Mike Kirkby

A physically based, variable contributing area model of basin hydrology / Un modèle à base physique de zone d'appel variable de l'hydrologie du bassin versant

A hydrological forecasting model is presented that attempts to combine the important distributed effects of channel network topology and dynamic contributing areas with the advantages of simple lumped parameter basin models. Quick response flow is predicted from a storage/contributing area relationship derived analytically from the topographic structure of a unit within a basin. Average soil water response is represented by a constant leakage infiltration store and an exponential subsurface water store. A simple non-linear routing procedure related to the link frequency distribution of the channel network completes the model and allows distinct basin sub-units, such as headwater and sideslope areas to be modelled separately. The model parameters are physically based in the sense that they may be determined directly by measurement and the model may be used at ungauged sites. Procedures for applying the model and tests with data from the Crimple Beck basin are described. Using only measured and estimated parameter values, without optimization, the model makes satisfactory predictions of basin response. The modular form of the model structure should allow application over a range of small and medium sized basins while retaining the possibility of including more complex model components when suitable data are available.

Testing a physically-based flood forecasting model (TOPMODEL) for three U.K. catchments

A previously developed model has been tested on three catchments: Crimple Beck (8 km2) near Harrogate, Hodge Beck (36 km2) on the North York Moors and the Wye headwater (10.5 km2) in central Wales. The model was originally validated on subcatchments within Crimple Beck. For this study forecasts were made over a period of one year, based only on rainfall and evaporation data. The model parameters were derived from a defined program of field measurements over a period of 2–4 weeks, and no formal optimization procedures were carried out before comparing forecasts with the measured stream discharge record. As a result of the comparisons, the model is seen as a useful approach for ungauged catchments of up to 500 km2 in humid-temperature climates.

Hillslope runoff processes and models

Abstract Hillslope hydrology is concerned with the partition of precipitation as it passes through the vegetation and soil between overland flow and subsurface flow. Flow follows routes which attenuate and delay the flow to different extents, so that a knowledge of the relevant mechanisms is important. In the 1960s and 1970s, hillslope hydrology developed as a distinct topic through the application of new field observations to develop a generation of physically based forecasting models. In its short history, theory has continually been overturned by field observation. Thus the current tendency, particularly among temperate zone hydrologists, to dismiss all Hortonian overland flow as a myth, is now being corrected by a number of significant field studies which reveal the great range in both climatic and hillslope conditions. Some recent models have generally attempted to simplify the processes acting, for example including only vertical unsaturated flow and lateral saturated flows. Others explicitly forecast partial or contributing areas. With hindsight, the most complete and distributed models have generally shown little forecasting advantage over simpler approaches, perhaps trending towards reliable models which can run on desk top microcomputers. The variety now being recognised in hillslope hydrological responses should also lead to models which take account of more complex interactions, even if initially with a less secure physical and mathematical basis than the Richards equation. In particular, there is a need to respond to the variety of climatic responses, and to spatial variability on and beneath the surface, including the role of seepage macropores and pipes which call into question whether the hillside can be treated as a Darcian flow system.

Sediment slugs: large-scale fluctuations in fluvial sediment transport rates and storage volumes

Variations in fluvial sediment transport rates and storage volumes have been described previously as sediment waves or pulses. These features have been identified over a wide range of temporal and spatial scales and have been categorized using existing bedform classifications. Here we describe the factors controlling the generation and propagation of what we term sediment slugs. These can be defined as bodies of clastic material associated with disequilibrium conditions in fluvial systems over time periods above the event scale. Slugs range in magnitude from unit bars (Smith, 1974) up to sedimentary features generated by basin-scale sediment supply disturbances (Trimble, 1981). At lower slug magnitudes, perturbations in sediment transport are generated by local riverbank and/or bed erosion. Larger-scale features result from the occurrence of rare high- magnitude geomorphic events, and the impacts on water and sediment production of tectonics, glaciation, climate change and anthropogenic influences. Simple sediment routing functions are presented which may be used to describe the propagation of sediment slugs in fluvial systems. Attention is drawn to components of the fluvial system where future research is urgently required to improve our quantitative understanding of drainage-basin sediment dynamics.

Modelling geomorphic response to environmental change in an upland catchment

In the UKs upland catchments river terraces and alluvial features indicate a history of periodic aggradation and degradation linked to Holocene changes in land use (primarily deforestation) and climate change (altering flood frequency and magnitude). Although both factors are important, calculating their individual effects is complicated by the likelihood of their concurrent alteration. To investigate the relative impacts of land use and climate change, a cellular model is applied to the upland catchments of Cam Gill Beck, above Starbotton, North Yorkshire. This is divided into 1 million 2 m by 2 m grid cells, to which a range of process laws are applied. These include approximate expressions for mass movement rates, soil creep, the influence of vegetation and hillslope hydrology, as well as fluvial erosion and deposition in ten grain-size fractions. This provides a good representation of valley floor geometry while retaining a fully dynamic interaction with the surrounding valley sides. Previous applications of this model have shown the detailed formation of bars and berms as well as examples of braiding, avulsion and channel range. Running on a Silicon Graphics Origin 2000 computer, an ensemble of simulations were completed, bracketing a wide range of environmental scenarios involving changes in flood frequency, magnitude and vegetation cover. Over time-scales ranging from 10 to 100 years, these showed that decreasing tree cover and increasing rainfall magnitude individually produced similar 25% to 100% increases in sediment discharge, whereas in combination they generated a 1300% rise. Furthermore, channels formed by the model in response to increased rainfall magnitudes are located where relic channels are found in Cam Gill Beck, implying that these are the products of previous periods of high rainfall magnitudes. Copyright

Gully processes and modelling

This article reviews previous investigations into gully and badland research and discusses processes and definitions in the context of existing research in southeast Spain. The theory of badland development is summarized and definitions are proposed which draw on previous work and continuing studies. The processes influencing gully and channel head morphology are then discussed including overland flow, hillslope processes, pipe initiation and enlargement, mass failures and the magnitude and frequency distribution of storm events. Finally, modelling of badland landscapes is discussed. The article highlights that much detailed research has been carried out on badlands, but long-term rates of gully development are not well understood. There are also gaps in our understanding of pipe network formation and collapse. In the short term theoretical modelling may provide the way forward and a direction for more holistic investigations.

The impact of rainstorms on floods in ephemeral channels in southeast Spain

Abstract This paper presents and discusses data on rainfall, stage and estimated discharge for a large flood occurring in two catchments in southeast Spain in September 1997. Rainfall and stage were recorded using automatic logging equipment and discharge was estimated using measurements of channel cross-sections and water depth estimated from trash lines. Total precipitation in the Rambla de Torrealvilla was 50 mm in 2 days with maximum rainfall intensities of 80 mm h −1 . Total rainfall in the Rambla de Nogalte was 195 mm in 3 days, with maximum intensities of 200 mm h −1 . In the Torrealvilla, this rainfall produced three flood peaks with maximum stage approaching 2.5 m. In the Nogalte, there was only one flood peak, which was 0.5 m deep. Estimated discharge varied widely throughout both catchments with maxima of 120 m 3 s −1 in the Torrealvilla and 60 m 3 s −1 in the Nogalte. Maximum discharges occurred at times of high rainfall intensity, but intensity alone did not explain why some tributaries had very small discharges. Variations in discharge in the ephemeral channels were due to combinations of lithology, morphology and land use. The predominantly marl catchment of the Torrealvilla had a lower threshold rainfall intensity than the schists of the Nogalte. Within each catchment sub-basins characterised by steep, gorge like terrain and sub-basins where agriculture had been abandoned both resulted in higher flood discharge. The contributing areas for the September storms were up to two thirds of tributary catchment areas. Comparison of rainfall data records shows that the September flood was the fifth largest on record and had a recurrence interval of 7 years. The largest (1973) flood, which is known to have caused substantial damage and a number of deaths, was only a 30-year event. The floods on the Torrealvilla destroyed at least two check dams and evidence suggests that these had little effect on reducing the impact of the floods.

Anticipating and managing future trade-offs and complementarities between ecosystem services

This paper shows how, with the aid of computer models developed in close collaboration with decision makers and other stakeholders, it is possible to quantify and map how policy decisions are likely to affect multiple ecosystem services in future. In this way, potential trade-offs and complementarities between different ecosystem services can be identified, so that policies can be designed to avoid the worst trade-offs, and where possible, enhance multiple services. The paper brings together evidence from across the Rural Economy and Land Use Programmes Sustainable Uplands project for the first time, with previously unpublished model outputs relating to runoff, agricultural suitability, biomass, heather cover, age, and utility for Red Grouse (Lagopus scotica), grass cover, and accompanying scenario narratives and video. Two contrasting scenarios, based on policies to extensify or intensify land management up to 2030, were developed through a combination of interviews and discussions during site visits with stakeholders, literature review, conceptual modeling, and process-based computer models, using the Dark Peak of the Peak District National Park in the UK as a case study. Where extensification leads to a significant reduction in managed burning and grazing or land abandonment, changes in vegetation type and structure could compromise a range of species that are important for conservation, while compromising provisioning services, amenity value, and increasing wildfire risk. However, where extensification leads to the restoration of peatlands damaged by former intensive management, there would be an increase in carbon sequestration and storage, with a number of cobenefits, which could counter the loss of habitats and species elsewhere in the landscape. In the second scenario, land use and management was significantly intensified to boost UK self-sufficiency in food. This would benefit certain provisioning services but would have negative consequences for carbon storage and water quality and would lead to a reduction in the abundance of certain species of conservation concern. The paper emphasizes the need for spatially explicit models that can track how ecosystem services might change over time, in response to policy or environmental drivers, and in response to the changing demands and preferences of society, which are far harder to anticipate. By developing such models in close collaboration with decision makers and other stakeholders, it is possible to depict scenarios of real concern to those who need to use the research findings. By engaging these collaborators with the research findings through film, it was possible to discuss adaptive options to minimize trade-offs and enhance the provision of multiple ecosystem services under the very different future conditions depicted by each scenario. By preparing for as wide a range of futures as possible in this way, it may be possible for decision makers to act rapidly and effectively to protect and enhance the provision of ecosystem services in the face of unpredictable future change.

A climatic index for soil erosion potential (CSEP) including seasonal and vegetation factors

Abstract The concept of Cumulative Erosion Potential (CEP) proposed by De Ploey, Kirkby and Ahnert in 1991 (Earth Surf. Process. Landforms, 16: 399–409) provides a simple climatic index of erosion potential based on annual rainfalls and their distribution, which is assumed to be exponential (or gamma with shape parameter 1). A modified CEP (CSEP) is presented here, extending the original in three ways. First, the index is disaggregated by month to include the effects of seasonality. Second, a mixed gamma(1) distribution is used to provide a better fit to the whole of the daily rainfall distribution. Third, the index is calculated both for a bare soil and for a natural vegetation cover, giving an additional index to the potential for managing erosion through landuse change. For the natural vegetation, the index is based on an estimate of equilibrium soil organic matter which is associated with differences in soil moisture storage capacities and derived from monthly rainfall and temperature values. The index thus remains a measure of climatic potential only, based on widely available monthly data on temperature, rainfall and number of rain days. It may be compared with the patterns shown by the European Soil Erosion Map and by the CORINE classification, which are dominated by a combination of climate and lithology.

Modelling the interactions between soil surface properties and water erosion

Abstract Interactions between soil surface properties, water runoff and erosion occur at many time and space scales. The paper focuses primarily on the effects of soil microtopography at a range of spatial scales and considers some new conceptual approaches to modelling its effect on runoff generation, flow concentration and sediment transport. In this paper, the local generation of runoff is considered through the simplifying concept of a discrete runoff threshold. The effect of random roughness is considered independently in the down-slope and cross-slope directions. Roughness elements measured in the cross-slope direction concentrate the flow within depressions, and create greater total sediment transport. Roughness measured in the down-slope direction represents elements which pond or impede the flow, reducing mean flow velocity and reducing sediment transport. This two-component approach to roughness provides a reasonable approximation to behaviour on fractally generated two-dimensional surfaces. If the roughness elements are assumed to be normally distributed, and independently random in the two directions, then explicit integrations can be made over the distributions, providing significant corrections to the relationship between mean flow depth and sediments transporting capacity. A second conceptual model is presented, exploring the implications of spatially random variations in surface flux capacity (storm total infiltration), surface (depression) storage and storm rainfall totals. It is demonstrated that some at-a-point runoff may, in principle, be generated, even where surface capacity appears to greatly exceed storm rainfall. In conclusion, it is argued that these effects, together with others not covered here, should be included in the next generation of soil erosion models.