Westward Propagation of Planetary waves observed from Topex/Poseidon: Theory and Implications

Roland A. deSzoeke and Dudley B. Chelton

College of Oceanic and Atmospheric Sciences

Oregon State University

ABSTRACT

Analyses of TOPEX/POSEIDON sea-level height fields clearly indicate westward propagation of long-wavelength (order 1000 km), long-period (order 1 year) disturbances in all ocean basins over wide latitude ranges. The westward phase speeds are well accounted for in most regions, except near the equator, and in the Antarctic circumpolar current, by linearized, quasigeostrophic theory that takes into account the modification of disturbances by stratification, and by mean, sheared, geostrophic motion. The stratification and motion fields are calculated from spline fits to the climatological hydrographic database. The stratification by mean sheared motion is crucial in the theory, accounting for a phase speed-up factor up to two over the standard (no motion) theory.

We suggest that the features in the mean ocean circulation that are responsible for the speed-up are the subsurface pools in which potential vorticity is homogenized along density surfaces over large horizontal extents. A simple mechanism will be illustrated whereby planetary wave modes tunnel across the homogeneous potential vorticity column and enhance their phase propagation speeds. The implications of faster planetary waves in the adjustment of the ocean to seasonal and interannual forcing will be discussed.

 

FIGURE 1: Time-longitude diagrams of sea-level height from TOPEX/POSEIDON show westward propagation of waves with long periods and wavelengths. These examples are from the North Pacific at 21‘N, 32‘N, 39‘N.

Figure 1: (!Click on the thumbnail to see a bigger version of the Figure!)

 

FIGURE 2: The observed phase propagation speeds are up to twice what the standard theory for long baroclinic Rossby waves predicts (see sidebar).

Figure 2: (!Click on the thumbnail to see a bigger version of the Figure!)

 

 

FIGURE 3: An extended theory that takes into account the effect on planetary wave propagation of the vertical shear associated with the mean circulation improves the agreement with observations significantly (see sidebar).

Figure 3: (!Click on the thumbnail to see a bigger version of the Figure!)

 

 

 

STANDARD ROSSBY-WAVE THEORY

The standard theory for baroclinic Rossby waves predicts westward phase speeds of

The baroclinic Rossby radius, Lr, was calculated in every degree square of the ocean, using the NODC historical hydrographic data set to give vertical density profiles. The standard Rossby wave phase propagation speed is shown in Fig. A-1.

 

Figure A1: (Click on the thumbnail to see a bigger version of the Figure)

 

 

EXTENDED PLANETARY-WAVE THEORY

The extended theory for baroclinic disturbances propagating through a mean flow U(z) gives an equation for the perturbation stream function y:

This equation was solved for conditions prevailing in every degree-square of the ocean, using the NODC historical hydrographic data set to give vertical density profiles, and meridional density gradients, from which N(z) and U(z) were calculated. (Examples are shown in Fig. A-2.) This furnishes vertical modes for y, and its westward phase propagation speed (Fig. A-3).

 

Figure A2: (Click on the thumbnail to see a bigger version of the Figure)

 

 

Figure A3: (Click on the thumbnail to see a bigger version of the Figure)

 

 

 

What feature in the mean circulation is responsible for this propagation speed up?

 

FIGURE 4: Mid-depth potential vorticity in midlatitudes is homogeneous. This figure shows the depth ranges over which such homogeneous potential vorticity layers are found (judged from KefferÆs [JPO (1985), 15, 509] maps), superimposed on a hydrographic density section in the Pacific Ocean.

Figure 4: (!Click on the thumbnail to see a bigger version of the Figure!)
 

 

FIGURE 5: A simple three-layered model was devised to illustrate the effect of homogeneous potential vorticity layers on planetary-wave propagation. The mean thickness of the middle layer increases poleward to keep potential vorticity constant. The potential vorticity gradient in the surface layer especially is enhanced.

A very simple result is obtained. The propagation speed of long planetary waves in this model is

where c1 (c2) is the propagation speed of a simple Rossby wave on the first (second) interface as though the other interface were absent: U is the vertical average of the mean velocity.

Figure 5: (!Click on the thumbnail to see a bigger version of the Figure!)

 

 

FIGURE 6: The dependence of the speed-up ratio (c1+c2)/c0 as a function of

is shown. For realistic choices of r1, r2, r3, and D1, D2, D3, values of the speed-up ratio in excess of 1.5 can be readily obtained.

Figure 6: (!Click on the thumbnail to see a bigger version of the Figure!)

 

 

FIGURE 7: A histogram of the speed-up ratio calculated from extended theory applied to the detailed degree-square density and velocity profiles. The bound of 2 is scarcely ever exceeded. Speed-up ratios of 1.3-1.5 are quite common.

Figure 7: (!Click on the thumbnail to see a bigger version of the Figure!)

 

 

FIGURE 8: Modifications of the standard planetary-wave dispersion relation by vertical shear (for the three-layer model). The maximum possible wave frequency is almost double that of the standard theory. This means that a much wider range of frequencies may be off-resonant in midlatitudes than has been thought. For example, annual to interannual periodicities may be able to propagate freely in subpolar latitudes. This has significant implications for the adjustment of the ocean at these periodicities.

Figure 8: (!Click on the thumbnail to see a bigger version of the Figure!)

 

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