** Jeffrey Anderson**

NCAR Data Assimilation Research Section

**Friday, 21 November, 2008**

**Foothills Laboratory 2, Room 1001**

**Lecture 10:00am**

### Nonlinear, Non-Gaussian Ensemble Filters for Data Assimilation

Both the deterministic and perturbed observation ensemble
Kalman filters that are used in geophysics are predicated
on assumptions that the joint prior distributions of model
state variables and observations are Gaussian. Nevertheless,
these methods have proved to be successful in situations
where the prior is not Gaussian. In this case, these filters
still assume that a least squares fit is appropriate for
approximating the prior relation between an observation
and a state variable.

Two new ensemble filter algorithms are described and
tested. The first relaxes the assumptions that the prior
observation distribution and the observation likelihood
are gaussian. This algorithm is shown to be competitive
with existing ensemble methods even when things are
nearly Gaussian. The new method facilitates the assimilation
of bounded quantities and observations that do not have
gaussian observational error distributions.

The second new algorithm also relaxes the assumption that
the relation between an observation and a state variable is
linear. This algorithm is a hybrid ensemble/particle filter
that works for large geophysical assimilation problems.
Performance is superior in cases where the relation
between observations and state variables is significantly
nonlinear. However, the traditional ensemble filters are
better for linear or weakly nonlinear applications.
Possible directions for further improved ensemble algorithms
are outlined.