AbstractWe present 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 non-orthogonally 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 between the irregular grid on which non-orthogonal 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 non-negative definite as part of the solution of the inverse problem. We apply this approach to three example sets of data, using non-orthogonally 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 parameterizations of the non-orthogonally 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.
Journal of Atmospheric and Oceanic Technology – American Meteorological Society
Published: Sep 19, 2017
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