A Surface Quasi-Geostrophic-Based Dynamical-Statistical Framework to Retrieve Interior Temperature/Salinity From Ocean Surface

Conventional methods to reconstruct ocean interior temperature/salinity (T/S) from surface data are mostly "pure data-driven." On the other hand, the reconstruction methods based on surface quasi-geostrophic (SQG) dynamics present promising results in retrieving mesoscale density structures. It is rarely considered to incorporate SQG-based reconstructions to facilitate the estimation of subsurface T/S. Since the SQG equation does not contain explicit terms of T/S, a density incorporation tool of least square-multivariate empirical orthogonal functions (LS-mEOFs) algorithm is proposed to retrieve T/S fields based on concurrent surface T/S and vertical density reconstructions. The LS-mEOFs plus SQG-based density reconstruction is developed into a novel dynamical-statistical framework of subsurface T/S reconstruction. In this study, the framework is evaluated based on the eddy-resolving ocean general circulation model for the Earth simulator simulation. The density reconstructions of SQG, interior + SQG (isQG), and SQG-mEOF-R are incorporated respectively. The results are compared with two linear algorithms of multivariate linear regression and mEOF-R and two machine learning algorithms of fruit fly optimized generalized regression neural network and random forest. The LS-mEOFs plus isQG and LS-mEOFs plus SQG-mEOF-R present robust T/S reconstruction in the selected regions of Northwest Pacific and Southeast Pacific. Especially, the Southeast Pacific is abundant of subsurface-intensified eddies, where the T/S fields are poorly retrieved by machine learning algorithms. It is encouraging that the SQG-based dynamical-statistical framework can outperform the machine learning algorithms in retrieving those complicated T/S structures. The proposed framework is applicable to 3D mesoscale T/S reconstruction with the advent of surface water and ocean topography mission.