Effect of training sample size, sampling design and prediction model on soil mapping with proximal sensing data for precision liming

Abstract

Site-specific estimation of lime requirement requires high-resolution maps of soil organic carbon (SOC), clay and pH. These maps can be generated with digital soil mapping models fitted on covariates observed by proximal soil sensors. However, the quality of the derived maps depends on the applied methodology. We assessed the effects of (i) training sample size (5–100); (ii) sampling design (simple random sampling (SRS), conditioned Latin hypercube sampling (cLHS) and k-means sampling (KM)); and (iii) prediction model (multiple linear regression (MLR) and random forest (RF)) on the prediction performance for the above mentioned three soil properties. The case study is based on conditional geostatistical simulations using 250 soil samples from a 51 ha field in Eastern Germany. Lin’s concordance correlation coefficient (CCC) and root-mean-square error (RMSE) were used to evaluate model performances. Results show that with increasing training sample sizes, relative improvements of RMSE and CCC decreased exponentially. We found the lowest median RMSE values with 100 training observations i.e., 1.73%, 0.21% and 0.3 for clay, SOC and pH, respectively. However, already with a sample size of 10, models of moderate quality (CCC > 0.65) were obtained for all three soil properties. cLHS and KM performed significantly better than SRS. MLR showed lower median RMSE values than RF for SOC and pH for smaller sample sizes, but RF outperformed MLR if at least 25–30 or 75–100 soil samples were used for SOC or pH, respectively. For clay, the median RMSE was lower with RF, regardless of sample size.

Sample Size Optimization for Digital Soil Mapping: An Empirical Example

“…Concordance increased quickly, while RMSE decreased quickly, as a function of sample size. This aligns with similar studies that show model performance metrics improve quickly at smaller sample sizes and then gradually level off [12,20]. In general, the sample plans selected with cLHS and FSCS outperformed those created with SRS in terms of both performance metrics at smaller sample sizes.…”

“…For example, Bouasria et al [14] showed minimal difference in RF model performance when comparing sample plans developed from cLHS and SRS to predict aboveground biomass, and Loiseau et al [83] noted no substantial difference in quantile RF predictions of sand, silt, and clay between SRS and cLHS sample plans. Schmidinger et al [12] noted higher RMSE and lower CCC with SRS compared to cLHS and FSCS at smaller sample sizes, whereas the differences decreased as sample sizes increased until all three sampling designs showed the same performance. To the contrary, Ma et al [82] showed that the overall accuracy of soil class prediction with RF was better with FSCS than it was with cLHS and SRS.…”

“…Techniques to estimate optimal sample size are critical to supporting soil management, crop productivity, and environmental conservation. Several applications include the prediction of crop yields [8,9], spatial variability of soil properties at the farm scale [10,11], and precision agriculture prescriptions [12,13] in agricultural systems. Sample size plays a critical role in predictive modeling of aboveground biomass and species distribution in forest systems [14,15] and in the calibration of models to predict soil properties from spectroscopy data [16,17] in soil science.…”