Jim Freer

Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology

It may be endemic to mechanistic modelling of complex environmental systems that there are many different model structures and many different parameter sets within a chosen model structure that may be behavioural or acceptable in reproducing the observed behaviour of that system. This has been called the equifinality concept. The generalised likelihood uncertainty estimation (GLUE) methodology for model identification allowing for equifinality is described. Prediction within this methodology is a process of ensemble forecasting using a sample of parameter sets from the behavioural model space, with each sample weighted according to its likelihood measure to estimate prediction quantiles. This allows that different models may contribute to the ensemble prediction interval at different time steps and that the distributional form of the predictions may change over time. Any effects of model nonlinearity, covariation of parameter values and errors in model structure, input data or observed variables, with which the simulations are compared, are handled implicitly within this procedure. GLUE involves a number of choices that must be made explicit and can be therefore subjected to scrutiny and discussion. These include ways of combining information from different types of model evaluation or from different periods in a data assimilation context. An example application to rainfall-runoff modelling is used to illustrate the methodology, including the updating of likelihood measures.

The role of bedrock topography on subsurface storm flow

We conducted a detailed study of subsurface flow and water table response coupled with digital terrain analysis (DTA) of surface and subsurface features at the hillslope scale in Panola Mountain Research Watershed (PMRW), Georgia. Subsurface storm flow contributions of macropore and matrix flow in different sections along an artificial trench face were highly variable in terms of timing, peak flow, recession characteristics, and total flow volume. The trench flow characteristics showed linkages with the spatial tensiometer response defining water table development upslope. DTA of the ground surface did not capture the observed spatial patterns of trench flow or tensiometric response. However, bedrock surface topographic indices significantly improved the estimation of spatial variation of flow at the trench. Point-scale tensiometric data were also more highly correlated with the bedrock surface-based indices. These relationships were further assessed for temporal changes throughout a rainstorm. Linkages between the bedrock indices and the trench flow and spatial water table responses improved during the wetter periods of the rainstorm, when the hillslope became more hydrologically connected. Our results clearly demonstrate that in developing a conceptual framework for understanding the mechanisms of runoff generation, local bedrock topography may be highly significant at the hillslope scale in some catchments where the bedrock surface acts as a relatively impermeable boundary.

Equifinality and uncertainty in physically based soil erosion models : application of the GLUE methodology to WEPP-the water erosion prediction project-for sites in the UK and USA.

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.

Modelling the hydrological response of Mediterranean catchments, Prades, Catalonia. The use of distributed models as aids to hypothesis formulation

This paper attempts to extend the physical arguments underlying the distributed TOPMODEL concepts in an application to the strongly seasonal contributing area responses in two adjacent small mediterranean catchments in the Prades region of Catalonia, Spain. A perceptual model of hydrological response in these catchments is used to suggest possible modifications of the model in a hypothesis testing framework, including an attempt to modify the topographic index approach to reflect the expansion of the effective area of subsurface flow during the wetting-up sequence. It is found that slight improvements in modelling efficiency are possible but that different model parameter distributions are appropriate for different parts of the record. The model was much more successful for the catchment producing the higher runoff volumes.

Rethinking the contribution of drained and undrained grasslands to sediment-related water quality problems.

Grass vegetation has been recommended for use in the prevention and control of soil erosion because of its dense sward characteristics and stabilizing effect on the soil. A general assumption is that grassland environments suffer from minimal soil erosion and therefore present little threat to the water quality of surface waters in terms of sediment and sorbed contaminant pollution. Our data question this assumption, reporting results from one hydrological year of observations on a field-experiment monitoring overland flow, drain flow, fluxes of suspended solids, total phosphorus (TP), and molybdate-reactive phosphorus (<0.45 mum) in response to natural rainfall events. During individual rainfall events, 1-ha grassland lysimeters yield up to 15 kg of suspended solids, with concentrations in runoff waters of up to 400 mg L(-1). These concentrations exceed the water quality standards recommended by the European Freshwater Fisheries Directive (25 mg L(-1)) and the USEPA (80 mg L(-1)) and are beyond those reported to have caused chronic effects on freshwater aquatic organisms. Furthermore, TP concentrations in runoff waters from these field lysimeters exceeded 800 mug L(-1). These concentrations are in excess of those reported to cause eutrophication problems in rivers and lakes and contravene the ecoregional nutrient criteria in all of the USA ecoregions. This paper also examines how subsurface drainage, a common agricultural practice in intensively managed grasslands, influences the hydrology and export of sediment and nutrients from grasslands. This dataset suggests that we need to rethink the conceptual understanding of grasslands as non-erosive landscapes. Failure to acknowledge this will result in the noncompliance of surface waters to water quality standards.

Investigating the uncertainty in predicting responses to atmospheric deposition using the model of acidification of groundwater in catchments (MAGIC) within a generalised likelihood uncertainty estimation (GLUE) framework

This study investigates the uncertainty associated with the modelled response of a catchment to historic and predicted future acidic deposition for the period 1851–2041. The MAGICmodel is applied within a GLUE framework to the 3.88 km2 Afon Gwy catchment at Plynlimon, Wales. Nine million Monte Carlo simulations resulted in 5700 being accepted as behaviouralas defined by a fuzzy measure comparing observed to simulated variables. Model output and parameter sensitivity analysis indicate that, for this example where weathering rates are low,model dynamics are limited compared to control exerted by modelinitial conditions and by the specified acidic deposition boundary conditions. The results show that despite the small number of behavioural simulations, they are widely spread acrossthe ranges for most of the parameters varied. The GLUE methodology allows simulated prediction ranges for important variables to be presented as quantitative likelihood weighteduncertainty estimates rather than a single prediction for eachvariable over time.

Struggling with Epistemic Uncertainties in Environmental Modelling of Natural Hazards

Epistemic uncertainties create difficulties for the quantitative estimation of uncertainties associated with environmental models. The nature of the issues involved is discussed, particularly in how to assign likelihood values to models when the forcing data and evaluation data might both be subject to epistemic uncertainties. A case study of a rainfall-runoff model of the River Brue catchment is developed with the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. Model evaluation is carried out using limits of acceptability set from considerations of the available data prior to running a model, while the errors associated with a model are treated non-parametrically for different parts of the hydrograph.