We have constructed spatial structure functions for oceanographic variables, collected during 15 cruises off the coast of Vancouver Island, Canada over a 3 year period (1979–81), to determine the appropriate correlation function and unresolved noise level for objective mapping according to the Gauss-Markov theorem. The assumption of quasigeostrophic flow has been tested by comparing the longitudinal and transverse velocity shear structure functions derived from geopotential height fields with those derived from 6 current meter moorings. In addition objective maps of geopotential height imply current shears similar to the directly observed shear vectors, as would be expected under geostrophic control. Structure functions of geopotential height, temperature, salinity, and log-transformed phytoplankton chlorophyll a pigment concentration all have a broad maximum near a separation of 30 km, consistent with a dominant eddy wavelength of ≃60 km, also the estimated wavelength of the most unstable baroclinic disturbance. The sensitivity of the objective maps generated using the Gauss-Markov theorem to different correlation functions, length scales and noise levels was tested: where the sampling was well distributed, the patterns changed little.Temporal structure functions (for data from 25 cruises) of geopotential height, temperature and salinity are roughly cyclic with minima at time lags of 1 and 2 years. The structure functions increase monotonically with lags up to at least 90 days indicating that temporal changes during a ship survey (several days) are sufficiently small that the maps can be regarded as synoptic. Finally, a composite kinetic energy spectrum from a long term (≃3 years) current meter mooring at the edge of the continental shelf has well defined peaks in a band with 10–50 day periods (which we believe represents the mesoscale eddies with ≃60km wavelength), and at the annual and the major tidal and inertial periods.
Denman, Kenneth L., and Howard J. Freeland. 1985. "Correlation scales, objective mapping and a statistical test of geostrophy over the continental shelf." Journal of Marine Research 43, (3). https://elischolar.library.yale.edu/journal_of_marine_research/1785