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In arid and semi-arid regions where surface water resources are scarce, groundwater is crucial. Accurate mapping of groundwater depth is vital for sustainable management practices. This study evaluated the performance of three spatial interpolation techniques – inverse distance weighting (IDW), ordinary kriging (OK), and radial basis functions (RBF) – in predicting groundwater depth distribution across Dire Dawa City, Ethiopia. The results demonstrated the superiority of the RBF method, exhibiting the lowest RMSE (3.21 m), MAE (0.16 m), and the highest R2 (0.99) compared to IDW and OK. The IDW method emerged as the next best performer (RMSE = 4.68 m, MAE = 0.16 m, R2= 0.97), followed by OK (RMSE = 5.32 m, MAE = 0.42 m, R2= 0.95). The RBF's superior accuracy aligns with findings from other semi-arid regions, underscoring its suitability for data-scarce areas like Dire Dawa. This comparative evaluation provides valuable insights for selecting the optimal interpolation method for groundwater depth mapping, supporting informed decision-making in local water resource management.The methodological approach comprised: • Implementation of three interpolation techniques, namely, inverse distance weighting (IDW), ordinary kriging (OK), and radial basis functions (RBF), utilizing 56 groundwater depth measurements from locations dispersed throughout the study area. • Cross-validation through randomly withholding 20 % of the data for validation purposes. • Comparison of the techniques based on statistical measures of accuracy, including root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2).

The significant reduction of surface water resources and recent recurrent droughts have increased the reliance on groundwater sources, leading to a decline in their quality. In this study, 28 samples of well water from different locations in Khanmirza, Lordegan, Borujen, Ardal and Kiar were collected in 2020-2021 and underwent chemical analysis in the laboratory. To evaluate the quality of the samples for use in agricultural, drinking and industrial sectors, the Wilcox diagram, Schuler diagram and Langlier index were used. Using interpolation methods, the chemical properties of the samples taken within the study area were examined and qualitative zoning maps were prepared using Kriging and inverse distance weighting methods. The results showed that according to the Wilcox diagram, most of the samples are within the range of C2S1 and are suitable for agricultural purposes. According to the Schuler diagram, these samples are within the range of good quality for drinking and based on the Langlier index, they are within the range of precipitating and consumable. This study helps decision-makers to have a clear view and plan comprehensively and effectively for the exploitation and preservation of groundwater resources, taking into account the qualitative maps of groundwater.

Flow duration curve represents the percentage of time that a river flow is equal to or greater. As these curves provide a direct response to the behavior of water resources in a basin, which is used widely in hydropower projects, it is important to predict flow duration curves in no metering basins, named "ungagged basins." The geostatistical approach to predict the values of these curves in non-measured stations shows the expansion of the range of studies in this topic. The aim of this study is to predict the flow duration curve over long periods of time in a basin with ungauged regions using probability kriging, inverse distance weighting (IDW) and maximum likelihood (ML) methods. Flow data from 38 flow measuring stations in the Dez Basin were used to map different discharges of the flow duration curve, and as a result, in order to complete their values, zone and quantify them, three different values of Q10, Q50 and Q90 of the flow duration curve acquired. The results show that as the flow rate increases (or the time percentage decreases), the amount of computational error increases and in all cases, the probability kriging method has a smaller error (0.96) than the IDW (1.65) and ML (1.15) methods. [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]

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.)

Spatial interpolation is a required method to generate a continuous surface such as Digital Elevation Model (DEM) because field investigation for most of the surface's part is time-consuming with a high demand in both human resources and monetory cost. One of the most used deterministic interpolation models is Inverse Distance Weighting (IDW) model. The model takes several neighbors' information, and the weights are constructed based on the distance between the interpolated point and the neighbors' points. From the machine learning model, Artificial Neural Networks (ANNs) model has also been used for spatial interpolation. The input of ANNs model is also one of the parameters that need to be defined when building the model. This paper evaluated the effect of the number of inputs (neighbors) on the elevation interpolation accuracy. We applied IDW and ANNs to interpolate the elevation of Balikpapan City, Indonesia. The results show that the accuracy increases significantly when the number of inputs is between one and three. However, after three inputs, additional input would not change the accuracy significantly. ANNs performed better than IDW. For three or more inputs, the MAE of ANNs and IDW interpolations are below 1.1 and around 2 meters, respectively. [ABSTRACT FROM AUTHOR]

In the present study, simple and ordinary kriging methods, inverse distance and linear regression based on digital elevation model of the earth were evaluated for estimating annual rainfall using twenty-year statistics of precipitation data (1998-2018) in 33 rainfall stations in Chaharmahal and Bakhtiari province. For this purpose, first in ArcMAP, for each model in Kriging method, its variogram was calculated and using two-way evaluation technique, the error of the maps was estimated. The best method among geostatistical methods was conventional kriging method with Gaussian model. MAE, MBE and RMSE statistical indices for this method were 74.44, 0.48 and 93.72, respectively. Then, rainfall and altitude data of the stations were used using a linear regression model in Curve Expert environment. Finally, in order to determine the best model for spatial distribution of precipitation as well as comparing statistical and geostatistical methods, linear regression and ordinary kriging models were compared with each other and the MAE, MBE and RMSE statistical indices for regression method obtained were 115, 3 and 155, respectively. As a result, due to the accuracy, precision and error rate of the prepared maps, the most suitable method for interpolation of annual precipitation is the conventional kriging method with Gaussian model.

[Display omitted] • Introduced IRW and its Python package for improved geochemical mapping considering elevation changes. • Compared IRW with IDW, highlighting better interpolation accuracy. • Evaluated using As, Cu, and Ba to demonstrate improved correlation with actual values. • Reduced spatial uncertainty in geochemical maps, enhancing anomaly and mineralization pattern identification. The extent and volume of geochemical sampling are inherently constrained by numerous factors, including budgetary limitations, analytical costs, and access restrictions. These constraints result in sampling networks that vary in density and regularity, dividing regions into sampled and unsampled areas. The creation of continuous geochemical maps is essential for geochemical prospectivity, which aims to identify geochemical anomalies, distinguish between background levels and anomalies, and define mineralization patterns. Therefore, it is necessary to interpolate data from sampled areas to estimate values in unsampled regions. Although several interpolation models exist, including Inverse Distance Weighting and various kriging methods, Inverse Distance Weighting is often used in two-dimensional ground modeling because, unlike kriging methods, Inverse Distance Weighting has no smoothing effect on edges. Inverse Distance Weighting's reliance solely on horizontal Euclidean distances between samples overlooks critical factors such as topography and the ensuing effects on dilution, transportation, and element mobility, rendering it less effective over varied elevations. This study introduces Inverse Radius Weighting, a new interpolation technique that incorporates both Euclidean and elevation fluctuations, therefore Pythagorean distance, to help with better geological interpretations. We assessed the efficacy of Inverse Radius Weighting compared to Inverse Distance Weighting across three elements with varying mobility (Arsenic − highly mobile, Copper − moderately mobile, and Barium − nearly immobile), using different numbers of neighbors and by comparing three different evaluation measures, namely R2, Mean Absolute Error and Mean Absolute Percentage Error. By evaluating the spatial uncertainty of the generated maps and selecting the configurations with the least uncertainty as the final maps, our analysis reveals an improvement in correlation between interpolated and actual values with Inverse Haversine Radius Weighting. With this advancement, Inverse Haversine Radius Weighting overcomes the limitations of traditional Inverse Distance Weighting by accounting for elevation and its associated effects, thereby paving the way for more accurate and geochemically meaningful interpolation in geochemical prospectivity mapping. [ABSTRACT FROM AUTHOR]

Context: Obtaining accurate and precise maps of landscape features often requires intensive spatial sampling and interpolation. The data required to generate reliable interpolated maps varies with sampling density and landscape heterogeneity. However, there has been no rigorous examination of sampling density relative to landscape characteristics and interpolation methods. Objectives: Our objective was to characterize the 3-way relationship among sampling density, interpolation method, and landscape heterogeneity on interpolation accuracy and precision in simulated and in situ landscapes. Methods: We simulated landscapes of variable heterogeneity and sampled at increasing densities using gridded and random strategies. We applied three local interpolation methods (i.e., Inverse Distance Weighting, Universal Kriging, and Nearest Neighbor) to the sampled data and estimated accuracy (slope and intercept) and precision (R2) between interpolated surfaces and the original surface. Finally, we applied these analyses to in situ data using a normalized difference vegetation index raster collected from pasture with various resolutions. Results: In our simulations, all interpolation methods and sampling strategies yielded similar accuracy and precision except in the case of Universal Kriging with random sampling. Additionally, low heterogeneity and increasing sample density improved both accuracy and precision, with cross-validation slopes and R2 values approaching optimal values. In situ analysis demonstrated that heterogeneity decreased with resolution. Nearest Neighbor under both sampling strategies and Universal Kriging using the gridded sampling strategy had the highest accuracy and precision. Decreased heterogeneity and increased sampling density improved accuracy and precision for all combinations of interpolation method and sampling strategies. Conclusions: Heterogeneity of the landscape is a major influence on the accuracy and precision of interpolated maps. There is a need to create structured tools to aid in determining sampling design most appropriate for interpolation methods across landscapes of various heterogeneity. [ABSTRACT FROM AUTHOR]

The focus of this paper is on developing localized growth factors for estimating annual average daily traffic (AADT) of a local, functionally classified road (referred to herein as a local road). Statewide, regional-level, and county-level median and mean growth factors were computed and compared with localized growth factor estimates from spatial interpolation methods, such as Ordinary Kriging, inverse distance weighted (IDW), and natural neighbor (NN) interpolation. The use of Ordinary Kriging-based localized growth factor is recommended for a local road AADT estimation. If count-based local road AADT (c-AADT) figures for previous years are available, they, along with localized growth factors for those years, should be used to estimate the local road AADT (e-AADT) for the reporting year. The estimated AADT (e-AADT) for the base year and localized growth factors from the base year to the reporting year must be used for estimating e-AADT of a non-covered local road link for the reporting year. The c-AADT or e-AADT of the local road link can be used to compute vehicle miles traveled (VMT) for reporting purposes. The proposed methodology reduces the costs and other resources required for traffic data collection and for e-AADT accounting for spatial variations. [ABSTRACT FROM AUTHOR]

Conventional methods of spatial prediction, such as Kriging, require assumptions such as stationarity and isotropy, which are not easy to evaluate, and often do not hold for spatial data. For these methods, the spatial dependency structure between data should be accurately modeled, which requires expert knowledge in spatial statistics. On the other hand, spatial prediction using artificial neural network (ANN) has attracted considerable interest due to ANN's ability in learning from data without the need for complex and specialized assumptions. However, ANN models require suitable input variables for better and efficient spatial prediction. This paper aims to improve the accuracy of ANNs spatial prediction using neighboring information. Given the general principle that "closer spatial data are more dependent", we tried to somehow enter data dependency into the network by using the neighboring observations. We proposed a hybrid model of ANN and inverse distance weighting, based on nearby observations. We also proposed an ANN-based model for spatial prediction based on weighted values of nearby observations. The accuracy of the models was compared through a simulation study. The results showed that using neighboring information to train ANN, dramatically increases the prediction accuracy. [ABSTRACT FROM AUTHOR]

Copyright of Ordnance Industry Automation is the property of Editorial Board for Ordnance Industry Automation 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.)

Abstract: Groundwater monitoring plays a significant role in groundwater management. This study presents an optimization method for designing groundwater-level monitoring networks. The proposed design method was used in the Eshtehard aquifer, in central Iran. Three scenarios were considered to optimize the locations of the observation wells: (1) designing new monitoring networks, (2) redesigning existing monitoring networks, and (3) expanding existing monitoring networks. The kriging method was utilized to determine groundwater levels at non-monitoring locations for preparing the design data base. The optimization of the groundwater monitoring network had the objectives of (1) minimizing the root mean square error and (2) minimizing the number of wells. The non-dominated sorting genetic algorithm (NSGA-II) was applied to optimize the network. Inverse distance weighting interpolation was used in NSGA-II to estimate the groundwater levels while optimizing network design. Results of the study indicate that the proposed method successfully optimizes the design of groundwater monitoring networks that achieve accuracy and cost-effectiveness.

• An error decomposition and fusion framework is proposed for daily precipitation estimation. • Geographically weighted regression and geographical difference analysis is implemented. • Improved precipitation estimates are achieved by the merging product. • The merging product demonstrates its superiority in accurately estimating winter precipitation and high-value precipitation. • The influence of GPCC station data on the accuracy of the merging product has been considered. Near-real-time satellite precipitation products (SPPs) possess inherent application prospects in the hydro-meteorological field due to their convenient acquisition and accessibility. Integrating gauge-based measurements with near-real-time SPPs is an effective approach for achieving precise spatial precipitation estimates at daily scale. This study proposed a newly developed error decomposition and fusion framework, named EDGWR, which integrates error decomposition and geographically weighted regression (GWR). The final merged product, denoted as IMERG-EDGWR, was obtained from the near-real-time Integrated Multi-satellitE Retrievals for Global Precipitation Measurement Early Run (IMERG-E) product. IMERG-EDGWR was compared with the raw IMERG-E, near-real-time IMERG-L, post-real-time IMERG-F, global multi-source merged precipitation data (MSWEP), interpolated results (IDW and OK), and direct application of GWR outcomes (IMERG-GWR), utilizing the daily ground measurements from 12 meteorological stations located in the Yellow River source region (YRSR). The evaluation results from 2014 to 2018 revealed that IMERG-EDGWR exhibited significant enhancements over the raw IMERG-E, surpassed the research-level IMERG-F, and generally outperformed IDW, OK, MSWEP, and IMERG-GWR. Notably, IMERG-EDGWR enhances the detection of heavy precipitation events, refining estimates of both magnitude and frequency for precipitation over 25 mm. During the winter season, IMERG-EDGWR produced the most accurate precipitation estimates with notable improvement of precipitation detection capabilities. An experiment reducing input data by excluding gauge observations from the GPCC dataset tested the robustness of the EDGWR algorithm, confirming its superiority even with diminished input data. The merging framework proposed in this study constitutes an efficacious and implementable solution to enhance the accuracy of near-real-time SPPs and is expected to be implemented in different regions in future research. [ABSTRACT FROM AUTHOR]

This study included the testing of normal (Gaussian) distribution of input data and, consequently, spatially interpolating maps of chemical components and cement modules in the flysch. This deposit contains the raw material for cement production. The researched area is located in southern Croatia, near Split, as part of the exploited field "St. Juraj–St. Kajo". There are six lithological units: (1) alternation of marls and sandstones with inclusions of conglomerates, (2) marl, (3) calcsiltite, (4) calcarenite, (5) marl with nummulites, (6) debrites, and (7) clayey marl. All of them are deposited in the (a) northern and (b) southern beds. Only debrites are divided into the (a) western and (b) eastern layers. Those lithological units were divided technologically based on their cement modules (lime saturation factor (LSF), silicate module (SM), and aluminate module (AM)). The average thicknesses were analysed, followed by normality tests (Kolmogorov–Smirnov (K–S) and Shapiro–Wilk (S–W)) of the chemical analyses: CaO, SiO2, Al2O3, Fe2O3, MgO, SO3, Na2O, K2O, CaCO3 (%) and three cement modules (LSF, SM, AM), available in the six lithological units. The normality tests were applied based on a number of input data. The further interpolation was performed using two methods, kriging and inverse distance weighting, mapping CaO (%), SiO2 (%), and LSF (−) in three different lithological units. The interpolation methods were selected based on two criteria: (a) normality test pass or fail and (b) the amount of data. In total, 144 tests were calculated, including sets from 7 to 36 points. The results show the current situation in the quarry, after decades of production, making reliable the future predictions of cement raw material exploitation. [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]

Humans and animals are both susceptible to highly pathogenic avian influenza (HPAI) viruses. In the future, HPAI has the potential to be a source of zoonoses and pandemic disease drivers. It is necessary to identify areas of high risk that are more vulnerable to HPAI infections. In this study, we applied unbiased predictions based on known information to find points of localities with a high probability of point prevalence rate. To carry out such predictions, we utilized the inverse distance weighting (IDW) and kriging method, with the help of the R statistical computing program. The provinces of Jeollanam-do, Gyeonggi-do, Chungcheongbuk-do and Ulsan have high anticipated risk. This research might aid in the management of avian influenza threats associated with various potential risks. [ABSTRACT FROM AUTHOR]

Mapping soil organic carbon (SOC) and its uncertainty are essential for agricultural soil management. The current study was carried out to quantify and map the spatial variability of SOC in an Agro-Ecosystem region (~ 170 km2) in Northeast Iran using Ordinary Kriging (OK), Empirical Bayesian Kriging (EBK), and Inverse Distance Weighting (IDW) techniques. In the study area, a total of 288 soil surface samples (0–20 cm depth) were collected. Results showed that the mean SOC was 0.728% with high variability (CV = 44.78%), and also SOC was found to be deviant from a normal distribution as revealed by Kolmogorov–Smirnov (K-S) test, with positive skewness. Due to the deviation from the normal distribution, and for the purpose of modeling, the data were log-transformed to approximate a normal distribution. The best fit empirical variogram was the Exponential model. Among the various interpolation techniques, estimation with EBK approach was the fairly reliable (RMSE = 0.3156; ME = 0.004), followed by OK (RMSE = 0.3162; ME = 0.003), and IDW (RMSE = 0.3199; ME = 0.005). Moreover, results showed that the spatial analysis of SOC had a strong spatial dependency for this study. Thus, the results revealed that the simple interpolation approach was a fast method and highly suitable for the spatial prediction of SOC in this study. [ABSTRACT FROM AUTHOR]

The aim of this study was to evaluate the spatial distribution of soil infiltration using geostatistics methods in a regional scale on 400 hectares of Mansour Abad Plain, in Larestan region, Fars Province. Sampling and parameters measurement were done for 78 points in a regular grid with a distance of 100*100 meters; for these variables, the best variogram model between linear, exponential, Gaussian and spherical models with the highest R2 and the lowest error was determined using GS+ and ArcGIS software. In this study, soil infiltration (cm/min) using the double ring method and some other soil properties including soil electrical conductivity (dS/m), pH, saturation percentage (%SP), particle size percentage (sand, silt and clay), and calcium (meq/lit), magnesium (meq/lit), sodium (meq/lit) were measured and determined. The spatial distribution of Kostiakov and Philip models parameters and theri zoning were determined using the geostatistic method. The results showed that, among different soil properties, the final infiltration rate had a high degree of variability in the study area, and the decision was based on the usual averaging methods, which could have a lot of error. Among applied infiltration models, Kostiakov model and Philip model were the best empirical and physical infiltratin models, respectively, in the studied area. The best semivariogram model for the steady state infiltration rate was Philip model, with the coeficients of S and A, and a coefficient of Kostiakove model was gaussian; for the b coefficient, Kostiakove model was exponential. Spatial structure of the final infiltration rate, a and b coefficients of Kostiakove model, and S and A coefficients of the Philip model, was strong. The best interpolation method for the final infiltration rate was cokriging with the cofactor of silt percentage, for the S coefficient of Philip model was inverse distance weighting (IDW); for a and b coefficients of Kostiakove model, kriging and IDW were suitable, respectively.

Surface interpolation techniques are usually used to create continuous data (i.e. raster data) from distributed set of point data over a geographical region. There are deterministic and stochastic (geostatistical) interpolation techniques can be used to create spatial raster surface. In this paper, the comparison between the Inverse Distance Weight (IDW) interpolation method as deterministic method and the Kriging interpolation method as stochastic method is done to determine the best performance for measuring levels of ground water in Baghdad Governorate. Spatial raster surface surfaces as ground water prediction maps are generated from each method by using average ground water level measured at 206 wells in the study area. These maps are shown spatial variation in the ground water levels and they have complete different. The IDW method results a refined map and lesser error than the Kriging method. Thus, the analysis shows that the IDW gives better real performance of measuring levels of ground water in Baghdad Governorate.

High-accuracy watershed features can be used as hydrological parameters of a distributed hydrological model and a nonpoint source pollution model. A total of 3,863 elevation points in Haizi Watershed, China, are collected to produce a basic digital elevation model (DEM). Spline, kriging, and inverse distance weighting methods are selected to interpolate different sample sizes obtained by different sampling methods. A total of 105 DEMs are constructed to extract river networks, outfalls, and watersheds. The accuracies of watershed features are evaluated by using root-mean-square error, and the errors of outfall position, river network closure (crossings of the actual and the extracted river networks), river network density, and watershed area. The results show that the accuracies of DEMs and watershed features increase with an increase in sample size. Sample size, sampling method, and interpolation method have significant impacts on the accuracies of DEMs, outfall position, river network closure, and watershed area. Sample size is most important for deriving watershed features. The optimal combinations of sample size, sampling method, and interpolation method can improve the accuracies of watershed features. [ABSTRACT FROM AUTHOR]

Humans and animals are both susceptible to highly pathogenic avian influenza (HPAI) viruses. In the future, HPAI has the potential to be a source of zoonoses and pandemic disease drivers. It is necessary to identify areas of high risk that are more vulnerable to HPAI infections. In this study, we applied unbiased predictions based on known information to find points of localities with a high probability of point prevalence rate. To carry out such predictions, we utilized the inverse distance weighting (IDW) and kriging method, with the help of the R statistical computing program. The provinces of Jeollanam-do, Gyeonggi-do, Chungcheongbuk-do and Ulsan have high anticipated risk. This research might aid in the management of avian influenza threats associated with various potential risks.

Air pollution can significantly accelerate the process of material corrosion, which may cause significant economic losses and serious safety incidents. Atmospheric corrosion maps provide atmospheric corrosivity in a given geographic scope, which can guide the designers to select the most suitable anti-corrosion materials for outdoor projects, also provide useful information for maintenance. This article investigated mapping of atmospheric corrosivity in Shandong Province, China. In order to obtain atmospheric corrosivity data, 100 exposure corrosion test sites were established in Shandong according to International Standard Organization (ISO) 8565. Hot-dip galvanized steel samples were exposed for 1 year in the test sites. Taking the results of exposure corrosion test as the data, inverse distance weighting (IDW) and ordinary kriging (OK) interpolation algorithm were used to estimate the atmospheric corrosivity of Shandong Province according to ISO 9223. The validity of OK and IDW was compared in developing atmospheric corrosion maps of Shandong Province on a 1 × 1 km resolution. The cross-validation results showed that OK interpolation algorithm with Gaussian semivariogram model get the best result in the prediction of corrosion rate. When the corrosion category was used as the criterion, the IDW interpolation algorithm of power 4 performed best, predicted results of 74 sites (n = 100) were consistent with observed. However, high mean relative errors (MRE more than 37%) and relatively low correlation (R2 about 24%) indicated that the prediction results of the two interpolation algorithms had a large error, which was caused by the low data density and the complicated corrosive factors of the atmosphere. [ABSTRACT FROM AUTHOR]

Estimating soil hydraulic properties are so important for hydrological modeling, designing irrigation-drainage systems and soil transmission of soluble salts and pollutants, although measurements of such parameters have been found costly and time-consuming. Owing to a high spatial variability of soil hydraulic characteristics, a large number of soil samples are required for proper analysis. Nowadays, geostatistical methods are used to estimate soil parameters on the basis of limited data. The purpose of this research is to investigate the spatial variability of the permeability coefficient in different soil textures (26 soil samples) found in the Kurdistan region of Iraq. The parameter values obtained indicated a normal trend in particle size distribution, whereas the values of permeability coefficient showed aberrant distribution patterns. Geostatistical analysis results indicated the best fitted theoretical model was Gaussian model and the proportion of sill/(sill + nugget) was 0.17 indicated strong spatial dependency of soil permeability. Furthermore, the optimal distance for estimating the soil permeability coefficient was 109,119 meters. A comparison of the kriging and IDW interpolation methods showed that both methods can estimate soil permeability with high accuracy and less error. The prediction maps of the applied methods indicated that high soil permeability rates were recorded in the south-east of the Kurdistan region of Iraq compared to low soil permeability rates recorded in the remainder of this region. It is recommended other interpolation methods such as co-kriging and indicator or simple kriging methods could be used to simulate data in large scale areas as well.

Elevation is the main information of the earth, and different models are provided for a better understanding of the earth. To have a digital elevation model (DEM), the height of the area must be gathered. However, it is not always possible to conduct a comprehensive survey in the area and calculate the whole surface. The best way is surveying some points, then estimating the elevation using these points. The purpose of this paper is to use interpolation methods to estimate elevation. In this paper, the three usual methods are chosen and introduced, then their performances are compared. These methods include inverse distance weighting (IDW), the Kriging method, and artificial neural network (ANN). The results show that the ANN models the elevation better than the two other methods with root mean square error (RMSE) equals to 5.9 m. [ABSTRACT FROM AUTHOR]

Spatial analysis of hydrological data often requires the interpolation of a variable from point samples. Commonly used methods for solving this problem include Inverse Distance Weighting (IDW) and Kriging (KG). IDW is easily extensible, has a competitive computational cost with respect to KG, hence it is usually preferred for this task. This paper proposes the optimization of finding the IDW parameter using a nature-inspired metaheuristic, namely Particle Swarm Optimization (PSO). The performance of the improved algorithm is evaluated in a complex scenario and benchmarked against the KG algorithm for 51 precipitation series from the Dobrogea region (Romania). Apart from facilitating the process of applying IDW, the PSO implementation for Optimizing IDW (OIDW) is computationally lighter than the traditional IDW approach. Compared to Kriging, OIDW is straightforward to be implemented and does not require the difficult process of identification of the most appropriate variogram for the given data. [ABSTRACT FROM AUTHOR]

As a typical spatial interpolation method with high efficiency and simplicity, inverse distance weighting (IDW) is almost a standard estimator in numerous fields such as geosciences and environmental science. However, it ignores the data-to-data correlation, which directly leads to unfavorable estimates with irregularly distributed samples. To address this issue, we propose a novel approach, termed dual IDW (DIDW). First, the average distance from one sample to others is employed to measure the data redundancy. Second, we impose an additional exponent on the average distance to make its importance adjustable. Last, this data-to-data distance is incorporated into the traditional IDW to account for the spatial configuration of neighborhoods in the interpolation. Consequently, DIDW flexibly takes both data-to-unknown and data-to-data distances into account. Only those samples that are close to the estimated location but apart from other sampled data would be assigned with large estimation weights. Details of its application and the validity are illustrated using a case study based on the public Walker Lake dataset. Our results indicate that the developed methods not only improve the interpolation accuracy significantly compared with the traditional IDW, but also slightly outperform ordinary kriging in the case where the sample dataset is too small to capture an appropriate spatial continuity, demonstrating that DIDW is valuable to be applied in a broader context. [ABSTRACT FROM AUTHOR]

Spatial trends of rainfall and reference evapotranspiration (ETo) are crucial for sustainable water resources management. Rainfall and ETo trends were evaluated and estimated using FAO Penman Monteith model and their spatial distributions were mapped across the Southeast Nigeria. Two spatial interpolation techniques, Inverse Distance Weighting (IDW) and Kriging in ArcGIS were employed for monthly, annual and seasonal rainfall and ETo. Results showed that rainfall increased gradually from North to South while ETo increased from South to North of the study area. ETo was found to be higher during dry seasons as the average rise in temperature within the period of study stood at 1.1%. There was a positive correlation of the predicted results obtained by the IDW and kriging methods with measured rainfall and ETo data, evaluated at R = 0.87(rainfall) and R = 0.83 (ETo) for IDW method, and R = 0.92 (rainfall) and R = 0.50 (ETo) for kriging method. This study provides background information on rainfall, ETo and climatic conditions for climate change studies, efficient crop water and environmental management. [ABSTRACT FROM AUTHOR]

This research aims to estimate baseflow (BF) and baseflow index (BFI) in ungauged basins in the southern part of Thailand. Three spatial interpolation methods (namely, inverse distance weighting (IDW), kriging, and spline) were utilized and compared in regard to their performance. Two baseflow separation methods, i.e., the local minimum method (LM) and the Eckhardt filter method (EF), were investigated. Runoff data were collected from 65 runoff stations. These runoff stations were randomly selected and divided into two parts: 75% and 25% for the calibration and validation stages, respectively, with a total of 36 study cases. Four statistical indices including mean absolute error (MAE), root mean squared error (RMSE), correlation coefficient (r), and combined accuracy (CA), were applied for the performance evaluation. The findings revealed that monthly and annual BF and BFI calculated by EF were mostly lower than those calculated by LM. Furthermore, IDW gave the best performance among the three spatial interpolation techniques by providing the highest r-value and the lowest MAE, RMSE, and CA values for both the calibration and validation stages, followed by kriging and spline, respectively. We also provided monthly and annual BF and BFI maps to benefit water resource management.

Regression tree models have been shown to provide the most accurate estimates of distributed snow water equivalent (SWE) when intensive field observations are available. This work presents a comparison of regression tree models using different source digital elevation models (DEMs) and different combinations of independent variables. Different residual interpolation techniques are also compared. The analysis was performed in the 19.1 km2 Tokopah Basin, located in the southern Sierra Nevada of California. Snow depth, the dependent variable of the statistical models, was derived from three snow surveys (April, May and June 1997), with an average of 328 depth measurements per survey. Estimates of distributed SWE were derived from the product of the snow depth surfaces, the average snow density (54 measurements on average) and the fractional snow covered area (obtained from the Landsat Thematic Mapper and the Airborne Visible/Infrared Imaging Spectrometer). Independent variables derived from the standard US Geological Survey DEM yielded the lowest overall model deviance and lowest error in snow depth prediction. Simulations using the Shuttle Radar Topography Mission DEM and the National Elevation Dataset DEM were improved when northness was substituted for solar radiation in five of six cases. Co-kriging with maximum upwind slope and elevation proved to be the best method for distributing residuals for April and June, respectively. Inverse distance weighting was the best residual distribution method for May. Copyright © 2004 John Wiley & Sons, Ltd.

Numerous methods have been used in the spatial prediction of soil salinity. However, the most suitable method is still unknown in arid irrigation regions. In this paper, 78 locations were sampled in salt-affected land caused by irrigation in an arid area in northern China. The geostatistical characteristics of the soil pH, Sodium Adsorption Ratio (SAR), Total Salt Content (TSC), and Soil Organic Matter (SOM) of the surface (0–20 cm) and subsurface (20–40 cm) layers were analyzed. The abilities of the Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and CoKriging (CK) interpolation methods were compared, and the Root Mean Square Error (RMSE) was used to justify the results of the methods. The results showed that the spatial distributions of the soil properties obtained using the different interpolation methods were similar. However, the surface layer exhibits more spatial heterogeneity than the subsurface layer. Based on the RSME, the nugget/sill value and range significantly affected which method was the most suitable. Lower nugget/sill values and lower ranges can be fitted using the IDW method, but higher nugget/sill values and higher ranges can be fitted using the OK method. These results provide a valuable reference for the prediction of soil salinity.

During the development of uranium deposits that use in-situ leaching extraction method, mineralogical and lithological structure of sub terrain media remains unknown and is limited to the data along the wells. In order to optimize the development process, the scheme of geotechnological polygon should be positioned by taking into account lithological and mineralogical characteristics of the deposit. Given article describes results of modeling of lithological and mineralogical structure of uranium deposit by using inverse distance weighting and kriging methods, that are widely used in oil and gas industry. These algorithms are part of interpolation module of geotechnological simulator software that was developed and integrated to the Institute of High Technology (KazAtomProm, Kazakhstan) for the purpose of optimization of the processes of uranium deposits development and production. The results show that these two methods can be practically used in Kazakhstan’s uranium industry and the comparison show that values of uranium concentration, permeability coefficient and lithological rock type provided by kriging algorithm are more reliable and closer as compared with other method when applied on the uranium deposit. The developed software that focuses on uranium deposits would eventually reduce costs of Kazakhstan’s mines related to purchasing of costly CAD systems and drilling expensive exploration wells.

Variable Annuity (VA) products expose insurance companies to considerable risk becauseof the guarantees they provide to buyers of these products. Managing and hedging these risks requireinsurers to find the values of key risk metrics for a large portfolio of VA products. In practice, manycompanies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations arecomputationally demanding, forcing insurance companies to invest hundreds of thousands of dollars incomputational infrastructure per year. Moreover, existing academic methodologies are focused on fairvaluation of a single VA contract, exploiting ideas in option theory and regression. In most cases, thecomputational complexity of these methods surpasses the computational requirements of MC simulations.Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In thispaper, we present a framework for valuing such portfolios based on spatial interpolation. We providea comprehensive study of this framework and compare existing interpolation schemes. Our numericalresults show superior performance, in terms of both computational effciency and accuracy, for thesemethods compared to nested MC simulations. We also present insights into the challenge of findingan effective interpolation scheme in this framework, and suggest guidelines that help us build a fullyautomated scheme that is effcient and accurate.

The aim of this study was to evaluate the spatial distribution of soil infiltration using geostatistics methods in a regional scale on 400 hectares of Mansour Abad Plain, in Larestan region, Fars Province. Sampling and parameters measurement were done for 78 points in a regular grid with a distance of 100*100 meters; for these variables, the best variogram model between linear, exponential, Gaussian and spherical models with the highest R2 and the lowest error was determined using GS+ and ArcGIS software. In this study, soil infiltration (cm/min) using the double ring method and some other soil properties including soil electrical conductivity (dS/m), pH, saturation percentage (%SP), particle size percentage (sand, silt and clay), and calcium (meq/lit), magnesium (meq/lit), sodium (meq/lit) were measured and determined. The spatial distribution of Kostiakov and Philip models parameters and theri zoning were determined using the geostatistic method. The results showed that, among different soil properties, the final infiltration rate had a high degree of variability in the study area, and the decision was based on the usual averaging methods, which could have a lot of error. Among applied infiltration models, Kostiakov model and Philip model were the best empirical and physical infiltratin models, respectively, in the studied area. The best semivariogram model for the steady state infiltration rate was Philip model, with the coeficients of S and A, and a coefficient of Kostiakove model was gaussian; for the b coefficient, Kostiakove model was exponential. Spatial structure of the final infiltration rate, a and b coefficients of Kostiakove model, and S and A coefficients of the Philip model, was strong. The best interpolation method for the final infiltration rate was cokriging with the cofactor of silt percentage, for the S coefficient of Philip model was inverse distance weighting (IDW); for a and b coefficients of Kostiakove model, kriging and IDW were suitable, respectively. [ABSTRACT FROM AUTHOR]

Abstract Model developments to assess different air pollution exposures within cities are still a key challenge in environmental epidemiology. Background air pollution is a long-term resident and low-level concentration pollution difficult to quantify, and to which population is chronically exposed. In this study, hourly time series of four key air pollutants were analysed using Hidden Markov Models to estimate the exposure to background pollution in Madrid, from 2001 to 2017. Using these estimates, its spatial distribution was later analysed after combining the interpolation results of ordinary kriging and inverse distance weighting. The ratio of ambient to background pollution differs according to the pollutant studied but is estimated to be on average about six to one. This methodology is proposed not only to describe the temporal and spatial variability of this complex exposure, but also to be used as input in new modelling approaches of air pollution in urban areas. Highlights • Background air pollution represents a low and long-term exposure to pollution to which population is chronically exposed. • This fraction of air pollution was studied at temporal and spatial scales in Madrid, from 2001 to 2017. • Applied models provide a robust approach for the complex estimation of background air pollution. • The combination of these models with other modelling approaches or for studying other forms of pollution is suggested. [ABSTRACT FROM AUTHOR]

Spatial analysis of hydrological data often requires the interpolation of a variable from point samples. Commonly used methods for solving this problem include Inverse Distance Weighting (IDW) and Kriging (KG). IDW is easily extensible, has a competitive computational cost with respect to KG, hence it is usually preferred for this task. This paper proposes the optimization of finding the IDW parameter using a nature-inspired metaheuristic, namely Particle Swarm Optimization (PSO). The performance of the improved algorithm is evaluated in a complex scenario and benchmarked against the KG algorithm for 51 precipitation series from the Dobrogea region (Romania). Apart from facilitating the process of applying IDW, the PSO implementation for Optimizing IDW (OIDW) is computationally lighter than the traditional IDW approach. Compared to Kriging, OIDW is straightforward to be implemented and does not require the difficult process of identification of the most appropriate variogram for the given data.

Knowledge of the spatial distribution of soil properties is the major issues in identifying, program planning, management and utilization of soil and water resources. This study was carried out to investigate the spatial variability of some important soil physical quality indices including sand, silt, clay, mean weight diameter of aggregates (MWD), organic carbon (OC), saturated hydraulic conductivity (Ks), saturated water content (θs) and bulk density (Db) in the three adjacent land uses i.e. forest, agriculture and range land located at Fandoghlou region of Ardabil. Totally, 100 soil samples were systematically (100 × 100 m grade) taken from 0-15 cm depth in spring 2013. At first, the accuracy of Kriging and inverse distance weighting (IDW) geostatisticaly methods in mapping of studied parameters was evaluated then the final map was presented. The values of nugget effect to sill ratio for clay, sand and silt were 0.5, 0.47 and 0.49, respectively so these parameters have an average spatial structure. The values of above mentioned ratio for OC, Db, θs, Ks, and MWD were obtained 0.002, 0.014, 0.0007, 0.05 and 0.008, respectively, indicating strong spatial structure. According to the R2 criteria, Kriging method in estimating clay, sand and silt and IDW method in estimating MWD, OC, Ks ،θs and Db had the highest accuracy. The final map indicated that forest land had higher OC, MWD and Ks and lower Db compared with agriculture and range land. The results of this research showed that soil physical quality of the studied region in agriculture and range land uses was lower than forest lands.

The objective of this study is estimating the groundwater quality for Konya city center and mapping their spatial variation in terms of suitability for drinking purposes, about 184 groundwater wells data had been taken from Konya city municipality during 2014 for Konya city center that involving pH, electrical conductivity (EC), Turbidity, calcium (Ca2+), magnesium (Mg2+), chloride (Cl-), sulphate (SO4 2-), nitrate (NO3 -), total alkalinity (TA) and total hardness (TH), and analyzed with reference to the World Health Organization (WHO) limits and (TS266) Turkish Standards, The geographic information system-based spatial distribution maps of different major parameters had been created by testing Geostatistical analyses within ArcGIS version 10.5 environment, the analyzed data was validated by the best-fitted models. The WQI values of the study area were found in the range of 27.28 and 72.99 that classified between good and poor water quality, about 93.413% of the total groundwater samples fall in the suitable limited for drinking water as good water quality, whereas 6.587% of the total groundwater samples get poor water quality. [ABSTRACT FROM AUTHOR]

In this paper, we show the relationship between two seemingly unrelated approximation techniques. On the one hand, a certain class of Gaussian process-based interpolation methods, and on the other hand inverse distance weighting, which has been developed in the context of spatial analysis where there is often a need for interpolating from irregularly spaced data to produce a continuous surface. We develop a generalization of inverse distance weighting and show that it is equivalent to the approximation provided by the class of Gaussian process-based interpolation methods. The equivalence is established via an elegant application of Riesz representation theorem concerning the dual of a Hilbert space. It is thus demonstrated how a classical theorem in linear algebra connects two disparate domains. [ABSTRACT FROM AUTHOR]

A variety of spatially continuous rainfall products are available but little evaluation of their accuracy has been published for areas with high spatial variability in rainfall. Five gridded rainfall products (PRISM, RTMA, and the interpolated Florida Automated Weather Network, FAWN, rainfall layers based on three interpolated methods) were assessed for Florida State. Point-to-pixel and pixel-to-pixel comparisons were performed to compare the five products. On average, the PRISM and RTMA products resulted in a better fit with the daily FAWN rainfall datasets, while FAWN-based interpolated products resulted in a better fit with the monthly FAWN rainfall datasets based on point-to-pixel analysis. Inverse distance weighting and ordinary kriging methods performed slightly better than the thin plate spline method in predicting daily rainfall. In general, monthly and seasonal rainfall amounts from PRISM and RTMA products were higher and lower, respectively, than reference rainfall amounts from FAWN gauge stations and FAWN-based interpolated products. [ABSTRACT FROM AUTHOR]

Spatial interpolation of fire weather variables from station data allow fire danger indices to be mapped continuously across the landscape. This information is crucial to fire management agencies, particularly in areas where weather data are sparse. We compare the performance of several standard interpolation methods (inverse distance weighting, spline, and geostatistical interpolation methods) for estimating output from the Canadian Fire Weather Index (FWI) system at unmonitored locations. We find that geostatistical methods (kriging) generally outperform the other methods, particularly when elevation is used as a covariate. We also find that interpolation of the input meteorological variables and the previous day's moisture codes to unmonitored locations followed by calculation of the FWI output variables is preferable to first calculating the FWI output variables and then interpolating, in contrast to previous studies. Alternatively, when the previous day's moisture codes are estimated from interpolated weather, rather than directly interpolated, errors can accumulate and become large. This effect is particularly evident for the duff moisture code and drought moisture code due to their significant autocorrelation. [ABSTRACT FROM AUTHOR]