systems. This commentary advocates using the method of multiple working hypotheses for systematic and stringent testing of model alternatives in hydrology. We discuss how the multiple-hypothesis approach provides the flexibility to formulate alternative representations (hypotheses) describing both individual processes and the overall system. When combined with incisive diagnostics to scrutinize multiple model representations against observed data, this provides hydrologists with a powerful and systematic approach for model development and improvement. Multiple-hypothesis frameworks also support a broader coverage of the model hypothesis space and hence improve the quantification of predictive uncertainty arising from system and component nonidentifiabilities. As part of discussing the advantages and limitations of multiplehypothesis frameworks, we critically review major contemporary challenges in hydrological hypothesis-testing, including exploiting different types of data to investigate the fidelity of alternative process representations, accounting for model structure ambiguities arising from major uncertainties in environmental data, quantifying regional differences in dominant hydrological processes, and the grander challenge of understanding the self-organization and optimality principles that may functionally explain and describe the heterogeneities evident in most environmental systems. We assess recent progress in these research directions, and how new advances are possible using multiple-hypothesis methodologies.Citation: Clark, M. P., D. Kavetski, and F. Fenicia (2011), Pursuing the method of multiple working hypotheses for hydrological modeling, Water Resour. Res., 47, W09301,

[1] Parameter estimation in rainfall-runoff models is affected by uncertainties in the measured input/output data (typically, rainfall and runoff, respectively), as well as model error. Despite advances in data collection and model construction, we expect input uncertainty to be particularly significant (because of the high spatial and temporal variability of precipitation) and to remain considerable in the foreseeable future. Ignoring this uncertainty compromises hydrological modeling, potentially yielding biased and misleading results. This paper develops a Bayesian total error analysis methodology for hydrological models that allows (indeed, requires) the modeler to directly and transparently incorporate, test, and refine existing understanding of all sources of data uncertainty in a specific application, including both rainfall and runoff uncertainties. The methodology employs additional (latent) variables to filter out the input corruption given the model hypothesis and the observed data. In this study, the input uncertainty is assumed to be multiplicative Gaussian and independent for each storm, but the general framework allows alternative uncertainty models. Several ways of incorporating vague prior knowledge of input corruption are discussed, contrasting Gaussian and inverse gamma assumptions; the latter method avoids degeneracies in the objective function. Although the general methodology is computationally intensive because of the additional latent variables, a range of modern numerical methods, particularly Monte Carlo analysis combined with fast Newton-type optimization methods and Hessian-based covariance analysis, can be employed to obtain practical solutions.

[1] This paper evaluates the use of field data on the spatial variability of snow water equivalent (SWE) to guide the design of distributed snow models. An extensive reanalysis of results from previous field studies in different snow environments around the world is presented, followed by an analysis of field data on spatial variability of snow collected in the headwaters of the Jollie River basin, a rugged mountain catchment in the Southern Alps of New Zealand. In addition, area-averaged simulations of SWE based on different types of spatial discretization are evaluated. Spatial variability of SWE is shaped by a range of different processes that occur across a hierarchy of spatial scales. Spatial variability at the watershed-scale is shaped by variability in near-surface meteorological fields (e.g., elevation gradients in temperature) and, provided suitable meteorological data is available, can be explicitly resolved by spatial interpolation/extrapolation. On the other hand, spatial variability of SWE at the hillslope-scale is governed by processes such as drifting, sloughing of snow off steep slopes, trapping of snow by shrubs, and the nonuniform unloading of snow by the forest canopy, which are more difficult to resolve explicitly. Subgrid probability distributions are often capable of representing the aggregate-impact of unresolved processes at the hillslope-scale, though they may not adequately capture the effects of elevation gradients. While the best modeling strategy is case-specific, the analysis in this paper provides guidance on both the suitability of several common snow modeling approaches and on the choice of parameter values in subgrid probability distributions.