The 1998 Super El Niño: possibly a "rogue wave"?

In comments on WUWT, people often think freely and throw out all sorts of ideas. Like in any collection of people, some are bad, some are average, a few are good, and even fewer are noteworthy. However, one that was noteworthy recently was from a WUWT regular known as “hotrod” in the “NASA Deep Solar Minimum” thread.

He wrote:

The thing that has been nagging at me is, that the trace of a rogue wave in this link, looks a lot like the 1998 temperature spike. On thinking about it, if a [rogue] wave is possible in the ocean, is it not conceivable that the same sort of behavior could exist in an average temperature plot for a body like the earth, as it oscillates around an average temperature? This like the PDO and AMO are just different types of periodic motion.

He was referring to what has now become known as the Draupner Wave, named for the oil platform that recorded it on January 1st, 1995.

In the case of the Draupner Wave, it has an amplitude about 3x that of the average background wave amplitude. It was created when the amplitudes of some waves of dissimilar amplitude and period combined in sync to form a new wave peak for an instant. That instant passed and the sea went back to normal background amplitude.

In the case of the 1998 Super El Niño, there is a similar sort of event where the temperature peak is about 3x that of the background peaks. This plot of the RSS Global Temperature Anomaly below (done by Barry Wise) shows the 1998 super event in red:

Barry writes:

The 1997/98 El Niño temperature spike seems to have had a long lasting effect that is dissipating. This graph shows what the trend was before the event and how the trend was affected by it. The dashed red line is the trend with all of the data and the purple is the trend based on the data before the area highlighted in red. Notice that there appears to be a decaying oscillation. If correct we’re in the third peak which is less than the previous two, and is much closer to the purple trend line.

[Note: I should point out that Barry’s method creates a different result than if the 97/98 El Nino data is removed, and before and after trend lines are plotted (h/t to Tom P) the resultant effect of the 1998 Super El Niño is less apparent. See comments for more discussion.]

Certainly there appears some similarity between the Draupner Wave and the 1998 Super El Niño worldwide temperature spike. And certainly we have a number of periodic systems and forcings going on here on Earth that are sinusoidal by their nature. They span short (high frequency) and long (low frequency) periods. Here are a few that I’ve thought of, short and long, but by no means is it a complete list.

Diurnal solar insolation and temperature variation, daily and monthly lunar tide cycles, seasonal variation of solar insolation by hemisphere, seasonal variation of temperatures by hemisphere, seasonal biomass variations, seasonal sea ice variations, seasonal albedo variations, 11 and 22 year solar cycles, Earth’s length of day variations, El Nino Southern Oscillation, North Atlantic Oscillation, Pacific Decadal Oscillation, Atlantic Multidecadal Oscillation, and at very long periods, Milankovitch cycles.

There are many many cycles on earth that are known, some yet to be discovered. Almost all of them have a root cause in periodic circular motions such as planetary rotation and orbital motion in our solar system and the variances of orbital eccentricity, obliquity, and precession. For example, the graph below shows how these different waves eventually synchronize to cause cycles of ice ages on earth.

To illustrate how sinusoidal cycles can conspire to produce peaks and valleys in amplitude, this interactive Java sinusoidal generator allows you to combine three different waves of varying phase, amplitude, and wavelength and see the resultant wave that forms from them:

During my limited experimentation above I couldn’t get the generator to produce a Draupner type wave, but as you can see in the screencap above, I was able to illustrate how a new peak can be generated (in blue)  that is larger than any of the source wave peaks.

Here is an example of how “wave focusing” can occur to produce a Draupner type peak:

Lest you think this essay is about childs play with sinusoids, I’ll point out that there have been some serious works done on the mathematics behind the creation of “rogue waves”.  For example there’s this brief discussion from the link commenter “hotrod” originally provided:

BBC Two, on November 14, 2002, aired a program on this phenomenon and its recent mathematical analysis. Freak waves, also “rogue waves,” “monster waves,” are extraordinarily tall and steep waves that appear sporadically and wreck havoc with shipping. One is suspected to have washed away the German cargo München which went down with all hands in the midst of a routine voyage in 1978. More recently, the cruise ship Caledonian Star was struck by a 30m wave on March 2, 2001. The standard analysis of ocean waves predicts a Gaussian-like distribution of heights; extreme heights, although possible, should be very rare – a 30m wave is expected once in ten thousand years, according to the BBC. But these waves occur much more frequently than predicted. The program focused on new methods of analysis, and on the work of the mathematician A. R. Osborne (Fisica Generale, Torino). Osborne has applied the inverse scattering transform, which he describes as “nonlinear Fourier analysis,” to the time series analysis of wave data. He conducted simulations using the nonlinear Schrödinger equation and found near agreement with the standard analysis, except that “every once in a while a large rogue wave rises up out of the random background noise.” His paper, available online, gives an example of such a simulation:

From CIM Bulletin #14  at http://at.yorku.ca/i/a/a/h/51.htm

Here’s a paper (PDF) on the Draupner wave  titled:  THE SHAPE OF THE DRAUPNER WAVE OF 1STJANUARY 1995 from Paul Taylor, Department of Engineering Science, University of Oxford. Taylor did a mathematiucal analysis of the Draupner wave, created a model to approximate the formation of it, and concluded that: “The New Year wave is ~ 1 in 2×10^5 waves” which when you think about it, makes it fairly common especially when you view it in context to images like the one below:

So it seems that such amplified rogue waves are fairly common in the nature of our oceans. That’s quite a journey from them one time being considered “mystical” by science.

Another scientific paper (PDF) of interest is: Physical Mechanisms of the Rogue Wave Phenomenon by Christian Kharif and Efim Pelinovsky of IRPHE in France and the Institute of Applied Physics in Russia, respectively. They conclude (emphasis mine):

All the physical scenarios of possible extreme wave generation (focusing, wave-current interaction, modulational instability), in fact, were known but only now (during the last 5 years) they are “dressed” by mathematical models of various levels (linear, weakly nonlinear, fully nonlinear models). Results of numerical simulations show the behaviour of each mechanism taking into account the random character of the wind waves in the ocean. Computations provide also the probability of rogue wave occurrence for simplified conditions. The many results are very sensitive to the model parameters (shape of wave spectrum, various corrections of the weakly nonlinear evolution models, accuracy of numerical schemes for long49 time computations).

Given that rogue waves were once thought to be the fantasy of imaginative sailors and fishermen, and given that science has now only addressed the problem once one was measured in 1995, it illustrates how something once thought to be impossible is now possible once it is measured, better understood, and studies published about it.

By the same logic, things like the Pacific Decadal Oscillation weren’t discovered until fairly recently. The PDO was named by Steven R. Hare, of the University of Washington, who noticed it while studying salmon production patterns (See BAMS article, PDF). Almost simultaneously the PDO climate pattern was also found by Yuan Zhang. This happened in 1997. It is one more natural cycle added to the many that were already known such as the El Niño-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO)

Perhaps it is not an unreasonable to consider that on occasion, some of these cycles conspire to produce extreme ocean events like the 1998 Super El Niño.

And, given the difficulty in predicting exactly when natural cycles might coincide to produce such an event, perhaps this is why they are so hard to predict. For example, there was Dr. James Hansen’s 2006 prediction about a “super El Niño” that would rival the 1983 and 1997-1998 El Niño events.

In March 2006, Hansen wrote a paper claiming the following:

We suggest that an El Niño is likely to originate in 2006 and that there is a good chance it will be a “super El Niño”, rivaling the 1983 and 1997-1998 El Niños, which were successively labeled the “El Niño of the century” as they were of unprecedented strength in the previous 100 years.

We all know now that prediction was a bust.  While there was in fact a 2006-2007 El Niño event. In the words of climatologist Mike McPhadden the event:

“started late, ended early and was below average strength”

Hansen’s prediction of a “super” event “rivaling the 1983 and 1997-1998 El Niños” never came true. Undeterred, Hansen is still predicting the onset of an El Niño event that will drive global temperatures to a new record high in 2009 or 2010. (h/t to Roger Pielke Jr on Prometheus)

Perhaps the applications of the studies of rogue ocean waves might be useful in figuring out if the 1998 event was in fact a synchronicity of natural cycles, linear, non-linear, and chaotic for a brief time, and if so, applied towards forecasting future super El Niño and La Niña events. I think it is worth considering. – Anthony