Jim E Freer

BAYESIAN ESTIMATION OF UNCERTAINTY IN RUNOFF PREDICTION AND THE VALUE OF DATA : AN APPLICATION OF THE GLUE APPROACH

This paper addresses the problem of evaluating the predictive uncertainty of TOPMODEL using the Bayesian Generalised Likelihood Uncertainty Estimation (GLUE) methodology in an application to the small Ringelbach research catchment in the Vosges, France. The wide range of parameter sets giving acceptable simulations is demonstrated, and uncertainty bands are presented based on different likelihood measures. It is shown how the distributions of predicted discharges are non-Gaussian and vary in shape through time and with discharge. Updating of the likelihood weights using Bayes equation is demonstrated after each year of record and it is shown how the additional data can be evaluated in terms of the way they constrain the uncertainty bands.

A decade of Predictions in Ungauged Basins (PUB)—a review

Abstract The Prediction in Ungauged Basins (PUB) initiative of the International Association of Hydrological Sciences (IAHS), launched in 2003 and concluded by the PUB Symposium 2012 held in Delft (23–25 October 2012), set out to shift the scientific culture of hydrology towards improved scientific understanding of hydrological processes, as well as associated uncertainties and the development of models with increasing realism and predictive power. This paper reviews the work that has been done under the six science themes of the PUB Decade and outlines the challenges ahead for the hydrological sciences community. Editor D. Koutsoyiannis Citation Hrachowitz, M., Savenije, H.H.G., Blöschl, G., McDonnell, J.J., Sivapalan, M., Pomeroy, J.W., Arheimer, B., Blume, T., Clark, M.P., Ehret, U., Fenicia, F., Freer, J.E., Gelfan, A., Gupta, H.V., Hughes, D.A., Hut, R.W., Montanari, A., Pande, S., Tetzlaff, D., Troch, P.A., Uhlenbrook, S., Wagener, T., Winsemius, H.C., Woods, R.A., Zehe, E., and Cudennec, C., 2013. A decade of Predictions in Ungauged Basins (PUB)—a review. Hydrological Sciences Journal, 58 (6), 1198–1255.

Toward a generalization of the TOPMODEL concepts: Topographic indices of hydrological similarity

Preliminary studies of the application of TOPMODEL to the 36-ha Ringelbach catchment suggested that the original form of exponential transmissivity function leading to the In (a/tan β) topographic index and first-order hyperbolic base flow recession curve is not appropriate to this catchment. Two alternative forms of topographic index and soil-topographic index are developed based on parabolic and linear transmissivity functions, leading to the more frequently observed second-order hyperbolic and exponential recession curves, respectively. It is shown how these can be used in the same way as the original to relate catchment average water table depths to local water table depths so that patterns of saturation can be evaluated. Two companion [Ambroise et al., this issue; Freer et al., this issue] papers show how the new parabolic index is used in the prediction of Ringelbach discharges, and how the limitations of the model are reflected in the estimated predictive uncertainties using the Generalised Likelihood Uncertainty Estimation (GLUE) approach.

Sensitivity analysis of environmental models

Sensitivity Analysis (SA) investigates how the variation in the output of a numerical model can be attributed to variations of its input factors. SA is increasingly being used in environmental modelling for a variety of purposes, including uncertainty assessment, model calibration and diagnostic evaluation, dominant control analysis and robust decision-making. In this paper we review the SA literature with the goal of providing: (i) a comprehensive view of SA approaches also in relation to other methodologies for model identification and application; (ii) a systematic classification of the most commonly used SA methods; (iii) practical guidelines for the application of SA. The paper aims at delivering an introduction to SA for non-specialist readers, as well as practical advice with best practice examples from the literature; and at stimulating the discussion within the community of SA developers and users regarding the setting of good practices and on defining priorities for future research. We present an overview of SA and its link to uncertainty analysis, model calibration and evaluation, robust decision-making.We provide a systematic review of existing approaches, which can support users in the choice of an SA method.We provide practical guidelines by developing a workflow for the application of SA and discuss critical choices.We give best practice examples from the literature and highlight trends and gaps for future research.

A unified approach for process-based hydrologic modeling: 1. Modeling concept

This work advances a unified approach to process-based hydrologic modeling to enable controlled and systematic evaluation of multiple model representations (hypotheses) of hydrologic processes and scaling behavior. Our approach, which we term the Structure for Unifying Multiple Modeling Alternatives (SUMMA), formulates a general set of conservation equations, providing the flexibility to experiment with different spatial representations, different flux parameterizations, different model parameter values, and different time stepping schemes. In this paper, we introduce the general approach used in SUMMA, detailing the spatial organization and model simplifications, and how different representations of multiple physical processes can be combined within a single modeling framework. We discuss how SUMMA can be used to systematically pursue the method of multiple working hypotheses in hydrology. In particular, we discuss how SUMMA can help tackle major hydrologic modeling challenges, including defining the appropriate complexity of a model, selecting among competing flux parameterizations, representing spatial variability across a hierarchy of scales, identifying potential improvements in computational efficiency and numerical accuracy as part of the numerical solver, and improving understanding of the various sources of model uncertainty.

Flood-plain mapping: a critical discussion of deterministic and probabilistic approaches

Abstract Different methodologies for flood-plain mapping are analysed and discussed by comparing deterministic and probabilistic approaches using hydrodynamic numerical solutions. In order to facilitate the critical discussion, state-of-art techniques in the field of flood inundation modelling are applied to a specific test site (River Dee, UK). Specifically, different flood-plain maps are derived for this test site. A first map is built by applying an advanced deterministic approach: use of a fully two-dimensional finite element model (TELEMAC-2D), calibrated against a historical flood extent, to derive a 1-in-100 year flood inundation map. A second map is derived by using a probabilistic approach: use of a simple raster-based inundation model (LISFLOOD-FP) to derive an uncertain flood extent map predicting the 1-in-100 year event conditioned on the extent of the 2006 flood. The flood-plain maps are then compared and the advantages and disadvantages of the two different approaches are critically discussed. Citation Di Baldassarre, G., Schumann, G., Bates, P. D., Freer, J. E. & Beven, K. J. (2010) Flood-plain mapping: a critical discussion of deterministic and probabilistic approaches. Hydrol. Sci. J. 55(3), 364–376.

Base cation concentrations in subsurface flow from a forested hillslope: The role of flushing frequency

A 20-m-wide trench was excavated to bedrock on a hillslope at the Panola Mountain Research Watershed in the Piedmont region of Georgia to determine the effect of upslope drainage area from the soil and bedrock surfaces on the geochemical evolution of base cation concentrations in subsurface flow. Samples were collected from ten 2-m sections and five natural soil pipes during three winter rainstorms in 1996. Base cation concentrations in hillslope subsurface flow were generally highest early and late in the storm response when flow rates were low, but during peak flow, concentrations varied little. Base cation concentrations in matrix flow from the 10 trench sections were unrelated to the soil surface drainage area and weakly inversely related to the bedrock surface drainage area. Base cation concentrations in pipe flow were lower than those in matrix flow and were also consistent with the inverse relation to bedrock surface drainage area found in matrix flow. The left side of the trench, which has the highest bedrock surface drainage area, had consistently lower mean base cation concentrations than the right side of the trench, which has the lowest bedrock surface drainage area. During moderate size rain events of about 20–40 mm, subsurface flow occurred only on the left side of the trench. The greater volume of water that has flowed through the left side of the trench appears to have resulted in greater leaching of base cations from soils and therefore lower base cation concentrations in subsurface flow than in flow from the right side of the trench. Alternatively, a greater proportion of flow that bypasses the soil matrix may have occurred through the hillslope on the left side of the trench than on the right side. Flushing frequency links spatial hillslope water flux with the evolution of groundwater and soil chemistry.

Stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology: Conditioning on head observations

A stochastic methodology to evaluate the predictive uncertainty in well capture zones in heterogeneous aquifers with uncertain parameters is presented. The approach is based on the generalized likelihood uncertainty estimation methodology. The hydraulic conductivity is modeled as a random space function allowing for the uncertainty that stems from the imperfect knowledge of the parameters of the correlation structure. Parameters are sampled from prior distributions and are used for the generation of a large number of hydraulic conductivity fields, which are subsequently used to solve the groundwater flow equation. A likelihood is calculated for every simulation, based on some goodness-of-fit measure between simulated heads and available observations. Using inverse particle tracking, a capture zone is determined which is assigned the likelihood calculated for that particular simulation. Statistical analysis of the ensemble of all simulations enables the predictive uncertainty of the well capture zones to be defined. Results are presented for a hypothetical test case and different likelihood definitions used in the conditioning process. The results show that the delineated capture zones are most sensitive to the mean hydraulic conductivity and the variance, whereas the integral scale of the variogram is the parameter with the smallest influence. For all likelihood measures the prior uncertainty is reduced considerably by introducing the observation heads, but the reduction is most effective for the very selective likelihood definition. The method presented can be used in real applications to quantify the uncertainty in the location and extent of well capture zones when little or no information is available about the hydraulic properties, through the conditioning on head observations.

New method developed for studying flow on hillslopes

Hillslope hydrologists have long assumed that the downslope movement of water and solutes can best be described by surface topography since gravitational potential largely dominates hydraulic gradients in steep terrain. Hence with the increased availability of Digital Terrain Maps (DTMs), surface topography is driving many popular hydrological models and is being used to estimate flow pathways in hydrological and geochemical models. This method may suffice at the catchment scale, but at the hillslope scale, flow pathways are not always determined by surface topography. It is at this critical scale (100–10,000 m2) that water flux and the chemical composition of soil water and groundwater can be measured as they move downslope. The complex interactions between water and solutes along hillslope subsurface flow paths have not been well documented. New evidence suggests that for steep hillslopes with thin soils, the fundamental control on hillslope flow paths is the bedrock surface.

A high‐resolution global flood hazard model

Abstract Floods are a natural hazard that affect communities worldwide, but to date the vast majority of flood hazard research and mapping has been undertaken by wealthy developed nations. As populations and economies have grown across the developing world, so too has demand from governments, businesses, and NGOs for modeled flood hazard data in these data‐scarce regions. We identify six key challenges faced when developing a flood hazard model that can be applied globally and present a framework methodology that leverages recent cross‐disciplinary advances to tackle each challenge. The model produces return period flood hazard maps at ∼90 m resolution for the whole terrestrial land surface between 56°S and 60°N, and results are validated against high‐resolution government flood hazard data sets from the UK and Canada. The global model is shown to capture between two thirds and three quarters of the area determined to be at risk in the benchmark data without generating excessive false positive predictions. When aggregated to ∼1 km, mean absolute error in flooded fraction falls to ∼5%. The full complexity global model contains an automatically parameterized subgrid channel network, and comparison to both a simplified 2‐D only variant and an independently developed pan‐European model shows the explicit inclusion of channels to be a critical contributor to improved model performance. While careful processing of existing global terrain data sets enables reasonable model performance in urban areas, adoption of forthcoming next‐generation global terrain data sets will offer the best prospect for a step‐change improvement in model performance.