An exact adjoint for the full-scale Bryan-Cox primitive equation model is applied to assimilate the North Atlantic climatologies. The inverse calculation aims at searching a steady state oceanic general circulation consistent with observations, by controlling the model input parameters (such as the initial states and the upper thermal and haline boundary conditions). Two climatological hydrographies (Levitus (1982) and Fukumori and Wunsch (1991)) are used for the assimilation. This enables the examination of the sensitivity of the assimilated results to data quality. In addition, the consistency between the climatological hydrography and fluxes is discussed by examining the fits between the optimally estimated surface fluxes and the fluxes calculated by Oberhuber (1988). The efforts made in the study are directed toward assessing the effectiveness of the combined OGCM/ adjoint approach in estimating the state of the ocean from climatologies and identifying the associated problems. The major findings of the study include: (1) The results show that the full OGCM dynamics substantially helps the model in better simulating the frontal structure of the Gulf Stream system and the large-scale features of the velocity field, thus demonstrating the advantage of the full OGCM and its exact adjoint. (2) The study finds that the optimized temperature field has a systematic error structure in the vertical—the upper ocean is cooler and the deep ocean is warmer compared to the climatology. Our analysis indicates that the cool surface layer is a correction imposed by the optimization to reduce large data misfits in the deep ocean due to the deep warming. This deep warming is an outcome of using the steady state assumption, the annual mean climatology and the relaxation boundary condition at the model northern boundary. The annual mean hydrography has a surface water warmer than the observed winter surface water, and a deep ocean whose properties are determined by the surface water at high latitudes. Due to the imposed model northern boundary condition, the modeled deep waters are formed through the artificial sinking of surface waters with annual-mean temperature in the relaxation zone. This process leads to a warm deep ocean and large model-data discrepancies in the vast deep layer. In order to reduce the misfits as required by the optimal procedure, the surface layer which is the source for the modeled deep water needs to be cooler. The strong and deep vertical mixing formed in the model provides the means for an effective cooling. The results further show that the surface cooling is stronger for the experiment assimilating the Fukumofi and Wunsch hydrography because this climatology has an even warmer surface water due to the use of the summer-dominated data source. (3) The experiments assimilating the Levitus hydrography illustrate two anomalous features, one is a strong zonally integrated upwelling in the midlatitude and the other a very noisy flux estimation. The analysis shows that both features are induced by the smeared representation of the Gulf Stream frontal structure in the Levitus hydrography, which indicates that data quality is one of the important factors in obtaining satisfactory results from the assimilation. (4) Although the requirements for a global minimum are only partially satisfied, the experiments show that, comparing with the Levitus hydrography, the Fukumori and Wunsch hydrography is dynamically more compatible with the Oberhuber climatological fluxes.
Yu, Lisan, and Paola Malanotte-Rizzoli. 1996. "Analysis of the North Atlantic climatologies using a combined OGCM/adjoint approach." Journal of Marine Research 54, (5). https://elischolar.library.yale.edu/journal_of_marine_research/2203