Title: PC Proxy: A New Method of 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 ozone measurements from
the Polar Aerosol and Ozone Measurement (POAM) 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 ppmv 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 0.30 ppmv 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 at the end of winter.