Mathematical Functions to Model the Depth Distribution of Soil Organic Carbon in a Range of Soils from New South Wales, Australia under Different Land Uses
Abstract
:1. Introduction
1.1. Mathematical Depth Functions
1.2. Conceptual Basis for Different Depth Zones in the Depth Distribution of Soil Organic Carbon
1.2.1. Phase A—Surface Soil
1.2.2. Phase B—Subsurface, Upper Subsoil
1.2.3. Phase C—Subsoil
1.2.4. Phase D—Deep Subsoil
1.3. Aims
2. Methods
2.1. Site Descriptions
2.2. Statistical Analysis
2.2.1. Fitting Curves to Depth Distributions
2.2.2. Evaluating SOC Distributions within Depth Segments Using Semi-Log Plots
3. Results
3.1. Statistical Fitting of Functions
3.2. Interpretation of the Two-Phase Exponential Function
3.3. Semi-Log Plots of SOC v’s Depth
3.4. Comparison of Results from Two-Phase Exponential Functions and Semi-Log Plots
4. Discussion
4.1. General
4.2. Effects of Land Use
4.3. Modelling SOC Profiles
4.4. Implications for Management and Policy
- At least two phases and sets of processes operating at different depths in the soil, and these are influenced by land use and soil type. A general implication of this is that it suggests a single measurement of SOC over a depth of 30 cm is going to contain soil materials with a wide range of SOC concentrations. Effective homogenization of the bulked sample before subsampling is an essential step in the measurement of SOC content and SOC stocks.
- Surface input of carbon is important under some land uses, especially woodlands, but less important under cropping, although stubble retention may provide limited amounts of biomass to the surface soils. The apparent failure of many stubble retention trials with direct drilling to increase SOC can be partially explained by the low level of shoot inputs provided by stubble retention and the lack of mechanisms to transport organic materials deeper into the profile [86]. The use of semi-log plots and a finer scale of SOC measurements with depth may provide a better understanding of the effects of direct drilling and stubble retention on the dynamics of SOC.
- SOC deeper in the subsoil can be subject to several inputs, but roots are probably the major source, even in Vertosols. Advection can transport dissolved SOC in liquid flow into the deeper subsoil [34], but given the drier climate associated with many of the soils, the amount of flow into the deeper soils is limited.
- At least three phases have been identified in the SOC profiles, near surface, mid depth and deep or baseline SOC. These have been identified by the nature of the SOC profiles [see Figure 5 and Figure 6]. In promoting land management practices to sequester carbon, an understanding of these phases is helpful. Woodland or native vegetation increases SOC in near surface layers, pasture in subsurface layers and the baseline or deep carbon is more difficult to influence. Cropping does not promote increases in SOC near surface. This is potentially a method to investigate the effects of different land management practices on SOC profiles.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Equation | Name | Mathematical Form |
---|---|---|
5 | Exponential | SOC = B exp (Cz) |
6 | Exponential | SOC = A + B exp (Cz) |
7 | Two phase exponential | SOC = B exp (Cz) + D exp (Ez) |
8 | Two phase exponential | SOC = A + B exp (Cz) + D exp (Ez) |
9 | Power function | SOC = BzC |
10 | Power function | SOC = A + BzC |
11 | Inverse | SOC = B/(1 + BCz) |
12 | Inverse | SOC = A + B/(1 + BCz) |
Parent Material | Location | Grid Reference | Soil Type | Land Use | Sampling Depth [cm] | MAR [mm] | MAT C | Site Number |
---|---|---|---|---|---|---|---|---|
New England Tablelands | ||||||||
Bingara Metasediments BM | Yeral/pinetrees | −29.79, 150.70 | Red Chromosol | Woodland | 100 | 745 | 18.2 | BM1 |
Yeral/pinetrees | −29.79, 150.70 | Red Chromosol | Pasture | 100 | 745 | 18.2 | BM1 | |
Yeral/pinetrees | −29.79, 150.70 | Red Chromosol | Cropping | 100 | 745 | 18.2 | BM1 | |
Dingwall | −29.82, 150.45 | Red Chromosol | Woodland | 100 | 745 | 18.2 | BM2 | |
Dingwall | −29.82, 150.45 | Red Chromosol | Pasture | 100 | 745 | 18.2 | BM2 | |
Dingwall | −29.82, 150.45 | Red Chromosol | Cropping | 100 | 745 | 18.2 | BM2 | |
Rockvale Metasediments RM | Rockvale | −30.48, 151.69 | Yellow Chromosol | Woodland | 80 | 792 | 13.7 | RM-W1 to W5 |
Rockvale | −30.48, 151.69 | Yellow Chromosol | Pasture | 80 | 792 | 13.7 | RM-P1 to P5 | |
Tulimba Metasediments TM | Tullimba | −30.48, 151.19 | Yellow Chromosol | Woodland | 70 | 643 | 14.7 | TM1 |
Tullimba | −30.48, 151.19 | Yellow Chromosol | Pasture | 70 | 643 | 14.7 | TM2 | |
Guyra Basalt Tertiary basalt GB | Kirby | −30.43, 151.63 | Dermosol | Woodland | 85 | 792 | 13.7 | GB1 |
Kirby | −30.43, 151.63 | Dermosol | Native pasture | 85 | 792 | 13.7 | GB1 | |
Glendon | −30.18, 151.62 | Black Ferrosol | Woodland | 95 | 913 | 12.2 | GB2 | |
Glendon | −30.18, 151.62 | Black Ferrosol | Native pasture | 95 | 913 | 12.2 | GB2 | |
Newby Park basalt Tertiary basalt NPB | Armidale | −30.51, 151.63 | Brown Dermosol | Woodland | 100 | 792 | 13.7 | NPB-W1 to W5 |
Armidale | −30.51, 151.63 | Brown Dermosol | Native pasture | 100 | 792 | 13.7 | NPB-P1 to P5 | |
Camerons Granite CG | Kingstown | −30.57, 151.23 | Yellow Chromosol | Woodland | 100 | 640 | 14.3 | CG1 |
Kingstown | −30.57, 151.23 | Yellow Chromosol | Pasture | 100 | 640 | 14.3 | CG1 | |
Central West NSW, Australian Greenhouse Office [AGO]—land clearing | ||||||||
Granite colluvium | Tallebung, NW of Condobolin | −32.91, 146.65 | Red Kandodsol | Woodland | 100 | 407 | 17.3 | AGO1 |
Granite colluvium | Tallebung, NW of Condobolin | −32.91, 146.65 | Red Kandosol | Cropping [cleared 3 years] | 100 | 407 | 17.3 | AGO2 |
Granite colluvium | Tallebung, NW of Condobolin | −32.85, 146.57 | Red Kandosol | Woodland | 100 | 408 | 17.3 | AGO3 |
Granite colluvium | Tallebung, NW of Condobolin | −32.91, 146.65 | Red Kandosol | Cropping [cleared 3 years] | 100 | 408 | 17.3 | AGO4 |
Granite colluvium | Tallebung, NW of Condobolin | −32.66, 146.64 | Red Kandosol | Woodland | 100 | 416 | 17.1 | AGO5 |
Granite colluvium | Tallebung, NW of Condobolin | −32.66, 146.64 | Red Kandosol | Pasture | 100 | 416 | 17.1 | AGO6 |
Granite colluvium | Tallebung, NW of Condobolin | −32.66, 146.64 | Red Kandosol | Cropping [cleared > 25 years] | 100 | 416 | 17.1 | AGO7 |
Central West NSW, Australian Greenhouse Office [AGO]—land clearing [Murphy et al. 2003] | ||||||||
Girilambone Beds | Tottenham | −32.22; 147.33 | Red Kandosol | Woodland | 100 | 475 mm | 17.4 | AGO8 |
Girilambone Beds | Tottenham | −32.22; 147.33 | Red Kandosol | Cropping [cleared > 25 years] | 100 | 475 mm | 17.4 | AGO9 |
Quaternary Alluvium | Dandaloo/ Narromine | −32.20; 147.56 | Grey Vertosol | Woodland | 100 | 481 mm | 17.3 | AGO10 |
Quaternary Alluvium | Dandaloo/ Narromine | −32.20; 147.56 | Grey Vertosol | Cropping [cleared 20 years] | 100 | 481 mm | 17.3 | AGO11 |
Girilambone Beds | Girilambone | −31.24; 146.94 | Red Kandosol | Woodland | 100 | 415 mm | 18.3 | AGO12 |
Girilambone Beds | Girilambone | −31.24; 146.94 | Red Kandosol | Cropping [cleared 9 years] | 100 | 415 mm | 18.3 | AGO13 |
Girilambone Beds | Nyngan | −31.61; 147.11 | Red Kandosol | Woodland | 100 | 437 mm | 17.9 | AGO14 |
Girilambone Beds | Nyngan | −31.61; 147.11 | Red Kandosol | Cropping [cleared 8 years] | 100 | 437 | 17.9 | AGO15 |
Quaternary Alluvium | Coonamble | −31.17; 148.73 | Grey Vertosol | Woodland | 100 | 541 | 17.4 | AGO16 |
Quaternary Alluvium | Coonamble | −31.17; 148.73 | Grey Vertosol | Cropping [cleared > 25 years] | 100 | 541 | 17.4 | AGO17 |
Quaternary Alluvium | Walgett | −30.14; 148.09 | Grey Vertosol | Woodland | 100 | 447 | 19.2 | AGO18 |
Quaternary Alluvium | Walgett | −30.14; 148.09 | Grey Vertosol | Cropping [cleared 6 years] | 100 | 447 | 19.2 | AGO19 |
Quaternary Alluvium | Walgett | −30.14; 148.09 | Grey Vertosol | Cropping [cleared > 25 years] | 100 | 447 | 19.2 | AGO22 |
Quaternary Alluvium | Walgett | −30.04; 147.85 | Grey Vertosol | Cropping [cleared 6 years] | 100 | 436 | 19.3 °C | AGO20 |
Quaternary Alluvium | Walgett | −30.04; 147.85 | Grey Vertosol | Cropping [cleared 6 years] | 100 | 436 | 19.3 | AGO21 |
Central West NSW, Little River Hydrological Study [LR] [McKenzie 2002] | ||||||||
Cowra Trough Metasediments | Yeoval 1; Arthurville | −32.35; 148.45 | Brown Sodosol | Pasture-lucerne | 140 | 583 | 16.6 | LR1 |
Yeoval 7; Cumnock | −32.89; 148.90 | Red Dermosol | Cropping | 140 | 613 | 16.6 | LR7 | |
Yeoval Granite | Yeoval 2; Yeoval | −32.81; 148.61 | Red Kandosol | Pasture-lucerne | 140 | 581 | 16.6 | LR2 |
Yeoval 3; Yeoval | −32.76; 148.61 | Red Chromosol | Pasture | 120 | 581 | 16.6 | LR3 | |
Yeoval 4; Yeoval | −32.79; 148.45 | Rudosol/Tenosol | Pasture | 37 | 581 | 16.6 | LR4 | |
Yeoval 5; Yeoval | −32.79; 148.45 | Yellow Chromosol | Pasture | 130 | 581 | 16.6 | LR5 | |
Dulladerry Rhyolite | Yeoval 6; Cumnock | −32.96; 148.62 | Yellow Chromosol | Cropping | 130 | 613 | 16.6 | LR6 |
Model | Equation Number. (See Table 1) | Land Use | Number of Profiles Fitted | % Profiles Fitted | MeanSEE | Mean adj R2 | 10th Percentile Adj R2 | 90th Percentile Adj R2 | Term Values | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | |||||||||
1 Exponential | 6 | Cropping | 16 | 100 | 0.120 | 0.90 | 0.68 | 0.99 | – | 1.660 | −0.039 | – | – |
SOC = B exp (Cz) | Pasture | 33 | 100 | 0.202 | 0.91 | 0.83 | 0.99 | – | 2.675 | −0.080 | – | – | |
Woodland | 36 | 100 | 0.329 | 0.91 | 0.77 | 0.99 | – | 4.881 | −0.081 | – | – | ||
2 Exponential | 7 | Cropping | 15 | 94 | 0.073 | 0.98 | 0.94 | 0.99 | 0.150 | 1.729 | −0.067 | – | – |
SOC = A + B exp (Cz) | Pasture | 33 | 100 | 0.110 | 0.97 | 0.93 | 0.99 | 0.245 | 2.750 | −0.125 | – | – | |
Woodland | 36 | 100 | 0.155 | 0.97 | 0.77 | 0.99 | 0.402 | 5.108 | −0.128 | – | – | ||
3 Two-phase exponential | 8 | Cropping | 15 | 94 | 0.056 | 0.99 | 0.96 | 0.99 | – | 1.880 | −0.227 | 0.690 | −0.016 |
SOC = B exp (Cz) + D exp (Ez) | Pasture | 31 | 94 | 0.090 | 0.98 | 0.91 | 0.99 | – | 2.815 | −0.192 | 0.690 | −0.013 | |
Woodland | 35 | 97 | 0.118 | 0.99 | 0.95 | 0.99 | – | 5.243 | −0.200 | 0.934 | −0.012 | ||
4 Two-phase exponential | 9 | Cropping | 14 | 88 | 0.065 | 0.98 | 0.94 | 0.99 | 0.047 | 1.706 | −0.273 | 0.937 | −0.025 |
SOC = A + B exp (Cz) + D exp (Ez) | Pasture | 27 | 82 | 0.106 | 0.96 | 0.87 | 0.99 | 0.140 | 5.403 | −0.427 | 0.861 | −0.035 | |
Woodland | 25 | 69 | 0.159 | 0.97 | 0.90 | 0.99 | 0.082 | 5.496 | −0.217 | 2.122 | −0.024 | ||
5 Power | 10 | Cropping | 16 | 100 | 0.151 | 0.87 | 0.62 | 0.96 | – | 2.578 | −0.451 | – | – |
SOC = B zC | Pasture | 33 | 100 | 0.161 | 0.94 | 0.84 | 0.99 | – | 4.024 | −0.603 | – | – | |
Woodland | 36 | 100 | 0.208 | 0.96 | 0.90 | 0.99 | – | 7.914 | −0.661 | – | – | ||
6 Power | 11 | Cropping | 9 | 56 | 0.108 | 0.89 | 0.20 | 0.99 | −1.550 | 4.273 | −0.287 | – | – |
SOC = A + B zC | Pasture | 31 | 94 | 0.114 | 0.97 | 0.90 | 0.99 | −0.301 | 3.802 | −0.424 | – | – | |
Woodland | 34 | 94 | 0.179 | 0.99 | 0.91 | 0.99 | −0.724 | 8.310 | −0.534 | – | – | ||
7 Inverse | 12 | Cropping | 16 | 100 | 0.096 | 0.93 | 0.79 | 0.99 | – | 2.145 | 0.050 | – | – |
SOC = B/(B + Cz) | Pasture | 33 | 100 | 0.123 | 0.96 | 0.93 | 0.99 | – | 4.115 | 0.071 | – | – | |
Woodland | 33 | 92 | 0.176 | 0.97 | 0.91 | 0.99 | – | 6.147 | 0.048 | – | – | ||
8 Inverse | 13 | Cropping | 16 | 100 | 0.070 | 0.96 | 0.85 | 0.99 | −0.233 | 2.835 | 0.058 | – | – |
SOC = A + B/(B + Cz) | Pasture | 33 | 100 | 0.103 | 0.97 | 0.93 | 0.99 | −0.038 | 4.504 | 0.081 | – | – | |
Woodland | 32 | 89 | 0.152 | 0.98 | 0.93 | 0.99 | −0.026 | 8.609 | 0.055 | – | – |
Model | Equation See Text | Land Use | SOC Profile Number | SEE | Adj R2 | Estimated Model Parameters | ||||
---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | ||||||
5 Exponential | 5 | Cropping | AGO 19 | 0.069 | 0.79 | - | 0.636 | −0.0122 | - | - |
SOC = B exp (Cz) | Woodland | AGO 18 | 0.213 | 0.71 | - | 1.290 | −0.0244 | - | - | |
6 Exponential | 6 | Cropping | AGO 19 | 0.012 | 0.99 | 0.282 | 0.518 | −0.0629 | - | - |
SOC = A + B exp (Cz) | Woodland | AGO 18 | 0.095 | 0.94 | 0.382 | 1.837 | −0.1582 | - | - | |
7 Two-phase exponential | 7 | Cropping | AGO 19 | 0.013 | 0.99 | - | 0.518 | −0.0630 | 0.283 | 0.0000 |
SOC = B exp (Cz) + D exp (Ez) | Woodland | AGO 18 | 0.017 | 0.99 | - | 2.069 | −0.3040 | 0.695 | −0.0102 | |
8 Two-phase exponential | 8 | Cropping | AGO 19 | 0.014 | 0.99 | 0.282 | 0.3255 | −0.0624 | 0.1925 | −0.0636 |
SOC = A + B exp (Cz) + D exp (Ez) | Woodland | AGO 18 | 0.013 | 0.99 | −1.243 | 2.047 | −0.2836 | 1.8923 | −0.0025 | |
9 Power | 9 | Cropping | AGO 19 | 0.033 | 0.95 | - | 0.969 | −0.2789 | - | - |
SOC = B zC | Woodland | AGO 18 | 0.052 | 0.98 | - | 2.494 | −0.4821 | - | - | |
10 Power | 10 | Cropping | AGO 19 | 0.032 | 0.96 | −0.550 | 1.443 | −0.1282 | - | - |
SOC = A + B zC | Woodland | AGO 18 | 0.046 | 0.99 | 1.163 | 2.619 | −0.6303 | - | - | |
11 Inverse | 11 | Cropping | AGO 19 | 0.048 | 0.90 | - | 0.717 | 0.0343 | - | - |
SOC = B/(1 + B * Cz) | Woodland | AGO 18 | 0.131 | 0.89 | - | 1.860 | 0.0510 | - | - | |
12 Inverse | 12 | Cropping | AGO 19 | 0.021 | 0.98 | 0.196 | 0.650 | 0.1343 | - | - |
SOC = A + B/(1 + B * Cz) | Woodland | AGO 18 | 0.055 | 0.98 | 0.270 | 3.293 | 0.1709 | - | - |
Semi Log Plot: Segments Fitted as loge(SOC) = b + mz; Backtransformed as G = exp (b) | Two Phase: Fitted as SOC = A + B exp (Cz) + D exp (Ez) | ||||||||
---|---|---|---|---|---|---|---|---|---|
Phase | Depth [cm] | G | m | SEE | R2 | Parameter Estimates | SEE | R2 | |
AGO 18; Land use = woodland; n = 11. Paired site with AGO 19 | |||||||||
a | 0–7.5 | 2.278 | −0.1302 | 0.013 | 0.99 | B = 2.048 | C = −0.2877 | 0.013 | 0.998 |
b | 15–25 | 0.790 | −0.0172 | D = 1.892 | E = −0.0025 | ||||
c | 35–95 | 0.781 | −0.0120 | A = -1.243 | |||||
AGO 19; Land use = cropping; n = 11. Paired site with AGO 18 | |||||||||
a | 0–25 | 0.760 | −0.0279 | 0.025 | 0.99 | B = 0.325 | C = −0.0624 | 0.014 | 0.99 |
b | 35–95 | 0.356 | −0.0027 | D = 0.193 | E = −0.0636 | ||||
A = 0.282 | |||||||||
AGO 14; Land use = woodland; n = 11. Paired site with AGO 15 | |||||||||
a | 0–7.5 | 3.667 | −0.1742 | 0.032 | 0.99 | B = 47.110 | C = −1.4822 | 0.060 | 0.99 |
b | 15–35 | 1.831 | −0.0435 | D = 1.252 | E = −0.0319 | ||||
c | 45–75 | 0.806 | −0.0180 | A = 0.068 | |||||
d | 85–95 | 4.862 | −0.0407 | Front of added SOC | |||||
AGO 15; Land use = cropping; n = 11. Paired site with AGO 14 | |||||||||
a | 0–35 | 1.335 | −0.0397 | 0.033 | 0.99 | B = 1.134 | C = −0.0509 | 0.024 | 0.99 |
b | 35–95 | 0.615 | −0.0176 | D = 0.192 | E = −0.0077 | ||||
A = 0.025 | |||||||||
Bingara–Yeral/Pinetrees–woodland; n = 9 | |||||||||
a | 0–7.5 | 6.416 | −0.1695 | 0.328 | 0.70 | B = 82.436 | C = −1.4947 | 0.234 | 0.94 |
b | 15–35 | 1.656 | −0.0155 | D = 1.715 | E = −0.0687 | ||||
c | 45–55 | 0.506 | 0.0112 | A = 0.789 | |||||
d | 65–75 | 70.142 | −0.0654 | Front of added SOC | |||||
Bingara–Yeral/Pinetrees–pasture; n = 11 | |||||||||
a | 0–7.5 | 2.756 | −0.0904 | 0.346 | 0.84 | B = 13.089 | C = −1.2287 | 0.141 | 0.94 |
b | 15–95 | 1.515 | −0.0229 | D = 1.694 | E = −0.0244 | ||||
A = −0.001 | |||||||||
Bingara–Yeral/Pinetrees–cropping; n = 11 | |||||||||
a | 0–15 | 2.223 | −0.0761 | 0.129 | 0.97 | B = 1.715 | C = −0.1113 | 0.059 | 0.98 |
b | 25–55 | 0.895 | −0.0205 | D = 0.448 | E = −0.0133 | ||||
c | 65–95 | 0.326 | −0.0039 | A = 0.088 | |||||
Guyra Basalt–Woodland; n = 10 | |||||||||
a | 0–7.5 | 10.276 | −0.1342 | 0.111 | 0.99 | B =9.355 | C=−0.3397 | 0.604 | 0.99 |
b | 15–35 | 3.322 | −0.0188 | D=4.978 | E =−0.0145 | ||||
c | 45–65 | 6.741 | −0.0411 | Front of added SOC | A=−1.450 | ||||
d | 75–85 | 271.106 | −0.0967 | Front of added SOC | |||||
Guyra Basalt–Pasture; n = 10 | |||||||||
a | 0–7.5 | 6.329 | −0.0628 | 0.111 | 0.99 | B = 2.433 | C =−0.1637 | 0.197 | 0.99 |
b | 15–35 | 3.987 | −0.0350 | D = 4.248 | E = −0.0400 | ||||
c | 45–85 | 2.276 | −0.0318 | A = −0.023 | |||||
Guyra Basalt–Cropping; n = 10 | |||||||||
a | 0–7.5 | 4.821 | −0.0747 | 0.237 | 0.95 | B = 3.204 | C = −0.1273 | 0.115 | 0.99 |
b | 15–25 | 2.720 | −0.0334 | D = 1.877 | E = −0.0226 | ||||
c | 35–85 | 2.049 | −0.0285 | A = −0.098 | |||||
AGO Site 16–Woodland; n = 11 | |||||||||
a | 0–7.5 | 4.428 | −0.1305 | 0.113 | 0.99 | B = 3.972 | C = −0.2904 | 0.192 | 0.96 |
b | 15–45 | 1.340 | −0.0135 | D = 25.373 | E = −0.0005 | ||||
c | 55–75 | 5.564 | −0.0332 | Front of added SOC | A = −24.069 | ||||
d | 85–95 | >>200 | −0.1837 | Front of added SOC | |||||
AGO Site 17–Cropping; n = 11 | |||||||||
a | 0–7.5 | 1.001 | −0.0498 | 0.043 | 0.99 | No fit | |||
b | 15–45 | 0.731 | −0.0012 | No fit | |||||
c | 55–75 | 5.569 | −0.0361 | Front of added SOC | No fit | ||||
d | 85–95 | >>200 | −0.2680 | Front of added SOC |
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Murphy, B.W.; Wilson, B.R.; Koen, T. Mathematical Functions to Model the Depth Distribution of Soil Organic Carbon in a Range of Soils from New South Wales, Australia under Different Land Uses. Soil Syst. 2019, 3, 46. https://doi.org/10.3390/soilsystems3030046
Murphy BW, Wilson BR, Koen T. Mathematical Functions to Model the Depth Distribution of Soil Organic Carbon in a Range of Soils from New South Wales, Australia under Different Land Uses. Soil Systems. 2019; 3(3):46. https://doi.org/10.3390/soilsystems3030046
Chicago/Turabian StyleMurphy, Brian W., Brian R. Wilson, and Terry Koen. 2019. "Mathematical Functions to Model the Depth Distribution of Soil Organic Carbon in a Range of Soils from New South Wales, Australia under Different Land Uses" Soil Systems 3, no. 3: 46. https://doi.org/10.3390/soilsystems3030046