Four-dimensional data assimilation with a wide range of scales
Article
English
OPEN
Tanguay, Monique
;
Bartello, Peter
;
Gauthier, Pierre
(2011)
A number of experiments investigating four-dimensional variational data assimilation using the adjoint method are presented. It has been proposed that the method will be able to produce improved initial conditions in data-sparse regions. In order to describe the flow in a region where there is little data, it is necessary for observational information either to be advected into the region, or to cascade downscale from larger scales characterizing the separation between observations. We focus on the latter and examine the method's ability to “fill in” small-scale detail determined dynamically from large-scale data. We choose to examine barotropic β-plane flow since it is one of the simplest geophysical settings involving a wide range of scales. In the limit of small error, predictability studies have shown that exponential error growth occurs along the gradients of two highly-correlated realizations. When the realizations have decorrelated, error statistics saturate at climatological levels. By appealing to the adjoint of the linearized equations, the adjoint method accounts for the former behaviour, but not the latter. When the assimilation period exceeds the validity timescale of the linearization, the assimilated fields show spectra which are spuriously shallow in the small scales, following the basic-state gradients. Moreover, it is essential to note that the validity timescale of the linearization is a function of lengthscale. Therefore, for a given assimilation period there is a scale below which useful initial conditions cannot be obtained. Equivalently, for a given model resolution, there is an assimilation period beyond which the exact initial conditions cannot be recovered. Some speculation on the optimal resolution at which to. perform 4D data assimilation as a function of the assimilation period is offered.DOI: 10.1034/j.1600-0870.1995.00204.x