Incremental mixed lognormal-Gaussian 4D VAR
Abstract
One of the advances that allowed 4DVAR to be operational for synoptic numerical weather prediction was the introduction of incremental 4DVAR. This method assumes that the errors are additive and Gaussian in nature. However, as work recently has shown, there are errors which are multiplicative. A full field version of the 4DVAR equations have been derived and tested in a toy problem for the situation where there is a mix of Gaussian and lognormal background and observational errors. It is not straight-forward, however, to extend the incremental theory to multiplicative errors. One approach which has been suggested recently involves using a transform for the increment. It is shown here that the increment that is found is not the 'incremental mode', i.e. the most likely state for the increment, but rather a median state for the increment. To overcome the multiplicative nature of the errors we present a geometric tangent linear approximation which enables us to linearize the observation operator with respect to a consistent lognormal multiplicative increment. In this paper we present an equivalent incremental version of the mixed lognormal-Gaussian which is based upon finding the most-likely state for additive increments for the Gaussian variables and lognormal for the multiplicative lognormal variables. We test this new approach with the Lorenz 1963 model under different size observational errors and observation window lengths.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFMNG12A..06F
- Keywords:
-
- 4468 NONLINEAR GEOPHYSICS Probability distributions;
- heavy and fat-tailed;
- 3315 ATMOSPHERIC PROCESSES Data assimilation