[1] When quantifying model prediction uncertainty, it is statistically convenient to represent model errors that are normally distributed with a constant variance. The Box-Cox transformation is the most widely used technique to normalize data and stabilize variance, but it is not without limitations. In this paper, a log-sinh transformation is derived based on a pattern of errors commonly seen in hydrological model predictions. It is suited to applications where prediction variables are positively skewed and the spread of errors is seen to first increase rapidly, then slowly, and eventually approach a constant as the prediction variable becomes greater. The log-sinh transformation is applied in two case studies, and the results are compared with one-and two-parameter Box-Cox transformations.Citation: Wang, Q. J., D. L. Shrestha, D. E. Robertson, and P. Pokhrel (2012), A log-sinh transformation for data normalization and variance stabilization, Water Resour. Res., 48, W05514,

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[1] Environmental models have become increasingly complex with greater attention being given to the spatially distributed representation of processes. Distributed models have large numbers of parameters to be specified, which is typically done either by recourse to a priori methods based on observable physical watershed characteristics, by calibration to watershed input-state-output data, or by some combination of both. In the case of calibration, the high dimensionality of the parameter search space poses a significant identifiability problem. This article discusses how this problem can be addressed, utilizing additional information about the parameters through a process known as regularization. Regularization, in its broadest sense, is a mathematical technique that utilizes additional information or constraints about the parameters to reduce problems related to over-parameterization. This article develops and applies a regularization approach to the calibration of a version of the Hydrology Laboratory Distributed Hydrologic Model (HL-DHM) developed by the US National Weather Service. A priori parameter estimates derived using the approach by Koren et al. (2000) were used to develop regularization relationships to constrain the feasible parameter space and enable existing global optimization techniques to be applied to solve the calibration problem. In a case study for the Blue River basin, the number of unknowns to be estimated was reduced from 858 to 33, and this calibration strategy improved the model performance while preserving the physical realism of the model parameters. Our results also suggest that the commonly used parameter field ''multiplier'' approach may often not be appropriate.Citation: Pokhrel, P., H. V. Gupta, and T. Wagener (2008), A spatial regularization approach to parameter estimation for a distributed watershed model, Water Resour. Res., 44, W12419,

[1] Hydrologic models require the specification of unknown model parameters via calibration to historical input-output data. For spatially distributed models, the large number of unknowns makes the calibration problem poorly conditioned. Spatial regularization can help to stabilize the problem by facilitating inclusion of additional information. While a common regularization approach is to apply a scalar multiplier to the prior estimate of each parameter field, this can cause problems by simultaneously changing both the mean and the variance of the distribution. This paper explores a multiple-criteria regularization approach that facilitates adjustment of the mean, variance, and shape of the parameter distribution, using prior information to constrain the problem while providing sufficient degrees of freedom to enable model performance improvements. We also test simple squashing functions to help in maintaining conceptually reasonable parameter values throughout the spatial domain. We apply the method to three basins in the context of the Distributed Model Intercomparison Project (DMIP2), obtaining considerable performance improvements at the basin outlet. However, the prior parameter estimates are found to give much better performance at the interior points (treated as ungauged), suggesting that the spatial information has not been properly exploited. The results also suggest that basin outlet hydrographs may not be particularly sensitive to spatial parameter variability and that an overall basin mean value may be sufficient for flow forecasting at the outlet, although not at the interior points. We discuss weaknesses in our study approach and suggest diagnostically more powerful strategies to be pursued.Citation: Pokhrel, P., and H. V. Gupta (2010), On the use of spatial regularization strategies to improve calibration of distributed watershed models, Water Resour. Res., 46, W01505,

Abstract. Statistical methods traditionally applied for seasonal streamflow forecasting use predictors that represent the initial catchment condition and future climate influences on future streamflows. Observations of antecedent streamflows or rainfall commonly used to represent the initial catchment conditions are surrogates for the true source of predictability and can potentially have limitations. This study investigates a hybrid seasonal forecasting system that uses the simulations from a dynamic hydrological model as a predictor to represent the initial catchment condition in a statistical seasonal forecasting method. We compare the skill and reliability of forecasts made using the hybrid forecasting approach to those made using the existing operational practice of the Australian Bureau of Meteorology for 21 catchments in eastern Australia. We investigate the reasons for differences. In general, the hybrid forecasting system produces forecasts that are more skilful than the existing operational practice and as reliable. The greatest increases in forecast skill tend to be (1) when the catchment is wetting up but antecedent streamflows have not responded to antecedent rainfall, (2) when the catchment is drying and the dominant source of antecedent streamflow is in transition between surface runoff and base flow, and (3) when the initial catchment condition is near saturation intermittently throughout the historical record.