Scale Dependence of Subsurface Horizontal Density Gradients as Observed In-Situ Across Four Orders of Magnitude

Horizontal sampling of the ocean has been sparse for decades because of technical limitations. This can contribute to an incomplete depiction and misleading understanding of the hydrography. This is a particular concern for complex submesoscale and smaller scale flow structures that influence stratification and vertical transport of properties.

We use high resolution observations from a Triaxus towed undulating vehicle and develop a statistical subsampling pipeline in order to present the first multi-scale investigation of subsurface and interior horizontal density variability in a global context. Hydrographic transects were performed between 2018 and 2022 with vertical ranges extending from near-surface values down to depths varying between 50 and 350m in the oceanographically distinct regimes of the Arctic marginal ice zone, of a coastal upwelling area, of the equatorial Atlantic, and of the Antarctic Circumpolar Current. The investigation of lateral density gradient fields follows a baseline spanning four orders of magnitude, from 2m to 25km. Our main objectives are to determine the scaling properties of density fronts and to identify oceanic regimes that are susceptible to an underestimation of their thermohaline variability.

We find that the amplitude of horizontal density gradients increases non-linearly as the horizontal resolution is increased, closely following a proposed power law over all observed scales. This relation is applicable throughout all study regions allowing for a potential prediction of the gradient distribution for scales not resolved by measurements. Submesoscale density gradients are of higher amplitude along the base of shallow mixed layers, and in the presence of subsurface currents, frontal systems, and eddies. The latter two create strong lateral anisotropies in the density field, masking other contributions to the multi-scale spread of gradients. Furthermore, the gradient fields are primarily driven by salinity variability at high northern latitudes and by temperature variability in regions closer to the equator; in the Southern Ocean temperature and salinity largely compensate. The decay rate of the estimated gradients with increasing horizontal distance is related to fractal properties and a scale-dependent compensation of the density field.

This highlights that there is a certain arbitrariness regarding the strengths of density gradients in the present literature. We recommend that the employed horizontal resolution always be quoted alongside values of the horizontal density gradient.