Advanced ENSO Theory: The Delayed Oscillator
Evolution of Kelvin and Rossby Waves
As mentioned earlier, the Kelvin and Rossby wave signals propagate at
different speeds. The Kelvin wave travels eastward and in our idealized
case has speed on the order of 2.9 meters per second. This means that a
Kelvin wave will cross the Pacific Ocean, which extends from approximately
120° East to 80° West (17,760 Kilometers in distance), in about
70 days. The Rossby mode travels westward at one third the speed of the
Kelvin wave, or about 0.93 meters per second. Thus a Rossby wave takes approximately
210 days to cross the Pacific.
The time evolution for the idealized experiment is shown in Figures 6 and
7, at 25-day and 50-day intervals, respectively. After 25 days (Figure 6
upper left panel), the Kelvin wave (red and gold shading) has moved from
the central Pacific forcing region to the east. At the same time, the Rossby
wave (blue and green shading) has propagated to the west, but over a much
shorter distance. Over days 50 through 100 the Kelvin wave reaches the eastern
boundary and reflects as a Rossby wave with positive sea surface height anomalies.
At the same time, the Rossby wave continues to propagate slowly to the west
becoming visibly distorted by day 100 (associated with the interaction with
the basin boundary).
Figures 6 and 7. Ocean surface height
anomaly (cm)
(Note that the shading levels in Figure 7 have been decreased
from those of Figure 6 so that we can continue to trace the evolution of
the waves which are continuing to be damped by diffusion as time evolves.)
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Figure 6
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Figure 7
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25 days
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125 days
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50 days
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175 days
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75 days
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225 days
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100 days
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275 days
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By day 125 (Figure 7), the Rossby wave has reached the western boundary
and is starting to reflect as a same-signed Kelvin wave. We now see a time
evolution similar to before, with a Kelvin wave propagating eastward along
the equator (this time starting from the western boundary) and a Rossby wave
propagating westward from the eastern boundary. However, now the Kelvin wave
has negative sea surface height anomalies, and is an upwelling wave. Over
the period from day 125 to day 275 the Kelvin wave propagates from the western
to the eastern boundary resulting in negative sea surface height anomalies
along the equator in the east. During this same period, the reflected Rossby
wave has traveled from near 120° West to 170° West.
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