A least-square regression analysis is applied for the estimation of velocity streamfunction field based on discretely sampled current meter data. The coefficients of a streamfunction that is expanded in terms of trigonometric basis function are obtained by enforcing the horizontal non-divergence of two-dimensional flow field. This method avoids interpolation and gives a root-mean-square (rms) residual of fit which includes the divergent part and noisiness of oceanic data. The implementation of the method is done by employing a boundaryfitted, curvilinear orthogonal coordinate which facilitates the specification of boundary conditions. An application is successfully made to the Texas-Louisiana shelf using the 32 months current meter data (31 moorings) observed as a part of the Texas-Louisiana Shelf and Transport Processes Study (LATEX). The rms residual of the fitting is relatively small for the shelf, which indicates the field is well represented by the streamfunction.

An objective method for the generation of velocity streamfunction is presented for dealing with discretely sampled oceanic data. The method treats a Poisson equation (forced by vorticity) derived from Helmholtz theorem in which streamfunction is obtained by isolating the non-divergent part of the two-dimensional flow field. With a mixed boundary condition and vorticity field estimated from observed field, the method is implemented over the Texas-Louisiana shelf based on the current meter data of the Texas-Louisiana Shelf Circulation and Transport Processes Study (LATEX) measured at 31 moorings for 32 months (April 1992 - November 1994). The resulting streamfunction pattern is quite consistent with observations. The streamfunction field by this method presents an opportunity to initialize and to verify computer models for local forecasts of environmental flow conditions for oil spill, nutrient and plankton transports as well as opportunity to understand shelf-wide low-frequency currents.