The "scatter" of the stratification: a simple metric to study the finescale structure of the oceanic density field

Abstract. A new metric, hereafter the «scatter» of the stratification, is introduced to study the finescale structure present in the observed oceanic density field. It is based on the linear regression of buoyancy against depth over a layer of specified thickness h = O(10–100 m). The scatter η is defined as the fraction of the total buoyancy variance contained in the residuals (0 ≤ η ≤ 1). Thus a small scatter indicates that the buoyancy profile is linear to a very good approximation on the vertical scale h, while it is a poor description of the buoyancy field on that scale when the scatter approaches unity. The new metric includes a formal method to estimate instrument errors on buoyancy, and to isolate the scatter arising from physical effects from the scatter due to instrument errors. The scatter can also be related to the potential energy (E_m) present in the buoyancy field on vertical scales within the [h/2, 2h] interval. Specifically, it compares this energy with that (E^*_m) needed to remove the stratification of the layer (low scatter when E_m << E^*_m, large scatter when E_m is comparable or larger than E^*_m).

The method is applied to a set of repeated hydrographic sections in the North Atlantic between Greenland and Portugal (OVIDE 2002–2023). It is found that the background Garrett-Munk (GM) internal wavefield contributes to low values of scatter (η < 0.1 with E_m ∼ E_m^GM << E^*_m), that thermohaline intrusions in the Irminger Sea raise the scatter slightly above this value (0.1 ≤ η ≤ 0.2 with E_m^GM ≤ E_m ≤ E^*_m), while the interaction of tidal (Reykjanes Ridge) and mesoscale (East Thulean Rise) flows with topography, the western boundary current regime of the East Greenland – Irminger Current and double diffusive convective events below the core of the Mediterranean Water all increase it even further (η > 0.2 and E_m^GM << E_m ∼ E^*_m). The Iberian Abyssal Plain is found to be a region where the stratification is so low that only a small amount of wave activity is needed to create a large scatter. The probability density function of η does not show gaps but changes shape depending on the value of h.

It is hoped that the scatter of the stratification can offer a useful benchmark for high resolution numerical models of the oceans, and can help detect and understand changes in oceanic stratification, particularly in the abyss where finite instrument errors and low stratification pose significant challenges, among many other possible applications of the method.