Material Transport in Oceanic Gyres. Part III: Randomized Stochastic Models

Abstract

Transport models are required for simulating the subgrid-scale transport by mesoscale eddies, which are typically not resolved in coarse-grid representations of the ocean circulation. Here, a new transport model from the class of stochastic models is formulated and its performance is tested against an eddy-resolving solution of the ocean circulation. The new approach overcomes drawbacks of the standard Markov models by broadening the range of simulated motions and by allowing transitions from one type of motion to another. The stochastic transport models yield random motion of individual passive particles, and the probability density function of the particle population may be interpreted as the concentration of a passive tracer. The models are developed for simulating observed transports of material by turbulent flows in the presence of coherent fluid structures, and they use only few internal parameters characterizing particular type of turbulence. The idea of stochastic randomization is introduced in the hierarchy of inhomogeneous and nonstationary stochastic models, and it is illustrated with the first kinematic-time parameter in the second-order Markov model. The principal property of the randomized stochastic hierarchy is its capability to simulate a broad range of intermediate-time, nondiffusive, single-particle dispersion behaviors involving a variety of timescales and length scales. This property is missing in the standard, nonrandomized hierarchy of Markov models which, as shown in a previous study, introduces errors in Lagrangian velocity correlation function and the corresponding material spreading process. The randomization implies that the parameter is represented by a probability distribution rather than a fixed average value. The probability distribution represents different populations of mesoscale fluctuations coexisting within a geographical region. The randomization effects are first studied in a homogeneous situation. Then, the performance of the inhomogeneous stochastic model is tested against passive tracer transport simulated by the fluid-dynamic, eddy-resolving ocean model. It is shown that the randomized model performs systematically better than the nonrandomized one, although only modestly so in some transport measures. Also, systematic differences are found between the direct solution of the stochastic model and the corresponding diffusion process with the eddy diffusivity estimated from the stochastic model. A local algorithm is proposed for estimating all the model parameters.