Generalized Likelihood Uncertainty Estimation Research Articles

Understanding uncertainties when inferring mean transit times of water trough tracer-based lumped-parameter models in Andean tropical montane cloud forest catchments

Abstract. Weekly samples from surface waters, springs, soil water and rainfall were collected in a 76.9 km2 mountain rain forest catchment and its tributaries in southern Ecuador. Time series of the stable water isotopes δ18O and δ2H were used to calculate mean transit times (MTTs) and the transit time distribution functions (TTDs) solving the convolution method for seven lumped-parameter models. For each model setup, the generalized likelihood uncertainty estimation (GLUE) methodology was applied to find the best predictions, behavioral solutions and parameter identifiability. For the study basin, TTDs based on model types such as the linear–piston flow for soil waters and the exponential–piston flow for surface waters and springs performed better than more versatile equations such as the gamma and the two parallel linear reservoirs. Notwithstanding both approaches yielded a better goodness of fit for most sites, but with considerable larger uncertainty shown by GLUE. Among the tested models, corresponding results were obtained for soil waters with short MTTs (ranging from 2 to 9 weeks). For waters with longer MTTs differences were found, suggesting that for those cases the MTT should be based at least on an intercomparison of several models. Under dominant baseflow conditions long MTTs for stream water ≥ 2 yr were detected, a phenomenon also observed for shallow springs. Short MTTs for water in the top soil layer indicate a rapid exchange of surface waters with deeper soil horizons. Differences in travel times between soils suggest that there is evidence of a land use effect on flow generation.

Parameter uncertainty analysis of reservoir operating rules based on implicit stochastic optimization

Reservoir operating rules are often derived using either a fitting or a simulation-based optimization method in the context of implicit stochastic optimization. Analysis of the parameter uncertainty in reservoir operating rules and their impact is necessary for robust solutions. In the present study, parameter uncertainty for reservoir operating rules is analyzed using two statistical methods, linear regression (LR) and Bayesian simulation (BS). LR estimates the confidence interval based on fitting the operating rules to the optimal deterministic solution. BS deals with the operating rule parameters as stochastic variables and treats the goodness-of-fit to the optimal deterministic solution or the operation profits as the likelihood measure. Two alternative techniques, the generalized likelihood uncertainty estimation (GLUE) and Markov Chain Monte Carlo method (MCMC), are implemented for the BS uncertainty analysis. These methods were applied to the operating rules of China’s Three Gorges Reservoir. The LR performed less than the BS, and the MCMC outperformed the GLUE. Even for the BS methods, the operation profits criterion was better than the goodness-of-fit criterion for deriving the reservoir operating rules.

Using CV-GLUE procedure in analysis of wetland model predictive uncertainty

This study develops a procedure that is related to Generalized Likelihood Uncertainty Estimation (GLUE), called the CV-GLUE procedure, for assessing the predictive uncertainty that is associated with different model structures with varying degrees of complexity. The proposed procedure comprises model calibration, validation, and predictive uncertainty estimation in terms of a characteristic coefficient of variation (characteristic CV). The procedure first performed two-stage Monte-Carlo simulations to ensure predictive accuracy by obtaining behavior parameter sets, and then the estimation of CV-values of the model outcomes, which represent the predictive uncertainties for a model structure of interest with its associated behavior parameter sets. Three commonly used wetland models (the first-order K–C* model, the plug flow with dispersion model, and the Wetland Water Quality Model; WWQM) were compared based on data that were collected from a free water surface constructed wetland with paddy cultivation in Taipei, Taiwan. The results show that the first-order K–C* model, which is simpler than the other two models, has greater predictive uncertainty. This finding shows that predictive uncertainty does not necessarily increase with the complexity of the model structure because in this case, the more simplistic representation (first-order K–C* model) of reality results in a higher uncertainty in the prediction made by the model. The CV-GLUE procedure is suggested to be a useful tool not only for designing constructed wetlands but also for other aspects of environmental management.

Monte Carlo-based calibration and uncertainty analysis of a coupled plant growth and hydrological model

Abstract. Computer simulations are widely used to support decision making and planning in the agriculture sector. On the one hand, many plant growth models use simplified hydrological processes and structures – for example, by the use of a small number of soil layers or by the application of simple water flow approaches. On the other hand, in many hydrological models plant growth processes are poorly represented. Hence, fully coupled models with a high degree of process representation would allow for a more detailed analysis of the dynamic behaviour of the soil–plant interface. We coupled two of such high-process-oriented independent models and calibrated both models simultaneously. The catchment modelling framework (CMF) simulated soil hydrology based on the Richards equation and the van Genuchten–Mualem model of the soil hydraulic properties. CMF was coupled with the plant growth modelling framework (PMF), which predicts plant growth on the basis of radiation use efficiency, degree days, water shortage and dynamic root biomass allocation. The Monte Carlo-based generalized likelihood uncertainty estimation (GLUE) method was applied to parameterize the coupled model and to investigate the related uncertainty of model predictions. Overall, 19 model parameters (4 for CMF and 15 for PMF) were analysed through 2 × 106 model runs randomly drawn from a uniform distribution. The model was applied to three sites with different management in Müncheberg (Germany) for the simulation of winter wheat (Triticum aestivum L.) in a cross-validation experiment. Field observations for model evaluation included soil water content and the dry matter of roots, storages, stems and leaves. The shape parameter of the retention curve n was highly constrained, whereas other parameters of the retention curve showed a large equifinality. We attribute this slightly poorer model performance to missing leaf senescence, which is currently not implemented in PMF. The most constrained parameters for the plant growth model were the radiation-use efficiency and the base temperature. Cross validation helped to identify deficits in the model structure, pointing out the need for including agricultural management options in the coupled model.

Prediction limits of a catchment hydrological model using different estimates of ETp

Summary A joint deterministic–stochastic protocol based on Monte Carlo simulations (MCS) was applied to the modelling of a medium size catchment using two significantly different sets of potential evapotranspiration (ET p ) data, estimated through a Penman-based method. Modelling error was accounted using the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. Both, water routing and water balance related parameters were considered in the analysis. The research revealed that the hypothesis of the less correct ET p data set being appropriate for the current modelling could not be rejected since model parameters adjusted to compensate for the use of significantly different ET p data sets. The GLUE analysis demonstrated that the model predictions exhibited some sensitivity to the hydraulic conductivity of one of the geological layers. Furthermore, the study revealed a considerable error attached to the simulation of both high and low flows, as well as, piezometric levels, for every ET p data set, which was most likely magnified by the coarse time and spatial scales used in the current modelling.

입자군집최적화 알고리듬을 이용한 효율적인 TOPMODEL의 불확실도 분석

멀티모달 최적화 알고리듬의 일종인 ISPSO와 불확실도 분석기법인 GLUE를 결합한 ISPSO-GLUE 기법을 TOPMODEL의 불확실도 분석에 적용하였으며, 그 결과를 GLUE 기법과 비교하였다. 두 기법 모두 같은 횟수만큼 모형을 실행하였을 때 ISPSO-GLUE 기법의 누적성능이 더 좋아지는 시점을 발견할 수 있었으며, 그 이후로도 ISPSO-GLUE 기법은 GLUE 기법과는 달리 점진적인 성능의 향상을 보여 주었다. 두 기법이 비슷한 모양과 양상의 95% 불확실도 구간을 생성하였다. 하지만 ISPSO-GLUE 기법이 약5.4배 더 많은 관측치를 포함하는 것으로 나타났으며 GLUE 기법에 비해 훨씬 적은횟수의 모형실행으로도 좋은 성능의 불확실도 구간을 얻을 수 있는 것으로 나타났다. ISPSO-GLUE 기법과 비교했을 때GLUE 기법이 최대 첨두유량의 감쇠곡선 부분에서 불확실도를 과대평가하였다. 이 시간대에 대해서는 GLUE의 경우 불확실도 를 줄이기 위해 더 많은 행동모형들을 찾을 필요가 있다. ISPSO-GLUE 기법이 정량적인 성능평가에서 훨씬 많은 관측치를 포함할 수 있었다는 것은 이 기법의 가능성을 잘 보여 주었다고 할 수 있으며, 특히 계산적으로 값비싼 수문모형에서는 보다 큰 성능의 차이를 보일 것으로 기대된다. We applied the ISPSO-GLUE method, which integrates the Isolated-Speciation-based Particle Swarm Optimization (ISPSO) with the Generalized Likelihood Uncertainty Estimation (GLUE) method, to the uncertainty analysis of the Topography Model (TOPMODEL) and compared its performance with that of the GLUE method. When we performed the same number of model runs for the both methods, we were able to identify the point where the performance of ISPSO-GLUE exceeded that of GLUE, after which ISPSOGLUE kept improving its performance steadily while GLUE did not. When we compared the 95% uncertainty bounds of the two methods, their general shapes and trends were very similar, but those of ISPSO-GLUE enclosed about 5.4 times more observed values than those of GLUE did. What it means is that ISPSOGLUE requires much less number of parameter samples to generate better performing uncertainty bounds. When compared to ISPSO-GLUE, GLUE overestimated uncertainty in the recession limb following the maximum peak streamflow. For this recession period, GLUE requires to find more behavioral models to reduce the uncertainty. ISPSO-GLUE can be a promising alternative to GLUE because the uncertainty bounds of the method were quantitatively superior to those of GLUE and, especially, computationally expensive hydrologic models are expected to greatly take advantage of the feature.

Evaluation of the hydrology of the IBIS land surface model in a semi‐arid catchment

AbstractThis paper evaluates the Integrated BIosphere Simulator (IBIS) land surface model using daily soil moisture data over a 3‐year period (2005–2007) at a semi‐arid site in southeastern Australia, the Stanley catchment, using the Monte Carlo generalized likelihood uncertainty estimation (GLUE) approach. The model was satisfactorily calibrated for both the surface 30 cm and full profile 90 cm. However, full‐profile calibration was not as good as that for the surface, which results from some deficiencies in the evapotranspiration component in IBIS. Relatively small differences in simulated soil moisture were associated with large discrepancies in the predictions of surface runoff, drainage and evapotranspiration. We conclude that while land surface schemes may be effective at simulating heat fluxes, they may be ineffective for prediction of hydrology unless the soil moisture is accurately estimated. Sensitivity analyses indicated that the soil moisture simulations were most sensitive to soil parameters, and the wilting point was the most identifiable parameter. Significant interactions existed between three soils parameters: porosity, saturated hydraulic conductivity and Campbell ‘b’ exponent, so they could not be identified independent of each other. There were no significant differences in parameter sensitivity and interaction for different hydroclimatic years. Even though the data record contained a very dry year and another year with a very large rainfall event, this indicated that the soil model could be calibrated without the data needing to explore the extreme range of dry and wet conditions. IBIS was much less sensitive to vegetation parameters. The leaf area index (LAI) could affect the mean of daily soil moisture time series when LAI < 1, while the variance of the soil moisture time series was sensitive to LAI > 1. IBIS was insensitive to the Jackson rooting parameter, suggesting that the effect of the rooting depth distribution on predictions of hydrology was insignificant. Copyright © 2014 John Wiley & Sons, Ltd.

Imidacloprid concentrations in paddy rice fields in northern Vietnam: measurement and probabilistic modeling

Uncertainties associated with pesticide exposure forecasts arise from many sources such as spatial and temporal variability of factors influencing pesticide behavior, inaccuracies in the measurement or estimation of input parameters and deficiencies in model structure. It is well acknowledged that, at least to some extent, simulation uncertainties should be accounted for when technical and political strategies are developed to mitigate pesticide exposure. We monitored the fate of the insecticide imidacloprid in a paddy rice field in Chieng Khoi watershed, Northern Vietnam. Pesticide fate was modeled using a new dynamic model together with the General Likelihood Uncertainty Estimation (GLUE) approach. A 95 % prediction uncertainty (PU) band was computed accounting for uncertainties in pesticide parameters, management practices, and weather conditions. As assessment criterion we used the Nash and Sutcliffe modeling efficiency (NSE). Measured paddy water concentrations of imidacloprid reached up to 53 μg L−1, paddy soil concentrations up to 9 μg kg−1. Calculated PU bands were in good agreement with field measurements. The field-scale model was extended to simulate pesticide fate in connected paddies. Imidacloprid concentrations in the afflux of the stream were estimated to be up to 83 μg L−1 under the current management practice in the research area. The loss of imidacloprid to the stream was assessed to range between 21 and 68 % of applied mass. Future studies, however, should focus on assessing loads of pesticides further widely used in connected paddies to help decision makers and farmers to adjust management strategies of protecting the environment.

Uncertainty-based multi-criteria calibration of rainfall-runoff models: a comparative study

This study compares formal Bayesian inference to the informal generalized likelihood uncertainty estimation (GLUE) approach for uncertainty-based calibration of rainfall-runoff models in a multi-criteria context. Bayesian inference is accomplished through Markov Chain Monte Carlo (MCMC) sampling based on an auto-regressive multi-criteria likelihood formulation. Non-converged MCMC sampling is also considered as an alternative method. These methods are compared along multiple comparative measures calculated over the calibration and validation periods of two case studies. Results demonstrate that there can be considerable differences in hydrograph prediction intervals generated by formal and informal strategies for uncertainty-based multi-criteria calibration. Also, the formal approach generates definitely preferable validation period results compared to GLUE (i.e., tighter prediction intervals that show higher reliability) considering identical computational budgets. Moreover, non-converged MCMC (based on the standard Gelman–Rubin metric) performance is reasonably consistent with those given by a formal and fully-converged Bayesian approach even though fully-converged results requires significantly larger number of samples (model evaluations) for the two case studies. Therefore, research to define alternative and more practical convergence criteria for MCMC applications to computationally intensive hydrologic models may be warranted.

Process-based simple model for simulating sugarcane growth and production

Dynamic simulation models can increase research efficiency and improve risk management of agriculture. Crop models are still little used for sugarcane (Saccharum spp.) because the lack of understanding of their capabilities and limitations, lack of experience in calibrating them, difficulties in evaluating and using models, and a general lack of model credibility. This paper describes the biophysics and shows a statistical evaluation of a simple sugarcane processbased model coupled with a routine for model calibration. Classical crop model approaches were used as a framework for this model, and fitted algorithms for simulating sucrose accumulation and leaf development driven by a source-sink approach were proposed. The model was evaluated using data from five growing seasons at four locations in Brazil, where crops received adequate nutrients and good weed control. Thirteen of the 27 parameters were optimized using a Generalized Likelihood Uncertainty Estimation algorithm using the leave-one-out cross-validation technique. Model predictions were evaluated using measured data of leaf area index, stalk and aerial dry mass, and sucrose content, using bias, root mean squared error, modeling efficiency, correlation coefficient and agreement index. The model well simulated the sugarcane crop in Southern Brazil, using the parameterization reported here. Predictions were best for stalk dry mass, followed by leaf area index and then sucrose content in stalk fresh mass.

GLUE based marine X-band weather radar data calibration and uncertainty estimation

The Generalized Likelihood Uncertainty Estimation methodology (GLUE) is investigated for radar rainfall calibration and uncertainty assessment. The method is used to calibrate radar data collected by a Local Area Weather Radar (LAWR).In contrast to other LAWR data calibrations, the method combines calibration with uncertainty estimation. Instead of searching for a single set of calibration parameters, the method uses the observations to construct distributions of the calibration parameters. These parameter sets provide valuable knowledge of parameter sensitivity and the uncertainty.Two approaches are analyzed; the static calibration approach, where the LAWR is calibrated once for a long period and the dynamic approach, where the estimate is continuously adjusted based on ground observations.The analysis illustrates that the static calibration performs insufficiently, whereas the dynamic adjustment improves the performance significantly.It is found that even if the dynamic adjustment method is used the uncertainty of rainfall estimates can still be significant.

Effect of Baseflow Separation on Uncertainty of Hydrological Modeling in the Xinanjiang Model

Based on the idea of inputting more available useful information for evaluation to gain less uncertainty, this study focuses on how well the uncertainty can be reduced by considering the baseflow estimation information obtained from the smoothed minima method (SMM). The Xinanjiang model and the generalized likelihood uncertainty estimation (GLUE) method with the shuffled complex evolution Metropolis (SCEM-UA) sampling algorithm were used for hydrological modeling and uncertainty analysis, respectively. The Jiangkou basin, located in the upper of the Hanjiang River, was selected as case study. It was found that the number and standard deviation of behavioral parameter sets both decreased when the threshold value for the baseflow efficiency index increased, and the high Nash-Sutcliffe efficiency coefficients correspond well with the high baseflow efficiency coefficients. The results also showed that uncertainty interval width decreased significantly, while containing ratio did not decrease by much and the simulated runoff with the behavioral parameter sets can fit better to the observed runoff, when threshold for the baseflow efficiency index was taken into consideration. These implied that using the baseflow estimation information can reduce the uncertainty in hydrological modeling to some degree and gain more reasonable prediction bounds.

Uncertainty Quantification of Hydrologic Model

Generalized Likelihood Uncertainty Estimation (GLUE), a simplified Bayesian method, was adopted to determine the parametric uncertainty in hydrological modeling. A preliminary analysis of the summer flows of the Kootenay Watershed, Canada, was modeled to portray a typical uncertainty analysis procedure. SLURP, a robust hydrologic model was chosen for this procedure. The results demonstrated the viability of applying the GLUE method in conjunction with the SLURP hydrological model, following which the posterior probability distributions of the parameters was analyzed. The performance of this technique was verified by examining the flows’ prediction intervals for a period of 2 years, enabling valid future hydrological forecasting for the watershed.

Flood modelling: parameterisation and inflow uncertainty

This paper presents an analysis of uncertainty in hydraulic modelling of floods, focusing on the inaccuracy caused by inflow errors and parameter uncertainty. In particular, the study develops a method to propagate the uncertainty induced by, firstly, application of a stage–discharge rating curve and, secondly, parameterisation of a one-dimensional hydraulic model by way of the power function and the conditioning of Manning's roughness coefficients. The proposed methodology was applied to a 98 km reach of the River Po, Italy. Model performance was evaluated using two independent sets of observed water levels in the river reach within a generalised likelihood uncertainty estimation framework. The inflow uncertainty was found to have a greater contribution to the overall uncertainty of the 1D model than the roughness parameters. Independent parameter conditioning and validation, as well as the uncertainty analysis, showed satisfactory model performance. When conditioned on one flood event, the model adequately simulated flood levels and high water marks for another (independent) event, as the observations were within 90% confidence interval of the simulation ensemble.

Impacts of climate and catastrophic forest changes on streamflow and water balance in a mountainous headwater stream in Southern Alberta

Abstract. Rivers in Southern Alberta are vulnerable to climate change because much of the river water originates as snow in the eastern slopes of the Rocky Mountains. Changes in likelihood of forest disturbance (wildfire, insects, logging, etc.) may also have impacts that are compounded by climate change. This study evaluates the impacts of climate and forest changes on streamflow in the upper parts of the Oldman River in Southern Alberta using a conceptual hydrological model, HBV-EC (Hydrologiska Byråns attenbalansavdelning, Environment Canada), in combination with a stochastic weather generator (LARS-WG) driven by GCM (global climate model) output climate data. Three climate change scenarios (A1B, A2 and B1) are selected to cover the range of possible future climate conditions (2020s, 2050s, and 2080s). The GCM projected less than a 10% increase in precipitation in winter and a similar amount of precipitation decrease in summer. These changes in projected precipitation resulted in up to a 200% (9.3 mm) increase in winter streamflow in February and up to a 63% (31.2 mm) decrease in summer flow in June. Flow also decreased in July and August, when irrigation is important; these reduced river flows during this season could impact agriculture production. The amplification in the streamflow is mostly driven by the projected increase in temperature that is predicted to melt winter snow earlier, resulting in lower water availability during the summer. Uncertainty analysis was completed using a guided GLUE (generalized likelihood uncertainty estimation) approach to obtain the best 100 parameter sets and associated ranges of streamflows. The impacts of uncertainty in streamflows were higher in spring and summer than in winter and fall. Forest change compounded the climate change impact by increasing the winter flow; however, it did not reduce the summer flow.

Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation

Abstract. In recent years, a strong debate has emerged in the hydrologic literature regarding how to properly treat nontraditional error residual distributions and quantify parameter and predictive uncertainty. Particularly, there is strong disagreement whether such uncertainty framework should have its roots within a proper statistical (Bayesian) context using Markov chain Monte Carlo (MCMC) simulation techniques, or whether such a framework should be based on a quite different philosophy and implement informal likelihood functions and simplistic search methods to summarize parameter and predictive distributions. This paper is a follow-up of our previous work published in Vrugt and Sadegh (2013) and demonstrates that approximate Bayesian computation (ABC) bridges the gap between formal and informal statistical model–data fitting approaches. The ABC methodology has recently emerged in the fields of biology and population genetics and relaxes the need for an explicit likelihood function in favor of one or multiple different summary statistics that measure the distance of each model simulation to the data. This paper further studies the theoretical and numerical equivalence of formal and informal Bayesian approaches using discharge and forcing data from different watersheds in the United States, in particular generalized likelihood uncertainty estimation (GLUE). We demonstrate that the limits of acceptability approach of GLUE is a special variant of ABC if each discharge observation of the calibration data set is used as a summary diagnostic.

An Interval-Deviation Approach for hydrology and water quality model evaluation within an uncertainty framework

Summary Uncertainty assessment is becoming one of the main topics in hydrology and water resources. In this study, an Interval-Deviation Approach (IDA) was designed and incorporated into the process of model evaluation. The proposed IDA was validated in a real application of the Soil and Water Assessment Tool (SWAT) and Generalized Likelihood Uncertainty Estimation (GLUE) in the Three Gorges Reservoir Area (TGRA), China. Compared with the traditional point-to-point comparison between measured and predicted data, the main superiority of the IDA is its innovative theory that models should be evaluated by each absolute distance between the paired uncertainty intervals or probability distribution for each measured and predicted data. In addition, the IDA can be used to quantify the possible range of model performance in a real application of the SWAT. This proposed IDA can be useful for error form indicators and models by providing a substitute method to facilitate enhanced evaluation of watershed models within an uncertainty framework.

Extending the ROMUL model to simulate the dynamics of dissolved and sorbed C and N compounds in decomposing boreal mor

Organic matter (OM) decomposition plays a key role in maintaining the carbon (C) and nutrient balance of forest ecosystems. When including nutrients and C compounds in coupled soil water and solute transport models, decomposition needs to be explicitly quantified. To meet this requirement, we extended the ROMUL decomposition model with routines that describe: (i) the fractionation of the total C and nitrogen (N) released by ROMUL into their intermediate decomposition products and end products, (ii) the biodegradation of the intermediate decomposition products into the end products, and (iii) the adsorption/desorption of the compounds on the surfaces of OM. The resulting model was tested against data on the measured amounts of C and N compounds in soil water (dissolved concentrations) and in the extractable pool (total dissolved and sorbed amount) of mor samples during incubation in a laboratory. The parameterisation and structural competence of the model, as well as the quality of the underlying data, were analysed using the generalised likelihood uncertainty estimation (GLUE) procedure. Certain combinations of parameter values were found necessary to produce eligible simulation results due to a complex interplay of the model parameters. The model proved sensitive to most parameters, and the highest identification potential was found for parameters controlling the adsorption of high molecular weight organic C and N, the fractionation of total N into ammonium and organic N, and the biodegradation of high-molecular-weight organic N. The model was structurally compatible with the measured concentrations of different C and N compounds in soil water. The results demonstrate that reliable estimates of the extractable pools of C and N compounds are particularly important for the model. Additional data, as well as fixing the values for a subset of model parameters, would enhance the parameter identifiability and enable further analyses of the structural competence of the model.

GLUE: 20 years on

AbstractThis paper reviews the use of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology in the 20 years since the paper by Beven and Binley in Hydrological Processes in (1992), which is now one of the most highly cited papers in hydrology. The original conception, the on‐going controversy it has generated, the nature of different sources of uncertainty and the meaning of the GLUE prediction uncertainty bounds are discussed. The hydrological, rather than statistical, arguments about the nature of model and data errors and uncertainties that are the basis for GLUE are emphasized. The application of the Institute of Hydrology distributed model to the Gwy catchment at Plynlimon presented in the original paper is revisited, using a larger sample of models, a wider range of likelihood evaluations and new visualization techniques. It is concluded that there are good reasons to reject this model for that data set. This is a positive result in a research environment in that it requires improved models or data to be made available. In practice, there may be ethical issues of using outputs from models for which there is evidence for model rejection in decision making. Finally, some suggestions for what is needed in the next 20 years are provided. © 2013 The Authors.Hydrological Processespublished by John Wiley & Sons, Ltd.

Informal uncertainty analysis (GLUE) of continuous flow simulation in a hybrid sewer system with infiltration inflow – consistency of containment ratios in calibration and validation?

Abstract. Monitoring of flows in sewer systems is increasingly applied to calibrate urban drainage models used for long-term simulation. However, most often models are calibrated without considering the uncertainties. The generalized likelihood uncertainty estimation (GLUE) methodology is here applied to assess parameter and flow simulation uncertainty using a simplified lumped sewer model that accounts for three separate flow contributions: wastewater, fast runoff from paved areas, and slow infiltrating water from permeable areas. Recently GLUE methodology has been critisised for generating prediction limits without statistical coherence and consistency and for the subjectivity in the choice of a threshold value to distinguish "behavioural" from "non-behavioural" parameter sets. In this paper we examine how well the GLUE methodology performs when the behavioural parameter sets deduced from a calibration period are applied to generate prediction bounds in validation periods. By retaining an increasing number of parameter sets we aim at obtaining consistency between the GLUE generated 90% prediction limits and the actual containment ratio (CR) in calibration. Due to the large uncertainties related to spatio-temporal rain variability during heavy convective rain events, flow measurement errors, possible model deficiencies as well as epistemic uncertainties, it was not possible to obtain an overall CR of more than 80%. However, the GLUE generated prediction limits still proved rather consistent, since the overall CRs obtained in calibration corresponded well with the overall CRs obtained in validation periods for all proportions of retained parameter sets evaluated. When focusing on wet and dry weather periods separately, some inconsistencies were however found between calibration and validation and we address here some of the reasons why we should not expect the coverage of the prediction limits to be identical in calibration and validation periods in real-world applications. The large uncertainties result in wide posterior parameter limits, that cannot be used for interpretation of, for example, the relative size of paved area vs. the size of infiltrating area. We should therefore try to learn from the significant discrepancies between model and observations from this study, possibly by using some form of non-stationary error correction procedure, but it seems crucial to obtain more representative rain inputs and more accurate flow observations to reduce parameter and model simulation uncertainty.