On the Validity of Commonly Used Covariance and Variogram Functions on the Sphere

Huang, Chunfeng; Zhang, Haimeng; Robeson, Scott M.

doi:10.1007/s11004-011-9344-7

Cited by 83 publications

(63 citation statements)

References 26 publications

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“…Other studies that use a product-sum covariance model typically assume the validity of this covariance model on a sphere (e.g., Zeng et al, 2013Zeng et al, , 2016. Results from Huang et al (2011) explicitly validate the exponential covariance model on a sphere, as well as sums of the products of exponential covariance models and constants (provided that the constants are positive). The first term of the product-sum covariance model used in this study (Eq.…”

Section: Characterization Of Spatio-temporal Covariancementioning

confidence: 95%

“…Most covariance models were originally designed for Euclidean space, and their validity in other coordinate systems cannot be assumed per se. Huang et al (2011) examined the validity of several theoretical covariance models in spherical coordinate systems. However, this evaluation has not been done for the spatio-temporal product-sum covariance model.…”

Section: Characterization Of Spatio-temporal Covariancementioning

confidence: 99%

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Spatio-temporal approach to moving window block kriging of satellite data v1.0

et al. 2017

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Abstract. Numerous existing satellites observe physical or environmental properties of the Earth system. Many of these satellites provide global-scale observations, but these observations are often sparse and noisy. By contrast, contiguous, global maps are often most useful to the scientific community (i.e., Level 3 products). We develop a spatio-temporal moving window block kriging method to create contiguous maps from sparse and/or noisy satellite observations. This approach exhibits several advantages over existing methods: (1) it allows for flexibility in setting the spatial resolution of the Level 3 map, (2) it is applicable to observations with variable density, (3) it produces a rigorous uncertainty estimate, (4) it exploits both spatial and temporal correlations in the data, and (5) it facilitates estimation in real time. Moreover, this approach only requires the assumption that the observable quantity exhibits spatial and temporal correlations that are inferable from the data. We test this method by creating Level 3 products from satellite observations of CO 2 (XCO 2 ) from the Greenhouse Gases Observing Satellite (GOSAT), CH 4 (XCH 4 ) from the Infrared Atmospheric Sounding Interferometer (IASI) and solar-induced chlorophyll fluorescence (SIF) from the Global Ozone Monitoring Experiment-2 (GOME-2). We evaluate and analyze the difference in performance of spatio-temporal vs. recently developed spatial kriging methods.

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Section: Characterization Of Spatio-temporal Covariancementioning

confidence: 95%

Section: Characterization Of Spatio-temporal Covariancementioning

confidence: 99%

Spatio-temporal approach to moving window block kriging of satellite data v1.0

et al. 2017

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“…A parametric function, the theoretical variogram, is fitted to the raw variogram using non-linear least squares. For the prototypical applications presented here, an exponential variogram function with a nugget effect was used, because it yields a valid covariance function on a sphere (Huang et al, 2011), provided a good match to the known physical characteristics of the observations, and fit the observed variability well:…”

Section: Characterization Of Spatial Covariancementioning

confidence: 99%

Mapping of satellite Earth observations using moving window block kriging

et al. 2015

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Abstract. Global gridded maps (a.k.a. Level 3 products) of Earth system properties observed by satellites are central to understanding the spatiotemporal variability of these properties. They also typically serve either as inputs into biogeochemical models or as independent data for evaluating such models. Spatial binning is a common method for generating contiguous maps, but this approach results in a loss of information, especially when the measurement noise is low relative to the degree of spatiotemporal variability. Such "binned" fields typically also lack a quantitative measure of uncertainty.Geostatistical mapping has previously been shown to make higher spatiotemporal resolution maps possible, and also provides a measure uncertainty associated with the gridded products. This study proposes a flexible moving window block kriging method that can be used as a tool for creating high spatiotemporal resolution maps from satellite data. It relies only on the assumption that the observed physical quantity exhibits spatial correlation that can be inferred from the observations. The method has several innovations relative to previously applied methods: (1) it provides flexibility in the spatial resolution of the contiguous maps, (2) it is applicable for physical quantities with varying spatiotemporal coverage (i.e., density of measurements) by utilizing a more general and versatile data sampling approach, and (3) it provides rigorous assessments of the uncertainty associated with the gridded products. The method is demonstrated by creating Level 3 products from observations of columnintegrated carbon dioxide (XCO 2 ) from the GOSAT (Greenhouse Gases Observing Satellite) satellite, and solar induced fluorescence (SIF) from the GOME-2 (Global Ozone Monitoring Experiment-2) instrument.

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“…For example, some widely used covariance functions in Euclidean space have been shown to be invalid (not positive-definite) on the sphere (Huang et al, 2011;Gneiting, 2013). Although the Earth is more precisely described as an ellipsoid, nearly all types of spatial analysis at the global scale are well modeled using spherical geometry (Tobler, 2002;Schaffrin et al, 2003;Banerjee, 2005).…”

Section: Theorymentioning

confidence: 99%