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Groundwater Arsenic Discontinuity
Published in M. Manzurul Hassan, Arsenic in Groundwater, 2018
Kriging is mainly designed to model spatial variability. It is a generic term for a range of least squares methods to provide the “best linear unbiased predictions” (BLUP), best in the sense of minimum variance (Oliver and Webster, 2014). Interpolation methods can be used in the estimation of spatial continuity of variables to infer the values to nonsampling locations. This estimation method in geostatistics is known as kriging, an interpolation approach that provides an optimal estimative of regionalized variables with minimum variance and without bias, using a theoretical variogram (Bressan et al., 2009; Ghosh and Parial, 2014; Isaaks and Srivastana, 1989). Kriging is useful for estimating spatial interaction of various data (Im and Park, 2013; Martin and Simpson, 2005). Kriging is a method for linear optimum appropriate interpolation with a minimum mean square error. It is known to be an exact estimator in the sense that observation points are correctly reestimated (Uyan and Cay, 2013).
Long-Term Spatiotemporal Evolution and Coordinated Control of Air Pollutants in a typical mega-mountain city of Cheng-Yu Region under the “Dual Carbon” Goal
Published in Journal of the Air & Waste Management Association, 2023
Xiaoju Li, Luqman Chuah Abdullah, Shafreeza Sobri, Mohamad Syazarudin, Siti Aslina Hussain, Tan Poh Aun, Jinzhao Hu
represents the estimation value at the point , represents the observation value of points near of the , represents the weight coefficient of the observation value and the relative point . Kriging method is used to spatially interpolate the historical data of annual average atmospheric pollutant concentration to get the spatial distribution map of pollution (Chen et al., 2018; Davuliene et al., 2021; Gui et al., 2019). Two assumptions for Kriging method to provide best linear unbiased prediction: 1. Stationarity – the joint probability distribution does not vary across the study space. 2.Isotropy – uniformity in all directions. The generated data will be discussed on their spatial and temporal variation characteristics, trends of pollutants, followed by comparisons on their spatial correlations between 2014 and 2020.
Inherent variability assessment from sparse property data of overburden soils and intermediate geomaterials using random field approaches
Published in Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2022
Opeyemi E. Oluwatuyi, Rebecca Holt, Rasika Rajapakshage, Shaun S. Wulff, Kam Ng
Kriging is used in spatial statistics to obtain predictions for unsampled locations. Kriging utilises best linear unbiased prediction (BLUP) at an unobserved location based upon the observed data. This study describes and performs universal kriging due to the presence of covariates (R: krige{gstat}) (Bivand et al. 2008). The BLUP for universal kriging is given by: where is the observed spatial location, is the unobserved spatial location to be predicted, is the generalised least squares estimate from Equation (9), is the REML estimate of , is value of the design matrix at , is the value of the geomaterial parameter at , and is a vector of covariances with entries for (Pebesma 2004; Bivand et al. 2008). If there is no nugget, then the predictions at observed locations will match the observed values. However, if a nugget is present, then the predictions at observed locations may not match the observed values (Banerjee, Carlin, and Gelfand 2014).
Improvement of Kriging interpolation with learning kernel in environmental variables study
Published in International Journal of Production Research, 2022
Te Xu, Yongxia Liu, Lixin Tang, Chang Liu
In summary, Kriging has been broadly used in many fields. As is known to all, Kriging could provide the best linear unbiased prediction of intermediate values once the raw data satisfy the second-order stationarity assumption that data come from a stationary random process (Arcidiacono et al. 2017). It means that the covariance of spatial variation is the same between these two data points when they are chosen by the same distance and direction. The spatial variation trend among data points is generally obtained by the multiple linear regression method once the form of variogram is given. In the real world, it is impossible to know the form of variogram in advance; thus, a few particular function models are suggested to be utilised as a kernel function, such as spherical model, exponential model and Gaussian model. However, when there are drastic changes (drifts like geological faults) or noise in raw data, the pre-assumed kernel function may not be able to characterise the real form of the variogram.