Reconstructing temperature and salinity structure in the ocean interior from sea surface parameters obtained from satellites and other sources is an important issue and is used in operational-based ocean data assimilation systems. Sea surface height (SSH) is the most important parameter in the estimation of internal structure because it is the integral information of water temperature and salinity. In this study, the variational method proposed by Fujii and Kamachi (2003) using the vertically coupled modes of the temperature-salinity empirical orthogonal function (EOF) is applied to ARGO float data and hydrographic observation data along the south coast of Japan to investigate the characteristics of errors depending on the SSH. Based on the results, an estimation method that incorporates stratification from the additional information of SSH is also proposed. ARGO float data were used to create the vertical mode of EOF. The period was 2001-2019, and the domain was 120°E to 150°E and 20°N to 35°N. In accordance with Fujii and Kamachi (2003), the 1100 m depth data were decomposed into 20 layers and the values at each depth were interpolated using the Akima method.
The ocean interior structure was reconstructed from surface data at the ARGO float observation points used as training data for the EOF calculation, and error characteristics were investigated. It was confirmed that the errors in the temperature and salinity profiles increased as the absolute value of the anomaly of SSH from climatological values (SSHa) increased. Comparison of the individual profiles confirms that the results reconstructed by the EOF smoothly estimate the lens structure of the ocean interior due to eddies and do not adequately reflect the stratification. A correlation was confirmed between SSHa and the vertical density gradient, a parameter related to the stratification of the ocean interior. By approximating SSHa with a quadratic function of the vertical density gradient, a method to incorporate stratification structure from SSHa observations to reconstruct temperature and salinity was applied. The method is based on the cost function proposed by Fujii and Kamachi (2003) with the addition of a fourth term that incorporates information on stratification structure.
The reconstruction and evaluation of the the ocean interior were conducted using hydrographic observation data crossing the Kuroshio Current along the south coast of Japan, using the method proposed by Fujii and Kamachi (2003) and adding a term related to the stratification structure to the method, respectively, and the results were compared. The addition of the new term improved the reproducibility of the stratification structure associated with eddies, especially around 600 m depth, and reduced the error. On the other hand, the salinity error increased slightly at depths shallower than 300 m. In the current method, SSHa, one-dimensional information on the sea surface related to the stratification structure, is used, assuming SSH observations by a nadir altimeter. By incorporating 2D SSH by SWOT, etc., for which observations have started, and applying it to the cost function, it is thought that reconstruction that more closely reflects the real stratification structure will be possible.