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George L. Mellor
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George L. Mellor

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A semi-empirical theory, used to predict buoyancy effects in a density-stratified and shear-driven flow, is also applied to the case of a boundary layer with curvature. Curved flow data are available and interesting in their own right since it can be seen that the Reynolds stress is reduced to zero at a critical “curvature Richardson” number predicted reasonably well by the theory.

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George L. Mellor

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George L. Mellor

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The first part of this paper is generic; it demonstrates a problem associated with one-dimensional, ocean surface layer model comparisons with ocean observations. Unlike three-dimensional simulations or the real ocean, kinetic energy can inexorably build up in one-dimensional simulations, which artificially enhances mixing. Adding a sink term to the momentum equations counteracts this behavior. The sink term is a surrogate for energy divergence available to three-dimensional models but not to one-dimensional models.

The remainder of the paper deals with the Mellor–Yamada boundary layer model. There exists prior evidence that the model’s summertime surface temperatures are too warm due to overly shallow mixed layer depths. If one adds a sink term to approximate three-dimensional model behavior, the warming problem is exacerbated, creating added incentive to seek an appropriate model change. Guided by laboratory data, a Richardson-number-dependent dissipation is introduced and this simple modification yields a favorable improvement in the comparison of model calculations with data even with the momentum sink term in place.

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George L. Mellor

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This is a revision of a previous paper dealing with three-dimensional wave-current interactions. It is shown that the continuity and momentum equations in the absence of surface waves can include waves after the addition of three-dimensional radiation stress terms, a fairly simple alteration for numerical ocean circulation models. The velocity that varies on time and space scales, which are large compared to inverse wave frequency and wavenumber, is denoted by û α and, by convention, is called the “current.” The Stokes drift is labeled u and the mean velocity is U αû α + u . When vertically integrated, the results here are in agreement with past literature.

Surface wind stress is empirical, but transfer of the stress into the water column is a function derived in this paper. The wave energy equation is derived, and terms such as the advective wave velocity are weighted vertical integrals of the mean velocity. The wave action equation is not an appropriate substitute for the wave energy equation when the mean velocity is depth dependent.

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George L. Mellor

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By considering the complex of one-point, turbulent moment equations for velocity, pressure and temperature, it appears possible to predict some properties of diabatic, density-stratified planetary layers using empirical information obtained from laboratory turbulence data in the absence of density stratification. In this paper attention is focused on the near-surface, constant-flux layer. The results, like the empirical input, are simple and, hopefully, will be instructive and useful in the formulation of improved and possibly more complicated models in the future.

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George L. Mellor

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Sommeria and Deardorff (1977) have derived turbulence closure relations which should be important to cloud modeling. To obtain these relations they have hade to invoke some analytical approximations and data from numerical statistical experiments. In the present paper, the analytical approximations have been eliminated. Somewhat surprisingly, results obtained here agree exactly with those obtained by the previous authors. Other new and useful relations are presented.

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Tal Ezer and George L. Mellor

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A three-dimensional data assimilation scheme is described and tested, using the Geosat altimeter data and a high-resolution, primitive equation, numerical ocean model of the Gulf Stream region. The assimilation scheme is based on an optimal interpolation approach in which data along satellite tracks are continuously interpolated horizontally and vertically into the model grid and assimilated with the model prognostic fields. Preprocessed correlations between surface elevation anomalies and subsurface temperature and salinity anomalies are used to project surface information into the deep ocean; model and data error estimates are used to optimize the assimilation. Analysis fields derived from the Navy's Optimum Thermal Interpolation System are used to initialize the model and to provide some estimate of errors.

To evaluate the effectiveness of the assimilation scheme, the errors of model oceanic fields (surface elevation, Gulf Stream axis, temperature) with data assimilation are compared with errors without data assimilation (i.e., a pure forecast). Although some mesoscale meanders and rings are not well produced by the assimilation model, consistent reduction of errors by the assimilation is demonstrated. The vertical distribution of errors reveals that the scheme is most effective in nowcasting temperatures at middepth (around 500 m) and less effective near the surface and in the deep ocean. The scheme is also more effective in nowcasting the Gulf Stream axis location than in nowcasting temperature variations. A comparison of the assimilation scheme during two periods shows that the nowcast skill of the assimilated model is reduced in May–September 1988, compared to May–July 1987, due to poor coverage of the altimeter data during 1988.

This paper is one step toward a dynamic model and data assimilation system, which when fully developed, should provide useful nowcast and forecast information.

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Tal Ezer and George L. Mellor

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Satellite-derived surface data have become an important source of information for studies of the Gulf Stream system. The question of just how useful these datasets are for nowcasting the subsurface thermal fields, however, remains to be fully explored. Three types of surface data—sea surface temperature (SST), sea surface height (SSH), and Gulf Stream position (GSP)—are used here in a series of data assimilation experiments to test their usefulness when assimilated into a realistic primitive equation model. The U.S. Navy’s analysis fields from the Optimal Thermal Interpolation System are used to simulate the surface data and to evaluate nowcast errors. Correlation factors between variations of the surface data and variations of the subsurface temperature are used to project the surface information into the deep ocean, using data and model error estimates and an optimal interpolation approach to blend model and observed fields.

While assimilation of each surface data source shows some skill in nowcasting the subsurface fields (i.e., reducing errors compared to a control case without assimilation), SSH data reduce errors more effectively in middepths (around 500 m), and SST data reduce errors more effectively in the upper layers (above 100 m). Assimilation of GSP is effective in nowcasting the deep Gulf Stream, while the model dynamics produce eddies that are not included in the GSP analysis. An attempt to optimally combine SST and SSH data in the assimilation shows an improved skill at all depths compared to assimilation of each set of data separately.

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Tal Ezer and George L. Mellor

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A primitive equation regional model is used to study the effects of surface and lateral forcing on the variability and the climatology of the Gulf Stream system. The model is an eddy-resolving, coastal ocean model that includes thermohaline dynamics and a second-order turbulence closure scheme to provide vertical mixing. The surface forcing consists of wind stroll and beat fluxes obtained from the Comprehensive Ocean-Atmosphere Data Set (COADS). Sensitivity studies am performed by driving the model with different forcing (e.g., annual versus zero surface forcing or monthly versus annual forcing). The model climatology, obtained from a five-year simulation of each case, is then compared to observed climatologies obtained from satellite-derived SST and hydrocast data.

The experiments in which surface best flux and wind stress were neglected show less realistic Gulf Stream separation and variability, compared with experiments in which annual or seasonal forcing are used. A similar unrealistic Gulf Stream separation is also obtained when the slope-water inflow at the northeast boundary is neglected. The experiments suggest that maintaining the density structure and the concomitant geostrophic flow in the northern recirculation gyre plays an important role in the separation of the Gulf Stream. The maintenance of the recirculation gyre is affected by beat transfer, wind stress and slope-water inflow. The beat transfer involves several processes: lateral eddy monster, surface heat gm and vertical mixing. Further improvement of the Gulf Stream separation and climatology are obtained when seasonal changes in the lateral temperature and salinity boundary conditions are included.

The seasonal climatology of the model calculations compare reasonably well with the observed climatology. Although total transports on open boundaries are maintained at climatological values, there are, nevertheless, large seasonal and spatial variations of Gulf Stream transport between Cape Hatteras and 62°W. These changes are accompanied by transport changes in the northern recirculation gyre.

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