Keith Beven

• Professor (Full) at Lancaster University

The Limits of Acceptability approach has been demonstrated to be an effective conditioning tool due to its capacity to consider epistemic uncertainty. However, its application faces two challenges—the low efficiency when random sampling is used and the difficulty in setting limits prior to calibration. Here an algorithm DREAM(LoAX) was developed an...

Few studies attempt to measure changes to discharge hydrographs during floods resulting from nature-based Solutions (NbS) for risk mitigation. The Q-NFM project in the UK has sought to measure and compare such changes for a wide range of NbS pilots applied to managed grasslands and woodlands. Also measured were underlying shifts in key hydrological...

The starting point for this study is the simulation study of Metcalfe et al. (2018) which suggested that retention times of the order of 10 h are required for natural flood management storage features to have a maximum effect on large flow peaks. A analysis of the celerity characteristics for some log jams at Tebay Gill, Cumbria (upland UK), sugges...

This study proposes using a Turing-like test for model evaluations and invalidations based on evidence of epistemic uncertainties in event runoff coefficients. Applying the consequent “limits of acceptability” results in all the 100 000 model parameter sets being rejected. However, applying the limits, together with an allowance for timing errors,...

There is a general trend toward the increasing inclusion of uncertainty estimation in the environmental modelling domain. We present the Consortium on Risk in the Environment: Diagnostics, Integration, Benchmarking, Learning and Elicitation (CREDIBLE) Uncertainty Estimation (CURE) toolbox, an open-source MATLABTM toolbox for uncertainty estimation...

This commentary discusses a framework for the benchmarking of hydrological models for different purposes when the datasets for different catchments might involve epistemic uncertainties. The approach might be expected to result in an ensemble of models that might be used in prediction (including models of different types) but also provides for mode...

While it is known that antecedent conditions and rainfall profiles contribute to the nonlinearity of streamflow response and that hydrograph shape can be dependent on the nature of rainfall inputs, how antecedent conditions (with similar rainfall inputs) impact hydrograph shape is less known. Here, a data-based mechanistic (DBM) approach is applied...

There is a general trend for increasing inclusion of uncertainty estimation in the environmental modelling domain. We present the CREDIBLE Uncertainty Estimation (CURE) Toolbox, an open source MATLABTM toolbox for uncertainty estimation aimed at scientists and practitioners that are not necessarily experts in uncertainty estimation. The toolbox foc...

This paper has taken a distributed modelling approach to examine the potential for hillslope storage bunds as a Natural Flood Management (NFM) strategy to mitigate the effects of downstream flooding if deployed extensively in the 209 km2 River Kent catchment in Cumbria (UK). To do so, a novel invalidation approach has been taken to calibrate an ens...

Part 1 of this study discussed the concept of using a form of Turing‐like Test for model evaluation, together with eight principles for implementing such an approach. In this part, the framing of fitness‐for‐purpose as a Turing‐like Test is discussed, together with an example application of trying to assess whether a rainfall‐runoff model might be...

Model invalidation is a good thing. It means that we are forced to reconsider either model structures or the available data more closely, that is to challenge our fundamental understanding of the problem at hand. It is not easy, however, to decide when a model should be invalidated, when we expect that the sources of uncertainty in environmental mo...

The representation of rainfall is important for hydrological modelling, particularly for spatially distributed models. Accurate estimation of rainfall is particularly challenging in mountainous regions where observations are often sparse relative to the spatial variability of rainfall, making interpolation challenging. In these regions, orographic...

There is a no lack of significant open questions in the field of hydrology. How will hydrological connectivity between freshwater bodies be altered by future human alterations to the hydrological cycle? Where does water go when it rains? Or what is the future space-time variability of flood and drought events? However, the answers to these question...

Inspired by a quotation from Howard Cook in 1946, this paper traces the evolution of the infiltration theory of runoff from the work of Robert Horton and LeRoy Sherman in the 1930s to the early digital computer models of the 1970s and 1980s. The reasons for the popularity of the infiltration theory are considered and its impact on the way in which...

After some background about what I have learned from a career in hydrological modelling, I present some opinions about how we might make progress in improving hydrological models in future including how to decide whether a model is fit for purpose; how to improve process representations in hydrological models; and how to take advantage of Models of...

The concept ‘models of everywhere’ was first introduced in the mid 2000s as a means of reasoning about the environmental science of a place, changing the nature of the underlying modelling process, from one in which general model structures are used to one in which modelling becomes a learning process about specific places, in particular capturing...

Natural flood management (NFM) has recently invigorated the hydrological community into redeploying its process understanding of hydrology and hydraulics to try to quantify the impacts of many distributed, ‘nature-based’ measures on the whole-catchment response. Advances in spatial data analysis, distributed hydrological modelling and fast numerica...

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, p...

This paper reviews the issues involved in treating hydrology as an example of an inexact science faced with significant epistemic uncertainties. It proposes a novel method for developing limits of acceptability for testing hydrological models as hypotheses about how a catchment hydrological system might function. The approach is based only on an an...

In this chapter, the concept of equifinality of model representations is discussed, from a background of model applications in the environmental sciences. Equifinality in this context is used to indicate that there may be many different model structures, parameter sets and auxiliary conditions that might appear to give equivalent output predictions...

Models must effectively represent velocities and celerities if they are to address the old‐water paradox. Celerity information is recorded indirectly in hydrograph observations, while velocity information is more difficult to measure and simulate effectively, requiring additional assumptions and parameters. Velocity information can be obtained from...

Ertsen discusses the representation of reality and uncertainty in our paper, raising three critical points. In response to the first, we agree that discussion of different interpretations of the concept of uncertainty is important when developing perceptual models – making different uncertainty interpretations explicit was a key motivation behind o...

This paper discusses how epistemic uncertainties are considered in a number of different natural hazard areas including floods, landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. In each case it is common practice to treat most uncertainties in the form of aleatory p...

Part 1 of this paper has discussed the uncertainties arising from gaps in knowledge or limited understanding of the processes involved in different natural hazard areas. Such deficits may include uncertainties about frequencies, process representations, parameters, present and future boundary conditions, consequences and impacts, and the meaning of...

Part 1 of this paper has discussed the uncertainties arising from gaps in knowledge or limited understanding of the processes involved in different natural hazard areas. Such deficits may include uncertainties about frequencies, process representations, parameters, present and future boundary conditions, consequences and impacts, and the meaning of...

This paper discusses how epistemic uncertainties are currently considered in the most widely occurring natural hazard areas, including floods, landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. Our aim is to provide an overview of the types of epistemic uncertainty i...

The Nierji Basin, in the north-east of China, is one of the most important basins in the joint operation of the entire Songhua River, containing a major reservoir used for flood control. It is necessary to forecast the flow of the basin during periods of flood accurately and with the maximum lead time possible. This paper presents a flood forecasti...

River discharge and nutrient measurements are subject to aleatory and epistemic uncertainties. In this study we present a novel method for estimating these uncertainties in co‐located discharge and phosphorus (P) measurements. The ‘voting point’ based method constrains the derived stage‐discharge rating curve both on the fit to available gaugings a...

Enhanced hillslope storage is utilised in “natural” flood management in order to retain overland storm run-off and to reduce connectivity between fast surface flow pathways and the channel. Examples include excavated ponds, deepened or bunded accumulation areas, and gullies and ephemeral channels blocked with wooden barriers or debris dams. The per...

These data support the forthcoming journal article "A new method, with application, for analysis of the impacts on flood risk of widely-distributed enhanced hillslope storage" by Peter Metcalfe, Keith Beven, Barry Hankin. This is currently in press for Hydrology and Earth System Science. They are Dynamic TOPMODEL runs comprise time series of simul...

The global proliferation of harmful algal blooms poses an increasing threat to water resources, recreation and ecosystems. Predicting the occurrence of these blooms is therefore needed to assist water managers in making management decisions to mitigate their impact. Evaluation of the potential for forecasting of algal blooms using the phytoplankton...

There is a need to model and predict the transfer of phosphorus (P) from land to water, but this is challenging because of the large number of complex physical and biogeochemical processes involved. This study presents, for the first time, a ‘limits of acceptability’ approach of the Generalized Likelihood Uncertainty Estimation (GLUE) framework to...

This opinion piece argues that in respect of testing models as hypotheses about how catchments function, there is no existing methodology that adequately deals with the potential for epistemic uncertainties about data and hydrological processes in the modeling processes. A rejectionist framework is suggested as a way ahead, wherein assessments of u...

In seasonal flow forecasting applications, one factor which can help predictability is a significant hydrological response time between rainfall and flows. On account of storage influences, large lakes therefore provide a useful test case although, due to the spatial scales involved, there are a number of modelling challenges related to data availa...

Excess nutrients in surface waters, such as phosphorus (P) from agriculture, result in poor water quality, with adverse effects on ecological health and costs for remediation. However, understanding and prediction of P transfers in catchments have been limited by inadequate data and over-parameterised models with high uncertainty. We show that, wit...

Phosphorus losses from land to water will be impacted by climate change and land management for food production, with detrimental impacts on aquatic ecosystems. Here we use a unique combination of methods to evaluate the impact of projected climate change on future phosphorus transfers, and to assess what scale of agricultural change would be neede...

Subsurface flow is often recognized as a dominant runoff generation process. However, observing subsurface properties, and understanding how they control flow pathways, remains challenging. This paper investigates how surface slope and bedrock cleavage control subsurface flow pathways in a slate bedrock headwater catchment in Luxembourg, characteri...

Climate projections for the future indicate that the United Kingdom will experience hotter, drier summers and warmer, wetter winters, bringing longer dry periods followed by rewetting. This will result in changes in phosphorus (P) mobilization patterns that will influence the transfer of P from land to water. We tested the hypothesis that changes i...

Excessive algal blooms, some of which can be toxic, are the most obvious symptoms of nutrient enrichment and can be exacerbated by climate change. They cause numerous ecological problems and also economic costs to water companies. The process-representation of the algal community model PROTECH was tested within the extended Generalised Likelihood U...

Characterizing, understanding and better estimating uncertainties are key concerns for drawing robust conclusions when analyzing changing socio-hydrological systems. Here we suggest developing a perceptual model of uncertainty that is complementary to the perceptual model of the socio-hydrological system and we provide an example application to flo...

Studies for the prevention and mitigation of floods require information on discharge and extent of inundation, commonly unavailable or uncertain, especially during extreme events. This study was initiated by the devastating flood in Tegucigalpa, the capital of Honduras, when Hurricane Mitch struck the city. In this study we hypothesized that it is...

Hillslope Runoff Attenuation Features (RAFs) are soft-engineered overland flow interception structures utilised in natural flood management, designed to reduce connectivity between fast overland flow pathways and the channel. The performance of distributed networks of these features is poorly understood. Extensive schemes can potentially retain lar...

Excess nutrients in surface waters, such as phosphorus (P) from agriculture, result in poor water quality, with adverse effects on ecological health and costs for remediation. However, understanding and prediction of P transfers in catchments have been limited by inadequate data and over-parameterised models with high uncertainty. We show that, wit...

In seasonal flow forecasting applications, one factor which can help predictability is a significant hydrological response time between rainfall and flows. On account of storage influences, large lakes therefore provide a useful test case although, due to the spatial scales involved, there are a number of modelling challenges related to data availa...

Flooding is a very costly natural hazard in the UK and is expected to increase further under future climate change scenarios. Flood defences are commonly deployed to protect communities and property from flooding, but in recent years flood management policy has looked towards solutions that seek to mitigate flood risk at flood-prone sites through t...

Most conceptual rainfall–runoff models use as input spatially averaged rainfall fields which are typically associated with significant errors that affect the model outcome. In this study, it is hypothesized that a simple spatially and temporally averaged event–dependent rainfall multiplier can account for errors in the rainfall input. The potential...

Nature-based approaches to flood risk management are increasing in popularity. Evidence for the effectiveness at the catchment scale of such spatially-distributed, upstream measures is inconclusive, however. It also remains an open question whether, under certain conditions, the individual impacts of a collection of flood mitigation interventions c...

Modelling of environmental processes is subject to a high degree of uncertainty due to the incorporation of random errors and a lack of knowledge about how processes operate at the scale of interest. Use of uncertain data when identifying and calibrating a model can lead to disinformative data being included in the procedure, resulting in uncertain...

We developed a parsimonious topography-based hydrologic model coupled with a soil biogeochemistry submodel in order to improve understanding and prediction of soluble reactive phosphorus (SRP) transfer in agricultural headwater catchments. The model structure aims to capture the dominant hydrological and biogeochemical processes identified from mul...

The relationship between tracer velocities and wave or wetting front celerities is essential to understand water flowing from hillslopes to the stream. The connection between maximum velocity and celerities estimated by means of experimental techniques has not been explored. To assess the pattern of infiltrating water front and dominant flow direct...

The permeability architecture of the critical zone exerts a major influence on the hydrogeochemistry of the critical zone. Water flow path dynamics drive the spatiotemporal pattern of geochemical evolution and resulting streamflow concentration-discharge (C-Q) relation, but these flow paths are complex and difficult to map quantitatively. Here we c...

Prevention and mitigation of floods require information on discharge and extent of inundation, commonly unavailable or uncertain, especially during extreme events. This study was initiated by the devastating flood in Tegucigalpa when Hurricane Mitch struck the city. In this study we hypothesised that it is possible to estimate, in a trustworthy way...

Prevention and mitigation of floods require information on discharge and extent of inundation, commonly unavailable or uncertain, especially during extreme events. This study was initiated by the devastating flood in Tegucigalpa when Hurricane Mitch struck the city. In this study we hypothesised that it is possible to estimate, in a trustworthy way...

Lake Malawi is the third largest lake in Africa and plays an important role in water supply, hydropower generation, agriculture and fisheries in the region. Lake level observations started in the 1890s and anecdotal evidence of variations dates back to the early 1800s. A chronology of lake level and outflow variations is presented together with upd...

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 modeling for a variety of purposes, including uncertainty assessment, model calibration and diagnostic evaluation, dominant control analysis and robust decis...

Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffus...

We hypothesise that climate change, together with intensive agricultural systems, will increase the transfer of pollutants from land to water and impact on stream health. This study builds, for the first time, an integrated assessment of nutrient transfers, bringing together a) high-frequency data from the outlets of two surface water-dominated, he...

We developed a parsimonious topography-based hydrologic model coupled with a soil biogeochemistry sub-model in order to improve understanding and prediction of Soluble Reactive Phosphorus (SRP) transfer in agricultural headwater catchments. The model structure aims to capture the dominant hydrological and biogeochemical processes identified from mu...

Uncertainties in natural hazard risk assessment are generally dominated by the sources arising from lack of knowledge or understanding of the processes involved. There is a lack of knowledge about frequencies, process representations, parameters, present and future boundary conditions, consequences and impacts, and the meaning of observations in ev...

Inferred rainfall sequences generated by a novel method of inverting a continuous time transfer function show a smoothed profile when compared to the observed rainfall, however, streamflow generated using the inferred catchment rainfall is almost identical to observed streamflow (Rt2 >97%). This paper compares the effective rainfall inferred by the...

In 2001, Beven and Freer introduced a "dynamic" variant of TOPMODEL that addressed some of the limitations of the original model whilst retaining its computational and parametric efficiency. The original assumption of a quasi-steady water table was replaced by time-dependent kinematic routing within hydrological similar areas. The new formulation a...

There is an emerging and urgent need for new approaches for the management of environmental challenges such as flood hazard in the broad context of sustainability. This requires a new way of working which bridges disciplines and organisations, and that breaks down science-culture boundaries. With this, there is growing recognition that the appropri...

We believe that there are too many models in hydrology and we should ask ourselves the question, if we are currently wasting time and effort in developing another model again instead of focusing on the development of a Community Hydrological Model. In other fields, this kind of models has been quite successful, but due to several reasons, no single...

The scientific literature has focused on uncertainty as randomness, while limited credit has been given to what we call here the “seventh facet of uncertainty”, i.e. lack of knowledge. This paper identifies three types of lack of understanding: (i) known unknowns, which are things we know we don’t know; (ii) unknown unknowns, which are things we do...

Catchment systems are interestingly nonlinear, but their dynamics are constrained from being unduly chaotic by mass and energy balance requirements. There have been no attempts in hydrology that we know of that have tried to map both the flow and transport dynamics of a catchment in any form of phase space. In part, this is because of the high dime...

This chapter deals primarily with hydrological flood modelling. Its history began in the mid-nineteenth century with the ‘Rational Method’ for peak flows attributed to Thomas Mulvany. Many different models have been developed, varying greatly in scope and level of detail, and are used for different purposes including science-driven testing of ideas...

The future has always been of great concern to humanity. The ecosystem approach to river basin management parallels the catchment management concept with its attention to the physical pathways of water, the movement of nutrients and pollutants and its consideration of the social, political and economic forces operating in the basin. NERC developed...

Field measurements of soil water content have many potential uses beyond merely monitoring changes in water storage of a soil profile. The neutron probe method has been applied widely to measure the effect of differences in evaporation losses from different vegetation on soil water balances. A number of key studies of unsaturated zone water balance...

Increasing pressures on the hydrological cycle from our changing planet have led to calls for a refocus of research in the sciences of hydrology and water resources. Opportunities for new and innovative research into these areas are being facilitated by advances in the use of cyberinfrastructure, such as the development of digital catchment observa...

This paper presents a discussion of some of the issues associated with the multiple sources of uncertainty and non-stationarity in the analysis and modelling of hydrological systems. Different forms of aleatory, epistemic, sematic and ontological uncertainty are defined. The potential for epistemic uncertainties to induce disinformation in calibrat...

The closure problem of representing hydrological boundary fluxes given the state of the system has been described as the scientific ‘Holy Grail’ of hydrology. This relationship between storage state and flux should be hysteretic and scale-dependant due to the differences between velocities and celerities in a hydrological system – effectively veloc...