Space–time variograms and a functional form for total air pollution measurements

Iaco, Sandra De; Myers, Donald E.; Posa, D.

doi:10.1016/s0167-9473(02)00081-6

Cited by 61 publications

(32 citation statements)

References 16 publications

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“…is somewhat more convenient in the fitting procedure (De Iaco et al, 2002b). Then the following is an obvious consequence of the preceding corollary.…”

Section: Product-sums and The Variogram Formmentioning

confidence: 72%

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Strict Positive Definiteness of a Product of Covariance Functions

Iaco

Myers

Posa

2011

Communications in Statistics - Theory and Methods

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Positive definiteness represents an admissibility condition for a function to be a covariance. Nevertheless, the more restricted condition of strict positive definiteness has received attention in literature, especially in spatial statistics, since it ensures that the kriging system has a unique solution. Most known covariance functions are isotropic but there are applications where isotropy is not appropriate, e.g., spacetime covariance functions. One way to construct non-isotropic covariance functions is to use a product or a product-sum. In this article, it is given a necessary as well as a sufficient condition for a product of two covariance functions to be strictly positive definite. This result is extended to the well-known product-sum covariance model.

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“…is somewhat more convenient in the fitting procedure (De Iaco et al, 2002b). Then the following is an obvious consequence of the preceding corollary.…”

Section: Product-sums and The Variogram Formmentioning

confidence: 72%

“…Some applications are found in De Iaco et al (2002b), Li et al (2009), andDe Iaco (2010). This non-separable family of space-time covariances has been built by applying the convexity property of the covariances family.…”

Section: Product-sums and The Variogram Formmentioning

confidence: 99%

Strict Positive Definiteness of a Product of Covariance Functions

Iaco

Myers

Posa

2011

Communications in Statistics - Theory and Methods

Self Cite

View full text Add to dashboard Cite

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“…In the separable model, the spatio-temporal covariance function is treated as either a sum or product of separate spatial and temporal covariance functions [30]. In the non-separable model, the spatio-temporal covariance function is treated as a non-linear, multiplicative version of the spatial and temporal covariance functions [6,10,[31][32][33]. However, spatio-temporal kriging methods assume that a space-time process has a constant mean and variance (i.e., second order stationarity) in space and time [13,15].…”

Section: Related Workmentioning

confidence: 99%

“…J. Geo-Inf. 2016, 5, 13 2 of 14 and regression-based methods [10][11][12]. Although space-time interpolation plays a key role in space-time modeling, existing methods mainly assume that space-time processes exhibit stationarity in space and time.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets

Deng

Zide

Liu

et al. 2016

IJGI

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Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984China ( -2009. Experimental results show that, for these datasets, the proposed method outperforms three state-of-the-art methods-e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.

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“…The spatiotemporal geostatistical approaches can offer several benefits including a larger data set to support stable parameter estimation and prediction and the exploitation of temporal as well as spatial autocorrelation in observed values, which is impossible in the spatial-only approach. The spatiotemporal geostatistical model has been applied in a range of fields including agricultural [19], atmospheric [20], and soil science [21].…”

Section: Introductionmentioning

confidence: 99%

A Regional Gap-Filling Method Based on Spatiotemporal Variogram Model of <inline-formula> <tex-math notation="TeX">$\hbox{CO}_{2}$</tex-math></inline-formula> Columns

Zeng

Lei

Hou

et al. 2014

IEEE Trans. Geosci. Remote Sensing

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A precise and high-resolution spatiotemporal distribution of atmospheric carbon dioxide (CO 2 ) is important in identifying and quantifying the CO 2 source and sinks on regional scales and emissions from discrete point sources. We propose the use of a regional gap-filling method by modeling the spatiotemporal correlation structures of column-averaged CO 2 dry air mole fractions (Xco 2 ) on a regional scale, using data from the Atmospheric CO 2 Observations from Space retrievals of the Greenhouse Gases Observing Satellite (ACOS-GOSAT) measurements over mainland China. The accuracy of the gap-filling results is verified by cross-validation and comparison with ground-based measurements. As the results of the spatiotemporal gap-filling method are applied to mainland China, the correlation coefficient (r 2 ) between the predicted values and true ones is greater than 0.85, the mean absolute prediction error is less than 1.5 ppm in cross-validation, and the seasonal cycle of the gap-filled data is generally in agreement with ground-based measurements. Finally, we compare the prediction accuracy based on our method with that based on the commonly used spatial-only kriging to further demonstrate the improved prediction accuracy. The applied regional gap-filling method, which makes full use of the multitemporal ACOS-GOSAT data, can generate a regional regular spatial distribution map of (Xco 2 ) at high spatial and temporal resolutions.Index Terms-Atmospheric CO 2 Observations from Space retrievals of the Greenhouse Gases Observing Satellite (ACOS-GOSAT), product-sum model, space-time kriging, Xco 2 .

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Space–time variograms and a functional form for total air pollution measurements

Cited by 61 publications

References 16 publications

Strict Positive Definiteness of a Product of Covariance Functions

Strict Positive Definiteness of a Product of Covariance Functions

A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets

A Regional Gap-Filling Method Based on Spatiotemporal Variogram Model of <inline-formula> <tex-math notation="TeX">$\hbox{CO}_{2}$</tex-math></inline-formula> Columns

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