Inverse Distance Weight

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

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The influence of distance weight on the inverse distance weighted method for ore-grade estimation

Scientific Reports ◽

10.1038/s41598-021-82227-y ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Zhan-Ning Liu ◽

Xiao-Yan Yu ◽

Li-Feng Jia ◽

Yuan-Sheng Wang ◽

Yu-Chen Song ◽

...

Keyword(s):

Estimation Accuracy ◽

Block Model ◽

Minkowski Distance ◽

Inverse Distance Weighted ◽

Grade Estimation ◽

M 10 ◽

Weight Calculation ◽

Distance Weighted ◽

Inverse Distance ◽

Ore Grade

AbstractIn order to study the influence of distance weight on ore-grade estimation, the inverse distance weighted (IDW) is used to estimate the Ni grade and MgO grade of serpentinite ore based on a three-dimensional ore body model and related block models. Manhattan distance, Euclidean distance, Chebyshev distance, and multiple forms of the Minkowski distance are used to calculate distance weight of IDW. Results show that using the Minkowski distance for the distance weight calculation is feasible. The law of the estimated results along with the distance weight is given. The study expands the distance weight calculation method in the IDW method, and a new method for improving estimation accuracy is given. Researchers can choose different weight calculation methods according to their needs. In this study, the estimated effect is best when the power of the Minkowski distance is 3 for a 10 m × 10 m × 10 m block model. For a 20 m × 20 m × 20 m block model, the estimated effect is best when the power of the Minkowski distance is 9.

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A simple approximation for inverse distance with application to the one‐center and two‐center Coulomb integrals

The Journal of Chemical Physics ◽

10.1063/1.449258 ◽

1985 ◽

Vol 83 (5) ◽

pp. 2616-2618 ◽

Cited By ~ 2

Author(s):

S. Noor Mohammad

Keyword(s):

Simple Approximation ◽

The One ◽

Coulomb Integrals ◽

Inverse Distance

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Analysis of Proximity Consequences of Coil Windings in Electromagnetic Forming

Journal of Manufacturing and Materials Processing ◽

10.3390/jmmp5020045 ◽

2021 ◽

Vol 5 (2) ◽

pp. 45

Author(s):

Siddhant Prakash Goyal ◽

Mohammadjavad Lashkari ◽

Awab Elsayed ◽

Marlon Hahn ◽

A. Erman Tekkaya

Keyword(s):

Proximity Effect ◽

Experimental Methods ◽

Electromagnetic Forming ◽

Velocity Measurements ◽

Local Curvature ◽

Metal Parts ◽

Sheet Metal Parts ◽

Geometrical Features ◽

Physical Phenomena ◽

Inverse Distance

Multiturn coils are required for manufacturing sheet metal parts with varying depths and special geometrical features using electromagnetic forming (EMF). Due to close coil turns, the physical phenomena of the proximity effect and Lorentz forces between the parallel coil windings are observed. This work attempts to investigate the mechanical consequences of these phenomena using numerical and experimental methods. A numerical model was developed in LS-DYNA. It was validated using experimental post-mortem strain and laser-based velocity measurements after and during the experiments, respectively. It was observed that the proximity effect in the parallel conductors led to current density localization at the closest or furthest ends of the conductor cross-section and high local curvature of the formed sheet. Further analysis of the forces between two coil windings explained the departure from the “inverse-distance” rule observed in the literature. Finally, some measures to prevent or reduce undesired coil deformation are provided.

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A Multimethod Analysis for Average Annual Precipitation Mapping in the Khorasan Razavi Province (Northeastern Iran)

Atmosphere ◽

10.3390/atmos12050592 ◽

2021 ◽

Vol 12 (5) ◽

pp. 592

Author(s):

Mehdi Aalijahan ◽

Azra Khosravichenar

Keyword(s):

Regional Planning ◽

Interpolation Method ◽

Absolute Error ◽

Rain Gauge ◽

Annual Precipitation ◽

Coefficient Of Determination ◽

Distance Weighting ◽

Average Annual Precipitation ◽

Inverse Distance

The spatial distribution of precipitation is one of the most important climatic variables used in geographic and environmental studies. However, when there is a lack of full coverage of meteorological stations, precipitation estimations are necessary to interpolate precipitation for larger areas. The purpose of this research was to find the best interpolation method for precipitation mapping in the partly densely populated Khorasan Razavi province of northeastern Iran. To achieve this, we compared five methods by applying average precipitation data from 97 rain gauge stations in that province for a period of 20 years (1994–2014): Inverse Distance Weighting, Radial Basis Functions (Completely Regularized Spline, Spline with Tension, Multiquadric, Inverse Multiquadric, Thin Plate Spline), Kriging (Simple, Ordinary, Universal), Co-Kriging (Simple, Ordinary, Universal) with an auxiliary elevation parameter, and non-linear Regression. Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and the Coefficient of Determination (R2) were used to determine the best-performing method of precipitation interpolation. Our study shows that Ordinary Co-Kriging with an auxiliary elevation parameter was the best method for determining the distribution of annual precipitation for this region, showing the highest coefficient of determination of 0.46% between estimated and observed values. Therefore, the application of this method of precipitation mapping would form a mandatory base for regional planning and policy making in the arid to semi-arid Khorasan Razavi province during the future.

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Spatial Distribution of Soil Nutrients in Farmland in a Hilly Region of the Pearl River Delta in China Based on Geostatistics and the Inverse Distance Weighting Method

Agriculture ◽

10.3390/agriculture11010050 ◽

2021 ◽

Vol 11 (1) ◽

pp. 50

Author(s):

Rumi Wang ◽

Runyan Zou ◽

Jianmei Liu ◽

Luo Liu ◽

Yueming Hu

Keyword(s):

Spatial Distribution ◽

Pearl River Delta ◽

Pearl River ◽

Weighting Method ◽

Farmland Protection ◽

The Pearl River Delta ◽

Hilly Region ◽

Distance Weighting ◽

The Pearl River ◽

Inverse Distance

Soil nutrients are essential factors that reflect farmland quality. Nitrogen, phosphorus, and potassium are essential elements for plants, while silicon is considered a “quasi-essential” element. This study investigated the spatial distribution of plant nutrients in soil in a hilly region of the Pearl River Delta in China. A total of 201 soil samples were collected from farmland topsoil (0–20 cm) for the analysis of total nitrogen (TN), available phosphorus (AP), available potassium (AK), and available silicon (ASi). The coefficients of variation ranged from 47.88% to 76.91%. The NSRs of TN, AP, AK, and ASi were 0.15, 0. 07, 0.12, and 0.13, respectively. The NSRs varied from 0.02 to 0.20. All variables exhibited weak spatial dependence (R2 < 0.5), except for TN (R2 = 0.701). After comparing the prediction accuracy of the different methods, we used the inverse distance weighting method to analyze the spatial distribution of plant nutrients in soil. The uniform spatial distribution of AK, TN overall showed a trend of increasing from northeast to southwest, and the overall spatial distribution of AP and ASi showed that the northeast was higher than the southwest. This study provides support for the delimitation of basic farmland protection areas, the formulation of land use spatial planning, and the formulation of accurate farmland protection policies.

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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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A Few GIS Clarifications on Tornado Density Mapping

Journal of Applied Meteorology and Climatology ◽

10.1175/jamc-d-15-0141.1 ◽

2016 ◽

Vol 55 (2) ◽

pp. 283-296 ◽

Cited By ~ 9

Author(s):

Yongxin Deng ◽

Brendan Wallace ◽

Derek Maassen ◽

Johnathan Werner

Keyword(s):

Uncertainty Modeling ◽

The United States ◽

Distance Decay ◽

Geographical Information ◽

Density Mapping ◽

Probability Mapping ◽

Density Maps ◽

Distance Weighted ◽

Inverse Distance ◽

Eastern Half

AbstractA geographical information system (GIS) perspective is taken to examine conceptual and methodological complications present in tornado density and probability mapping. Tornado density is defined as the inverse-distance-weighted count of tornado touchdown points or tornado-affected cells within a neighborhood area. The paper first adds a few geographic elements into the tornado definition and then characterizes tornado density as a density field in GIS that depends on predefined, modifiable areas to exist. Tornado density is therefore conceptually distinguished from both individual tornadoes and tornado probability. Three factors are identified to be vital in tornado density mapping: the neighborhood size, the distance decay function, and the choice of tornado properties. Correspondingly, 12 neighborhood sizes ranging from 20 to 360 km are tested, four distance decay functions are compared, and two tornado properties—tornado touchdown locations and pathlengths—are separately incorporated in mapping. GIS interpretations, clarifications, and demonstrations are provided for these factors to reach a thorough understanding of how the factors function and affect the resultant tornado density maps. Historical tornado data of the eastern half of the United States from 1973 to 2013 are used in these demonstrations. Uncertainty and propagation analyses are recommended for future tornado density and probability mapping, and a Monte Carlo simulation using tornado pathlength data is conducted as an example of uncertainty modeling. In all, tornado density mapping is diagnosed as a largely subjective activity, and the mapper needs to make multiple choices according to the mapping purpose, scale, and the involved tornado record data.

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