Geostatistical Interpolation Methods Research Articles

Research Progress on Spatiotemporal Interpolation Methods for Meteorological Elements

With the development of mathematical statistics, people have developed the spatiotemporal interpolation methods based on the spatial interpolation method or the temporal interpolation method. These methods fully consider the comprehensive effects of time series changes and spatial distribution to better handle complicated and changeable meteorological element data. This article systematically reviews the current research progress of spatiotemporal interpolation methods for spatiotemporal sampling data of meteorological origin. Spatiotemporal interpolation methods of meteorological elements are classified into three categories: spatiotemporal geostatistical interpolation methods, spatiotemporal deterministic interpolation methods, and spatiotemporal mixed interpolation methods. This article summarizes the theoretical concept and practical application of the spatiotemporal interpolation methods of meteorological elements, analyzes the advantages and disadvantages of using spatiotemporal interpolation methods for estimating or forecasting meteorological elements, combined through some measures and their application to explain the accuracy of the spatiotemporal interpolation methods; and discusses the problems and challenges of spatiotemporal interpolation. Finally, the future research focus of spatiotemporal interpolation methods is proposed. This article provides a valuable method reference for estimating or predicting meteorological elements such as precipitation in unsampled points.

Influence of geostatistical interpolation method and cell-size resolution on CO2 storage capacity estimates: Application to saline aquifers with sparse data availability in Israel

The primary focus for future large-scale projects targeting the sequestration of CO2 lies in underground saline aquifers. In southern Israel, two such aquifers were identified as suitable for CO2 storage, however, the data available for these aquifers is limited and sparse. To confront this challenge, geostatistical interpolation techniques are often used to fill in the data gaps. In this study, we evaluate the impact of the interpolation method and cell size on the storage capacity of these two saline aquifers. Eight interpolation techniques are used to estimate three parameters of the aquifers (thickness, depth, and porosity), which serve as the basis for evaluating the CO2 storage capacity, utilizing the US-DOE-NETL equation. Our findings show that the choice of the interpolation method and cell size has a significant impact on the calculated CO2 storage capacity, and therefore stress the importance of documenting these parameters. Our evaluation also shows that shallow CO2 storage sites exhibit a greater sensitivity to depth relative to deeper storage sites. The results of our study are applicable to early-stage assessments of regional CO2 storage capacity in which data is limited. Calculated CO2 storage capacities for the two aquifers indicate their continued suitability for CO2 sequestration in Israel.

Spatial distribution of groundwater fluoride and arsenic and its related disease in typical drinking endemic regions

c exposure to geogenic fluoride and arsenic iChronic exposure to geogenic fluoride and arsenic in groundwater has a deleterious influence on the health of billions of people globally. The health status of residents impacted by connected diseases is urgently needed. A twelve-year study was carried out to identify the spatial distribution pattern of high fluoride/arsenic groundwater in an arid/semi-arid area and to estimate the population exposed to related disease. A geostatistical interpolation method and a disease inversion model were used. The results indicated that fluoride/arsenic-rich groundwater primarily accumulated in basins of Shanxi Province. Groundwater fluoride exposure provided a health concern to 3.16 million persons (9.08 % of the population), including 2.50 million children at risk of dental caries. Exposure to groundwater arsenic caused a health risk to 4.38 million inhabitants (12.58 % of total), with 1.92 million at risk of lung cancer, 1.87 million at risk of bladder cancer, and 0.29 million at risk of skin cancer, respectively. The pollution and impact of groundwater fluoride and arsenic vary greatly among residents in different environments, and accurate assessment of the affected population is of great significance for residents' health and water quality management. Our research study complements the critical data on the disease risks associated with geogenic-contaminated groundwater and provides scientific basis of water quality management for policy makers.

Ranking of the utility of selected geostatistical interpolation methods in conditions of highly skewed seismic data distributions: a case study of the Baltic Basin (Poland)

Ranking of the utility of selected geostatistical interpolation methods in conditions of highly skewed seismic data distributions: a case study of the Baltic Basin (Poland)

Evaluation of land suitability for soybean production using GIS-based multi-criteria approach in Kudan Local Government area of Kaduna State Nigeria

The demand for food production in achieving Sustainable Development Goals, such as poverty eradication and food security and nutrition in developing countries like Nigeria has led to intensive agriculture, resulting in decreased soil quality and environmental challenges. To address these issues, land suitability evaluation plays a crucial role in designing sustainable land use and management systems. This evaluation provides valuable insights for farmers and policymakers to optimize soybean production, enhance crop yield, and promote sustainable agricultural development. The research covers 39,057 ha (ha) and it considers multiple criteria such as soil properties, slope, Normalized Difference Vegetation Index (NDVI), and land use/land cover (LULC) of the study area. Soil data and land use/land cover information were obtained and processed using geostatistical techniques and interpolation methods in ArcGIS. An Analytical Hierarchy Process (AHP) was employed to determine the overall importance of the evaluation criteria. This study revealed that 14.14% of the area falls into the moderately suitable class, a significant proportion (83.77%) of the area is marginally suitable for growing soybean, and the remaining proportion (2.09%) is deemed unsuitable. Drainage condition was identified as one of the major limiting factors for soybean cultivation in the region. Management practices such as drainage construction, organic residue incorporation, and appropriate fertilizer application were suggested to improve land suitability. The outcome of this study has shown that integrating RS and GIS techniques in land suitability assessment facilitates evidence-based decision-making and supports effective land use planning for increased agricultural productivity and environmental sustainability.

The Effect of Drought Phenomenon on the Surface of Groundwater Aquifer in Qazvin Plain in Iran

As one of the most catastrophic atmospheric events, drought affects various aspects of the environment. Groundwater resources are one of the sectors that are influenced by long-term droughts and have received insufficient attention compared to other aspects of the environment. Rainfall data collected by 23 metrological stations for 20 years (2005, 2010, 2015, 2020) was used to investigate the drought event and its situation in Qazvin Plain, the central plateau of Iran. Drought characteristics are evaluated using the 24-month standardized precipitation index (SPI). The results of SPI indicated that insufficient precipitation, excessive use of groundwater for irrigation, and utilization of uncontrolled wells caused a significant reduction in groundwater aquifers from 2015 to 2020. To assess the performance of the SPI, a five-year moving average of available precipitation data was calculated, and the result confirmed the outcomes of the SPI. Appropriate geostatistical interpolation methods are used to generate maps of drought zoning. Based on the results of this investigation in the northeastern part of the study area, June and November had the highest and lowest rates of drought, respectively. The linear regression between the annual average of precipitation and the changes in groundwater aquifer level exposed a significant correlation of R2 = 0.4253. Furthermore, linear regression between 24-month SPI and groundwater aquifer level indicated a correlation of R2 = 0.614. Considering the results of this study, the reduction of groundwater aquifer levels in Qazvin Plain from 2015 to 2015 exposed a significant negative difference compared to previous years (2005 to 2010).

Improving Rainfall Fields in Data-Scarce Basins: Influence of the Kernel Bandwidth Value of Merging on Hydrometeorological Modeling

Accurate rainfall fields are important for several hydrological and meteorological applications. In poorly instrumented basins, the lack of rain gauges heavily affects the spatial rainfall estimation, yet neither remote sensed nor climate model estimates are good enough for management applications. To tackle this problem, we investigate the impacts of combining both sources of information by varying the kernel bandwidth value of the double smoothing merging algorithm and analyzing the error of the rainfall fields. We explored the correlation between rain gauge density and bandwidth and compared the results against classical geostatistical interpolation methods based solely on in-situ measurements. Propagation of rainfall error into hydrological modelling is usual, and therefore we evaluated the influence of the bandwidth in streamflow simulations implementing two hydrological models. The hydrological evaluation considered the analysis of hydrological signatures rather than just performance metrics. We found that there is a clear correlation between kernel bandwidth and monitoring network density and that the bandwidth also affects hydrological performance. Simple bilinear downscaling did not produce a significant difference in meteorological or hydrological errors, and rain gauge network configuration also impacts the error of the field. We conclude that merging outperforms the results of classical interpolation methods, in some cases by 20% or 50%, suggesting the suitability of the method for being applied in data-scarce domains.

Optimal GIS interpolation techniques and multivariate statistical approach to study the soil-trace metal(loid)s distribution patterns in the agricultural surface soil of Matehuala, Mexico

Soils in the past mining areas are susceptible to trace metal(loid)s deposition and pose a health risk to humans. The purpose of this work is to evaluate the distribution patterns and contamination characteristics of trace metal(loid)s in the agricultural surface soils of past mining regions. The contaminated site is near an abandoned mining area, which is surrounded by land used for maize cultivation. The multivariate statistical approach and GIS interpolation techniques are often used in spatial distribution mapping to predict metal(loid)s concentrations for arsenic (As) and other trace metals (i.e., Al, Fe, Mn, and Sr) in areas that have not been sampled. The mean relative error (MRE) and root mean square error (RMSE) values were used to evaluate and correlate the efficiency of deterministic interpolation (Inverse Distance Weighting- IDW, Local Polynomial- LP, and Radial Basis Functions- RBF) as well as geostatistical interpolation methods (Ordinary Kriging- OK and Empirical Bayesian Kriging- EBK). The results revealed that all interpolation techniques predicted the mean concentration of trace metal(loid)s in soil with moderate accuracy. It was found that agricultural soils contained arsenic enrichment (up to 185 mg/kg), up to five times the background concentrations (35 mg/kg), and 8.5 times the Mexican guidelines (22 mg/kg). The statistical analysis with the cross-validation method revealed that IDW and LP consistently provided the most accurate predictions of trace metal(loid)s concentrations while OK, EBK, and RBF techniques are less accurate. Overall, these GIS interpolation techniques help in the prediction of trace metal(loid)s concentrations at unexplored sites and establish the requirement for the amelioration of agricultural surface soil.

Mapping soil arsenic pollution at a brownfield site using satellite hyperspectral imagery and machine learning.

Heavy metal contamination is ubiquitous in brownfields. Traditional site investigation employs geostatistical interpolation methods (GIMs) to predict the distribution of soil pollutants after soil sampling and chemical analysis. However, the heterogeneity of soil pollution in brownfields makes the assumptions of GIMs no longer valid and further undermines the accuracy of soil investigation. In the present study, a satellite hyperspectral image processing and machine learning method was developed to map arsenic pollution at a brownfield site. To eliminate the noise caused by atmospheric factors and increase the efficiency of spectral data, 1.3 million spectral indexes (SIs) were constructed and 1171 of them were selected due to their high correlations with soil arsenic. Five machine learning methods, i.e., Random forest (RF), ExtraTrees, Adaptive Boosting, Extreme Gradient Trees, and Gradient Descent Boosting Trees (GDB) were built to predict soil arsenic. The RF method was found to render the best performance (r = 0.78), reducing 30 % of prediction errors compared with traditional GIMs. RF also maintained a relatively higher level of accuracy (r = 0.56) when the sampling grids increased to 100 m, which was higher than that of GIMs under a 50 m sampling grid (r = 0.42), revealing that the proposed method can provide more accurate results with fewer sampling points, namely less investigation cost. It was indicated that the second derivate was the most efficient preprocessing method to remove spectral noise and normalized difference (ND) was the most reliable spectral index construction strategy. Based on uncertainty analysis, the heterogeneity of soil arsenic distribution was considered the most influential factor causing prediction errors. This study demonstrates that machine learning based on satellite visible and near-infrared reflectance spectroscopy (VNIR) is a promising approach to map soil arsenic contamination at brownfield sites with high accuracy and low cost.

Evaluation of Different Topographic Parameters Extracted from the Digital Elevation Measurements with the Use of Geostatistical Interpolation Methods

Evaluation of Different Topographic Parameters Extracted from the Digital Elevation Measurements with the Use of Geostatistical Interpolation Methods

Spatiotemporal Analysis of Groundwater Resources in the Saïss Aquifer, Morocco

In recent decades, the Saïss plain, in the northwest of Morocco, has experienced a noticeable increase in water demand due to a very significant population growth and economic development, as well as the climate change effects. With the aim of reaching optimal and dynamic management of these water resources, it is essential to have comprehensive and reliable information on the state of the aquifer systems in the region. To achieve this, we assessed a geostatistical analysis of groundwater level data, and created a multivariate regression model. Indeed, in this study, a spatiotemporal analysis of groundwater depth based on piezometric measurements of 45 wells was carried out for the period from 2005 to 2020. It compares and evaluates eight geostatistical interpolation methods and solves the problem of data gaps of the piezometric measurement by completing the chronological series of the groundwater level between 2005 and 2020 using the ARIMA model. The results demonstrate that the variation in the groundwater level between 2005 and 2020 indicates that the water table level is decreased in certain areas, but it has improved or remained constant in other areas. These results emphasize an urgent need for a dynamic management for the conservation of groundwater resources in certain areas of the region under this study.

Probabilistic approach for seismic microzonation integrating 3D geological and geotechnical uncertainty

A novel probabilistic methodology for regional seismic site characterization is proposed and applied to a region with highly heterogeneous surficial geology and varying soil sediment thickness and stiffness. The method combines various sources of geological and geotechnical uncertainties to develop a three-dimensional (3D) shear-wave velocity ( Vs) model and evaluate the associated uncertainties. A 3D geological model of the unconsolidated deposits was developed using geostatistical interpolation and simulation methods. Sequential indicator simulations produced a quantitative geologic model that explicitly quantified geological uncertainties based on the likelihood of specific soil types occurring. In situ measurements and multivariate statistical analysis allowed the development of empirical correlations between Vs, geotechnical parameters, depth, and soil types. The resulting 3D Vs values were estimated on the basis of Vs-depth correlations and the probability of occurrence of each soil type. In this approach, the propagated uncertainty was also quantified by considering the combined variance. Seismic microzonation mapping was then conducted by transforming the 3D Vs model into two-dimensional (2D) maps that represent the spatial distributions of the time-averaged shear-wave velocity of the top 30 m ( Vs,30) and the fundamental site period ( T0), along with their respective uncertainties using Monte Carlo simulations. The results indicate that microzonation maps and their uncertainties are influenced by the thickness, occurrence probability, and geotechnical properties of soils. The proposed method can be used to assess the probabilistic seismic risk at local and regional scales in areas with geologically and geotechnically complex soil properties.

Socio-Economic Characteristics of Urban Tuberculosis Areas in Petaling, Selangor: A Current Spatial Exploratory Scenario

World Health Organization (WHO) has estimated one-third of the world population as potentially infected with tuberculosis (TB) in 2020. Almost nine (9) million people are detected with TB with approximately two (2) million deaths every year. Selangor state reported among the highest cases of current TB trend in Malaysia. Poverty, immunosuppressive and co-morbidities would relate to the recent TB scenario and urban socioeconomic status (SES) in the state. The study was conducted to exploratory analyse the contemporary effects of SES on the disease in Petaling using a geospatial approach. The main SES factors applied in this study are level of job, income, and education, while Empirical Bayesian Kriging (EBK) of geostatistical interpolation and correlation analysis method were utilised to visualize and estimate the SES-based risk index map and determine the possible socio-economic characteristics. Based on a five likert scale and index method, the risk map was categorised into proposed five (5) classes from Class 1 (blue = very low risk) to Class 5 (red = very high risk). The overall risk map was suggested in a Class 3 (medium-low level) as closely consistent with the correlation analysis (r = 0.37), suggesting that both TB cases and SES factors increased in response to each other but have a medium - weak direct implication. The result has shown that overall SES factor does not greatly affect the local TB cases in 2017, but further study need to be explored on the other potential mediating variables.

Long-Term (1990–2013) Changes and Spatial Variations of Cropland Runoff across China

Quantitative information on regional cropland runoff is important for sustainable agricultural water quantity and quality management. This study combined the Soil Conservation Service Curve Number (SCS-CN) method and geostatistical approaches to quantify long-term (1990–2013) changes and regional spatial variations of cropland runoff in China. Estimated CN values from 17 cropland study sites across China showed reasonable agreement with default values from the National Engineering Handbook (R2 = 0.76, n = 17). Among four commonly used geostatistical interpolation methods, the inverse distance weighting (IDW) method achieved the highest accuracy (R2 = 0.67, n = 209) for prediction of cropland runoff. Using default CN values and the IDW method, estimated national annual cropland runoff volume and runoff depth in 1990–2013 were 253 ± 25 km3 yr−1 and 182 ± 15 mm yr−1, respectively. Estimated cropland runoff depth gradually increased from the drier northwest inland region to the wetter southeast coastal region (range: 2–1375 mm yr−1). Regionally, eastern, central and southern China accounted for 39% of the cultivated area and 53% of the irrigated land area and contributed to 68% of the national cropland runoff volume. In contrast, northwestern, northern, southwestern and northeastern China accounted for 61% of the cultivated area and 47% of the irrigated land area and contributed to 32% of the runoff volume. Rainfall was the main source (72%) of cropland runoff for the entire nation, while irrigation became the main source of cropland runoff in drier regions (northwestern and southwestern China). Over the 24-year study period, estimated cropland runoff depth showed no significant trends, whereas cropland runoff volume and irrigation-contributed percentages decreased by 7% and 35%, respectively, owing to implementation of water-saving irrigation technologies. To reduce excessive runoff and increase water utilization efficiencies, regionally specific water management strategies should be further promoted. As the first long-term national estimate of cropland runoff in China, this study provides a simple framework for estimating regional cropland runoff depth and volume, providing critical information for guiding developments of management practices to mitigate agricultural nonpoint source pollution, soil erosion and water scarcity.

Mapping Soil Properties at a Regional Scale: Assessing Deterministic vs. Geostatistical Interpolation Methods at Different Soil Depths

To determine which interpolation technique is the most suitable for each case study is an essential task for a correct soil mapping, particularly in studies performed at a regional scale. So, our main goal was to identify the most accurate method for mapping 12 soil variables at three different depth intervals: 0–5, 5–10 and >10 cm. For doing that, we have compared nine interpolation methods (deterministic and geostatistical), drawing soil maps of the Spanish region of Extremadura (41,635 km2 in size) from more than 400 sampling sites in total (e.g., more than 500 for pH for the depth of 0–5 cm). We used the coefficient of determination (R2), the mean error (ME) and the root mean square error (RMSE) as statistical parameters to assess the accuracy of each interpolation method. The results indicated that the most accurate method varied depending on the property and depth of study. In soil properties such as clay, EBK (Empirical Bayesian Kriging) was the most accurate for 0–5 cm layer (R2 = 0.767 and RMSE = 3.318). However, for 5–10 cm in depth, it was the IDW (Inverse Distance Weighted) method with R2 and RMSE values of 0.689 and 5.131, respectively. In other properties such as pH, the CRS (Completely Regularized Spline) method was the best for 0–5 cm in depth (R2 = 0.834 and RMSE = 0.333), while EBK was the best for predicting values below 10 cm (R2 = 0.825 and RMSE = 0.399). According to our findings, we concluded that it is necessary to choose the most accurate interpolation method for a proper soil mapping.

Spatial Distribution and Migration Characteristics of Heavy Metals in Grassland Open-Pit Coal Mine Dump Soil Interface.

The open-pit coal mine dump in the study area contains many low-concentration heavy metal pollutants, which may cause pollution to the soil interface. Firstly, statistical analysis and geostatistical spatial interpolation methods described heavy metal pollution’s spatial distribution. The mine dump heavy metal pollution distribution is strongly random due to disorderly piles, but it is closely related to slope soil erosion. Furthermore, the soil deposition area is where pollutants accumulate. For example, all heavy metal elements converge at the bottom of the dump. Usually, the pollution in the lower part is higher than that in the upper part; the pollution in the lower step is higher than the upper step; the pollution in the soil deposition locations such as flat plate and slope bottom is higher than the soil erosion locations such as slope tip and middle slope. Finally, the hyperspectral remote sensing method described heavy metals pollution’s migration characteristics, that the pollutants could affect the soil interface by at least 1 km. This study provides a basis for preventing and controlling critical parts of mine dump heavy metal pollution and pollution path control.

The Effect of Drought Phenomenon on the Surface of Groundwater Aquifer in Qazvin Plain in Iran

As one of the most catastrophic atmospheric events, drought affects various aspects of the environment. Groundwater resources are one the sectors that are influenced by long-term droughts and received insufficient attention compared to other aspects of the environment. Rainfall data collected by 23 metrological stations for 20 years (2005, 2010, 2015,2020) was used to investigate the drought event and its situation in Qazvin plain, the central plateau of Iran. Drought characteristics are evaluated using the 24-month standardized precipitation index (SPI). The results of SPI indicated that insufficient precipitation, excessive use of groundwater for irrigation, and utilization of uncontrolled wells caused a significant reduction in groundwater aquifers from 2015 to 2020. To assess the performance of the SPI, a five-year moving average of available precipitation data was calculated, and the result confirmed the outcomes of SPI. Appropriate geostatistical interpolation methods are used to generate maps of drought zoning. Based on the results of this investigation in the northeastern part of the study area, June and November had the highest and the lowest rate of drought, respectively. The linear regression between the annual average of precipitation and the changes of groundwater aquifer level exposed a significant correlation of R2 = 0.4253. Furthermore, linear regression between 24-month SPI and groundwater aquifer level indicated a correlation of R2 = 0.614. Considering the results of this study, the reduction of groundwater aquifer levels in Qazvin plain from 2015 to 2015 exposed a significant negative difference compared to previous years (2005 to 2010).

Application of geostatistical models to identify spatial distribution of groundwater quality parameters.

Groundwater quality management is a priority in arid and semi-arid zones where water is scarce. Leachate from open dumping of municipal solid wastes may threaten groundwater quality. This research aimed at assessing groundwater quality of the aquifer of Shur river basin in Tehran province, Iran. The pollution potential of leachate from a landfill, located at the center of the basin, was estimated to assess its impact on the aquifer. Samples from 38 wells and 2 leachate ponds around the landfill were analyzed for their physico-chemical parameters and heavy metals. Leachate Pollution Index (LPI) and Water Quality Index (WQI) were calculated and multivariate statistical techniques were employed through geostatistical models to predict the spatial variability of groundwater quality and assess its contamination sources. The groundwater quality map was developed by GIS Interface. LPI indicated that leachate from the closed cell (LPI = 36) was more contaminating than that of the active site (LPI = 25). Kriging and cokriging geostatistical interpolation methods were applied to groundwater quality parameters. The best interpolation model was then identified through cross-validation with RMSE and GSD criteria. Cokriging yielded more accurate results than kriging. Spatial distribution maps showed high groundwater contamination and degraded water quality mainly in the central part of the basin, where the landfill was. Also, 293.7ha of the study area possessed poor and very poor water quality, unsuitable for drinking. This study implicated multiple approaches for groundwater quality assessment and estimated its spatial structure as an effort toward effective groundwater quality management in Shur river basin.

Groundwater Quality Monitoring Using In-Situ Measurements and Hybrid Machine Learning with Empirical Bayesian Kriging Interpolation Method

This article discusses the assessment of groundwater quality using a hybrid technique that would aid in the convenience of groundwater (GW) quality monitoring. Twenty eight (28) GW samples representing 62 barangays in Calapan City, Oriental Mindoro, Philippines were analyzed for their physicochemical characteristics and heavy metal (HM) concentrations. The 28 GW samples were collected at suburban sites identified by the coordinates produced by Global Positioning System Montana 680. The analysis of heavy metal concentrations was conducted onsite using portable handheld X-Ray Fluorescence (pXRF) Spectrometry. Hybrid machine learning—geostatistical interpolation (MLGI) method, specific to neural network particle swarm optimization with Empirical Bayesian Kriging (NN-PSO+EBK), was employed for data integration, GW quality spatial assessment and monitoring. Spatial map of metals concentration was produced using the NN-PSO-EBK. Another, spot map was created for observed metals concentration and was compared to the spatial maps. Results showed that the created maps recorded significant results based on its MSEs with values such as 1.404 × 10−4, 5.42 × 10−5, 6.26 × 10−4, 3.7 × 10−6, 4.141 × 10−4 for Ba, Cu, Fe, Mn, Zn, respectively. Also, cross-validation of the observed and predicted values resulted to R values range within 0.934–0.994 which means almost accurate. Based on these results, it can be stated that the technique is efficient for groundwater quality monitoring. Utilization of this technique could be useful in regular and efficient GW quality monitoring.

Priestorová analýza dát z povrchového zberu na lokalite Vráble-Fidvár

The goal of this study is to introduce selected methods of spatial analysis and their contribution to evaluation of fieldwalking data. Spatial analysis encompasses various methods suitable for identification, objective evaluation and visualization of spatial patterns which are present in obtained data. This article primarily deals with sampled data, collected during a 2007 fieldwalking campaign. The dataset consisting of potsherds was spatially autocorrelated, using the global and local Moran’s I coefficient, which was used to identify clusters of finds. Spatial pattern of the settlement was visualised by geostatistical interpolation method – kriging.