Alexander L. Kurapov

The M2 Internal Tide off Oregon: Inferences from Data Assimilation

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 3 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 M2 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 s21, 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 m22 at times over the slopes of Stonewall Bank.

Combined Effects of Wind-Driven Upwelling and Internal Tide on the Continental Shelf

Abstract Internal tides on the continental shelf can be intermittent as a result of changing hydrographic conditions associated with wind-driven upwelling. In turn, the internal tide can affect transports associated with upwelling. To study these processes, simulations in an idealized, alongshore uniform setup are performed utilizing the hydrostatic Regional Ocean Modeling System (ROMS) with conditions corresponding, as closely as possible, to the central Oregon shelf. “Wind only” (WO), “tide only” (TO), and “tide and wind” (TW) solutions are compared, utilizing cases with constant upwelling-favorable wind stress as well as with time-variable observed stress. The tide is forced by applying cross-shore barotropic flow at the offshore boundary with intensity sufficient to generate an internal tide with horizontal velocity amplitudes near 0.15 m s−1, corresponding to observed levels. The internal tide affects the subinertial circulation, mostly through the changes in the bottom boundary layer variability, re...

Spatial and Temporal Variability of the M2 Internal Tide Generation and Propagation on the Oregon Shelf

AbstractA 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 M2 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 stratific...

Representer‐based variational data assimilation in a nonlinear model of nearshore circulation

[1] A representer-based variational data assimilation (DA) method is implemented with a shallow-water model of circulation in the nearshore surf zone and tested with synthetic data. The behavior of the DA system is evaluated over a 1-hour time interval that is large compared to timescales characteristic of instability growth and eddy interactions. True reference solutions, from which the synthetic data are sampled, correspond to fully developed unsteady nonlinear flows driven by a steady spatially varying forcing representing the effect of breaking waves. Forcing and initial conditions are adjusted to fit the data. The convergence of the nonlinear optimization algorithm and the accuracy of the forcing and state estimates depend on the choice of the forcing error covariance C. In a weakly nonlinear (equilibrated waves) regime, using C that allows only a steady forcing correction yields a convergent and accurate solution. In a more strongly nonlinear regime, the DA system cannot find sufficient degrees of freedom in the steady forcing to control eddy variability. Implementing a bell-shaped temporal correlation function in C with the 1-min decorrelation scale yields a convergent linearized inverse solution that describes correctly the spatiotemporal variability in the eddy field. The corresponding estimate of forcing, however, is not satisfactory. Accurate estimates of both the flow and the forcing can be achieved by implementing a composite C with a temporal correlation separated into an O(1) steady and small amplitude time-variable parts.

Distant effect of assimilation of moored currents into a model of coastal wind‐driven circulation off Oregon

[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.

Data assimilation in a baroclinic coastal ocean model: Ensemble statistics and comparison of methods

The performance of data assimilation methods in an idealized three-dimensional time-dependent coastal baroclinic model is assessed by computing ensemble error statistics. The analytical representer solution allows for computation of posterior error statistics for the variational generalized inverse method (GIM) as well as sequential methods such as the Kalman filter (KF) and optimal interpolation (OI). Computations can be made in a straightforward way, given the statistics of errors in the model equations and data. The GIM yields solutions with significantly smaller variance than that given by KF or OI if the data contain valuable information about the past flow. This is the case, for instance, when a large fraction of the model error is due to uncertainty in the wind stress. In the scope of the model presented here, the plausibility of simplifications made in a practical OI scheme is analyzed. The unified study of the GIM, KF, and OI allows for the demonstratation of how the forecast error covariance used in a practical OI sequential scheme may be optimized with the use of lagged covariances for the model solution. The effect of the misspecified input error statistics on the solution quality is also assessed. In some practically relevant cases the use of future data by the GIM, in contrast to KF and OI, compensates for incorrectly specified input error covariances.

Modeling Bottom Mixed Layer Variability on the Mid-Oregon Shelf during Summer Upwelling

Abstract Results from a model of wind-driven circulation are analyzed to study spatial and temporal variability in the bottom mixed layer (BML) on the mid-Oregon shelf in summer 2001. The model assimilates acoustic Doppler profiler velocities from two cross-shore lines of moorings 90 km apart to provide improved accuracy of near-bottom velocities and turbulence variables in the area between the mooring lines. Model results suggest that the response of the BML thickness to upwelling- and downwelling-favorable winds differs qualitatively between an area of “simple” bathymetric slope at 45°N and a wider shelf area east of Stonewall Bank (44.5°N). At 45°N, the BML grows in response to downwelling-favorable conditions, in agreement with known theories. East of Stonewall Bank, the BML thickness is increased following upwelling events. In this area, the southward upwelling jet detaches from the coast and flows over a wider part of the Oregon shelf, creating conditions for Ekman pumping near the bottom. Based on ...

Coastal Ocean Forecasting: science foundation and user benefits

The advancement of Coastal Ocean Forecasting Systems (COFS) requires the support of continuous scientific progress addressing: (a) the primary mechanisms driving coastal circulation; (b) methods to achieve fully integrated coastal systems (observations and models), that are dynamically embedded in larger scale systems; and (c) methods to adequately represent air-sea and biophysical interactions. Issues of downscaling, data assimilation, atmosphere-wave-ocean couplings and ecosystem dynamics in the coastal ocean are discussed. These science topics are fundamental for successful COFS, which are connected to evolving downstream applications, dictated by the socioeconomic needs of rapidly increasing coastal populations.

Evaluation of directly wind‐coherent near‐inertial surface currents off Oregon using a statistical parameterization and analytical and numerical models

Directly wind-coherent near-inertial surface currents off the Oregon coast are investigated with a statistical parameterization of observations and outputs of a regional numerical ocean model and three one-dimensional analytical models including the slab layer, Ekman, and near-surface averaged Ekman models. The transfer functions and response functions, statistically estimated from observed wind stress at NDBC buoys and surface currents derived from shored-based high-frequency radars, enable us to isolate the directly wind-forced near-inertial surface currents. Concurrent observations of the wind and currents are crucial to evaluate the directly wind-forced currents. Thus, the wind stress and surface current fields obtained from a regional ocean model, which simulates variability of the wind and surface currents on scales comparable to those in observations, are analyzed with the same statistical parameterization to derive the point-by-point transfer functions and response functions. Model and data comparisons show that the regional ocean model describes near-inertial variability of surface currents qualitatively and quantitatively correctly. The estimated response functions exhibit decay time scales in a range of 3–5 days, and about 40% of the near-inertial motions are explained by local wind stress. Among the one-dimensional analytical models, the near-surface averaged Ekman model explains the statistically derived wind-current relationship better than other analytical models.

Intensified Diurnal Tides along the Oregon Coast

AbstractIntensified diurnal tides are found along portions of the Oregon shelf (U.S. West Coast) based on analyses of high-frequency (HF) radar surface current data and outputs of a 1-km resolution ocean circulation model. The K1 tidal currents with magnitudes near 0.07 m s−1 over a wider part of the shelf (Heceta Bank complex; 44°–44.5°N), previously predicted by Erofeeva et al., are confirmed here by newly available HF radar data. Intensified diurnal tides are also found along the narrow shelf south of Heceta Bank. In the close vicinity of Cape Blanco (42.8°N), diurnal tidal currents (K1 and O1 constituents combined) may reach 0.3 m s−1. Appreciable differences in diurnal tide intensity are found depending on whether the model is forced with tides and winds (TW) or only tides. Also, diurnal variability in wind forcing is found to affect diurnal surface velocities. For the case forced by tides alone, results strongly depend on whether the model ocean is stratified [tides only, stratified (TOS)] or not [t...