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This investigation estimates a regional Mean Sea Surface (MSS) model, named SY21MSS, over the eastern Mediterranean Sea using satellite altimetry data from nine Exact Repeat Missions (ERM) and two Geodetic Missions (GM). Two interpolation methods, Least Squares Collocation (LSC) and Ordinary Kriging (OK), were employed, and statistical metrics were applied to assess their performance within a 15 km buffer from the coast. The comparison between LSC and OK techniques in the context of regional MSS modeling primarily centers on the covariance functions used by these methods. Furthermore, generalized cross-validation results indicate that OK outperforms LSC in this region. Consequently, the study recommends adopting the Kriging-based model for calculating regional MSS models in this region due to its superior performance. The investigation further explored the disparities between estimated regional MSS models and the global model DTU18MSS, highlighting a pronounced similarity between OK-SY21MSS and DTU18MSS, as evidenced by a lesser standard deviation (SD) difference compared to LSC-SY21MSS. The practical implications of this research underscore the importance of selecting an appropriate interpolation technique based on data characteristics and study area specifics. While both LSC and OK techniques are deemed viable for MSS modeling, the study emphasizes the superior performance of OK, particularly concerning covariance functions. Additionally, the results emphasize caution when applying global models in regions with significant local variations. [ABSTRACT FROM AUTHOR]

Fine-resolution spatio-temporal maps of near-surface urban air temperature (Ta) provide crucial data inputs for sustainable urban decision-making, personal heat exposure, and climate-relevant epidemiological studies. The recent availability of IoT weather station data allows for high-resolution urban Ta mapping using approaches such as interpolation techniques or machine learning (ML). This study is aimed at executing these approaches and traditional numerical modeling within a practical and operational framework and evaluate their practicality and efficiency in cases where data availability, computational constraints, or specialized expertise pose challenges. We employ Netatmo crowd-sourced weather station data and three geospatial mapping approaches: (1) Ordinary Kriging, (2) statistical ML model (using predictors primarily derived from Earth Observation Data), and (3) weather research and forecasting model (WRF) to predict/map daily Ta at nearly 1-km spatial resolution in Warsaw (Poland) for June–September and compare the predictions against observations from 5 meteorological reference stations. The results reveal that ML can serve as a viable alternative approach to traditional kriging and numerical simulation, characterized by reduced complexity and higher computational speeds within the domain of urban meteorological studies (overall RMSE = 1.06 °C and R2 = 0.94, compared to ground-based meteorological stations). The results have implications for identifying the urban regions vulnerable to overheating and evidence-based urban management in response to climate change. Due to the open-sourced nature of the applied predictors and input parsimony, the ML method can be easily replicated for other EU cities. [ABSTRACT FROM AUTHOR]

The accurate prediction of soil contamination in abandoned mining areas is necessary to address their environmental risks. This study employed a combined model of machine learning and geostatistics to predict the spatial distribution of soil contamination using heavy metal data collected in an abandoned metal mine. An exploratory data analysis was used to identify patterns in the collected data, the root mean squared error (RMSE) and coefficient of determination (R2) were used to verify the predicted values, and the model was validated using K-fold cross-validation. The prediction results were produced as a map by applying hyperparameter tuning to Random Forest (RF) and Ordinary Kriging (OK) through GridSearchCV using optimal parameter selections. Furthermore, the prediction residuals of the RF model were calculated, and the RF prediction map and OK interpolation results of the RF prediction residuals were summarized to construct an RF–OK prediction map. The RMSE and R2 values for the RF, OK, and RF–OK interpolation models were 66.214, 65.101, and 52.884 mg/kg and 0.867, 0.871, and 0.915, respectively. In addition, the optimization results with the minimum RMSE and maximum R2 were obtained through hyperparameter tuning. The proposed RF–OK hybrid model demonstrated superior prediction performance compared to the individual models. [ABSTRACT FROM AUTHOR]

Ordinary kriging (OK) is a popular interpolation method for its ability to simultaneously minimize error variance and deliver statistically optimal and unbiased predictions. In this work, the adaptive moving window kriging with K-means clustering (AMWKK) technique is developed to improve the estimation obtained from the moving window kriging based on the K-means clustering proposed by Abedini et al. This technique specifically addresses the challenge of selecting appropriate windows for target points located near the borders, which can potentially be the source of errors. The AMWKK algorithm introduces a dynamic clustering approach within the moving window kriging, where each target site sequentially serves as a cluster centroid. The OK is then applied within the cluster encompassing the target point, ensuring localized and adaptive interpolation. The proposed method is compared with ordinary kriging and other moving window kriging variant approaches to estimate Thailand's mean annual pressure and humidity in 2018. The results indicate superior estimation capabilities of the AMWKK approach in terms of distinct quantitative performance statistics. The advantage of using the AMWKK method for spatial interpolation can be attributed to the fact that it facilitates the automatic tuning of the window size at any estimation point. The algorithm is particularly effective when observations in the same cluster as target points are sparse. [ABSTRACT FROM AUTHOR]

Thematic maps are essential tools in precision agriculture to demonstrate the information of spatially distributed phenomena. A thematic map can be created from sampling data, a standard procedure for soil attributes. Interpolation methods are used to estimate data in unknown locations, such as inverse distance weighting (IDW) and ordinary Kriging (OK). For both interpolators, it is essential to use the appropriate parameters to estimate values in non-sampled locations, either the exponent value and the number of neighbors for IDW, or the theoretical model adjusted to the experimental semivariogram for OK. Thus, this trial aims at adopting additional criteria in selecting interpolators and evaluating their performance. AgDataBox platform's data interpolation module was improved, where the process of selecting the interpolator and determining its parameters considers the criteria (i) effective spatial dependence index, (ii) the first semivariance significance index, and (iii) slope of the model ends index. The experimental data come from an experiment in two agricultural areas in Brazil, using grids with good sampling density (2.7, 2.6, and 3.5 points per ha). It was observed that, usually, the application method of the three new criteria selected different models for a dataset and this must be considered in the interpolator selection process. Thematic maps varied from 0.1 to 64%, according to the coefficient of relative deviation, when comparing the three methods of applying the selection criteria. [ABSTRACT FROM AUTHOR]

Patterns of spatial heterogeneity in forests and other fire-prone ecosystems are increasingly recognized as critical for predicting fire behavior and subsequent fire effects. Given the difficulty in sampling continuous spatial patterns across scales, statistical approaches are common to scale from plot to landscapes. This study compared the performance of four spatial interpolation methods (SIM) for mapping fine-scale fuel loads: classification (CL), multiple linear regression (LR), ordinary kriging (OK), and regression kriging (RK). These methods represent commonly used SIMs and demonstrate a diversity of non-geostatistical, geostatistical, and hybrid approaches. Models were developed for a 17.6-hectare site using a combination of metrics derived from spatially mapped trees, surface fuels sampled with an intensive network of photoload plots, and topographic variables. The results of this comparison indicate that all estimates produced unbiased spatial predictions. Regression kriging outperformed the other approaches that either relied solely on interpolation from point observations or regression-based approaches using auxiliary information for developing fine-scale surface fuel maps. While our analysis found that surface fuel loading was correlated with species composition, forest structure, and topography, the relationships were relatively weak, indicating that other variables and spatial interactions could significantly improve surface fuel mapping. [ABSTRACT FROM AUTHOR]

The accurate prediction of soil contamination in abandoned mining areas is necessary to address their environmental risks. This study employed a combined model of machine learning and geostatistics to predict the spatial distribution of soil contamination using heavy metal data collected in an abandoned metal mine. An exploratory data analysis was used to identify patterns in the collected data, the root mean squared error (RMSE) and coefficient of determination (R2) were used to verify the predicted values, and the model was validated using K-fold cross-validation. The prediction results were produced as a map by applying hyperparameter tuning to Random Forest (RF) and Ordinary Kriging (OK) through GridSearchCV using optimal parameter selections. Furthermore, the prediction residuals of the RF model were calculated, and the RF prediction map and OK interpolation results of the RF prediction residuals were summarized to construct an RF–OK prediction map. The RMSE and R2 values for the RF, OK, and RF–OK interpolation models were 66.214, 65.101, and 52.884 mg/kg and 0.867, 0.871, and 0.915, respectively. In addition, the optimization results with the minimum RMSE and maximum R2 were obtained through hyperparameter tuning. The proposed RF–OK hybrid model demonstrated superior prediction performance compared to the individual models.

The deformation characteristic of the arch dam can directly reflect its service performance, which can be analyzed on the basis of the dam deformation field. However, restricted by the limited number of dam monitoring points and the inhomogeneity of materials, an accurate measurement of arch dam deformation field is difficult to estimate by using the existing common methods, such as the spatial interpolation methods and the finite element method (FEM). With the aim of ensuring arch dam structure safety, the ordinary kriging interpolation method, combined with FEM, is proposed for arch dam deformation field estimation, in this study. Given the inversion of the computation parameters of the arch dam, FEM is used to calculate the basic arch dam deformation. Subsequently, the ordinary kriging interpolation method is introduced to estimate the spatial variance deformation at each point of the arch dam. One superhigh arch dam in China is selected as a case study; two additional methods are introduced as comparisons that are based on a numerical experiment and the actual monitoring data. The experimental results show that the proposed method considerably improves the accuracy and computational efficiency of the arch dam deformation field estimation and that it is of great practical importance for characterizing the deformation behavior of arch dams. [ABSTRACT FROM AUTHOR]

Kriging has been shown to be the best interpolator to interpolate maps in precision agriculture. However, Kriging requires a high number of sampling points to generate accurate maps. Recently, machine learning (ML) techniques have shown the potential to produce maps with a lower number of sampling points. In addition, using ML map generation can be automated and use much more feature information to improve map quality. Therefore, the objective of this study was to implement a ML technique and compare it to IDW and to Ordinary Kriging (OK). The ML algorithm used was the Support Vector Machine (SVM). Software based on the SVM method was developed (Smart-Map) using the Python language. This software was tested in an area of 204 ha cultivated with soybeans. The performance of the SVM method was compared to traditional interpolation methods, IDW and Ordinary Kriging (OK). Based on the analysis of 10 soil attributes, OK had better performance than IDW and the ML method when the Moran's I (Index) values were significant and higher than 0.67. With a low density of points and low degrees of spatial autocorrelation, the ML method performed better than IDW and OK. [ABSTRACT FROM AUTHOR]

This study assessed the health of the mangrove ecosystem and mapped the spatial variation in selected variables sampled across the Matang Mangrove Forest Reserve (MMFR) by using a geostatistical technique. A total of 556 samples were collected from 56 sampling points representing mangrove biotic and abiotic variables. All variables were used to generate the semivariogram model. The predicted variables over the entire MMFR have an overall prediction accuracy of 85.16% (AGB), 90.78% (crab abundance), 97.3% (soil C), 99.91% (soil N), 89.23% (number of phytoplankton species), 95.62% (number of diatom species), 99.36% (DO), and 87.33% (turbidity). Via linear weight combination, the prediction map shows that mangrove ecosystem health in Kuala Trong throughout the Sungai Kerang is excellent (5: MQI > 1.5). Some landward areas of Kuala Trong were predicted to have moderate health (3: −0.5 ≤ MQI ≤ 0.5), while Kuala Sepetang was predicted to have the bad ecosystem health (2: −1.5 ≤ MQI ≤ −0.5), with active timber harvesting operations and anthropogenic activities in the landward areas. The results of this method can be utilised to carry out the preferred restoration, through appropriate management and facilities distribution, for improving the ecosystem health of mangroves. [ABSTRACT FROM AUTHOR]

Accurate spatial distribution information of rainfall is essential to rainfall‐induced hazard predictions and statistical interpolation methods may serve as a useful tool to produce a detailed distribution from coarse data sources. Although numerous comparison studies about different interpolation methods have been conducted on irregular rain‐gauge networks, there is a need to perform such work on the increasingly available gridded rainfall data. Carried out in the Emilia‐Romagna region (Italy) from 2008 to 2018, this study aims to examine accurate and appropriate interpolation methods to produce finer rainfall surface maps based on the 0.25° × 0.25° ERA5 gridded precipitation datasets. Five interpolation techniques, namely Thiessen polygons, Inverse Distance Weighting (IDW), Thin Plate Spline (TPS), Ordinary Kriging (OK) and ordinary Co‐Kriging (CoK), have been selected and compared at different time scales (annual, monthly and annual maximum daily precipitation). To assess the accuracy, the leave‐one‐out‐cross‐validation test was used by using the indexes of Bias, correlation coefficient, the Nash‐Sutcliffe Efficiency, Root Mean Square Error and the Kling‐Gupta Efficiency (KGE). Additionally, visual inspections are employed to evaluate the plausibility of the interpolated maps. Results show: (a) All five interpolation methods have certain capabilities to improve spatial resolution, but they fail on accuracy at the daily scale. The OK generally outperforms the other four methods, while TPS shows better performance through the visual inspection at the monthly scale; (b) Unlike in the case of the interpolation using conventional point‐based rain‐gauge data, the multivariate method CoK is inferior to the univariate ones and the p‐power of the IDW also differs and (c) Winter and spring results are better than those of summer and autumn. This study has provided useful guidance on choosing suitable rainfall interpolation methods for gridded datasets, which can be expanded in other regions and data sources to explore the generality of the conclusions. [ABSTRACT FROM AUTHOR]

Spatial interpolation methods usually differ in their underlying mathematical concepts. Each has inherent advantages and disadvantages, and choosing a method should be based on the type of data to be analyzed. This paper, therefore, compares and evaluates the performances of well-established interpolation techniques that can be used to estimate monthly rainfall in Thailand. The approaches analyzed include inverse distance weighting (IDW), inverse exponential weighting (IEW), multiple linear regression (MLR), artificial neural networks (ANN), and ordinary kriging (OK) methods. In addition, a search of the nearest stations has also been conducted for some of the aforementioned schemes. A k-fold cross-validation is exploited to assess the efficiency of each method. Results show that ANN might be the least desirable choice as it underperformed, with the remaining methods being roughly comparable. Considering both accuracy and computational flexibility, the IEW approach with a restricted number of neighboring stations is recommended in this study. [ABSTRACT FROM AUTHOR]

Background. Several studies have demonstrated that chromium (Cr) and cadmium (Cd) have adverse impacts on the environment and human health. These elements are present in electronic waste (e-waste) recycling sites. Several interpolation methods have been used to evaluate geographical impacts on humans and the environment. Objectives. The aim of the present paper is to compare the accuracy of inverse distance weighting (IDW) and ordinary kriging (OK) in topsoil analysis of e-waste recycling sites in Douala, Cameroon. Methods. Selecting the proper spatial interpolation method is crucial for carrying out surface analysis. Ordinary kriging and IDW are interpolation methods used for spatial analysis and surface mapping. Two sets of samples were used and compared. The performances of interpolation methods were evaluated and compared using cross-validation. Results. The results showed that the OK method performed better than IDW prediction for the spatial distribution of Cr, but the two interpolation methods had the same result for Cd (in the first set of samples). Results from Kolmogorov-Smirnov and Shapiro-Wilk tests showed that the data were normally distributed in the study area. The p value (0.302 and 0.773) was greater than 0.05 for Cr and for Cd (0.267 and 0.712). In the second set of samples, the OK method results (for Cd and Cr) were greatly diminished and the concentrations dropped, looking more like an average on the maps. However, the IDW interpolation gave a better representation of the concentration of Cd and Cr on the maps of the study area. For the second set of samples, OK and IDW for Cd and Cr had more similar results, especially in terms of root mean square error (RMSE). Conclusions. Many parameters were better identified from the RMSE statistic obtained from cross-validation after exhaustive testing. Inverse distance weighting appeared more adequate in limited urban areas. Competing Interests. The authors declare no competing financial interests

Assessing spatial variability of drought-prone areas is important for disaster preparedness and impact management. This study applied state-of-the-art geographically weighted regression hybridized with kriging method (GWRKrig) to map the spatial variability of drought-prone areas in the northwest of Iran based on the Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI). Rainfall and evapotranspiration data from 47 synoptic stations over 20 years were used to generate SPI and SPEI, and topographical (altitude) data were used for GWRKrig. The results obtained using GWRKrig were compared with that of standalone GWR, regression kriging (RegKrig), and ordinary kriging (Krig) methods. The GWRKrig method emerged as a promising tool for spatial interpolation of drought indices based on performance evaluation measures, namely, the root mean squared error (RMSE) and coefficient of determination (R2). The SPEI-based drought intensity interpolated via GWRKrig revealed relatively precise spatial variability of drought zones. The method proposed in this study would assist in the accurate delineation of drought-prone areas, which is the foremost venture in the planning hierarchy of drought management schemes and their implementation. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) modeling of geological surfaces, such as coal seams and strata horizons, from sparsely sampled data collected in the field, is a crucial task in geological modeling. Interpolation is a common approach for this task to construct continuous geological surface models. However, this problem becomes challenging considering the impact of the faults on geological surfaces. Existing methods tend to solve this problem through three steps, including interpolating stratum and fault surface, applying a fault modeling method to modify the geological surface, and optimizing the modified surface to pass sample points fallen into the fault displacement zone. This paper presents a more concise method to generate a faulted geological surface, in which 1) a constrained Delaunay triangulated irregular network (CD-TIN) is constructed to facilitate the neighborhood search process of the ordinary kriging (OK) interpolation, 2) the CD-TIN is also directly constrained by horizon cut-off lines formed from theoretical fault displacement profiles, and 3) subsequently, neighbors of the location to be estimated are selected effectively in the CD-TIN considering the fault topology. The proposed method significantly improves the time efficiency of the OK interpolation by utilizing the CD-TIN and incorporates fault effects directly into the interpolation process by inserting fault horizontal cut-off lines into CD-TIN. Moreover, by integrating the fault effects directly into the interpolation process, the surface modeling process is accomplished in a single stage instead of two separate stages of interpolation first and then modifying the surface in the fault area. By this strategy, the proposed method significantly improves the time efficiency of the OK interpolation algorithm and achieves more accurate modeling of the faulted geological surface. Experiments were designed to compare the performance of our method with several commonly used approaches, and the results indicate that the proposed TIN-constrained OK method achieves better accuracy and efficiency in modeling faulted geological surfaces than other methods. This method could also be used in geospatial interpolation studies, such as meteorological data interpolation.

This study applies statistical methods to interpolate missing values in a data set of radiative energy fluxes at the surface of Earth. We apply Random Forest (RF) and seven other conventional spatial interpolation models to a global Surface Solar Radiation (SSR) data set. We apply three categories of predictors: climatic, spatial, and time series variables. Although the first category is the most common in research, our study shows that it is actually the last two categories that are best suited to predict the response. In fact, the best spatial variable is almost 40 times more important than the best climatic variable in predicting SSR. Furthermore, the 10‐fold cross validation shows that the RF has a Mean Absolute Error (MAE) of 10.2 Wm−2 and a standard deviation of 1.5 Wm−2. On the other hand, the average MAE of the conventional interpolation methods is 21.3 Wm−2, which is more than twice as large as the RF method, in addition to an average standard deviation of 6.4 Wm−2, which is more than four times larger than the RF standard deviation. This highlights the benefits of using machine learning in environmental research. Key Points: Random forest model is capable of reproducing historical records of surface solar radiation with high accuracy and great stabilityThe most influential predictor for the value at one geographical location is the average of its nearest five neighborsThe proposed approach maintains good performance even in a setting with sparse and uneven data points [ABSTRACT FROM AUTHOR]

Determining and predicting both the spatial and temporal variability of soil moisture content is a critical factor in crop production in semi-arid agricultural systems. The objective of this research was to predict the spatial distribution of soil moisture content using ordinary kriging (OK), regression kriging (RK) and cokriging (CK) models. For that purpose, the soil moisture was monitored in the wet period (March, April and May) and dry period (August, September and October) in Kadınhanı district of Konya Province, Turkey. In each monthly sampling period of the study, a total of 278 samples were collected from locations within an area of 29,608.6 ha. The coefficients of variation (CV) of the soil moisture in dry and wet soil conditions were 0.39 and 0.20, respectively. Soil texture, bulk density (BD) and land use were the most important factors influencing soil moisture. In addition, dry soil generally had a smaller nugget effect than wet soil. Overall, CK was able to better estimate the soil moisture content than OK and RK, as evidenced by the smaller mean absolute error (MAE) and mean square error (MSE). RK estimation is more vulnerable to error than CK and OK estimations because the low coefficients of determination in the regression equation lead to increased error and lower confidence in the estimates. The insights generated by the modeling utilized in this study can assist land use planners, land managers and farmers to more efficiently predict, manage and utilize soil moisture content and hence produce larger crops more sustainably. [ABSTRACT FROM AUTHOR]

Bathymetric data plays a major role in obtaining accurate results in hydrodynamic modeling of rivers, estuaries, and coasts. Bathymetries are commonly generated by spatial interpolation methods of data on a model grid. Sparse and limited data will impact the quality of the interpolated bathymetry. This study proposes an efficient spatial interpolation framework for producing a channel bathymetry from sparse, cross-sectional data. The proposed approach consists of three steps: (1) anisotropic bed topography data locations transformed to an orthogonal and smooth grid coordinate system that is aligned with its riverbanks and thalweg; (2) sample data are linearly interpolated to generate river bathymetry; and (3) the generated river bathymetry is converted into its original coordinates. The proposed approach was validated with a high spatial resolution topography of the Tieu estuarine branch. In addition, the proposed approach is compared with other spatial interpolation methods such as ordinary kriging, inverse distance weighting, and kriging with external drift. The proposed approach gives a nearly unbiased topography and a strongly reduced RMSE compared with the other methods. In addition, it accurately reproduces the thalweg. The proposed approach appears to be efficiently applicable for regions with sparse cross-sections. Moreover, river topography generated by the proposed approach is smooth including important morphologic features, making it suitable for two- and three-dimensional hydrodynamic modeling. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Soil Sciences & Agricultural Engineering is the property of Egyptian National Agricultural Library (ENAL) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

[Display omitted] • An alternative ZTD model to grid-wise VMF1 product over Europe, through spatial interpolation of the site-wise VMF1 product. • Performance of Ordinary Kriging and IDW methods for predicting ZTDs. • Refining the data quality of gridded VMF1 product in the GNSS stations. This study proposes an alternative approach to the grid-wise VMF1 over Europe, through spatial interpolation of the site-wise VMF1 product. The performance of Ordinary Kriging and IDW was evaluated for predicting ZTD. Using 2020 data collected at 24 GNSS stations, two scenarios were constructed for February and August. Ordinary Kriging and IDW predictions were performed by making model adjustments via performance metrics and method successes were compared. The results showed that the ordinary kriging achieved a success rate of 83.2 %, while the IDW method achieved 77.1 % success. We compared the results with the grid-wise VMF1 to control the accuracy of spatial interpolations. Finally, the methods proposed as alternatives to gridded VMF1 were verified through the CSRS-PPP (ZTD). Ordinary-Kriging (RMSE Feb : [0.92–2.95 cm]; RMSE Aug : [1.76–3.85 cm]) was in better compliance with the CSRS-PPP (ZTD) , compared to the grid-wise VMF1 (RMSE Feb : [1.59–3.01 cm]; RMSE Aug : [2.32–3.93 cm]). These results support that the quality of gridded products can be improved by spatial interpolations. [ABSTRACT FROM AUTHOR]

Investigation on spatial distribution of tree growth characteristics in different forest stands, has a fundamental role in assessing possible harvest planning considering potential of the stands. The aim of this study is mapping the spatial distribution of forest characteristics such as stand volume growth, diameter, growth, ingrowth) and determining the amount of tree mortality in the district three of Sangdeh region within a period of 5 years. Two methods of Ordinary Kriging (OK) and weighted Inverse Distance (IDW) interpolation were applied for mapping. For this purpose, we calculated the increment using direct measurement in 130 permanent sample plots. The results of this study showed that the mean volume increment, diameter increment, ingrowth and annual mortality were 5.65 cubic meters per hectare per year, 0.48 cm, 3.5 and 4.2 stems per hectare per year, respectively. For volume increment, the IDW method by power one and with a root mean square error 0.29 cubic meters per hectare per year, for diameter increment, ingrowth and annual mortality the ordinary Kriging method with a root mean square error 0.219 cm per year, 1.4 and 2.8 nha-1y-1 showed better results, respectively. Overall the results showed that geostatistical methods are efficient methods for mapping forest growth characteristics.

People are increasingly exposed to electromagnetic radiation with the rapid development of technologies such as broadcasting and mobile communication system. There is a concern that long-term exposure at low levels may be associated with various non-specific physical symptoms and ecological effects on animals and plants. It is extremely important to measure and analyze the electromagnetic radiation levels in order to protect people from the possible effects of electromagnetic radiation. A large-scale assessment of the effects of electromagnetic radiation on health or on ecology requires the ambient electromagnetic radiation levels over areas too vast to cover with conventional measurement methods. In this article, detailed information about the measurement tools and measurement method are given. The electromagnetic radiation exposure levels were measured on the main streets in the dense urban areas of Beijing, the capital of China. We apply ordinary kriging as an interpolation technique to assess the electromagnetic radiation exposure in large outdoor areas based on car-mounted measurements along the surrounding roads. The electromagnetic radiation exposure levels for larger areas can be investigated visually on the electromagnetic pollution map, which can assist decision makers by identifying the hotspots. [ABSTRACT FROM AUTHOR]

Spatial interpolation methods are frequently used to characterize soil attributes' spatial variability. However, inconclusive results, about the comparative performance of these methods, have been reported in the literature. Therefore, the present study aimed to analyze the efficiency of ordinary kriging (OK) and inverse distance weighting (IDW) methods in estimating the soil penetration resistance (SPR), soil bulk density (SBD), and soil moisture content (SM) using two distinct sampling grids. The soil sampling was performed on a 5.7 ha area in Southeast Brazil. For data collection, a regular grid with 145 points (20 x 20 m) was created. Soil samples were taken at a 0.20 m layer depth. In order to compare the accuracy of OK and IDW, another grid was created from the initial grid (A), by eliminating one interspersed line, which resulted in a grid with 41 sampled points (40 x 40 m). Results showed that sampling grid A presented less errors than B, proving that the more sampling points, the lower the errors that are associated with both methods will be. Overall, the OK was less biased than IDW only for SBD (A) and SM (B) maps, whereas IDW outperformed OK for the other attributes for both sampling grids. [ABSTRACT FROM AUTHOR]

• The Ordinary Kriging (OK) method can be regarded as an instance of the Radial Basis Function (RBF) interpolation framework. • Four different functions have been implemented in the RBF interpolation framework to carry out core power mapping. • Measurements from DayaBay Unit 1 PWR are used to verify the accuracy of the RBF interpolation framework. Reactor core power mapping can be regarded as an interpolation problem of scattered data which is common in many scientific and engineering fields, and the Radial Basis Function (RBF) method provides an excellent tool for interpolating multidimensional scattered data and thus an appropriate approach for power mapping. By using the dual form of the RBF interpolation expression, this study shows that the Ordinary Kriging (OK) method authors utilized before can be regarded as an instance of RBF framework. Moreover, Gaussian function, multiquadric function, inverse quadratic function and inverse multiquadric function have been implemented in RBF interpolation framework to carry out core power mapping. Measurements from DayaBay Unit 1 PWR are used to verify the accuracies of these four RBF functions, and comparisons are made among these four methods and the OK method. The reconstructed assembly power distribution results and the calculation speeds show that the RBF interpolation framework is suitable for on-line core power distribution monitoring. [ABSTRACT FROM AUTHOR]

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Understanding the spatial distribution of organic and/or inorganic contaminants is crucial to facilitate decision-making of rehabilitation strategies in order to ensure the most appropriate management of contaminated sites in terms of contaminant removals efficiencies and operating costs. For these reasons, various interpolation methods [Thiessen Polygon (TP) method, inverse of distance (IDW) method, ordinary kriging (OK), as well as sequential Gaussian simulations (SGS)] were used to better understand the spatial distribution of As, Cr, Cu, pentachlorophenol (PCP) and dioxins and furans (PCDD/F) found onto a specific industrial site. These methods do not only vary in complexity and efficiency but also lead to different results when using values coming from the same characterization campaign. Therefore, it is often necessary to evaluate their relevance by performing a comparative analysis. The results showed that ordinary kriging (OK) was a better estimator of the mean and more advanced compared to the two other methods of interpolation (TP and IDW). However, it appeared that SGS has the same power than OK but it also permitted to calculate a reliable value of the probabilities of exceeding regulatory cut-offs of contamination. Image 1 • Fate and behavior of PCP, PCDD/F, As, Cr and Cu on an treated wood storage site. • Mapping the spatial distribution of (in-)organic contaminants on an industrial site. • Comparison of interpolation and SGS method to assess volume of contaminated soils. • SGS was the most suitable method for risk assessment of contaminated soil. [ABSTRACT FROM AUTHOR]

After a series of intentional Global Positioning System (GPS) jamming attacks impacted a large area of South Korea, the Ministry of Oceans and Fisheries of South Korea considers long-range navigation (Loran) and enhanced Loran (eLoran) as a maritime backup navigation system. Despite its robustness to signal jamming, the positioning accuracy of Loran/eLoran is lower than that of GPS. Because the signal delay due to the land path, which is called the additional secondary factor (ASF), is the largest unknown component of Loran/eLoran, it is necessary to account for temporal and spatial ASF errors to ensure high accuracy. The generation of ASF maps based on ASF survey data in a service area is the most convenient way to mitigate spatial ASF error, but the quality of ASF maps depends on the applied interpolation algorithm. It is desirable to generate high-quality ASF maps based on ASF measurements at only a few survey points, because extensive ASF surveys are expensive and time consuming and require considerable effort. This paper proposes kriging methods for satisfying this objective and shows their superior performance during a field test in Incheon, Korea. In particular, universal kriging with the proposed drift model showed a better performance than linear interpolation, inverse distance weighing, and ordinary kriging when the test vehicle was close to a coastline. The positioning accuracy with the ASF maps generated by the proposed universal kriging along a 5-km route during the field test was 25.24 m (95%). The land vehicle used for the test experienced significant signal-to-noise ratio (SNR) degradation owing to the noise caused by its engine. A vessel without such SNR degradation is expected to achieve higher accuracy. [ABSTRACT FROM AUTHOR]

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Abstract Modeling of the variogram is a critical step for most geostatistical methods. However, most of the prevalent variogram-based solutions are designed without sufficient consideration of the effect of the interpolation process on their application. This paper proposes an automated variogram modeling framework, which simultaneously considers the fit of the experimental variogram and interpolation accuracy in the modeling variogram interpolation result. The variogram modeling framework can be treated as a nonlinear optimization problem with two sub-goals. The first is to optimize the goodness of fit between the experimental and theoretical variogram values under the conditions of their designated parameters. Second, we seek to optimize the difference between measured values and the associated kriging estimates with the candidate variogram model. A typical case study was chosen using a public dataset to test the proposed method, which was implemented using a genetic algorithm, and its performance was compared with the ones of other commonly applied variogram modeling approaches. As expected, the traditional variogram modeling method that only considers fitting standard experimental variograms showed severe sensitivity to errors in data and parameters; classical cross-validation modeling results tended to overlook the experimental variograms. By contrast, the proposed method succeeded in producing variogram models with robust, high-quality kriging estimates and favorable fitness of experimental variograms in a more powerful and flexible way. Highlights • A method with high reliability in variogram fitting and interpolation is proposed. • The method can produce a robust variogram model in an automated and flexible way. • A case study towards adjustment of all typical model parameters is illustrated. • The traditional solutions cannot always yield reasonable and stable results. [ABSTRACT FROM AUTHOR]

Abstract: Aim: Recognition that statistical models do not always reliably predict habitat suitability under future climate scenarios is leading increasingly to explicit incorporation of the physiological constraints that underlie species’ distributions into spatially explicit predictions. However, computational intensity constrains the use of high‐resolution, process‐explicit models. We examined whether geostatistical analysis can effectively interpolate a biophysical model, reducing the computational investment typically required for using mechanistic methods to inform physiological predictions. Location: New Zealand [40°40′00″ S 174°00′00″ E]. Methods: We used a spatially explicit, mechanistic microclimate model to predict hourly temperatures at five soil depths under two scenarios of climate warming. Using the predicted soil temperatures as input to a biophysical model of temperature‐dependent embryonic development, we estimated incubation temperatures and corresponding hatchling sex ratios for tuatara, a reptile with temperature‐dependent sex determination, at a submetre horizontal spatial resolution. We then applied ordinary kriging, a robust method of geostatistical interpolation, to estimate predictions throughout the full extent of our study location, an additional 480,000+ microsites, and validated the interpolation against an independent set of predictions. Results: Ordinary kriging accurately predicted spatial variability in incubation temperatures. Mean predictions were similar between methods, and error in the geospatial model generally decreased with increasing soil depth. Error was higher for the geospatial model of the ‘maximum warming’, compared with the ‘minimum warming’, scenario of climate change. Main conclusions: Our results show that ordinary kriging can be a reliable method for interpolating variability in high‐resolution predictions. However, the effects of error on the accuracy of interpolated predictions will become more severe as values approach a physiological threshold, such as the minimum and maximum incubation temperatures that result in extreme sex ratio bias. For distribution models, the widths of geographic areas predicted to be suitable for, in this case, maintaining balanced sex ratios, compared to those predicted to be unsuitable, may be narrower than in reality. [ABSTRACT FROM AUTHOR]

patial interpolation, in the context of spatial analysis, can be defined as the derivation of new data from already known information, a technique frequently used to predict and quantify spatial variation of a certain property or parameter. In this study we compared the performance of Inverse Distance Weighted (IDW), Ordinary Kriging and Natural Neighbor techniques, applied in spatial interpolation of precipitation parameters (pH, electrical conductivity and total dissolved solids). These techniques are often used when the area of interest is relatively small and the sampled locations are regularly spaced. The methods were tested on data collected in Iasi city (Romania) between March – May 2013. Spatial modeling was performed on a small dataset, consisting of 7 sample locations and 13 different known values of each analyzed parameter. The precision of the techniques used is directly dependent on sample density as well as data variation, greater fluctuations in values between locations causing a decrease in the accuracy of the methods used. To validate the results and reveal the best method of interpolating rainfall characteristics, leave-one – out cross-validation approach was used. Comparing residues between the known values and the estimated values of pH, electrical conductivity and total dissolved solids, it was revealed that Natural Neighbor stands out as generating the smallest residues for pH and electrical conductivity, whereas IDW presents the smallest error in interpolating total dissolved solids (the parameter with the highest fluctuations in value).

Copyright of Tecnología y Ciencias del Agua is the property of Instituto Mexicano de Tecnologia del Agua (IMTA) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Geological properties usually vary spatially, but they are often measured sparsely in engineering geology practice, particularly for projects with medium or relatively small sizes. Spatial interpolation is, therefore, frequently performed to estimate the geological properties of interest at unobserved locations. Among a variety of interpolation methods (e.g., ordinary kriging (OK), polynomial interpolation (PI), cubic spline interpolation (CSI) and inverse distance weighting (IDW)), OK is one of the widely used methods, and it requires modeling of spatial structure of the measurement data points using a semi-variogram. However, the accuracy of the semi-variogram is affected by data size, and it may give unreliable estimates when the measurement data are sparse. This poses a challenge in applications where the measurement data are sparse, such as site characterization. To address this challenge, Bayesian compressive sampling (BCS) has been recently developed, which is able to reconstruct a complete signal from a remarkably few number of measurement data points on that signal. Unlike OK, BCS does not require characterization of spatial structure from the available measurement data before the interpolation. Therefore, the difficulties associated with modeling a semi-variogram from sparse data in OK are bypassed in BCS. A comparative study is performed in this paper to compare the effectiveness of BCS with OK, PI, CSI and IDW using simulated data and real cone penetration test data. In addition, an approach is presented in this paper to objectively select the most appropriate basis function in BCS. It is found that the BCS method is more suitable and performs better than the OK, PI, CSI and IDW methods when the measurement data are limited and sparse, such as interpretation of geological data or site characterization data. [ABSTRACT FROM AUTHOR]

Efficient soil management practices depend on the spatial distribution of soil properties which varies significantly even within the same field. Considering that it is impossible for any monitoring technique to provide spatially continuous data, spatial interpolation plays an indispensable role in estimating the missing values where no actual value was measured. The objective of this study was to evaluate various interpolation techniques for the estimation of selected soil chemical properties in a study area located about 85km to the north west of Cairo, Egypt. The studied soil properties included soil salinity, available phosphorus and nitrogen. The interpolation techniques included two commonly used techniques namely, Ordinary Kriging (OK) and Inverse Distance Weighting (IDW). The Artificial Neural Networks (ANN) method, which is considered a somewhat new approach was also evaluated. Soil samples were collected at approximately 200×200 m grids at 0-25 cm depth. The cross-validation method was used for evaluating the selected methods utilizing root mean square error (RMSE) and mean relative error (MRE). This study revealed that ANN had the highest accuracy followed by OK then IDW in terms of both RMSE and MRE when interpolating the studied soil properties. Nevertheless, these results are dependent on the accuracy of the designed network which must have an overall accuracy of coefficient of correlation (R) more than 0.80 between the predicted and the actual data. It also revealed that the best IDW with the highest accuracy must have a power of 2 for salinity and nitrogen and a power of 3 for phosphorus. [ABSTRACT FROM AUTHOR]

This paper compares continuous surfaces obtained by the interpolation of standard penetration test values (Nspt) by depth using deterministic and geostatistical models. The evaluation of the interpolation methods was based on the percent areas of the compactness classes by depth obtained in each method and on the percent errors calculated from the differences between the measured and interpolated Nspt. The Nspt values were obtained from 228 standard penetration tests (SPT) in situ investigations carried out in quaternary sandy marine sediments located along the Brazilian northeast coast. The boreholes are well distributed in an area of 10.9 km, covering six districts of João Pessoa City (Paraíba State, Brazil). The interpolations and analyses were conducted using geographic information system and spreadsheet software. The interpolations of Nspt values were made at depths of 1, 3, 6 and 15 m. The interpolated Nspt values obtained for each depth were classified into five soil compactness classes. The general boundaries of the compactness classes and their percent areas by depth were similar for both methods with some localized differences. Both methods presented high average percent errors and standard deviations, with a slight advantage to the geostatistical model (ordinary kriging). The minimum average percent error and standard deviation occurred at a depth of 3 m for both methods, with a slight advantage to the deterministic method (spline modified). Both methods also indicated a peculiar high soil resistance of the marine sediments at a depth of 6 m and significant areas of loose soils at a depth of 15 m in one of the districts analyzed. Both methods showed similar potential for practical applications for the initial phases of a project, not ruling out more specific SPT tests, but can optimize them. [ABSTRACT FROM AUTHOR]

Plane-of-array (PoA) irradiation data is a requirement to simulate the energetic performance of photovoltaic devices (PVs). Normally, solar data is only available as global horizontal irradiation, for a limited number of locations, and typically in hourly time resolution. One approach to handling this restricted data is to enhance it initially by interpolation to the location of interest; next, it must be translated to PoA data by separately considering the diffuse and the beam components. There are many methods of interpolation. This research selects ordinary kriging as the best performing technique by studying mathematical properties, experimentation and leave-one-out-cross validation. Likewise, a number of different translation models has been developed, most of them parameterised for specific measurement setups and locations. The work presented identifies the optimum approach for the UK on a national scale. The global horizontal irradiation will be split into its constituent parts. Divers separation models were tried. The results of each separation algorithm were checked against measured data distributed across the UK. It became apparent that while there is little difference between procedures (14 Wh/m2 mean bias error (MBE), 12 Wh/m2 root mean square error (RMSE)), the Ridley, Boland, Lauret equation (a universal split algorithm) consistently performed well. The combined interpolation/separation RMSE is 86 Wh/m2). [ABSTRACT FROM AUTHOR]

Soil salinity is one of the important soil properties that has asignificant effect on many processes such as plant grows. The objectives ofthis paper are to estimate soil salinity and to map the salinity risk inMeiankangi located in Sistan plain. Soilelectrical conductivity was measured on soil samples taken from 122 sitesdistributed radiometry across to study area. The geostatistical methods ofordinary kriging and indicator kriging were used for salinity mapping. Thelatter was used to map the probability that soil salinity exceeds a criticalthreshold. The methods were evaluated using cross-validation. The validation ofused methods were evaluated using root mean square error (RMSE( and mean bias error (MBE).The results showed that both methods were similar for predict soil salinity.The probability maps of exceeding 2, 4 and 8 ds/m were generated usingindicator kriging. Given the critical threshold of 2 ds/m, almost all theregions have a probability of salinity of more than 0.5. The results showed that the salinity is moderate across the study area.Overall the obtained results indicated that unlike ordinary kriging, indicatorkriging is able to map the salinity risk. These maps are very helpful indecision such as land classification and management.

Copyright of Rudarsko-Geolosko-Naftni Zbornik is the property of Faculty of Mining, Geology & Petroleum Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study applied a geostatistical approach to quantify above-ground biomass (AGB) of the Labanan Concession Forest in East Kalimantan, Indonesia. Forest inventory data collected via transect sampling were converted to AGB, and two approaches of estimating the spatial distributions of biomass, the global and stratified approaches, were compared. The global approach does not take local varying structures into account, whereas the stratified approach accounts for the heterogeneity of land cover types. Thus, AGBs estimated from each land cover type were pooled for the stratified approach. Ordinary kriging was performed to predict AGB at unsampled locations. The total estimates of AGB and RMSCVEs for the global and stratified methods were 13,512,392.2 tons (161.92 ton/ha) and 13,607,205.5 tons (163.05 ton/ha), respectively, for AGB and 81.0 ton/ha and 81.2 ton/ha, respectively, for RMSCVE. Considering the different environmental conditions for each land cover type, the stratified method was expected to better capture the spatial structure particular to each land cover type, leading to more accurate estimates of AGB. However, the results suggest the degree of accuracy for the two methods was nearly similar. [ABSTRACT FROM AUTHOR]

A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania's South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW) method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications. [ABSTRACT FROM AUTHOR]

The saline groundwater irrigation is an important problem in the arid and semiarid region because it can cause soil salinization and reduce crop productivity. The accurate spatial distribution of groundwater salinity can be helpful to managers and decision makers. In this study, the mapping of salinity risk through groundwater electrical conductivity (EC) irrigation was performed based on data collected from 88 wells in the Lower-Cheliff plain (Algeria). The EC data showed a normal distribution based on elementary statistics. The EC classified using Riverside method point out a high risk of groundwater salinity (Class C3) or very high risk (Class C4) for soil salinization. The EC estimated by ordinary kriging method (OK) revealed on one hand, an underprediction of a high value, on the other hand, an overprediction of low value. The methodology of nonparametric and nonlinear of indicator kriging (IK) was performed by three thresholds: EC > 2.25, EC > 3, and EC > 5 dS=m. The map has been obtained from the combination of the local conditional cumulative distribution function (CCDF). The interpolated map by IK indicates the same overall spatial distribution of salinity with the one obtained by OK, enlightening differences in the shape and size of the area. The comparison between the groundwater EC estimated by OK and the one using IK demonstrates that IK has a better spatial prediction of salinity in terms of area and uncertainty. The groundwater salinity map was improved and accurately predicted by IK interpolation method. [ABSTRACT FROM AUTHOR]

Rainfall data provide an essential input for most hydrologic analyses and designs for effective management of water resource systems. However, in practice, missing values often occur in rainfall data that can ultimately influence the results of hydrologic analysis and design. Conventionally, stochastic interpolation methods such as kriging are the most frequently used approach to estimate the missing rainfall values where the variogram model that represents spatial correlations among data points plays a vital role and significantly impacts the performance of the methods. In the past, the standard variogram models in ordinary kriging were replaced with the universal function approximator-based variogram models, such as artificial neural networks (ANN). In the current study, applicability of genetic programming (GP) to derive the variogram model and use of this GP-derived variogram model within ordinary kriging for spatial interpolation was investigated. Developed genetic programming-based ordinary kriging (GPOK) was then applied for estimating the missing rainfall data at a rain gauge station using the historical rainfall data from 19 rain gauge stations in the Middle Yarra River catchment of Victoria, Australia. The results indicated that the proposed GPOK method outperformed the traditional ordinary kriging as well as the ANN-based ordinary kriging method for spatial interpolation of rainfall. Moreover, the GP-derived variogram model is shown to have advantages over the standard and ANN-derived variogram models. Therefore, the GP-derived variogram model seems to be a potential alternative to variogram models applied in the past and the proposed GPOK method is recommended as a viable option for spatial interpolation. [ABSTRACT FROM AUTHOR]