Four-dimensional temperature, salinity and mixed layer depth in the Gulf Stream, reconstructed from remote sensing with physics-informed deep learning.

Despite the ever-growing amount of ocean's data, the interior of the ocean remains poorly sampled, especially in regions of high variability such as the Gulf Stream. The use of neural networks to interpolate properties and understand ocean processes is highly relevant. We introduce OSnet (Ocean Stratification network), a new ocean reconstruction system aimed at providing a physically consistent analysis of the upper ocean stratification. The proposed scheme is a bootstrapped multilayer perceptron trained to predict simultaneously temperature and salinity (T-S) profiles down to 1000m and the Mixed Layer Depth (MLD) from satellite data covering 1993 to 2019. The inputs are sea surface temperature and sea level anomaly, complemented with mean dynamic topography, bathymetry, longitude, latitude and the day of the year. The in-situ profiles are from the CORA database and include Argo floats and ship-based profiles. The prediction of the MLD is used to adjust a posteriori the vertical gradients of predicted T-S profiles, thus increasing the accuracy of the solution and removing vertical density inversions. The root mean square error of the predictions compared to the observed in situ profiles is of 0.66 °C for temperature, 0.11 psu for salinity and 39 m for the MLD.
The prediction is generalized on a 1/4° daily grid, producing four-dimensional fields of temperature and salinity, with their associated confidence interval issued from the bootstrap. The maximum of uncertainty is located north of the Gulf Stream, between the shelf and the current, where the variability is large. To validate our results we compare them with the observation-based Armor3D weekly product and the physics-based ocean reanalysis Glorys12. The OSnet reconstructed field is coherent even in the pre-ARGO years, demonstrating the good generalization properties of the network. It reproduces the warming trend of surface temperature, the seasonal cycle of surface salinity and presents coherent patterns of temperature, salinity and MLD. While OSnet delivers an accurate interpolation of the ocean's stratification, it is also a tool to study how the interior of the ocean's behaviour reflects on the surface data. We can compute the relative importance of each input for each T-S prediction and analyse how the network learns which surface feature influences most which property and at which depth. Our results are promising and demonstrate the power of deep learning methods to improve the predictions of ocean interior properties from observations of the ocean surface.