I updated the codes to add a new driver to estimate optimal observations, OPT_OBSERVATIONS. Many thanks to Gordon for implementing this option. This driver is an enhanced adjoint sensitivity algorithm, but the tangent linear is used and initialized from the adjoint final record (initial time). As in the AD_SENSITIVITY case, the user need to define the chosen functional or index, J, in terms of the space and/or time integrals of the model state, S(zeta,u,v,T,…). Small changes, dS, in S will lead to changes dJ in J:
dJ = (dJ/dzeta) dzeta + (dJ/du) du + (dJ/dv) dv + (dJ/dt) dT ...
and
dJ/dS = transpose(R) S
where transpose(R) is the adjoint propagator. It implies that the sensitivity for ALL variables, parameters, and space-time points can be computed from a single integration of the adjoint model.
As in AD_SENSITIVITY, the user needs to provide the adjoint sensitivity scope arrays Rscope, Uscope, and Vscope in the GRID NetCDF file. It also needs to provide the basic state trajectory (nonlinear solution) that is used to linearize the adjoint and tangent linear models.