Application of Nonlinear Constraints in a Three-Dimensional Variational Ocean Analysis

Two kinds of nonlinear constraints, not previously studied in oceanography, have been adopted with the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar) in a three-dimensional oceanic variational analysis in the equatorial Pacific. One is the constraint for the variational Quality Control (QC) procedure and the other is used to avoid density and temperature inversions. Estimation of the large heat content anomaly in the upper ocean related to El Nino and La Nina phenomena is improved with the variational QC. For example, it prevents unusual but correct observation data on the thermocline deepening in the 1997/98 El Nino from being ignored. As a result, it improves the temperature field estimation in the eastern equatorial Pacific. The constraint for avoiding inversions prevents the low salinity layer at the surface and the barrier layer in the eastern equatorial Pacific in the El Nino period from being destroyed by the convective adjustment procedure performed after minimizing the cost function. Incorporating nonlinear constraints in variational analyses is thus a strong candidate for increasing the accuracy of analysis.