Comparison of common spatial interpolation methods for analyzing pollutant spatial distributions at contaminated sites

Evaluation of the prediction effectiveness for geochemical mapping using machine learning methods: A case study from northern Guangdong Province in China

This study compares seven machine learning models to investigate whether they improve the accuracy of geochemical mapping compared to ordinary kriging (OK). Arsenic is widely present in soil due to human activities and soil parent material, posing significant toxicity. Predicting the spatial distribution of elements in soil has become a current research hotspot. Lianzhou City in northern Guangdong Province, China, was chosen as the study area, collecting a total of 2908 surface soil samples from 0 to 20 cm depth. Seven machine learning models were chosen: Random Forest (RF), Support Vector Machine (SVM), Ridge Regression (Ridge), Gradient Boosting Decision Tree (GBDT), Artificial Neural Network (ANN), K-Nearest Neighbors (KNN), and Gaussian Process Regression (GPR). Exploring the advantages and disadvantages of machine learning and traditional geological statistical models in predicting the spatial distribution of heavy metal elements, this study also analyzes factors affecting the accuracy of element prediction. The two best-performing models in the original model, RF (R2 = 0.445) and GBDT (R2 = 0.414), did not outperform OK (R2 = 0.459) in terms of prediction accuracy. Ridge and GPR, the worst-performing methods, have R2 values of only 0.201 and 0.248, respectively. To improve the models' prediction accuracy, a spatial regionalized (SR) covariate index was added. Improvements varied among different methods, with RF and GBDT increasing their R2 values from 0.4 to 0.78 after enhancement. In contrast, the GPR model showed the least significant improvement, with its R2 value only reaching 0.25 in the improved method. This study concluded that choosing the right machine learning model and considering factors that influence prediction accuracy, such as regional variations, the number of sampling points, and their distribution, are crucial for ensuring the accuracy of predictions. This provides valuable insights for future research in this area.

Integrated pollution analysis, pollution area identification and source apportionment of heavy metal contamination in agricultural soil

Given the global prevalence of soil heavy metal contamination, knowledge concerning of soil environmental quality assessment, pollution area identification and source apportionment is critical for implementation of soil pollution prevention and safe utilization strategies. In this study, soil static environmental capacity (QI) for heavy metals was selected to evaluate pollution risks in agricultural soils of Wenzhou, southeast China. Combined with geostatistical methods, the pollution area was identified along with uncertainty analysis. Potential sources were quantitatively apportioned using a positive matrix factorization model (PMF). Results showed that agricultural soils in this study were mainly contaminated by Cd and Pb based on both Nemerow and QI indices. The environmental capacity assessment found more than 90% areas were identified as polluted soils for Qi-Zn, Qi-Cd and Qi-Pb, with minor uncertain areas. Cu was identified as having a high proportion of uncertain pollution area status, which was similar to the results of the integrated environmental capacity for all metals. PMF results indicated that industrial discharge, agrochemicals and parent material accounted for 32.1%, 32.2% and 35.7% of heavy metal accumulation in soils, respectively. Implementation of strict policies to reduce anthropogenic source emissions and remediate soil pollution are crucial to minimize metal pollution inputs, improve agricultural soil quality and enhance food safety.

Screening and optimization of interpolation methods for mapping soil-borne polychlorinated biphenyls

There is yet no scientific consensus, and for now, on how to choose the optimal interpolation method and its parameters for mapping soil-borne organic pollutants. Take the polychlorinated biphenyls (PCBs) for instance, we present the comparison of some classic interpolation methods using a high-resolution soil monitoring database. The results showed that empirical Bayesian kriging (EBK) has the highest accuracy for predicting the total PCB concentration, while root mean squared error (RMSE) in inverse distance weighting (IDW) is among the highest in these interpolation methods. The logarithmic transformation of non-normally distributed data contributed to enhance considerably the semivariogram for modeling in kriging interpolation. The increasing of search neighborhood reduced IDW's RMSE, but slightly affected in ordinary kriging (OK), while both of them resulted in over smooth of prediction map. The existence of outliers made the difference between two points increase sharply, and thereby weakening spatial autocorrelation and decreasing the accuracy. As predicted error increased continuously, the prediction accuracy of different interpolation methods reached unanimity gradually. The attempt of the assisted interpolation algorithm did not significantly improve the prediction accuracy of the IDW method. This study constructed a standardized workflow for interpolation, which could reduce human error to reach higher interpolation accuracy for mapping soil-borne PCBs.

Groundwater heavy metal(loid)s risk prediction based on topsoil contamination and aquifer vulnerability at a zinc smelting site

Groundwater pollution is a recurrent problem in abandoned non-ferrous metal smelting sites, and its severity is influenced by topsoil contamination, hydrogeological characteristics, and hydrogeochemical conditions. In such unique areas, traditional methods for evaluating groundwater pollution risk are biased, as the long production history of these sites have led to highly polluted and heterogeneous soil and groundwater. Herein, based on a typical lead-zinc smelting site, As, Pb, Zn, Cd, Mn, and Ni were found to be the predominant heavy metal (loid)s in groundwater, with respective exceedance rates of 44.4%, 50.0%, 72.2%, 88.9%, 88.9%, and 61.1%. Combined with the groundwater pollution characteristics, the representative hydrogeochemical factors were screened out to optimize the following aquifer vulnerability evaluation using the AHP-DRASTICH method. A comprehensive evaluation model (DI-NCPI) for groundwater pollution risk was established by combining the DRASTICH index (DI) obtained after optimization and the Nemerow comprehensive contamination index (NCPI) of topsoil. The fit between DI-NCPI and groundwater heavy metal (loid) pollution index reached 0.956, which laterally confirms that the model has some reference value. In terms of distribution, the high-risk and very high-risk zones were mainly concentrated in the zinc smelting system, located in the southeastern and central-western parts of the site. These areas have relatively high levels of topsoil contamination and aquifer vulnerability and require focused attention in site remediation. This research highlights the importance of combining topsoil contamination and aquifer vulnerability to evaluate groundwater pollution risk in smelting areas. It provides a more targeted reference for groundwater remediation strategies in abandoned smelting sites, as well as severely polluted industrial areas.

Exploring the Spatial Pattern of Urban Forest Ecosystem Services based on i-Tree Eco and Spatial Interpolation: A Case Study of Kyoto City, Japan

Urban forest, as an essential urban green infrastructure, is critical in providing ecosystem services to cities. To enhance the mainstreaming of ecosystem services in urban planning, it is necessary to explore the spatial pattern of urban forest ecosystem services in cities. This study provides a workflow for urban forest planning based on field investigation, i-Tree Eco, and geostatistical interpolation. Firstly, trees across an array of land use types were investigated using a sampling method. Then i-Tree Eco was applied to quantify ecosystem services and ecosystem service value in each plot. Based on the ecosystem services estimates for plots, four interpolation methods were applied and compared by cross-validation. The Empirical Bayesian Kriging was determined as the best interpolation method with higher prediction accuracy. With the results of Empirical Bayesian Kriging, this study compared urban forest ecosystem services and ecosystem service value across land use types. The spatial correlations between ecosystem service value and four types of point of interest in urban places were explored using the bivariate Moran's I statistic and the bivariate local indicators of spatial association. Our results show that the residential area in the built-up area of Kyoto city had higher species richness, tree density, ecosystem services, and total ecosystem service value. Positive spatial correlations were found between ecosystem service value and the distribution of urban space types including the tourist attraction distribution, urban park distribution, and school distribution. This study provides a specific ecosystem service-oriented reference for urban forest planning based on land use and urban space types.

Optimization of spatial prediction and sampling strategy of site contamination based on Thiessen polygon coupling interpolation

Contaminated sites pose a serious threat to the ecological environment and human health. Because of the presence of multiple peaks in the pollution data of some contaminated sites, as well as strong spatial heterogeneity and skewness in their distribution, the accuracy of spatial interpolation prediction is low. This study proposes a method for investigating highly skewed contaminated sites, which uses Thiessen polygons coupled with geostatistics and deterministic interpolation to optimize the spatial prediction and sampling strategy of sites. An industrial site in Luohe is used as an example to validate the proposed method. The results indicate that using 40 × 40 m as the minimum initial sampling unit can obtain data that is representative of the regional pollution situation. Evaluation indexes reveal that the ordinary kriging (OK) method for interpolation prediction accuracy and the radial basis function_inverse distance weighted (RBF_IMQ) method for pollution scope prediction provides the best results, which can effectively improve the spatial prediction accuracy of pollution in the study area. Each accuracy indicator is enhanced by 20-70% after supplementing 11 sampling points in the suspect region, and the identification of the pollution scope approaches 95%. This method offers a novel approach for investigating highly biased contaminated sites, which can optimize the spatial prediction accuracy of pollution and reduce economic costs.

Estimation of Polycyclic Aromatic Hydrocarbons in Groundwater from Campania Plain: Spatial Distribution, Source Attribution and Health Cancer Risk Evaluation

The aim of this study was to evaluate the concentrations of polycyclic aromatic hydrocarbons (PAHs) in 1168 groundwater samples of the Campania Plain (Southern Italy), taken using a municipal environmental pressure index (MIEP), and to analyze the distribution of these compounds to determine source PAHs using ratios of isomers diagnostic. Lastly, this study also aimed to estimate the potential health cancer risk in groundwaters. The data indicated that the highest concentration of PAHs was found in groundwater from Caserta Province and the contents of BghiP, Phe, and Nap were detected in the samples. The spatial distribution of these pollutants was evaluated using the Jenks method; moreover, the data indicated that incremental lifetime cancer risk ILCR_ingestion ranged from 7.31 × 10^-20 to 4.96 × 10^-19, while ILCR_dermal ranged from 4.32 × 10^-11 to 2.93 × 10^-10. These research findings may provide information about the Campania Plain's groundwater quality and aid in the development of preventative measures to lessen PAH contamination in groundwater.

Delineating and identifying risk zones of soil heavy metal pollution in an industrialized region using machine learning

The ability to control the risk of soil heavy metal pollution is limited by the inability to accurately depict their spatial distributions and to reasonably delineate the risk zones. To overcome this limitation and develop machine learning methods, a hybrid data-driven method supported by random forest (RF) and fuzzy c-means with the aid of inverse distance weighted interpolation was proposed to delineate and further identify risk zones of soil heavy metal pollution on the basis of 577 soil samples and 12 environmental covariates. The results indicated that, compared to multiple linear regression, RF had a better prediction performance for As, Cd, Cr, Cu, Hg, Ni, Pb, and Zn, with the corresponding R² values of 0.86, 0.85, 0.78, 0.85, 0.84, 0.78, 0.79 and 0.76, respectively. The relative concentrations (predicted concentrations divided by risk screening values) of Cd (17.69), Cr (1.38), Hg (0.31), Pb (6.52), and Zn (8.24) were relatively high in the north central part of the study area. There were large differences in the key influencing factors and their contributions among the eight heavy metals. Overall, industrial enterprises (21.60% for As), soil pH (31.60% for Cd), and population (15.50% for Cr) were the key influencing factors for the heavy metals in soil. Four risk zones, including one high risk zone, one medium risk zone, and two low risk zones were delineated and identified based on the characteristics of the eight heavy metals and their influencing factors, and accordingly discriminated risk control strategies were developed. In the high risk zone, it will be necessary to strictly control the discharge of heavy metals from the various industrial enterprises and mines by the adoption of cleaner production practices, centralizedly treat the domestic wastes from residents, substantially reduce the irrigation of polluted river water, and positively remediate the Cd, Cr, and Ni-polluted soil.

An experimental investigation on the effect of soluble sugar degradation on the of domestic-source-contaminated soil sites formation and evolution

The percolation-degradation process of soluble domestic pollution is very important for the evolution of soil properties and the formation of contaminated sites. The main objective of this study is to investigate the influence of glucose seepage-degradation on the permeability of clay through an indoor percolation test in combination with thermogravimetric measurement with glucose as a representative domestic contaminant soluble sugar. We can conclude that the permeability of clay was significantly impacted by the seepage-degradation of soluble sugar. With a focus on the role of soluble sugars in domestic source pollutants on clay, the formation and evolution of the domestic source contaminated soil site went through three main stages: "generation of domestic source contaminated liquid & formation of S-C zone", "contraction of S-C zone & formation of E-C zone and C zone", and "disappearance of S-C zone & contraction of E-C zone and C zone". The clay permeability decreased, the migration range shrinked, and the pollution level of the clay near the source of the contaminants increased with increasing soluble sugar solution concentration.

Optimizing spatial interpolation method and sampling number for predicting cadmium distribution in the largest shallow lake of North China

Cadmium (Cd) pollution has been widely recognized in lake ecosystems. Although the accurate prediction of the spatial distributions of Cd in lakes is important for controlling Cd pollution, the traditional monitoring methods of setting discrete and limited sampling points cannot actually reflect the continuous spatial distribution characteristics of Cd. In this study, we set up 93 sampling points in Baiyangdian Lake (BYDL), and collected surface water, overlying water and sediment samples from each sampling point. Cd contents were measured to predict their spatial distributions in different environmental components by three interpolation methods, inverse distance weighted (IDW), radial basis function (RBF) and ordinary kriging (OK), and the effects of different sampling numbers on the interpolation accuracy were also assessed to optimize the interpolation method and sampling number. The results showed that the interpolation accuracy of IDW decreased with increasing power values. The best basis function for RBF was IMQ, and the best semivariogram models for OK were the spherical model and stable model. The best interpolation method for the waters and sediments was RBF-IMQ compared with OK and IDW. Within the sampling number range of 50-93, the interpolation accuracy for Cd in surface water increased with the increase in sampling number. Comparatively, the interpolation accuracy was the highest for overlying water and sediments when the sampling number was 60. The findings of this work provide a combined sampling and spatial interpolation method for monitoring the spatial distribution and pollution levels of Cd in the waters and sediments of shallow lakes.

Diagnosing trace metals contamination in ageing stormwater constructed wetlands by portable X-ray Fluorescence Analyzer (pXRF)

In the context of stormwater management in urban areas, more knowledge is needed about sustainable urban drainage systems (SUDS)' long-term performance. This article reports robust calibration of a portable X-ray Fluorescence Analyzer (pXRF) for a purpose of metal accumulation diagnosis in two stormwater constructed wetlands (SCWs). Two 9-year-old SCWs located in Eastern France and composed of a sedimentation pond and a vertical-flow reed-bed filter (RBF#1) respectively a horizontal-flow RBF (RBF#2) are studied. A focus is made on the RBFs where five target metals (Cr, Cu, Ni, Pb, Zn) are monitored to fulfill three objectives: i) develop a robust analyzing method for both field and laboratory scale; ii) compute a distribution mapping of the metals on the substrate; and iii) identify and quantify contamination hotspots. pXRF measurements present an opportunity for a quick field diagnosis of such ageing systems once calibrated. An optimal 63 s beam shooting time was selected for analyses, and optimal particle size distribution was set below 250 μm. As water content is known to be a critical factor influencing measuring quality, correction factors were determined to allow for field campaign up to 30 % of water content. Metals are more accumulated in RBF#1 than in RBF#2 because of the particle size distribution and hydraulic regime of the RBFs. Moreover, RBF#1 displays a higher metal accumulation at the water supply outputs while the distribution pattern in RBF#2 is more diffuse. Only 34 %, resp. 22 % of RBF#1 and RBF#2 surface is contaminated, with corresponding concentrations ranging among the highest 50 % and 25 % concentrations. Eventually, the RBF#1 upper layer (0-5 cm) higher organic matter content generates more metal retention than its deeper layer whereas in RBF#2 metal concentration is homogeneous along depth. These results can be useful to optimize the long-term maintenance and possibly the sizing of such systems.

An improved non-stationary geostatistical method for three-dimensional interpolation of Benzo(a)pyrene at a contaminated site

Intense industrial activities and complex hydrogeological conditions at contaminated sites make accurate three-dimensional (3D) mapping challenging. The cause is the non-stationarity in the variance of soil pollutants in geographical space (G-space), making the stationary hypothesis required by the Kriging method unsatisfactory. To handle the variance non-stationarity, a Variance-Octree-Kriging (VOK) method was proposed. VOK is a spatial deformation method that constructs a stationary deformation space (D-space) by stretching and shrinking the G-spaces with low and high spatial correlation, respectively. VOK method consists of 3D stratification in G-space, space scaling and transformation, and ordinary Kriging (OK) in D-space. 3D stratification uses variance octree (VOT) to generate a set of anchor points in the G-space. The spatial scaling and transformation use the virtual force algorithm (VFA) and thin-plate spline to evenly distribute the anchor points and obtain the D-space, where the OK is implemented. The method was applied to predict the distribution of soil Benzo(a)pyrene (BaP) at a contaminated site in North China Plain. The results show that the interpolation accuracy of VOK was 9% higher than that of OK. The VOK method also changed the spatial structure from anisotropic to isotropic. The root mean squared error (RMSE) of fill, silt and clay layers decreased by 4.67%, 11.39%, and 20.46%, respectively. This method is applicable to the 3D interpolation of pollutants at contaminated sites, with the advantages of high interpolation accuracy and the ability to handle the non-stationarity in variance.

Effectiveness of predicting the spatial distributions of target contaminants of a coking plant based on their related pollutants

The prediction accuracy of the spatial distribution of soil pollutants at a site is relatively low. Related pollutants can be used as auxiliary variables to improve the prediction accuracy. However, little relevant research has been conducted on site soil pollution. To analyze the prediction accuracy of target pollutants combined with auxiliary pollutants, Cu, toluene, and phenanthrene were selected as the target pollutants for this study. Based on geostatistical analysis and spatial analysis, the following results were obtained. (1) The reduction in the root mean square errors (RMSEs) for Cu, toluene, and phenanthrene with multivariable cokriging was 68.4%, 81.6%, and 81.2%, respectively, which are proportional to the correlation coefficient of the relationship between the auxiliary pollutants and the target pollutants. (2) The RMSEs calculated for the multivariable cokriging were lower than those obtained by only combining one related pollutants, and two co-variables should be better. (3) The predicted results for Cu, phenanthrene, and toluene and their corresponding related pollutants are more accurate than the results obtained not using the related pollutants. (4) In the interpolation process, the RMSEs for Cu, toluene, and phenanthrene with multivariable cokriging basically increase as the neighborhood sample data increases, and then they become stable. (5) When 84, 61, and 34 sample points were removed, the RMSEs for Cu, toluene, and phenanthrene, respectively, with multivariable cokriging were close to the RMSEs of the target pollutants based on the total samples. The results are of great significance to improving the prediction accuracy of the spatial distribution of soil pollutants at coking plant sites.

Identification and uncertainty analysis of high-risk areas of heavy metals in sediments of the Yangtze River estuary, China

In this study, ordinary kriging (OK) and indicator kriging (IK) were used to analyze the uncertainty associated with high-risk areas of seven heavy metals (As, Cd, Cr, Cu, Hg, Pb, and Zn) in sediments of the Yangtze River estuary during four seasons. The OK results showed that the high-risk areas of Cd, Cr, Cu, Hg, and Pb had a high proportion, with the highest corresponding to Cr pollution (up to 60%). Predictions based on IK revealed that the proportion of high-risk areas of Cr, Cd, and Hg pollution were high, especially that of Cr was higher than 90%. However, there were uncertainties between the OK and IK results. The uncertainty results revealed that the uncertainty areas of Cr pollution were relatively large, accounting for about 30%, while those of Cd, Cu, and Hg pollution were lower than 10%.

Quantitative analysis of the main sources of pollutants in the soils around key areas based on the positive matrix factorization method

Quantitative identification of the main sources of heavy metals and polycyclic aromatic hydrocarbons (PAHs) in soils around multiple types of key areas is of great significance for blocking pollution sources. However, there is a lack of more comprehensive relevant research. In this study, Beijing was taken as the research area and four main sources were identified using the positive matrix factorization (PMF) method. The concentration of Pb, PAHs, Cr, and Hg in soils was significantly affected by the presence of landuse type, road traffic, natural factor, and industrial production, respectively, and the farmland, distance to main road, Proterozoic Changcheng-Jixian parent material and cinnamon soil type, and the gross industrial production make greater contributions to these four factors respectively than other variables. Moreover, the uncertainty of the PMF indicates that this four-factor PMF solution is stable and appropriate. These results provide support for the comprehensive control of soil environmental risks.

Effectiveness of predicting spatial contaminant distributions at industrial sites using partitioned interpolation method

Soil pollution at industrial sites is an important issue in China and in most other regions of the world. The accurate prediction of the spatial distribution of pollutants at contaminated industrial sites is a requirement for the development of most soil remediation strategies, and is commonly performed using spatial interpolation methods. However, significant and abrupt variations in the spatial distribution of pollutants decrease prediction accuracy. During this study, the use of partition interpolation methods was applied to benzo fluoranthene in four soil layers at a contaminated site to determine their ability to improve prediction accuracy in comparison to unpartitioned methods. The examined methods for partitioned interpolation included inverse distance weighting (IDW), radial basis function (RBF), and ordinary kriging (OK). The prediction results of the three methods for partitioned interpolation were compared, and the applicability of partition interpolation was determined. The prediction error associated with the partitioned interpolation methods decreased by 70% compared to unpartitioned interpolation. The prediction accuracy of IDW-based partition interpolation was higher than that of RBF- and OK-based partition interpolation techniques, and it was suitable for identification of highly polluted areas. Partition interpolation is also applicable to 12 other PAHs controlled by USEPA that can be detected, and the prediction effects could also verify this interpolation choice. In addition, the results also demonstrated that the more the maximum concentration deviated from the "norm", the greater the prediction error was caused by the smoothing effects of the interpolation models. These results suggest that the partition interpolation with IDW method can be effectively used to obtain relatively accurate spatial contaminant distribution information, and to identify highly polluted areas.

Random Forest Spatial Interpolation

For many decades, kriging and deterministic interpolation techniques, such as inverse distance weighting and nearest neighbour interpolation, have been the most popular spatial interpolation techniques. Kriging with external drift and regression kriging have become basic techniques that benefit both from spatial autocorrelation and covariate information. More recently, machine learning techniques, such as random forest and gradient boosting, have become increasingly popular and are now often used for spatial interpolation. Some attempts have been made to explicitly take the spatial component into account in machine learning, but so far, none of these approaches have taken the natural route of incorporating the nearest observations and their distances to the prediction location as covariates. In this research, we explored the value of including observations at the nearest locations and their distances from the prediction location by introducing Random Forest Spatial Interpolation (RFSI). We compared RFSI with deterministic interpolation methods, ordinary kriging, regression kriging, Random Forest and Random Forest for spatial prediction (RFsp) in three case studies. The first case study made use of synthetic data, i.e., simulations from normally distributed stationary random fields with a known semivariogram, for which ordinary kriging is known to be optimal. The second and third case studies evaluated the performance of the various interpolation methods using daily precipitation data for the 2016–2018 period in Catalonia, Spain, and mean daily temperature for the year 2008 in Croatia. Results of the synthetic case study showed that RFSI outperformed most simple deterministic interpolation techniques and had similar performance as inverse distance weighting and RFsp. As expected, kriging was the most accurate technique in the synthetic case study. In the precipitation and temperature case studies, RFSI mostly outperformed regression kriging, inverse distance weighting, random forest, and RFsp. Moreover, RFSI was substantially faster than RFsp, particularly when the training dataset was large and high-resolution prediction maps were made.