# Quantification of Erosion in Selected Catchment Areas of the Ruzizi River (DRC) Using the (R)USLE Model

^{1}

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^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Implementation of Freely Available Datasets into (R)USLE

^{−1}· h

^{−1}· yr

^{−1}.

_{i}is the mean monthly rainfall (mm) and p is the mean annual rainfall (mm).

^{−1}· MJ

^{−1}· mm

^{−1}.

_{csand}is the factor of low soil erodibility due to coarse-grained sand particles in the soil; f

_{cl-si}is the factor for low soil erodibility due to high clay-silt ratios; f

_{orgc}is the factor for reduced soil erodibility due to high carbon content; f

_{hisand}is the factor for reduced soil erodibility due to very high sand content; m

_{s}is the percentage of sand with grain sizes of 0.05–2 mm; m

_{silt}is the percentage of silt with grain sizes of 0.002–0.05 mm; m

_{c}is the percentage of clay with grain sizes of <0.0002 mm; orgC is the percentage of organic carbon.

_{i.j}is the slope length factor with coordinates i.j for one grid cell; A

_{i.j}is the flow accumulation area at the inlet of a grid cell counting the number of cells of the part of the catchment with flow orientation into the respective grid cell; D is the size of a grid cell (m); the exponent m represents the ratio β of rill erosion, which caused by overland flow to inter-rill erosion caused by the impact of raindrops; θ is the slope angle in degrees; a

_{i.j}is the aspect or exposition of the grid cell.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Author(s), Region, Formula | Model | Factor |
---|---|---|

[17], Chemoga WS, Ethiopia and [18], Awassa, Central Ethiopia | USLE | Rainfall erosivity (R) |

R = −8.12 + (0.562 × P) | (2) | |

[19], Kulhan, India | USLE | Rainfall erosivity (R) |

R = P × 0.5 | (3) | |

[16], Kivu, DRC and Rwanda | USLE | Rainfall-runoff erosivity (R) |

R = 38.46 + 3.48 × P | (4) |

^{−1}h

^{−1}per year); P is the mean annual rainfall (mm).

Author(s), Region, Formula | Model | Factor |
---|---|---|

[20], Nethravathi, Southwest India ** | RUSLE | Soil erodibility (K) |

K = 27.66 × m^{1.14} × 10^{−8} × (12 − a) + 0.0043 × (b − 2) + 0.0033 × (c − 3) | (7) | |

$m=silt\left(in\%\right)+veryfinesand\left(in\%\right)\times \left(100-clay\left(in\%\right)\right)$ | (7a) |

_{csand}is the factor of low soil erodibility due to coarse-grained sand particles in the soil; f

_{cl-si}is factor for low soil erodibility due to high clay-silt ratios; f

_{orgc}is the factor for reduced soil erodibility due to high carbon content; f

_{hisand}is the factor for reduced soil erodibility due to very high sand content; m

_{s}is the percentage of sand with grain sizes of 0.05–2 mm; m

_{silt}is the percentage of silt with grain sizes of 0.002–0.05 mm; m

_{c}is the percentage of clay with grain sizes of <0.0002 mm; orgC is the percentage of organic carbon. ** a is organic matter in %; b is a structure code in which (1) is very structured or particulate, (2) is fairly structured, (3) is slightly structured, and (4) is solid; c is the profile permeability code in which (1) is rapid, (2) is moderate to rapid, (3) is moderate, (4) is moderate to slow, (5) is slow, and (6) very slow.

Author(s), Region, Formula | Model | Factor |
---|---|---|

[16], Kivu, DRC and Rwanda * | USLE | Slope Length and Steepness Factor (LS) |

${L}_{i,j}=\frac{{\left({A}_{i,j-in}+{D}^{2}\right)}^{m+1}-{A}_{i,j-in}^{m+1}}{{D}^{m+2}\times {x}_{i,j}^{m}\times {\left(22.13\right)}^{m}}$ | (8) | |

$m=\frac{\beta}{1+\beta}$ | (8a) | |

$\beta =\frac{sin\theta /0.0896}{3{\left(sin\theta \right)}^{0.8}+0.56}$ | (8b) | |

${x}_{i,j}=\left(sin{a}_{i,j}+\mathrm{cos}{a}_{i,j}\right)$ | (8c) | |

${s}_{i,j}=10.8sin{\theta}_{i,j}+0.03,\mathrm{tan}{\theta}_{i,j}9\%$ | (9a) | |

${s}_{i,j}=16.8sin{\theta}_{i,j}-0.50,\mathrm{tan}{\theta}_{i,j}9\%$ | (9b) | |

[17], Blue Nile Basin, Ethiopia ** | USLE | Topographic factor (LS) |

$LS={\left(\frac{\lambda}{22.13}\right)}^{m}\times \left(0.065+0.045\times x+0.0065\times {x}^{2}\right)$ | (10) | |

[20], Nethravathi, Southwest India | RUSLE | Topographic factor (LS) |

$LS={\left(\frac{{Q}_{a}M}{22.13}\right)}^{y}\times \left(0.065+0.045\times {S}_{g}+0.0065\times {S}_{g}{}^{2}\right)$ | (11) | |

[2], Palouse, Idaho, US *** | RUSLE | Topographic factor (LS) |

$LS={\left(\frac{\lambda}{22.13}\right)}^{0.5}\times \left(10.8sin\theta +0.03\right)$ s < 9% | (12a) | |

$LS={\left(\frac{\lambda}{22.13}\right)}^{0.5}\times {\left(\frac{sin\theta}{0.0896}\right)}^{0.6}$ s > 9% | (12b) |

_{i.j}is the slope length factor with coordinates i.j for one grid cell; A

_{i.j}is the flow accumulation area at the inlet of a grid cell counting the number of cells of the part of the catchment with flow orientation into the respective grid cell; D is the size of a grid cell (m); the exponent m represents the ratio β of rill erosion which caused by overland flow to inter-rill erosion caused by the impact of raindrops; θ is the slope angle in degrees; a

_{i.j}is the aspect or exposition of the grid cell. Karamage et al. [16] were using the formula of slope steepness factor based on McCool et al. [27] who differentiate between slope angles of less and more than 9% to consider also steep angles in their study area along the East African Rift. ** λ is the distance between onset of runoff and the receiving channel; m is an exponent depending on the slope steepness, this factor will not be calculated as by Karamage et al. [16] but assigned due to slope angle in percent (0 to 5% will be assigned with values of 0.2 to 0.5) which is according to Wischmeier and Smith [1]; x is the slope angle in percentage. *** Q

_{a}is the flow accumulation grid with the grid size M; y is an exponent depending on the slope angle (see explanation above for exponent m); S

_{g}is the slope angle in percentage.

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**Figure 1.**Location of the study area on the African continent (

**A**), in Eastern Africa (

**B**), and in the Ruzizi catchment area in the Eastern DRC near Bukavu at Lake Kivu (

**C**).

**Figure 2.**Resulting maps of the single factors for RUSLE calculations; (

**A**) mean R factor calculated after Prasannakumar et al. [15]; (

**B**) K factor calculated after Karamage et al. [16]; (

**C**) LS factor calculated after Karamage et al. [16]; C factor calculated using the definitions of Malaysian Department of Agriculture (2010, cited from [23]) for rainy (

**D**) and dry seasons (

**E**); (

**F**) P factor [49].

Factor | Data Set | Provider | Spatial Resolution | Publication Year/Since |
---|---|---|---|---|

R | CHIRPS v2.0 (precipitation) | NASA, NOAA | 0.05° (5500 m) | 1981–recent (v2.0) |

K | AfSIS—Soil Grids (soil) | ISRIC | 250 m | 2017 |

L and S | SRTMv3 (DEM) | NASA | 1 second (30 m) | 2000, 2015 (v3) |

C | Sentinel 2a (multispectral: supervised classification is necessary) | ESA | 10 m | Mid–2015–recent |

P | Results of C calculations to be matched with DEM (see L and S calculations) |

**Table 2.**C factor for selected land cover classes in Malaysia [23:41ff] and assigned values used in this study.

Land Cover Type | C Factor [23] | January C Factor | August C Factor |
---|---|---|---|

Rangeland | 0.23 | ||

Forest / tree | |||

50% cover | 0.39 | ||

100% cover | 0.03 | 0.03 | 0.03 |

Bushes / scrub | |||

50% cover | 0.35 | ||

100% cover | 0.03 | 0.03 | 0.15 |

Grassland 100% cover | 0.03 | 0.03 | 0.30 |

Mining areas | 1.00 | 1.00 | 1.00 |

Agricultural crop | 0.38 | 0.38 | 0.40 |

Paddy (with water) | 0.01 | 0.01 | 0.01 |

Urbanized areas | |||

Low density (50% green area) | 0.25 | ||

Medium density (25% green area) | 0.15 | 0.15 | 0.15 |

High density (5% green area) | 0.05 | ||

Impervious (Parking lot, road, etc.) | 0.01 | 0.01 | 0.01 |

**Table 3.**Classes of Maximum Likelihood Classification and respective C factors, mainly based on the Malaysian Department of Agriculture (2010 [23:41], see Table 2).

Land Cover Class | Remarks | Area of Training Samples (% of 6.49 km²) | Area of Land Cover Class (% of 2300 km²) | C Factor | |
---|---|---|---|---|---|

January | August | ||||

Settlement, road | < 5% Vegetation | 20.60 | 7.82 | 0.01 | 0.01 |

Village | < 50% Vegetation | 1.34 | 9.04 | 0.15 | 0.15 |

Pit | 0% Vegetation, mostly artisanal mining | 0.24 | 0.04 | 1.00 | 1.00 |

Rice field | Mostly represented as areas with dense vegetation in a wetland-like area along flat valleys | 5.73 | 3.14 | 0.01 | 0.01 |

Crop land | Individual species were not distinguished | 25.74 | 17.71 | 0.38 | 0.40 |

Grass land | Wide areas, mainly along steep slopes in the hinterland of Ruzizi Valley, burning activities during the dry seasons | 12.83 | 29.98 | 0.03 | 0.30 |

Bush land | Low trees and bushes (Miombo woodland), natural vegetation in the region, some areas are burned during dry season | 5.94 | 19.22 | 0.03 | 0.15 |

Forest | Dense forests, mainly as riparian forest along Ruzizi tributaries | 4.75 | 9.96 | 0.03 | 0.03 |

Water | Mainly Ruzizi River and Lake Kivu | 22.82 | 3.10 | 0.00 | 0.00 |

**Table 4.**P factor under different conservation support practices [49].

Slope (%) | Contouring | Strip-Cropping | Terracing |
---|---|---|---|

0.0–7.0 | 0.55 | 0.27 | 0.10 |

7.0–11.3 | 0.60 | 0.30 | 0.12 |

11.3–17.6 | 0.80 | 0.40 | 0.16 |

17.6–26.8 | 0.90 | 0.45 | 0.18 |

> 26.8 | 1.00 | 0.50 | 0.20 |

Factor | Units | Min | Max | Mean |
---|---|---|---|---|

R [15] | MJ · mm · ha^{−1} · h^{−1} · yr^{−1} | 762.08 | 915.80 | 845.70 |

K [16] | t · ha · h · ha^{−1} · MJ^{−1} · mm^{−1} | 0.13 | 0.15 | 0.14 |

LS [16] | dimensionless | 0.03 | 17.10 | 3.60 |

L | 0.99 | 2.30 | 1.10 | |

S | 0.03 | 13.40 | 3.30 | |

C (rainy season) [23] | dimensionless | 0.00 | 1.00 | 0.27 |

C (dry season) [23] | dimensionless | 0.00 | 1.00 | 0.28 |

P (terracing) [16] | dimensionless | 0.10 | 1.00 | 0.48 |

RUSLE | RUSLE with P Factor | |||||||
---|---|---|---|---|---|---|---|---|

Catchments | Area | % | Max | Mean | Sum | Max | Mean | Sum |

(ha) | (t/yr/ha) | (t/yr) | (t/yr/ha) | (t/yr) | ||||

Ruzizi I | 3,176.92 | 26.38 | 463.62 | 40.50 | 128,654.89 | 431.07 | 24.55 | 77,983.04 |

Ruzizi II | 8,866.82 | 73.62 | 1,162.23 | 50.58 | 448,469.38 | 1109.95 | 29.29 | 259,726.87 |

Ruzizi I and II | 12,043.74 | 100.00 | 1,162.23 | 47.92 | 577,124.27 | 1109.95 | 28.04 | 337,709.91 |

Ruzizi I: LULC | ||||||||

Settlement, road | 272.11 | 8.57 | 383.70 | 17.54 | 4772.31 | |||

Village | 218.87 | 6.89 | 423.52 | 67.07 | 14,679.69 | |||

Pits | 0.48 | 0.01 | 74.33 | 32.44 | 15.45 | |||

Rice | 184.39 | 5.80 | 229.22 | 6.31 | 1162.78 | |||

Crops | 602.89 | 18.98 | 463.62 | 102.89 | 62,028.67 | 92.72 | 18.84 | 11,356.82 |

Grass land | 982.24 | 30.92 | 431.07 | 30.06 | 29,522.31 | |||

Bush land | 510.88 | 16.08 | 386.29 | 19.63 | 10,026.72 | |||

Forest | 405.07 | 12.75 | 363.39 | 15.92 | 6446.95 | |||

Area sum | 3176.92 | 100.00 | 128,654.89 | 77,983.04 | ||||

Ruzizi II: LULC | ||||||||

Settlement, road | 546.98 | 6.17 | 714.52 | 27.02 | 14,780.46 | |||

Village | 697.27 | 7.86 | 792.87 | 73.67 | 51,365.04 | |||

Pits | 5.33 | 0.06 | 1109.95 | 384.68 | 2051.70 | |||

Rice | 225.73 | 2.55 | 183.04 | 9.01 | 2033.38 | |||

Crops | 1875.24 | 21.5 | 1162.23 | 123.92 | 232,381.04 | 232.45 | 23.27 | 43,638.53 |

Grass land | 2733.66 | 30.83 | 600.82 | 33.27 | 90,956.95 | |||

Bush land | 2004.77 | 22.61 | 524.92 | 20.34 | 40,782.23 | |||

Forest | 777.85 | 8.77 | 449.30 | 18.15 | 14,118.57 | |||

Area sum | 8866.82 | 100.00 | 448,469.38 | 259,726.87 |

Ruzizi I Sub-Catchment (31.76 km²) | Soil Loss in t/ha/yr | t/yr | ||
---|---|---|---|---|

Author, Model | Min | Max | Mean | Sum |

[3], USLE | 0.01 | 1000 | 27.08 | 86,194.81 |

own calculations following exactly [3], USLE | 0.25 | 3998.20 | 164.52 | 523,695.85 |

C factor from [2], R factor from [1], RUSLE | 0.00 | 463.62 | 40.50 | 128,654.89 |

**Table 8.**(R)USLE results for cropland at a slope of 15–20% and 25–30% in comparison to field work on a slope of 28%.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Eisenberg, J.; Muvundja, F.A. Quantification of Erosion in Selected Catchment Areas of the Ruzizi River (DRC) Using the (R)USLE Model. *Land* **2020**, *9*, 125.
https://doi.org/10.3390/land9040125

**AMA Style**

Eisenberg J, Muvundja FA. Quantification of Erosion in Selected Catchment Areas of the Ruzizi River (DRC) Using the (R)USLE Model. *Land*. 2020; 9(4):125.
https://doi.org/10.3390/land9040125

**Chicago/Turabian Style**

Eisenberg, Joachim, and Fabrice A. Muvundja. 2020. "Quantification of Erosion in Selected Catchment Areas of the Ruzizi River (DRC) Using the (R)USLE Model" *Land* 9, no. 4: 125.
https://doi.org/10.3390/land9040125