[1] The conventional treatment of uncertainty in rainfall-runoff modeling primarily attributes uncertainty in the input-output representation of the model to uncertainty in the model parameters without explicitly addressing the input, output, and model structural uncertainties. This paper presents a new framework, the Integrated Bayesian Uncertainty Estimator (IBUNE), to account for the major uncertainties of hydrologic rainfall-runoff predictions explicitly. IBUNE distinguishes between the various sources of uncertainty including parameter, input, and model structural uncertainty. An input error model in the form of a Gaussian multiplier has been introduced within IBUNE. These multipliers are assumed to be drawn from an identical distribution with an unknown mean and variance which were estimated along with other hydrological model parameters by a Monte Carlo Markov Chain (MCMC) scheme. IBUNE also includes the Bayesian model averaging (BMA) scheme which is employed to further improve the prediction skill and address model structural uncertainty using multiple model outputs. A series of case studies using three rainfall-runoff models to predict the streamflow in the Leaf River basin, Mississippi, are used to examine the necessity and usefulness of this technique. The results suggest that ignoring either input forcings error or model structural uncertainty will lead to unrealistic model simulations and incorrect uncertainty bounds.Citation: Ajami, N. K., Q. Duan, and S. Sorooshian (2007), An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction, Water Resour.
Multi-model ensemble strategy is a means to exploit the diversity of skillful predictions from different models. This paper studies the use of Bayesian model averaging (BMA) scheme to develop more skillful and reliable probabilistic hydrologic predictions from multiple competing predictions made by several hydrologic models. BMA is a statistical procedure that infers consensus predictions by weighing individual predictions based on their probabilistic likelihood measures, with the better performing predictions receiving higher weights than the worse performing ones. Furthermore, BMA provides a more reliable description of the total predictive uncertainty than the original ensemble, leading to a sharper and better calibrated probability density function (PDF) for the probabilistic predictions. In this study, a nine-member ensemble of hydrologic predictions was used to test and evaluate the BMA scheme. This ensemble was generated by calibrating three different hydrologic models using three distinct objective functions. These objective functions were chosen in a way that forces the models to capture certain aspects of the hydrograph well (e.g., peaks, mid-flows and low flows). Two sets of numerical experiments were carried out on three test basins in the US to explore the best way of using the BMA scheme. In the first set, a single set of BMA weights was computed to obtain BMA predictions, while the second set employed multiple sets of weights, with distinct sets corresponding to different flow intervals. In both sets, the streamflow values were transformed using Box-Cox transformation to ensure that the probability distribution of the prediction errors is approximately Gaussian. A split sample approach was used to obtain and validate the BMA predictions. The test results showed that BMA scheme has the advantage of generating more skillful and equally reliable probabilistic predictions than original ensemble. The performance of the expected BMA predictions in terms of daily root mean square error (DRMS) and daily absolute mean error (DABS) is generally superior to that of the best individual predictions. Furthermore, the BMA predictions employing multiple sets of weights are generally better than those using single set of weights.
An important goal of spatially distributed hydrologic modeling is to provide estimates of streamflow (and river levels) at any point along the river system. To encourage collaborative research into appropriate levels of model complexity, the value of spatially distributed data, and methods suitable for model development and calibration, the US National Weather Service Hydrology Laboratory (NWSHL) is promoting the distributed modeling intercomparison project (DMIP). In particular, the project is interested in how spatially distributed estimates of precipitation provided by the next generation radar (NEXRAD) network, high resolution digital elevation models (DEM), soil, land-use and vegetation data can be integrated into an improved system for distributed hydrologic modeling that provides more accurate and informative flood forecasts.The goal of this study is to explore four questions: Can a semi-distributed approach improve the streamflow forecasts at the watershed outlet compared to a lumped approach? What is a suitable calibration strategy for a semi-distributed model structure, and how much improvement can be obtained? What is the minimum level of spatial complexity required, above which the improvement in forecast accuracy is marginal? What spatial details must be included to enable flow prediction at any point along the river network?The study compares lumped, semi-lumped and semi-distributed versions of the SAC-SMA (Sacramento Soil Moisture Accounting) model for the Illinois River basin at Watts (OK). A kinematic wave scheme is used to rout the flow along the river channel to the outlet. A Multi-step Automatic Calibration Scheme (MACS) using the Shuffled Complex Evolution (SCE-UA) optimization algorithm is applied for model calibration. The calibration results reveal that moving from a lumped model structure, driven by spatially averaged NEXRAD data over the entire basin, to a semi-distributed model structure, with forcing data averaged over each sub-basin while having identical parameters for all the sub-basins, improves the simulation results. However, varying the parameters between sub-basins does not further improve the simulation results, either at the outlet or at an interior testing point. q
This paper examines several multimodel combination techniques that are used for streamflow forecasting: the simple model average (SMA), the multimodel superensemble (MMSE), modified multimodel superensemble (M3SE), and the weighted average method (WAM). These model combination techniques were evaluated using the results from the Distributed Model Intercomparison Project (DMIP), an international project sponsored by the National Weather Service (NWS) Office of Hydrologic Development (OHD). All of the multimodel combination results were obtained using uncalibrated DMIP model simulations and were compared against the best-uncalibrated as well as the best-calibrated individual model results. The purpose of this study is to understand how different combination techniques affect the accuracy levels of the multimodel simulations. This study revealed that the multimodel simulations obtained from uncalibrated single-model simulations are generally better than any single-member model simulations, even the best-calibrated single-model simulations. Furthermore, more sophisticated multimodel combination techniques that incorporated bias correction step work better than simple multimodel average simulations or multimodel simulations without bias correction.
Media-related public awareness of extreme drought in California is linked to changes in urban water use behavior.
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