Mapping Soil Properties at a Regional Scale: Assessing Deterministic vs. Geostatistical Interpolation Methods at Different Soil Depths
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Dataset Characteristics and Variables Selection
2.3. Data Preprocessing and Statistical Analysis
2.4. Interpolation Methods
- Inverse Distance Weighting (IDW), which works on the assumption that closer points are more similar to each other than those further away. This method uses the values surrounding some unmeasured point to predict, giving greater weight to the closer points [48].
- Four Radial Basis Functions: Completely Regularized Spline (CRS), Spline With Tension (SWT), Multiquadric (M-Q) and Inverse Multiquadric (IM-Q). These are exact interpolation techniques, i.e., the surface must pass through each of the measured values. Each function will give an interpolation surface with a different shape and different results [49].
- Local Polynomial Interpolation (LPI), which works by fitting many polynomials within the specified overlapping neighbourhoods as opposed to Global Polynomial Interpolation (GPI) [50].
- Ordinary Kriging (OK), which works on the assumption that a constant mean is unknown throughout the process [51].
- Simple Kriging (SK), which assumes stationarity from the beginning of a known mean. Hence, mathematically speaking, it is the simplest but least general method [52].
- Empirical Bayesian Kriging (EBK) tends to maximum likelihood estimation. This allows us to measure the evidence and the uncertainty of the emulator [49].
2.5. Assessment of the Interpolation Methods Reliability
3. Results
3.1. Descriptive Statistics
3.2. Optimal Interpolation Method by Soil Property
3.2.1. Particle Size Distribution
3.2.2. Selected Chemical and Sorption Complex Properties
3.2.3. Selected Elements Content
3.3. General Assessment of the Interpolation Methods
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
References
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Soil Property | Depth (cm) | n * | Unit | Method |
---|---|---|---|---|
0–5 | 495 | % | Soil Survey Laboratory Methods Manual [38] | |
Clay | 5–10 | 393 | ||
>10 | 326 | |||
0–5 | 424 | |||
Silt | 5–10 | 392 | ||
>10 | 328 | |||
0–5 | 333 | |||
Sand | 5–10 | 294 | ||
>10 | 239 | |||
0–5 | 509 | 1:2.5 soil/water | ||
pH | 5–10 | 449 | ||
>10 | 349 | |||
0–5 | 445 | Cmol kg−1 | MAPA [39] | |
CEC | 5–10 | 402 | ||
>10 | 306 | |||
0–5 | 314 | |||
Calcium | 5–10 | 262 | ||
>10 | 171 | |||
0–5 | 319 | |||
Magnesium | 5–10 | 226 | ||
>10 | 178 | |||
0–5 | 284 | |||
Sodium | 5–10 | 262 | ||
>10 | 185 | |||
0–5 | 265 | % | Dumas [40] | |
Available N | 5–10 | 254 | ||
>10 | 205 | |||
0–5 | 176 | ppm | Olsen et al. [41] | |
Available P | 5–10 | 155 | ||
>10 | 94 | |||
0–5 | 296 | Cmol kg−1 | Ammonium acetate at pH 7 (USDA) [42] | |
Potassium | 5–10 | 243 | ||
>10 | 190 | |||
0–5 | 420 | % | Walkley and Black wet combustion [43] | |
SOM | 5–10 | 419 | ||
>10 | 303 |
Variable | Depth | N | Mean | Min. | Max. | CV (%) |
---|---|---|---|---|---|---|
Clay (%) | 0–5 cm | 495 | 15 | 1 | 50 | 55 |
5–10 cm | 393 | 19 | 2. | 81 | 65 | |
>10 cm | 326 | 22.811 | 3 | 77 | 59. | |
Silt (%) | 0–5 cm | 424 | 33 | 1 | 70 | 46 |
5–10 cm | 392 | 33 | 1 | 71 | 49 | |
>10 cm | 328 | 31 | 3 | 74 | 54 | |
Sand (%) | 0–5 cm | 333 | 47 | 6 | 91 | 27 |
5–10 cm | 294 | 43 | 4 | 89 | 32 | |
>10 cm | 239 | 41 | 2 | 85 | 38 | |
pH (1:2.5) | 0–5 cm | 509 | 5.93 | 4.00 | 8.20 | 14 |
5–10 cm | 449 | 6.01 | 3.70 | 9.1 | 15 | |
>10 cm | 349 | 6.14 | 4.20 | 9.30 | 16 | |
CEC (Cmol kg−1) | 0–5 cm | 445 | 15.52 | 0.81 | 80.46 | 67 |
5–10 cm | 402 | 15.57 | 2.00 | 69.66 | 76 | |
>10 cm | 306 | 16.34 | 2.00 | 61.60 | 70 | |
Ca (Cmol kg−1) | 0–5 cm | 314 | 6.78 | 0.41 | 61.87 | 116 |
5–10 cm | 262 | 6.90 | 0.17 | 62.00 | 142 | |
>10 cm | 171 | 8.85 | 0.18 | 55.59 | 137 | |
Mg (Cmol kg−1) | 0–5 cm | 319 | 1.80 | 0.07 | 12.30 | 87 |
5–10 cm | 226 | 1.77 | 0.05 | 25.00 | 93 | |
>10 cm | 178 | 2.29 | 0.03 | 16.62 | 104 | |
Na (Cmol kg−1) | 0–5 cm | 284 | 0.65 | 0.07 | 2.92 | 100 |
5–10 cm | 262 | 0.40 | 0.04 | 2.13 | 144 | |
>10 cm | 185 | 0.43 | 0.02 | 2.54 | 129 | |
N (%) | 0–5 cm | 265 | 0.23 | 0.02 | 0.95 | 87 |
5–10 cm | 254 | 0.13 | 0.01 | 0.38 | 85 | |
>10 cm | 205 | 0.09 | 0.00 | 0.26 | 97 | |
P (ppm) | 0–5 cm | 176 | 22.10 | 0.40 | 69.00 | 53 |
5–10 cm | 155 | 15.12 | 0.40 | 67.00 | 44 | |
>10 cm | 94 | 11.84 | 0.40 | 48.30 | 51. | |
K (Cmol kg−1) | 0–5 cm | 296 | 0.57 | 0.03 | 3.40 | 77. |
5–10 cm | 243 | 0.42 | 0.02 | 2.12 | 87 | |
>10 cm | 190 | 0.42 | 0.02 | 2.91 | 95 | |
SOM (%) | 0–5 cm | 420 | 3.62 | 0.10 | 20.80 | 76 |
5–10 cm | 419 | 1.86 | 0.10 | 14.50 | 98 | |
>10 cm | 303 | 1.21 | 0.10 | 6.00 | 82 |
0–5 cm | 5–10 cm | >10 cm | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Variable | Method | ME | R2 | RMSE | ME | R2 | RMSE | ME | R2 | RMSE |
Clay (%) | IDW | −0.249 | 0.723 | 3.554 | 0.265 | 0.689 | 5.131 | 1.393 | 0.648 | 5.205 |
CRS | 0.239 | 0.725 | 3.505 | 1.119 | 0.663 | 5.313 | 1.870 | 0.639 | 5.800 | |
SWT | 0.223 | 0.731 | 3.456 | 1.123 | 0.638 | 5.321 | 1.822 | 0.642 | 5.771 | |
M-Q | 0.200 | 0.721 | 4.002 | 0.147 | 0.575 | 6.357 | 0.740 | 0.580 | 6.503 | |
IM-Q | 3.964 | 0.650 | 3.964 | 0.690 | 0.641 | 5.569 | 2.524 | 0.562 | 6.590 | |
LPI | 0.223 | 0.663 | 4.046 | 0.970 | 0.584 | 5.799 | 2.077 | 0.607 | 6.153 | |
OK | 0.220 | 0.728 | 3.523 | 0.570 | 0.625 | 5.480 | 1.946 | 0.578 | 6.376 | |
SK | 0.390 | 0.674 | 4.157 | 0.388 | 0.603 | 5.865 | 2.367 | 0.591 | 6.101 | |
EBK | 0.198 | 0.767 | 3.318 | 0.238 | 0.639 | 5.525 | 1.807 | 0.613 | 5.972 | |
Silt (%) | IDW | 0.267 | 0.831 | 6.222 | −0.486 | 0.897 | 5.103 | 1.168 | 0.905 | 6.595 |
CRS | −0.163 | 0.823 | 6.363 | −1.365 | 0.895 | 5.287 | −0.564 | 0.923 | 6.438 | |
SWT | −0.110 | 0.825 | 6.331 | −1.357 | 0.895 | 5.280 | −0.418 | 0.919 | 6.344 | |
M-Q | 0.489 | 0.807 | 6.775 | −0.627 | 0.889 | 5.494 | 0.239 | 0.908 | 5.804 | |
IM-Q | −0.416 | 0.734 | 7.835 | −1.629 | 0.847 | 6.375 | −2.209 | 0.761 | 10.051 | |
LPI | −0.423 | 0.793 | 7.234 | −1.415 | 0.856 | 6.158 | −1.823 | 0.862 | 8.939 | |
OK | −0.264 | 0.820 | 6.458 | −1.420 | 0.882 | 5.626 | −0.609 | 0.921 | 5.605 | |
SK | −0.094 | 0.815 | 6.563 | −1.537 | 0.884 | 5.582 | 0.244 | 0.923 | 6.020 | |
EBK | −0.329 | 0.820 | 6.488 | −1.040 | 0.892 | 5.383 | −0.444 | 0.929 | 5.725 | |
Sand (%) | IDW | 0.847 | 0.657 | 5.290 | 0.200 | 0.816 | 5.217 | −1.818 | 0.750 | 7.039 |
CRS | 0.290 | 0.739 | 4.627 | 0.730 | 0.804 | 5.459 | −1.703 | 0.748 | 7.072 | |
SWT | 0.204 | 0.723 | 4.727 | 0.832 | 0.810 | 9.637 | −1.706 | 0.748 | 7.069 | |
M-Q | 0.884 | 0.608 | 6.406 | 0.280 | 0.826 | 5.729 | −1.392 | 0.732 | 7.544 | |
IM-Q | −0.740 | 0.535 | 6.233 | 0.664 | 0.700 | 6.680 | −2.077 | 0.514 | 9.782 | |
LPI | 1.065 | 0.602 | 6.279 | 1.164 | 0.738 | 6.881 | −0.247 | 0.615 | 8.851 | |
OK | 0.471 | 0.680 | 5.094 | 1.460 | 0.720 | 6.790 | −1.505 | 0.780 | 6.586 | |
SK | 0.719 | 0.677 | 5.133 | 0.740 | 0.693 | 6.878 | −1.437 | 0.799 | 6.354 | |
EBK | 1.083 | 0.637 | 5.602 | 0.759 | 0.816 | 5.258 | −1.794 | 0.764 | 6.906 |
0–5 cm | 5–10 cm | >10 cm | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Variable | Method | ME | R2 | RMSE | ME | R2 | RMSE | ME | R2 | RMSE |
pH (1:2.5) | IDW | −0.030 | 0.809 | 0.350 | 0.071 | 0.808 | 0.349 | 0.015 | 0.803 | 0.413 |
CRS | −0.031 | 0.834 | 0.333 | 0.069 | 0.826 | 0.331 | 0.034 | 0.803 | 0.412 | |
SWT | −0.006 | 0.794 | 0.364 | 0.068 | 0.827 | 0.330 | 0.033 | 0.804 | 0.411 | |
M-Q | −0.033 | 0.726 | 0.413 | 0.030 | 0.803 | 0.356 | 0.007 | 0.796 | 0.443 | |
IM-Q | 0.013 | 0.720 | 0.424 | 0.070 | 0.767 | 0.381 | 0.061 | 0.730 | 0.487 | |
LPI | −0.064 | 0.772 | 0.399 | 0.028 | 0.744 | 0.837 | −0.014 | 0.761 | 0.455 | |
OK | −0.029 | 0.806 | 0.352 | 0.041 | 0.823 | 0.328 | 0.021 | 0.782 | 0.441 | |
SK | −0.043 | 0.813 | 0.362 | 0.054 | 0.804 | 0.348 | 0.030 | 0.757 | 0.465 | |
EBK | −0.018 | 0.823 | 0.335 | 0.064 | 0.816 | 0.342 | 0.024 | 0.825 | 0.399 | |
CEC (Cmol kg−1) | IDW | 1.396 | 0.854 | 3.778 | 1.741 | 0.683 | 4.676 | 0.706 | 0.690 | 4.470 |
CRS | 1.444 | 0.823 | 3.990 | 2.019 | 0.713 | 4.555 | 1.025 | 0.671 | 4.625 | |
SWT | 1.438 | 0.825 | 3.976 | 2.018 | 0.713 | 4.553 | 1.021 | 0.671 | 4.620 | |
M-Q | 1.402 | 0.744 | 5.706 | 1.893 | 0.665 | 5.188 | 0.418 | 0.641 | 4.763 | |
IM-Q | 1.508 | 0.760 | 4.436 | 1.720 | 0.704 | 4.538 | 1.405 | 0.601 | 5.239 | |
LPI | 1.158 | 0.670 | 5.015 | 1.819 | 0.700 | 4.560 | 0.575 | 0.646 | 4.901 | |
OK | 1.296 | 0.821 | 4.108 | 1.690 | 0.702 | 4.533 | 0.804 | 0.679 | 4.583 | |
SK | 1.866 | 0.770 | 4.486 | 1.649 | 0.703 | 4.576 | 1.120 | 0.704 | 4.637 | |
EBK | 1.441 | 0.819 | 4.199 | 1.833 | 0.728 | 4.567 | 0.864 | 0.697 | 4.415 | |
Ca (Cmol kg−1) | IDW | 0.006 | 0.833 | 2.263 | 0.639 | 0.973 | 1.879 | −0.521 | 0.959 | 2.326 |
CRS | 0.254 | 0.960 | 1.153 | 0.451 | 0.952 | 2.280 | 0.040 | 0.905 | 2.610 | |
SWT | 0.178 | 0.964 | 1.078 | 0.469 | 0.956 | 2.137 | 0.056 | 0.904 | 2.621 | |
M-Q | 0.105 | 0.963 | 1.078 | 0.368 | 0.897 | 3.305 | −0.812 | 0.968 | 2.254 | |
IM-Q | 0.235 | 0.964 | 1.093 | 0.369 | 0.911 | 3.208 | 0.232 | 0.830 | 3.664 | |
LPI | −0.079 | 0.819 | 2.509 | 0.169 | 0.912 | 3.217 | −0.665 | 0.961 | 2.473 | |
OK | 0.053 | 0.967 | 1.055 | 0.325 | 0.917 | 2.744 | −0.272 | 0.959 | 2.241 | |
SK | 0.298 | 0.970 | 1.010 | 0.332 | 0.901 | 3.614 | 0.075 | 0.905 | 2.727 | |
EBK | 0.084 | 0.977 | 0.864 | 0.676 | 0.947 | 2.233 | −0.400 | 0.964 | 1.955 | |
Mg (Cmol kg−1) | IDW | 0.112 | 0.439 | 0.907 | 0.147 | 0.605 | 0.539 | 0.347 | 0.708 | 0.781 |
CRS | 0.268 | 0.448 | 0.814 | 0.246 | 0.554 | 0.613 | 0.417 | 0.688 | 0.822 | |
SWT | 0.265 | 0.422 | 0.872 | 0.251 | 0.551 | 0.618 | 0.417 | 0.694 | 0.816 | |
M-Q | 0.224 | 0.291 | 1.183 | −0.052 | 0.432 | 0.577 | 0.370 | 0.365 | 1.186 | |
IM-Q | 0.294 | 0.360 | 0.995 | 0.222 | 0.551 | 0.661 | 0.429 | 0.754 | 0.782 | |
LPI | 0.303 | 0.413 | 0.827 | 0.229 | 0.485 | 0.650 | 0.362 | 0.659 | 0.833 | |
OK | 0.135 | 0.504 | 0.789 | 0.102 | 0.770 | 0.534 | 0.553 | 0.605 | 0.988 | |
SK | 0.301 | 0.569 | 0.741 | 0.274 | 0.333 | 0.724 | 0.370 | 0.535 | 0.939 | |
EBK | 0.158 | 0.395 | 0.955 | 0.027 | 0.534 | 0.561 | 0.398 | 0.449 | 1.105 | |
Na (Cmol kg−1) | IDW | 0.069 | 0.828 | 0.210 | 0.074 | 0.505 | 0.142 | 0.105 | 0.044 | 0.196 |
CRS | 0.030 | 0.888 | 0.167 | 0.064 | 0.511 | 0.138 | 0.110 | 0.104 | 0.198 | |
SWT | 0.040 | 0.891 | 0.169 | 0.067 | 0.503 | 0.138 | 0.116 | 0.089 | 0.201 | |
M-Q | 0.008 | 0.801 | 0.227 | 0.040 | 0.400 | 0.174 | 0.085 | 0.077 | 0.239 | |
IM-Q | 0.087 | 0.904 | 0.202 | 0.055 | 0.369 | 0.175 | 0.134 | 0.039 | 0.227 | |
LPI | 0.048 | 0.755 | 0.248 | 0.102 | 0.107 | 0.203 | 0.139 | 0.011 | 0.226 | |
OK | 0.016 | 0.865 | 0.178 | 0.050 | 0.369 | 0.137 | 0.130 | 0.004 | 0.234 | |
SK | 0.048 | 0.855 | 0.190 | 0.111 | 0.303 | 0.174 | 0.130 | 0.103 | 0.201 | |
EBK | 0.036 | 0.820 | 0.213 | 0.096 | 0.071 | 0.200 | 0.120 | 0.011 | 0.218 |
0–5 cm | 5–10 cm | >10 cm | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Variable | Method | ME | R2 | RMSE | ME | R2 | RMSE | ME | R2 | RMSE |
N (%) | IDW | 0.010 | 0.577 | 0.058 | −0.003 | 0.128 | 0.039 | 0.002 | 0.685 | 0.024 |
CRS | 0.006 | 0.590 | 0.056 | −0.001 | 0.119 | 0.039 | 0.005 | 0.645 | 0.026 | |
SWT | 0.006 | 0.597 | 0.056 | −0.001 | 0.116 | 0.039 | 0.005 | 0.649 | 0.026 | |
M-Q | 0.006 | 0.362 | 0.076 | −0.009 | 0.064 | 0.051 | 0.002 | 0.541 | 0.031 | |
IM-Q | 0.010 | 0.598 | 0.060 | −0.009 | 0.064 | 0.051 | 0.002 | 0.545 | 0.029 | |
LPI | 0.010 | 0.463 | 0.067 | 0.003 | 0.039 | 0.045 | 0.009 | 0.587 | 0.032 | |
OK | 0.004 | 0.603 | 0.056 | 0.000 | 0.142 | 0.038 | 0.005 | 0.595 | 0.028 | |
SK | 0.006 | 0.634 | 0.053 | 0.004 | 0.161 | 0.033 | 0.008 | 0.442 | 0.034 | |
EBK | 0.005 | 0.584 | 0.060 | −0.003 | 0.038 | 0.040 | 0.004 | 0.495 | 0.032 | |
P (ppm) | IDW | −1.741 | 0.836 | 6.917 | −0.780 | 0.739 | 5.508 | 5.518 | 0.319 | 14.143 |
CRS | 0.840 | 0.840 | 6.726 | 1.557 | 0.519 | 6.911 | 7.561 | 0.590 | 14.615 | |
SWT | 0.705 | 0.838 | 6.710 | 1.727 | 0.582 | 7.024 | 7.433 | 0.587 | 14.374 | |
M-Q | 1.131 | 0.841 | 10.297 | −0.630 | 0.673 | 8.475 | 12.242 | 0.584 | 27.097 | |
IM-Q | 2.255 | 0.523 | 10.859 | 2.975 | 0.278 | 9.382 | 6.655 | 0.625 | 8.811 | |
LPI | −0.731 | 0.780 | 7.672 | 3.034 | 0.411 | 8.716 | 4.663 | 0.243 | 12.556 | |
OK | −0.006 | 0.811 | 7.378 | 0.616 | 0.745 | 5.366 | 7.387 | 0.151 | 17.555 | |
SK | −0.355 | 0.850 | 7.336 | 0.929 | 0.685 | 6.385 | 7.141 | 0.420 | 17.683 | |
EBK | 1.145 | 0.831 | 8.679 | 0.929 | 0.685 | 6.385 | 8.544 | 0.579 | 16.123 | |
K(Cmol kg−1) | IDW | −0.015 | 0.729 | 0.170 | 0.041 | 0.547 | 0.147 | 0.001 | 0.617 | 0.146 |
CRS | 0.000 | 0.723 | 0.173 | 0.040 | 0.582 | 0.133 | 0.032 | 0.571 | 0.158 | |
SWT | 0.013 | 0.686 | 0.185 | 0.050 | 0.522 | 0.150 | 0.033 | 0.575 | 0.158 | |
M-Q | −0.032 | 0.657 | 0.192 | 0.002 | 0.444 | 0.158 | 0.004 | 0.637 | 0.143 | |
IM-Q | 0.023 | 0.642 | 0.203 | 0.052 | 0.366 | 0.194 | 0.046 | 0.552 | 0.185 | |
LPI | −0.005 | 0.666 | 0.188 | 0.042 | 0.529 | 0.159 | 0.032 | 0.584 | 0.140 | |
OK | −0.020 | 0.716 | 0.174 | 0.027 | 0.512 | 0.154 | 0.021 | 0.557 | 0.146 | |
SK | 0.052 | 0.690 | 0.187 | 0.049 | 0.578 | 0.141 | 0.038 | 0.586 | 0.145 | |
EBK | −0.012 | 0.719 | 0.172 | 0.020 | 0.524 | 0.139 | 0.017 | 0.579 | 0.140 | |
SOM (%) | IDW | 0.105 | 0.754 | 0.957 | 0.31 | 0.704 | 0.754 | 0.109 | 0.662 | 0.548 |
CRS | −0.041 | 0.67 | 1.033 | 0.268 | 0.631 | 0.784 | 0.083 | 0.577 | 0.557 | |
SWT | −0.078 | 0.673 | 1.043 | 0.267 | 0.627 | 0.776 | 0.084 | 0.578 | 0.555 | |
M-Q | −0.07 | 0.683 | 1.072 | 0.175 | 0.441 | 0.881 | 0.043 | 0.506 | 0.630 | |
IM-Q | −0.052 | 0.46 | 1.287 | 0.264 | 0.449 | 0.888 | 0.022 | 0.267 | 0.667 | |
LPI | 0 | 0.454 | 1.343 | 0.318 | 0.435 | 0.945 | 0.131 | 0.402 | 0.628 | |
OK | 0.001 | 0.707 | 0.97 | 0.175 | 0.624 | 0.79 | 0.082 | 0.588 | 0.531 | |
SK | −0.07 | 0.680 | 1.006 | 0.199 | 0.474 | 0.852 | 0.091 | 0.598 | 0.548 | |
EBK | −0.008 | 0.684 | 1.001 | 0.221 | 0.657 | 0.715 | 0.046 | 0.492 | 0.565 |
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Barrena-González, J.; Lavado Contador, J.F.; Pulido Fernández, M. Mapping Soil Properties at a Regional Scale: Assessing Deterministic vs. Geostatistical Interpolation Methods at Different Soil Depths. Sustainability 2022, 14, 10049. https://doi.org/10.3390/su141610049
Barrena-González J, Lavado Contador JF, Pulido Fernández M. Mapping Soil Properties at a Regional Scale: Assessing Deterministic vs. Geostatistical Interpolation Methods at Different Soil Depths. Sustainability. 2022; 14(16):10049. https://doi.org/10.3390/su141610049
Chicago/Turabian StyleBarrena-González, Jesús, Joaquín Francisco Lavado Contador, and Manuel Pulido Fernández. 2022. "Mapping Soil Properties at a Regional Scale: Assessing Deterministic vs. Geostatistical Interpolation Methods at Different Soil Depths" Sustainability 14, no. 16: 10049. https://doi.org/10.3390/su141610049