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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 multiscale observations in a research catchment (Kervidy–Naizin, 5 km2). Groundwater fluctuations, responsible for the connection of soil SRP production zones to the stream, were simulated with a fully distributed hydrologic model at 20 m resolution. The spatial variability of the soil phosphorus content and the temporal variability of soil moisture and temperature, which had previously been identified as key controlling factors of SRP solubilization in soils, were included as part of an empirical soil biogeochemistry sub-model. The modelling approach included an analysis of the information contained in the calibration data and propagation of uncertainty in model predictions using a generalized likelihood uncertainty estimation (GLUE) "limits of acceptability" framework. Overall, the model appeared to perform well given the uncertainty in the observational data, with a Nash–Sutcliffe efficiency on daily SRP loads between 0.1 and 0.8 for acceptable models. The role of hydrological connectivity via groundwater fluctuation and the role of increased SRP solubilization following dry/hot periods were captured well. We conclude that in the absence of near-continuous monitoring, the amount of information contained in the data is limited; hence, parsimonious models are more relevant than highly parameterized models. An analysis of uncertainty in the data is recommended for model calibration in order to provide reliable predictions.

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 parameter estimation and ambiguity in the outcomes. Rainfall-runoff modelling where a single rain-gauge is often assumed to be representative of the potentially highly variable (in both space and time) rainfall field is a good example. The noisy pattern of rainfall inputs is transformed by the catchment into streamflow. The streamflow pattern is dependent on the spatio-temporal pattern of rainfall and of the dominant processes operating within the catchment. Inverse modelling of the catchment dynamics, that is, inferring catchment rainfall from streamflow, provides a possible means of improving the estimated rainfall input because all rain falling on the catchment becomes streamflow, and thus, providing improved forecasts of the streamflow output. A combination of inverse modelling, time series analysis, spatial analysis and spectral analysis may also help to provide an insight into the complex processes operating within the catchment system. This paper applies a novel method for inferring true catchment rainfall from streamflow highlighting that the streamflow is better estimated using inferred rainfall than observed rainfall (from a single gauge) because a single gauge only gives a partial description of the rainfall field. However reducing uncertainty in this way comes at a price, in this case, the reduction in time-resolution of the inferred rainfall series.

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.

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, semantic, and ontological uncertainty are defined. The potential for epistemic uncertainties to induce disinformation in calibration data and arbitrary non-stationarities in model error characteristics, and surprises in predicting the future, are discussed in the context of other forms of non-stationarity. It is suggested that a condition tree is used to be explicit about the assumptions that underlie any assessment of uncertainty. This also provides an audit trail for providing evidence to decision makers.

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 don’t know we don’t know; and (iii) wrong assumptions, things we think we know, but we actually don’t know. Here we discuss each of these with reference to the study of the dynamics of human–water systems, which is one of the main topics of Panta Rhei, the current scientific decade of the International Association of Hydrological Sciences (IAHS), focusing on changes in hydrology and society. In the paper, we argue that interdisciplinary studies of socio-hydrological dynamics leading to a better understanding of human–water interactions can help in coping with wrong assumptions and known unknowns. Also, being aware of the existence of unknown unknowns, and their potential capability to generate surprises or black swans, suggests the need to complement top-down approaches, based on quantitative predictions of water-related hazards, with bottom-up approaches, based on societal vulnerabilities and possibilities of failure.

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 parameter estimation and ambiguity in the outcomes. Rainfall-runoff modelling where a single rain-gauge is often assumed to be representative of the potentially highly variable (in both space and time) rainfall field is a good example. The noisy pattern of rainfall inputs is transformed by the catchment into streamflow. The streamflow pattern is dependent on the spatio-temporal pattern of rainfall and of the dominant processes operating within the catchment. Inverse modelling of the catchment dynamics, that is, inferring catchment rainfall from streamflow, provides a possible means of improving the estimated rainfall input because all rain falling on the catchment becomes streamflow, and thus, providing improved forecasts of the streamflow output. A combination of inverse modelling, time series analysis, spatial analysis and spectral analysis may also help to provide an insight into the complex processes operating within the catchment system. This paper applies a novel method for inferring true catchment rainfall from streamflow highlighting that the streamflow is better estimated using inferred rainfall than observed rainfall (from a single gauge) because a single gauge only gives a partial description of the rainfall field. However reducing uncertainty in this way comes at a price, in this case, the reduction in time-resolution of the inferred rainfall series.

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 don’t know we don’t know; and (iii) wrong assumptions, things we think we know, but we actually don’t know. Here we discuss each of these with reference to the study of the dynamics of human–water systems, which is one of the main topics of Panta Rhei, the current scientific decade of the International Association of Hydrological Sciences (IAHS), focusing on changes in hydrology and society. In the paper, we argue that interdisciplinary studies of socio-hydrological dynamics leading to a better understanding of human–water interactions can help in coping with wrong assumptions and known unknowns. Also, being aware of the existence of unknown unknowns, and their potential capability to generate surprises or black swans, suggests the need to complement top-down approaches, based on quantitative predictions of water-related hazards, with bottom-up approaches, based on societal vulnerabilities and possibilities of failure.

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, semantic, and ontological uncertainty are defined. The potential for epistemic uncertainties to induce disinformation in calibration data and arbitrary non-stationarities in model error characteristics, and surprises in predicting the future, are discussed in the context of other forms of non-stationarity. It is suggested that a condition tree is used to be explicit about the assumptions that underlie any assessment of uncertainty. This also provides an audit trail for providing evidence to decision makers.

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 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, headwater (~ 10 km²) agricultural catchments, b) event-by-event analysis of nutrient transfers, c) concentration duration curves for comparison with EU Water Framework Directive water quality targets, d) event analysis of location-specific, sub-daily rainfall projections (UKCP, 2009), and e) a linear model relating storm rainfall to phosphorus load. These components, in combination, bring innovation and new insight into the estimation of future phosphorus transfers, which was not available from individual components. The data demonstrated two features of particular concern for climate change impacts. Firstly, the bulk of the suspended sediment and total phosphorus (TP) load (greater than 90% and 80% respectively) was transferred during the highest discharge events. The linear model of rainfall-driven TP transfers estimated that, with the projected increase in winter rainfall (+ 8% to + 17% in the catchments by 2050s), annual event loads might increase by around 9% on average, if agricultural practices remain unchanged. Secondly, events following dry periods of several weeks, particularly in summer, were responsible for high concentrations of phosphorus, but relatively low loads. The high concentrations, associated with low flow, could become more frequent or last longer in the future, with a corresponding increase in the length of time that threshold concentrations (e.g. for water quality status) are exceeded. The results suggest that in order to build resilience in stream health and help mitigate potential increases in diffuse agricultural water pollution due to climate change, land management practices should target contro

This thesis is an in depth investigation of the history of the acceptance of Einstein’s Theory of General Relativity by scientists and by the public through the media. It emphasises the key role that Australia played in that acceptance and in the verification of General Relativity. This contribution came from the 1922 total solar eclipse across the continent as well as the discovery in 2003 at Parkes Radio Telescope of the first, and to this date only, pair of pulsars in mutual orbit. This system provides a unique opportunity to plumb the theory in a much stronger gravitational field regime than previously. This historical scrutiny provides an insight into scientific revolutions in general. The examination of this particular development may then act as a template for the study of other scientific revolutions. One of the key findings is that the Theory of General Relativity was prematurely accepted. The main argument of the thesis is for 1928 being the year when sufficient evidence existed for scientists to begin accepting the theory based on gravitational deflection of light instead of the commonly accepted date of 1919. Emphasis is given to the explorations of the 1922 eclipse parties in Australia and the activities of the eight groups measuring light deflection at this eclipse. This work is gathered together here for the first time. The upshot is that it was 1928 before the results were published in full and a conclusion could be drawn. It is also established that the situation for Mercury needed a much longer time period to near the end of the twentieth century before a decisive verdict could be made. Similar to the situation for light deflection, it is found that 1928 is also the year in which spectroscopic data from spectral line frequency shifts of the Sun and white dwarfs had accumulated sufficiently so that a strong conclusion on the third of the classical tests of General Relativity could be made. From the late 1960s the radio region of the spectrum was emp

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 allows a more flexible discretisation, variable upslope drainage areas and spatially variable physical properties. There has, however, never been a freely distributable version of dynamic TOPMODEL. Here, we describe a new, open source, version developed in the R environment. It incorporates handling of geo-referenced spatial data that allows it to integrate with modern GIS. It makes use of data storage and vectorisation features of the language that will allow efficient scaling of the problem domain. The implementation is evaluated with data from a small catchment. The formulation of the model in terms of a flow distribution matrix is described and its use illustrated for treatment of surface and subsurface flow routing. The model uses an improved implicit solution for updating the subsurface storages and fluxes. The paper focuses on the robustness of the predicted output variables to changes in the time and space discretisations.

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 community model has been developed in the field of hydrology yet. The concept, strength, and weakness of a community model were discussed at the Chapman Conference on Catchment Spatial Behaviour and Complex Organisation held in Luxembourg in September 2014. This discussion as well as our own opinions about the potential of a community models or at least the necessary discussion to establish one are debated in this commentary.

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 dimensionality of the space–time patterns of response; in part because there is sufficient uncertainty about the input and output fluxes estimated by measurement that this might be expected to obscure any attractor-like behaviour. In this study we explore the basin of the catchment attractor for the Multiple Interacting Pathway (MIPs) model that in previous papers has been shown to give good results for the small Gårdsjön catchment in Sweden. MIPs is based on particle tracking techniques and gives results for both the flow responses and for the travel and residence time responses of water in the catchment. Here it is used to provide consistent values of fluxes, total storage, travel time distributions and residence time distributions for a long simulation period. The nature of those responses in storage and input dimensions is then investigated. The results suggest that the range of behaviours is hysteretic in interesting ways and constrained by the forcing inputs, with space filling of trajectories in the basin of attraction as should be expected of a forced dissipative system. The range of behaviours exhibited defines a space that the responses of any simpler emulator model will need to span.

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.

What we see now in the landscape is the result of a long history of events with varying degrees of persistence. We have only limited access to much of that history and we know that many current events have only a minimal impact on what we see. Even rather extreme events may have impacts that are not very long-lasting but can have the effect of changing the antecedent states for future events. That means that sampling of sequences of events might be important in understanding the evolution of the catchments. In some cases, however, extreme events can have an impact on the system that persists over hundreds or thousands of years. Any evolution of the landscape is then constrained by those past events, however much it might be also constrained by self-organisational principles. It might be difficult to verify those principles given the epistemic uncertainties about past histories and system properties that are generic to the studies that are possible within a research project or career. These arguments are investigated in a simple slab model of landslip failures in a hillslope hollow subject to stochastic forcing over long periods of time. The complementarity of an event-persistence approach to hydro-eco-geomorphological systems is captured in suggestions for future research questions.

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 observatories. This is enabling research into hydrological issues such as flooding to be approached differently. The ability to combine different sources of data, knowledge, and modeling capabilities from different groups such as scientists, policy makers, and the general public has the potential to provide novel insights into the way individual catchments respond at different temporal and spatial scales. While the potential benefits of the digital catchment observatory are large, this new way of carrying out research into hydrological sciences is likely to prove challenging on many levels. Along with the obvious technical and infrastructural challenges to this work, an important area for consideration is how to enable a digital observatory to work for a range of potential end-users, paving the way for new areas of research through developing a platform effective for engagement and knowledge exchange. Using examples from the recent local-scale hydrological exemplar in the Environmental Virtual Observatory pilot project (http://www.evo-uk.org), this commentary considers a number of issues around the communication between and engagement of different users, the use of local knowledge and uncertainty with cloud-based models, and the potential for decision support and directions for future research.

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 allows a more flexible discretisation, variable upslope drainage areas and spatially variable physical properties. There has, however, never been a freely distributable version of dynamic TOPMODEL. Here, we describe a new, open source, version developed in the R environment. It incorporates handling of geo-referenced spatial data that allows it to integrate with modern GIS. It makes use of data storage and vectorisation features of the language that will allow efficient scaling of the problem domain. The implementation is evaluated with data from a small catchment. The formulation of the model in terms of a flow distribution matrix is described and its use illustrated for treatment of surface and subsurface flow routing. The model uses an improved implicit solution for updating the subsurface storages and fluxes. The paper focuses on the robustness of the predicted output variables to changes in the time and space discretisations.

What we see now in the landscape is the result of a long history of events with varying degrees of persistence. We have only limited access to much of that history and we know that many current events have only a minimal impact on what we see. Even rather extreme events may have impacts that are not very long-lasting but can have the effect of changing the antecedent states for future events. That means that sampling of sequences of events might be important in understanding the evolution of the catchments. In some cases, however, extreme events can have an impact on the system that persists over hundreds or thousands of years. Any evolution of the landscape is then constrained by those past events, however much it might be also constrained by self-organisational principles. It might be difficult to verify those principles given the epistemic uncertainties about past histories and system properties that are generic to the studies that are possible within a research project or career. These arguments are investigated in a simple slab model of landslip failures in a hillslope hollow subject to stochastic forcing over long periods of time. The complementarity of an event-persistence approach to hydro-eco-geomorphological systems is captured in suggestions for future research questions.