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 and delineating soil temperature regimes of China using pedotransfer function

Soil temperature regime (STR) is important for soil classification and land use. Generally, STR is delineated by estimating the mean annual soil temperature at a depth of 50 cm (MAST50) according to the Chinese Soil Taxonomy (CST). However, delineating the STR of China remains a challenge due to the difficulties in accurately estimating MAST50. The objectives of this study were to explore environmental factors that influence the spatial variation of MAST50 and generate an STR map for China. Soil temperature measurements at 40 and 80 cm depth were collected from 386 National Meteorological Stations in China during 1971–2000. The MAST50 was calculated as the average mean annual soil temperature (MAST) from 1971–2000 between 40 and 80 cm depths. In addition, 2 048 mean annual air temperature (MAAT) measurements from 1971 to 2000 were collected from the National Meteorological Stations across China. A zonal pedotransfer function (PTF) was developed based on the ensemble linear regression kriging model to predict the MAST50 in three topographic steps of China. The results showed that MAAT was the most important variable related to the variation of MAST50. The zonal PTF was evaluated with a 10% validation dataset with a mean absolute error (MAE) of 0.66°C and root mean square error (RMSE) of 0.78°C, which were smaller than the unified model with MAE of 0.83°C and RMSE of 0.96°C, respectively. This study demonstrated that the zonal PTF helped improve the accuracy of the predicted MAST50 map. Based on the prediction results, an STR map across China was generated to provide a consistent scientific base for the improvement and application of CST and land use support.

Hybrid modelling of random forests and kriging with sentinel-2A multispectral imagery to determine urban brightness temperatures with high resolution

ABSTRACT Herein, a random-forest-based Kriging downscaling method (RFRKriging) was tested to increase the spatial resolution of Landsat 8 thermal-infrared remote sensing (TIRS) brightness temperature (T b) over the central areas of Guangzhou, China. The 240-m Landsat 8 T b was upscaled from the resampled 30-m Landsat 8 T b by using the spatial averaging method. T b was downscaled based on its relationship to spectral reflectance in visible/near-infrared and shortwave infrared bands, spectral indices, including normalized difference vegetation index (NDVI), normalized difference building index (NDBI), and modified normalized difference water index (MNDWI), digital elevation model (DEM), longitude, latitude, impervious surface, vegetation, and soil fractions. The linear regression Kriging (LRKriging) and NDVI-based thermal sharpening algorithm (TsHARP) regression Kriging (TsHARPKriging) were also implemented. Relative to the reference data from the resampled Landsat 8 T b, the RFRKriging produced satisfactory downscaling results with respect to the maximum coefficient of determination (R 2), the minimum root-mean-square error (RMSE), and the minimum ratio between RMSE and the correspondent Landsat 8 T b standard deviation (RSD). RFRKriging captured T b differences over roads, forests, water bodies, and buildings and enhanced the spatial details of downscaled T b in all urban areas. Furthermore, integrating the multi-type predictor variables from 10-m Sentinel-2A and 30-m Landsat 8 image sets, RFRKriging was further applied to downscale 30-m Landsat 8 T b to 10 m. Then, it was upscaled to 30 m and assessed with the original 30-m Landsat 8 T b. RFRKriging was an effective and practical method for increasing the spatial resolution, with a low RSD of 0.254, a low RMSE of 0.525 K and a high R 2 of 0.935. The RSD of less than 0.5 indicates that RFRKriging could achieve an acceptable downscaling accuracy. Furthermore, RFRKriging enhances the spatial details of a 10-m T b in complex urban environments while maintaining the intrinsic information and spatial patterns of a downscaled T b. Due to the unavailability of the 30-m and 10-m T b truth, this study may only provide a quantitative assessment from some theoretical experiments. Also, a comparison of the RFRKriging downscaled T b with the resampled Landsat 8 T b was performed. The results suggest that the proposed RFRKriging downscaling method shows better downscaling performance with more spatial details than the cubic convolution method applied by the National Aeronautics and Space Administration (NASA) Centre.

Spatial distribution of soil carbon stocks in a semi-arid region of India

We predicted total carbon (TC) stocks in the 0–30 cm soil depth of two southern states in India using field observations, environmental covariates and geospatial approaches. We compared the Geographically Weighted Regression Kriging (GWRK) with Linear Regression Kriging (LRK) approach to predict the TC stocks. Greater spatial heterogeneity in TC stocks (2–15 kg m−2) were predicted with lower estimation errors (RMSE = 2 kg m−2 R2 = 0.63) in GWRK in comparison to the LRK approach (RMSE = 3 kg m−2, R2 = 0.55). The average decrease in the prediction error was 39% in GWRK in comparison to the LRK approach. The total TC stock in the 0–30 cm depth of the study area was estimated at 1.5 Pg C with upper and lower prediction intervals of 1 and 2 Pg C, respectively. The cropland stored largest (65%, 1 Pg C) amount of TC stocks followed by forest (21%, 0.31 Pg C) and plantation (8%, 0.12 Pg C) land cover types. Among soil types the Alfisols stored largest (33%, 0.49 Pg C) amount of TC stocks followed by Inceptisols (23%; 0.35 Pg C) and Entisols (18%, 0.27 Pg C). The uncertainty in TC stock predictions ranged from 41 to 75% and 69 to 91% under various land covers and soil types, respectively. Highest uncertainties in predicted TC stocks were associated with the forest land cover type and Mollisols soil order. Similarly, lowest uncertainties were found in the built up areas and Aridisols soil order. Our results suggest that GWRK is a useful approach to spatially predict the TC stocks at regional scales.

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.

Geospatial Predictive Modelling for Climate Mapping of Selected Severe Weather Phenomena Over Poland: A Methodological Approach

The main purpose of the study is to introduce methods for mapping the spatial distribution of the occurrence of selected atmospheric phenomena (thunderstorms, fog, glaze and rime) over Poland from 1966 to 2010 (45 years). Limited in situ observations as well the discontinuous and location-dependent nature of these phenomena make traditional interpolation inappropriate. Spatially continuous maps were created with the use of geospatial predictive modelling techniques. For each given phenomenon, an algorithm identifying its favourable meteorological and environmental conditions was created on the basis of observations recorded at 61 weather stations in Poland. Annual frequency maps presenting the probability of a day with a thunderstorm, fog, glaze or rime were created with the use of a modelled, gridded dataset by implementing predefined algorithms. Relevant explanatory variables were derived from NCEP/NCAR reanalysis and downscaled with the use of a Regional Climate Model. The resulting maps of favourable meteorological conditions were found to be valuable and representative on the country scale but at different correlation (r) strength against in situ data (from r = 0.84 for thunderstorms to r = 0.15 for fog). A weak correlation between gridded estimates of fog occurrence and observations data indicated the very local nature of this phenomenon. For this reason, additional environmental predictors of fog occurrence were also examined. Topographic parameters derived from the SRTM elevation model and reclassified CORINE Land Cover data were used as the external, explanatory variables for the multiple linear regression kriging used to obtain the final map. The regression model explained 89 % of annual frequency of fog variability in the study area. Regression residuals were interpolated via simple kriging.

Climate vs. topography – spatial patterns of plant species diversity and endemism on a high‐elevation island

Summary Climate and topography are among the most fundamental drivers of plant diversity. Here, we assessed the importance of climate and topography in explaining diversity patterns of species richness, endemic richness and endemicity on the landscape scale of an oceanic island and evaluated the independent contribution of climatic and topographic variables to spatial diversity patterns. We constructed a presence/absence matrix of perennial endemic and native vascular plant species (including subspecies) in 890 plots on the environmentally very heterogeneous island of La Palma, Canary Islands. Species richness, endemic richness and endemicity were recorded, interpolated and related to climate (i.e. variables describing temperature, precipitation, variability and climatic rarity) and topography (i.e. topographic complexity, solar radiation, geologic age, slope and aspect). We used multimodel inference, spatial autoregressive models, variance partitioning and linear regression kriging as statistical methods. Species richness is best explained by both climatic and topographic variables. Topographic variables (esp. topographic complexity and solar radiation) explain endemic richness, and climatic variables (esp. elevation/temperature and rainfall seasonality) explain endemicity. Spatial patterns of species richness, endemic richness and endemicity were in part geographically decoupled from each other. Synthesis. We identified several topography‐dependent processes ranging from evolutionary processes (micro‐refugia, in situ speciation, pre‐adaptation to rupicolous conditions, dispersal limitations) to human‐induced influences (introduced herbivores, fire, land use) that possibly shape the endemic richness pattern of La Palma. In contrast, climate mainly drives endemicity, which is connected to ecological speciation and specialization to local conditions. We highlight the importance of incorporating climatic variability into future studies of plant species diversity and endemism. The spatial incongruence in hot spots of species richness, endemic richness and endemicity emphasizes the need for an integrated conservation approach acknowledging different diversity measures to protect the complete spectrum of diversity. High‐elevation islands such as La Palma are highly suitable to study drivers of diversity and endemism, as they offer environmental gradients of continental magnitude on the landscape scale of a single climatic mini‐continent and a large array of in situ‐speciated endemics.