A study of clod evolution in simulated rain on the basis of digital elevation models

Catena 160 (2018) 212–221

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A study of clod evolution in simulated rain on the basis of digital elevation models

MARK

E. Vanniera,⁎, O. Taconeta, R. Dusséauxa, F. Darbouxb,1 a b

LATMOS/IPSL, Université Versailles Saint-Quentin en Yvelines, France INRA, UR0272 "Science du sol", Centre de recherche Val de Loire, CS 40001, F-45075 Orléans Cedex 2, France

A R T I C L E I N F O

A B S T R A C T

Keywords: Surface roughness Silt loam soil Cloddiness Image analysis Splash erosion Swelling

Soil roughness is a key parameter to our understanding of soil properties and soil-water interaction, most of which occur at millimeter scales. Soil irregularities, such as aggregates, clods and interrill depressions, influence water infiltration and overland flow. The objective of this study is to observe and quantify clod evolution under cumulated precipitation. We prepared two soil trays with loose silt soil and pre-sieved clods put on top, at low and high concentrations. These trays were then subjected to a set of five successive artificial rainfalls. The digital elevation models (DEM) were recorded for each tray, at millimetric resolution, at the initial stage and after each subsequent rainfall. The clods were automatically segmented on the DEM and the diameter, surface area and volume of these clods were measured by computer. The isolated clods showed comparable behavior on both trays. The small clods were almost always decreasing in volume until they disappeared. The other clods swelled during the first rain or the first two rains, and then decreased in area and volume. The decrease was faster for volume than for area. This probably reflected a soil detachment phenomenon, which mostly affected the heights of the clods. On the high concentration tray, the close inter-proximity of the clods induced merging and the formation of blocks. The rate of decrease of clod volume as a function of cumulative precipitation could be modeled using exponential and linear equations. Small and intermediate-sized clods showed an exponential decrease that was smoother as the clod size increased. Large clod volume decrease was almost linear. We were further able to model the trend of the slope parameter of the exponential decrease, as a function of clod size. Our study has shown how the DEM recording and image analysis can be used to quantify the evolution of clods under rainfall, improve our understanding of clod dynamics under rainfall and roughness parameterization. The size dependency of clod volume decrease is important for soil conservation decisions. This will obviously affect crust formation, surface armoring, soil erosion and surface permeability to water and gas.

1. Introduction Soil microtopography underlies soil-water interaction such as erosion, deposition and infiltration, and in turn, many of these surface processes alter surface morphology. Hence, surface microtopography results from the interaction and feedback between soil and water mechanisms. Some studies have already been undertaken to predict the changes occurring when raindrops hit the soil surface and cause the breakdown of aggregates and clods by slaking, micro-cracking, mechanical disruption and transfer of soil fragments by splash (Bradford et al., 1987; Nearing et al., 1994; Bresson and Moran, 2004; Marzen et al., 2015). Other studies have focused on soil crust formation (Le Bissonnais et al., 1989; Freebairn et al., 1991; Bielders and Baveye,

⁎

1

1995; Le Bissonnais et al., 1995; Bresson et al., 2004; Gallardo-Carrera et al., 2007) or soil loss evaluation (Römkens et al., 2001; Licznar and Nearing, 2003; de Bie, 2005). After tillage implements, the surface of cultivated soil is built up at small scales from an arrangement of clods and aggregates. According to Römkens and Wang (1986), Huang and Bradford (1992) and Takken (2000), several types of surface roughness can be determined: Micro relief variations of the order of one millimeter are due to soil grains and aggregates. Surface variations of the order of 10 mm are due to cloddiness and are studied as random roughness. An oriented roughness of > 100 mm may also be present and caused by tillage (Allmaras et al., 1966). On a wider scale, surface variations define our very landscape. Here, our paper shall focus solely on cloddiness.

Corresponding author. E-mail address: [email protected] (E. Vannier). Presently at: Inra, Université de Lorraine, UMR 1120 “Laboratoire Sols et Environnement”, F-54505 Vandœuvre-lès-Nancy, France.

http://dx.doi.org/10.1016/j.catena.2017.09.017 Received 15 December 2016; Received in revised form 21 September 2017; Accepted 25 September 2017 Available online 01 October 2017 0341-8162/ © 2017 Elsevier B.V. All rights reserved.

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Major studies have already investigated the role of tillage practice in erosion or run-off control (Moldenhauer and Koswara, 1968; Lyles et al., 1969; Stuttard, 1984; Elwell, 1989; Darboux et al., 2001; Gómez and Nearing, 2005; Hemmat et al., 2007). Some of these studies (Moldenhauer and Koswara, 1968; Lyles et al., 1969; Stuttard, 1984; Elwell, 1989) examined the combined effects of clod size, clod density, soil texture and other soil properties when investigating clod resistance to breakdown by simulated rainfall. Stable clods lessen soil detachment due to raindrop impact, seal development and therefore run-off generation and soil loss. These experiments were performed in a laboratory with artificial soils prepared using air-dried clods. Measurements of soil cloddiness were mainly expressed in terms of different size ranges obtained by sieving. However, in Elwell (1989), a different approach was chosen. A process-orientated model following clod breakdown under rainfall was introduced. The height of an initial hemispherical clod was reduced due to soil erosion. Inferred variables related to clod geometry (height and diameter at ground level). These dimensions were deduced from elementary vertical measurements taken from above the tray. Then, the rate of detachment of the soil was estimated by regression analysis based on the average cumulated depth of soil detached against cumulative rainfall energy. Photogrammetry and laser scanners have been used to measure surface elevations at plot or micro plot scale. The derived digital elevation models (DEMs) are suitable to study the variations of soil surface roughness (Darboux et al., 2001; Jester and Klik, 2005; Haubrock et al., 2009; Eitel et al., 2011). In our recent studies (Taconet et al., 2010; Taconet et al., 2013; Chimi-Chiadjeu et al., 2014; Vannier et al., 2014), we demonstrated that it is possible to retrieve automatically the characteristics of clods from millimetric-resolution DEM of the soil surface using different segmentation methods. In the present paper, we shall consider the evolution of soil clods under simulated rainfall. The main objective is to demonstrate the capability of automatic analysis of soil surface DEM in modeling clod evolution under rainfall. Two indices of surface roughness characterizing the area and volume of the clods are defined. We relate them to previous studies of roughness evolution under cumulated precipitation, performed with different indices. Then, we use them to study the influence of clod initial concentration and finally, to introduce a trend modeling of clod evolution under simulated rainfall.

Fig. 1. DEM of the low clod concentration (LCC) tray.

Fig. 2. DEM of the high clod concentration (HCC) tray.

Table 1 Characteristics of rainfall simulations.

Rainfall Rainfall Rainfall Rainfall Rainfall

2. Materials and methods

n° n° n° n° n°

1 2 3 4 5

Intensity (mm·h− 1)

Duration (min)

Cumulated rainfall P (mm)

33 33 42 42 42

60 60 38 51 90

33 66 93 129 192

2.1. Soil preparation arrangement (Table 1). Initial intensity was 33 mm·h− 1 (56 sweeps/ min). During the first rainfall, every clod reached saturation. At the very beginning of the second rainfall, percolation was visually observed from the bottom outlet of both trays. Then, in order to speed up clod erosion, rain intensity was increased to 42 mm·h− 1 (72 sweeps/min). The three ensuing rains were stopped once the soil surfaces seemed to have evolved visually. We could see a smoothing and leveling of clods until disappearance of some of them. The HCC tray was also subjected to the formation of blocks of clods as will be presented later in more detail. For each stage, the soil surface elevation was recorded with an instantaneous-profile laser scanner (Darboux and Huang, 2003) at a grid spacing of 0.5 mm in x and y, and of 0.1 mm in z. Briefly, the scanner consisted in lasers generating a line on the soil surface and a camera set at an angle. The shape of the laser line recorded by the camera allowed the measurement of the surface geometry along a profile in the x-z plane. The laser-camera assembly was moved automatically along a rail (x-axis), allowing for the measurement of the whole surface geometry. Since the horizontal spatial resolution (i.e. the ability of the scanner to measure laps) was better than 0.5 mm, the spacing of 0.5 mm in xy was maintained. With a rough surface, there were about 20% of missing data points due to shadow effect, i.e. the laser is hidden from the

Two trays of a 50 × 50 cm2 surface area and a depth of 10 cm were used. Their permeable bottom allowed for water percolation. The trays were prepared with soil collected from the top 15 cm of the A horizon of an Alfisol (Soil Survey Division Staff, 1993). This silt loam soil had a composition of 11% of clay, 60% of silt and 29% of sand, and an organic matter content of 2%. Initial soil moisture was 2.4% of the total soil mass. Using a hand scoop, the trays were filled with loose soil, creating a structure similar to a seedbed (except for the rows). Air-dried clods of various sizes were set upon the soil surfaces. On each tray, a different clod concentration was used: the low clod concentration (LCC) tray had a clod concentration of 530 m− 2 (Fig. 1) and the high clod concentration (HCC) tray of 805 m− 2 (Fig. 2). Soil surface evolution was performed with a laboratory rainfall simulator, similar in design to the one described in Foster et al. (1979). It was equipped with 4 oscillating nozzles (Spraying Systems Co., Wheaton, Illinois, USA. Veejet type 6550) fed at 0.7 bar with deionised water. The simulator was located 6.1 m above the soil surface, allowing raindrops to reach the soil surface with a velocity close to their terminal velocity. Raindrops had a median size diameter of 1.5 mm. Rainfall intensity was set by adjusting the number of sweeps per minute. A set of five successive rainfalls of two intensities and different durations was carried out in order to produce changes in surface elevations and clod 213

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include also the proportion of the category Cnamong the whole set of clods, the numerator is calculated with all i ∈ Cn, and the denominator is calculated with all i ∈ {C1 ∪ C2 ∪ C3}. We then considered the normalized volume variation of clods, given by the expression:

camera by the roughness (Darboux and Huang, 2003). To reduce the amount of missing points, two records, with a rotation of 180° between them, were taken for each DEM retrieval. The frames were trimmed and the pair of records were repositioned by intercorrelation. They were then merged by taking the data found exclusively on each record and averaging the repetitive data. The remaining 7% of missing data points were estimated by the nearest neighbor interpolation. The main absolute difference between the common elevation points of a pair of records was slightly < 1 mm. So, the vertical precision of the final DEM was 1 mm. Thus, the elevations were re-scaled at a 1 mm resolution. In order to avoid an edge effect and to allow for an individual clod survey, the dimensions of our studied DEMs were 32.5 × 32.5 cm2. The delimitated areas tried to reduce the number of truncated clods.

VV (j ) =

We performed automatic clod delineation by an elevation thresholding on the DEM. Indeed, the pixels belonging to clods are labelled after the segmentation by thresholding. Since pre-sieved clods were set upon a horizontal soil surface, this surface is used as reference for elevations. And clods have positive elevations. So the clods are detected as having elevations superior to 1 mm, which is the vertical precision of the final DEM. This led to a binary image that was segmented to obtain the contours of clods by the Matlab function “contour”. This function captures the level lines of connected pixels that have the same value in the image. A minimum length of 20 mm was required for the contour perimeter so as to avoid those small aggregates that make up the surface of the soil supporting the clods. Only the clods fully contained in the image were detected. The borderline clods were not taken into account. Then, the characteristics of clods were evaluated using the elevation values from the DEM, for the selected data points belonging to each clod. Some clods were very close together and were not separated by DEM analysis. They constitute what we call blocks of clods. There appeared to be three categories of segmented objects:

s(j ) = ae−bP (j)

(3)

s (j ) = α − βP (j )

(4)

where s(j) represents the modeled data, a and b are parameters of the exponential model, and α and β are parameters of the linear model: a and α are amplitude coefficients, b and β are slope coefficients. These parameters are estimated by the least squares method. When applied to the clod normalized volume (or area) variation of clods VV(j) (or AV(j)), which is dimensionless, we obtained:

– C1: Single clods that were present upon the surface from the initial stage to their disappearance or to the final stage if not disappeared; – C2: Stable blocks of clods that were present upon the surface from the initial stage to the final stage; – C3: Unstable clods and blocks, including single clods at the initial stage that merge with a block after one of the five rainfalls, denoted rainfall n° j, with 1 ≤ j ≤ 5, blocks that merge together after rainfall n° j, blocks or clods that split into two parts after rainfall n° j and clods that appear after rainfall n° j.

b=−

∆s (j ) 1 ∙ ∆P (j ) s (j )

(5)

β=−

∆s (j ) ∆P (j )

(6)

Thus, β can be interpreted as the rate of decrease of clod volume (or area) with cumulated precipitation, in mm− 1. With exponential modeling, b represents the rate of decrease of clod volume (or area), related to clod volume (respectively area), also in mm− 1. For a small value of b (and if bP(j) stays small) the linear approximation of the exponential leads us to compare a and α and ab and β. Now, P(j) is contingent upon rainfall intensity and time. If DR appoints the rate of soil detachment for the unit areas of 32.5 × 32.5 cm2 of both trays and provided that the rain intensity is constant throughout the trend study, it can be stated DR that β is proportional to μ . ∑ V (0) , where μ is the bulk density. Please

Statistical roughness parameters are limited in their ability to describe rough surface breakdown (Bertuzzi et al., 1990). The percentage of ground area occupied by clods has been suggested by Elwell (1989) as an index of surface roughness in soil loss. Elwell (1989) also studied and modeled the variation of clod volume with rainfall energy as a function of the initial clod diameter. We therefore introduce the normalized area variation of clods as:

i i

notice here, that immediately after the end of rainfall j = 2, the intensity of the rain was set at 42 mm·h− 1 and was kept at this value till the end (Table 1). Thereafter, every modeling of AV(j) and VV(j) decrease was performed from the end of rainfall j = 2 to the end of rainfall j = 5, and hence for a constant rain intensity. In order to check the validity of Eqs. (3) and (4), we defined a reliability factor ε:

∑i Ai (j ) ∑i Ai (0)

(2)

where Vi(j) is the volume enclosed in clod (or block) n° i at stage after rainfall n° j and Vi(0) is the initial volume enclosed in clod (or block) n° i. As for AVCn, we shall denote VVCn the normalized volume variation calculated within the subset of clods Cn. AV(j) and VV(j) are normalized indices and are dimensionless. Some authors like Zobeck and Onstad (1987), Guzha (2004) and de Oro and Buschiazzo (2011) have observed that random roughness (RR), which was estimated with standard deviation of heights, decreases exponentially with the increase in cumulated precipitation P. Bauer et al. (2015) also included a linear model of the roughness decrease. So, we further investigated modeling both indices AV(j) and VV(j) as exponential and linear functions of P(j) according to the following equations:

2.2. Soil surface analysis

AV (j ) =

∑i Vi (j ) ∑i Vi (0)

(1)

ε=

where Ai(j) is the area filled by clod (or block) n° i at stage after rainfall n° j, 0 ≤ j ≤ 5 and Ai(0) is the initial area filled by clod (or block) n° i. Let us notice that, by definition, as the normalization is performed with the initial stage, AV does not take into account the area of clods that will appear after rainfall n°j, with j > 0. Indeed these clods are very small and disappear during the subsequent rainfall, so they are present only for one stage. By default, the sums are calculated within the whole set of clods of a tray, i ∈ {C1 ∪ C2 ∪ C3}. AV can also be computed within a subset of clods Cn. It is then denoted AVCn. In that case, in order to

∑j (so (j ) − sm (j ))2 ∑j (so (j ))2

(7)

where so(j) is the j observed data and sm(j) is the j modeled data. ɛ measures the normalized deviation between observed and modeled data. Smaller values of ɛ indicate a more valid model. Approximating clods as half spheres, the diameter of clod i at stage after rainfall n° j is estimated by: th

di (j ) = 2.

214

3

3. Vi (j ) 2. π

th

(8)

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3. Results and discussion

diminution of their number correspond either to the disappearance of some clods or to the merging of a clod with a block of category C3. A large clod has a specific behavior. After rainfall j = 2, it breaks up but still sticks together (it becomes what Roger-Estrade et al., 2004 call a “φ clod”). During the following rainfalls, the breaking up goes on dislocating it, and finally, the φ clod smooths. No blocks were present at the initial stage. The C3 clods and blocks represent 5% of the clods at the initial stage. Their evolution was mainly caused by rearrangement of the blocks by splitting or merging. A small clod was also newly detected after rainfall j = 2. Several phenomena intervened at the same time and could be globally neutral for the cardinal of C3. As will be seen later, it is the small-sized clods that disappear. We observed a slight acceleration in disappearances after rainfall j = 3. This might be caused by the increase in intensity (Table 1). However, the two rates of intensity employed, i.e. 33 mm·h− 1 and 42 mm·h− 1, stay close together. The linear trend in the decrease of clod volume for large clods (see the next section) shows that the change in intensity has no impact on this category of clod. The clod evolution in the HCC tray was more complex because blocks were present since the initial stage, owing to the locally-higher clod concentration (Table 2). A growing portion of the C1 clods disappeared after the successive rainfalls. At the final stage, 53% of them have disappeared. It is more than for the LCC tray (38%) and can be explained by the smaller size of the clods on the HCC tray. The blocks being of a large size, the total amount of rain is not sufficient to make them disappear. Concerning the C3 clods and blocks, more phenomena of splitting and merging took place due to the proximity of the clods on the HCC tray. The cardinal of C3 does not reflect this fact because reductions by merging are compensated for by augmentations from splitting.

3.1. Evolution of clods with cumulated precipitation

3.2. Quantification of surface roughness

The soil was initially dry and got saturated during the first rainfall. Considering clod evolution, three phenomena came to light: the disappearance of a clod, the appearance of a clod and the merging of clods to form a block. For the HCC tray, a fourth phenomenon also occurred: the evolution of a block. At the initial stage, for the LCC tray, 58 clods were fully contained within the image of the soil surface and were automatically detected (Fig. 3). There were 55 clods belonging the category C1 and 3 clods belonging to the category C3 (Table 2). The equivalent diameter of the clods (Eq. (8)) spreads from 3.6 mm to 76.0 mm. The median is 18.6 mm. The HCC tray is characterized by a greater clod concentration of 805 m− 2 (against 530 m− 2 for the LCC tray). At the initial stage, 54 clods or blocks of clods, including 10 blocks, were automatically detected. There were 34 clods of category C1, 3 blocks of category C2 and 17 remaining clods and blocks of category C3 (Table 2). The C1 clod diameters spread from 5.1 mm to 40.0 mm. The median is 14.2 mm, meaning that the C1 clods of the HCC tray were mostly smaller than those of the LCC tray. Table 2 represents summarily the evolution of the three categories of clods C1, C2 and C3 on the LCC and the HCC trays. The C1 clods of the LCC tray represent 95% of the clods. The

Let us now consider the trends of the roughness indices AV and VV as a function of cumulated precipitation. As shown by Fig. 4a, for the LCC tray, the normalized area covered by the clod bases AV increases rapidly by 22% after 33 mm of rainfall. It then increases slightly before decreasing after 66 mm of rainfall. At the final stage, the clod bases stay more spread-out than at the initial stage. Similar behavior of increased roughness before decrease has been observed by Dalla Rosa et al. (2012) for conventional tilled soils subjected to simulated rainfall. They used a different roughness index, called RI that was derived from the semivariogram of the soil DEM. RI increased until about 50 mm of cumulated precipitation and then decreased. For clods and blocks on the HCC tray, AV increased by 17.5% (against 22% for the LCC tray) for 33 mm of rainfall (Fig. 4b). Indeed, the swelling phenomenon responsible for the AV increase after the first rainfall, was limited on this tray due to the local proximity of clods and blocks, and to the presence of smaller clods. The normalized area variation then decreased for the second rain to the fourth one and ended by a slight increase. At the final stage, the whole clods and blocks were slightly more spread-out than at origin, as it was already the case for the LCC tray. Modeling of AV decrease was performed after the 2nd rainfall (66 mm), for all clods present at the initial stage and for the clods of the

47 34

2

50 7

38

1

39

30

24

52 29

15

100

6

31

16

50

37

54

41

12

40

32 49 48

21

55

y (mm)

11

150

10 18

46

43 23

28

4

53 20

14

200

44

57 50 27

30

45 3

33

8

20

19

36

42 58

250 22

26

35

51

25

9

10

40

13

56

300

5

17

0 0

50

100

150

200

250

300

x (mm)

Fig. 3. Top view of the automatic delineation of clods on the DEM of the LCC tray, at the initial stage.

This simple approximation has been applied before (Kamphorst et al., 2005). In the present paper, it is used only to get an order of magnitude of the size of clods. The clods could be modeled more accurately by half ellipsoids, but this would introduce additional parameters (Vannier et al., 2014).

Table 2 Evolution of the number of clods on the LCC and HCC trays, for the three categories of clods C1, C2 and C3, at the initial stage and after each rainfall. Tray LCC

HCC

C1 C2 C3 C1 C2 C3

Clods Blocks Objects Clods Blocks Objects

Initial stage

Rainfall 1

Rainfall 2

Rainfall 3

Rainfall 4

Rainfall 5

55 0 3 34 3 17

52 0 4 32 3 9

49 0 5 30 3 12

41 0 2 26 3 13

37 0 2 21 3 12

34 0 1 16 3 12

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Fig. 4. Normalized area variation of clods as a function of cumulated rainfall for the LCC tray a) and the HCC tray b).

Table 3 Parameters of normalized area variation of clods as a function of cumulated rainfall, with exponential model (a and b) and linear model (α and β). ɛ is the reliability factor denoting the deviation between data and model. Tray LCC HCC

a AV AVC1 AV AVC1 AVC2 AVC3

1.33 1.28 1.21 0.47 0.12 0.63

ɛ

b −3

1.1 × 10 1.1 × 10− 3 1.0 × 10− 3 3.3 × 10− 3 7.7 × 10− 4 6.5 × 10− 5

α −3

3.0 × 10 2.6 × 10− 3 4.4 × 10− 2 1.7 × 10− 3 2.1 × 10− 2 6.5 × 10− 2

1.32 1.27 1.19 0.49 0.12 0.64

β

ɛ −3

1.3 × 10 1.2 × 10− 3 1.1 × 10− 3 1.0 × 10− 3 8.3 × 10− 5 3.9 × 10− 5

2.1 × 10− 3 1.6 × 10− 3 4.5 × 10− 2 1.0 × 10− 2 2.2 × 10− 2 6.5 × 10− 2

exponential model, only a is dependent on the area variation magnitude, we get b = 3.3 × 10− 3 irrespective of the normalization. The values of ɛ show that the exponential model is more suitable for the C1 clods on this tray. The values of ɛ for the other categories of clods are very comparable for both models. The C2 blocks are not much eroded as shown by the low values of b and β. Due to the presence of large blocks, the category C3 of objects represents 57% of the normalized area variation. This is the highest difference between the HCC and the LCC trays. With this category, the area variation is oscillating (i.e. increasing, then decreasing, and then increasing again) due to merging and splitting competing with swelling and erosion. The exponential modeling is thus not suitable to this category, as shown by a more elevated value of ɛ (Table 3). During the first rainfall, the volume filled by the overall clods and blocks VV increased by 12% on the LCC tray and by 11% on the HCC tray; it then decreased (Fig. 5a and b). After the last rainfall, clods and blocks occupied 87% of the initial volume on both trays. It shows that area evolution goes along with height decrease. Total loss of volume between the first and final rainfalls amounts to 25% and 24% for the LCC and the HCC tray, respectively. This can be explained by the disappearance of some clods, the lowering of clod heights and soil detachment. The total volume of soil, vl, lost between the first and last rainfall amounts to 1.02 × 105 mm3 for the LCC tray against 7.82 × 104 mm3 for the HCC tray. Knowing the bulk density of clods, μ, and supposing that soil moisture stays constant during the following rainfalls, it is possible to determine the mass lost ml by multiplying μ by v l. When modeling the variation of VV and VVC1 with cumulated precipitation according to Eq. (3) for the LCC tray, inferred values of a and

different categories (Table 3). The overall parameters for AV of both trays are very close together. Parameter b represents the rate of decrease. Its low value (around 10− 3) shows that this rate is almost linear. As, will be shown later, this is due to the presence of large clods. The linear and exponential models are therefore in good agreement since a and α on the one hand, and ab and β on the other hand, are comparable. The slope parameter of the exponential model b has the same order of magnitude as found by Bauer et al. (2015) for a silt loam soil, and with both roughness indices based on the standard deviation of the heights, RC and RR. For the LCC tray, the parameters for AV and AVC1 (Table 3) are close together as it can be seen also on Fig. 4a. The low values of ɛ show that exponential and linear models are relevant, and that linear model is slightly more suitable (lower ɛ). The parameters a and b of AV model of the HCC tray are slightly smaller than those of the LCC tray (Table 3). It can be explained by the presence of large blocks that are less eroded than the smaller objects. We can also notice that the values of ɛ are higher than for the LCC tray. This is due to the instability of the clods and blocks of the C3 category, which represent more than half of the area variation. Let us now analyze in more detail what takes place for each category of clods and blocks (Fig. 4b and Table 3). For the C1 clods, fitting AVC1 with an exponential from rainfall j = 2 to rainfall j = 5 leads to a = 0.47 and b = 3.3 × 10− 3, with ɛ = 1.7 × 10− 3. Linear fit yields α = 0.49, β = 1.0 × 10− 3 and ɛ = 1.0 × 10− 2. Intercepts are very close for both models. With the linear model, the slope β is sensitive to the magnitude of the area variation (β has to be compared to ab). We would have hadβ = 3.1 × 10− 3 (and ɛ = 1.0 × 10− 2) if AVC1 were normalized within C1 instead of within{C1 ∪ C2 ∪ C3}. With the

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Fig. 5. a) Normalized volume variation of clods as a function of cumulated rainfall for the LCC tray a) and the HCC tray b).

Table 4 Parameters of normalized volume variation of clods as a function of cumulated rainfall, with exponential model (a and b) and linear model (α and β). ɛ is the reliability factor denoting the deviation between data and model. Tray LCC HCC

a VV VVC1 VV VVC1 VVC2 VVC3

1.20 1.05 1.19 0.31 0.12 0.76

ɛ

b −3

1.7 × 10 1.6 × 10− 3 1.8 × 10− 3 3.7 × 10− 3 1.7 × 10− 3 1.4 × 10− 3

α −3

2.3 × 10 2.4 × 10− 3 4.3 × 10− 2 5.2 × 10− 3 9.8 × 10− 3 5.9 × 10− 2

b are respectively a = 1.20 and b = 1.7 × 10− 3, ɛ = 2.3 × 10− 3 and a = 1.05, b = 1.6 × 10− 3, and ɛ = 2.4 × 10− 3 (Table 4). Decrease is faster than for area. It is also possible to model linearly VV and VVC1 with α = 1.18, β = 1.6 × 10− 3 and ɛ = 1.2 × 10− 3 and α = 1.03, β = 1.4 × 10− 3 and ɛ = 1.6 × 10− 3. Here the intercepts a and α are very close together, and ab is 20 to 28% higher than β. For the LCC tray, linear model is more suitable than exponential one. For the HCC tray, fitting VV as a function of cumulative precipitation, among the whole set of clods and among each category of clods, shows the same behavior as was already observed with AV (Fig. 4b and Table 3). Again, the values of ɛ show that the exponential model is more suitable for the C1 clods, and the values of ɛ for the other categories of clods are very comparable for both models (Table 4). We can notice that for the categories C2 and C3, the decrease is larger in volume than in area, as shown by higher slopes parameters. The partition between the C1 clods and the C3 objects is different in area and in volume (see amplitude parameters). It can be explained by smaller elevations of the C1 clods, reducing the volume, and higher elevations of the C3 objects, enhancing the volume. As the normalized indices AV and VV do not take into account the clods that appear after a rainfall, we completed the study by taking into account the clod coverage of the soil surfaces by all clods. It makes thus a change for the C3 category. The evolution in clod coverage, expressed as a percentage of soil surface, is given in Table 5. The increase in coverage-percentage indicates the expansion of the clod bases. After rainfall j = 1, spreading competes with the disappearance of the clods. We retrieve the overall trend of increase until rainfall j = 2 and then decrease, already observed with AV and VV. Nevertheless, the dynamic of clods and blocks is different depending on their category. The clod and block coverage for the HCC tray was close to that of the LCC tray, being slightly higher (see Table 5). This can be explained, for a locally-higher concentration of clods on the HCC tray, by a smaller

β

ɛ −3

1.18 1.03 1.15 0.29 0.12 0.75

1.2 × 10− 3 1.6 × 10− 3 4.6 × 10− 2 7.8 × 10− 3 1.2 × 10− 2 6.1 × 10− 2

1.6 × 10 1.4 × 10− 3 1.7 × 10− 3 7.1 × 10− 4 1.6 × 10− 4 7.9 × 10− 4

Table 5 Clod coverage of all the clods, expressed as a percentage of the DEM surface, at each stage of the soil surface. Tray LCC

HCC

Overall C1 Clods C3 Objects Overall C1 Clods C2 Blocks C3 Objects

Initial stage

Rain 1

Rain 2

Rain 3

Rain 4

Rain 5

24.7% 23.7% 1.0% 26.1% 8.6% 2.5% 15.0%

30.2% 29.0% 1.2% 30.6% 10.3% 3.0% 17.3%

30.4% 29.3% 1.1% 30.8% 9.8% 3.0% 18.0%

29.6% 28.5% 1.1% 27.5% 9.0% 2.8% 15.7%

28.6% 27.4% 1.2% 26.2% 8.0% 2.7% 15.5%

26.5% 25.5% 1.0% 26.7% 6.5% 2.7% 17.5%

size. Contrary to the C1 clods of the LCC tray, which represent 95% of the clods and follow the general trend, the C1 clods have lost 24% of their initial coverage after the rainfall j = 5. It can be explained by the smaller size. The C2 blocks follow the evolution of AVC2, which is increasing and then decreasing more and more slightly, remaining more spread-out than at origin. As the number of clods appearing after a rainfall is small and as these appeared clods are of small size, clod coverage for the C3 category follows the evolution of AVC3, which is oscillating. To see in more detail the partition between spreading, reduction and disappearance, the cumulative distribution functions of the equivalent diameter of the clods (Eq. (8)) were estimated for the C1 category, for which it is not biased by the instability of clods, and on the LCC tray, where these clods are more numerous than on the HCC tray. The cumulative distribution functions of diameters at the initial stage and after rainfall j = 1 show an increase in diameters caused by rain, except for the smaller clods that have a decreasing diameter (Fig. 6a). This phenomenon coincides with the increase observed in both area and volume of the clods. After rainfall j = 1, the y-intercept expresses the 217

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1 individual volume

0.8 initial stage after rainfall 1 after rainfall 2

0.6 0.4 0.2 0

a)

0

10

20

30

40 50 diameter (mm)

60

70

1

0.5

0

80

a)

1

40

60

120 140 80 100 cumulated precipitation (mm)

160

180

200

small clods

overall volume

0.8

after rainfall 3 after rainfall 4 after rainfall 5

0.6 0.4 0.2

b)

20

1

0.8

0

0

exponential modeling 0.6 0.4 0.2

0

10

20

30

40 50 diameter (mm)

60

70

0

80

b)

Fig. 6. Cumulative distribution functions of diameters as a function of cumulated rainfall for the LCC tray, at the first three stages a) and at the following stages b).

0

20

40

60

80 100 120 140 cumulated precipitation (mm)

160

180

200

Fig. 7. a) Normalized variation of small-sized clod volume as a function of cumulated rainfall for the LCC tray. b) Overall variation of small-sized clod volume as a function of cumulated rainfall.

percentage of clods that have disappeared, i.e. 5%. The cumulative distribution functions of the diameters after rainfall j and rainfall j + 1 show that the diameter of most of the clods remained stable, and a decrease in the diameter of a growing portion of the smaller clods (Fig. 6a and b). This decreasing trend may also be observed on the variation curves of both the area and volume of the clods. At the final stage, the y-intercept, i.e. the percentage of clods that have disappeared was 38%.

Table 6 Parameters a and b of exponential model of normalized volume decrease as a function of cumulated rainfall, for the isolated clods (C1) and the three classes of clod size. ɛ is the reliability factor denoting the deviation between data and model. Tray LCC

3.3. Volume rate of decrease as a function of clod size

HCC

Let us now consider the evolution in the volume of the individual clods of the category C1 as a function of their size. As for the preceding section, Eq. (3) was run with volumes measured from the end of rainfall j = 2 to the end of rainfall j = 5. During this process, the rain intensity applied was constant and set to 42 mm·h− 1. The clods of C1 of the LCC tray were separated into three classes of equal cardinal. We thus had a first class C1s of small clods of volume < 540 mm3 (equivalent diameter of 12.7 mm for half a sphere using Eq. (8)), a second class C1m of middle-sized clods of volume ranging between 540 and 3570 mm3 (between 12.7 and 23.9 mm in diameter), and a last class C1l of large clods of volume > 3570 mm3 (23.9 mm in diameter). The cardinal of the three classes was respectively 18, 19 and 18. As for the LCC tray, the clods belonging to the category C1 of the HCC tray were also separated into three classes, with the same inferred size limits. The first class of small clods C1s, contained 12 clods. The second class of middle-sized clods C1m, included 17 clods. And the last class of large clods C1l, had 5 clods. Small clods of volume < 540 mm3 (12.7 mm in diameter) have a rapidly decreasing volume. Fig. 7a represents the individual clod volumes normalized by the volume at the initial stage, with the mean slope in bold, for the LCC tray. Fig. 7b shows the normalized volume variation on the small-sized clods VVC1s with exponential modeling. Here the purpose is not to take into account the proportion of C1s clods among C1 but to follow the clod evolution, so the normalization in VVC1s was performed among the class C1s. Model parameters were a = 10.1, b = 0.047 and ɛ = 5.9 × 10− 2 (Table 6). Values of b are higher than those of VVC1 (1.6 × 10− 3), obtained with the whole clods of C1, proving that the smaller clods have a faster rate of decrease in volume and that this decrease is not linear. All these clods but one disappeared after 129 mm of rainfall. The parameters of exponential model for the volume variation of the clods of C1s on the HCC tray were a = 6.78, b = 0.045 and ɛ = 6.3 × 10− 2 (Table 6). These values are close (for a) or very close (for b and ɛ) to that of the LCC tray, leading us

Small clods Intermediate-sized clods Large clods Small clods Intermediate-sized clods Large clods

a

b

ɛ

10.1 1.88 1.18 6.78 2.01 1.29

4.7 × 10− 2 7.7 × 10− 3 1.2 × 10− 3 4.5 × 10− 2 10.4 × 10− 3 2.1 × 10− 3

5.9 × 10− 2 1.5 × 10− 2 6.6 × 10− 3 6.3 × 10− 2 6.6 × 10− 2 7.4 × 10− 3

to consider that the small clods have the same behavior on both trays. Intermediate-sized clods of volume ranging between 540 (12.7 mm in diameter) and 3570 mm3 (23.9 mm in diameter) have a slower decrease on average, proven by the parameter b being smaller than for the small-sized clods. Model parameters are a = 1.88, b = 7.7 × 10− 3 and ɛ = 1.5 × 10− 2 for the LCC tray (Table 6, Fig. 8a and b). Again, volume decrease is not linear. The total amount of rainfall is not sufficient to make the clods disappear. Their average final volume amounts to 45% of the initial volume. For the clods of C1m on the HCC tray, the fit yielded a = 2.01, b = 10.4 × 10− 3 and ɛ = 6.6 × 10− 2. Decreases are rather comparable for both trays. Smaller values of a and b show that the intermediate-sized clods were less eroded than the small ones. Large-sized clods of volume > 3570 mm3 (23.9 mm in diameter) have an even slower rate of decrease, with a = 1.18, b = 1.2 × 10− 3 and ɛ = 6.6 × 10− 3 for the LCC tray (Table 6, Fig. 9a and b). Decrease is likewise linear. At the final stage, the average volume amounts to 94% of the initial volume. For large clods of the HCC tray, we got a = 1.29, b = 2.1 × 10− 3 and ɛ = 7.4 × 10− 3. The large clods of the category C1l are scarce, because clods of the HCC tray are mainly smaller than on the LCC tray, and because the unstable objects of the category C3 are numerous on the HCC tray. We can notice that the volume decrease tends to linearize as the size of clods increases (i.e. b gets smaller) and that among the categories of intermediate and largesized clods, clods seems to be a little more eroded on the HCC tray than on the LCC tray, asserted by higher values of b on the HCC tray (Table 6). This can be explained by the smaller size of clods on the HCC tray, for the intermediate and large-size classes. On average, under rainfall, the volume of small clods always decreases and swelling is not observed after the first rainfall of 60 min, as 218

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individual volume

1.5

Removing the fraction of clods with a diameter of < 8 mm in the Ida silt loam and the Kenyon loam samples increased the rainfall energy necessary to initiate run-off. That is to say that the smaller clods have a rapid rate of soil detachment, as we also found in the present paper for clods of diameter < 12.7 mm. The fraction of clods of diameters ranging from 30 to 40 mm in every type of soil in Moldenhauer (1970) did not undergo much erosion, as was the case for clods of diameter > 23.9 mm in the present study. The possible reasons for this are that: 1) the surface area exposed to rainfall is much lower for big clods (compared to their volume) than for small clods and 2) wetting is slower for big clods since water has a longer way to reach their center. In Elwell (1989), for a ferric Luvisol in Zimbabwe, only clods with diameters above 25 mm were considered. These clods showed a linear decrease in depth of soil detached with cumulative rainfall energy. Smaller clods were not monitored. So, a partition can be raised between clods larger than 25 mm in diameter, compared to smaller clods. For big clods > 25 mm in diameter, the linear decrease in clod dimension shown by parameters related to soil detachment [RADB in Elwell, 1989, or parameter b in the present study] shows that the rate of soil detachment is constant with cumulative rainfall energy or precipitation.

1

0.5

a)

0

0

20

40

60

80 100 120 140 cumulated precipitation (mm)

160

180

200

1.5

overall volume

intermediate-sized clods exponential modeling

1

0.5

0

0

20

40

60

b)

80

100

120

140

160

180

200

cumulated precipitation (mm)

Fig. 8. a) Normalized variation of middle-sized clod volume as a function of cumulated rainfall for the LCC tray. b) Overall variation of middle-sized clod volume as a function of cumulated rainfall.

3.4. Modeling of isolated clods of both trays as a function of clod size Interestingly, the clods of the category C1, which are single isolated clods that did not interact with other clods, have the same behavior on both trays. Since the parameters a and b of Eq. (3) are different for all three classes of clod size, C1s, C1m and C1l, it means that we are able to further model the decrease of clod volume as a function of cumulated precipitation by modeling parameters a and b, according to clod size. The rate of volume decrease, parameter b, can be modeled with a hyperbolic law:

individual volume

1.2 1 0.8 0.6 0.4 0.2 0

a)

0

20

40

60

120 140 80 100 cumulated precipitation (mm)

160

180

200

b=

overall volume

1 0.8 0.6 large clods

0.2

exponential modeling

0

b)

0

20

40

60

80 100 120 140 cumulated precipitation (mm)

160

180

(9)

where v0 denotes the mean volume of the subset of clods under scrutiny at their initial stage, in mm3, and f and g are parameters, in mm2 and in mm3 respectively. The C1 clods of both trays were gathered into a single set. Then, an initial subset was extracted with 19 clods of volume < 162 mm3 (diameter of 8.5 mm). After, the threshold on the volume was gradually increased in order to increase the cardinal of the subset, and thereby the mean volume of clods, evenly. Least squared estimation of parameters yielded f = 6.82, g = −94.4, and ɛ = 0.09. The satisfactory fit can be seen on Fig. 10. There is a good adequacy between the observed values of parameter b and their computed ones. The observed data can also be approximated by two straight lines (Fig. 10). They are determined with Eq. (10):

1.2

0.4

f v0 + g

200

Fig. 9. a) Normalized variation of large clod volume as a function of cumulated rainfall for the LCC tray. b) Overall variation of large clod volume as a function of cumulated rainfall.

b = γ − ηv0

for the other clods. This raises two hypothesis: either 1) swelling is apparent in the first minutes and then gives way to volume decrease, and hence cannot be observed after 60 min; or 2) swelling is negligible for small clods of diameter < 12.7 mm. The phenomenon of swelling was noticed for intermediate and large clods in the same proportions (from 1.0 to 1.4 of the initial volume). However, the rate of decrease in the volume of intermediate-sized clods remains quite high. By comparison, volume decrease is moderate for large-sized clods. According to Lyles et al. (1969), where the soil and rainfall characteristics studied were comparable to those of the present paper, clod size is a major factor influencing soil detachment during rain. Indeed, small clods are more sensitive to breakdown by raindrop impact than large clods, because of clod saturation (time and degree) that occurs earlier than for bigger clods. We found the same behavior in the present study. Moldenhauer (1970) also observed that increase in minimum clod size leads to smaller wash erosion for Ida silt loam and Kenyon loam soils. He claimed that one measure representative of clod breakdown under rainfall is the precipitation energy necessary to initiate run-off.

(10) −3

The y-intercepts are γ = 0.14 and γ = 7.3 × 10 and the slopes are η = 3.6 × 10− 4 and η = 1.1 × 10− 6, with reliability factors ε = 2.7 × 10− 2 and ε = 1.5 × 10− 2, respectively. The two straight lines indicate limit behavior for the rate of decrease of clod volume b, with the two extreme classes of clod size, the smallest and the biggest. The first straight line was assessed with the subset of the smallest clods with a mean volume of < 350 mm3 (11 mm in diameter) (Fig. 10). These small clods showed a low swell or no swell, and a rapid decrease in volume, as was previously observed for the subsets of clods lesser than 12.7 mm. The second straight line was assessed with the subset including the largest clods, of mean volume > 1350 mm3 (17.3 mm in diameter), for which swelling is noticeable and soil detachment is moderate and slow. Therefore, as shown by the curve, the size dependency of clod volume decrease tends to reduce. The very low value of b validates the linear approximation of the exponential model and confirms a linear trend of volume decrease as a function of cumulative precipitation. It tallies with the observation that the soil 219

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C1 clods hyperbola linear approximations

Fig. 10. Parameter b of exponential model of normalized volume decrease as a function of the mean volume of the clod subset for isolated clods (C1) of both trays.

0.1

parameter b

0.08

0.06

0.04

0.02

0

0

1000 1350

350

2000

3000

4000

5000

6000

mean volume of clods (mm3)

observed clod dynamics. The size dependency of clod volume decrease is important for soil conservation decision. A fine tilth is often required for plant emergence but it would increase the clod slumping that is even greater when the clods are small. When clods are larger, the rate of decrease of the clod volume (parameter b) tends to decrease more and more slowly as a function of mean of clod volume. When b is small enough, the variation of clod volume as a function of cumulative precipitation gets linear. It corresponds to a constant rate of detachment of soil. However, if the dependency of b on the mean clod volume tends to reduce on average, the decrease of clod volume still undergoes individual variations. It can be seen in the spread of volume variations as a function of cumulative precipitation (Fig. 9a). That will obviously affect crust formation, surface armoring, soil erosion and surface permeability to water and gas.

detachment rate seems constant for clods > 23.9 mm in diameter in the preceding section. The amplitude parameter a has a very strong decrease and then nears a steady state (Fig. 11). The observed data can be approximated by straight lines (Eq. (10) with a instead of b) of y-intercepts γ = 33.3 and γ = 1.89 and of slopes η = 9.0 × 10− 2 and η = 1.5 × 10− 4, with reliability factors ε = 6.6 × 10− 3 and ε = 2.9 × 10− 3, respectively. As for parameter b, the straight lines of a as a function of the mean volume of the clods show a rapid decrease in volume of the smallest clods and a slow variation for the largest clod. One can notice that the second behavior of a occurs for lesser volumes than for b (about 770 mm3 or 14.3 mm in diameter). By evenly increasing the mean clod volume of a subset, we were able to make a more accurate study of the clod volume rate of decrease as a function of clod size. Both parameters a and b exhibit rather binary behavior. There is the trend of the small clods of < 11 mm in diameter, that are rapidly decreasing, as demonstrated by the larger values of a and b. The decrease of clod volume is even greater when the clods are small. Then there is the trend of large clods whose diameter exceeds about 17 mm, and whose values for a and b vary more slowly. Between these two trends, a transition takes place for intermediate-sized clods. While the soil surfaces were quite artificial in design (clods put on top of loose soil), practical conclusions can be drawn based on the

4. Conclusion In the present paper, we have studied the evolution of soil clods under simulated rainfall, with the help of DEM recording and image processing. The clods were automatically segmented on the DEM images after each rainfall and computer measurements were taken of the surface area and volume of these clods. The isolated clods showed comparable behavior on both trays of

16 C1 clods linear approximations

14

12

parameter a

10

8

6

4

2

0

0

350

770

1000

2000

3000

4000

5000

mean volume of clods (mm3)

220

6000

Fig. 11. Parameter a of exponential model of normalized volume decrease as a function of the mean volume of the clod subset for isolated clods (C1) of both trays.

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different clod concentration. The spreading of the clod bases went along with the reduction of clod heights and the disappearance of the smaller clods. After 60 min of rain, no swelling was visible for the smaller clods. The volume of these clods was only decreasing with the succession of rainfalls. The other clods swelled during the first rainfall event or during the first two rainfall events (i.e. during 60 to 120 min), and then decreased in area and volume. The volume decreased faster than the area. It most likely reflected a soil-detachment phenomenon that eroded the height of the clods. On the high clod concentration tray, the close inter-proximity of the clods induced merging and the formation of blocks. Therefore the evolution of clods was more complex on this tray. Within the category of unstable clods and blocks, the area or volume variation began to increase and decrease, but it ended by an increase. This was due to merging and splitting competing with swelling and erosion. It is possible to measure the volume of soil loss per clod and per block between stages, from the first rainfall to the final one (with constant moisture) and to relate this volume of soil loss to erosion. By applying exponential and linear equations, we were able to model clod-area and clod-volume rate of decrease as a function of cumulative precipitation. Taking clod size into account when modeling the volume of the isolated clods of both trays confirmed that the volume decreased faster for the small clods than for the larger ones, in agreement with results exhibited by previous authors. This raises again the compromise between tillage requirements and soil conservation. It was possible to further model the slope parameter b of the exponential decrease of volume, as a function of clod size. The behavior of b, with a very low value, was in agreement with our findings for the linear trends of large clods. It confirmed that the rate of soil detachment was constant throughout the life of these large clods as was already mentioned by Elwell, 1989. With DEM recording and image processing, it was thereby possible to revisit the survey of clod change under rain and propose new roughness indices. Soil roughness is a key parameter to our understanding of soil properties and soil-water interaction, most of which occur at millimeter scales. The size dependency of clod volume decrease is important for soil conservation decisions. That will obviously affect crust formation, surface armoring, soil erosion and surface permeability to water and gas. Future work will tackle a more in-depth analysis of the roughness of natural soil surfaces. Acknowledgments Grateful thanks to Bernard Renaux (INRA) for his technical expertise. This study was funded by the French program: “Programme National de Télédétection Spatiale” (AO2010-499016). References Allmaras, R.R., Burwell, R.E., Larson, W.E., Holt, R.F., Nelson, W.W., 1966. Total porosity and random roughness of the interrow zone as influenced by tillage. In: Conservation Research Report No 7. Agricultural Research Service, U.S. Department of Agriculture (22 p.). Bauer, T., Strauss, P., Grims, M., Kamptner, E., Mansberger, R., Spiegel, H., 2015. Longterm agricultural management effects on surface roughness and consolidation of soils. Soil Tillage Res. 151, 28–38. Bertuzzi, P., Rauws, G., Courault, D., 1990. Testing roughness indices to estimate soil surface roughness changes due to simulated rainfall. Soil Tillage Res. 17, 87–99. Bielders, C.L., Baveye, P., 1995. Processes of structural crust formation on coarse-textured soils. Eur. J. Soil Sci. 46, 221–232. Bradford, J.M., Ferris, J.E., Remley, P.A., 1987. Interrill soil erosion processes: II. Relationship of splash detachment to soil properties. Soil Sci. Soc. Am. J. 51, 1571–1575. Bresson, L.M., Moran, C.J., 2004. Micromorphological study of slumping in a hardsetting seedbed under various wetting conditions. Geoderma 118, 277–288. Bresson, L.M., Moran, C.J., Assouline, S., 2004. Use of bulk density profiles from Xradiography to examine structural crust models. Soil Sci. Soc. Am. J. 68, 1169–1176. Chimi-Chiadjeu, O., Le Hégarat-Mascle, S., Vannier, E., Taconet, O., Dusséaux, R., 2014. Automatic clod detection and boundary estimation from digital elevation model images using different approaches. Catena 118, 73–83.

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