The M2 Internal Tide off Oregon: Inferences from Data Assimilation

Abstract

A linearized baroclinic, spectral-in-time tidal inverse model has been developed for assimilation of surface currents from coast-based high-frequency (HF) radars. Representer functions obtained as a part of the generalized inverse solution show that for superinertial flows information from the surface velocity measurements propagates to depth along wave characteristics, allowing internal tidal flows to be mapped throughout the water column. Application of the inverse model to a 38 km ϫ 57 km domain off the mid-Oregon coast, where data from two HF radar systems are available, provides a uniquely detailed picture of spatial and temporal variability of the M 2 internal tide in a coastal environment. Most baroclinic signal contained in the data comes from outside the computational domain, and so data assimilation (DA) is used to restore baroclinic currents at the open boundary (OB). Experiments with synthetic data demonstrate that the choice of the error covariance for the OB condition affects model performance. A covariance consistent with assumed dynamics is obtained by nesting, using representers computed in a larger domain. Harmonic analysis of currents from HF radars and an acoustic Doppler profiler (ADP) mooring off Oregon for May-July 1998 reveals substantial intermittence of the internal tide, both in amplitude and phase. Assimilation of the surface current measurements captures the temporal variability and improves the ADP/solution rms difference. Despite significant temporal variability, persistent features are found for the studied period; for instance, the dominant direction of baroclinic wave phase and energy propagation is always from the northwest. At the surface, baroclinic surface tidal currents (deviations from the depth-averaged current) can be 10 cm s Ϫ1 , 2 times as large as the depth-averaged current. Barotropic-to-baroclinic energy conversion is generally weak within the model domain over the shelf but reaches 5 mW m Ϫ2 at times over the slopes of Stonewall Bank.

The Cascade of Tidal Energy from Low to High Modes on a Continental Slope

“…To connect our modes with the Laplace tidal equations, the vertical structure functions obey a linear free surface and flat bottom (Miles 1974). Previous studies have derived surface and internal-tide energy equations by separating terms involving depth averages and residuals (e.g., Kurapov et al 2003). Here, this methodology is extended by deriving energy equations for each vertical mode.…”

“…Internal-tide generation (e.g., Kurapov et al 2003;Kelly et al 2010) is the rate of work done by the surface tide on the internal tide and can be obtained from (7) by setting m 5 0 (the surface-tide mode) and summing n from 1 to ' (the internal-tide modes),…”

Assimilation of HF radar surface currents to optimize forcing in the northwestern Mediterranean Sea

“…Various assimilation methods have been developed based on nudging (Lewis et al, 1998), Kalman filtering using parametrized (Paduan and Shulman, 2004;Shulman and Paduan, 2009) or ensemble (Breivik and Saetra, 2001;Oke et al, 2002b;Barth et al, 2008a) error covariances, and the application of adjoint-based methods (Kurapov et al, 2003;Hoteit et al, 2009).…”

Coastal observing and forecasting system for the German Bight – estimates of hydrophysical states

“…demanding problems. The assimilation techniques proposed in literature include optimal interpolation (e.g., Breivik and Saetra, 2001), more sophisticated statistical approaches (e.g., Oke et al, 2002;Paduan and Shulman, 2004;Barth et al, 2008Barth et al, , 2010, variational techniques (e.g., Sentchev et al, 2006;Yaremchuk and Sentchev, 2009;Scott et al, 2000;Kurapov et al, 2003) and adhoc methods (e.g., Lewis et al, 1998).…”