Search results for: ordinary kriging interpolation

Authors: Nguyen Tien Thanh, Günter Meon

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Precipitation plays a key role in water cycle, defining the local climatic conditions and in ecosystem. It is also an important input parameter for water resources management and hydrologic models. With spatial continuous data, a certainty of discharge predictions or other environmental factors is unquestionably better than without. This is, however, not always willingly available to acquire for a small basin, especially for coastal region in Vietnam due to a low network of meteorological stations (30 stations) on long coast of 3260 km2. Furthermore, available gridded precipitation datasets are not fine enough when applying to hydrologic models. Under conditions of global warming, an application of spatial interpolation methods is a crucial for the climate change impact studies to obtain the spatial continuous data. In recent research projects, although some methods can perform better than others do, no methods draw the best results for all cases. The objective of this paper therefore, is to investigate different spatial interpolation methods for daily precipitation over a small basin (approximately 400 km2) located in coastal region, Southern Vietnam and find out the most efficient interpolation method on this catchment. The five different interpolation methods consisting of cressman, ordinary kriging, regression kriging, dual kriging and inverse distance weighting have been applied to identify the best method for the area of study on the spatio-temporal scale (daily, 10 km x 10 km). A 30-year precipitation database was created and merged into available gridded datasets. Finally, observed changes in constructed precipitation were performed. The results demonstrate that the method of ordinary kriging interpolation is an effective approach to analyze the daily precipitation. The mixed trends of increasing and decreasing monthly, seasonal and annual precipitation have documented at significant levels.

Keywords: interpolation, precipitation, trend, vietnam

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Authors: Abbas Hani, Maryam Jassasizadeh

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The concentrations of Cd, Pb, and Ni were determined from 40 soil samples collected in surface soils of Khark Island. Geostatistic methods and GIS were used to identify heavy metal sources and their spatial pattern. Principal component analysis coupled with correlation between heavy metals showed that level of mentioned heavy metal was lower than the standard level. Then the data obtained from the soil analyzing were studied for the purposes of normal distribution. The best way of interior finding for cadmium and nickel was ordinary kriging and the best way of interpolation of lead was inverse distance weighted. The result of this study help us to understand heavy metals distribution and make decision for remediation of soil pollution.

Keywords: geostatistics, ordinary kriging, heavy metals, GIS, Khark

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Authors: Pengwei Qiao, Sucai Yang, Wenxia Wei

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Soil pollution has become an important issue in China. Accurate spatial distribution prediction of pollutants with interpolation methods is the basis for soil remediation in the site. However, a relatively strong variability of pollutants would decrease the prediction accuracy. Theoretically, partition interpolation can result in accurate prediction results. In order to verify the applicability of partition interpolation for a site, benzo (b) fluoranthene (BbF) in four soil layers was adopted as the research object in this paper. IDW (inverse distance weighting)-, RBF (radial basis function)-and OK (ordinary kriging)-based partition interpolation accuracies were evaluated, and their influential factors were analyzed; then, the uncertainty and applicability of partition interpolation were determined. Three conclusions were drawn. (1) The prediction error of partitioned interpolation decreased by 70% compared to unpartitioned interpolation. (2) Partition interpolation reduced the impact of high CV (coefficient of variation) and high concentration value on the prediction accuracy. (3) The prediction accuracy of IDW-based partition interpolation was higher than that of RBF- and OK-based partition interpolation, and it was suitable for the identification of highly polluted areas at a contaminated site. These results provide a useful method to obtain relatively accurate spatial distribution information of pollutants and to identify highly polluted areas, which is important for soil pollution remediation in the site.

Keywords: accuracy, applicability, partition interpolation, site, soil pollution, uncertainty

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming

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Authors: Lazhar Belkhiri, Ammar Tiri, Lotfi Mouni

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In this research, we analyzed the groundwater quality index in the El Milia plain, Kebir Rhumel Basin, Algeria. Thirty-three groundwater samples were collected from wells in the El Milia plain during April 2015. In this study, pH and electrical conductivity (EC) were conducted at each sampling well. Eight hydrochemical parameters such as calcium (Ca), magnesium (Mg), sodium (Na), potassium (K), chlorid (Cl), sulfate (SO4), bicarbonate (HCO3), and Nnitrate (NO3) were analysed. The entropy water quality index (EWQI) method was employed to evaluate the groundwater quality in the study area. Moran’s I and the ordinary kriging (OK) interpolation technique were used to examine the spatial distribution pattern of the hydrochemical parameters in the groundwater. It was found that the hydrochemical parameters Ca, Cl, and HCO3 showed strong spatial autocorrelation in the El Milia plain, indicating a spatial dependence and clustering of these parameters in the groundwater. The groundwater quality was evaluated using the entropy water quality index (EWQI). The results showed that approximately 86% of the total groundwater samples in the study area fall within the moderate groundwater quality category. The spatial map of the EWQI values indicated an increasing trend from the south-west to the northeast, following the direction of groundwater flow. The highest EWQI values were observed near El Milia city in the center of the plain. This spatial pattern suggests variations in groundwater quality across the study area, with potentially higher risks near the city center. Therefore, the results obtained in this research provide very useful information to decision-makers.

Keywords: entropy water quality index (EWQI), moran’s i, ordinary kriging interpolation, el milia plain

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Authors: Aafaf El Jazouli, Ahmed Barakat, Rida Khellouk

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Mapping of soil degradation is derived from field observations, laboratory measurements, and remote sensing data, integrated quantitative methods to map the spatial characteristics of soil properties at different spatial and temporal scales to provide up-to-date information on the field. Since soil salinity, texture and organic matter play a vital role in assessing topsoil characteristics and soil quality, remote sensing can be considered an effective method for studying these properties. The main objective of this research is to asses soil degradation by combining remote sensing data and laboratory analysis. In order to achieve this goal, the required study of soil samples was taken at 50 locations in the upper basin of Oum Er Rbia in the Middle Atlas in Morocco. These samples were dried, sieved to 2 mm and analyzed in the laboratory. Landsat 8 OLI imagery was analyzed using physical or empirical methods to derive soil properties. In addition, remote sensing can serve as a supporting data source. Deterministic potential (Spline and Inverse Distance weighting) and probabilistic interpolation methods (ordinary kriging and universal kriging) were used to produce maps of each grain size class and soil properties using GIS software. As a result, a correlation was found between soil texture and soil organic matter content. This approach developed in ongoing research will improve the prospects for the use of remote sensing data for mapping soil degradation in arid and semi-arid environments.

Keywords: Soil degradation, GIS, interpolation methods (spline, IDW, kriging), Landsat 8 OLI, Oum Er Rbia high basin

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Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Ekrem Canli, Thomas Glade

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The precise prediction of rainfall in space and time is a key element to most landslide early warning systems. Unfortunately, the spatial variability of rainfall in many early warning applications is often disregarded. A common simplification is to use uniformly distributed rainfall to characterize aerial rainfall intensity. With spatially differentiated rainfall information, real-time comparison with rainfall thresholds or the implementation in process-based approaches might form the basis for improved landslide warnings. This study suggests an automated workflow from the hourly, web-based collection of rain gauge data to the generation of spatially differentiated rainfall predictions based on kriging. Because the application of kriging is usually a labor intensive task, a simplified and consequently automated variogram modeling procedure was applied to up-to-date rainfall data. The entire workflow was carried out purely with open source technology. Validation results, albeit promising, pointed out the challenges that are involved in pure distance based, automated geostatistical interpolation techniques for ever-changing environmental phenomena over short temporal and spatial extent.

Keywords: kriging, landslide early warning system, spatial rainfall prediction, variogram modelling, web scraping

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: Rongli Gai, Zhiyuan Chang

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At this stage, in view of various situations in the interpolation process, most researchers use self-adaptation to adjust the interpolation process, which is also one of the current and future research hotspots in the field of CNC machining. In the interpolation process, according to the overview of the spline curve interpolation algorithm, the adaptive analysis is carried out from the factors affecting the interpolation process. The adaptive operation is reflected in various aspects, such as speed, parameters, errors, nodes, feed rates, random Period, sensitive point, step size, curvature, adaptive segmentation, adaptive optimization, etc. This paper will analyze and summarize the research of adaptive imputation in the direction of the above factors affecting imputation.

Keywords: adaptive algorithm, CNC machining, interpolation constraints, spline curve interpolation

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Sahabeh Safarpour, Khiruddin Abdullah, Hwee San Lim, Mohsen Dadras

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Air pollution is a growing problem arising from domestic heating, high density of vehicle traffic, electricity production, and expanding commercial and industrial activities, all increasing in parallel with urban population. Monitoring and forecasting of air quality parameters are important due to health impact. One widely available metric of aerosol abundance is the aerosol optical depth (AOD). The AOD is the integrated light extinction coefficient over a vertical atmospheric column of unit cross section, which represents the extent to which the aerosols in that vertical profile prevent the transmission of light by absorption or scattering. Seasonal aerosol optical depth (AOD) values at 550 nm derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor onboard NASA’s Terra satellites, for the 10 years period of 2000-2010 were used to test 7 different spatial interpolation methods in the present study. The accuracy of estimations was assessed through visual analysis as well as independent validation based on basic statistics, such as root mean square error (RMSE) and correlation coefficient. Based on the RMSE and R values of predictions made using measured values from 2000 to 2010, Radial Basis Functions (RBFs) yielded the best results for spring, summer, and winter and ordinary kriging yielded the best results for fall.

Keywords: aerosol optical depth, MODIS, spatial interpolation techniques, Radial Basis Functions

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Authors: Thanh Van Hoang, Tien Yin Chou, Yao Min Fang, Yi Min Huang, Xuan Linh Nguyen

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Reliable information on the spatial distribution of annual rainfall and temperature is essential in research projects relating to urban and regional planning. This research presents results of a classification of temperature and rainfall in the Red River Delta of northern Vietnam based on measurements from seven meteorological stations (Ha Nam, Hung Yen, Lang, Nam Dinh, Ninh Binh, Phu Lien, Thai Binh) in the river basin over a thirty-years period from 1982-2011. The average accumulated rainfall trends in the delta are analysed and form the basis of research essential to weather and climate forecasting. This study employs interpolation based on the Kriging Method for daily rainfall (min and max) and daily temperature (min and max) in order to improve the understanding of sources of variation and uncertainly in these important meteorological parameters. To the Kriging method, the results will show the different models and the different parameters based on the various precipitation series. The results provide a useful reference to assist decision makers in developing smart agriculture strategies for the Red River Delta in Vietnam.

Keywords: spatial interpolation method, ArcGIS, temperature variability, rainfall variability, Red River Delta, Vietnam

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Authors: Carla Idely Palencia-Aguilar

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Artificial wetlands play an important role at Guasca Municipality in Colombia, not only because they are used for the agroindustry, but also because more than 45 species were found, some of which are endemic and migratory birds. Remote sensing was used to determine the changes in the area occupied by water of artificial wetlands by means of Aster and Modis images for different time periods. Evapotranspiration was also determined by three methods: Surface Energy Balance System-Su (SEBS) algorithm, Surface Energy Balance- Bastiaanssen (SEBAL) algorithm, and Potential Evapotranspiration- FAO. Empirical equations were also developed to determine the relationship between Normalized Difference Vegetation Index (NDVI) versus net radiation, ambient temperature and rain with an obtained R2 of 0.83. Groundwater level fluctuations on a daily basis were studied as well. Data from a piezometer placed next to the wetland were fitted with rain changes (with two weather stations located at the proximities of the wetlands) by means of multiple regression and time series analysis, the R2 from the calculated and measured values resulted was higher than 0.98. Information from nearby weather stations provided information for ordinary kriging as well as the results for the Digital Elevation Model (DEM) developed by using PCI software. Standard models (exponential, spherical, circular, gaussian, linear) to describe spatial variation were tested. Ordinary Cokriging between height and rain variables were also tested, to determine if the accuracy of the interpolation would increase. The results showed no significant differences giving the fact that the mean result of the spherical function for the rain samples after ordinary kriging was 58.06 and a standard deviation of 18.06. The cokriging using for the variable rain, a spherical function; for height variable, the power function and for the cross variable (rain and height), the spherical function had a mean of 57.58 and a standard deviation of 18.36. Threatens of eutrophication were also studied, given the unconsciousness of neighbours and government deficiency. Water quality was determined over the years; different parameters were studied to determine the chemical characteristics of water. In addition, 600 pesticides were studied by gas and liquid chromatography. Results showed that coliforms, nitrogen, phosphorous and prochloraz were the most significant contaminants.

Keywords: DEM, evapotranspiration, geostatistics, NDVI

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Authors: Selvakumar Ulaganathan, Ivo Couckuyt, Francesco Ferranti, Tom Dhaene, Eric Laermans

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Variable-fidelity surrogate modelling offers an efficient way to approximate function data available in multiple degrees of accuracy each with varying computational cost. In this paper, a Kriging-based variable-fidelity surrogate modelling approach is introduced to approximate such deterministic data. Initially, individual Kriging surrogate models, which are enhanced with gradient data of different degrees of accuracy, are constructed. Then these Gradient enhanced Kriging surrogate models are strategically coupled using a recursive CoKriging formulation to provide an accurate surrogate model for the highest fidelity data. While, intuitively, gradient data is useful to enhance the accuracy of surrogate models, the primary motivation behind this work is to investigate if it is also worthwhile incorporating gradient data of varying degrees of accuracy.

Keywords: Kriging, CoKriging, Surrogate modelling, Variable- fidelity modelling, Gradients

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Authors: Yelbek B. Utepov, Assel T. Mukhamejanova, Aliya K. Aldungarova, Aida G. Nazarova, Sabit A. Karaulov, Nurgul T. Alibekova, Aigul K. Kozhas, Dias Kazhimkanuly, Akmaral K. Tleubayeva

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This research focuses on enhancing geotechnical surveying for foundation design through the spatial interpolation of intermediate soil properties. Traditional geotechnical practices rely on discrete data from borehole drilling, soil sampling, and laboratory analyses, often neglecting the continuous nature of soil properties and disregarding values in intermediate locations. This study challenges these omissions by emphasizing interpolation techniques such as Kriging, Inverse Distance Weighting, and Spline interpolation to capture the nuanced spatial variations in soil properties. The methodology is applied to geotechnical survey data from two construction sites in Astana, Kazakhstan, revealing continuous representations of Young's Modulus, Cohesion, and Friction Angle. The spatial heatmaps generated through interpolation offered valuable insights into the subsurface environment, highlighting heterogeneity and aiding in more informed foundation design decisions for considered cites. Moreover, intriguing patterns of heterogeneity, as well as visual clusters and transitions between soil classes, were explored within seemingly uniform layers. The study bridges the gap between discrete borehole samples and the continuous subsurface, contributing to the evolution of geotechnical engineering practices. The proposed approach, utilizing open-source software geographic information systems, provides a practical tool for visualizing soil characteristics and may pave the way for future advancements in geotechnical surveying and foundation design.

Keywords: soil mechanical properties, spatial interpolation, inverse distance weighting, heatmaps

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Authors: Sheikh Samsuzzhan Alam

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The present study investigates the selection of variogram model in analyzing spatial variations of environmental variables with the trend. Sometimes, the autofitted theoretical variogram does not really capture the true nature of the empirical semivariogram. So proper exploration and analysis are needed to select the best variogram model. For this study, an open source data collected from California Soil Resource Lab1 is used to explain the problems when fitting a theoretical variogram. Five most commonly used variogram models: Linear, Gaussian, Exponential, Matern, and Spherical were fitted to the experimental semivariogram. Ordinary kriging methods were considered to evaluate the accuracy of the selected variograms through cross-validation. This study is beneficial for selecting an appropriate theoretical variogram model for environmental variables.

Keywords: anisotropy, cross-validation, environmental variables, kriging, variogram models

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Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Srijanani Anurag Prasad

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The Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) was built by combining interpolation data from the Iterated Function System (IFS). The interpolation data in a CHFIS comprises a row and/or column of uncertain values when a single point is entered. Alternatively, a row and/or column of additional points are placed in the given interpolation data to demonstrate the node added CHFIS. There are three techniques for inserting new points that correspond to the row and/or column of nodes inserted, and each method is further classified into four types based on the values of the inserted nodes. As a result, numerous forms of node insertion can be found in a CHFIS.

Keywords: fractal, interpolation, iterated function system, coalescence, node insertion, knot insertion

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Authors: Shahpar Yilmaz, Yasir Nadeem, Syed A. Mehdi

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Searching for a record in a dataset is always a frequent task for any data structure-related application. Hence, a fast and efficient algorithm for the approach has its importance in yielding the quickest results and enhancing the overall productivity of the company. Interpolation search is one such technique used to search through a sorted set of elements. This paper proposes a new algorithm, an advancement over interpolation search for the application of search over a sorted array. Pattern Recognition Search or PR Search (PRS), like interpolation search, is a pattern-based divide and conquer algorithm whose objective is to reduce the sample size in order to quicken the process and it does so by treating the array as a perfect arithmetic progression series and thereby deducing the key element’s position. We look to highlight some of the key drawbacks of interpolation search, which are accounted for in the Pattern Recognition Search.

Keywords: array, complexity, index, sorting, space, time

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Authors: Farzaneh Khorram, Xavier Emery

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In this paper, it is aimed to create a crushing consumption energy (CCE) block model and determine the blocks with the potential to have the maximum grinding process energy consumption for the study area. For this purpose, a joint estimate (co-kriging) and joint simulation (turning band method and plurigaussian methods) to predict the CCE based on its correlation with SAG power index (SPI), A×B, and ball mill bond work Index (BWI). The analysis shows that TBCOSIM and plurigaussian have the more realistic results compared to cokriging. It seems logical due to the nature of the data geometallurgical and the linearity of the kriging method and the smoothing effect of kriging.

Keywords: plurigaussian, turning band, cokriging, geometallurgy

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Authors: Zeyu Zhou, Xiaojun Bi

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Due to the limited environmental parameters and the limited resolution of the sensor, the universal existence of the mixed pixels in the process of remote sensing images restricts the spatial resolution of the remote sensing images. Sub-pixel mapping technology can effectively improve the spatial resolution. As the bilinear interpolation algorithm inevitably produces the edge blur effect, which leads to the inaccurate sub-pixel mapping results. In order to avoid the edge blur effect that affects the sub-pixel mapping results in the interpolation process, this paper presents a new edge-directed interpolation algorithm which uses the covariance adaptive interpolation algorithm on the edge of the low-resolution image and uses bilinear interpolation algorithm in the low-resolution image smooth area. By using the edge-directed interpolation algorithm, the super-resolution of the image with low resolution is obtained, and we get the percentage of each sub-pixel under a certain type of high-resolution image. Then we rely on the probability value as a soft attribute estimate and carry out sub-pixel scale under the ‘hard classification’. Finally, we get the result of sub-pixel mapping. Through the experiment, we compare the algorithm and the bilinear algorithm given in this paper to the results of the sub-pixel mapping method. It is found that the sub-pixel mapping method based on the edge-directed interpolation algorithm has better edge effect and higher mapping accuracy. The results of the paper meet our original intention of the question. At the same time, the method does not require iterative computation and training of samples, making it easier to implement.

Keywords: remote sensing images, sub-pixel mapping, bilinear interpolation, edge-directed interpolation

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Authors: M. Uysal, M. Yilmaz, I. Tiryakioğlu

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Digital Terrain Model (DTM) is a digital numerical representation of the Earth's surface. DTMs have been applied to a diverse field of tasks, such as urban planning, military, glacier mapping, disaster management. In the expression of the Earth' surface as a mathematical model, an infinite number of point measurements are needed. Because of the impossibility of this case, the points at regular intervals are measured to characterize the Earth's surface and DTM of the Earth is generated. Hitherto, the classical measurement techniques and photogrammetry method have widespread use in the construction of DTM. At present, RADAR, LiDAR, and stereo satellite images are also used for the construction of DTM. In recent years, especially because of its superiorities, Airborne Light Detection and Ranging (LiDAR) has an increased use in DTM applications. A 3D point cloud is created with LiDAR technology by obtaining numerous point data. However recently, by the development in image mapping methods, the use of unmanned aerial vehicles (UAV) for photogrammetric data acquisition has increased DTM generation from image-based point cloud. The accuracy of the DTM depends on various factors such as data collection method, the distribution of elevation points, the point density, properties of the surface and interpolation methods. In this study, the random data reduction method is compared for DTMs generated from image based point cloud data. The original image based point cloud data set (100%) is reduced to a series of subsets by using random algorithm, representing the 75, 50, 25 and 5% of the original image based point cloud data set. Over the ANS campus of Afyon Kocatepe University as the test area, DTM constructed from the original image based point cloud data set is compared with DTMs interpolated from reduced data sets by Kriging interpolation method. The results show that the random data reduction method can be used to reduce the image based point cloud datasets to 50% density level while still maintaining the quality of DTM.

Keywords: DTM, Unmanned Aerial Vehicle (UAV), uniform, random, kriging

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Authors: Singara Singh Kasana, Pankaj Garg

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In this paper, a blind data hiding technique based on interpolation of sub sampled versions of a cover image is proposed. Sub sampled image is taken as a reference image and an interpolated image is generated from this reference image. Then difference between original cover image and interpolated image is used to embed secret data. Comparisons with the existing interpolation based techniques show that proposed technique provides higher embedding capacity and better visual quality marked images. Moreover, the performance of the proposed technique is more stable for different images.

Keywords: interpolation, image subsampling, PSNR, SIM

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Authors: James Adewale, Joshua Sunday

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In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods.

Keywords: predictor, corrector, collocation, interpolation, approximate solution, independent solution, zero stable, consistent, convergent

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Authors: Ahmed F. Elaksher, Islam Omar

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In this project, we used MOLA-based DEMs to orthorectify HiRISE optical images. The MOLA data was interpolated using the kriging interpolation technique. Corresponding tie points were then digitized from both datasets. These points were employed in co-registering both datasets using GIS analysis tools. Different transformation models, including the affine and projective transformation models, were used with different sets and distributions of tie points. Additionally, we evaluated the use of the MOLA elevations in co-registering the MOLA and HiRISE datasets. The planimetric RMSEs achieved for each model are reported. Results suggested the use of 3D-2D transformation models.

Keywords: photogrammetry, Mars, MOLA, HiRISE

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Authors: Pedro Mauricio Acosta, Carlos Andrés Caro

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This research presents the regionalization of IDF curves for the department of Boyacá, Colombia, which comprises 16 towns, including the provincial capital, Tunja. For regionalization adjustment parameters (U and alpha) of the IDF curves stations referred to in the studied area were used. Similar regionalization is used by the interpolation of intensities. In the case of regionalization by parameters found by the construction of the curves intensity, duration and frequency estimation methods using ordinary moments and maximum likelihood. Regionalization and interpolation of data were performed with the assistance of Arcgis software. Within the development of the project the best choice to provide a level of reliability such as to determine which of the options and ways to regionalize is best sought. The resulting isolines maps were made in the case of regionalization intensities, each map is associated with a different return period and duration in order to build IDF curves in the studied area. In the case of the regionalization maps parameters associated with each parameter were performed last.

Keywords: intensity duration, frequency curves, regionalization, hydrology

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Authors: Sakshi Dhumale, Madhushree C., Amba Shetty

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The effect of station density on the geostatistical prediction of groundwater levels is of critical importance to ensure accurate and reliable predictions. Monitoring station density directly impacts the accuracy and reliability of geostatistical predictions by influencing the model's ability to capture localized variations and small-scale features in groundwater levels. This is particularly crucial in regions with complex hydrogeological conditions and significant spatial heterogeneity. Insufficient station density can result in larger prediction uncertainties, as the model may struggle to adequately represent the spatial variability and correlation patterns of the data. On the other hand, an optimal distribution of monitoring stations enables effective coverage of the study area and captures the spatial variability of groundwater levels more comprehensively. In this study, we investigate the effect of station density on the predictive performance of groundwater levels using the geostatistical technique of Ordinary Kriging. The research utilizes groundwater level data collected from 121 observation wells within the semi-arid Berambadi watershed, gathered over a six-year period (2010-2015) from the Indian Institute of Science (IISc), Bengaluru. The dataset is partitioned into seven subsets representing varying sampling densities, ranging from 15% (12 wells) to 100% (121 wells) of the total well network. The results obtained from different monitoring networks are compared against the existing groundwater monitoring network established by the Central Ground Water Board (CGWB). The findings of this study demonstrate that higher station densities significantly enhance the accuracy of geostatistical predictions for groundwater levels. The increased number of monitoring stations enables improved interpolation accuracy and captures finer-scale variations in groundwater levels. These results shed light on the relationship between station density and the geostatistical prediction of groundwater levels, emphasizing the importance of appropriate station densities to ensure accurate and reliable predictions. The insights gained from this study have practical implications for designing and optimizing monitoring networks, facilitating effective groundwater level assessments, and enabling sustainable management of groundwater resources.

Keywords: station density, geostatistical prediction, groundwater levels, monitoring networks, interpolation accuracy, spatial variability

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Authors: Yasuyuki Takahashi, Maya Yamashita, Kyoko Saito

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In general, dynamic SPECT data acquisition needs a few minutes for one rotation. Thus, the time-activity curve (TAC) derived from the dynamic SPECT is relatively coarse. In order to effectively shorten the interval, between data points, we adopted a 180-degree interpolation method. This method is already used for reconstruction of the X-ray CT data. In this study, we applied this 180-degree interpolation method to SPECT and investigated its effectiveness.To briefly describe the 180-degree interpolation method: the 180-degree data in the second half of one rotation are combined with the 180-degree data in the first half of the next rotation to generate a 360-degree data set appropriate for the time halfway between the first and second rotations. In both a phantom and a patient study, the data points from the interpolated images fell in good agreement with the data points tracking the accumulation of 99mTc activity over time for appropriate region of interest. We conclude that data derived from interpolated images improves the apparent time resolution of dynamic SPECT.

Keywords: dynamic SPECT, time resolution, 180-degree interpolation method, 99mTc-GSA.

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Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

Abstract:

Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

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