Inferring physical parameters from Lagrangian trajectories using stochastic processes

We demonstrate how the theory of stochastic processes can be used to quantify physical features and test hypotheses from observed or modeled Lagrangian trajectories. We propose a simple technique for constructing physically motivated stochastic processes, and then estimating the parameters from observed data. Applications of our approach include new techniques for estimating diffusivity, inertial oscillations, and the decay rate of frequency spectra, amongst others. For example, we demonstrate that a basic four-parameter stochastic process captures the anisotropy of Lagrangian velocities in a quasi-geostrophic forced-dissipative turbulence simulation, and that the estimated anisotropy timescale can be used to infer the Rhines scale of the system. We also highlight how stochastic processes can be used to infer physical features of other datasets, such as trajectories obtained from the Global Drifter Program.

The stochastic models we propose are simple, ranging from 3 to 6 parameters depending on the application. This allows for an easy physical interpretation of each parameter, and allows parameters to be estimated from relatively short trajectories. This is useful when data is sparse or when the trajectory is traversing an inhomogeneous environment. Our models handle many of the practicalities of observed data, such as nonstationarity, anisotropy and inhomogeneity, as we demonstrate with examples. The stochastic approach is then combined with statistical theory to construct confidence intervals of the parameter estimates, as well as performing various hypothesis tests, such as testing for anisotropy, or for the presence of frequency-shifted inertial oscillations due to eddies.