[1] Estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions. Residual errors are often assumed to be independent and to be adequately described by a Gaussian probability distribution with a mean of zero and a constant variance. Here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed. A formal generalized likelihood function is presented, which extends the applicability of previously used likelihood functions to situations where residual errors are correlated, heteroscedastic, and non-Gaussian with varying degrees of kurtosis and skewness. The approach focuses on a correct statistical description of the data and the total model residuals, without separating out various error sources. Application to Bayesian uncertainty analysis of a conceptual rainfall-runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors. When applied to daily rainfall-runoff data from a humid basin we find that (1) residual errors are much better described by a heteroscedastic, first-order, auto-correlated error model with a Laplacian distribution function characterized by heavier tails than a Gaussian distribution; and (2) compared to a standard least-squares approach, proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference. Application to daily rainfall-runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that (1) multiplicative bias factors can be used to compensate for some of the largest errors and (2) a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near-zero flows. We conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well.Citation: Schoups, G., and J. A. Vrugt (2010), A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors, Water Resour.

[1] In hydrological tracer studies, the gamma distribution can serve as an appropriate transit time distribution (TTD) as it allows more flexibility to account for nonlinearities in the behavior of catchment systems than the more commonly used exponential distribution. However, it is unclear which physical interpretation can be ascribed to its two parameters (a, b). In this study, long-term tracer data from three contrasting catchments in the Scottish Highlands were used for a comparative assessment of interannual variability in TTDs and resulting mean transit times (MTT = ab) inferred by the gamma distribution model. In addition, spatial variation in the long-term average TTDs from these and six additional catchments was also assessed. The temporal analysis showed that the b parameter was controlled by precipitation intensities above catchment-specific thresholds. In contrast, the a parameter, which showed little temporal variability and no relationship with precipitation intensity, was found to be closely related to catchment landscape organization, notably the hydrological characteristics of the dominant soils and the drainage density. The relationship between b and precipitation intensity was used to express b as a time-varying function within the framework of lumped convolution integrals to examine the nonstationarity of TTDs. The resulting time-variant TTDs provided more detailed and potentially useful information about the temporal dynamics and the timing of solute fluxes. It was shown that in the wet, cool climatic conditions of the Scottish Highlands, the transit times from the time-variant TTD were roughly consistent with the variations of MTTs revealed by interannual analysis.

This study investigates the possible correspondence between catchment structure, as represented by perceptual hydrological models developed from fieldwork investigations, and mathematical model structures, selected on the basis of reproducing observed catchment hydrographs. Three Luxembourgish headwater catchments are considered, where previous fieldwork suggested distinct flow‐generating mechanisms and hydrological dynamics. A set of lumped conceptual model structures are hypothesized and implemented using the SUPERFLEX framework. Following parameter calibration, the model performance is examined in terms of predictive accuracy, quantification of uncertainty, and the ability to reproduce the flow–duration curve signature. Our key research question is whether differences in the performance of the conceptual model structures can be interpreted based on the dominant catchment processes suggested from fieldwork investigations. For example, we propose that the permeable bedrock and the presence of multiple aquifers in the Huewelerbach catchment may explain the superior performance of model structures with storage elements connected in parallel. Conversely, model structures with serial connections perform better in the Weierbach and Wollefsbach catchments, which are characterized by impermeable bedrock and dominated by lateral flow. The presence of threshold dynamics in the Weierbach and Wollefsbach catchments may favour nonlinear models, while the smoother dynamics of the larger Huewelerbach catchment were suitably reproduced by linear models. It is also shown how hydrologically distinct processes can be effectively described by the same mathematical model components. Major research questions are reviewed, including the correspondence between hydrological processes at different levels of scale and how best to synthesize the experimentalist's and modeller's perspectives. Copyright © 2013 John Wiley & Sons, Ltd.

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The sustainability of irrigated agriculture in many arid and semiarid areas of the world is at risk because of a combination of several interrelated factors, including lack of fresh water, lack of drainage, the presence of high water tables, and salinization of soil and groundwater resources. Nowhere in the United States are these issues more apparent than in the San Joaquin Valley of California. A solid understanding of salinization processes at regional spatial and decadal time scales is required to evaluate the sustainability of irrigated agriculture. A hydro-salinity model was developed to integrate subsurface hydrology with reactive salt transport for a 1,400-km 2 study area in the San Joaquin Valley. The model was used to reconstruct historical changes in salt storage by irrigated agriculture over the past 60 years. We show that patterns in soil and groundwater salinity were caused by spatial variations in soil hydrology, the change from local groundwater to snowmelt water as the main irrigation water supply, and by occasional droughts. Gypsum dissolution was a critical component of the regional salt balance. Although results show that the total salt input and output were about equal for the past 20 years, the model also predicts salinization of the deeper aquifers, thereby questioning the sustainability of irrigated agriculture.regional hydrology ͉ salinization ͉ vadose zone