Eight runoff plots, located within a small catchment within the Walnut Gulch ExperimentalWatershed, southern Arizona, were constructed to test the argument that sediment yield (kg m − − − − −2 ) decreases as plot length increases. The plots ranged in length from 2 m to 27·78 m. Runoff and sediment loss from these plots were obtained for ten natural storm events. The pattern of sediment yield from these plots conforms to the case in which sediment yield first increases as plot length increases, but then subsequently decreases. Data from the present experiment indicate that maximum sediment yield would occur from a plot 7 m long. Analysis of both runoff and sediment yield from the plots indicates that the relationship of sediment yield to plot length derives both from the limited travel distance of individual entrained particles and from a decline in runoff coefficient as plot length increases. Particlesize analysis of eroded sediment confirms the role of travel distance in controlling sediment yield. Whether in response to the finite travel distance of entrained particles or the relationship of runoff coefficient to plot length, the experiment clearly demonstrates that the erosion rates for hillslopes and catchments cannot be simply extrapolated from plot measurements, and that alternative methods for estimating large-area erosion rates are required. Copyright Figure 1. Design of small plots.rates and travel distances of entrained particles, Parsons et al. (2004) proposed a conceptual model for soil erosion that leads to scale dependency in erosion rates. For interrill flow, they argued that this interaction would cause sediment yield initially to increase as area (length) increased, but subsequently to decrease. This paper reports on a field experiment to test this argument. MethodologyEight runoff plots were constructed within a small catchment located within the Walnut Gulch Experimental Watershed, southern Arizona. The catchment was vegetated with a desert shrub community dominated by Larrea tridentata and Acacia constricta. Four of the plots (named Hardy, Costello, Pete and Morecambe) were designed to be the same size (2 m long by 1 m wide). Slight variations in the construction of the plots resulted in actual plot sizes ranging from 2·08 m 2 to 2·11 m 2 . The side and upper plot boundaries were constructed using aluminium flashing inserted into a shallow trench dug into the soil and buttressed by concrete either side of the flashing. On the downslope side of each plot a triangular metal sheet directed runoff from the plot into a reservoir, of approximately 100 litres capacity, buried into the soil. Within this reservoir was a 13-litre bucket into which flow first fell and then overflowed into the reservoir. The metal sheet and reservoir were covered so that no rain falling onto them could enter the reservoir, nor could any sediment be splashed onto the sheet or into the reservoir. The design of these plots is shown in Figure 1. Water and sediment collected in the reservoirs were measured following each runof...

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The process basis of existing soil-erosion models is shown to be ill-founded. The existing literature builds directly or indirectly on Bennett's (1974) paper, which provided a blueprint for integrated catchment-scale erosion modelling. Whereas Bennett recognized the inherent assumptions of the approach suggested, subsequent readings of the paper have led to a less critical approach. Most notably, the assumption that sediment movement could be approximated by a continuity equation that related to transport in suspension has produced a series of submodels that assume that all movement occurs in suspension. For commonly occurring conditions on hillslopes, this case is demonstrably untrue both on theoretical grounds and from empirical observations. Elsewhere in the catchment system, it is only partially true, and the extent to which the assumption is reasonable varies both spatially and temporally. A second ground-breaking paper -that of Foster and Meyer (1972) -was responsible for subsequent uncritical application of a first-order approximation to deposition based on steady-state analysis and again a weak empirical basis. We describe in this paper an alternative model (MAHLERAN -Model for Assessing Hillslope-Landscape Erosion, Runoff And Nutrients) based upon particle-travel distance that overcomes existing limitations by incorporating parameterizations of the different detachment and transport mechanisms that occur in water erosion in hillslopes and small catchments. In the second paper in the series, we consider the sensitivity and general behaviour of MAHLERAN, and test it in relation to data from a large rainfall-simulation experiment. The third paper of the sequence evaluates the model using data from plots of different sizes in monitored rainfall events. From this evaluation, we consider the scaling characteristics of the current form of MAHLERAN and suggest that integrated modelling, laboratory and field approaches are required in order to advance the state of the art in soil-erosion modelling. Wainwright et al., 2001;Parsons et al., 2004Parsons et al., , 2006b. We have argued elsewhere (Parsons et al., 2004) that these problems arise from a fundamental misconception, and thus misrepresentation, of the component processes that make up soil erosion. The aim of this paper is, therefore, to review the conceptual basis of existing models and to propose an alternative model that addresses the problems inherent in existing approaches. Figure 2. Comparison of information on (a) travel distances and (b) virtual velocities from Hassan et al. (1992) for concentrated flows and Parsons et al. (1998) for unconcentrated flows. See the text for further discussion.822 J. Wainwright et al.Figure 4. Summary of the calculation algorithm used in MAHLERAN. The main components in terms of detachment and the use of travel distance and virtual velocity to estimate sediment discharge are highlighted. 824 J. Wainwright et al.appropriate erosion and deposition rates have been calculated. The sediment mass-balance Equation (6) is equiva...

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Current estimates of rates of soil erosion by water derived from plots are incompatible with estimates of long-term lowering of large drainage basins. Traditional arguments to reconcile these two disparate rates are flawed. The flux of sediment leaving a specified area cannot be converted to a yield simply by dividing by the area, because there is no simple relationship between flux and area. Here, we develop an approach to the determination of erosion rates that is based upon the entrainment rates and travel distances of individual particles. The limited available empirical data is consistent with the predictions of this approach. Parameterization of the equations to take account of such factors as gradient and sediment supply is required to proceed from the conceptual framework to quantitative measurements of erosion. However, our conceptual model solves the apparent paradox of the sediment delivery ratio, resolves recent discussion about the validity of erosion rates made using USLE erosion plots, and potentially can reconcile erosion rates with known lifespans of continents. Our results imply that previous estimates of soil erosion are fallacious.