## 2 Materials
### In Situ Data
#### 2.2.3 Surface Roughness  
The surface roughness was measured using a 2 m long needle profilometer after each tillage event. Tillage was either plowed, stubble-disked, narrowed, prepared cloudy or prepared smooth. The profilometer is composed of 201 needles spaced 1 cm apart. These needles replicate the micro-relief of the ground by landing on the surface, and a photograph records the soil profile. For each change in the surface state, two profiles were collected parallel to the direction of the tillage of the plot, and two others were collected perpendicularly.  
Figure 4: Surface texture measurements (black dots) displayed on the United States Department of Agriculture (USDA) classification system with the following classes: clay (Cl), silty clay (SiCl), sandy clay (SaCl), clay loam (CILo), silty clay loam (SiClLo), sandy clay loam (CaCILo), loam (Lo), silty loam (SiLo), sandy loam (SaLo), silt (Si), loamy sand (LoSa) and sand (Sa).  
Pairs of pictures were digitized and associated to obtain 4 m long profiles. The first-order trend was removed to subtract the effect of the local slope due to non-parallelism between the soil and the profilometer. A statistical description of the roughness is provided by the root-mean-square height (h\({}_{\text{rms}}\)). The dependence between two successive points of the roughness profile was estimated through the exponential or Gaussian correlation function, defining a distance for which the correlation between points no longer exists, or the correlation length (l\({}_{\text{c}}\)).  
The values of h\({}_{\text{rms}}\) and l\({}_{\text{c}}\), derived from parallel and perpendicular profiles and grouped into four categories according to tillage practices, are presented in Figure 5. The values are highest in the perpendicular direction, as evidenced by the average h\({}_{\text{rms}}\) of 2.2 cm (vs. 1.5 cm in the parallel direction) or l\({}_{\text{c}}\) of 7.7 cm (vs. 4.4 cm). The 'plowed' surface state presents the highest values of h\({}_{\text{rms}}\) (with averages of 3.4 and 4.4 cm in the parallel and perpendicular directions) and differs from other levels of roughness. It represents 11% of the collected profiles and is associated with high variability, as evidenced by the values of the coefficients of variation between 25 and 45%, depending on the parameter (h\({}_{\text{rms}}\) or l\({}_{\text{c}}\)) and the direction considered. The'stubble disked' and 'harrowed' surface states represent, respectively, 14 and 23% of the collected profiles. They are associated with fairly close h\({}_{\text{rms}}\) values, with an average of 1.5 and 1.8 cm in the parallel direction and 2.7 and 2.4 cm in the perpendicular direction. They are therefore difficult to separate, especially as they have high dispersion, with coefficients of variation greater than 30%. The 'prepared' surface states account for more than half of the roughness measurements (25% for the 'cloddy' state and 27% for'smooth'). They are associated with fairly close h\({}_{\text{rms}}\) values, less than 2 cm on average. The l\({}_{\text{c}}\) values are more mixed, with greater averages for the'smooth' state compared to 'cloddy' (with 4.4 vs. 2.5 cm in the parallel direction and 8.5 vs. 6.0 cm in the perpendicular direction).