# PC proxy: a method for dynamical tracer reconstruction

## Abstract

A detailed development of the principal component proxy method of dynamical tracer reconstruction is presented, including error analysis. The method works by correlating the largest principal components of a matrix representation of the transport dynamics with a set of sparse measurements. The Lyapunov spectrum was measured and used to quantify the lifetime of each principal component. The method was tested on the 500 K isentropic surface with stratospheric ozone concentration measurements from the Polar Aerosol and Ozone Measurement III satellite instrument during October and November 1998 and compared with the older proxy tracer method which works by correlating measurements with a single other tracer or proxy. Using a 60 day integration time and five (5) principal components, cross validation of globally reconstructed ozone and comparison with ozone sondes returned root-mean-square errors of 0.16 and 0.36 ppmv, respectively. This compares favourably with the classic proxy tracer method in which a passive tracer equivalent latitude field was used for the proxy and which returned RMS errors of 0.22 and 0.59 ppmv for cross-validation and sonde validation respectively. The method seems especially effective for shorter lived tracers and was far more accurate than the classic method at predicting ozone concentration in the Southern hemisphere over the same time period. It is also more effective when reconstruction is performed over the entire Earth rather than a single hemisphere allowing for seamless reconstruction of global fields.

## Keywords

Transport dynamics Interpolation methods Satellite remote sensing Assimilation models Flow tracers Numerical analysis Ozone Applied linear algrebra## Notes

### Acknowledgements

Thanks to the National Center for Environmental Prediction and the National Center for Atmospheric Research for the reanalysis data used in the simulations. Thanks also to World Ozone and Ultraviolet Data Center and Environment Canada for ozone sonde data. And thanks especially to my former colleagues at the Naval Research Laboratory for POAM III ozone data. Contour maps were created with Generic Mapping Tools (GMT) while scatter plots and historgrams were done in Open Office.

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