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Yoo, JG, Kim SY, Cornuelle BD, Kosro PM, Kurapov AL.  2017.  A Noninterpolated Estimate of Horizontal Spatial Covariance from Nonorthogonally and Irregularly Sampled Scalar Velocities. Journal of Atmospheric and Oceanic Technology. 34:2407-2430.   10.1175/jtech-d-17-0100.1   AbstractWebsite

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.

Hoteit, I, Cornuelle B, Kim SY, Forget G, Kohl A, Terrill E.  2009.  Assessing 4D-VAR for dynamical mapping of coastal high-frequency radar in San Diego. Dynamics of Atmospheres and Oceans. 48:175-197.   10.1016/j.dynatmoce.2008.11.005   AbstractWebsite

The problem of dynamically mapping high-frequency (HF) radar radial velocity observations is investigated using a three-dimensional hydrodynamic model of the San Diego coastal region and an adjoint-based assimilation method. The HF radar provides near-real-time radial velocities from three sites covering the region offshore of San Diego Bay. The hydrodynamical model is the Massachusetts Institute of Technology general circulation model (MITgcm) with 1 km horizontal resolution and 40 vertical layers. The domain is centered on Point Loma, extending 117 km offshore and 120 km alongshore. The reference run (before adjustment) is initialized from a single profile of T and S and is forced with wind data from a single shore station and with zero heat and fresh water fluxes. The adjoint of the model is used to adjust initial temperature, salinity, and velocity, hourly temperature, salinity and horizontal velocities at the open boundaries, and hourly surface fluxes of momentum, heat and freshwater so that the model reproduces hourly HF radar radial velocity observations. Results from a small number of experiments suggest that the adjoint method can be successfully used over 10-day windows at coastal model resolution. It produces a dynamically consistent model run that fits HF radar data with errors near the specified uncertainties. In a test of the forecasting capability of the San Diego model after adjustment, the forecast skill was shown to exceed persistence for up to 20 h. (C) 2008 Elsevier B.V. All rights reserved.