Table 2 Descriptive statistics of transformed variables and the corresponding transformation
Parameters | Tukey’s power transformation | Minimum | Median | Mean | Maximum | CV (%) | Skewness | Kurtosis |
|---|---|---|---|---|---|---|---|---|
Dependent Variables | ||||||||
 Clay | (x - 5)^(0.375) | 6.54 | 8.46 | 8.44 | 10.01 | 9.23 | 0.000 | 2.20 |
 Sand | (x)^(0.3) | 1.56 | 2.47 | 2.47 | 3.51 | 16.52 | −0.009 | 2.39 |
 Silt | (63 - x)^(0.5) | 4.05 | 5.75 | 5.76 | 7.28 | 11.25 | −0.054 | 2.67 |
Independent Variables or Predictors | ||||||||
 Analytical hillshading | (x + 2)^(0.075) | 1.06 | 1.08 | 1.08 | 1.11 | 0.82 | 0.002 | 3.30 |
 Aspect | x | 0.12 | 3.28 | 3.23 | 6.28 | 56.45 | −0.041 | 1.79 |
 Catchment area | -(x - 12)^(−0.075) | −0.71 | −0.60 | −0.60 | −0.45 | −9.13 | 0.005 | 2.47 |
 Channel network base level | (x + 1)^(0.125) | 1.24 | 1.70 | 1.68 | 2.20 | 15.01 | 0.175 | 1.71 |
 Curvature classification | (23 - x)^(1.6) | 76.16 | 113.98 | 114.87 | 150.93 | 19.82 | −0.058 | 1.75 |
 Elevation | log10(x) | 0.64 | 1.83 | 1.76 | 2.73 | 30.02 | 0.024 | 1.60 |
 Flow accumulation | (x - 15)^(0.075) | 1.40 | 1.66 | 1.65 | 2.238 | 11.38 | 0.207 | 2.34 |
 Landsat 8 Band 1 | -(−x)^(−1) | 12.54 | 23.61 | 24.00 | 31.39 | 11.17 | 0.108 | 5.01 |
 Landsat 8 Band 10 | (x - 13)^(0.375) | 1.25 | 1.54 | 1.52 | 1.86 | 6.06 | −0.093 | 4.30 |
 Landsat 8 Band 11 | (x - 10)^(0.125) | 0.97 | 1.09 | 1.09 | 1.19 | 2.89 | −0.018 | 4.53 |
 Landsat 8 Band 2 | -(x)^(−0.8) | −15.75 | −11.98 | −12.13 | −7.82 | −11.63 | −0.016 | 3.40 |
 Landsat 8 Band 3 | -(x)^(−0.55) | −5.28 | −4.42 | −4.45 | −3.46 | −7.48 | 0.006 | 3.14 |
 Landsat 8 Band 4 | -(x)^(−0.375) | −3.37 | −2.86 | −2.89 | −2.36 | −6.83 | −0.029 | 2.69 |
 Landsat 8 Band 5 | -(x + 1)^(−2.475) | −0.59 | −0.49 | −0.49 | −0.36 | −8.27 | 0.008 | 3.11 |
 Landsat 8 Band 6 | -(x + 1)^(−10) | −0.32 | −0.21 | −0.21 | −0.07 | −20.91 | 0.022 | 2.95 |
 Landsat 8 Band 7 | -(x)^(−0.725) | −8.06 | −6.01 | −6.05 | −3.76 | −11.85 | −0.037 | 3.34 |
 Latitude | log10(x) | 6.05 | 6.05 | 6.05 | 6.05 | 0.02 | 0.319 | 3.27 |
 Longitude | log10(x) | 5.74 | 5.75 | 5.75 | 5.75 | 0.03 | 0.190 | 3.26 |
 LS factor | log10(x) | −1.52 | −0.74 | −0.81 | 1.03 | −86.99 | 0.398 | 1.95 |
 Mass balance index | (3.4 - x)^(1.525) | 4.74 | 6.48 | 6.51 | 8.16 | 12.97 | −0.066 | 2.12 |
 Mountain ridge proximity | (x)^(0.95) | 159.10 | 3124.60 | 2895.20 | 6592.80 | 46.60 | 0.016 | 3.08 |
 MRVBF | (x - 3)^(3) | −27.00 | −27.00 | −14.58 | 8.00 | −89.63 | 0.253 | 1.36 |
 Mid-slope position | -(x - 3)^(−4) | −0.06 | −0.03 | −0.03 | −0.01 | −36.45 | 0.005 | 1.81 |
 NDVI | -(x - 1)^(−1) | 1.79 | 3.36 | 3.36 | 5.18 | 19.03 | 0.062 | 2.48 |
 Normalized height | -(x + 2)^(−7.575) | 0.00 | 0.00 | 0.00 | 0.00 | −62.97 | −0.004 | 1.54 |
 Overland flow distance | (x + 10)^(0.075) | 1.23 | 1.32 | 1.32 | 1.42 | 3.59 | 0.000 | 2.14 |
 Profile curvature | -(x + 1)^(−10) | −1.11 | −1.00 | −1.00 | −0.89 | −3.68 | 0.176 | 3.64 |
 S factor | log10(x) | −1.52 | −0.78 | −0.89 | 0.52 | −68.47 | 0.208 | 1.57 |
 SAGA wetness index | (x - 2)^(0.475) | 1.80 | 2.49 | 2.47 | 3.13 | 12.80 | −0.026 | 2.06 |
 Sky view factor | -(1 - x)^(−0.125) | −2.72 | −1.91 | −1.88 | −1.31 | −11.82 | 0.011 | 3.82 |
 Slope | (x)^(0.475) | 0.00 | 2.14 | 2.12 | 4.91 | 45.98 | 0.098 | 3.11 |
 Slope height | (x - 1)^(0.075) | 0.75 | 1.10 | 1.09 | 1.40 | 12.23 | −0.048 | 2.06 |
 Stream proximity | (x + 6)^(0.125) | 1.33 | 2.03 | 2.03 | 2.75 | 18.65 | −0.036 | 1.83 |
 Terrain ruggedness index | -(x + 1)^(−0.85) | −1.00 | −0.66 | −0.66 | −0.26 | −25.45 | 0.038 | 2.47 |
 Valley depth | -(x + 3)^(−0.325) | −0.65 | −0.42 | −0.42 | −0.18 | −22.37 | 0.017 | 2.89 |
 Vertical distance to channel network | (x)^(0.3) | 0.00 | 0.55 | 0.54 | 1.10 | 52.97 | −0.075 | 2.10 |
 Vertical overland flow distance | (x)^(0.175) | 0.65 | 1.15 | 1.14 | 1.60 | 16.23 | −0.043 | 2.81 |