Statistical Estimation of Flow Components and Diffusivity from Ocean Drifter Velocity Observations

Position and velocity measurements from freely-drifting surface buoys, known as drifters, provide a unique observational dataset for measuring ocean surface flow. The most immediate value of such observations is to aggregate data across drifters to determine the currents and the mean flow at given spatial locations. However, with more sophisticated models and statistical estimation techniques we can capture additional flow components from drifter data, as we shall demonstrate in this thesis. First, we shall demonstrate how data from closely-deployed collections of drifters can be jointly modelled to extract and identify mesoscale flow components—such as strain, vorticity, and divergence—as well as submesoscale components such as diffusivity, and background components such as inertial oscillations. We apply our methods to the LatMix deployment of drifters in the Sargasso Sea in 2011. Identification of so many flow components is made possible by considering the relative motions of the drifters with respect to each other, rather than in isolation. In the proceeding two chapters we shall build on these findings and provide evidence, both from simulation results and from analytically derived statistical properties, to demonstrate how the identification and estimation of flow components is expected to statistically behave as both the sampling features (e.g. number of drifters and length of deployment) and as both the sampling features (e.g. number of drifters and length of deployment) and the underlying flow field changes. Finally, we perform a separate analysis on Global Drifter Program data, where drifters are too far apart to be modelled relatively, and we instead perform a mean-flow and diffusivity separation using a novel estimator for estimating large-scale diffusivity which we propose from the spectral analysis of time series. A central goal of this thesis is to quantify the statistical error of parameter estimates of flow components, both in terms of bias and variance, and to then tune estimation methods to reduce these errors as much as possible. the underlying flow field changes. Finally, we perform a separate analysis on Global Drifter Program data, where drifters are too far apart to be modelled relatively, and we instead perform a mean-flow and diffusivity separation using a novel estimator for estimating large-scale diffusivity which we propose from the spectral analysis of time series. A central goal of this thesis is to quantify the statistical error of parameter estimates of flow components, both in terms of bias and variance, and to then tune estimation methods to reduce these errors as much as possible

Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories

Drifters deployed in close proximity collectively provide a unique observational data set with which to separate mesoscale and submesoscale flows. In this paper we provide a principled approach for doing so by fitting observed velocities to a local Taylor expansion of the velocity flow field. We demonstrate how to estimate mesoscale and submesoscale quantities that evolve slowly over time, as well as their associated statistical uncertainty. We show that in practice the mesoscale component of our model can explain much first and second-moment variability in drifter velocities, especially at low frequencies. This results in much lower and more meaningful measures of submesoscale diffusivity, which would otherwise be contaminated by unresolved mesoscale flow. We quantify these effects theoretically via computing Lagrangian frequency spectra, and demonstrate the usefulness of our methodology through simulations as well as with real observations from the LatMix deployment of drifters. The outcome of this method is a full Lagrangian decomposition of each drifter trajectory into three components that represent the background, mesoscale, and submesoscale flow