Separating Background, Mesoscale and Diffusive Flow from Lagrangian Drifter Trajectories

Surface drifters provide direct measurements of transport and dispersion, making them an invaluable tool for studying ocean circulation. We parameterise the flow to explain what causes a drifter to take a particular path, using the unknown part of the flow to calculate diffusivity. However, uneven sampling patterns and sparse spatial coverage offer unique challenges. The distance between drifters in the Global Drifter Program (GDP) are typically larger than most ocean features, so the primary quantities estimated are based on single particle statistics such as mean (background) velocity and the residual diffusivity. Experiments such as LatMix and GLAD provide a better understanding of the ocean due to drifters being deployed in close proximity. We can therefore disentangle the flow into more components to parameterise the mesoscale diffusivity, reducing the residual diffusivity estimates by several orders of magnitude.

We introduce a novel method to estimate diffusivity which is based on spectral estimation techniques from time series analysis. Specifically, we apply a smoothed spectral estimate and approximate the optimal smoothing window parameter from physical reasoning, to obtain diffusivity estimates with reduced variance and error.
We first apply this diffusivity estimator to the GDP, where we separate the background flow from diffusivity. This estimator provides smoother estimates across space and time due to the reduced variance, and the removal of background velocity reduces the diffusivity estimate as we gain more information about the flow.

We then present a model where the flow comprises of a background flow, a mesoscale component containing strain and vorticity, and diffusivity.
The model is applied to data from the LatMix experiment and uses multiple particles to produce estimates for both the mesoscale and sub-mesoscale parts of the flow. We show how the sub-mesoscale parameters reduce our diffusivity estimates from ~10⁴ m²/s to ~0.1 m²/s.