## Workshop 2: October 24-28, 2011

# Large-Scale Inverse Problems and Applications in the Earth Sciences

## Organizers

Mike Cullen, MET Office, Exeter, UK

Melina Freitag, University of Bath, UK

Stefan Kindermann, University of Linz, Austria

Hanna Katriina Pikkarainen, Johann Radon Institute, Austria

## Synopsis and Main Topics

This workshop will focus on the large inverse problems commonly arising in simulation and forecasting in the earth
sciences. For example, operational weather forecasting models have between 10^{7} and 10^{8} degrees
of freedom. Even so, these degrees of freedom represent grossly space-time averaged properties of the atmosphere.
Accurate forecasts require accurate initial conditions. With recent developments in satellite data, there are
between 10^{6} and 10^{7} observations each day. However, while these also represent space-time
averaged properties, the averaging implicit in the measurements is quite different from that used in the models.
In atmosphere and ocean applications, there is a physically-based model available which can be used to regularise
the problem. We assume that there is a set of observations with known error characteristics available over a period
of time. The basic deterministic technique is to fit a model trajectory to the observations over a period of time
to within the observation error. Since the model is not perfect the model trajectory has to be corrected, which
defines the data assimilation problem. The stochastic view can be expressed by using an ensemble of model trajectories,
and calculating corrections to both the mean value and the spread which allow the observations to be fitted by each
ensemble member. In other areas of earth science, only the structure of the model formulation itself is known and the
aim is to use the past observation history to determine the unknown model parameters.

The workshop will involve experts in the theory of inverse problems together with experts working on both theoretical and practical aspects of the techniques by which large inverse problems arise in the earth sciences.