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...

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

Understanding and forecasting the evolution of geophysical fluids is a major scientific and societal challenge. Forecasting algorithms should take into account all the available informations on the considered dynamical system. The Variational Data Assimilation (VDA) technique combines in a consistent way all these informations in an Optimality System in order to reconstruct the model inputs. VDA is currently used by the major meteorological centres. During the last two decades about thirty satellites were launched to improve the knowledge of the atmosphere and of the oceans. They continuously provide a huge amount of data that are still underused by numerical forecast systems. In particular, the dynamical evolution of some meteorological or oceanic features (such as eddies, fronts,. . .) that a human vision may easily detect is not optimally taken into account in realistic applications of VDA. Image Assimilation in VDA framework can be performed using pseudo-observation techniques : they provide some apparent velocity fields which are assimilated as classical observations. These measurements are obtained by some external procedures which are decoupled with the considered dynamical system. In this paper, we suggest a more consistent approach which directly incorporates image sequences into the Optimality System.

We analyze high-resolution (1 km) simulations of the western Pacific, Gulf of Mexico, and Arabian Sea to understand submesoscale eddy dynamics. A mask based on the Okubo–Weiss parameter isolates small-scale eddies, and we further classify those with |ζ/f| ≥ 1 as being submesoscale eddies. Cyclonic submesoscale eddies exhibit a vertical depth structure in which temperature anomalies from the large-scale background are negative. Peak density anomalies associated with cyclonic submesoscale eddies are found at a depth approximately twice the mixed layer depth (MLD). Within anticyclonic submesoscale eddies, temperature anomalies are positive and have peak density anomalies at the MLD. The depth–depth covariance structure for the cyclonic and anticyclonic submesoscale eddies have maxima over a shallow region near the surface and weak off diagonal elements. The observed vertical structure suggests that submesoscale eddies have a shallower depth profile and smaller vertical correlation scales when compared to the mesoscale phenomenon. We test a two-dimensional submesoscale eddy dynamical balance. Compared to a geostrophic dynamical balance using only pressure gradient and Coriolis force, including velocity tendency and advection produces lower errors by about 20%. In regions with strong tides and associated internal waves (western Pacific and Arabian Sea), using the mixed layer integrated small-scale steric height within the dynamical equations produces the lowest magnitude errors. In areas with weak tides (Gulf of Mexico), using small-scale sea surface height (SSH) produces the lowest magnitude errors. Recovering a submesoscale eddy with the correct magnitude and rotation requires integration of small-scale specific volume anomalies well below the mixed layer.