Olivier Planchon

A fast, simple and versatile algorithm to fill the depressions of digital elevation models

The usual numerical methods for removing the depressions of a Digital Elevation Model Ž. DEM gradually fill the depressions and merge the embedded ones. These methods are complex to implement and need large computation time, particularly when the DEM contains a high proportion of random noise. A new method is presented here. It is innovative because, instead of gradually filling the depressions, it first inundates the surface with a thick layer of water and then removes the excess water. The algorithm is simple to understand and to implement, requiring only a few tens of code lines. It is much faster than usual algorithms. Moreover, this method is versatile: depressions can be replaced with a surface either strictly horizontal, or slightly sloping. The first option is used for the calculation of depression storage capacity and the second one for drainage network extraction. The method is fully detailed and a pseudo-code is provided. Its practical computation time, evaluated on generated fractal surfaces, is asymptotically proportional to N 1.2 where N is the number of grid points. The theoretical computation time is asymptotically proportional to N 1.5 in all cases, with the exception of some exotic ones with no practical interest. By contrast, existing methods have a computation time asymptotically proportional to N 2 . Applications are done for both generated and measured surfaces with 256 cells to 6.2 million cells. q 2001 Elsevier Science B.V. All rights reserved.

Microrelief induced by tillage: measurement and modelling of Surface Storage Capacity

Abstract The micro-topography of a groundnut plot in Senegal has been recorded over a full cultivation cycle, using an automated device able to measure 16.2 m2 at every 5 cm with an accuracy of 1 mm. Tillage is horse drawn, perpendicular to the general slope, and generates oriented microreliefs. Surface Storage Capacity (SSC) was calculated on both raw and slope-detrended surfaces. Additionally, various boundary conditions (BC) were used: no-wall; three-wall (up, left and right); or mirror (the Digital Elevation Model (DEM) surrounded by eight alternately reversed images of itself). SSC is more affected by these variants than by the variations of microrelief itself. Whatever the calculation method, SSC (as well as random roughness), follows a decreasing exponential with cumulated rainfall, but the coefficients of the exponential differ widely to each other. This suggests that SSC values could be of little use when they are obtained on various slopes, arbitrarily detrended or not, and calculated with arbitrary BC. We suggest a simple geometric model to characterise the way microrelief empties as the slope increases. The model has two calibrated depth-ratio parameters, one in each direction. It gives a more coherent framework for calculation and use of SSC. The model was applied to one of the DEMs of the data set, sampled after the first rain following hoeing. With the mirror-BC and detrended slope, SSC was 3.6 mm. Microrelief was found to behave in the same proportions, when tilted, than a tetrahedral container 94 times wider than deeper in the tillage direction and 11 times perpendicularly. This model represents the volume of surface water that cannot flow in any direction. With three-wall-BC, SSC was 6.7 mm, 1.4 mm remaining on the plot whatever the slope angle, and 5.3 mm behaving the same as a container 69 times wider than deeper. A possible use of this model is illustrated with an attempt to upscale the sampled plot to the watershed to which it belongs.

Raindrop erosion of tillage induced microrelief: possible use of the diffusion equation

The purpose of this paper is to evaluate the possibility of using the diffusion equation for raindrop erosion modelling. We wanted in particular to know if such a model could provide accurate interpolations of microrelief between two known dates. In a theoretical section, we show that the assumption that soil particles follow parabolic trajectories when splashed by raindrop impacts leads to a diffusion equation. This equation suggests a linear relation between Dz, the variation of height between two dates, and the Laplacianr 2 z (r 2 za@ 2 z/@x 2 a@ 2 z/@y 2 ). This relation is confirmed by data from a simulated rainfall experiment carried out in the sandy soils of the Senegalese groundnut belt. Four square plots of side 4 m each were used. They were hoed with a traditional horse-drawn three-tined hoe. Three rains of 70 mm h ˇ1 lasting 30 min each were applied. An automated relief meter designed and constructed by the authors was used to measure the distribution of heights for every 5 cm before the first rain, and after the first and the third rains. The mean correlation coefficient of the model was 62% for the first rain and 46% for the next two rains. Besides raindrop erosion, compaction occurred during the first rain. Adding a crude description of compaction enhanced the mean of the correlation coefficients of the model up to 70% for the first rain. Furthermore, the coefficient of variation of the four adjusted total diffusion lessens from 10 to 6%. The simulated surfaces were smoother than the real ones, which was an expected result, but the surface storage capacity was overestimated. The latter result illustrates the role of runoff in shaping the flow paths it follows and, consequently, in lessening the surface storage capacity. The main conclusion is that the diffusion equation provides a promising frame for further development of models simulating microrelief evolution during rainfall. Another conclusion is that these models should integrate existing routines for runoff erosion at small scale in order to simulate surfaces with realistic hydraulic properties. # 2000 Published by Elsevier Science B.V.

FullSWOF: A software for overland flow simulation / FullSWOF : un logiciel pour la simulation du ruissellement

Overland flow on agricultural fields may have some undesirable effects such as soil erosion, flood, and pollutant transport. To better understand this phenomenon and limit its consequences, we developed a code using state-of-the-art numerical methods: Full Shallow Water equations for Overland Flow (FullSWOF ), an object-oriented code written in C++. It has been made open-source and can be downloaded from http://www.univ-orleans.fr/mapmo/soft/FullSWOF/. The model is based on the classical system of shallow water (SW) (or Saint–Venant system). Numerical difficulties come from the numerous dry/wet transitions and the highly variable topography encountered inside a field. The code includes run-on and rainfall inputs, infiltration (modified Green-Ampt equation), and friction (Darcy-Weisbach and Manning formulas). First, we present the numerical method for the resolution of the SW equations integrated in FullSWOF_2D (the two-dimensional version). This method is based on hydrostatic reconstruction scheme, coupled with a semi-implicit friction term treatment. FullSWOF_2D has been previously validated using analytical solutions from the Shallow Water Analytic Solutions for Hydraulic and Environmental Studies library (SWASHES). FullSWOF_2D is run on a real topography measured on a runoff plot located in Thies (Senegal). Simulation results are compared with measured data. This experimental benchmark demonstrates the capabilities of FullSWOF to simulate adequately overland flow. FullSWOF could also be used for other environmental issues, such as river floods and dam breaks.

Relationship between raindrop erosion and runoff erosion under simulated rainfall in the Sudano-Sahel: consequences for the spread of nematodes by runoff

This paper presents a rainfall simulation experiment carried out on three 50 m2 plots in the Senegalese groundnut belt. One plot was not cultivated. Groundnut and millet had previously been grown in the other two. The experiment consisted of three rain events applied over 5 days at the end of the dry season. Erosion was monitored inside the plots by the use of a relief meter and, at their outlets, by sampling the discharge. The number of indigenous nematodes, and an exotic species introduced before the first rain event, was monitored in the soil and in the discharge. This experiment allows, for the first time, a set of simple hypotheses to be proposed to explain the spread of nematodes by the runoff: raindrop impacts on the soil surface set them in suspension; then, their low bulk density and their relatively large size do not allow them to settle when the raindrops shake the water surface. Thus, nematodes follow the flow path where they are as far as its velocity remains significant. The biological aspects are decisive in the mobility of nematodes, which can vary by a factor of 100 depending on the trophic groups. A very high raindrop erosion occurred during the experiment, up to 60 tons per hectare for the first rain event after hoeing. This represents more than 40 per cent of the volume of soil previously moved by soil work. The geometric properties of the plough, and their hydraulic consequences, appear very ephemeral. And yet these large movements of soil inside the plots are little related to the sediment load at the outlet, which follows its own rules. Analysis of the results indicates that the carrying capacity of the runoff at the scale of 10 m2, on gentle slopes ploughed perpendicular to the slope, could not be directly calculable from the discharge. It could depend on the history of past discharges because the shape of the flow paths, which condition their carrying capacity, permanently interacts with the discharge. These interactions could explain the great difficulties encountered by the erosion models in the case of low discharges on non-cohesive soils. Copyright