Multi-model ensemble hydrologic prediction using Bayesian model averaging

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. © 2006 Elsevier Ltd. All rights reserved

Toward improved hydrologic prediction with reduced uncertainty using sequential multi-model combination

The contemporary usage of hydrologic models has been to rely on a single model to perform the simulation and predictions. Despite the tremendous progress, efforts and investment put into developing more hydrologic models, there is no convincing claim that any particular model in existence is superior to other models for various applications and under all circumstances. This results to reducing the size of the plausible model space and often leads to predictions that may well-represent some phenomena or events at the expenses of others. Assessment of predictive uncertainty based on a single model is subject to statistical bias and most likely underestimation of uncertainty. This endorses the implementation of multi-model methods for more accurate estimation of uncertainty in hydrologic prediction. In this study, we present two methods for the combination of multiple model predictors using Bayesian Model Averaging (BMA) and Sequential Bayesian Model Combination (SBMC). Both methods are statistical schemes to infer a combined probabilistic prediction that possess more reliability and skill than the original model members produced by several competing models. This paper discusses the features of both methods and explains how the limitation of BMA can be overcome by SBMC. Three hydrologic models are considered and it is shown that multi-model combination can result in higher prediction accuracy than individual models. © 2008 ASCE

Ensemble evaluation of hydrological model hypotheses

It is demonstrated for the first time how model parameter, structural and data uncertainties can be accounted for explicitly and simultaneously within the Generalized Likelihood Uncertainty Estimation (GLUE) methodology. As an example application, 72 variants of a single soil moisture accounting store are tested as simplified hypotheses of runoff generation at six experimental grassland field-scale lysimeters through model rejection and a novel diagnostic scheme. The fields, designed as replicates, exhibit different hydrological behaviors which yield different model performances. For fields with low initial discharge levels at the beginning of events, the conceptual stores considered reach their limit of applicability. Conversely, one of the fields yielding more discharge than the others, but having larger data gaps, allows for greater flexibility in the choice of model structures. As a model learning exercise, the study points to a “leaking” of the fields not evident from previous field experiments. It is discussed how understanding observational uncertainties and incorporating these into model diagnostics can help appreciate the scale of model structural error

Statistical post-processing of hydrological forecasts using Bayesian model averaging

Accurate and reliable probabilistic forecasts of hydrological quantities like runoff or water level are beneficial to various areas of society. Probabilistic state-of-the-art hydrological ensemble prediction models are usually driven with meteorological ensemble forecasts. Hence, biases and dispersion errors of the meteorological forecasts cascade down to the hydrological predictions and add to the errors of the hydrological models. The systematic parts of these errors can be reduced by applying statistical post-processing. For a sound estimation of predictive uncertainty and an optimal correction of systematic errors, statistical post-processing methods should be tailored to the particular forecast variable at hand. Former studies have shown that it can make sense to treat hydrological quantities as bounded variables. In this paper, a doubly truncated Bayesian model averaging (BMA) method, which allows for flexible post-processing of (multi-model) ensemble forecasts of water level, is introduced. A case study based on water level for a gauge of river Rhine, reveals a good predictive skill of doubly truncated BMA compared both to the raw ensemble and the reference ensemble model output statistics approach.Comment: 19 pages, 6 figure

Response of hydrological processes to input data in high alpine catchment : an assessment of the Yarkant River basin in China

Most studies of input data used in hydrological models have focused on flow; however, point discharge data negligibly reflect deviations in spatial input data. To study the effects of different input data sources on hydrological processes at the catchment scale, eight MIKE SHE models driven by station-based data (SBD) and remote sensing data (RSD) were implemented. The significant influences of input variables on water components were examined using an analysis of the variance model (ANOVA) with the hydrologic catchment response quantified based on different water components. The results suggest that compared with SBD, RSD precipitation resulted in greater differences in snow storage in the different elevation bands and RSD temperatures led to more snowpack areas with thinner depths. These changes in snowpack provided an appropriate interpretation of precipitation and temperature distinctions between RSD and SBD. For potential evapotranspiration (PET), the larger RSD value caused less plant transpiration because parameters were adjusted to satisfy the outflow. At the catchment scale, the spatiotemporal distributions of sensitive water components, which can be defined by the ANOVA model, indicate that this approach is rational for assessing the impacts of input data on hydrological processes

Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation

There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices

Assessment of Epistemic Uncertainty in Flood Inundation Modeling

Flooding is one of the most devastating natural disasters in the world and it exacerbated during the past decades. In order to reduce the loss of lives and properties from repeating flooding events, reliable flood predictions are required. Currently, there exist a series of hydrodynamic models that have different model structures which solve different forms of governing equations in one- (1D), two- (2D) or three- (3D) dimensions, thus providing various possible predictions for decision makers to choose from. Even for the same model, depending on how the model is implemented for a specific parameter set, input data and channel geometry representation, the prediction is different. Therefore, investigating the reducible uncertainty (epistemic uncertainty) in flood inundation modeling and finding a proper way to generate robust predictions are very crucial for future modelers. In this dissertation, epistemic uncertainty sources from model structure, model parameter and model input are investigated and evaluated by using stream reaches ranging from reach scale to watershed scale in different geographical settings. The three objectives of this dissertation are to: (1) evaluate the impact of hydrodynamic model structure uncertainty on predicted water stages and inundation extents under different geophysical settings, and explore the influence of channel and floodplain roughness on model performance respectively, (2) investigate and apply a multi-model combing approach, Bayesian model averaging (BMA), to produce reliable predictions by considering four uncertainty sources including channel width, channel cross-sectional shape, channel roughness and flow forcing and (3) separate and prioritize different uncertainty sources, including DEM resolution, channel width, channel cross-sectional shape, channel roughness and flow forcing, based on their relative influences using hierarchical Bayesian model averaging (HBMA). In the first objective, the performance of four hydraulic models including HEC-RAS 1D, HEC-RAS 2D, LISFLOOD-FP diffusive and LISFLOOD-FP subgrid are evaluated at four rivers that have different geophysical settings in the United States. The results show that HEC-RAS 2D does not perform well at low channel roughness condition. However, at high channel roughness condition, the performance of HEC-RAS 2D and HEC-RAS 1D are comparable. The performance of the subgrid version of LISFLOOD-FP (LS) is more stable under different channel roughness conditions, and in general it performs better than the diffusive version (LD) in simulating floodplain inundation. Moreover, applying distributed floodplain roughness does not necessarily improve model performances. In the second objective, LISFLOOD-FP subgrid model is applied for a relatively large catchment-Black River watershed in Missouri and Arkansas considering four uncertainty sources using BMA approach. The results indicate that although BMA deterministic prediction may not always outperform all the model members in the ensemble, this approach is able to provide a relatively robust water stage prediction. Typically, BMA deterministic prediction behaves better than most of the member predictions in the ensemble and ensemble mean prediction. BMA has better performance than ensemble mean prediction for high-chance flood regions at Black River watershed. On the other hand, there is no significant difference between two types of probabilistic flood maps for low-chance flood regions. In the third objective, LISFLOOD-FP subgrid model is also set up in the Black River watershed to find out the relative influence of five different uncertainty sources. The results demonstrate that channel width and topographical data resolution have largest impact on the hydrodynamic model predictions. These two sources are followed by flow forcing, which has relatively greater influence than channel cross-sectional shape and model parameter. However, when model weights are taken into account, input (topography and input forcing) and model parameter (roughness) have larger impact on prediction variance than model structure (channel shape and width)