Generalized Likelihood Uncertainty Estimation Method Research Articles

Evaluation of Sweet Corn Yield and Nitrogen Leaching with CERES-Maize Considering Input Parameter Uncertainties

A study was conducted to evaluate the ability of the CERES-Maize model in the Decision Support System for Agrotechnology Transfer (DSSAT) to simulate sweet corn (Zea mays L. var. saccharata) yield and nitrogen leaching in Florida, considering input parameter uncertainties. In this type of biological system modeling, uncertainties in predictions with respect to input parameter uncertainty are often not reported. Thus, the result of model verification could be misleading if there are large uncertainties in field observations, since single model prediction values cannot comprehensively represent heterogeneous field conditions. Instead, comparisons between the distributions of model simulations and field observations were recommended in this study. A two-factor split-plot field experiment was conducted with three nitrogen fertilizer levels (185, 247, and 309 kg N ha-1) and two irrigation levels (I1 and I2; I2 = 1.5 I1, where I1 is the irrigation demand calculated based on a daily soil water balance). Yield response to different nitrogen fertilizer and irrigation management levels was evaluated, and the cumulative nitrogen leaching was estimated for each of the treatments based on a nitrogen balance. Next, the field experiment treatments were simulated with the calibrated CERES-Maize model using parameter sets generated from parameter distributions derived with the generalized likelihood uncertainty estimation (GLUE) method in a previous study. Simulated dry matter yields and cumulative nitrogen leaching were compared to field-measured or estimated values. Measured total and marketable yields were not affected by irrigation level. Estimated nitrogen leaching increased significantly with higher levels of irrigation and nitrogen fertilizer application. The calibrated CERES-Maize model accurately predicted the phenology dates, with an error of 0 and 1 day for anthesis and maturity dates, respectively. The prediction uncertainties (due to uncertain input parameter values), as measured by the standard deviation (SD) in predicted anthesis and maturity dates, were only 1 and 2 days after planting, respectively. The model also accurately predicted the changes in dry matter yield caused by different nitrogen and irrigation levels, with a relative absolute error (RAE) less than 12% for all but one treatment. Due to the uncertainties in soil and genetic parameters, the prediction SD of simulated dry yields ranged from 655 kg ha-1 at I1 to 960 kg ha-1 at I2, while the observation SD ranged from 220 to 463 kg ha-1 for measured dry yields. The uncertainties in simulated dry yield were higher than the uncertainties of measured values due to relatively high variations in estimated genetic coefficients. The model performance could be improved further if the variations in estimated genetic coefficients could be reduced. The difference between the simulated and estimated nitrogen leaching amounts was significant and complex, ranging from -31 to 43 kg N ha-1 with an average absolute difference of 15.3%. This discrepancy was probably due to both the errors in estimation of potential nitrogen leaching in the field experiment using a mass balance approach and the inaccuracy of model predictions. Nevertheless, the increase in nitrogen leaching resulting from higher nitrogen fertilizer levels was correctly predicted. The uncertainties in simulated N leaching covered more than 67% of the uncertainties of estimated leaching for all but one treatment, indicating that estimated soil parameters via the GLUE method were able to represent the heterogeneity of field soil. In general, the CERES-Maize model is able to simulate sweet corn production under different management conditions sufficiently to allow exploration of tradeoffs between crop yield and nitrogen leaching for sweet corn production in Florida.

In lieu of the paired catchment approach: Hydrologic model change detection at the catchment scale

The paired catchment approach has been the predominant method for detecting the effects of disturbance on catchment‐scale hydrology. Notwithstanding, the utility of this approach is limited by regression model sample size, variability between paired catchments, type II error, and the inability of locating a long‐term suitable control. An increasingly common practice is to use rainfall‐runoff models to discern the effect of disturbance on hydrology, but few hydrologic model studies (1) consider problems associated with model identification, (2) use formal statistical methods to evaluate the significance of hydrologic change relative to variations in rainfall and streamflow, and (3) apply change detection models to undisturbed catchments to test the approach. We present an alternative method to the paired catchment approach and improve on stand‐alone hydrologic modeling to discern the effects of forest harvesting at the catchment scale. Our method combines rainfall‐runoff modeling to account for natural fluctuations in daily streamflow, uncertainty analyses using the generalized likelihood uncertainty estimation method to identify and separate hydrologic model uncertainty from unexplained variation, and GLS regression change detection models to provide a formal experimental framework for detecting changes in daily streamflow relative to variations in daily hydrologic and climatic data. We include statistical analyses of climate variation and a two‐part evaluation to explore model performance and account for unexplained variation. Evaluations consisted of applying our method to a control catchment and to a period prior to harvesting in a treated catchment to demonstrate that our method was capable of capturing the absence of land use change in an undisturbed catchment and capturing the absence of land use change during a period of no disturbance in the harvested catchment. In addition, we explore the sensitivity of our method to model identification, number of simulations, and likelihood thresholds for model identification. We show that an increase in the number of model simulations does not necessarily result in increased change detection performance. Our method is a potentially useful alternative to the paired catchment approach where reference catchments are not possible and to stand‐alone hydrologic modeling for detecting the effects of land use change on hydrology.

Evaluation of the subjective factors of the GLUE method and comparison with the formal Bayesian method in uncertainty assessment of hydrological models

Quantification of uncertainty of hydrological models has attracted much attention in the recent hydrological literature. Different results and conclusions have been reported which result from the use of different methods with different assumptions. In particular, the disagreement between the Generalized Likelihood Uncertainty Estimation (GLUE) and the Bayesian methods for assessing the uncertainty in conceptual watershed modelling has been widely discussed. What has been mostly criticized is the subjective choice as regards the influence of threshold value, number of sample simulations, and likelihood function in the GLUE method. In this study the impact of threshold values and number of sample simulations on the uncertainty assessment of GLUE is systematically evaluated, and a comprehensive evaluation about the posterior distribution, parameter and total uncertainty estimated by GLUE and a formal Bayesian approach using the Metropolis Hasting (MH) algorithm are performed for two well-tested conceptual hydrological models (WASMOD and DTVGM) in an arid basin from North China. The results show that in the GLUE method, the posterior distribution of parameters and the 95% confidence interval of the simulated discharge are sensitive to the choice of the threshold value as measured by the acceptable samples rate (ASR). However, when the threshold value in the GLUE method is high enough (i.e., when the ASR value is smaller than 0.1%), the posterior distribution of parameters, the 95% confidence interval of simulated discharge and the percent of observations bracketed by the 95% confidence interval (P-95CI) for the GLUE method approach those values estimated by the Bayesian method for both hydrological models. Second, in the GLUE method, the insufficiency of number of sample simulations will influence the maximum Nash-Sutcliffe (MNS) efficiency value when ASR is fixed. However, as soon as the number of sample simulations increases to 2 x 10(4) for WASMOD and to 8 x 10(4) for the DTVGM model the influence of number of sample simulations on the model simulation results becomes of minor importance. Third, the uncertainty in simulated discharges resulting from parameter uncertainty is much smaller than that resulting from the model structure uncertainty for both hydrological models. Fourth, the goodness of model fit as measured by the maximum Nash-Sutcliffe efficiency value is nearly the same for the GLUE and the Bayesian methods for both hydrological models. Thus this study provides useful information on the uncertainty assessment of hydrological models. (C) 2010 Elsevier B.V. All rights reserved.

Characterization of Petroleum-Hydrocarbon Fate and Transport in Homogeneous and Heterogeneous Aquifers Using a Generalized Uncertainty Estimation Method

This paper presents a generalized uncertainty estimation method (GUEM) to characterize the fate and transport of petroleum-hydrocarbon contaminants in subsurface environments. Compared to the conventional methods, GUEM employs the Metropolis-Hastings sampling algorithm to replace the conventional Monte Carlo algorithm; this algorithm has the advantage of reducing computational cost in obtaining realizations of uncertain parameters. The GUEM method is applied to a hypothetical homogenous and a real-world heterogonous site for demonstration studies. The first demonstration shows that GUEM generates outputs with wider bounds than conventional uncertainty characterization methods. This avoids overestimation of lower bounds and underestimation of upper bounds of resulting modeling outputs. Results from the second demonstration implied that the groundwater would not be suitable for the drinking water source after three years of natural attenuation and remediation actions should be taken to guarantee the groundwater safety. Even after taking a three-year pump-and-treat remediation action, it would pose risks as one can conclude that the benzene concentrations would violate the regulated environmental guideline with a possibility of over 0.9, and enhanced remediation actions are still desired to be taken for improving the groundwater quality. Despite the advantages in characterizing the fate and transport of contaminants, GUEM could be improved by introducing two correlated random variables in the sampling process for enhancing simulation accuracy. It is also expected to be integrated with traditional methods such as Monte Carlo method and generalized likelihood uncertainty estimation method to deal with hybrid fuzzy-random and interval-random inputs, respectively.

강우자료의 불확실성을 고려한 강우 유출 모형의 적용

강우유출모형의 입력 자료로 사용되는 강우 관측 자료의 불확실성이 유량예측에 미치는 영향을 분석하기 위하여 모형변수 검정의 불확실성 연구에서 사용하는 GLUE (Generalized Likelihood Uncertainty Estimation)방법을 입력 자료 부분으로 확장하여 적용 하였다. 독일의 Weida 유역의 강우 관측 자료를 바탕으로 구조적 및 비구조적인 불확실성 부분을 각각 구조적인 오차 수정 과정과 DUE (Data Uncertainty Engine)을 통하여 강우자료를 구성하였다. 이를 유역의 수문학적 작용을 고려하기 위해 선정한 집중형 강우유출모형, PDM (Probability Distribution Model)에 MC (Monte Carlo)와 GLUE 방법을 활용하여 적용하였다. MC검정변수들의 검정 후 반응 표면(Posterior response surface)을 검토하고 GLUE 의 반응검정 모형변수(Behavioural model parameter set)를 선택, 간략한 GLUE 유량곡선들을 계산하였다. 계산된 GLUE 유량곡선들을 모두 합하여 앙상블 유량을 산정하고, 이 유량의 90 분위를 강우량자료 및 모형변수 검정의 불확실성을 고려한 신뢰구간으로 제시하였다. PDM 모형의 결과는 유량곡선의 전구간에서 안정적인 모의 능력을 보여주고 있으나, 첨두유량 부분이 적게 산정되는 문제점을 보이고 있다. 본 연구에서 상대적으로 적은 수의 강우 시나리오 및 반응검정 모형변수의 적용이라는 한계에도 불구하고, GLUE 방법을 강우관측자료의 불확실성 부분으로 확장하여 강우자료 및 변수 검정의 불확실성을 고려한 모의된 유량예측의 신뢰구간의 적용가능성을 보여주고 있다. The effects of rainfall input uncertainty on predictions of stream flow are studied based extended GLUE (Generalized Likelihood Uncertainty Estimation) approach. The uncertainty in the rainfall data is implemented by systematic/non-systematic rainfall measurement analysis in Weida catchment, Germany. PDM (Probability Distribution Model) rainfall runoff model is selected for hydrological representation of the catchment. Using general correction procedure and DUE(Data Uncertainty Engine), feasible rainfall time series are generated. These series are applied to PDM in MC(Monte Carlo) and GLUE method; Posterior distributions of the model parameters are examined and behavioural model parameters are selected for simplified GLUE prediction of stream flow. All predictions are combined to develop ensemble prediction and 90 percentile of ensemble prediction, which are used to show the effects of uncertainty sources of input data and model parameters. The results show acceptable performances in all flow regime, except underestimation of the peak flows. These results are not definite proof of the effects of rainfall uncertainty on parameter estimation; however, extended GLUE approach in this study is a potential method which can include major uncertainty in the rainfall-runoff modelling.

Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling

In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes.

An empirical method to improve the prediction limits of the GLUE methodology in rainfall–runoff modeling

The generalized likelihood uncertainty estimation (GLUE) method is one of the most widely used methods for investigating the uncertainties in the water resources and environmental modeling. However, some researches have found that the percentage of the observations falling within the prediction limits provided by the GLUE is much lower than the given certainty level used to produce these prediction limits in many cases. One possible reason contributing to such a low enveloping efficiency is the fact that, as the GLUE method indiscriminatingly accepts the simulation output of the hydrological model as its input, the errors in the simulation output of the hydrological model will be directly reflected in the prediction limits provided by the GLUE method. So, it is suggested in this paper to modify the original GLUE methodology by applying a new procedure designed to at least partially correct the simulation/prediction of the hydrological model prior to the derivation of the prediction limits at each time step, in an attempt to improve the efficiency of the GLUE prediction limits in enveloping the real-world observations. To test this simple concept, both the original GLUE and the suggested modified GLUE methods have been employed to produce the prediction limits of runoff on two different catchments. In terms of the containing ratio, i.e. the percentage of the observed data bracketed by the respective runoff prediction limits, the modified GLUE method has shown substantial improvements over the original method, in both the calibration and the verification periods.

Assessment of flood forecasting lead time based on generalized likelihood uncertainty estimation approach

Real time updating of rainfall-runoff (RR) models is traditionally performed by state-space formulation in the context of flood forecasting systems. In this paper, however, we examine applicability of generalized likelihood uncertainty estimation (GLUE) approach in real time modification of forecasts. Real time updating and parameter uncertainty analysis was conducted for Abmark catchment, a part of the great Karkheh basin in south west of Iran. A conceptual-distributed RR model, namely ModClark, was used for basin simulation, such that the basin’s hydrograph was determined by the superposition of runoff generated by individual cells in a raster-based discretization. In real time updating of RR model by GLUE method, prior and posterior likelihoods were computed using forecast errors that were obtained from the results of behavioral models and real time recorded discharges. Then, prior and posterior likelihoods were applied to modify forecast confidence limits in each time step. Calibration of parameters was performed using historical data while distribution of parameters was modified in real time based on new data records. Two scenarios of rainfall forecast including prefect-rainfall-forecast and no-rainfall-forecast were assumed in absence of a robust rainfall forecast model in the study catchment. The results demonstrated that GLUE application could offer an acceptable lead time for peak discharge forecast at the expense of high computational demand.

Constraining the Sheffield dynamic global vegetation model using stream‐flow measurements in the United Kingdom

The biospheric water and carbon cycles are intimately coupled, so simulating carbon fluxes by vegetation also requires modelling of the water fluxes, with each component influencing the other. Observations of river streamflow integrate information at the catchment scale and are widely available over a long period; they therefore provide an important source of information for validating or calibrating vegetation models. In this paper, we analyse the performance of the Sheffield dynamic global vegetation model (SDGVM) for predicting river streamflow and quantifying how this information helps to constrain carbon flux predictions. The SDGVM is run for 29 large catchments in the United Kingdom. Annual streamflow estimates are compared with long time-series observations. In 23 out of the 29 catchments, the bias between model and observations is less than 50 mm, equivalent to less than 10% of precipitation. In the remaining catchments, larger errors are because of combinations of unpredictable causes, in particular various human activities and measurement issues and, in two cases, unidentified causes. In one of the catchments, we assess to what extent a knowledge of annual streamflow can constrain model parameters and in turn constrain estimates of gross primary production (GPP). For this purpose, we assume the model parameters are uncertain and constrain them by the streamflow observations using the generalized likelihood uncertainty estimation method. Comparing the probability density function of GPP with and without constraint shows that streamflow effectively constrains GPP, mainly by setting a low probability to GPP values below about 1100 g C-1 m2 yr-1 . In other words, streamflow observations allow the rejection of low values of GPP, so that the potential range of possible GPP values is almost halved.

Estimating soil hydraulic properties and their uncertainty: the use of stochastic simulation in the inverse modelling of the evaporation method

The evaporation method is an easy and reliable procedure for measuring soil hydraulic properties. Inverse modelling has been used to analyse the evaporation data facilitating the prediction of soil hydraulic properties. The conventional approach to solve the inverse solution is the use of the nonlinear least-squares (NLLS) technique. A major problem with such inverse modelling approaches is nonidentifiability, which is a condition where different parameter sets can lead to a similar flow response. In addition, NLLS only attempts to find optimum parameters that give the best fit to the observed data while not recognising the uncertainties in the models and observations made. The discrepancies of the NLLS approach may be alleviated by adopting the concept of generalized likelihood uncertainty estimation (GLUE), which acknowledges that many parameter sets within a model will give similar output to satisfy a given objective function. This is illustrated in this paper by using the GLUE method for estimating soil water retention and hydraulic conductivity from an evaporation experiment encompassing a range of soil types ranging from sand to heavy clay. Results show that the GLUE methodology can provide the estimates of the hydraulic properties and along with its uncertainty. The water retention curve can be predicted well from the range of potential 0 to −1000 cm, but the uncertainty associated with the unsaturated hydraulic conductivity prediction is quite high.

A non-linear and stochastic response surface method for Bayesian estimation of uncertainty in soil moisture simulation from a land surface model

Abstract. This study presents a simple and efficient scheme for Bayesian estimation of uncertainty in soil moisture simulation by a Land Surface Model (LSM). The scheme is assessed within a Monte Carlo (MC) simulation framework based on the Generalized Likelihood Uncertainty Estimation (GLUE) methodology. A primary limitation of using the GLUE method is the prohibitive computational burden imposed by uniform random sampling of the model's parameter distributions. Sampling is improved in the proposed scheme by stochastic modeling of the parameters' response surface that recognizes the non-linear deterministic behavior between soil moisture and land surface parameters. Uncertainty in soil moisture simulation (model output) is approximated through a Hermite polynomial chaos expansion of normal random variables that represent the model's parameter (model input) uncertainty. The unknown coefficients of the polynomial are calculated using limited number of model simulation runs. The calibrated polynomial is then used as a fast-running proxy to the slower-running LSM to predict the degree of representativeness of a randomly sampled model parameter set. An evaluation of the scheme's efficiency in sampling is made through comparison with the fully random MC sampling (the norm for GLUE) and the nearest-neighborhood sampling technique. The scheme was able to reduce computational burden of random MC sampling for GLUE in the ranges of 10%-70%. The scheme was also found to be about 10% more efficient than the nearest-neighborhood sampling method in predicting a sampled parameter set's degree of representativeness. The GLUE based on the proposed sampling scheme did not alter the essential features of the uncertainty structure in soil moisture simulation. The scheme can potentially make GLUE uncertainty estimation for any LSM more efficient as it does not impose any additional structural or distributional assumptions.