Spatial variation of total column ozone on a global scale

TL;DR

This paper explores modeling the global spatial variation of total column ozone using axially symmetric processes and spherical harmonics, highlighting the challenges in capturing both large and small scale features.

Contribution

It demonstrates the use of spherical harmonics for modeling axially symmetric ozone data and discusses the limitations in fitting local variations.

Findings

Large scale features captured with few spherical harmonic terms

Model fits poorly at local scales despite capturing broad patterns

Highlights need for models that incorporate both large and small scale structures

Abstract

The spatial dependence of total column ozone varies strongly with latitude, so that homogeneous models (invariant to all rotations) are clearly unsuitable. However, an assumption of axial symmetry, which means that the process model is invariant to rotations about the Earth's axis, is much more plausible and considerably simplifies the modeling. Using TOMS (Total Ozone Mapping Spectrometer) measurements of total column ozone over a six-day period, this work investigates the modeling of axially symmetric processes on the sphere using expansions in spherical harmonics. It turns out that one can capture many of the large scale features of the spatial covariance structure using a relatively small number of terms in such an expansion, but the resulting fitted model provides a horrible fit to the data when evaluated via its likelihood because of its inability to describe accurately the process's local behavior. Thus, there remains the challenge of developing computationally tractable models that capture both the large and small scale structure of these data.