In a recent paper, Marcia Wyatt and Judith Curry posited about “Stadium Waves” and climate, suggesting that the ‘stadium-wave’ signal propagates like the cheer known as “the wave” at sporting events whereby sections of sports fans seated in a circular or oval stadium stand and sit as a ‘wave’ propagates through the audience. In a similar way, Wyatt and Curry’s ‘stadium wave’ climate signal propagates around the Northern Hemisphere through a network of ocean, ice, and atmospheric circulation elements that self-organize into a collective tempo. Some might call it a “beat frequency“.
You can read more about it here on WUWT’s coverage of the paper. You can watch a stadium wave in action below.
I came across the Wyatt and Curry article again recently, and it made me think about how stadium waves might be much like traffic waves on congested multi-lane city highways. Plus, I found an excellent interactive visualization that helps tell the story
You know what these events are; the situation where all of the sudden you find yourself braking, coming to a stop or near stop along with the other traffic, and you sit there or crawl along for a minute, resume, only to repeat again n times and then suddenly the pattern evaporates and you keep looking for whatever it was that cause the slowdown, only to find nothing.
Being curious late last night, I found that there was an excellent visualization for traffic waves that may also serve as a suitable visualization for Wyatt and Curry’s “stadium wave” in the atmosphere. This comes from a KQED blog called “The Lowdown”. Below is a screenshot of their interactive traffic wave model with my annotation. It reminds me of the top down look at the northern hemisphere we often see when looking at the circumpolar vortex.
You can interact with this visualization yourself here: http://blogs.kqed.org/lowdown/2013/11/12/traffic-waves
Matthew Green writes:
The simplest explanation for why traffic waves happen is that drivers have relatively slow reaction times: if the car in front of you suddenly slows down, it’ll likely take you a second or so to hit the brakes. The slower your reaction time, the harder you have to brake to compensate and keep a safe distance. The same goes for the car behind you, which has to brake even harder than you did in order to slow down faster. And so on down the road, in a domino-like effect.
The equation used in the car circle above is relatively complex. Known as the Intelligent Driver Model, it was first proposed in 2000 by researchers at Germany’s Dresden University of Technology. The creators made this Java applet demonstration. Formal equations to explain these traffic patterns in terms of individual behavior are called car following models. They were first developed by researchers at General Motors in the 1950s. The simplest such formula is:
where a is the car’s acceleration, Δv is the difference in velocity compared with the car behind it, T is reaction time and ƛ is some constant that researchers estimate from data. The equation says, “At time t, you accelerate at a rate proportional to the difference in speed between your car and the speed of the car you’re following, but with a gap of T seconds.”
So, put really simply, if you’re going faster than the car in front of you, then you slow down. And if you’re going slower, you speed up. This equation produces the graph below. At the 10-second mark, the grey car slows down, and the cars that brake later have to slow down to lower and lower minimum speeds. Each line shows the history of the speed of a different car. Drag the slider to graphically see a traffic wave unfold. Note how the cars at the bottom of the chart get closer together with time, as speed evens out.
In our atmosphere, “braking” could be equivalent to such events like rex block highs and cutoff lows, both of which are detached from the jet stream and impede atmospheric flow. That’s just one example for a short time scale we can observe in weather.
From our WUWT story on the paper, where they use the term “braking” to describe what starts the stadium wave:
Wyatt and Curry identified two key ingredients to the propagation and maintenance of this stadium wave signal: the Atlantic Multidecadal Oscillation (AMO) and sea ice extent in the Eurasian Arctic shelf seas. The AMO sets the signal’s tempo, while the sea ice bridges communication between ocean and atmosphere. The oscillatory nature of the signal can be thought of in terms of ‘braking,’ in which positive and negative feedbacks interact to support reversals of the circulation regimes. As a result, climate regimes — multiple-decade intervals of warming or cooling — evolve in a spatially and temporally ordered manner. While not strictly periodic in occurrence, their repetition is regular — the order of quasi-oscillatory events remains consistent. Wyatt’s thesis found that the stadium wave signal has existed for at least 300 years.
The stadium wave periodically enhances or dampens the trend of long-term rising temperatures, which may explain the recent hiatus in rising global surface temperatures.
“The stadium wave signal predicts that the current pause in global warming could extend into the 2030s,” said Wyatt, an independent scientist after having earned her Ph.D. from the University of Colorado in 2012.
Thank goodness we don’t get stuck in traffic that long.