A functional data analysis study of stratospheric ozone trends and ozone sonde measurement biases

Many environmental data sets may be considered as functional data.
For example each balloon-based flight of an ozonesonde, provides
measurements of the altitude-dependent ozone partial pressure
profile as the sonde ascends through the atmosphere.
A sequence of sonde launches provides observations from
a time series of ozone partial pressure "curves", with
each curve a function of altitude. The shape of these curves
evolves over time in response to complex dynamical and chemical
processes. I present a functional data analysis study
of altitude-dependent non-linear time trends in stratospheric
ozone, based on a time series of ozonesonde flights from
Hohenpeissenberg in Germany. I also investigate two specific modes of ozone variability, namely the Quasi-Biennial Oscillation and solar cycle.
Due to the large number of observations, this analysis
combines dimension reducing functional basis approximations,
with flexible spline-based additive models on the
low-dimensional basis function coefficient scale.



In the second part of my talk, I discuss data quality issues raised
during the first trend study, and ongoing work towards incorporating
unknown data biases and uncertainties into the trend studies.
Stratospheric ozone is measured by several categories of instruments,
operating on different space-time resolutions and sampling
schemes (including satellite, surface-based and sonde instruments).
Each instrument exhibits its own measurement error and
bias processes. Sonde measurements frequently are pre-processed
according to scientific beliefs or approximations of the instrument
biases, before being provided to the broader atmospheric
science community for further studies (such as trend estimation).
For many ozonesondes, such as those we initially analyzed, pre-processing included a controversial data-adjustment step aimed at improving agreement of the ozonesonde records with measurements from another instrument operating on a different spatial scale. I describe the
step that was taken for the data we initially analyzed, namely a simple flight-specific scalar multiplication of the sonde observations. Motivated by this, I present subsequent research with Eduardo Montoya (Cal State Bakersfield) to estimate an altitude-dependent bias profile through a constrained functional
linear model with a scalar response and functional explanatory variable. I briefly discuss estimation challenges in this model.