Multiple Linear Regression Kriging Research Articles

Improving a regional peat thickness map using soil apparent electrical conductivity measurements at the field-scale

IntroductionThe increased adoption of proximal sensors has helped to generate peat mapping products: they gather data quickly and can detect the peat-mineral later boundary. A third layer, made of sedimentary peat (limnic layers, gyttja), can sometimes be found in between them. This material is highly variable spatially and is associated with degraded soil properties when located near the surface.MethodsThis study aimed to assess the potential of direct current resistivity measurements to predict the maximum peat thickness (MPT), defined as the non-limnic peat thickness, to facilitate soil conservation and management practices at the field-scale. The results were also compared to a regional map of the MPT from a previous study used and also tested as a covariate. This study was conducted in a shallow (MPT = 8-138 cm) cultivated organic soil from Québec, Canada. The MPT was mapped using the apparent electrical conductivity (ECa) from a Veris Q2800, and a digital elevation model, with and without a regional MPT map (RM) as a covariate to downscale it. Three machine-learning algorithms (Cubist, Random Forest, and Support Vector Regression) were compared to ordinary kriging (OK), multiple linear regression, and multiple linear regression kriging (MLRK) models.Results and discussionThe best predictive performance was achieved with OK (Lin’s CCC = 0.89, RMSE = 13.75 cm), followed by MLRK-RM (CCC = 0.85, RMSE = 15.7 cm). All models were more accurate than the RM (CCC = 0.65, RMSE = 29.85 cm), although they underpredicted MPT > 100 cm. Moreover, the addition of the RM as a covariate led to a lower prediction error and higher accuracy for all models. Overall, a field-scale approach could better support precision soil conservation interventions by generating more accurate management zones. Future studies should test multi-sensor fusion and other geophysical sensors to further improve the model performance and detect deeper boundaries.

Mapping peat depth using a portable gamma-ray sensor and terrain attributes

Pristine peatlands being excellent storage for terrestrial Carbon (C) play a crucial role in regulating climate and water and provide several important ecosystem services. However, peatlands have been heavily altered (e.g., by draining the water table), increasing greenhouse gas (GHG) emissions. Restoring peatlands requires a comprehensive characterization, including knowledge of peat depth (PD; m). Traditionally, this requires the physical insertion of a push probe, which is time-consuming and labor-intensive. It has been shown that non-invasive proximal sensing techniques such as electromagnetic induction and ground penetrating radar can add value to PD data. In this research, we want to assess the potential of proximally sensed gamma-ray (γ-ray) spectrometry (i.e., potassium [K], thorium [Th], uranium [U], and the count rate [CR]) and terrain attributes data (i.e., elevation, slope, SAGAWI, and MRVBF) to map PD either alone or in combination across a small (10 ha) peatland area in ØBakker, Denmark. Here, the PD varies from 0.1 m in the south to 7.3 m in the north. We use various prediction models including ordinary kriging (OK) of PD, linear regression (LR), multiple LR (MLR), LR kriging (LRK), MLR kriging (MLRK) and empirical Bayesian kriging regression (EBKR). We also determine the minimum calibration sample size required by decreasing sample size in decrements (i.e., n = 100, 90, 80,…, 30). We compare these approaches using prediction agreement (Lin’s concordance correlation coefficient; LCCC) and accuracy (root mean square error; RMSE). The results show that OK using maximum calibration size (n = 108) had near perfect agreement (0.97) and accuracy (0.59 m), compared to LR (ln CR; 0.65 and 0.78 m, respectively) and MLR (ln K, Th, CR and elevation; 0.85 and 0.63 m). Improvements are achieved by adding residuals; LRK (0.95 and 0.71 m) and MLRK (0.96 and 0.51 m). The best results were obtained using EBKR (0.97 and 0.63 m) given all predictions were positive and no significant change in agreement and standard errors with the decrement of calibration sample size (e.g., n = 30). The results have implications towards C stocks assessment and improved land use planning to control GHG emissions and slow down global warming.

Predicting saturated hydraulic conductivity by pedo-transfer function and spatial methods in calcareous soils

Modeling soil saturated hydraulic conductivity (Ks) plays an important role to design and manage irrigation methods. Developing and evaluating accurate pedo-transfer functions (PTFs) for predicting difficult-to-measure soil properties such as Ks is an essential factor. This study aimed to develop aspatial models such as MLR (Multiple linear regression)-, ANN (Artificial neural network)-, and GMDH (Group method of data handling)-based PTFs and spatial methods such as Ordinary Kriging (OK), MLR- Kriging (MLR-K), ANN- Kriging (ANN-K), and GMDH-Kriging (GMDH-K) in GIS (Geographic information system) for predicting Ks in semi-arid soils. Soil infiltration was measured with a double-ring approach at 124 points with three replications at the field scale. After that, soil Ks was obtained by fitting the Green and Ampt infiltration model on soil infiltration data. In addition, for each point, easily measurable soil attributes such as texture, calcium carbonate equivalent, bulk density, soil moisture, saturated percent, organic matter, and gravel contents were measured. The results showed that the ANN-based PTFs yielded the better results with the highest E (0.605) and the lowest RMSE (0.055) than the MLR-based PTFs (E = 0.341 and RMSE = 0.068) and GMDH-based PTFs (E = 0.396 and RMSE = 0.065) for predicting Ks parameters. In addition, the hybrid spatial methods in this study, which include GMDH-K, MLR-K, and ANN-K provided more reliable estimation than the OK method. In overall, the best estimation of spatial method was ANN-K method, which had the highest E value (0.728) and the smallest RMSE value (0.044) for predicting the Ks parameters.

Comparison of a spatial, spatial and hybrid methods for predicting inter-rill and rill soil sensitivity to erosion at the field scale

Soil erosion prediction and conservation planning require detailed soil data under different environmental conditions. When such data are needed at the field scale, aspatial and spatial models could be used to predict soil erosion processes. This study was conducted to develop spatial models including geostatistical models (i.e. ordinary kriging (OK) and cokriging (CK)) and hybrid geostatistical models (i.e. multiple linear regression-kriging (MLRK) and artificial neural network-kriging (ANNK)) for estimating WEPP baseline soil sensitivity to erosion parameters for calcareous agricultural soils in northwest Iran. Inter-rill and rill erosion simulation experiments were carried out at 100 locations at the field scale with 3 replications. At each location, the soil properties (organic matter, calcium carbonate equivalent, sand, silt, clay, base infiltration rate) were measured and auxiliary data obtained from attributes derived from digital elevation models (elevation, slope, stream power index, wetness index and sediment transport index) and remote sensing data (three visible bands, NIR, SWIR (5 and 7 bands), NDVI indices). The MLR and ANN models were used to estimate baseline inter-rill soil sensitivity to erosion (Kib) and rill soil sensitivity to erosion (Krb and τcb) using two types of input data. For the first type of prediction models (type I), the measured soil properties and auxiliary data were used, whereas for the second type of models (type II), principal components (PCs) based on the soil and auxiliary data were used. In comparison to the models that were developed here, the WEPP inter-rill and rill soil sensitivity to erosion models showed a relatively poor performance. The ANN models developed here predicted Kib, Krb and τcb parameters better than the MLR models using both types of data (type I and II). Moreover, the results indicated that the ANNK model was the most appropriate spatial or hybrid model for predicting soil sensitivity to erosion parameters.

Spatial prediction and mapping of soil pH across a tropical afro-montane landscape

Soil pH is an indispensable part of the soil bionetwork, but so vulnerable to the dynamics of land-use change. Understanding the spatial and temporal distribution of soil pH is thus important for sustainable land use planning and management. In this study, we developed an approach based on geographically weighted regression-kriging (GWRK) to predict the continuous variation of soil pH up to 15 cm depth. The approach is compared to multiple linear regression-kriging (MLRK) using a total of 220 soil observations and 28 candidate auxiliary data, including climatic, topographic, and remotely sensed data. Results revealed that organic matter, sand, silt, temperature, and Landsat 8 operational land imager band 7 can explain the spatial variability of soil pH. GWR-based (local) models remarkably improved the prediction accuracy of soil pH compared to the MLR-based (global) models considering the root mean square error (i.e., 0.33 vs. 0.15; 0.37 vs. 0.17, respectively) and the coefficient of multiple determination (R2) (i.e., 0.59 vs. 0.74; 0.43 vs. 0.55, respectively). In conclusion, the use of GWR-based models revealed that the correlations between soil pH and environmental covariates were not stationary in space. Forested areas tended to be very strongly to moderately acidic, while croplands were slightly acidic to neutral. The GWR-based models demonstrated their utility in improving predictive soil mapping. These findings will support spatially-targeted soil pH management for improved food security and ecosystem health.

Effects of different sampling densities on geographically weighted regression kriging for predicting soil organic carbon

Geographically weighted regression kriging (GWRK) is a popular interpolation method, considering not only spatial parametric non-stationarity and relationship between target and explanatory variables, but also spatial autocorrelation of residuals. However, little attention has been paid to the effects of different sampling densities on GWRK technique for estimating soil properties. Objectives of this study were: (i) comparing the GWRK predictions with those obtained from multiple linear regression kriging (MLRK) and ordinary kriging (OK), and (ii) examining how different sampling densities affect the performance of GWRK for predicting soil organic carbon (SOC). Soil samples were simulated with four sampling densities, including 0.010, 0.020, 0.041, and 0.082 sites/km2. The results showed that GWRK made less prediction errors and outperformed MLRK and OK in the case of a high sampling density, with the root mean squared errors of GWRK<MLRK<OK and coefficient of determination of GWRK>MLRK>OK. However, in the case of a low sampling density, GWRK generated larger prediction errors, exhibiting a poorer performance than MLRK and OK. Accordingly, we conclude that GWRK can be considered as the best approach for predicting SOC in these three approaches with sufficient data points, but it has a poorer performance than the other methods with sparse data points.

Estimating Loess Plateau Average Annual Precipitation with Multiple Linear Regression Kriging and Geographically Weighted Regression Kriging

Estimating the spatial distribution of precipitation is an important and challenging task in hydrology, climatology, ecology, and environmental science. In order to generate a highly accurate distribution map of average annual precipitation for the Loess Plateau in China, multiple linear regression Kriging (MLRK) and geographically weighted regression Kriging (GWRK) methods were employed using precipitation data from the period 1980–2010 from 435 meteorological stations. The predictors in regression Kriging were selected by stepwise regression analysis from many auxiliary environmental factors, such as elevation (DEM), normalized difference vegetation index (NDVI), solar radiation, slope, and aspect. All predictor distribution maps had a 500 m spatial resolution. Validation precipitation data from 130 hydrometeorological stations were used to assess the prediction accuracies of the MLRK and GWRK approaches. Results showed that both prediction maps with a 500 m spatial resolution interpolated by MLRK and GWRK had a high accuracy and captured detailed spatial distribution data; however, MLRK produced a lower prediction error and a higher variance explanation than GWRK, although the differences were small, in contrast to conclusions from similar studies.