A transport‐distance approach to scaling erosion rates: 2. sensitivity and evaluation of Mahleran

Abstract

In the first paper in this series, we demonstrated that most process-based erosion models have a series of in-built assumptions that led us to question their true process basis. An alternative soil-erosion model (MAHLERAN -Model for Assessing Hillslope-Landscape Erosion, Runoff And Nutrients) based upon particle-travel distance has been presented in the first paper in this series and this paper presents the first of two evaluations of the model. Here, a sensitivity analysis shows that the numerical model is consistent with the analytical model of Parsons et al. (2004) and demonstrates that downslope patterns of sediment flux on hillslopes are a complex interaction of rainfall intensity, duration and pattern; hillslope gradient; surface roughness and sediment size. This result indicates that the spatial scaling of sediment transfers on hillslopes is a non-trivial problem and will vary from point to point and from event to event and thus from year to year. The model is evaluated against field data from a rainfall-simulation experiment on an 18 m × × × × × 35 m plot for which there are sub-plot-scale data on runoff hydraulics and sediment flux. The results show that the model is capable of reproducing the sedigraph with an overall normalized root-mean-square error of 18·4% and Nash-Sutcliffe efficiency of 0·90. Spatial and temporal patterns of particle-size distributions of the eroded sediment are also reproduced very well, once erosion parameters have been optimized for the specific soil conditions. Figure 2. Sensitivity analysis on a uniform, planar 100 m long × 30 m wide slope according to rainfall intensity considering both unconcentrated and concentrated erosion.Figure 6. Comparisons of spatial patterns of runoff and sediment production for the E2 event on the large shrubland plot at Walnut Gulch: (a) total runoff in litres at a point for the Equation (2) case; (b) total runoff in litres at a point for the Equation (3b) case; (c) total sediment movement in kilograms at a point for the Equation (2) case; (d) total sediment movement in kilograms at a point for the Equation (3b) case. This figure is available in colour online at www.interscience.wiley.com/journal/espl 974 J. Wainwright et al.Figure 7. Summary of discharge and erosion characteristics of the simulations of E2 on the large shrubland plot at Walnut Gulch. The x-axis represents the distance from the top of the plot (0 m) to the outlet at 35 m.Figure A1. Sensitivity analysis on a uniform, planar 100 m long × 30 m wide slope according to rainfall duration considering unconcentrated erosion only. The x-axis represents the distance from the top of the plot (0 m) to the outlet at 35 m. Each graph shows the sum of all the model cells at a given distance downslope for total flow discharge (m 3 ), sediment flux (kg m −1 ), sediment yield (kg m −2 ), detachment (kg), deposition (kg), net erosion (kg) and percentage of all detachment that is by raindrops (i.e. 100% = detachment entirely by raindrops, 0% = detachment entirely by concentrated flow erosion). 978 J...

Modeling fine‐scale soil surface structure using geostatistics

“…Data-capture techniques (proximal and terrestrial laser scanning, high-definition total station surveying) now exist to produce digital elevation models at very fine spatial resolutions [Jomaa et al, 2010]. Models such as MAHLERAN [Wainwright et al, 2008], take advantage of these data and operate at a 0.5 m spatial resolution in order to simulate the spatial variability of soil surface properties that may occur in a heterogeneous landscape. However, even at the 0.5 m resolution, the spatial structure of the landscape that has been shown to evolve through rainfall events herein, is not well represented.…”

Standing proud: a response to ‘Soil‐erosion models: where do we really stand?’ by Smithet al.

“…All models require this distinction to be addressed. In MAHLERAN, we attempt to do so explicitly, but as we have noted in Wainwright et al (2008aWainwright et al ( , 2008bWainwright et al ( , 2008cWainwright et al ( , 2009) the approach is in need of further development based on more iterations between theory, experiments, observation and prediction. However, in developing their discussion, Smith et al show another misreading of our paper.…”

“…These points are all discussed in detail in Wainwright et al (2009). Furthermore, the detailed model-evaluation exercise that we undertook in Wainwright et al (2008bWainwright et al ( , 2008c shows quite clearly how the approach can be used both to improve models and model parameterizations whilst being openly critical of the model under development.…”

“…The second extrapolation is a curious one regarding buoyant particles. Were one to wish to simulate buoyant particles (for example in the case of peat erosion: Evans and Warburton, 2001), then the limitations of existing parameterizations (as we discuss extensively in a broader context in Wainwright et al, 2008bWainwright et al, , 2008c would be apparent, and one would need to modify not only the calculation of virtual velocities under all fl ow conditions, but also the detachment and transport-distance components of the model.…”

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Our original papers (Wainwright et al, 2008a(Wainwright et al, , 2008b(Wainwright et al, , 2008c which prompted the comment by Smith et al identifi ed a need to revisit soil-erosion modelling concepts and applications. Our argument was based on a critique that demonstrated misunderstandings and untested assumptions in the literature over the last 35 years or so.

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