Analysis on observing optimization for the wind-driven circulation by an adjoint approach

The adjoint approach is a variational method which is often applied to data assimilation widely in meteorology and oceanography It is used for analyse s on observing optimization for the wind-driven Sverdrup circulation. The a djoint system developed by Thacker and Long (1992), which is based on the G FDL Byran-Cox model, includes three components, i.e. the forward model, the adjoint model and the optimal algorithm. The GFDL Byran-Cox model was inte grated for a long time driven by a batch of ideal wind stresses whose merid ional component is set to null and zonal component is a sine function of la titudes in a rectangle box with six vertical levels and 2 by 2 degree horiz ontal resolution. The results are regarded as a "real" representative of th e wind-driven Sverdrup circulation, from which the four dimensional fields are allowed to be sampled in several ways, such as sampling at the differen t levels or along the different vertical sections. To set the different sam ples, the fields of temperature, salinity and velocities function as the ob servational limit in the adjoint system respectively where the same initial condition is chosen for 4D VAR data assimilation. By examining the distanc e functions which measure the misfit between the circulation field from the control experiment of the adjoint system with a complete observation and t hose from data assimilation of adjoint approach in these sensitivity experi ments respectively, observing optimizations for the wind-driven Sverdrup ci rculation will be suggested under a fixed observational cost.