Digital Mapping of Soil Organic Matter and Cation Exchange Capacity in a Low Relief Landscape Using LiDAR Data

Abstract

Soil organic matter content (SOM) and cation exchange capacity (CEC) are important agronomic soil properties. Accurate, high-resolution spatial information of SOM and CEC are needed for precision farm management. The objectives of this study were to: (1) map SOM and CEC in a low relief area using only lidar elevation-based terrain attributes, and (2) compare the prediction accuracy of SOM and CEC maps created by universal kriging, Cubist, and random forest with Soil Survey Geographic (SSURGO) database. For this study, 174 soil samples were collected from a depth from 0 to 10 cm. The topographic wetness index, topographic position index, multi resolution valley bottom flatness, and multi resolution ridge top flatness indices generated from the lidar data were used as covariates in model predictions. No major differences were found in the prediction performance of all selected models. For SOM, the predictive models provided results with coefficient of determination (R²) (0.44–0.45), root mean square error (RMSE) (0.8–0.83%), bias (0–0.22%), and concordance correlation coefficient (ρ_c) (0.56–0.58). For CEC, the R² ranged from 0.39 to 0.44, RMSE ranged from 3.62 to 3.74 cmol_c kg⁻¹, bias ranged from 0–0.17 cmol_c kg⁻¹, and ρ_c ranged from 0.55 to 0.57. We also compared the results to the USDA Soil Survey Geographic (SSURGO) data. For both SOM and CEC, SSURGO was comparable with our predictive models, except for few map units where both SOM and CEC were either under or over predicted.

Core Ideas

• In a low relief environment, SOM and CEC variation were captured using lidar elevation data
• Universal kriging, random forest, and cubits predictive models performed similarly
• Predictive models provided more detailed spatial distribution of SOM and CEC compared to SSURGO

1. Introduction

Soil properties vary over space mainly related to factors such as climate, organisms, relief or topography, parent material and time [1]. In a relatively small area such as in our study site (~570 ha), most of these factor (also known as soil forming factors [1]) are considered constant with topography being the main driving force of soil variation. This is embodied in the catena concept [2] which states that soils follow predictable and repeatable pattern based on topography.

SOM content and CEC are important indicators for soil health and fertility. These properties influence plant growth and performance through soil water and soil nutrient redistribution. Therefore, accurate and spatially detailed maps of SOM and CEC are needed to support research decisions regarding crops and soil management at this study site. Also, detailed and accurate spatial soil information is needed for agricultural and ecological decision-making. Conventional, polygon-based soil maps are the main data source for these applications. In the United States, the Soil Survey Geographic (SSURGO) database [3] and the State Soil Geographic (STATSGO) database [3] maintained by the Natural Resources Conservation Service (NRCS) are extensively used for many applications. These polygon-based maps were originally developed for land management and may not be suitable for spatially accurate soil property maps [4] at field or farm levels. Map unit polygons often contain more than one major soil component as well as a few minor soil components, which reduces the map unit purity. For applications such as precision crop management and high throughput phenomics research, more detailed soil maps are needed that are currently available from the SSURGO database.

Digital soil mapping (DSM) is an approach for overcoming the limitations of conventional soil polygon maps and for improving the accuracy of soil property predictions at a finer resolution [5]. Digital soil maps are generated using different techniques (including geo-statistical algorithms) and stored within a geographic information system (GIS), which allows data to be used for further analysis and interpretation [6].

In this study, our goal was to map SOM content and CEC at the Purdue University Agronomy Center for Research and Education (ACRE). SOM content and CEC are important for plant nutrient availability and soil hydraulic properties, [7,8] and influence the phenotypic response and productivity of plants [9].

Several DSM methods have been used to map SOM and CEC using point samples, remote sensing indices, and terrain attributes derived from a digital elevation model (DEM) as inputs [7,8,9,10,11,12]. For example, the CEC was predicted based on a generalized linear model using environmental variables including local relief and geomorphic units as prediction covariates [12]. Linear and multiple linear regressions (MLR) models have been widely used for spatial prediction of soil organic carbon due to their simplicity in application and ease of interpretation [7,10]. For example, [13] applied regression kriging (MLR and kinging of residuals) to predict and map field-scale variability of soil organic carbon using terrain attributes as covariates while [14] utilized legacy soil map and Landsat 5 TM variables for predicting CEC in a flat landscape based on random forest and geostatistical (i.e., Cokriging) models. Other studies used generalized linear models [15], and machine learning algorithms such as artificial neural networks [15,16,17,18], random forest [11,19,20], and Cubist [8,17,19,20] for predicting SOM and CEC.

Mapping soil properties in low relief areas can be a challenge since soil forming factors, especially topography and vegetation, may not co-vary with soil properties over space to the level at which they can be used effectively in DSM [21]. Terrain attributes derived from high-resolution elevation data, however, can capture local soil spatial variation that is caused due to interaction of water flow and topography [15]. In much of the Midwestern United States, high-resolution elevation data based on light detection and ranging (LiDAR) are widely available making lidar and lidar-based terrain attributes convenient environmental covariates for DSM.

Lidar and lidar-based terrain attributes are not the only environmental covariates used in DSM studies. Environmental covariates derived from optical remote sensing systems (e.g., satellite and unmanned aerial vehicle imagery) are often used in DSM [15,17,22]. Optical measurements are ideal covariates for DSM in locations with high correlation between land surface reflectance and soil properties. For example, the use of remotely derived vegetation indices (e.g., normalized difference vegetation index and enhance vegetation index) can improve accuracy of soil organic matter in DSM models [23]. However, there are circumstances where optical remote sensing data is less viable in soil properties mapping. One such circumstance in on agricultural research farms where experimental plots are intensively managed irrespective to the variation in soil properties such that the subsequent variation in surface reflection often poorly correlate to variation in soil properties. Using Landsat remote sensing imagery derived covariates and terrain attributes [17] mapped soil organic carbon in a flat topographic area. The result showed a poor correlation of remote sensing covariates and strong correlation of terrain attributes with soil organic carbon.

The goals of this research were to (1) map SOM content and CEC in a low relief area using only lidar elevation-based terrain attributes, and (2) compare the prediction accuracy of SOM and CEC maps created by universal kriging, Cubist, and random forest with Soil Survey Geographic (SSURGO) database. The assumption is that at this scale (~570 ha), topography plays a major role in spatial distribution of soil properties such as SOM and CEC. In this study, we compared the performance of three predication models: universal kriging (UK), Cubist, and random forest (RF) to map SOM and CEC. We hypothesized that at this scale, terrain-driven hydrological flow patterns are the dominant process responsible for SOM and CEC differences in surface soils and that DSM models calibrated using lidar-derived terrain attributes should be capable of predicting the distribution of SOM and CEC at field and farm levels.

2. Materials and Methods

2.1. The Study Area

The Purdue Agronomy Center for Research and Education (ACRE) is an agronomic field research station located in Tippecanoe County Indiana, USA (40°29′ N, 86°59′ W) (Figure 1) and comprised 570 ha at the time this research was conducted. The mean annual temperature is 10 °C and mean total annual precipitation is 970 mm [24]. The average summer temperature (June to August) is 22.2 °C and average winter temperature (December to February) is −2.6 °C [24]. ACRE is located at the transition between the Eastern Hardwood Forests to the east and the prairies of the Great Plains to the west. Low relief, gently undulating Wisconsin age (15,000–20,000 years) till plain underlies the area [24]. The soils formed in ~50 cm of loess over loamy Wisconsin till and outwash. The site is in the mesic soil temperature regime and the udic soil moisture regime, but large areas of the study site have soils with an aquic soil moisture regime due to the presence of a seasonal high-water table [24]. Most of the soils are poorly and somewhat poorly drained. Mollisols occur over most of the study area, but Alfisols occur on the southern edge [24]. Corn and soybean are the major crops.

2.2. Soil Sampling and Analysis

As part of a previous, unpublished study, 174 soil samples were collected over the study area. Representative sampling locations were selected using the conditioned Latin hypercube sampling (cLHS) algorithm [22] using the clhs package [25] in R-software 3.5.1 [26]. The cLHS method is a stratified random procedure that selects sampling locations based on the probability distribution of environmental covariates. Topographic wetness index (TWI), topographic position index (TPI), multi resolution valley bottom flatness, and ridge top flatness (MrVBF and MrRTF) that were derived from the DEM were used as environmental covariates for cLHS design.

The samples were collected from a soil depth from 0 to 10 cm by using a Push probe in July 2015, oven-dried at 40 °C, crushed, and passed through a 2 mm sieve. At each sampling location, 15 sub-samples were collected within a meter radius and combined to create a composite sample for analysis. The samples were analyzed by A&L Great Lakes Laboratories, Inc., Fort Wayne, IN, USA, following the soil test procedures for the North Central Region [27]. Briefly, SOM was determined by loss on ignition at 360 °C with a base factor of 0.97 and SOM expressed on a weight percent basis (%), CEC (cmol_c kg⁻¹) was measured by sum of cations displaced by 1 M ammonium acetate solution at pH 7 by inductively coupled plasma mass spectrometry. For model building and spatial predictions, the data were randomly split, with 70% of the samples used for model calibration and 30% used for model evaluation (Figure 1).

2.3. Digital Elevation Model and Terrain Attributes

2.3.1. Digital Elevation Model

Digital elevation model for Tippecanoe County, IN acquired as a statewide governmental funded campaign in 2013 at 1.5 m × 1.5 m pixel resolution or dimensions using lidar was used, and it is freely available for download from the Indiana Spatial Data Portal (http://gis.iu.edu/, accessed on 10 December 2020). The lidar data were collected with Leica ALS70, Leica ALS80, Optech Galaxy PRIME, and Riegl LMS-Q1560 airborne sensors (Woolpert, 2020 [28]. The DEM was re-projected from the Indiana State Plane West Coordinate System (NAD_1983_StatePlane_Indiana_West_FIPS_1302_Feet) which uses dimensions in feet, to the Indiana Geospatial Coordinate System (InGCS) for the Tippecanoe and White Counties (NAD_1983_2011_InGCS_Tippecanoe-White_m) in meters. The InGCS has lower grid vs. ground distortion when compared to the State Plane Coordinate System (±80 ppm) [29] and thus is more appropriate for a small area such as ACRE.

Digital elevation models with pixel resolutions on the order of 1–2 m are often too detailed and noisy for modeling field-scale soil spatial variability [8]. For example, Ref. [30] found that pixel resolutions from 5–10 m are sufficient to capture the topography for digital soil mapping of a post-glaciated landscapes in northern Indiana. Our initial evaluation showed that within ACRE, anthropogenic micro-topographic features such as roads and field boundaries, that are on average 20 cm higher than the cultivated fields, unduly affected the DEM derived indices (Figure 2). We resampled the original 1.5 m DEM to 10 m using simple mean aggregation in ArcGIS 10.6 [31] to smooth out most of the anthropogenic features (Figure 2).

The watershed contributing water to ACRE obtained from the United States Geological Survey–National Hydrography Dataset (USGS-NHD) downloaded from the United States Department of Agriculture (USDA) Geospatial Data Gateway (GDG) (https://datagateway.nrcs.usda.gov/, accessed on 10 December 2020) for Tippecanoe County, IN was used to clip the elevation data. The watershed boundary rather than the ACRE farm boundary was used to reduce artifacts for the derived terrain attributes. The ACRE farm boundary was then used to clip the derived terrain attributes for further analysis.

2.3.2. Terrain Attributes

It is possible to generate many terrain attributes from a DEM, but it is important to limit their number to avoid redundancy, model overfitting and interpretations [32]. Suleymanov et al. (2021) [33] found that of 17 generated terrain attributes, only three of them (elevation, slope, and MrRTF) were most important for predicting the spatial variability of soil properties including SOM. We focused on those terrain attributes that have a close relationship to water redistribution across a post-glaciated landscape such as at ACRE and that are commonly used in DSM. We calculated the following terrain attributes using SAGA-GIS 2.1.4 [34]: topographic wetness index (TWI), topographic position index (TPI), multi-resolution valley bottom flatness index (MrVBF), multi-resolution ridge top flatness index (MrRTF) (Figure 3).

Topographic Wetness Index

The topographic wetness index quantifies potential moisture retention and redistribution properties of a landscape and shows relationship between topography and hydrological processes, mainly surface runoff in a watershed. It was calculated as TWI = ln (A_s/tanβ), where A_s is the specific catchment area (m²/m) and β is the slope angle, considering a multi-flow-direction algorithm. Higher values of TWI represent areas that accumulate water, such as depressions and drainage ways, while lower values represent areas that shed water, such as crests and ridges.

Topographic Position Index

The topographic position index [35] compares the elevation of a cell (Z₀) to the average elevation of its surrounding cells (Z_α) in a specific area as defined by circles of arbitrary radius (TPI = –₀ − Z_α). Positive values of TPI represent ridges, and negative values represent valleys, while values close to zero represent linear sloping areas between ridges and valleys. This index is scale dependent, and by using different radii it can differentiate small hummocks from larger ridges, as well as small depressions from wider valleys. We evaluated different radii to calculate TPI. The larger radii (150, 200, 300, and 500 m) resulted in smoothing of the landscape features, while smaller radii (30 and 60 m) generated linear artifacts and fragmented the actual landforms into small pieces. Based on visual interpretation and familiarity with the study location, a radius of a 100 m was found to best represent the landscape units of the study site.

Multiresolution Valley Bottom Flatness and Multiresolution Ridge Top Flatness

The MrVBF algorithm [36], identifies valley bottoms by utilizing the lowness and flatness characteristics. The lowness parameter is measured by ranking elevation with respect to a circular neighborhood area, and the flatness parameter is measured using the inverse of slope.

The slope threshold is a critical parameter in MrVBF calculations, and it depends on the DEM resolution. The suggested slope threshold for a DEM of 250 m resolution is 4%, while for a DEM of 25 m it is 16%, and for a DEM of 8 m it is 32% [36]. We compared slope thresholds of 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 16% (the default slope threshold of the algorithm) and based on our familiarity with the area and resulting terrain attributes in the field, a slope threshold of 2% was found to best represent the topography of the landscape. The MrRTF is a separate index but complementary to the MrVBF. It is derived in a similar way as MrVBF, except it identifies the upper parts of the landscape. As with MrVBF, the same slope threshold value (2%) was selected for MrRTF.

2.4. Data from the Soil Survey Geographic Database

For Tippecanoe County, the SSURGO database provides soil mapping information at a scale 1:15,840 [24]. In this study, low, representative, and high values of SOM and CEC for each mapping unit from SSURGO (

Table 1. The soil survey geographic (SSURGO) soil organic matter content (SOM) and cation exchange capacity (CEC) low, representative (Rep.), mean, and high values for 0–10 cm based on the spline function. Data is for the ACRE study site.

SSURGO Soil Map Unit			SOM			CEC
		Area	Low	Rep.	High	Low	Mean	High
		%	%			cmolc kg−1
Cm	Chalmers silty clay loam	33.9	3.5	4.9	6.5	18.2	28.5	38.8
CwB2	Crosby-Miami silt loams	0.4	1.0	2.4	3.1	2.5	7.0	12.2
Du	Drummer soils	17.6	3.3	4.9	6.5	22.4	29.2	36.2
Md	Mahalasville-Treaty complex	0.2	3.3	4.8	6.4	18.2	24.2	30.3
MsC2	Miami silt loam	0.2	1.1	2.1	3.3	4.7	9.2	16.0
Mu	Milford silty clay loam	4.2	3.5	5.7	6.7	25.4	31.1	36.7
Pg	Pella silty clay loam	1.6	4.8	4.7	7.1	22.9	28.9	34.9
Pk	Peotone silty clay loam	0.6	4.3	5.9	7.4	21.2	29.6	38.1
RcA	Raub-Brenton complex	22.1	1.9	2.9	4.2	12.5	17.4	22.3
RoB	Rockfield silt loam	4.6	1.1	1.6	2.1	6.7	12.2	17.6
SwA	Starks-Fincastle complex	3.6	0.9	2.1	2.9	7.1	12.8	18.6
TfB	Throckmorton silt loam	1.4	1.1	2.1	3.2	5.6	11.6	17.6
TmA	Toronto-Millbrook complex	8.7	1.9	2.9	3.8	10.9	16.7	22.5
Ua *	Udorthents, loamy	0.9	-	-	-	-	-	-

* The Ua is a disturbed and removed soil from its original place and was not considered.

) were compared to the predictions from the DSM models. The SSURGO SOM and CEC values were directly acquired from the Web Soil Survey website [37], except the mean value of CEC, which was calculated as the average of the low and high CEC values. The SSURGO values of soil properties have been derived from a combination of laboratory measured data and soil scientist expert knowledge [38]. Based on a conversion factor of 1.72, SOM in the SSURGO dataset was converted from soil organic carbon of the Walkley-Black method, while CEC was determined by summation of cations, which were displaced by ammonium acetate solution [39,40]. It is important to recognize that the SOM data comparison between DSM models and SSURGO might not be consistent due to the differences in laboratory methods and the conversion factors used to convert soil organic carbon from Walkley-Black to SOM.

The analysis were performed through various packages in R-software v. 3.5.1. To generate representative SOM and CEC data from a soil depth from 0 to 10 cm, the SSURGO data were harmonized by depth using mass-preserving splines function (ea_spline) of the ithir package 1.0 [41]. The spline function models the continuous depth distribution of soil properties based on discrete horizon observations [42]. The equal area spline function for modeling soil organic carbon content with depth has been proven to be useful in several studies [8,16,43]. For detailed information and mathematical expression of the spline function, see [16,44].

Since a map unit may have two or more components, we derived the final values of a map unit based on the weighted mean of each component. For instance, CwB2 (Crosby-Miami silt loams, 2 to 4 percent slopes, eroded) contains 64% Crosby and 33% Miami and 3% other minor components. Based on the spline function for the 0–10 cm depth, the SOM representative value for Crosby was 2.67% and 2.18% for Miami. The final SOM representative value of CwB2 for the 0–10 cm depth was derived as:

$$\mathrm{CwB}2 \mathrm{mapping} \mathrm{unit} \mathrm{mean} \mathrm{value} \mathrm{of} \mathrm{SOM} (\%)=\left(0.64\times 2.67\right)+\left(0.33\times 2.18\right)=2.43$$

(1)

2.5. Spatial Prediction Models

Three different models (universal kriging, Cubist, and random forest) were used to predict SOM content and CEC. All model training and evaluation was performed in R-software v. 3.5.1 [26].

Universal kriging, also known as regression kriging [45], is a hybrid approach to modeling, meaning that the prediction of a desired variable is made based on a combination of deterministic and stochastic components. The deterministic part of the regression relies on the covariate information, while the stochastic part relies on the spatial auto-correlation of the regression residual based on a variogram [42]. We ran backwards stepwise linear models to select appropriate terrain attributes for the deterministic part of UK. The gstat package 2.0.2 [46] was used for UK prediction of SOM and CEC.

Cubist is a machine learning tool that uses a rule-based regression algorithm for prediction [47]. It operates based on if, then, else statements. If a condition is matched, the next step is a prediction of the desired soil property by using ordinary least squares regression from the covariates within that subset [48]. However, if a condition is not met, then the next node of the tree is defined by the rule and the if, then, else sequence is repeated. The interpretation of a Cubist model is easy as it provides an explicit model stating the relative importance of the predictors. The Cubist 0.2.2 package [48] was used to predict SOM and CEC of the study area using 5 rules, 5 extrapolation, and 10 committees as suggested by (https://www.rulequest.com/cubist-unix.html, accessed on 10 December 2021).

The Random Forest (RF) [49], is an ensemble machine learning algorithm that predicts the property of interest based on covariates by creating multiple decision trees. The outcomes of the decision trees are then aggregated to provide the final prediction. A random and independent bootstrap sample of the training data is used to train each tree in the forest. From the bootstrap sample, a random subset (~2/3) is selected for training and the remaining points (~1/3), are used for validating the tree. Additionally, a random subset of the variables is selected to split the nodes of each tree [50]. In this study, we used 1000 trees for RF as suggested by [11,42]. The randomForest package 4.6.14 [51] was used to predict both SOM and CEC.

The spatial dependency of the residuals from universal kriging, cubist and RF predictions were modelled with variogram and their distributions were mapped using kriging interpolation. Kriging of residuals may capture spatial variability that was not represented by deterministic or linear models of UK. Variogram has three main parameters: nugget, sill, and range. The nugget is the variance unexplained by the variogram and referred to noise in the data or random error. Sill represents the maximum variability among the point pairs. The range represents the maximum distance of spatial autocorrelation. For UK, a spherical variogram, and for Cubist and RF, exponential variograms were fitted to krige the residual of SOM. For kriging the CEC residuals, a spherical variogram was fitted for all three predictive models. Residual kriging was carried out with gstat package 2.0.2 [46]. The final estimates of SOM and CEC were derived by adding kriged residuals and the predicted values from the corresponding models.

2.6. Validation of Model Performance

All of the predictive models were first evaluated with the calibration dataset from which they were generated (internal evaluation). A second random-hold-back independent evaluation was conducted using 30% of the data for testing the prediction performance of each model. Root mean square error (RMSE), mean error (ME) or bias, coefficient of determination (R²), and Lin’s concordance correlation coefficient (ρ_c) (Equations (2)–(5)) indices were used for validation

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\left(\frac{{{\displaystyle \sum }}_{i=1}^n{(ob{s}_i-pre{d}_i)}^2}{n}\right)}$$

(2)

$$\mathrm{M}\mathrm{E} \left(\mathrm{i}.\mathrm{e}., bias\right)=\frac{{{\displaystyle \sum }}_{i=1}^{n}ob{s}_i-pre{d}_i}{n}$$

(3)

$${\mathrm{R}}^2=\frac{{{\displaystyle \sum }}_{i=1}^n(ob{s}_i-\overline{obs}) \left(pre{d}_i-\overline{pred}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{(ob{s}_i-\overline{obs})}^2} \sqrt{{{\displaystyle \sum }}_{i=1}^n{(pre{d}_i-\overline{pred})}^2}}$$

(4)

$${\mathrm{\rho }}_{\mathrm{c}}=\frac{2\rho {\sigma }_{obs}\rho {\mathsf{\sigma }}_{\mathrm{pred}}}{{\mathsf{\sigma }}_{\mathrm{pred}}^2+{ \mathsf{\sigma }}_{\mathrm{obs}}^2+{\left({\mu }_{pred}+{\mu }_{obs}\right)}^2}$$

(5)

where obs_i are the observed values and pred_i are the predicted SOM and CEC values of at locatiIn i, μ_obs is the mean of the observed values, μ_pred is the mean of the predicted values, σ²_obs is the variance of the observed values, σ²_pred is the variance of predicted values, n is the number of the sampling locations, and ρ is the correlation coefficient among the observations and predictions [42].

The RMSE shows the accuracy of the prediction, and smaller values translate to higher accuracy. Bias shows the mean error of the prediction and is equal to zero for an unbiased prediction. The R², asses the ability of the model to explain the variability in the predictions, while Pearson’s correlation coefficient (ρ), measures the precision of the relationship between the predicted and observed values. The ρ_c [52], is a single statistic that measures both the precision and the accuracy of the relationship. The ρ_c is also known as the goodness of fit along a 45° line (1:1 line). The value of ρ_c falls between −1 and +1. A value of −1 indicates perfect negative agreement, while a value of +1 indicates perfect positive agreement between the predicted and observed values. A ρ_c value of zero shows that there is no agreement at all [42,52]. The strength of the agreement was evaluated using ρ_c based on the proposed scale from [53]. The goof function of the ithir package 1.0 [41] was used to compute these evaluation indices.

3. Results and Discussion

3.1. Descriptive Statistics

The mean SOM content was 4.2% and both calibration (4.2%) and validation (4.0%) mean SOM values were comparable. Similarly, the range values of SOM were comparable varying from 1.2 to 7.2% for all datasets (

Table 2. Summary statistics of soil organic matter content (SOM) and cation exchange capacity (CEC) data for the study area.

Statistical Index	SOM			CEC
	Whole Dataset	Calibration	Validation	Whole Dataset	Calibration	Validation
	%			cmolc kg−1
Minimum	1.2	1.9	1.2	9.9	11.1	9.9
1st Quartile	3.5	3.5	3.2	16.2	16.5	14.9
Median	4.0	4.0	4.2	20.1	20.1	20.1
Mean	4.2	4.2	4.0	19.9	20.1	19.5
3rd Quartile	4.8	4.9	4.6	23.2	23.3	23.0
Maximum	7.2	7.0	7.2	30.1	30.1	29.3
Standard Deviation	1.1	1.2	1.1	4.6	4.5	4.9

). The mean CEC values for the whole dataset (19.9 cmol_c kg⁻¹) and the calibration (20.1 cmol_c kg⁻¹) and validation (19.5 cmol_c kg⁻¹) datasets were comparable as were the range values varying from 9.9 to 30.1 cmol_c kg⁻¹.

As with SOM content and CEC, the differences between calibration and validation data sets for the terrain attributes were comparable (

Table 3. Summary statistics of terrain attributes for the study area.

Terrain Attributes	Dataset	Statistical Index
		Minimum	1st Quartile	Median	Mean	3rd Quartile	Maximum	Standard Deviation
TWI	Whole dataset	5.29	7.37	8.69	9.39	10.71	18.73	2.64
	Calibration	5.29	7.37	8.72	9.58	10.81	18.73	2.84
	Validation	6.04	7.51	8.41	8.93	10.25	15.31	2.04
TPI	Whole dataset	−0.46	−0.11	−0.03	−0.01	0.09	0.71	0.18
	Calibration	−0.45	−0.11	−0.04	0.00	0.09	0.62	0.18
	Validation	−0.46	−0.10	−0.03	−0.01	0.07	0.71	0.19
MrVBF	Whole dataset	0.00	0.37	1.60	1.62	2.75	5.24	1.33
	Calibration	0.00	0.46	1.74	1.72	2.80	4.96	1.28
	Validation	0.01	0.17	0.65	1.39	2.63	5.24	1.44
MrRTF	Whole dataset	0.00	0.14	0.74	1.64	2.98	4.99	1.76
	Calibration	0.00	0.15	1.16	1.84	3.65	4.99	1.84
	Validation	0.00	0.12	0.47	1.18	1.50	4.99	1.47

). The mean values for the calibration dataset were slightly higher compared to validation dataset for all terrain attributes However, there were no trends with regard to other statistical parameters.

3.2. Spatial Trend Modeling

Each model utilized different terrain attributes for SOM and CEC predictions. A backwards stepwise linear model selection was used for the UK model. Based on the following equations (Equations (6) and (7)), the backwards stepwise model selected TWI, TPI, and MrRTF for SOM, and TPI and MrVBF for CEC predictions.

$$\mathrm{SOM}(\%)=3.37+0.11\times \mathrm{TWI}-2.20\times \mathrm{TPI}-0.09\times \mathrm{MrRTF}$$

(6)

$$\mathrm{CEC} \left({\mathrm{cmol}}_{\mathrm{c}}{ \mathrm{kg}}^{-1}\right)=18.41-9.36\times \mathrm{TPI}+1.02\times \mathrm{MrVBF}$$

(7)

From a pedological standpoint, Equations (6) and (7) reveal meaningful relationships between terrain and SOM or CEC. Equation (6) shows that SOM is positively correlated to TWI or wet/low-lying areas of the landscape, while it is negatively correlated to TPI and MrRTF or higher/steeper areas of the landscape. Similarly, CEC (Equation (7)) is negatively correlated with TPI, but positively correlated with MrVBF or lower landscape positions.

Cubist utilized all four terrain attributes for SOM, and only TPI and MrVBF for CEC predictions. Out of ten models generated by Cubist for SOM and CEC predictions, we selected the models with the lowest prediction error. For example, the SOM model (Equation (8)) was applicable in 123 locations where the average SOM was 4.09% with a prediction error of 0.70%. The CEC model (Equation (10)) applied to the 123 training locations had a mean value of 20.12 cmol_c kg⁻¹ and predication error of 2.84 cmol_c kg⁻¹. The Cubist model provided slightly different models for SOM prediction based on the combination of four terrain attributes but produced identical models for CEC. Following are examples of Cubist models for SOM and CEC predictions.

$$\begin{gathered} If \mathrm{TWI}\le 13.76 \\ then \mathrm{S}\mathrm{O}\mathrm{M} (\%)=3.79+0.21x\mathrm{MrVBF} -1.17x \mathrm{TPI}-0.11x\mathrm{MrRTF} \end{gathered}$$

(8)

$$\begin{gathered} If \mathrm{TWI}>13.76 \\ then \mathrm{SOM} (\%)=7.74+0.02x\mathrm{MrVBF} -0.32xMrRTF \end{gathered}$$

(9)

$$\mathrm{CEC} \left({\mathrm{cmol}}_{\mathrm{c}}{ \mathrm{kg}}^{-1}\right)=18.84-9.30x\mathrm{TPI}+1.03x\mathrm{MrVBF}$$

(10)

The Cubist model also provided the relative importance (RI) of the terrain attributes in developing conditions rules (if then else rules) and in developing multivariate linear function. In SOM prediction, the RI of the four terrain attributes was 54% (TPI), 37% (MrRTF), 35% (TWI), and 34% (MrVBF) in the MLR function and 54% for TWI in rule conditions. Therefore, TWI is the most important predictor for the Cubist model for SOM prediction.

For CEC, the Cubist model did not estimate conditional rules and returned only a single regression equation (Equation (10)). Not surprisingly, due to the lack of conditional rules, the equation from Cubist is almost identical with the one from stepwise linear regression (Equation (7)). Subsequently, the UK and Cubist predictive models produced similar results for CEC (Table 3). This suggests that for our study area, the additional complexity of Cubist models is unwarranted as the relationship between soil properties and landscape can be described by a single regression equation without the need for complex conditional rules.

Random forest used all four terrain attributes for predicting both SOM and CEC. The varImpPlot function in the randomForest package 4.6.14 [51] shows the importance of terrain attributes for SOM and CEC predictions. For the RF predictions the most important terrain attributes for SOM predictions were TPI and TWI, while for CEC predictions TPI and MrVBF (Figure 4). Overall, TPI was the most important variable and MrRTF was the least important variable in all selected models.

Both the UK and Cubist models show that SOM and CEC increase as TWI and MrVBF increase and decrease as TPI and MrRTF values increase. Even though, RF utilized all four terrain attributes for SOM and CEC predictions, TPI and MrVBF were among the most important variables for both SOM and CEC, similar to UK and Cubist (Equations (6)–(10)). Ref. [17] reported that among the five terrain attributes (elevation, TWI, plan curvature, total catchment area, and channel network base level), TWI and total catchment area closely related to the soil organic carbon content in flat slope areas. They also stated that besides these two terrain attributes, soil nutrient indicators were other environmental covariates that showed close correlation with soil organic carbon content. Ref. [43] found that wetness index and MrVBF were among the most important terrain attributes that influenced spatial distribution of SOM. They also reported that beside terrain attributes, land use, soil type and precipitation were other environmental variables that influence SOM distribution. Ref. [54] also documented the influence of land use, soil type, and geology on soil organic carbon distribution. They also noted that after elevation, TWI was the second most important terrain attribute in soil organic carbon prediction. The influence of soil type, geology, elevation, and slope on soil organic carbon distribution in wet cultivated fields was also reported by [11] who found that most of the soil organic carbon variation at the surface (0–10 cm) was explained by topographic attributes, while in the subsurface (10–50 cm) it was best estimated by soil texture classes.

TWI had correlation of 0.49 with SOM, 0.43 with CEC, −0.56 with TPI, 0.01 with MrRTF, and 0.67 with MrVBF. TPI had correlation of −0.51 with SOM, −0.53 with CEC, −0.52 with MrVBF, and 0.19 with MrRTF. MrVBF had correlation of 0.46 with SOM, 0.52 with CEC, and 0.04 with MrRTF. MrRTF showed a correlation of −0.21 with SOM, −0.06 with CEC. Suleymanov et al. (2021) [33] reported 0.5 correlation between SOM and MrRTF and MrRTF was a key attribute for mapping soil organic carbon and thickness of humus. Ref. [15] also observed a correlation of 0.5 between soil properties including soil organic carbon and auxiliary information. Ref. [20] reported lower correlation (<−0.38) between DEM and soil attributes including CEC, and moderate to strong correlation (<0.60) between satellite bands of synthetic soil image and soil attributes. The legacy soil map showed better correlation (0.5) with CEC compared to Landsat 5 TM derived attributes (<0.44) in the flat landscape of a semiarid region of Brazil [14]. Similar to [17], we found that based on the whole dataset, SOM has a strong correlation with CEC (0.73).

3.3. Variogram of Model Residuals

Variogram parameters of the UK, Cubist and RF model residuals of SOM and CEC are presented in the

Table 4. Variogram parameters of universal kriging (UK), Cubist, and random forest (RF) model residuals to predict soil organic matter content (SOM) and cation exchange capacity (CEC).

Soil Property	DSM Model	Semi-Variogram Model	Nugget	Sill	Nugget:Sill	Range (m)
SOM	UK	Spherical	0.22	0.43	0.51	126.12
	Cubist	Exponential	0.18	0.39	0.46	175.00
	RF	Exponential	0.08	0.11	0.72	176.29
CEC	UK	Spherical	5.46	5.70	0.96	229.00
	Cubist	Spherical	5.23	5.86	0.89	307.60
	RF	Spherical	1.16	1.41	0.82	405.50

. The nugget is the variance unexplained by the variogram and referred to noise in the data or random error. Compared to SOM, all DSM models, particularly UK and Cubist demonstrated highest nugget values for CEC. Sill represents the maximum variability among the point pairs. The range represents the maximum distance of spatial autocorrelation. The range values were increased in order of UK, Cubist, and RF for both SOM and CEC. UK showed lower range or spatial autocorrelation for both SOM and CEC while, RF shows higher spatial autocorrelation for the stated soil properties. The nugget to sill ratio determines the strength of spatial autocorrelation [55,56,57,58]. According to [55], a nugget to sill ratio of less than 0.25 shows strong, 0.25–0.75 shows moderate, and greater than 0.75 shows weak spatial dependence or autocorrelation. According to the nugget:sill ratio, SOM showed moderate while, CEC showed weak spatial dependency. According to [58], higher nugget:sill ratio and longer ranges, indicates greater variability in soil properties and a need for more observations for better prediction.

3.4. Predictive Model Performance

Based on the 4 evaluation metrics (

Table 5. Universal kriging (UK), Cubist, and random forest (RF) accuracy assessment for organic matter content (SOM) and cation exchange capacity (CEC) predictions with calibration and validation datasets.

Prediction Model		SOM				CEC
		R2	Bias	RMSE	${\mathit{\rho }}_{\mathit{c}}$	R2	Bias	RMSE	${\mathit{\rho }}_{\mathit{c}}$
		%				cmolc kg−1
UK	Calibration	0.50	0.00	0.80	0.60	0.60	0.00	2.80	0.70
	Validation	0.44	0.22	0.83	0.56	0.39	0.05	3.74	0.55
Cubist	Calibration	0.50	0.00	0.80	0.70	0.60	0.00	2.80	0.70
	Validation	0.45	0.17	0.80	0.58	0.41	0.00	3.68	0.57
RF	Calibration	0.90	0.00	0.40	0.90	0.90	0.00	1.40	0.90
	Validation	0.45	0.17	0.80	0.56	0.44	0.17	3.62	0.56
SSURGO	Calibration	0.31	−0.14	1.11	0.56	0.51	3.88	6.06	0.53
	Validation	0.40	−0.03	0.99	0.62	0.56	3.85	5.78	0.58

) and scatter plots of measured versus predicted SOM (Figure 5) and CEC (Figure 6), we found no major differences in the prediction performance of all three models.

Also [19] found no major difference and reported similar R² and RMSE values for soil organic carbon estimation based on Cubist and RF. Similar conclusion was reported by [17], who noted that RF and Cubist showed similar predictive performance in soil organic carbon estimation.

For the calibration data, RF had lower RMSE, lower bias, higher R², and higher concordance than UK and Cubist for both SOM and CEC predictions. With RF, this was expected due to the ensemble approach, which can result in low bias and variance [59,60]. Ref. [17] reported that predicted and observed values of soil organic carbon on the RF scatter plot were closer to the central or 1:1 line compared to Cubist, artificial neural network, support vector machine, and multiple linear regression models. For the RF models, however, there was a significant change in model performance between calibration and evaluation data. Thus, the performance decreased by half during the evaluation and was comparable with the performance of UK and Cubist. For example, for SOM predictions, the R² of the RF prediction were 0.90 for the calibration dataset and decreased to 0.45 for the evaluation dataset which was similar to UK (0.44) and Cubist (0.45). This significant change between calibration and evaluation performance is strong evidence that the RF models may be over optimistic. This highlights one of the issues with modeling for DSM: if models are not evaluated rigorously (i.e., using independent evaluation rather than leave-one-out), model performance estimates may be overly optimistic. Ref. [43] also documented higher R² and lower RMSE based on calibration dataset compared to validation dataset. Therefore, we agree that an independent validation dataset is necessary for DSM prediction performance evaluation [54,61].

According to the scatter plots for SOM (Figure 5a–c) and CEC (Figure 6a–c), all three models tended to over predict at low values and under predict at high values. This behavior is less pronounced for RF models on the calibration data, but it is apparent for all models on the evaluation dataset. This lack of performance for all models may be due to several factors, which are discussed below.

One reason for this poor correlation may be the due to the history of the study location. ACRE serves as a research and education facility and consists of many smaller individual fields that are managed under highly variable practices (e.g., multiple tillage systems, nutrient application rates, and crop rotations). For example, ACRE is crisscrossed by a grid of roads and grassed field boundaries that are on average 20 cm higher than the adjoining fields, and by a dense network of underground drainage tiles. The impact of the roads on terrain attributes is evident as linear features in the terrain attribute maps (Figure 2). The high variation in management may lead to higher soil variability from field to field than expected. Training models using samples from highly variable fields can limit their predictive performance outside the sample areas [62]. To account for the effects of variable management history, we would need to incorporate environmental covariates that describe previous management of each field into our modeling framework. This sort of detailed field-by-field management history has not been recorded for the entire farm. Recent research from [63] conducted on a long-term soil monitoring network in Switzerland has highlighted the role of land use change, crop rotations and site conditions on soil organic carbon dynamics. Further research is needed to identify suitable covariates that describe agriculture management history [64].

Compounding the land use and management history, the relatively flat topography with subtle topographic variation (on average 1% slope based on a 3 × 3 pixel window) may also have contributed to relatively poor performance of all models. In many environments, chemical properties of surface soil and SOM are highly variable spatially, and distinct variations are often found within short distances of meters and/or decimeters [65,66]. Thus, the intensive land use and management history combined with relatively flat terrain may have diluted the influence of terrain in the distribution of SOM and CEC leading to poorer than expected model performance. Although the R² for evaluation were relatively low, ranging from 0.39 to 0.45 in our study, they were comparable with other studies that considered terrain/climatic data only [16,50,67]. Ref. [16], argues that for quantitative soil spatial models, R² values of 0.5 and less are not uncommon. The fact that models were based only on terrain attributes supports the idea that topography at this scale is still one of the major factors for predicting soil properties despite management. The RMSE values of all three models were lower compared to [11], which used RF for soil organic carbon prediction. They found a higher RMSE (1.72%) for the surface soil (0–10 cm) and lower (0.43) at the subsurface (10–50 cm). This suggests that the spatial distribution patterns of soil organic carbon particularly at the topsoil are highly variable. Ref. [14] reported that based on validation dataset, geostatistical model (i.e., Cokriging) provided better results (R² = 0.57 and RMSE = 7.22) compared to the RF (R² = 0.47 and RMSE = 7.89) in CEC prediction. However a higher performance of kriging over RF and cubist models on the prediction of soil organic carbon at field-scale was also reported by [68]. Unlike in our study, a high-sampling density would have favored kriging in their case.

3.5. Organic Matter Content and Cation Exchange Capacity Distribution in the Landscape

DSM model predictions of SOM (Figure 7) and CEC (Figure 8) were consistent with the distributions of SOM and CEC within the landscape based on theoretical and pedological principles. The maps of predicted SOM and CEC for all three models indicate higher values for SOM and CEC in lower landscape positions (i.e., foot and toeslopes), and lower values at higher and steeper landscape positions (i.e., shoulders and summits). Ref. [10] also reported higher accumulation of soil organic carbon in lower or concave areas. Lower areas receive more overland flow of nutrients and crop residue from the steeper areas leading to an increase in SOM and CEC over time. The steeper regions are subject to erosion and loss of nutrients and soil organic matter to the lower parts of the landscape. On the other hand, waterlogging in lower areas reduces the rate of soil organic matter decomposition and results in higher SOM and nutrient accumulation [69].

3.6. Predictive Models versus SSURGO

When comparing maps of SSURGO SOM and CEC to DSM maps, all maps generally show a similar trend: high SOM and CEC occurred on lower landscape positions (Figure 7 and Figure 8). Where these maps differ from SSURGO is in the extent of regions of high SOM and CEC and the level of detail within SSURGO map units. In SSURGO, the regions or map units of high SOM and CEC are larger in extent compared to the DSM maps. Generally, SSURGO overrepresented the areas with high SOM and CEC (Figure 7 and Figure 8). For example, SSURGO representative values had a median SOM of 4.9% compared to 4.1 and 4.2% for DSM maps (

Table 6. Summary statistics of universal kriging (UK), Cubist, random forest (RF), and soil survey geographic (SSURGO) organic matter content (SOM) and cation exchange capacity (CEC) maps.

Statistical Index	SOM				CEC
	UK	Cubist	RF	SSURGO	UK	Cubist	RF	SSURGO
	%				cmolc kg−1
Minimum	0.9	1.9	2.4	1.6	1.1	5.2	11.9	7.0
1st Quartile	3.8	3.8	3.7	2.9	17.7	17.6	17.5	17.4
Median	4.2	4.2	4.1	4.9	20.0	19.9	19.4	28.5
Mean	4.2	4.2	4.2	4.0	19.6	19.6	19.7	23.5
3rd Quartile	4.7	4.6	4.6	4.9	22.0	22.1	21.8	28.5
Maximum	7.8	7.2	6.5	5.9	28.6	28.1	27.8	31.1
Standard Deviation	0.7	0.8	0.7	1.2	3.2	3.3	2.8	6.6

). Similarly, the SSURGO mean values for CEC had a median of 28.5% while DSM maps had a median between 19.4 and 20.0% (Table 6). Additionally, the standard deviation of SSURGO SOM (1.2%) and CEC (6.6%) maps are higher compared to DSM Maps, which is less than 0.8% for SOM and 2.8–3.3% for CEC (Table 6). Some of the major reasons for the overrepresentation of the areas with high SOM and CEC are the scale 1:15,840 [24] of SSURGO mapping and the design of map units. The density of the point data combined with high resolution topographic data provides a more detailed map of the SOM and CEC distribution compared to SSURGO. Also, SSURGO SOM and CEC capture the variability of the soil property within a larger and much more generalized map units thus tend to overrepresent the ranges and their extent within individual soil polygons.

One interesting area of agreement between SSURGO and DSM maps is for CEC predictions in the southern quarter of the study area. In this area, both SSURGO and DSM models predicted the lowest CEC values. Even though sampling points were not concentrated at this part of the study site (Figure 1), DSM models still managed to predict these regions of low CEC. Low DSM-derived CEC predictions likely resulted from the low TPI in the study areas (see the spatial trend modeling section). While SSURGO was not developed using TPI specifically, SSURGO mapping did rely heavily on relationships between soils and slope positions, which TPI captures numerically. Agreement between DSM-predicted CEC and SSURGO maps highlights the importance of soil-landscape relationships in soil spatial distributions, even at field scale.

We compared SOM and CEC predicted by DSM techniques to SOM and CEC from the SSURGO soil map. According to Table 5, the prediction performance (i.e., R² and concordance) of SSURGO was analogous to the DSM prediction, however, SSURGO has higher bias and RMSE particularly for CEC prediction. It is also interesting that SSURGO show slightly better results for validation data when compared to calibration data. We also compared SOM and CEC contents predicted by DSM to the SOM and CEC contents within each map unit from SSURGO (Figure 9). Both SOM and CEC show that the three predictive models follow similar prediction trends in each of the SSURGO mapping units. Based on visual interpretation of boxplots (Figure 9a–c), the results of our models for SOM are consistent with the estimates from eight SSURGO mapping units; exceptions were CwB2, McS2, RoB, SwA, TfB, and TmA. SSURGO underrepresented the SOM for these map units while the other models predicted greater concentrations of SOM. Generally, SSURGO had a wider range in SOM and CEC values when compared to the prediction models (Figure 9). This was particularly the case for CEC estimates. The prediction of our models for CEC is consistent with only few of the SSURGO mapping units see: RcA, RoB, SwA, TfB, and TmA (Figure 9d–f). Based on visual inspection of the boxplots (Figure 9d–f), however, for most of the mapping units, our models either over- or under-predicted CEC.

There are several reasons for the inconsistencies of model predictions with SSURGO. First, SSURGO has inherent limitations; the soil variability is represented using aggregated polygon map units with one to four named components plus inclusions of other soils or non-soils areas that do not explicitly capture the underlying spatial variability of soils within polygons [69]. Thus, these inclusions reduce the purity of the map units and impact interpretation and modeling [70]. Second, the procedure for SOM analysis differed between the datasets. The Walkley-Black method was used for the SSURGO data, while the loss-on-ignition (LOI) method was used for our collected data. Due to incomplete digestion of soil organic carbon, the Walkley-Black method usually underestimates SOM [71,72]. Additionally, the SSURGO values might have been impacted by errors introduced by the spline interpolation. Third, the SSURGO database was developed based on historical soil survey data and may not accurately reflect the current status of soil properties, particularly SOM and CEC, which are relatively dynamic and altered by various factors such as land management, climate change, and seasonal variability [9,73,74]. Additionally, the data were produced over different time periods and therefore inherit inconsistencies [4]. A fourth reason for the inconsistency is that the surveyors who collected data for SSURGO may not have had enough soil observations for building their mental models of soil variability as the detailed scale that lidar may suggest. A fifth reason for the inconsistency is that SSURGO values are not purely derived from laboratory analysis, instead the data may have resulted from a combination of laboratory measurements and field observations of expert soil scientists [38,75]. Due to these shortcomings, using SSURGO data in quantitative modeling and/or for monitoring soil carbon stocks sequestration could be misleading, particularly at the farm scale for highly variable soils in post glaciated landscapes.

4. Conclusions

In this study we developed digital soil maps of organic matter and cation exchange capacity for a 570-ha research farm, the Purdue Agronomy Center for Research and Education (ACRE). Digital soil maps were developed using only terrain attributes derived from lidar based digital elevation model. We compared three model approaches for predicting spatial distribution of SOM and CEC: universal kriging (UK), Cubist, and Random Forest. All models performed similarly for both SOM and CEC. Considering the high variability in farm management practices and nutrient application, the prediction accuracies were considered reasonable. All three predictive models showed similar spatial patterns that were comparable to the SSURGO map unit extents. This highlights the strength of the soil-landscape models as captured by predictive models or the soil mental models of soil surveyors (SSURGO) for mapping SOM and CEC. Overall SSURGO had a wider range of predicted soil properties when compared to the DSM models. However, DSM showed a finer-resolution view of the distribution of soil properties at ACRE and would be more informative for field precision management than the comparatively coarse-scale SSURGO data.

The results of this study demonstrate that lidar data can be used to adequately predict SOM and CEC at the farm scale in this post-glaciated landscape. This result has important implication for DSM in areas where certain environmental covariates may not be suitable or available. Provided there is a coupling between terrain attributes and soil properties, and that sampling locations capture the relationships between landscape and soil properties, even relatively simple empirical models such as universal kriging, can adequately predict spatial distribution of SOM and CEC.