Soil Erosion Rate Calculator
Soil Erosion Rate Calculator, Computes soil loss due to rainfall and slope gradient.
Formulas Used
The soil erosion rate is calculated using the Universal Soil Loss Equation (USLE):
- Soil Erosion Rate:
\\[ A = R \cdot K \cdot LS \cdot C \cdot P \\]
Where:
- \\( A \\): Soil loss (t/ha/yr)
- \\( R \\): Rainfall erosivity factor (MJ mm/ha/h/yr)
- \\( K \\): Soil erodibility factor (t ha h/ha/MJ/mm)
- \\( LS \\): Topographic factor (dimensionless)
- \\( C \\): Cover management factor (0–1)
- \\( P \\): Support practice factor (0–1)
- Topographic Factor (LS):
\\[ LS = \left( \frac{L}{22.13} \right)^m \cdot \left( 0.065 + 0.045S + 0.0065S^2 \right) \\]
Where:
- \\( L \\): Slope length (m)
- \\( S \\): Slope steepness (%)
- \\( m \\): Exponent (0.5 for S > 5%, 0.4 for 3–5%, 0.3 for 1–3%, 0.2 for < 1%)
- Severity Level:
Based on \\( A \\):
- Low: \\( A \leq 2 \\) t/ha/yr
- Moderate: \\( 2 < A \leq 10 \\) t/ha/yr
- High: \\( 10 < A \leq 50 \\) t/ha/yr
- Severe: \\( A > 50 \\) t/ha/yr
Example Calculations
Example 1: Agricultural Field
Inputs: R = 200, K = 0.25, L = 100 m, S = 5%, C = 0.2, P = 0.5
Calculations:
- Determine \\( m \\): S = 5%, so \\( m = 0.4 \\)
- Topographic Factor (LS):
\\[ \left( \frac{100}{22.13} \right)^{0.4} \cdot \left( 0.065 + 0.045 \cdot 5 + 0.0065 \cdot 5^2 \right) \\]
\\[ \left( 4.517 \right)^{0.4} \cdot \left( 0.065 + 0.225 + 0.1625 \right) \approx 1.873 \cdot 0.4525 \approx 0.847 \\]
- Soil Erosion Rate: \\[ 200 \cdot 0.25 \cdot 0.847 \cdot 0.2 \cdot 0.5 \approx 423.5 \cdot 0.2 \cdot 0.5 \approx 4.235 \, \text{t/ha/yr} \\]
- Severity Level: Moderate (2–10 t/ha/yr)
Result: Soil Erosion Rate: 4.2 t/ha/yr (Moderate)
Example 2: Steep Unprotected Slope
Inputs: R = 500, K = 0.3, L = 150 m, S = 15%, C = 0.8, P = 1
Calculations:
- Determine \\( m \\): S = 15%, so \\( m = 0.5 \\)
- Topographic Factor (LS):
\\[ \left( \frac{150}{22.13} \right)^{0.5} \cdot \left( 0.065 + 0.045 \cdot 15 + 0.0065 \cdot 15^2 \right) \\]
\\[ \left( 6.777 \right)^{0.5} \cdot \left( 0.065 + 0.675 + 1.4625 \right) \approx 2.603 \cdot 2.2025 \approx 5.734 \\]
- Soil Erosion Rate: \\[ 500 \cdot 0.3 \cdot 5.734 \cdot 0.8 \cdot 1 \approx 860.1 \cdot 0.8 \approx 688.08 \, \text{t/ha/yr} \\]
- Severity Level: Severe (>50 t/ha/yr)
Result: Soil Erosion Rate: 688.1 t/ha/yr (Severe)
Example 3: Well-Managed Cropland
Inputs: R = 150, K = 0.15, L = 50 m, S = 2%, C = 0.05, P = 0.3
Calculations:
- Determine \\( m \\): S = 2%, so \\( m = 0.3 \\)
- Topographic Factor (LS):
\\[ \left( \frac{50}{22.13} \right)^{0.3} \cdot \left( 0.065 + 0.045 \cdot 2 + 0.0065 \cdot 2^2 \right) \\]
\\[ \left( 2.259 \right)^{0.3} \cdot \left( 0.065 + 0.09 + 0.026 \right) \approx 1.468 \cdot 0.181 \approx 0.266 \\]
- Soil Erosion Rate: \\[ 150 \cdot 0.15 \cdot 0.266 \cdot 0.05 \cdot 0.3 \approx 5.985 \cdot 0.05 \cdot 0.3 \approx 0.090 \, \text{t/ha/yr} \\]
- Severity Level: Low (≤2 t/ha/yr)
Result: Soil Erosion Rate: 0.1 t/ha/yr (Low)
How to Use the Calculator
Follow these steps to estimate the annual soil erosion rate:
- Enter Rainfall Erosivity (R): Input the rainfall erosivity factor (10–1000 MJ mm/ha/h/yr, e.g., 200). Use the decimal button (.) for precision.
- Enter Soil Erodibility (K): Input the soil erodibility factor (0.01–0.7 t ha h/ha/MJ/mm, e.g., 0.25). Use the decimal button for precision.
- Enter Slope Length (L): Input the slope length in meters (1–500, e.g., 100). Use the decimal button for precision.
- Enter Slope Steepness (S): Input the slope gradient in percentage (0.1–100, e.g., 10). Use the decimal button for precision.
- Enter Cover Management (C): Input the cover management factor (0.001–1, e.g., 0.2). Use the decimal button for precision.
- Enter Support Practice (P): Input the support practice factor (0.01–1, e.g., 0.5). Use the decimal button for precision.
- Calculate: Click “Calculate Soil Erosion Rate” to see the result.
- Interpret Result: The result shows the soil erosion rate in t/ha/yr with a severity level (Low: ≤2, Moderate: 2–10, High: 10–50, Severe: >50). If you see “Please fill in all fields,” ensure all inputs are valid.
- Share or Embed: Use the share buttons to post results on social media, copy the result, or get an embed code.
Note: This is a simplified model based on USLE. Actual soil erosion depends on additional factors like soil texture, rainfall intensity, and local conditions.