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1.
This paper aims to investigate the uncertainty in simulated extreme low and high flows originating from hydrological model structure and parameters. To this end, three different rainfall-runoff models, namely GR4J, HBV and Xinanjiang, are applied to two subbasins of Qiantang River basin, eastern China. The Generalised Likelihood Uncertainty Estimation approach is used for estimating the uncertainty of the three models due to parameter values, henceforth referred as parameter uncertainty. Uncertainty in simulated extreme flows is evaluated by means of the annual maximum discharge and mean annual 7-day minimum discharge. The results show that although the models have good performance for the daily flows, the uncertainty in the extreme flows could not be neglected. The uncertainty originating from parameters is larger than uncertainty due to model structure. The parameter uncertainty of the extreme flows increases with the observed discharge. The parameter uncertainty in both the extreme high flows and the extreme low flows is the largest for the HBV model and the smallest for the Xinanjiang model. It is noted that the extreme low flows are mostly underestimated by all models with optimum parameter sets for both subbasins. The largest underestimation is from Xinanjiang model. Therefore it is not reliable enough to use only one set of the parameters to make the prediction and carrying out the uncertainty study in the extreme discharge simulation could give an overall picture for the planners.  相似文献   

2.
In this paper we propose a methodology to include prior information in the estimation of effective soil parameters for modelling the soil moisture content in the unsaturated zone. Laboratory measurements on undisturbed soil cores were used to estimate the moisture retention curve and hydraulic conductivity curve parameters. The soil moisture content was measured at 25 locations along three transects and at three different depths (surface, 30 and 60 cm) on an 80×20 m hillslope for the year 2001. Soil cores were collected in 84 locations situated in three profile pits along the hillslope. For the estimation of the effective soil hydraulic parameters the joint probability distribution of measured parameter values was used as prior information. A two-horizon single column 1D MIKE SHE model based on Richards' equation was set-up for nine soil moisture measurement locations along the middle transect of the hillslope. The goal of the model is to simulate the soil moisture profile at each location. The shuffled complex evolution (SCE) algorithm has been applied to estimate effective model parameters using either wide parameter ranges, referred to as the ‘no-prior’ case, or the joint probability distribution of measured parameter values as prior information (‘prior’ case). When the prior information is incorporated in the SCE optimisation the goodness-of-fit of the model predictions is only slightly worse compared to when no-prior information is incorporated. However, the effective parameter estimates are more realistic when the prior information is incorporated. For both the no-prior and prior case the generalised likelihood uncertainty estimation procedure (GLUE) was subsequently used to estimate the uncertainty bounds (UB) on the model predictions. When incorporating the prior information more parameter sets were accepted for the estimation of the predictive uncertainty and the parameter values were more realistic. Moreover, UB better enclosed the observations. Thus, incorporating prior information in GLUE reduces the amount of model evaluations needed to obtain sufficient behavioural parameter sets. The results indicate the importance of prior information in the SCE and GLUE parameter estimation strategies.  相似文献   

3.
This research incorporates the generalized likelihood uncertainty estimation (GLUE) methodology in a high‐resolution Environmental Protection Agency Storm Water Management Model (SWMM), which we developed for a highly urbanized sewershed in Syracuse, NY, to assess SWMM modelling uncertainties and estimate parameters. We addressed two issues that have long been suggested having a great impact on the GLUE uncertainty estimation: the observations used to construct the likelihood measure and the sampling approach to obtain the posterior samples of the input parameters and prediction bounds of the model output. First, on the basis of the Bayes' theorem, we compared the prediction bounds generated from the same Gaussian distribution likelihood measure conditioned on flow observations of varying magnitude. Second, we employed two sampling techniques, the sampling importance resampling (SIR) and the threshold sampling methods, to generate posterior parameter distributions and prediction bounds, based on which the sampling efficiency was compared. In addition, for a better understanding of the hydrological responses of different pervious land covers in urban areas, we developed new parameter sets in SWMM representing the hydrological properties of trees and lawns, which were estimated through the GLUE procedure. The results showed that SIR was a more effective alternative to the conventional threshold sampling method. The combined total flow and peak flow data were an efficient alternative to the intensive 5‐min flow data for reducing SWMM parameter and output uncertainties. Several runoff control parameters were found to have a great effect on peak flows, including the newly introduced parameters for trees. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

4.
The level of model complexity that can be effectively supported by available information has long been a subject of many studies in hydrologic modelling. In particular, distributed parameter models tend to be regarded as overparameterized because of numerous parameters used to describe spatially heterogeneous hydrologic processes. However, it is not clear how parameters and observations influence the degree of overparameterization, equifinality of parameter values, and uncertainty. This study investigated the impact of the numbers of observations and parameters on calibration quality including equifinality among calibrated parameter values, model performance, and output/parameter uncertainty using the Soil and Water Assessment Tool model. In the experiments, the number of observations was increased by expanding the calibration period or by including measurements made at inner points of a watershed. Similarly, additional calibration parameters were included in the order of their sensitivity. Then, unique sets of parameters were calibrated with the same objective function, optimization algorithm, and stopping criteria but different numbers of observations. The calibration quality was quantified with statistics calculated based on the ‘behavioural’ parameter sets, identified using 1% and 5% cut‐off thresholds in a generalized likelihood uncertainty estimation framework. The study demonstrated that equifinality, model performance, and output/parameter uncertainty were responsive to the numbers of observations and calibration parameters; however, the relationship between the numbers, equifinality, and uncertainty was not always conclusive. Model performance improved with increased numbers of calibration parameters and observations, and substantial equifinality did neither necessarily mean bad model performance nor large uncertainty in the model outputs and parameters. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

5.
Despite the wealth of soil erosion models available for the prediction of both runoff and soil loss at a variety of scales, little quantification is made of uncertainty and error associated with model output. This in part reflects the need to produce unequivocal or optimal results for the end user, which will often be an unrealistic goal. This paper presents a conceptually simple methodology, Generalized Likelihood Uncertainty Estimation (GLUE), for assessing the degree of uncertainty surrounding output from a physically based soil erosion model, the Water Erosion Prediction Project (WEPP). The ability not only to be explicit about model error but also to evaluate future improvements in parameter estimation, observed data or scientific understanding is demonstrated. This approach is applied to two sets of soil loss/runoff plot replicates, one in the UK and one in the USA. Although it is demonstrated that observations can be largely captured within uncertainty bounds, results indicate that these uncertainty bounds are often wide, reflecting the need to qualify results that derive from ‘optimum’ parameter sets, and to accept the concept of equifinality within soil erosion models. Attention is brought to the problem of under‐prediction of large events/over‐prediction of small events, as an area where model improvements could be made, specifically in the case of relatively dry years. Finally it is proposed that such a technique of model evaluation be employed more widely within the discipline so as to aid the interpretation and understanding of complex model output. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

6.
This study describes the parametric uncertainty of artificial neural networks (ANNs) by employing the generalized likelihood uncertainty estimation (GLUE) method. The ANNs are used to forecast daily streamflow for three sub-basins of the Rhine Basin (East Alpine, Main, and Mosel) having different hydrological and climatological characteristics. We have obtained prior parameter distributions from 5000 ANNs in the training period to capture the parametric uncertainty and subsequently 125,000 correlated parameter sets were generated. These parameter sets were used to quantify the uncertainty in the forecasted streamflow in the testing period using three uncertainty measures: percentage of coverage, average relative length, and average asymmetry degree. The results indicated that the highest uncertainty was obtained for the Mosel sub-basin and the lowest for the East Alpine sub-basin mainly due to hydro-climatic differences between these basins. The prediction results and uncertainty estimates of the proposed methodology were compared to the direct ensemble and bootstrap methods. The GLUE method successfully captured the observed discharges with the generated prediction intervals, especially the peak flows. It was also illustrated that uncertainty bands are sensitive to the selection of the threshold value for the Nash–Sutcliffe efficiency measure used in the GLUE method by employing the Wilcoxon–Mann–Whitney test.  相似文献   

7.
Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km2), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R 2) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.  相似文献   

8.
Nearshore sandbars, located in <10 m water depth, can contain remarkably periodic alongshore undulations in both cross‐shore position and depth. In a double sandbar system, the alongshore spacing of these morphological patterns in the inner sandbar may be identical to those in the outer sandbar. Although this morphological coupling has been observed previously, its frequency and predominance remain unclear. In this paper, we use a 9.3‐year dataset of daily low‐tide time exposure images from the double‐barred beach at Surfers Paradise (Gold Coast, Australia) to analyse the temporal and spatial characteristics of morphological coupling within a double sandbar system. We distinguish five types of morphological coupling between the inner and outer sandbars, of which four coincide with a downstate progression of the outer bar. Coupling is either in‐phase (with a landward perturbation of the inner bar facing an outer‐bar horn) or out‐of‐phase (with a seaward perturbation of the inner bar facing an outer‐bar horn), where the coupled inner‐bar features either consist of rip channels or, predominantly, perturbations of the low‐tide terrace. Cross‐correlation of the image‐derived inner‐ and outer‐bar patterns shows coupling to be a common phenomenon in the double sandbar system studied here, with coupling in 40% of the observations. In contrast to previous observations of sandbar–shoreline coupling at single‐barred beaches, in‐phase coupling (85% of all coupled bar patterns) predominates over out‐of‐phase coupling (15%). Based on our observations and bathymetries assimilated from the images for a restricted set of coupling events, we hypothesize that the angle of offshore wave incidence, wave height and depth variations along the outer sandbar determine the type of flow pattern (cell circulations versus meandering currents) above the inner bar and hence steer the type of coupling. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

9.
In this paper we extend the generalized likelihood uncertainty estimation (GLUE) technique to estimate spatially distributed uncertainty in models conditioned against binary pattern data contained in flood inundation maps. Untransformed binary pattern data already have been used within GLUE to estimate domain‐averaged (zero‐dimensional) likelihoods, yet the pattern information embedded within such sources has not been used to estimate distributed uncertainty. Where pattern information has been used to map distributed uncertainty it has been transformed into a continuous function prior to use, which may introduce additional errors. To solve this problem we use here ‘raw’ binary pattern data to define a zero‐dimensional global performance measure for each simulation in a Monte Carlo ensemble. Thereafter, for each pixel of the distributed model we evaluate the probability that this pixel was inundated. This probability is then weighted by the measure of global model performance, thus taking into account how well a given parameter set performs overall. The result is a distributed uncertainty measure mapped over real space. The advantage of the approach is that it both captures distributed uncertainty and contains information on global likelihood that can be used to condition predictions of further events for which observed data are not available. The technique is applied to the problem of flood inundation prediction at two test sites representing different hydrodynamic conditions. In both cases, the method reveals the spatial structure in simulation uncertainty and simultaneously enables mapping of flood probability predicted by the model. Spatially distributed uncertainty analysis is shown to contain information over and above that available from global performance measures. Overall, the paper highlights the different types of information that may be obtained from mappings of model uncertainty over real and n‐dimensional parameter spaces. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

10.
Spatial patterns of rainfall are known to cause differences in observed flow. In this paper, the effects of perturbations in rainfall patterns on changes in parameter sets as well as model output are explored using the hydrological model Dynamic TOPMODEL for the Brue catchment (135 km2) in southwest England. Overall rainfall amount remains the same at each time step so the perturbations act as effectively treated errors in the spatial pattern. The errors were analysed with particular emphasis on when they could be detected under an uncertainty framework. Higher rainfall perturbations (multipliers of × 4 and greater) in the low lying and high areas of the catchment resulted in changes to event peaks and accompanying compensation in the baseflow. More significantly, changes in the effective model parameter values required by the best models to take account of the more extreme patterns were able to be detected by noting when distributions of parameters change under uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

11.
Cross-shore migratory behavior of nearshore sandbars is commonly studied with nearshore bathymetric-evolution models that represent underlying processes of hydrodynamics and sediment transport. These models, however, struggle to reproduce natural cross-shore sandbar behavior on timescales of a few days to weeks and have uncertain skill on longer scales of months to years. One particular concern for the use of models on prediction timescales that far exceed the timescale of the modeled processes is the exponential accumulation of errors in the nonlinear model equations. The relation between cross-shore sandbar migration, sandbar location and wave height has previously been demonstrated to be weakly nonlinear on timescales of several days, but it is unknown how this nonlinearity affects the predictability of long-term (months to years) cross-shore sandbar behavior. Here we study the role of nonlinearity in the predictability of sandbar behavior on timescales of a few days to several months with data-driven neural network models. Our analyses are based on over 5600 daily-observed cross-shore sandbar locations and daily-averaged wave forcings from the Gold Coast, Australia, and Hasaki, Japan. We find that neural network models are able to hindcast many aspects of cross-shore sandbar behavior, such as rapid offshore migration during storms, slower onshore return during quiet periods, seasonal cycles and annual to interannual offshore-directed trends. Although the relation between sandbar migration, sandbar location and wave height is nonlinear, sandbar behavior can be hindcasted accurately over the entire lifespan of the sandbars at the Gold Coast. Contrastingly, it is difficult to hindcast the long-term offshore-directed trends in sandbar behavior at Hasaki because of exponential accumulation of errors over time. Our results further reveal that during periods with low-wave conditions it becomes increasingly difficult to predict sandbar locations, while during high waves predictions become increasingly accurate.  相似文献   

12.
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.  相似文献   

13.
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14.
In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented using the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.  相似文献   

15.
A methodology to derive solute transport models at any flow rate is presented. The novelty of the proposed approach lies in the assessment of uncertainty of predictions that incorporate parameterisation based on flow rate. A simple treatment of uncertainty takes into account heteroscedastic modelling errors related to tracer experiments performed over a range of flow rates, as well as the uncertainty of the observed flow rates themselves. The proposed approach is illustrated using two models for the transport of a conservative solute: a physically based, deterministic, advection-dispersion model (ADE), and a stochastic, transfer function based, active mixing volume model (AMV). For both models the uncertainty of any parameter increases with increasing flow rate (reflecting the heteroscedastic treatment of modelling errors at different observed flow rates), but in contrast the uncertainty of travel time, computed from the predicted model parameters, was found to decrease with increasing flow rate.  相似文献   

16.
This paper proposes a new orientation to address the problem of hydrological model calibration in ungauged basin. Satellite radar altimetric observations of river water level at basin outlet are used to calibrate the model, as a surrogate of streamflow data. To shift the calibration objective, the hydrological model is coupled with a hydraulic model describing the relation between streamflow and water stage. The methodology is illustrated by a case study in the Upper Mississippi Basin using TOPEX/Poseidon (T/P) satellite data. The generalized likelihood uncertainty estimation (GLUE) is employed for model calibration and uncertainty analysis. We found that even without any streamflow information for regulating model behavior, the calibrated hydrological model can make fairly reasonable streamflow estimation. In order to illustrate the degree of additional uncertainty associated with shifting calibration objective and identifying its sources, the posterior distributions of hydrological parameters derived from calibration based on T/P data, streamflow data and T/P data with fixed hydraulic parameters are compared. The results show that the main source is the model parameter uncertainty. And the contribution of remote sensing data uncertainty is minor. Furthermore, the influence of removing high error satellite observations on streamflow estimation is also examined. Under the precondition of sufficient temporal coverage of calibration data, such data screening can eliminate some unrealistic parameter sets from the behavioral group. The study contributes to improve streamflow estimation in ungauged basin and evaluate the value of remote sensing in hydrological modeling. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

17.
The problems of calibrating soil hydraulic and transport parameters are well documented, particularly when data are limited. Programs such as CXTFIT, UUCODE and PEST, based on well established principles of statistical inference, will often provide good fits to limited observations giving the impression that a useful model of a particular soil system has been obtained. This may be the case, but such an approach may grossly underestimate the uncertainties associated with future predictions of the system and resulting dependent variables. In this paper, this is illustrated by an application of CXTFIT within the generalised likelihood uncertainty estimation (GLUE) approach to model calibration which is based on a quite different philosophy. CXTFIT gives very good fits to the observed breakthrough curves for several different model formulations, resulting in very small parameter uncertainty estimates. The application of GLUE, however, shows that much wider ranges of parameter values can provide acceptable fits to the data. The wider range of potential outcomes should be more robust in model prediction, especially when used to constrain field scale models.  相似文献   

18.
The physically based distributed hydrological models are ideal for hydrological simulations; however most of such models do not use the basic equations pertaining to mass, energy and momentum conservation, to represent the physics of the process. This is plausibly due to the lack of complete understanding of the hydrological process. The soil and water assessment tool (SWAT) is one such widely accepted semi-distributed, conceptual hydrological model used for water resources planning. However, the over-parameterization, difficulty in its calibration process and the uncertainty associated with predictions make its applications skeptical. This study considers assessing the predictive uncertainty associated with distributed hydrological models. The existing methods for uncertainty estimation demand high computational time and therefore make them challenging to apply on complex hydrological models. The proposed approach employs the concepts of generalized likelihood uncertainty estimation (GLUE) in an iterative procedure by starting with an assumed prior probability distribution of parameters, and by using mutual information (MI) index for sampling the behavioral parameter set. The distributions are conditioned on the observed information through successive cycles of simulations. During each cycle of simulation, MI is used in conjunction with Markov Chain Monte Carlo procedure to sample the parameter sets so as to increase the number of behavioral sets, which in turn helps reduce the number of cycles/simulations for the analysis. The method is demonstrated through a case study of SWAT model in Illinois River basin in the USA. A comparison of the proposed method with GLUE indicates that the computational requirement of uncertainty analysis is considerably reduced in the proposed approach. It is also noted that the model prediction band, derived using the proposed method, is more effective compared to that derived using the other methods considered in this study.  相似文献   

19.
This study investigates the recovery capabilities of a single-barred beach in the Pacific Mexican coast before and after the 2015–2016 El Niño winter. Concurrent hydrodynamic and morphological data collected over a 3-year period (August 2014–2017) were analysed to determine the subaerial-subtidal volumetric exchange and cross-shore subtidal sandbar migrations, in relation to the incident wave forcing. The beach presented a seasonal seaward and landward sandbar migration cycle. The sandbar migrated offshore during the energetic waves between November and February, and onshore during the milder wave period in spring, until welding to the subaerial beach around May. The transfer of sediment towards the subaerial section continued over the summer, reaching a complete recovery by September/October. Prior to El Niño, the subaerial beach successfully recovered by the end of summer 2015 through the landward sandbar migration process. The 2015–2016 energetic winter waves caused a subaerial volume loss of ~ 140 m3 m?1 (from October 2015 to March 2016), more than twice the amount eroded in the other winters, and the sandbar moved further offshore and to deeper depths (3–4 m) than the winter before. In addition, the energetic 2015–2016 winter waves lasted for 2 months longer than in other years, making the 2016 spring shorter. Consequently, during the onshore migration, the sandbar was unable of reaching shallow depths, and a large portion of sand remained in the subtidal beach. The subaerial beach recovered 60 and 65% of the loss in the 2016 and 2017 summers, respectively. It is concluded that the landward migration process of the sandbar during the spring is critical to ensure a full subaerial beach recovery over the mild wave period in summer. The recovery capabilities of the subaerial beach will depend on the cross-shore distance and depth where the sandbar is located, and on the duration of mild wave conditions required for the sandbar to migrate onshore.  相似文献   

20.
Satellites provide important information on many meteorological and oceanographic variables. State-space models are commonly used to analyse such data sets with measurement errors. In this work, we propose to extend the usual linear and Gaussian state-space to analyse time series with irregular time sampling, such as the one obtained when keeping all the satellite observations available at some specific location. We discuss the parameter estimation using a method of moment and the method of maximum likelihood. Simulation results indicate that the method of moment leads to a computationally efficient and numerically robust estimation procedure suitable for initializing the Expectation–Maximisation algorithm, which is combined with a standard numerical optimization procedure to maximize the likelihood function. The model is validated on sea surface temperature (SST) data from a particular satellite. The results indicate that the proposed methodology can be used to reconstruct realistic SST time series at a specific location and also give useful information on the quality of satellite measurement and the dynamics of the SST.  相似文献   

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