Regression Kriging Model Research Articles

Spatial Downscaling of Nighttime Land Surface Temperature Based on Geographically Neural Network Weighted Regression Kriging

Land surface temperature (LST) has a wide application in Earth Science-related fields, and spatial downscaling is an important method to retrieve high-resolution LST data. However, existing LST downscaling methods have difficulties in simultaneously constructing and expressing spatial non-stationarity, spatial autocorrelation, and complex non-linearity during the LST downscaling process, which limits the performance of the models. Moreover, there is a lack of research on high-resolution nighttime land surface temperature (NLST) reconstruction based on spatial downscaling, which does not meet the data needs for urban-scale nighttime urban heat island (UHI) studies. Therefore, this study combined Geographically Neural Network Weighted Regression (GNNWR) with Area-to-Point Kriging interpolation (ATPK) to propose a Geographically Neural Network Weighted Regression Kriging (GNNWRK) model for NLST downscaling. To verify the model’s generality and robustness, this study selected four study areas with different landform and climate type for NLST spatial downscaling experiments. The GNNWRK was compared with four benchmark downscaling methods, including TsHARP, Random Forest, Geographically Weighted Regression, and GNNWR. The results show that compared to these four benchmark methods, the GNNWRK method has higher accuracy in NLST downscaling, with a maximum Pearson’s Correlation Coefficient (Pcc) of 0.930 and a minimum Root Mean Square Error (RMSE) of 0.886 K. Moreover, the validation based on MODIS NLST data and ground-measured NLST data also indicates that the GNNWRK model can obtain more accurate, high-resolution NLST with richer and more detailed texture. This enhances the potential of NLST in studying the effects of urban nighttime heat islands at a finer scale.

Prediction of Spatial Distribution of Heavy Metals in Cultivated Soil Based on Multi-source Auxiliary Variables and Random Forest Model

Spatial prediction of the concentrations of soil heavy metals (HMs) in cultivated land is critical for monitoring cultivated land contamination and ensuring sustainable eco-agriculture. In this study, 32 environmental variables from terrain, climate, soil attributes, remote-sensing information, vegetation indices, and anthropogenic activities were used as auxiliary variables, and random forest (RF), regression Kriging (RK), ordinary Kriging (OK), and multiple linear regression (MLR) models were proposed to predict the concentrations of As, Cd, Cr, Cu, Hg, Ni, Pb, and Zn in cultivated soils. In comparison to those of RK, OK, and MLR, the RF model had the best prediction performance for As, Cd, Cr, Hg, Pb, and Zn, whereas the OK and RK models had highest prediction performance for Cu and Ni, respectively, showing that R2 was the highest, and mean absolute error (MAE) and root mean square error (RMSE) were the lowest. The prediction performance of the spatial distribution of soil HMs under different prediction methods was basically consistent. The high value areas of eight HMs concentrations were all distributed in the southern plain area. However, the RF model depicted the details of spatial prediction more prominently. Moreover, the importance ranking of influencing factors derived from the RF model indicated that the spatial variation in concentrations of the eight HMs in Lanxi City were mainly affected by the combined effects of Se, TN, pH, elevation, annual average temperature, annual average rainfall, distance from rivers, and distance from factories. Given the above, random forest models could be used as an effective method for the spatial prediction of soil heavy metals, providing scientific reference for regional soil pollution investigation, assessment, and management.

Mapping Gross Domestic Product Distribution at 1 km Resolution across Thailand Using the Random Forest Area-to-Area Regression Kriging Model

Accurate spatial distribution of gridded gross domestic product (GDP) data is crucial for revealing regional disparities within administrative units, thus facilitating a deeper understanding of regional economic dynamics, industrial distribution, and urbanization trends. The existing GDP spatial models often rely on prediction residuals for model evaluation or utilize residual distribution to improve the final accuracy, frequently overlooking the modifiable areal unit problem within residual distribution. This paper introduces a hybrid downscaling model that combines random forest and area-to-area kriging to map gridded GDP. Employing Thailand as a case study, GDP distribution maps were generated at a 1 km spatial resolution for the year 2015 and compared with five alternative downscaling methods and an existing GDP product. The results demonstrate that the proposed approach yields higher accuracy and greater precision in detailing GDP distribution, as evidenced by the smallest mean absolute error and root mean squared error values, which stand at USD 256.458 and 699.348 ten million, respectively. Among the four different sets of auxiliary variables considered, one consistently exhibited a higher prediction accuracy. This particular set of auxiliary variables integrated classification-based variables, illustrating the advantages of incorporating such integrated variables into modeling while accounting for classification characteristics.

Comparative study of feature selection methods for wind speed estimation at ungauged locations

Wind speed estimation at ungauged locations is one of the preliminary steps for wind resource assessment. With the availability of high-resolution Digital Elevation Models (DEM) and remote sensing data, the number of potential wind speed predictors has grown substantially. The adequate spatial scale of these predictors is unknown a priori, leading to the use of multiple spatial scales of predictors in wind speed estimation models. Implementing a feature selection method as a pre-processing step of the analysis is necessary to avoid overfitting and the resulting potential model underperformance. This paper evaluated six feature selection methods (forward stepwise regression, Least Absolute Shrinkage and Selection Operator (LASSO), Elastic Net, maximum relevance minimum redundancy (MRMR), Genetic algorithm, and recursive feature elimination using support vector regression) for the estimation of different wind speed quantiles across Canada. The selected features were used to fit a regression-kriging model, and the importance of the predictors was evaluated with their associated regression coefficients. The results of the study showed that LASSO and MRMR are the most efficient algorithms with the least number of parameters to tune and good generalization performance. The study found that some predictors were more important for specific exceedance probabilities. The most important predictors were the distance from the coast and surface roughness length, regardless of exceedance probability.

High-Resolution Precipitation Modeling in Complex Terrains Using Hybrid Interpolation Techniques: Incorporating Physiographic and MODIS Cloud Cover Influences

The inclusion of physiographic and atmospheric influences is critical for spatial modeling of orographic precipitation in complex terrains. However, attempts to incorporate cloud cover frequency (CCF) data when interpolating precipitation are limited. CCF considers the rain shadow effect during interpolation to avoid an overly strong relationship between elevation and precipitation in areas at equivalent altitudes across rain shadows. Conventional multivariate regression or geostatistical methods assume the precipitation–explanatory variable relationship to be steady, even though this relation is often non-stationarity in complex terrains. This study proposed a novel spatial mapping approach for precipitation that combines regression-kriging (RK) to leverage its advantages over conventional multivariate regression and the spatial autocorrelation structure of residuals via kriging. The proposed hybrid model, RK (GT + CCF), utilized CCF and other physiographic factors to enhance the accuracy of precipitation interpolation. The implementation of this approach was examined in a mountainous region of southern Syria using in situ monthly precipitation data from 57 rain gauges. The RK model’s performance was compared with conventional multivariate regression models (CMRMs) that used geographical and topographical (GT) factors and CCF as predictors. The results indicated that the RK model outperformed the CMRMs with a root mean square error of <8 mm, a mean absolute percentage error range of 5–15%, and an R2 range of 0.75–0.96. The findings of this study showed that the incorporation of MODIS–CCF with physiographic variables as covariates significantly improved the interpolation accuracy by 5–20%, with the largest improvement in modeling precipitation in March.

Evaluation of Radar Precipitation Products and Assessment of the Gauge-Radar Merging Methods in Southeast Texas for Extreme Precipitation Events

Many radar-gauge merging methods have been developed to produce improved rainfall data by leveraging the advantages of gauge and radar observations. Two popular merging methods, Regression Kriging and Bayesian Regression Kriging were utilized and compared in this study to produce hourly rainfall data from gauge networks and multi-source radar datasets. The authors collected, processed, and modeled the gauge and radar rainfall data (Stage IV, MRMS and RTMA radar data) of the two extreme storm events (i.e., Hurricane Harvey in 2017 and Tropical Storm Imelda in 2019) occurring in the coastal area in Southeast Texas with devastating flooding. The analysis of the modeled data on consideration of statistical metrics, physical rationality, and computational expenses, implies that while both methods can effectively improve the radar rainfall data, the Regression Kriging model demonstrates its superior performance over that of the Bayesian Regression Kriging model since the latter is found to be prone to overfitting issues due to the clustered gauge distributions. Moreover, the spatial resolution of rainfall data is found to affect the merging results significantly, where the Bayesian Regression Kriging model works unskillfully when radar rainfall data with a coarser resolution is used. The study recommends the use of high-quality radar data with properly spatial-interpolated gauge data to improve the radar-gauge merging methods. The authors believe that the findings of the study are critical for assisting hazard mitigation and future design improvement.

Mapping Topsoil Total Nitrogen Using Random Forest and Modified Regression Kriging in Agricultural Areas of Central China

Accurate understanding of spatial distribution and variability of soil total nitrogen (TN) is critical for the site-specific nitrogen management. Based on 4337 newly obtained soil observations and 33 covariates, this study applied the random forest (RF) algorithm and modified regression kriging (RF combined with residual kriging: RFK, hereafter) model to spatially predict and map topsoil TN content in agricultural areas of Henan Province, central China. According to the RFK prediction, topsoil TN content ranged from 0.52 to 1.81 g kg-1, and the farmland with the topsoil TN contents of 1.00-1.23 g kg-1 and 0.80-1.23 g kg-1 accounted for 48.2% and 81.2% of the total farmland area, respectively. Spatially, the topsoil TN in the study area was generally higher in the west and lower in the east. By using the Boruta variable selection algorithm, soil organic matter (SOM) and available potassium contents in topsoil, nitrogen deposition, average annual precipitation, livestock discharges, and topsoil pH were identified as the main factors driving the spatial distribution and variation of soil TN in the study area. The RF and RFK models used showed the expected performance and achieved acceptable TN prediction accuracy. In comparison, RFK performed slightly better than the RF model. The R2 and RMSE achieved by the RFK model were improved by 4.5% and 4.5%, respectively, compared with that by the RF model. However, the results suggest that RFK was inferior to the RF model in quantifying prediction uncertainty and thus may have a slight disadvantage in model reliability.

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.

Multivariate random forest for digital soil mapping

In digital soil mapping (DSM), soil maps are usually produced in a univariate manner, that is, each soil map is produced independently and therefore, when multiple soil properties are mapped the underlying dependence structure between these soil properties is ignored. This may lead to inconsistent predictions and simulations. For example, soil organic carbon (SOC) and total nitrogen (TN) maps produced independently may show unrealistic carbon–nitrogen (C:N) ratios. In the last decade the production of soil maps with machine learning models has become increasingly popular as these models are able to capture complex non-linear relationships between soil properties and environmental covariates. However, producing soil maps with multivariate machine learning models is still lacking and requires much investigation in DSM. In this paper we present the combined modelling of multiple soil properties with a multivariate random forest (MRF) model. We applied this model to mapping SOC and TN, and we compared it with results of two separate univariate random forest (RF) models. The comparison was done by means of stochastic simulations determined by sampling from the conditional distributions of the soil properties, given the covariates, as estimated by quantile regression forest. The results show that the MRF model is superior in terms of maintaining the dependence structure between SOC and TN, and consequently, is also able to produce more realistic C:N ratios. The models were also compared on the basis of prediction accuracy using commonly used accuracy metrics such as the root mean square error (RMSE). We found that the accuracy of the MRF model (RMSE-SOC=40.04, RMSE-TN=2.26, RMSE-CN=3.58) is comparable to that of the univariate RF models (RMSE-SOC=39.76, RMSE-TN=2.26, RMSE-CN=3.65). We performed the same comparisons between a regression co-kriging model and two separate regression kriging models, and made similar conclusions.

Spatial distribution and influencing factors of humus layer thickness of forest land in permafrost region of Northeast China

Humus has significant impacts on soil water dynamics, nutrient storage and plant growth. Studies have demonstrated that the humus layer is related to climate, soil properties, topography and other environmental factors. However, the thickness of the humus layer (HLT) and its spatial distributions are less investigated. Especially in boreal mountain forests underlain with permafrost, the environmental influences on HLT remain unclear. In a high-latitude watershed of boreal mountain forest in Northeast China, this study explores the effects of the environmental factors on HLT, and its relationships with permafrost types. The HLT distribution across the watershed is extracted using the geographically weighted regression kriging (GWRK) model. The elevation, slope, aspect, mean annual ground surface temperature and mean annual soil water content are determined to be statistically significant influencers factors of HLT. The elevation is the most important variable for HLT in this cold land, with an indirect effect on HLT through impacting ground surface temperature and soil water content. Topography casts more significant impact than ground surface temperature and soil water content. HLT ranges from 1.1 to 26.7 cm across three permafrost classes in the study area, decreasing with the discontinuity of permafrost types (continuous permafrost > sporadic permafrost > isolated patches). The findings suggest that the humus development is closely related to the permafrost type in northern high latitudes, and the permafrost degradation can lead to humus layer thinning under climate warming.

First soil organic carbon report of Paraguay

Assessing soil organic carbon (SOC) stocks at a national scale provides relevant information on soil fertility and soil functions, such as soil water retention capacity, nutrient availability, and soil structure. Our overall goal is to map the SOC stock at the topsoil layer (0–30 cm) in Paraguay, using spatial information of key environmental factors (Environmental Factors - EF; 119 variables) related to SOC and by performing a Regression Kriging (RK) model. We fitted a RK model with 954 sample points, evaluating and computing the model uncertainty of SOC predictions with 10% of independent sample points. Our results show that on average, the SOC stock across Paraguay was 4,46 ± 2,66 kg m−2 where the highest SOC is found in humid regions covered by broad-leaf forests (8.66 × 10−6); while the lowest SOC is found within water-limited ecosystems (1.97 × 10−6). We determined that soil type, climate, and vegetation land cover were the strongest SOC predictors. Since this study represents the first Paraguayan effort to develop a SOC monitoring framework, it also provides the first national SOC map with its associated uncertainty. Enabling a unique opportunity to fulfill relevant information gaps and the extended opportunity to be used to validate global and regional SOC products.

Digital Mapping of Soil Organic Carbon Based on Machine Learning and Regression Kriging.

In the last two decades, machine learning (ML) methods have been widely used in digital soil mapping (DSM), but the regression kriging (RK) model which combines the advantages of the ML and kriging methods has rarely been used in DSM. In addition, due to the limitation of a single-model structure, many ML methods have poor prediction accuracy in undulating terrain areas. In this study, we collected the SOC content of 115 soil samples in a hilly farming area with continuous undulating terrain. According to the theory of soil-forming factors in pedogenesis, we selected 10 topographic indices, 7 vegetation indices, and 2 soil indices as environmental covariates, and according to the law of geographical similarity, we used ML and RK methods to mine the relationship between SOC and environmental covariates to predict the SOC content. Four ensemble models-random forest (RF), Cubist, stochastic gradient boosting (SGB), and Bayesian regularized neural networks (BRNNs)-were used to fit the trend of SOC content, and the simple kriging (SK) method was used to interpolate the residuals of the ensemble models, and then the SOC and residual were superimposed to obtain the RK prediction result. Moreover, the 115 samples were divided into calibration and validation sets at a ratio of 80%, and the tenfold cross-validation method was used to fit the optimal parameters of the model. From the results of four ensemble models: RF performed best in the calibration set (R2c = 0.834) but poorly in the validation set (R2v = 0.362); Cubist had good accuracy and stability in both the calibration and validation sets (R2c = 0.693 and R2v = 0.445); SGB performed poorly (R2c = 0.430 and R2v = 0.336); and BRNN had the lowest accuracy (R2c = 0.323 and R2v = 0.282). The results showed that the R2 of the four RK models in the validation set were 0.718, 0.674, 0.724, and 0.625, respectively. Compared with the ensemble models without superimposed residuals, the prediction accuracy was improved by 0.356, 0.229, 0.388, and 0.343, respectively. In conclusion, Cubist has high prediction accuracy and generalization ability in areas with complex topography, and the RK model can make full use of trends and spatial structural factors that are not easy to mine by ML models, which can effectively improve the prediction accuracy. This provides a reference for soil survey and digital mapping in complex terrain areas.

A Comparison of Machine Learning and Geostatistical Approaches for Mapping Forest Canopy Height over the Southeastern US Using ICESat-2

The availability of canopy height information in the Ice, Cloud, and Land Elevation Satellite-2’s (ICESat-2’s) land and vegetation product, or ATL08, presents opportunities for developing full-coverage products over broad spatial scales. The primary goal of this study was to develop a 30-meter canopy height map over the southeastern US, for the Southeastern Plains ecoregion and the Middle Atlantic Coastal Plains ecoregion. More specifically, this work served to compare well-known modeling approaches for upscaling canopy information from ATL08 to develop a wall-to-wall product. Focusing on only strong beams from nighttime acquisitions, the h_canopy parameter was extracted from ATL08 data. Landsat-8 bands and derived vegetation indices (normalized difference vegetation index, enhanced vegetation index, and modified soil-adjusted vegetation index) along with National Land Cover Database’s canopy cover and digital elevation models were used to extrapolate ICESat-2 canopy height from tracks to the regional level. Two different modeling techniques, random forest (RF) and regression kriging (RK), were applied for estimating canopy height. The RF model estimated canopy height with a coefficient of determination (R2) value of 0.48, root-mean-square error (RMSE) of 4.58 m, mean absolute error (MAE) of 3.47 and bias of 0.23 for independent validation, and an R2 value of 0.38, RMSE of 6.39 m, MAE of 5.04 and bias of −1.39 when compared with airborne lidar-derived canopy heights. The RK model estimated canopy heights with an R2 value of 0.69, RMSE of 3.49 m, MAE of 2.61 and bias of 0.03 for independent validation, and an R value of 0.68, R2 value of 0.47, RMSE of 5.96m, MAE of 4.52 and bias of −1.81 when compared with airborne lidar-derived canopy heights. The results suggest feasibility for the implementation of the RK method over a larger spatial extent and potential for combining other remote sensing and satellite data for future monitoring of canopy height dynamics.

Using environmental covariates to predict soil organic carbon stocks in Vertisols of Sudan

Soil organic carbon (SOC) stocks account for nearly 75% of the active carbon pool in terrestrial ecosystems. SOC is also one of the most important soil quality components and has a vital role in agricultural productivity. The main objective of this study was to test the ability of regression kriging (RK) to predict the spatial distribution of SOC stocks in the Vertisols of Gezira State, Sudan using environmental covariates (ECOVs) and legacy soil data. The variables involved 2098 legacy soil datasets (LSDs). Seven ECOVs were used: precipitation (PR), temperature (T), normalized difference vegetation index (NDVI), land use/cover (LULC), digital elevation model (DEM), terrain slope (TS), and valley depth (VD), all downloaded from the repository of the United States Geology Survey (USGS) except PR and T. The RK model was validated using root mean squared error (RMSE), normalized root mean squared error (nRMSE), mean absolute error (MAE), mean squared error (MSE), and coefficient of determination (R2). The NDVI and topography were the major ECOVs affecting spatial SOC distribution and its stocks in the area. The results showed that low elevation areas had higher SOC content compared to higher regions and the SOC stocks were 4.14 Kg C ha−1, 0.86 Kg C ha−1, 0.11 Kg C ha−1, 0.02 Kg C ha−1, and 0.004 Kg C ha−1 at gradient levels of <5°, 5–10°, 10–15°, 15–20°, and < 20°, respectively. Additionally, the spatial prediction revealed that agricultural land use (cropland) had the greatest SOC stocks (4.49 Kg C ha−1), whereas grasslands and forest lands were the lowest (0.01 Kg C ha−1). The RK model performed fairly well (RMSE = 1.83 g kg−1; nRMSE = 36%; MAE = 1.7%; MSE = 3.63%; R2 = 0.98) and gave satisfactory results to predict SOC stocks in the top 30 cm of the Vertisols. The findings of this study highlight that Vertisols could play a vital role in climate change mitigation via high SOC stocks and ability for C sequestration. It was recommended that the RK model should be extended to include much denser LSDs and test it with additional ECOVs combined with most specific soil properties that would have significant influence on SOC stocks in Vertisols, particularly soil pH, clay content, and clay mineralogy to achieve higher accuracy.

Spatial non‐stationary effects of explanatory variables on soil bulk density in the critical zone of the Chinese Loess Plateau

AbstractBulk density (BD) is one of the most important soil physical properties in the hydrological processes of Earth's Critical Zone (CZ). The heterogeneity and related controlling factors of surface BD have received extensive research attention. However, it is unclear whether the effects of controlling factors on BD are homogeneous or vary spatially. This study quantified topsoil BD with a high‐density sampling strategy (10 m × 10 m; n = 1134) across the ShuangChaGou watershed in the critical zone of the Chinese Loess Plateau (CLP‐CZ). Stepwise multiple linear regression (SMLR), regression kriging (RK), random forest (RF) and geographically weighted regression (GWR) were established as modelling approaches to (i) compare the performance of these four models in explaining BD variation, (ii) assess the main factors driving BD, and (iii) evaluate the spatial non‐stationary relationship between BD and its explanatory variables. GWR explained the BD variation to the same extent as the RK model (35%), outperforming both the SMLR (15%) and RF models (19%). The variation in topsoil BD depended mainly on: soil organic carbon (SOC) content, normalised difference vegetation index (NDVI), plan curvature, and slope length. The spatial distribution of the local R2, regression coefficient magnitude, significance and sign calculated by GWR revealed that the effects of variables accounting for variation in BD varied spatially. The explanatory power of these variables in terms of BD variation was strongest in northern and northeastern areas of the watershed and weakest in southern areas of the watershed. Both significant negative and positive correlations between BD and silt content, NDVI, and plan curvature were found. This study enriched traditional research linked to the complicated relationships between BD and controlling factors by incorporating spatial non‐stationarity, which is useful for improving the accuracy of hydrological modelling in the CLP‐CZ and in similar CZs worldwide.Highlights Non‐stationary relationships between BD (N = 1134) and its explanatory variables were captured at the watershed scale. GWR model performed on par with the RK and better than the SMLR or RF model. Silt content, NDVI, and plan curvature showed both significant negative and positive effects on BD. Spatial non‐stationarity of BD should be considered for improving the performance of hydrological modeling.

Comparing spatial interaction models and flow interpolation techniques for predicting “cold start” bike‐share trip demand

AbstractBike‐sharing systems are expanding rapidly in metropolitan areas all over the world and individual systems are updated frequently over space and time to dynamically meet demand. Usage trends are important for understanding bike demand, but an overlooked issue is that of “cold starts” or the prediction of demand at a new station with no previous usage history. In this article, we explore a methodology for predicting the bike trips from and to a cold start station in the NYC Citi Bike system. Specifically, gravity‐type spatial interaction model and spatial interpolation models, including natural neighbor interpolation and kriging, are employed. The overall results come from experiments of a real‐world bike‐sharing system in NYC and indicate that the regression kriging model outperforms the other models by taking advantage of the robustness and interpretability of gravity‐type spatial interaction regression models and the capability of ordinary kriging to capture spatial dependence.

Validating a spatio-temporal model of observed neighborhood physical disorder

This study tested spatio-temporal model prediction accuracy and concurrent validity of observed neighborhood physical disorder collected from virtual audits of Google Street View streetscapes. We predicted physical disorder from spatio-temporal regression Kriging models based on measures at three dates per each of 256 streestscapes (n = 768 data points) across an urban area. We assessed model internal validity through cross validation and external validity through Pearson correlations with respondent-reported perceptions of physical disorder from a breast cancer survivor cohort. We compared validity among full models (both large- and small-scale spatio-temporal trends) versus large-scale only. Full models yielded lower prediction error compared to large-scale only models. Physical disorder predictions were lagged at uniform distances and dates away from the respondent-reported perceptions of physical disorder. Correlations between perceived and observed physical disorder predicted from the full model were higher compared to that of the large-scale only model, but only at locations and times closest to the respondent's exact residential address and questionnaire date. A spatio-temporal Kriging model of observed physical disorder is valid.

Measurement error-filtered machine learning in digital soil mapping

This paper presents a two-stage maximum likelihood framework to deal with measurement errors in digital soil mapping (DSM) when using a machine learning (ML) model. The framework is implemented with random forest and projection pursuit regression to illustrate two different areas of machine learning, i.e. ensemble learning with trees and feature-learning. In our proposed framework, a measurement error variance (MEV) is incorporated as a weight in the log-likelihood function so that measurements with a larger MEV receive less weight when a ML model is calibrated. We evaluate the performance of the error-filtered ML models with an error-filtered regression kriging model, in a comprehensive simulation study and in a real-world case study of Namibian data. From the results we show that prediction accuracy can be increased by using our proposed framework, especially when the MEVs are large and heterogeneous.

Squirrel-Cage Fan System Optimization and Flow Field Prediction Using Parallel Filling Criterion and Surrogate Model

In this study, the blade shape of the squirrel-cage fan system inside the range hood was optimized using the surrogate model to improve the maximum volume flow rate. The influence of computational fluid dynamics (CFD) noise was concerned. The regression Kriging model (RKM) was used as a surrogate model to reflect the relationship between the design parameters of the blade and the volume flow rate. The parallel filling criterion after re-interpolation was used to improve the optimization efficiency further and ensure global optimization. Through experimental verification, we found that the relative error between the volume flow rate of the optimal sample of RKM and the experiment was only 0.4%. Compared with the prototype, the maximum volume flow rate of the optimal sample of RKM was increased by 2.9%, and the efficiency under the corresponding working conditions was increased by 2%. RKM was used to predict the velocity field of the volute and impeller exit section to explore the feasibility of the RKM in the flow field prediction. Research shows that the RKM cannot accurately predict the velocity of each grid on the cross-section. Still, it can accurately predict the changing trend of the velocity.

Soil organic carbon prediction with terrain derivatives using geostatistics and sequential Gaussian simulation

This current study investigated the relationship between soil organic carbon (SOC) and terrain derivatives on soil developed on dissimilar lithology while comparing the best modelling approach. Sixty (n = 60) bulk soil samples were taken from the depth of 0–30 cm according to five identified basement complex materials and analyzed for SOC. The models considered are ordinary kriging (OK), principal components kriging (PCA_OK) and regression kriging (RK). For the prediction's accuracy, 2-fold, and leave one out (LOOCV) cross-validation was carried out. The study indicated SOC in soil developed on granite gneiss (2.12%) and Biottite hornblende gneiss (2.05%) to be significantly (p < 0.05) higher than those on other lithology materials. SOC was significantly and positively correlated with slope (r = 0.44), channel network (r = 0.46), elevation (r = 0.47) and relative slope length (r = 0.20). The RK model showed higher performances in estimating SOC considering 2-fold cross-validation (RMSE = 0.48, ME = − 0.02, MSE = 0.23 and MAE = 0.39). Relative difference (RD) was positive when RK was compared with OK and PCA_OK, further suggesting RK as a better performing model. RK improved the map's structure with terrain derivatives, but the area was generally low in SOC. Model limitations showed that OK requires larger samples to improve the quality of prediction. Also, RK significant dissatisfaction is that the regression model parameters and covariance function parameters need to be estimated simultaneously. Simultaneously, PCA_OK tries to reduce a large number of interdependent variables to smaller number variables. In comparison, the sequential Gaussian simulation (SGS) revealed that the possible simulation realizations discovered more detail information than the original interpolated maps except for RK. The study recommended that SGS and RK map be adopted when making a precise land management decision.