Nonstationary covariance models for global data

By Mikyoung Jun, Michael L. Stein. 2008

160 citations recorded by the source corpus.

With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of parametric covariance models that can capture the nonstationarity in global data, especially strong dependency of covariance structure on latitudes. We apply the Discrete Fourier Transform to data on regular grids, which enables us to calculate the exact likelihood for large data sets. Our covariance model is applied to global total column ozone level data on a given day. We discuss how our covariance model compares with some existing models.

Subfields: Artificial Intelligence, Environmental Engineering, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/72f57911ffb13e8cef9fd25ed42b19c75769162e

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Citations in the corpus

Non-Stationary Dependence Structures for Spatial Extremes (2014, background): “Jun and Stein (2007, 2008), Castruccio and Stein (2013) and Castruccio and Genton (2014) advocated a spectral approach that provides flexible non-stationary covariance models on the sphere.”
Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere (2016, methodology): “We have missing data and follow the same procedure proposed by Jun and Stein (2008) to handle them.”
A class of Matérn-like covariance functions for smooth processes on a sphere (2015, methodology): “Data in geophysical applications often exhibit strong dependence of covariance structure on latitude (Jun and Stein, 2008), and the spatial range or smoothness parameters may vary across space (Kleiber and Nychka, 2012; Jun, 2014).”
Bayesian Inference for the Spatial Random Effects Model (2011, unknown): “Jun and Stein (2008) used a closely related model to analyze global total column ozone data.”
Excursion probability of Gaussian random fields on sphere (2014, background): “One may use Steiner’s formula (Adler and Taylor [2], page 142) to compute the Lipschitz–Killing curvatures of T exactly.”
Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping (2011, methodology): “The most general model in Jun and Stein (2008) is on the form X(s) = P1(l2)X0(s) + ( P2(l2) ∂ ∂l2 + P3(l2) ∂ ∂l1 ) X1(s) (5.1) +P4(l2) ∂ ∂l1 X2(s), where Xi, i= 0,1,2, are i.i.d. Matérn fields in R 3, Pi, i= 1,2,3,4, are nonrandom functions depending on latitude, l1 denoted longitude and l2…”