In recent years, high-resolution ("eddying") global three-dimensional ocean general circulation models have begun to include astronomical tidal forcing alongside atmospheric forcing. Such models can carry an internal tide field with a realistic amount of nonstationarity, and an internal gravity wave continuum spectrum that compares more closely with observations as model resolution increases. Global internal tide and gravity wave models are important for understanding the three-dimensional geography of ocean mixing, for operational oceanography, and for simulating and interpreting satellite altimeter observations. Here we describe the most important technical details behind such models, including atmospheric forcing, bathymetry, astronomical tidal forcing, self-attraction and loading, quadratic bottom boundary layer drag, parameterized topographic internal wave drag, shallow-water tidal equations, and a brief summary of the theory of linear internal gravity waves. We focus on simulations run with two models, the HYbrid Coordinate Ocean Model (HYCOM) and the Massachusetts Institute of Technology general circulation model (MITgcm). We compare the modeled internal tides and internal gravity wave continuum to satellite altimeter observations, moored observational records, and the predictions of the Garrett-Munk (1975) internal gravity wave continuum spectrum. We briefly examine specific topics of interest, such as tidal energetics, internal tide nonstationarity, and the role of nonlinearities in generating the modeled internal gravity wave continuum. We also describe our first attempts at using a Kalman filter to improve the accuracy of tides embedded within a general circulation model. We discuss the challenges and opportunities of modeling stationary internal tides, non-stationary internal tides, and the internal gravity wave continuum spectrum for satellite altimetry and other applications. Introductionhis book chapter is about global modeling of oceanic internal tides and the oceanic internal gravity wave continuum. The chapter focuses on hydrodynamical modeling, rather than empirical modeling, of such motions. Due to the operational oceanography theme of the book in which this chapter resides, we focus on high-spatial-resolution numerical models run over relatively short time scales-i.e., simulations that could form the dynamical backbone of operational models-rather than on lower-resolution models run over decades or centuries for climate forecasting purposes. In this introductory section, after defining internal gravity waves and internal tides, we discuss the motivation for, requirements for, and history of global modeling of internal tides and the internal gravity wave continuum. A subsequent section focuses on the technical details underlying such models, such as atmospheric forcing, bathymetry, astronomical tidal forcing, self-attraction and loading, quadratic bottom boundary layer drag, parameterized topographic internal wave drag, shallow-water tidal equations, and a brief synopsis of internal wave theor...

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The ocean tidal velocity and elevation can be estimated concurrently with the ocean circulation by adding the astronomical tidal forcing, parameterized topographic internal wave drag, and self-attraction and loading to the general circulation physics. However, the accuracy of these tidal estimates does not yet match accuracies in the best data-assimilative barotropic tidal models. This paper investigates the application of an Augmented State Ensemble Kalman Filter (ASEnKF) to improve the accuracy of M 2 barotropic tides embedded in a 1/12.5° three-dimensional ocean general circulation model. The ASEnKF is an alternative to the techniques typically used with linearized tide-only models; such techniques cannot be applied to the embedded tides in a nonlinear eddying circulation. An extra term, meant to correct for errors in the tide model due to imperfectly known topography and damping terms, is introduced into the tidal forcing. Ensembles of the model are created with stochastically generated forcing correction terms. The discrepancies for each ensemble member with TPXO, an existing data-assimilative tide model, are computed. The ASEnKF method yields an optimal estimate of the model forcing correction terms, that minimizes resultant root mean square (RMS) tidal sea surface elevation error with respect to TPXO, as well as an estimate of the tidal elevation. The deep-water, global area-averaged RMS sea surface elevation error of the principal lunar semidiurnal tide M 2 is reduced from 4.4 cm in a best-case nonassimilative solution to 2.6 cm. The largest elevation errors in both the non-assimilative and ASEnKF

Eulerian velocity fields are derived from 300 drifters released in the Gulf of Mexico by The Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) during the summer 2012 Grand Lagrangian Deployment (GLAD) experiment. These data are directly assimilated into the Navy Coastal Ocean Model (NCOM) four-dimensional variational data assimilation (4DVAR) analysis system in a series of experiments to investigate their impact on the model circulation. The NCOM-4DVAR is a newly developed tool for data analysis, formulated for weak-constraint data assimilation based on the indirect representer method. The assimilation experiments take advantage of this velocity data along with other available data sources from in situ and satellite measurements of surface and subsurface temperature and salinity. Three different experiments are done: (i) A nonassimilative NCOM free run, (ii) an assimilative NCOM run that utilizes temperature and salinity observations, and (iii) an assimilative NCOM run that uses temperature and salinity observations as well as the GLAD velocity observations. The resulting analyses and subsequent forecasts are compared to assimilated and future GLAD velocity and temperature/salinity observations to determine the performance of each experiment and the impact of the GLAD data on the analysis and the forecast. It is shown that the NCOM-4DVAR is able to fit the observations not only in the analysis step, but also in the subsequent forecast. It is also found that the GLAD velocity data greatly improves the characterization of the circulation, with the forecast showing a better fit to future GLAD observations than those experiments without the velocity data included.