Aiming for the Optimum: Examining Complex Relationships Between Sampling Regime, Sampling Density and Landscape Complexity to Accurately Model Resource Availability

Abstract Context Obtaining accurate maps of landscape features often requires intensive spatial sampling and interpolation. The data required to generate reliable interpolated maps varies with spatial scale and landscape heterogeneity. However, there has been no rigorous examination of sampling density relative to landscape characteristics and interpolation methods.ObjectivesOur objective was to characterize the 3-way relationship among sampling density, interpolation method, and landscape heterogeneity on interpolation accuracy in simulated and in situ landscapes. MethodsWe simulated landscapes of variable heterogeneity and sampled at increasing densities using both systematic and random strategies. We applied each of three local interpolation methods: Inverse Distance Weighting, Universal Kriging, and Nearest Neighbor — to the sampled data and estimated accuracy (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 All interpolation methods and sampling strategies resulted in similar accuracy; however, low heterogeneity yielded the highest R2 values at high sampling densities. In situ results showed that Universal Kriging performed best with systematic sampling, and inverse distance weighting with random sampling. Heterogeneity decreased with resolution, which increased accuracy of all interpolation methods. Landscape heterogeneity had the greatest effect on accuracy.ConclusionsHeterogeneity of the original landscape is the most significant factor in determining the accuracy 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.

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Interpolation of Small Datasets in the Sandstone Hydrocarbon Reservoirs, Case Study of the Sava Depression, Croatia

Geosciences ◽

10.3390/geosciences9050201 ◽

2019 ◽

Vol 9 (5) ◽

pp. 201 ◽

Cited By ~ 3

Author(s):

Tomislav Malvić ◽

Josip Ivšinović ◽

Josipa Velić ◽

Rajna Rajić

Keyword(s):

Inverse Distance Weighting ◽

Challenging Problem ◽

Interpolation Methods ◽

Distance Weighting ◽

Hydrocarbon Fields ◽

Northern Croatia ◽

First Time ◽

Inverse Distance ◽

Selection Of

The interpolation of small datasets is challenging problem regarding the selection of interpolation methods and type of datasets. Here, for such analysis, the analysed data was taken in two hydrocarbon fields (“A” and “B”), located in the western part of the Sava Depression (in Northern Croatia). The selected reservoirs “L” (in the “A” Field) and “K” (“B”) are of Lower Pontian (Upper Miocene) age and belong to the Kloštar-Ivanić Formation. Due to strong tectonics, there are numerous tectonic blocks, each sampled with only a few wells. We selected two variables for interpolation—reservoirs permeabilities and injected volumes of field water. The following interpolation methods are described, compared and applied: Nearest Neighbourhood, Natural Neighbour (for the first time in the Sava Depression) and Inverse Distance Weighting. The last one has been recommended as the most appropriate in this study. Also, the presented research can be repeated in similar clastic environments at the same level hydrocarbon of exploration.

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EVALUATION OF SOIL GEOCHEMISTRY DATA OF CANCA (GÜMÜŞHANE-NE TURKEY) BY PROCESSING INVERSE DISTANCE WEIGHTING AND KRIGING INTERPOLATION METHODS-FIRST FINDINGS

Bulletin Of The Mineral Research and Exploration ◽

10.19111/bulletinofmre.430531 ◽

2018 ◽

pp. 10-20

Author(s):

Alaaddin VURAL

Keyword(s):

Inverse Distance Weighting ◽

Kriging Interpolation ◽

Soil Geochemistry ◽

Interpolation Methods ◽

Distance Weighting ◽

Inverse Distance

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Application of the Modified Shepard’s Method (MSM): A Case Study with the Interpolation of Neogene Reservoir Variables in Northern Croatia

Stats ◽

10.3390/stats3010007 ◽

2020 ◽

Vol 3 (1) ◽

pp. 68-83 ◽

Cited By ~ 1

Author(s):

Tomislav Malvić ◽

Josip Ivšinović ◽

Josipa Velić ◽

Jasenka Sremac ◽

Uroš Barudžija

Keyword(s):

Cross Validation ◽

Statistical Properties ◽

Inverse Distance Weighting ◽

Geological Mapping ◽

Interpolation Methods ◽

Geometrical Features ◽

Distance Weighting ◽

Northern Croatia ◽

Inverse Distance

Interpolation is a procedure that depends on the spatial and/or statistical properties of the analysed variable(s). It is a particularly challenging task for small datasets, such as in those with less than 20 points of data. This problem is common in subsurface geological mapping, i.e., in cases where the data is taken solely from wells. Successful solutions of such mapping problems depend on interpolation methods designed primarily for small datasets and the datasets themselves. Here, we compare two methods, Inverse Distance Weighting and the Modified Shepard’s Method, and apply them to three variables (porosity, permeability, and thickness) measured in the Neogene sandstone hydrocarbon reservoirs (northern Croatia). The results show that cross-validation itself will not provide appropriate map selection, but, in combination with geometrical features, it can help experts eliminate the solutions with low-probable structures/shapes. The Golden Software licensed program Surfer 15 was used for the interpolations in this study.

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Application of Modified Shepard's Method (MSM) case study with interpolation of Neogene reservoirs variables in the Northern Croatia

10.20944/preprints201912.0129.v1 ◽

2019 ◽

Author(s):

Tomislav Malvić ◽

Josip Ivšinović ◽

Josipa Velić ◽

Jasenka Sremac ◽

Uroš Barudžija

Keyword(s):

Cross Validation ◽

Statistical Properties ◽

Inverse Distance Weighting ◽

Geological Mapping ◽

Interpolation Methods ◽

Geometrical Features ◽

Distance Weighting ◽

Northern Croatia ◽

Inverse Distance

Interpolation is procedure that depends on spatial and/or statistical properties of analysed variable(s). It is special challenging task for data that included low number of samples, like dataset with less than 20 data. This problem is especially emphasized in the subsurface geological mapping, i.e. in the cases where data are taken solely from wells. Successful solutions of such mapping problems ask for knowledge about interpolation methods designed primarily for small datasets and dataset itself. Here are compared two methods, namely Inverse Distance Weighting and Modified Shepard’s Method, applied for three variables (porosity, permeability, thickness) measured in the Neogene sandstone hydrocarbon reservoirs (Northern Croatia). The results showed that pure cross-validation is not enough condition for appropriate map selection, but also geometrical features need to be considered, for datasets with less than 20 points.

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Ordinary kriging vs inverse distance weighting: spatial interpolation of the sessile community of Madagascar reef, Gulf of Mexico

PeerJ ◽

10.7717/peerj.4078 ◽

2017 ◽

Vol 5 ◽

pp. e4078 ◽

Cited By ~ 9

Author(s):

Salvador Zarco-Perello ◽

Nuno Simões

Keyword(s):

Remote Sensing ◽

Gulf Of Mexico ◽

Spatial Variability ◽

Ordinary Kriging ◽

Spatial Interpolation ◽

Prediction Errors ◽

Interpolation Methods ◽

Distance Weighting ◽

Inverse Distance

Information about the distribution and abundance of the habitat-forming sessile organisms in marine ecosystems is of great importance for conservation and natural resource managers. Spatial interpolation methodologies can be useful to generate this information from in situ sampling points, especially in circumstances where remote sensing methodologies cannot be applied due to small-scale spatial variability of the natural communities and low light penetration in the water column. Interpolation methods are widely used in environmental sciences; however, published studies using these methodologies in coral reef science are scarce. We compared the accuracy of the two most commonly used interpolation methods in all disciplines, inverse distance weighting (IDW) and ordinary kriging (OK), to predict the distribution and abundance of hard corals, octocorals, macroalgae, sponges and zoantharians and identify hotspots of these habitat-forming organisms using data sampled at three different spatial scales (5, 10 and 20 m) in Madagascar reef, Gulf of Mexico. The deeper sandy environments of the leeward and windward regions of Madagascar reef were dominated by macroalgae and seconded by octocorals. However, the shallow rocky environments of the reef crest had the highest richness of habitat-forming groups of organisms; here, we registered high abundances of octocorals and macroalgae, with sponges, Millepora alcicornis and zoantharians dominating in some patches, creating high levels of habitat heterogeneity. IDW and OK generated similar maps of distribution for all the taxa; however, cross-validation tests showed that IDW outperformed OK in the prediction of their abundances. When the sampling distance was at 20 m, both interpolation techniques performed poorly, but as the sampling was done at shorter distances prediction accuracies increased, especially for IDW. OK had higher mean prediction errors and failed to correctly interpolate the highest abundance values measured in situ, except for macroalgae, whereas IDW had lower mean prediction errors and high correlations between predicted and measured values in all cases when sampling was every 5 m. The accurate spatial interpolations created using IDW allowed us to see the spatial variability of each taxa at a biological and spatial resolution that remote sensing would not have been able to produce. Our study sets the basis for further research projects and conservation management in Madagascar reef and encourages similar studies in the region and other parts of the world where remote sensing technologies are not suitable for use.

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Assessment of Ordinary Kriging and Inverse Distance Weighting Methods for Modeling Chromium and Cadmium Soil Pollution in E-Waste Sites in Douala, Cameroon

Journal of Health and Pollution ◽

10.5696/2156-9614-10.26.200605 ◽

2020 ◽

Vol 10 (26) ◽

pp. 200605

Author(s):

Romaric Emmanuel Ouabo ◽

Abimbola Y. Sangodoyin ◽

Mary B. Ogundiran

Keyword(s):

Urban Areas ◽

Ordinary Kriging ◽

Cross Validation ◽

Interpolation Method ◽

Waste Recycling ◽

Inverse Distance Weighting ◽

P Value ◽

Interpolation Methods ◽

Distance Weighting ◽

Inverse Distance

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

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Assessment of Spatial Prediction Techniques Accuracy for Elevation Determination in Akure South Local Government, Ondo State

European Journal of Engineering Research and Science ◽

10.24018/ejers.2020.5.5.1805 ◽

2020 ◽

Vol 5 (5) ◽

pp. 550-553

Author(s):

Victor Ayodele Ijaware ◽

Adebayo T. Adeboye

Keyword(s):

Polynomial Interpolation ◽

Inverse Distance Weighting ◽

Universal Kriging ◽

Empirical Bayesian ◽

Bayesian Kriging ◽

Empirical Bayesian Kriging ◽

Local Polynomial ◽

Distance Weighting ◽

Elevation Data ◽

Inverse Distance

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) is a cooperative effort between NASA and Japan's Ministry of Economy Trade and Industry (METI), with the collaboration of scientific and industry organizations in both countries. The ASTER instrument provides a more robust remote sensing imaging capability when compared to the older Landsat Thematic Mapper. This paper deals with the accuracy assessment of elevation data obtained using ASTER from each of the eleven (11) selected extrapolation/interpolation algorithms: Inverse Distance Weighting, Natural Neighbor, Spline Regular, Spline Tension, Universal Kriging, Empirical Bayesian Kriging, Topo to Raster, global (trend surface), local polynomial, kernel interpolation with barriers and radial basis functions in Digital Elevation Model (DEM) surface creation. The data were compared with reference to ground control points of differential GPS measurements in the study area. The error statistics were generated between DGPS measurements and Extracted elevation data from each selected interpolation method. It was observed that Spline Regular Interpolation shown the best overall accuracy of ±11.520m when elevation data extracted from Inverse distance weighting, Natural Neighbour, Spline T, Topo to Raster, Universal Kriging, Empirical Bayesian kriging, Global polynomial interpolation (GPI), local polynomial interpolation (LPI), Radial basis function and Kernel interpolation of ±15.170, ±14.340, ±12.336, ±13.551, ±14.707, ±13.711, ±15.363, ±13.964, ±13.590 and ±15.376 respectively when compared with elevation values from GPS method. The study recommends capacity building in the form of workshop, training, and flexible integration of point elevation data to DEM.

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Interpolation of Small Datasets in the Sandstone Hydrocarbon Reservoirs, Case Study from the Sava Depression, Croatia

10.20944/preprints201902.0260.v1 ◽

2019 ◽

Author(s):

Tomislav Malvić ◽

Josip Ivšinović ◽

Josipa Velić ◽

Rajna Rajić

Keyword(s):

Laboratory Tests ◽

Secondary Phase ◽

Inverse Distance Weighting ◽

Tectonic Block ◽

Interpolation Methods ◽

Distance Weighting ◽

Hydrocarbon Fields ◽

First Time ◽

Inverse Distance

Here are analysed data taken in two hydrocarbon fields ("A" and "B"), located in the western part of Sava Depression (North Croatia). They are in the secondary phase of production. The selected reservoirs "L" (in the “A” Field) and "K" (“B”) are of the Lower Pontian (Upper Miocene) age and belong to Klo&scaron;tar-Ivanić Formation. Due to strong tectonics, there are numerous tectonic block, relatively rarely sampled with well and laboratory tests. Here are selected two variables for interpolation - reservoirs permeabilities and the injected volumes of field water. The following interpolation methods are described, compared and applied: Nearest Neighbourhood, Natural Neighbour (the first time in the Sava Depression) and Inverse Distance Weighting. The last one has been proven as the most appropriate for datasets with size lower than 20 points.

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Comparison of Different Interpolation Methods for Prediction of Soil Salinity in Arid Irrigation Region in Northern China

Agronomy ◽

10.3390/agronomy11081535 ◽

2021 ◽

Vol 11 (8) ◽

pp. 1535

Author(s):

Tonggang Fu ◽

Hui Gao ◽

Jintong Liu

Keyword(s):

Soil Salinity ◽

Subsurface Layer ◽

Salt Content ◽

Spatial Prediction ◽

Northern China ◽

Sodium Adsorption Ratio ◽

Interpolation Methods ◽

Distance Weighting ◽

Total Salt Content ◽

Inverse Distance

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.

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