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

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.

[1]  Alan S. Willsky,et al.  Multiscale Autoregressive Models and Wavelets , 1999, IEEE Trans. Inf. Theory.

[2]  K. C. Chou,et al.  Multiscale systems, Kalman filters, and Riccati equations , 1994, IEEE Trans. Autom. Control..

[3]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[4]  Michael L. Stein,et al.  Some statistical methods for analyzing the TOMS data , 1998 .

[5]  E. Kolaczyk.  Bayesian Multiscale Models for Poisson Processes , 1999 .

[6]  N. Cressie.  Fitting variogram models by weighted least squares , 1985 .

[7]  P. Bhartia,et al.  Nimbus-7 Total Ozone Mapping Spectrometer (TOMS) Data Products User`s Guide , 1993 .

[8]  Paul W. Fieguth,et al.  Fractal estimation using models on multiscale trees , 1996, IEEE Trans. Signal Process..

[9]  G. C. Tiao,et al.  Modeling Satellite Ozone Data , 1995 .

[10]  Charles Madrid,et al.  The Nimbus 7 user's guide , 1978 .

[11]  S. Lauritzen.  Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models , 1992 .

[12]  Alan S. Willsky,et al.  Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination , 1995, IEEE Trans. Image Process..

[13]  Alan S. Willsky,et al.  Multiscale smoothing error models , 1995, IEEE Trans. Autom. Control..

[14]  Glen Jaross,et al.  Earth probe total ozone mapping spectrometer (TOMS): data products user's guide , 1998 .

[15]  J. London.  The observed distribution of atmospheric ozone and its variations , 1985 .

[16]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[18]  Y. Meyer.  Wavelets and Operators , 1993 .

[19]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[20]  G. MallatS..  A Theory for Multiresolution Signal Decomposition , 1989 .

[21]  ControlHsin-Cheng HuangNoel CressieABSTRACT.  Multiscale Graphical Modeling in Space: Applications to Command and Control , 2000 .

[22]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[23]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[24]  A.S. Willsky,et al.  Multiscale autoregressive models and the stochastic realization problem , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).

[25]  Gad Levy,et al.  Space and time aliasing structure in monthly mean polar-orbiting satellite data , 1995 .