4DVAR Balance Operator

[arango]

We added the balance operator (BALANCE_OPERATOR option) to the 4DVAR algorithms. This formulation follows the methodology described by Weaver et al. (2006). It basically computes the off diagonal correlation/covariances terms used during variational data assimilation. The balance operator computes the multivariate covariances based on several balance relationships.

The balance operator is used to computed the unobserved variables information from the directly observed data. The ocean state vector is split between balanced and unbalanced components, except for temperature which is treated in totality and used as the starting point to establish the balanced part of the other variables. The multivariate formulation is obtained by establishing linear balance relationships between temperature and the other state increments using T-S empirical formulas, the linear equation of state, hydrostatic balance, and geostrophic balance.

Many thanks to Andy Moore and Javier Zavala for their help implementing this operator. This code is still in the early stages and it is likely to change in the future. It now released so the Beta-testers can start hacking it.