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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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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

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Masamichi Inoue
and
James J. O'Brien

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A dynamical forecast model which has been applied to the onset of the 1982/83 El Niño is applied to the decay of this event. The timing of the decay is well predicted, illustrating the flexibility of the dynamical forecast model which could handle an unusual El Niño, i.e., the 1982/83 event with significant wind changes outside a well-recognized site for usual El Niño related wind changes. The results suggest the need to include zonal winds from the entire equatorial Pacific. It appears that the dynamical forecast model based on a linear numerical model forced by ship winds can be used to forecast the timing of the onset and decay of a major El Niño.

The evolution of the 1982/83 El Niño is described using the dynamical model forced by the observed wind. The equatorial Pacific Ocean response during this event is basically that to an eastward translating zonal band of westerly wind anomalies. The observed double peaks in the sea-level record in the eastern Pacific in early 1983 appear to be due to the observed amplitude modulation of the wind anomalies east of 140°W, confirming the previous findings of Tang and Weisberg. It appears that the first Kelvin wave pulse generated in the western Pacific in early 1982 was reflected as a Rossby wave from the eastern boundary. The propagation of this Rossby wave into the central Pacific in July 1982 coincides with the dramatic intensification of the westerly wind anomalies in that region. This suggest a possible air-sea interaction leading to the major onset of this El Niño.

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James J. O'brien
and
Fred Parham

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In the last several years many scientists have been using poorly resolved coupled models to study the El Niño- Southern Oscillation (ENSO). It has been very common to state that an ENSO cycle found in a model cannot have oceanic Kelvin waves as a mechanism because such waves do not exist in an ocean model with coarse grid spacing. In this note we demonstrate that equatorial Kelvin waves can exist in models with coarse grids.

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Masamichi Inoue
and
James J. O'Brien

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The feasibility of a forecasting scheme for predicting the onset of a major El Ni-o in the ocean is demonstrated using the linear numerical model of Busalacchi and O'Brien and the interannual components of the shipboard observed wind for 1961-82. The model upper layer thickness anomaly in the eastern Pacific, which was used as the predictand, was estimated after three months of steady wind integration. A lag time of three months is used to permit the propagation of a large El Niflo-type Kelvin wave across the Pacific Ocean. If the necessary wind changes required to generate a large El Niflo type Kelvin wave have already taken place in the western and/or central Pacific, El Niflo could be predicted one to three months in advancefrom knowledge of the wind field alone. Starting from November 1963, three-month steady-wind integrations were performed for the wind condition of each of the seven months (November to May), for each of the 15 years extending from 1964 to 1978. This period includes four El Ni-o years. The probability distribution function of the three-month running mean of the upper layer thickness anomaly in the eastern Pacific was estimated separately for the El Nifio and the non-El Nub groups using "bootstrap" estimates. The separation of the two probability distribution functions allows for the establishment of a criterion for forecasting El Nifio. An independent wind data set for the period 1979-82, which includes the onset of the 1982/83 El Nub, was used to test the feasibility of the forecasting scheme. If the null hypothesis is that a sample year is a non-El Niflo year and based on a forecast criterion of false positive error (false alarm rate) ~ 0.01, which corresponds to false negative error ~ 0.52-0.86 (which corresponds to a probability of detecting the occurrence of an El Niflo ~ 0.14-0.48), the 1982/83 El Niflo would be forecast to be underway following the analysis of the April 1982 surface wind field. Since the objective is to establish a forecasting scheme for predicting the onset of a major El Niflo, the forecast scheme is chosen to be one of low risk and low power in prediction performance.

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Richard Grotjahn
and
James J. O'Brien

Abstract

The errors introduced by the use of various numerical schemes for solving mathematical models have generally been only vaguely determined previously by numerical modelers. A method for a more quantitative analysis of the inaccuracies is outlined. The error associated with some simple schemes is analyzed for several linear hyperbolic systems representative of typical problems in meteorology and oceanography. Results of previous studies of phase velocity inaccuracies are confirmed and form a basis for an extension of the analysis to group velocities. Significant angular and magnitude errors are found in the group velocity. Directional errors of 180° are found for some waves. Since the group velocity is the propagation speed of the energy, such errors may have severe consequences in a numerical model. When analysis was made of complex systems of equations, results found for simple systems reappeared. Thus, studies of simple systems may provide useful indications of behavior in more complex problems where the analysis may have to be limited. Only the long waves, i.e., those resolved by many grid points, are represented with any reasonable accuracy.

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