We have been trying to understand the decadal-scale fluctuations in sea level along the U.S. coasts. Coastal effects are usually quite complicated, so we began our work by studying the variability in the open ocean. We have used a simple wind-forced model in which the local Ekman pumping drives variability in the thermocline, and the Rossby waves carry this signal to the west. We only consider periods longer than a few years; motions from higher-frequency eddies are not present in the model results shown here.
The first surprise was that the very-low-frequency wind variability, as a function of longitude, has a peak on both sides of the ocean. At periods closer to annual, it had been known that the variability had a single peak near the middle of the ocean. The transition to a second- mode-like behavior occurs at periods longer than a few years, as can be seen in Figure 1. (WARNING: THIS FIGURE IS A LARGE FILE APPROX. 145K).
In this presentation, the figure shows the power in wind curl from the COADS data along 32 N as a function of frequency, x axis, and as a function of longitude; the axis that goes into the page, and slightly to the right. We have smoothed the spectrum as appropriate at higher frequencies, with progressively less smoothing toward low frequencies. The uncertainty of the spectral energy in the lowest frequency points, at a period of 512 mo, is full-scale. Poor spectral estimates, but that's what has driven the ocean, and our model. To suppress noise, we integrated the wind stress around 4 degree boxes to determine curl.
There is a great deal of power in the vicinity of the annual term. However, we did in fact remove the power at exactly 12.0 months from the spectrum before any smoothing (or equivalently, from the data); this leakage of power into adjacent frequency bands appears to be a real feature of the wind. An annual peak is a feature only of many years of data.
The sea level record at Bermuda begins in the 1930s, although there is a gap during the early war years. The wind data are much better after 1945. Our comparison begins in the 50s, after the long waves that began on the African coast have had time to cross the ocean. The model wave speeds were determined from the Levitus (smoothed) density field, and have not been tuned to enhance this result.
Figure 2 shows a comparison between our model results and Bermuda sea level, corrected to uniform atmospheric pressure. The comparison is surprisingly good. Our model is based on a vertical modal decomposition; we find that all the signal is in the first mode. The signal in Figure 2 can be interpreted as sea level, or equally as the variability in the main thermocline.
If we make a comparison of model output (as in Fig 2) using the mean wind forcing, as a function of time but averaged across the ocean, rather than using the full horizontal resolution in the wind field, the model does poorly. Similarly, if we use only the local forcing near Bermuda, the model does poorly, as one might have expected.
It is possible, then, under the assumption that what comes out of our simple model has something to do with the ocean, to show the full signal as a function of time and longitude, again across 32 north, as shown in Figure 3. (WARNING: THIS FIGURE IS APPROX. 30K). Several features are striking. First, the spectrum (not shown; you have to imagine it) does not look quite like the spectrum of the wind. It peaks at periods shorter than the record length. Second, there is a large change in the amplitude of ocean variability from one time period to another. The largest peak-to-peak variations are roughly one quarter of the amplitude of the change in sea level across the Gulf Stream.
Acknowledgments.
This work should appear in the June 1995 Journal of Physical Oceanography. We are continuing this work; it is supported by NOAA, for which we are most grateful. We thank Prof. Allan Clarke for his long-standing cooperation and for many helpful discussions.
For a more detailed description of this research contact:
sturges@atlantic.ocean.fsu.edu or bg@atlantic.ocean.fsu.edu
