p. 263, first paragraph: Replace the text,
The middle panel shows the “building blocks” from which the solution is made up:
an eastward propagating Kelvin wave and a westward propagating n = 1 equatorial Rossby wave, as described in Section 9.4. In the solution shown in the bottom panel, the Kelvin wave is dominant to the east of the mass source and the Rossby wave is dominant to the west of it. The Rossby wave is seen to be responsible for the anticyclonic gyres at the longitude of and to the west of the deep convection over the warm pool and the Kelvin wave is responsible for the equatorial ridge of high pressure waves accompanied by westerlies to the east of it. In the steady state solution the waves are damped as they propagate away from the mass source at the same rate as they are being forced by it.4 We will show how this circulation develops in Section 15.3.
by:
The middle panel shows the “building blocks” that are instrumental in the development of the solution: an eastward propagating Kelvin wave and a westward propagating n = 1 equatorial Rossby wave, as described in Section 9.4. In the solution shown in the bottom panel, the Kelvin wave is dominant to the east of the mass source and the Rossby wave is dominant to the west of it. The Rossby wave is seen to be responsible for the anticyclonic gyres at the longitude of and to the west of the deep convection over the warm pool and the Kelvin wave produces an equatorial ridge of high pressure accompanied by westerlies to the east of it. The formation of these waves is shown in Animation 10.2.5-6, which was created using a primitive equation model forced by a circular heat source on the equator. In this integration the basic state flow is a state of rest, as in the steady state solutions of Matsuno (1966) and Gill (1980).
To understand how the time dependent response evolves into the steady state solution, it is necessary to consider longer time integrations. Animation 12.1-7a shows the same integration as in 10.2.5-6, but extended out to 30 days. Owing to the strong damping, with an e-folding tine of just 2 days, the Kelvin wave is attenuated as it propagates eastward and after a week or so, the damping of the Kelvin wave response balances the eastward advection and the solution approaches a steady state that resembles the Gill solution. However, when the damping rate is reduced to a more realistic value, with an e-folding time of 2-3 weeks, the Kelvin wave propagates farther and farther eastward before it comes into equilibrium with the damping, as shown in Animations 12.1-7b,c. The extended eastward dispersion of the Kelvin wave gives rise to a zonally symmetric component of the steady state solution, with a narrow westerly jet along the equator accompanied by a ridge of high pressure. This feature is maintained by the equatorward transport of westerly momentum by the Rossby wave gyres to the west of the heat source. In Gill’s analysis the shallow water wave equation is linearized about a state of rest, so a zonally symmetric equatorial westerly jet would not develop, even if the damping were reduced.
Prescribing a zonally symmetric basic state flow with westerlies in the initial condition of the integrations with the primitive equation model adds another element of complexity to the solution, as shown in Animations 12.1.7d,e. Rossby waves emanating from the heat source disperse along great circles and perturb the flow to the east of the heat source, as in the solutions with the model based on the barotropic vorticity equation shown in Fig. 1d of Sardeshmukh and Hoskins (1988). The zonally symmetric component of the response is not as strong as in Animation 12.1-7c, presumably because the poleward transport of westerly momentum by the planetary waves dispersing back into the equatorial belt along great circles cancels some of the equatorward transport by the anticyclonic gyres to the west of the heat source.