As is apparent from the preceding discussion, a number of key problems (e.g., the “closure” problem, determining Eulerian statistics from Lagrangian statistics, dealing with array bias and diffusion bias) are still open that relate to the use of Lagrangian data in the description of the ocean circulation. They suggest a variety of directions for statistical research, ranging from statistical analysis for oceanographic data to probabilistic modeling for processes in the ocean. Some specific considerations are the following:
Filtering and parameter estimation for random fields governed by randomly perturbed ordinary and partial differential equations, with emphasis on numerical methods for nonlinear filtering, spectral methods, and others;
The study of single-particle statistics in inhomogeneous and nonstationary turbulent flows;
The study of multiparticle statistics;
The Lagrangian approach to turbulence;
The derivation of closed-form equations for moments of passive scalars; and
The exploration of the time evolution of distributions of passive scalars, with emphasis on intermittence (“patchiness”).