This paper presents a least squares method to estimate the horizontal (isotropic or anisotropic) spatial covariance of two-dimensional orthogonal vector components, without introducing an intervening mapping step and biases, from the spatial covariance of the nonorthogonally and irregularly sampled raw scalar velocities. The field is assumed to be locally homogeneous in space and sampled in an ensemble so the unknown spatial covariance is a function of spatial lag only. The transformation between the irregular grid on which nonorthogonal scalar projections of the vector are sampled and the regular orthogonal grid on which they will be mapped is created using the geometry of the problem. The spatial covariance of the orthogonal velocity components of the field is parameterized by either the energy (power) spectrum in the wavenumber domain or the lagged covariance in the spatial domain. The energy spectrum is constrained to be nonnegative definite as part of the solution of the inverse problem. This approach is applied to three example sets of data, using nonorthogonally and irregularly sampled radial velocity data obtained from 1) a simple spectral model, 2) a regional numerical model, and 3) an array of high-frequency radars. In tests where the true covariance is known, the proposed direct approaches fitting to parameterization of the nonorthogonally and irregularly sampled raw data in the wavenumber domain and spatial domain outperform methods that map the data to a regular grid before estimating the covariance.

A coastal ocean climatology of temperature and salinity in the Southern California Bight is estimated from conductivity-temperature-depth (CTD) and bottle sample profiles collected by historical California Cooperative Oceanic Fisheries Investigation (CalCOFI) cruises (1950-2009; quarterly after 1984) off southern California and quarterly/monthly nearshore CTD surveys (within 30 km from the coast except for the surfzone; 1999-2009) off San Diego and Los Angeles. As these fields are sampled regularly in space, but not in time, conventional Fourier analysis may not be possible. The time dependent temperature and salinity fields are modeled as linear combinations of an annual cycle and its five harmonics, as well as three standard climate indices (El Nino-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), North Pacific Gyre Oscillation (NPGO)), the Scripps Pier temperature time series, and a mean and linear trend without time lags. Since several of the predictor indices are correlated, the indices are successively orthogonalized to eliminate ambiguity in the identification of the contributed variance of each component. Regression coefficients are displayed in both vertical transects and horizontal maps to evaluate (1) whether the temporal and spatial scales of the two data sets of nearshore and offshore observations are consistent and (2) how oceanic variability at a regional scale is related to variability in the nearshore waters. The data-derived climatology can be used to identify anomalous events and atypical behaviors in regional-scale oceanic variability and to provide background ocean estimates for mapping or modeling. (C) 2015 Elsevier Ltd. All rights reserved.