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James J. O'Brien

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James J. O'Brien

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JAMES J. O'BRIEN

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James J. O'Brien

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This paper is a continuation of a theoretical description of upwelling and mixing induced in a stratified, rotating, two-layer ocean by momentum transfer from an intense, stationary, axially-symmetric atmospheric vortex. A second model which includes mixing is considered. The dynamic internal response of the ocean is assumed to be axially symmetric which permits consideration of the solution in two independent variables, radial distance and time. Numerical integration via the method of characteristics is utilized to obtain values of depth-averaged radial and tangential velocities, depth of the upper layer, and density contrast for a period of two days. Transfer of momentum between the air and the sea and between the upper and lower layers of the ocean is included. Transfer of heat and salt between the two ocean layers is simulated. Transfer of heat and moisture with the atmosphere is not considered.

The mechanism of energy transfer to and from the atmosphere and to and from the lower layer is examined in detail. This indicates that the total energy varies only with the inertial period. The energy associated with the effect of mixing is an order of magnitude smaller than that associated with turbulent dissipation. However, turbulent mixing of heat and salt modifies the density structure throughout the wind-forced region of the ocean, while intense upwelling is confined to within twice the radius of maximum hurricane winds.

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James J. O'Brien

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The kinematic method for determining vertical velocity ω in pressure coordinates is reviewed. Alternative objective procedures are derived for obtaining ω, and an analytical solution to the pressure-differentiated continuity equation is found. A variational formulation leads to a generalized objective adjustment for divergence estimates which yields improved, physically realistic estimates of ω. Case studies for intense mesoscale convection demonstrate the utility of an adjustment scheme based on the simplest hypothesis, namely, that the errors in divergence estimates are a linear function of pressure.

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James J. O'Brien

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James J. O'Brien and Robert O. Reid

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This study is concerned with the theoretical description of upwelling induced in a stratified, rotating, two-layer ocean by momentum transfer from an intense stationary, axially-symmetric atmospheric vortex. The dynamic internal response of the ocean is assumed to be axially-symmetric which permits consideration of the solution in two independent variables, radial distance and time. Numerical integration via the method of characteristics is utilized to obtain values of radial velocity, tangential velocity, and depth of the upper layer for a period of two days. Transfer of momentum between the air and the sea and between the upper and lower layers are allowed. Transfer of heat and moisture with the atmosphere is not considered.

A general model is derived which leads to a hierarchy of models of increasing complexity. The detailed solution of the first of these is illustrated.

Results agree qualitatively with observations taken in the Gulf of Mexico following hurricane Hilda, 1964. Intense upwelling is confined to within twice the radius of maximum winds. The displaced warm central waters produce some downwelling adjacent to the upwelled region. The degree of upwelling is time-dependent and the hurricane-force winds must act on the ocean for several hours before significant upwelling occurs. The model indicates a strong coupling of the radially propagating internal wave mode and the vortex mode of the system. This coupling confines the significant internal disturbances to within the wind-forced region.

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Antonio J. Busalacchi and James J. O'Brien

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A simple linear model of the tropical Pacific Ocean is used to simulate the oceanic response to time-dependent wind stress forcing. A linear, one-layer, reduced-gravity transport model on an equatorial beta-plane is incorporated. The non-rectangular model basin extends from 18°N to 12°S. Bottom topography, thermohaline and thermodynamic effects are neglected.

The equatorial response, particularly at the eastern boundary, is studied along the same lines as Kindle. Annual and semiannual harmonics of the zonal equatorial wind stress calculated by Meyers are used to force the model. The east-west slope of the model pycnocline is compared with depth observations of the 14°C isotherm. The linear model generates a semiannual eastern boundary response remote from any region with strong second harmonies of the zonal wind stress. This response supports Meyers' hypothesis that at the eastern boundary the semiannual displacement of the thermocline is due to remote forcing.

The major application of the model is forced by mean monthly wind stresses based on 10 years of observations over the tropical Pacific. The resulting meridional profile of the pycnocline depth is similar to Wyrtki's profile of dynamic height. The equatorial system of troughs and ridges is evident in the pycnocline profile. The seasonal variation of the major equatorial surface currents is compared with the observations. An annual Rossby wave emanating from the eastern boundary is found to modify the location and variability of the Countercurrent Trough. The presence of an anomalous eastward flow centered south of the equator in the eastern equatorial Pacific is supported by Tsuchiya's maps of the dynamic topography of this region.

The results of the two model applications indicate that the dynamics inherent in linear theory are capable of simulating some of the major features of the equatorial response and those of the equatorial surface current system.

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David M. Legler and James J. O'Brien

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A simple algorithm is developed and tested to derive a regularly spaced wind field in a limited arm from simulated multi-orbit scatterometer data. The data are generated by sampling a time-varying known wind field, the 1000-mb FGGE data, from a simulated scatterometer. A simple assimilation technique is used to derive a regularly spaced wind field representation of two-day averages from the simulated data. This technique averages the generated scatterometer data in time and space and uses a low-pass filter in primarily the zonal direction. The resultant vectors were compared to the known two-day averages calculated from the FGGE data. To test the technique, synthetic noise was added to the generated data to simulate scatterometer inaccuracies in speed and direction.

Three cases were tested. In the first case, the simulated scatterometer data contained no noise or errors. The average magnitude of the difference wind field, known minus resultant, was less than the natural variability of the known windfield. In the second case, random white noise with standard deviation of 2 m s−1 (and then 4 m s−1) about a zero mean were added to each sampled vector component simulating inaccuracies in speed and direction inherent in scatterometer sampling. The added noise made little difference on the resultant wind field representation. In the third case, spatially correlated noise was added to each simulated swath simulating data with noise in both speed and direction to reflect errors due to sampling a wind field containing both synoptic and mesoscale components. The standard deviation of the spatially correlated noise was initially 2 m s−1 in each vector component. The average magnitude of the difference vectors increased slightly. In addition, when the noise was increased to 3 m s−1 in each component, the error did not increase significantly.

To test the results on another time period, a final case was run with a 24-hour time window. When spatially correlated noise and random white noise, each with standard deviations of 3 m s−1, were added to the sampled vector component the error did not increase significantly over the noise-free case.

This assimilation technique provides representations of two-day averages on a 100 km regularly spaced grid, and might therefore be applicable to large-scale ocean or atmospheric models. The results of this technique signify the level of importance of errors resulting from the application of assimilation schemes on scatterometer data. These errors appear to be more significant and limiting to the application of scatterometer data than errors from scatterometer inaccuracy.

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John C. Kindle and James J. O'Brien

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A common observation in major coastal upwelling regions is a reversal of the mean longshore current with depth during active upwelling. A numerical model and a simple analytical model applied to a two-layer ocean on a beta-plane indicate that this undercurrent cannot exist for upwelling off an east-west (zonal) coastline. The models are applied to the coastal upwelling occurring on the Campeche Bank during the period from March to September. The beta-plane solutions for upwelling along an east-west coastline resemble f-plane solutions for a meridional (N–S) coastline. In particular, the hypothesis explaining the undercurrent of Hurlburt and Thompson cannot hold for upwelling along a zonal coastline. The results in this paper form a new hypothesis which could be tested by measuring currents on the Campeche Bank during active upwelling.

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