Multiresolution models for nonstationary spatial covariance functions

Nychka, Douglas; Wikle, Christopher K.; Royle, J. Andrew

doi:10.1191/1471082x02st037oa

Cited by 172 publications

(124 citation statements)

References 8 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…Based on a Monte Carlo sample of 600 FHDA simulated fields, a mixture of exponentials (6) The thin plate spline model was fit (using Tps from the R [15] package fields (Nychka et al [14])) with a linear drift and the smoothing parameter chosen by generalized cross-validation.…”

Section: Seasonal Model Resultsmentioning

confidence: 99%

Statistical models for monitoring and regulating ground‐level ozone

Gilleland¹,

Nychka²

2005

Environmetrics

Self Cite

View full text Add to dashboard Cite

The U.S. Environmental Protection Agency's (EPA) National Ambient Air Quality Standard (NAAQS) for ground-level ozone is now based on the fourth-highest daily maximum 8-hour average ozone level (FHDA).Standard geostatistical models may not be appropriate for interpolating such a statistic off of a network of monitoring sites. In this paper we compare the performance of different statistical models in predicting this standard at locations where monitors are not located. We give special attention to two models: a daily model that uses an autoregression to account for spatial and temporal dependence, and a seasonal model that assumes the FHDA field is Gaussian and employs spatial statistical techniques. Based on five seasons of ozone data collected in and around North Carolina, we find that the daily model is superior enough to the seasonal model to warrant its added complexity.

show abstract

Section: Seasonal Model Resultsmentioning

confidence: 99%

Statistical models for monitoring and regulating ground‐level ozone

Gilleland¹,

Nychka²

2005

Environmetrics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the third regularization space, wavelet space, regularization in physical space and spectral space can be carried out simultaneously with wavelets, which are localized in both physical space and spectral space. In wavelet space, sample covariances were regularized with diagonal covariance matrices (Fisher and Andersson, 2001;Deckmyn and Berre, 2005) and matrices having diagonal elements and some off-diagonal elements (Nychka et al, 2002;Rhodin and Anlauf, 2007). Similar to compactly supported correlation functions, wavelets can filter out spurious noise on sample covariances (Pannekoucke et al, 2007).…”

Section: Regularizationmentioning

confidence: 99%

Covariance regularization in inverse space

Ueno

Tsuchiya

2009

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

ABSTRACT:In data assimilation, covariance matrices are introduced in order to prescribe the weights of the initial state, model dynamics, and observation, and suitable specification of the covariances is known to be essential for obtaining sensible state estimates. The covariance matrices are specified by sample covariances and are converted according to an assumed covariance structure. Modelling of the covariance structure consists of the regularization of a sample covariance and the constraint of a dynamic relationship. Regularization is required for converting the singular sample covariance into a non-singular sample covariance, removing spurious correlation between variables at distant points, and reducing the required number of parameters that specify the covariances. In previous studies, regularization of sample covariances has been carried out in physical (grid) space, spectral space, and wavelet space. We herein propose a method for covariance regularization in inverse space, in which we use the covariance selection model (the Gaussian graphical model). For each variable, we assume neighbouring variables, i.e. a targeted variable is directly related to its neighbours and is conditionally independent of the non-neighbouring variables. Conditional independence is expressed by specifying zero elements in the inverse covariance matrix. The non-zero elements are estimated numerically by the maximum likelihood using Newton's method. Appropriate neighbours can be selected with the AIC or BIC information criteria. We address some techniques for implementation when the covariance matrix has a large dimension. We present an illustrative example using a simple 3 × 3 matrix and an application to a sample covariance obtained from sea-surface height observations.

show abstract

“…Scalable spatial and spatio-temporal approaches in the recent literature include a hierarchical Bayesian spatio-temporal model with multiresolution wavelet basis functions and two data sources of different support [12]; science-based orthogonal eigenfunctions and multiresolution basis functions to capture residual dependencies [13]; modelling nonstationary covariance functions with multiresolutional wavelet models [14]; a hierarchical Bayesian model with FFT representation of Spatial Random Effects [15]; spectral parameterization of a spatial Poisson process [16]; approximate optimal prediction with dimension reduction through conditioning on a small set of space-filling locations [17]; a bivariate dynamic process-convolution model [18]; Fixed Rank Kriging based on the Spatial Random Effects model [7]; modelling with nonstationary covariance models using the discrete Fourier transform [19]; Fixed Rank Filtering and Fixed Ranked Smoothing based on the Kalman filter and the Spatio-Temporal Random Effects model [20]; and linking Gaussian fields and Gaussian Markov random fields using stochastic partial differential equations [21].…”

Section: Multivariate Spatial Data Fusionmentioning

confidence: 99%

Multivariate Spatial Data Fusion for Very Large Remote Sensing Datasets

2017

View full text Add to dashboard Cite

Global maps of total-column carbon dioxide (CO 2 ) mole fraction (in units of parts per million) are important tools for climate research since they provide insights into the spatial distribution of carbon intake and emissions as well as their seasonal and annual evolutions. Currently, two main remote sensing instruments for total-column CO 2 are the Orbiting Carbon Observatory-2 (OCO-2) and the Greenhouse gases Observing SATellite (GOSAT), both of which produce estimates of CO 2 concentration, called profiles, at 20 different pressure levels. Operationally, each profile estimate is then convolved into a single estimate of column-averaged CO 2 using a linear pressure weighting function. This total-column CO 2 is then used for subsequent analyses such as Level 3 map generation and colocation for validation. In principle, total-column CO 2 in these applications may be more efficiently estimated by making optimal estimates of the vector-valued CO 2 profiles and applying the pressure weighting function afterwards. These estimates will be more efficient if there is multivariate dependence between CO 2 values in the profile. In this article, we describe a methodology that uses a modified Spatial Random Effects model to account for the multivariate nature of the data fusion of OCO-2 and GOSAT. We show that multivariate fusion of the profiles has improved mean squared error relative to scalar fusion of the column-averaged CO 2 values from OCO-2 and GOSAT. The computations scale linearly with the number of data points, making it suitable for the typically massive remote sensing datasets. Furthermore, the methodology properly accounts for differences in instrument footprint, measurement-error characteristics, and data coverages.

show abstract

Multiresolution models for nonstationary spatial covariance functions

Cited by 172 publications

References 8 publications

Statistical models for monitoring and regulating ground‐level ozone

Statistical models for monitoring and regulating ground‐level ozone

Covariance regularization in inverse space

Multivariate Spatial Data Fusion for Very Large Remote Sensing Datasets

Contact Info

Product

Resources

About