Reconstruction of oceanic flow characteristics from quasi‐Lagrangian data: 1. Approach and mathematical methods

Abstract

We describe a nontraditional method for processing data derived from quasi-Lagrangian tracers. The approach relies on a representation of the thermohydrodynamic field as a set of a finite number of functions (modes) with the subsequent computation of mode amplitudes from quasi-Lagrangian data. This requires special methods for calculating mode components of the thermohydrodynamic field from Lagrangian observations. Also, because of the quasi-Lagrangian nature of the data there are special problems caused by the need to filter in both space and time and to account for motions unresolved by such observations. The former problem is addressed by a filtering procedure based on a variational criteria and Pontryagin's principle. To handle the latter problem, a subgrid parameterization scheme appropriate for Lagrangian data is proposed. 1.Lagrangian" will be used to designate this setting. Of course, real probes in the surface layer also will respond differently than do generic parcels to accelerations arising from winds and waves. These effects can be quantified and minimized through engineering studies. The emphasis here is on procedures for recovering mesoscale and general circulation features from quasi-Lagrangian data, and so the latter effects will not be addressed.The present approach falls into the third category in that it utilizes the deterministic character of Lagrangian data and is complementary to numerical modeling. It differs, however, from the approach taken by Kitwan et al. [ 1988, 1990] in that no a priori transformation between Eulerian and Lagrangian frames is required. It can also be applied to basin-scale data sets, whereas the Kirwan, et al. methodology is "local." The analysis utilizes mathematical tools that are standard for Eulerian data and models. In doing so, it addresses the important issue of how to filter the trajectory data in a manner consistent with Eulerian data analysis. This is a fundamental problem in oceanography, as Eulerian data lend themselves naturally to discerning time scales while Lagrangian data encapsulate both time and space information.In view of these issues, a detailed airing of the mathematical basis of this approach is appropriate. This is provided in the next three sections. Section 2 gives some background and rationale, section 3 provides the general formulation, and section 4 shows how to obtain the mode structure of the velocity field. In section 5 the mathematical formalisms developed in the previous sections are applied to the problem of obtaining the mode representation of temperature data.Up to this point the mathematical approach is an adaptation of methods from classical theoretical physics. The next two sections (6 and 7) address problems peculiar to quasi-Lagrangian data. Methods based on a variational principle for filtering the observations in both space and time are discussed in section 6. Quasi-Lagrangian data are discrete and subject to aliasing by motions whose scales are less than the sampling rate. Section 7 addresses the issue of parame-9733 V. ...

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