Fast, Resolution-Consistent Spatial Prediction of Global Processes From Satellite Data

Abstract

Polar orbiting satellites remotely sense the earth and its atmosphere, producing datasets that give daily global coverage. For any given day, the data are many and measured at spatially irregular locations. Our goal in this article is to predict values that are spatially regular at different resolutions; such values are often used as input to general circulation models (GCMs) and the like. Not only do we wish to predict optimally, but because data acquisition is relentless, our algorithm must also process the data very rapidly. This article applies a multiresolution autoregressive tree-structured model, and presents a new statistical prediction methodology that is resolution consistent (i.e., preserves "mass balance" across resolutions) and computes spatial predictions and prediction (co)variances extremely fast. Data from the Total Ozone Mapping Spectrometer (TOMS) instrument, on the Nimbus-7 satellite, are used for illustration. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Fast, Resolution-Consistent Spatial Prediction of Global Processes From Satellite DataHsin-Cheng HUANG , Noel CRESSIE, and John GABROSEK Polar orbitingsatellitesremotely sense the earth and its atmosphere,producingdatasets that give daily global coverage. For any given day, the data are many and measured at spatially irregular locations. Our goal in this article is to predict values that are spatially regular at different resolutions; such values are often used as input to general circulation models (GCMs) and the like. Not only do we wish to predict optimally, but because data acquisition is relentless, our algorithm must also process the data very rapidly. This article applies a multiresolutionautoregressivetree-structuredmodel, and presents a new statistical prediction methodology that is resolution consistent (i.e., preserves "mass balance" across resolutions) and computes spatial predictions and prediction (co)variances extremely fast. Data from the Total Ozone Mapping Spectrometer (TOMS) instrument, on the Nimbus-7 satellite, are used for illustration.

Combining Incompatible Spatial Data

“…In view of this, Fieguth et al (1995) modeled Q(s) as a function that decreases geometrically with scale, and many such models are conceivable. Huang, Cressie, and Gabrosek (2000) developed heterogeneous tree models that also allow the variance of the spatial tree process to change with scale. The basic algorithm used for prediction in multiscale tree models provides implicit forms for the covariance of X4s5 at any particular scale and also cross-covariances between X4s5 at different scales.…”

Integrating and Interpreting Aerosol Observations and Models within the PARAGON Framework

“…Wikle et al (2001) used Bayesian hierarchical models to combine satellite data at high resolution with model-generated data at coarse resolution to estimate tropical ocean surface winds. Huang et al (2002) employed a Bayesian hierarchical model in the development of a multiresolution Kalman filter for producing statistically optimal estimates of ozone from Total Ozone Mapping Spectrometer data at multiple nested resolutions.…”

“…The challenge for research into complex phenomena such as aerosol-climate interaction is to combine these disparate data into an integrated whole (Kahn and Braverman 1999;Huang et al 2002). The ultimate goal is to establish a complete dataset that will effectively confront and constrain ever more realistic global three-dimensional models.…”

Application of Hierarchical Matrices to Linear Inverse Problems in Geostatistics

“…One approach is to use covariance tapering [25,26], in which the correct covariance matrix is tapered using an appropriately chosen compactly supported radial basis function which results in a sparse approximation of the covariance matrix that can be solved using sparse matrix algorithms. Another approach is to choose classes of covariance functions for which kriging can be done exactly using a multiresolution spatial process [27][28][29]. Other approaches include fixed rank kriging [30] Before we proceed, we would like to clarify the notations.…”