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.

We present seafloor pressure records from the Cascadia Subduction Zone, alongside oceanographic and geophysical models, to evaluate the spatial uniformity of bottom pressure and optimize the geometry of sensor networks for resolving offshore slow‐slip transients. Seafloor pressure records from 2011 to 2015 show that signal amplitudes are depth‐dependent, with tidally filtered and detrended root‐mean‐squares of <2 cm on the abyssal plain and >6 cm on the continental shelf. This is consistent with bottom pressure predictions from circulation models and comparable to deformation amplitudes from offshore slow slip observed in other subduction zones. We show that the oceanographic component of seafloor pressure can be reduced to ≤1‐cm root‐mean‐square by differencing against a reference record from a similar depth, under restrictions that vary with depth. Instruments at 100–250 m require depths matched within 10 m at separations of <100 km, while locations deeper than 1,400 m are broadly comparable over separations of at least 300 km. Despite the significant noise reduction from this method, no slow slip was identified in the dataset, possibly due to poor spatiotemporal instrument coverage, nonideal deployment geometry, and limited depth‐matched instruments. We use forward predictions of deformation from elastic half‐space models and hindcast pressure from circulation models to generate synthetic slow‐slip observational records and show that a range of slip scenarios produce resolvable signals under depth‐matched differencing. For future detection of offshore slow slip in Cascadia, we recommend a geometry in which instruments are deployed along isobaths to optimize corrections for oceanographic signals.

[1] An optimal interpolation (OI) sequential algorithm is implemented for a threedimensional primitive equation model to assimilate current measurements from acoustic Doppler profilers moored on the Oregon shelf as a part of the Coastal Ocean Advances in Shelf Transport (COAST) upwelling experiment (May-August 2001). A stationary estimate of the forecast error covariance required by the OI is computed based on the error covariance in the model solution not constrained by data assimilation. Lagged model error covariances are used to account for the effect of previously assimilated data. The forecast error covariance has a shorter alongshore spatial scale than the model error covariance unconstrained by the data, as an effect of propagating dynamical modes. Assimilation of currents from one or two of the moorings located on the path of the upwelling jet helps to improve the model data rms error and correlation at the mooring sites located at an alongshore distance of 90 km, south or north from the assimilation sites. The coastal jet is deflected offshore over Heceta Bank, and assimilation of data from an inner-shelf mooring in the jet separation zone does not help to improve prediction in the far field. Larger improvements are obtained for the first part of the study period (yeardays 146-190). In the second part (days 191-237) the geometry of our limited area model possibly limits prediction accuracy. In numerical experiments involving assimilation of data from only one mooring the actual and expected rms error improvements are compared, providing a consistency test for the forecast error covariance.

A 1-km-horizontal-resolution model based on the Regional Ocean Modeling System is implemented along the Oregon coast to study average characteristics and intermittency of the M 2 internal tide during summer upwelling. Wind-driven and tidally driven flows are simulated in combination, using realistic bathymetry, atmospheric forcing, and boundary conditions. The study period is April through August 2002, when mooring velocities are available for comparison. Modeled subtidal and tidal variability on the shelf are in good quantitative agreement with moored velocity time series observations. Depth-integrated baroclinic tidal energy flux (EF), its divergence, and topographic energy conversion (TEC) from the barotropic to baroclinic tide are computed from high-pass-filtered, harmonically analyzed model results in a series of 16-day time windows. Model results reveal several ''hot spots'' of intensive TEC on the slope. At these locations, TEC is well balanced by EF divergence. Changes in background stratification and currents associated with winddriven upwelling and downwelling do not appreciably affect TEC hot spot locations but may affect intensity of internal tide generation at those locations. Relatively little internal tide is generated on the shelf. Areas of supercritical slope near the shelf break partially reflect baroclinic tidal energy to deeper water, contributing to spatial variability in seasonally averaged on-shelf EF. Despite significant temporal and spatial variability in the internal tide, the alongshore-integrated flux of internal tide energy onto the Oregon shelf, where it is dissipated, does not vary much with time. Approximately 65% of the M 2 baroclinic tidal energy generated on the slope is dissipated there, and the rest is radiated toward the shelf and interior ocean in roughly equal proportions. An experiment with smoother bathymetry reveals that slope-integrated TEC is more sensitive to bathymetric roughness than on-shelf EF.