DIVA

"DIVA (Data-Interpolating Variational Analysis) allows the spatial interpolation of data (analysis) in an optimal way, comparable to optimal interpolation (OI). In comparison to OI it takes into account coastlines, sub-basins and advection. Calculations are highly optimized and rely on a finite element resolution. Tools to generate the finite element mesh are provided as well as tools to optimize the parameters of the analysis. Quality control of data can be performed and error fields can be calculated. Also detrending of data is possible. Finally 3D and 4D extensions are included with emphasis on direct computations of climatologies from ODV spreadsheet files.

DIVA uses a finite-element method to solve a variational principle which takes into account

1. the distance between analysis and data (observation constraint),
2. the regularity of the analysis (smoothness constraint),
3. physical laws (behaviour constraint).

The advantage of the method over classic interpolation methods is multiple:

• the coastline are taken into account during the analysis, since the variational principle is solved only in the region covered by the sea. This prevents the information from traveling across boundaries (e.g., peninsula, islands, etc) and then produce artificial mixing between water masses.
• the numerical cost is not dependent on the number of data, but on the number of degrees of freedom, itself related to the size of the finite-element mesh. 

http://www.data-assimilation.net/mediawiki/index.php/DIVA

http://www.data-assimilation.net/mediawiki/index.php/Software