Generalized inversion of the Gent-Cane model of the tropical Pacific with Tropical Atmosphere-Ocean (TAO) data

We here describe the results of our latest effort to reanalyze TAO monthly mean Surface and subsurface temperature observations constrained by a tropical Pacific ocean model, and simultaneously to evaluate the physical consistency of the observations and the model. Both tasks are executed by weak-constraint, four-dimensional variational assimilation of the observations into the model. In this study our reanalysis employs the reduced-gravity Gent-Cane model, combined with the 'KPP-interior' parameterization of vertical turbulent fluxes. With the limited vertical resolution adopted in previous studies of this model, the 'W4DVAR' or inverse method fails to produce an acceptable reanalysis, as the dynamical residuals are too large locally ill space and time. Moreover, the objective significance test that is an essential product of the inversion rejects the model, even though the model is imposed only as a weak constraint, as convincingly as the even simpler Zebiak-Cane model was rejected (Bennett et al., 1998, 2000). In order to obtain a locally plausible reanalysis of the observations, we have to employ significantly finer vertical resolution. The calculations are extremely expensive and technically difficult, ill the interests of efficiency and convergence, we solve the fixed-interval smoothing problem for 3-month intervals (during the 1997-1998 El Ni (n) over tildeo, December 1996-March 1998), and we impose the continuity equations for layer thickness as strong constraints. We present detailed results for just one such experiment which shows the model in the best light. The resulting fits to the monthly-mean data are within our prior error assumptions and so constitute a highly plausible reanalysis. However, the significance test statistic for the inversion exceeds its expected value by many tens of standard deviations, forcing us to the inference that the model cannot ill fact be reconciled with the observations. The paradox of locally small residuals and a large test statistic is explained by an analysis of the degrees of freedom allowed in the weak constraints.