Statistical analysis of the best GIS interpolation method for bearing capacity estimation in An-Najaf City, Iraq

AbstractThe presence of an economical solution to predict soil behaviour is essential for new construction areas. This paper aims to investigate the ultimate interpolation method for predicting the soil bearing capacity of An-Najaf city-Iraq based on field investigation information. Firstly, the engineering bearing capacity was calculated based on the in-site N-SPT values using dynamic loading for 464 boreholes with depths of 0–2 m, using the Meyerhof formula. The data then were classified and imported to the GIS program to apply the interpolation methods. Four deterministic and two geostatistical interpolation methods were applied to produce six bearing capacity maps. The statistical analyses were performed using two methods: the common cross-validation method by the coefficient of determination (R2) and root mean square error (RMSE), where the results showed that ordinary kriging (OK) is the ultimate method with the least RMSE and highest R2. These results were confusing so, the backward elimination regression (BER) procedure was applied to gain the definite result. The results of BER show that among all the deterministic methods, the IDW is the optimal and most significant interpolation method. The result of geostatistical methods shows that EBK is the best method in our case than the OK method. BER also applied to all six methods and shows that IDW is the ultimate significant method. The results indicate no general ultimate interpolation method for all cases and datasets type; therefore, the statistical analyses must be performed for each case and dataset.

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COMPARAÇÃO ENTRE MÉTODOS DE INTERPOLAÇÃO ESPACIAL PARA A ESTIMATIVA DA DISTRIBUIÇÃO DE PRECIPITAÇÃO NO CEARÁ-BRASIL

Irriga ◽

10.15809/irriga.2020v25n1p131-142 ◽

2020 ◽

Vol 25 (1) ◽

pp. 131-142

Author(s):

Danilo Batista Nogueira ◽

Alexsandro Oliveira Da Silva ◽

Ana Paula Nunes Da Silva

Keyword(s):

Mean Square Error ◽

Pearson Correlation ◽

Performance Criterion ◽

Coefficient Of Determination ◽

Mean Square ◽

Data Set ◽

Semivariogram Model ◽

Interpolation Methods ◽

Geostatistical Methods ◽

Rain Gauges

COMPARAÇÃO ENTRE MÉTODOS DE INTERPOLAÇÃO ESPACIAL PARA A ESTIMATIVA DA DISTRIBUIÇÃO DE PRECIPITAÇÃO NO CEARÁ-BRASIL DANILO BATISTA NOGUEIRA1; ALEXSANDRO OLIVEIRA DA SILVA 2 E ANA PAULA NUNES DA SILVA 3 1 Departamento de Engenharia Agrícola, Universidade Federal do Ceará, Avenida Mister Hull, S/N-Campus do Pici, Centro de Ciências Agrárias, Bloco 804, CEP 60455-760, Fortaleza, Ceará, Brasil, [email protected] 2 Departamento de Engenharia Agrícola, Universidade Federal do Ceará, Avenida Mister Hull, S/N-Campus do Pici, Centro de Ciências Agrárias, Bloco 804, CEP 60455-760, Fortaleza, Ceará, Brasil, [email protected] 3 Departamento de Engenharia Agrícola, Universidade Estadual do Amapá, Avenida Presidente Vargas, N 650, Centro de Ciências Agrárias, CEP 68906-970, Macapá, Amapá, Brasil, [email protected] 1 RESUMO A distribuição espacial de precipitação ainda é largamente representada por métodos geoestatísticos de interpolação e em áreas de semiárido necessita de estudos recorrentes por conta de sua variabilidade temporal e espacial. Diante disto, visando o aperfeiçoamento dos métodos de interpolação e o desenvolvimento de mapas no estado do Ceará, o presente trabalho teve como objetivo analisar a acurácia de cinco métodos de interpolação: Inverso do Quadrado da Distância (IQD), Krigagem com um semivariograma esférico, Krigagem com um semivariograma exponencial, Vizinho natural e Spline regularizada. Para isto foram utilizados dados de precipitação média anual de um período de vinte anos (1991 a 2010) de 252 postos pluviométricos. Como forma de determinação do método mais adequado optou-se pela técnica de validação cruzada como critério de comparação, determinando o erro médio quadrático (RMSE), o coeficiente de determinação (r²), o coeficiente de correlação de Pearson (r), o índice de concordância (d) e o índice de desempenho (c) entre os dados estimados e os dados observados. Os resultados apontam que a interpolação por Krigagem exponencial apresentou critério de desempenho classificado como bom e um menor erro quadrático médio (164,09 mm), mostrando ser esse o interpolador de melhor representatividade espacial para o conjunto de dados. Keywords: geoestatística, postos pluviométricos, variáveis regionalizadas. NOGUEIRA, D. B.; SILVA, A. O.; SILVA, A. P. N. COMPARISON OF SPATIAL INTERPOLATION METHODS FOR THE ESTIMATION OF PRECIPITATION DISTRIBUTION IN CEARÁ -BRAZIL 2 ABSTRACT The spatial distribution of precipitation is still largely represented by geostatistical methods of interpolation and in semiarid areas it requires recurrent studies due to their temporal and spatial variability. Therefore, aiming at the improvement of interpolation methods and the improvement of rainfall maps in the state of Ceará, this study aimed to analyze the accuracy of five interpolation methods: Inverse of Square Distance (ISD), Kriging with a spherical semivariogram model, Kriging with a exponential semivariogram model, Natural neighbor and Spline regularized. For that, data of annual average rainfall of a period of twenty years (1991 to 2010) of 252 rain gauges were used. As a form of evaluation and determination of the most appropriate method, the technique of cross-validation was chosen as the criterion of comparison, determining the root mean square error (RMSE), coefficient of determination (r²), Pearson correlation coefficient (r), concordance index (d) and performance index (c) between the estimated data and the observed data. The results show that the interpolation by exponential Kriging method presented performance criterion classified as good and lower mean square error (164,09), showing that it is the interpolator of better spatial representation for the data set under study. Keywords: statistical, rain gauges, regionalized variables.

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Comparison of Spatial Interpolation Methods for Mapping Daily Air Temperature

10.5194/egusphere-egu21-13970 ◽

2021 ◽

Author(s):

Lasyamayee L Sahoo ◽

Subashisa Dutta

Keyword(s):

Minimum Temperature ◽

Evaluation Method ◽

Heat Waves ◽

Interpolation Method ◽

Climatic Variability ◽

Labour Productivity ◽

The State ◽

Coefficient Of Determination ◽

Maximum Temperature ◽

Interpolation Methods

<p>The sparsely distributed meteorological centers fails to provide enough information regarding spatial patterns. Even at places where dense meteorological stations are available, it is difficult to develop realistic gridded data due to the complex topography and climatic variability. Some of the climate as well as hydrological model require spatially continuous datasets as inputs. It is possible to obtain a continuous surface of raster datasets with the help of interpolation methods where each value is assigned based on surrounding values using specific mathematical formulas. For present study, various interpolation methods, like Inverse distance weighted, ordinary krigging, thin plate smoothing spline; has been compared for maximum and minimum temperature. Error in the interpolated data was analyzed by independent cross validation method, in which measurements like root mean square error (RMSE), mean squared relative error (MSRE), coefficient of determination (r<sup>2</sup>) and coefficient of efficiency (CE) were adopted for performance evaluation. Method with minimum error was chosen for developing the final map. It provides an effective way for mapping the meteorological variables in a topographically diverse region. In this case, an Indian state Odisha is chosen as study area. The state consists of 10 different agro-climatic zones and sees several weather systems across the year. The area suffers with floods, drought, heat waves and costal erosion almost every year with variable intensity. Strong heat waves in summer affect the human health, agriculture, construction efficiency and labour productivity. As three-fourth of the state is filled with mountains and high lands, monitoring network is sparsely distributed. Despite small latitudinal difference, temperature changes considerably with respect to both space and time. Here interpolation method plays a vital role to avoid uncertainty in modelling. Based on the generated maps, vulnerable areas on the basis of maximum temperature in summer and minimum temperature in winter is identified. Several indicators and vulnerability indices has been used.</p>

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Comparison of interpolation methods based on Geographic Information System (GIS) in the spatial distribution of seawater intrusion

Jurnal Natural ◽

10.24815/jn.v20i2.16440 ◽

2020 ◽

Vol 20 (2) ◽

pp. 24-30

Author(s):

MAULINA TANJUNG ◽

SAUMI SYAHREZA ◽

MUHAMMAD RUSDI

Keyword(s):

Electrical Conductivity ◽

Spatial Distribution ◽

Seawater Intrusion ◽

Coastal Area ◽

Polynomial Interpolation ◽

Interpolation Method ◽

Coefficient Of Determination ◽

Interpolation Methods ◽

Empirical Bayesian Kriging ◽

Banda Aceh

The study of monitoring seawater intrusion and groundwater quality in a coastal area needs to be done regularly to prevent the clean water crisis problems in the future. Accurate and reliable interpolation of seawater intrusion over a region is the requirement of an efficient monitoring. In this study, different interpolation methods were investigated and compared to determine the best interpolation method for predicting the spatial distribution of seawater intrusion in the coastal area of Banda Aceh. Groundwater electrical conductivity (EC) was analyzed to identify the contamination of seawater intrusion into the coastal aquifers. Four interpolation methods such as Empirical Bayesian Kriging (EBK), Global Polynomial Interpolation (GPI), Inverse Distance Weighting (IDW), and Local Polynomial Interpolation (LPI), were used to create the spatial distribution of the groundwater electrical conductivity. The accuracy of interpolation methods was evaluated by using a cross-validation technique through the coefficient of determination (R2) and the Root Mean Square Error (RMSE). The results showed that IDW performed the most accurate prediction values and the best surface which were indicated by the least RMSE and the highest R2 value. It can be concluded that IDW interpolation method is the best method for interpolating the groundwater electrical conductivity associated with seawater intrusion in the coastal area of Banda Aceh.

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Filling Missing Data Using Interpolation Methods: Study on the Effect of Fitting Distribution

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.594-595.889 ◽

2013 ◽

Vol 594-595 ◽

pp. 889-895 ◽

Cited By ~ 3

Author(s):

M.N. Noor ◽

A.S. Yahaya ◽

N.A. Ramli ◽

Abdullah Mohd Mustafa Al Bakri

Keyword(s):

Missing Data ◽

Human Error ◽

Goodness Of Fit ◽

Missing Values ◽

Mean Squared Error ◽

Interpolation Method ◽

Coefficient Of Determination ◽

Time Data ◽

Data Set ◽

Interpolation Methods

The presence of missing values in statistical survey data is an important issue to deal with. These data usually contained missing values due to many factors such as machine failures, changes in the siting monitors, routine maintenance and human error. Incomplete data set usually cause bias due to differences between observed and unobserved data. Therefore, it is important to ensure that the data analyzed are of high quality. A straightforward approach to deal with this problem is to ignore the missing data and to discard those incomplete cases from the data set. This approach is generally not valid for time-series prediction, in which the value of a system typically depends on the historical time data of the system. One approach that commonly used for the treatment of this missing item is adoption of imputation technique. This paper discusses three interpolation methods that are linear, quadratic and cubic. A total of 8577 observations of PM10 data for a year were used to compare between the three methods when fitting the Gamma distribution. The goodness-of-fit were obtained using three performance indicators that are mean absolute error (MAE), root mean squared error (RMSE) and coefficient of determination (R2). The results shows that the linear interpolation method provides a very good fit to the data.

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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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Research about Influencing Factor on Interpolation Accuracy in Data Exchange of Fluid-Structure Interaction

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.318.100 ◽

2013 ◽

Vol 318 ◽

pp. 100-107

Author(s):

Zhen Shen ◽

Biao Wang ◽

Hui Yang ◽

Yun Zheng

Keyword(s):

Data Exchange ◽

Shape Function ◽

Interpolation Method ◽

Matching Condition ◽

Optimal Interpolation ◽

Complex Interpolation ◽

Interpolation Function ◽

Interpolation Methods ◽

Interpolation Accuracy ◽

Lower Accuracy

Six kinds of interpolation methods, including projection-shape function method, three-dimensional linear interpolation method, optimal interpolation method, constant volume transformation method and so on, were adoped in the study of interpolation accuracy. From the point of view about the characterization of matching condition of two different grids and interpolation function, the infuencing factor on the interpolation accuracy was studied. The results revealed that different interpolation methods had different interpolation accuracy. The projection-shape function interpolation method had the best effect and the more complex interpolation function had lower accuracy. In many cases, the matching condition of two grids had much greater impact on the interpolation accuracy than the method itself. The error of interpolation method is inevitable, but the error caused by the grid quality could be reduced through efforts.

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Image Interpolation Algorithm Based on Edge Features

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.50-51.564 ◽

2011 ◽

Vol 50-51 ◽

pp. 564-567

Author(s):

Yun Feng Yang ◽

Xiao Guang Wei ◽

Zhi Xun Su

Keyword(s):

Interpolation Method ◽

Spline Interpolation ◽

Weighted Average ◽

Image Interpolation ◽

Interpolation Process ◽

Edge Information ◽

B Spline ◽

Interpolation Methods ◽

Distance Weighted ◽

Edge Features

Image interpolation is used widely in the computer vision. Holding edge information is main problem in the image interpolation. By using bilinear and bicubic B-spline interpolation methods, a novel image interpolation approach was proposed in this paper. Firstly, inverse distance weighted average method was used to reduce image’s noise. Secondly, edge detection operator was used to extract image's edges information. It can help us to select different interpolation methods in the image interpolation process. Finally, we selected bilinear interpolation approach at non-edge regions, and bicubic B-spline interpolation method was used near edges regions. Further more, control vertexes were computed from pixels with calculation formula which has been simplified in the B-spline interpolation process. Experiments showed the interpolated image by the proposed method had good vision results for it could hold image's edge information effectively.

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Interpolation methods for thematic maps of soybean yield and soil chemical attributes

Semina Ciências Agrárias ◽

10.5433/1679-0359.2017v38n2p1059 ◽

2017 ◽

Vol 38 (2) ◽

pp. 1059 ◽

Cited By ~ 1

Author(s):

Nelson Miguel Betzek ◽

Eduardo Godoy de Souza ◽

Claudio Leones Bazzi ◽

Ricardo Sobjak ◽

Vanderlei Artur Bier ◽

...

Keyword(s):

Precision Agriculture ◽

Interpolation Method ◽

Thematic Maps ◽

Relative Deviation ◽

Error Matrix ◽

Soybean Yield ◽

Interpolation Methods ◽

Sample Data ◽

Chemical Attributes ◽

Deviation Coefficient

The application of precision agriculture considers the values of non-sampled places by the interpolation of sample data. The accuracy with which the maps of spatial distribution of yield and the soil attributes are produced in the interpolation process influences their application and utilization. This paper aimed to compare three interpolation methods (inverse of the distance, inverse of the square distance, and ordinary kriging) in the construction of thematic maps of soybean yield and soil chemical attributes. A set of data referred to 55 sampling units for the construction maps of soybean yield and of eight soil chemical attributes, by different interpolation methods. The comparison was made based on the error matrix, by calculating the Kappa and Tau indices, beyond the relative deviation coefficient (RDC). It was noticed that the inverse of the square distance was the interpolator that less influenced the data behavior, and the best interpolation method dependent of the variability of the studied attribute. The kriging and the inverse of the square distance were considered the methods that presented the best results in the interpolation of data.

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A new method for interpolating linear features in aeromagnetic data

Geophysics ◽

10.1190/geo2018-0156.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. JM15-JM24 ◽

Cited By ~ 2

Author(s):

Tomas Naprstek ◽

Richard S. Smith

Keyword(s):

Field Data ◽

Interpolation Method ◽

Source Code ◽

Synthetic Data ◽

Aeromagnetic Data ◽

Derivative Expansion ◽

Linear Features ◽

Interpolation Methods ◽

Minimum Curvature ◽

Linear Nature

When aeromagnetic data are interpolated to make a gridded image, thin linear features can result in “boudinage” or “string of beads” artifacts if the anomalies are at acute angles to the traverse lines. These artifacts are due to the undersampling of these types of features across the flight lines, making it difficult for most interpolation methods to effectively maintain the linear nature of the features without user guidance. The magnetic responses of dikes and dike swarms are typical examples of the type of geologic feature that can cause these artifacts; thus, these features are often difficult to interpret. Many interpretation methods use various enhancements of the gridded data, such as horizontal or vertical derivatives, and these artifacts are often exacerbated by the processing. Therefore, interpolation methods that are free of these artifacts are necessary for advanced interpretation and analysis of thin, linear features. We have developed a new interpolation method that iteratively enhances linear trends across flight lines, ensuring that linear features are evident on the interpolated grid. Using a Taylor derivative expansion and structure tensors allows the method to continually analyze and interpolate data along anisotropic trends, while honoring the original flight line data. We applied this method to synthetic data and field data, which both show improvement over standard bidirectional gridding, minimum curvature, and kriging methods for interpolating thin, linear features at acute angles to the flight lines. These improved results are also apparent in the vertical derivative enhancement of field data. The source code for this method has been made publicly available.

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Experimental Investigation on Anchorage Mechanisms of Self-Locked Anchor under Combined Tension and Shear

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.163-167.3600 ◽

2010 ◽

Vol 163-167 ◽

pp. 3600-3603

Author(s):

Ying Li ◽

Dong Zi Pan ◽

Lian Zhang

Keyword(s):

Experimental Investigation ◽

Bearing Capacity ◽

Fracture Pattern ◽

Ultimate Bearing Capacity ◽

Design Codes ◽

Design Recommendations ◽

Experimental Parameters ◽

Current Design ◽

New Construction ◽

New Type

Self-locked anchor is a new type of underreamed anchor, and which is more and more frequently used in both new construction and structural retrofitting or strengthening projects. Nevertheless, current design codes do not contain suitable design recommendations for these anchors. This study investigates the anchorage mechanisms of self-locked anchor under combined tension and shear loadings. The experimental parameters mainly include anchor diameters (Φ16 and Φ20) and loading angles (0°, 30°, 45°, and 60°). The present results indicate the characters of axial and transverse deformations, the ultimate bearing capacity, the fracture pattern of anchor, and the breakout model of concrete.

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