  Studies on stratospheric ozone have attracted much attention due to its
serious impacts on climate changes and its important role as a tracer of
Earth's global circulation. Tropospheric ozone as a main atmospheric pollutant
damages human health as well as the growth of vegetation. Yet there is still a
lack of a theoretical framework to fully describe the variation of ozone. To
understand ozone's spatiotemporal variance, we introduce the eigen microstate
method to analyze the global ozone mass mixing ratio (OMMR) between 1979-01-01
and 2020-06-30 at 37 pressure layers. We find that eigen microstates at
different geopotential heights can capture different climate phenomena and
modes. Without deseasonalization, the first eigen microstates capture the
seasonal effect and reveal that the phase of the intra-annual cycle moves with
the geopotential heights. After deseasonalization, by contrast, the collective
patterns from the overall trend, ENSO, QBO, and tropopause pressure are
identified by the first few significant eigen microstates. The theoretical
framework proposed here can also be applied to other complex Earth systems.
