Polar Plots, from Jim Sogi

October 31, 2008 |

 Winter surf is starting up. Surf prediction is almost as important, (to me) as stock prediction. One of the tools for surf prediction are polar plots of wind and swell direction from the offshore buoys. A few years back Chair mentioned polar coordinates and plots. These can be done in R. I thought a simple plot of the direction and angle of market price might be helpful in some models to predict. For waves, NOAA uses data from offshore data buoys and says:

Spectra and source term are presented for selected output locations in the form of polar plots. The radial lines in the polar plots depict the directional resolution of the model. The concentric circles are plotted at 0.05 Hz intervals, where the innermost circle corresponds to 0.05 Hz and the outermost circle corresponds to 0.25 Hz. Wave energy plotted in the lower left quadrant travels in SW directions etc. The blue arrow in the center of the plots depicts wind speed and direction. Colors represent wave energy density for spectra and rates of change of energy density for source terms and are plotted at a logarithmic scale where the contours separating the colors increase by a factor of 2.

This application might be good for markets as a different sort of plot on the question, "Is the market going up or down, and how fast?". Surf direction and speed is critical to choose the spot, and equipment. Market direction and intensity is critical, but hard to predict. Surf travels generally from north to south in the winter. Market forces generally tend to travel East to West. Perhaps a polar plot of the prevailing market winds, and the concentrations of energy might be helpful in predicting market direction and intensity.

Jeff Watson writes:

As a serious student of surf prediction, I note and live by the seasonality of the swells. Different seasons bring swells from different directions, and Sogi-San is lucky to live in a place that gets swell from all 360 degrees, ensuring year round surf somewhere in the islands. Surf prediction is easy at my location as we have roughly two primary causes of swell; Cold fronts and hurricanes. We only have a window of roughly 90 degrees where conditions will produce rideable waves I check our weather maps daily and look at all the buoy information from the NOAA, whether it's surf season or not. From my location it is pretty easy to predict when we will get swells, although predicting the size gets rather tricky. To predict the size takes a lot of experience, comparisons of past data, and a firm grasp of current weather conditions…much like looking at the markets. Although it's anecdotal, I find it much easier to predict the possibility of waves than future market action.

One thing of note, sometimes mysto swells will appear out of nowhere, lasting only a very short time, with no apparent cause, disappearing as quickly as they arrive much to the chagrin of the locals. The swells that hit with no warning cause a lot of surfers to miss out on waves, because they aren't positioned to hit the swell. The markets do the same thing with movements that come out of nowhere, surprising the participants who are out of position, causing the players to be frantic while trying to catch the move which is usually missed. All of this, whether with the waves or markets, sometimes comes with no valid explanation. When I talk to groms about the waves and swell, I sometimes resort to using the cliche, "It is what it is." The same thing can be said about market moves.

Vinh Tu adds:

Mathematically, angles are even closer to correlations. Two series of t observations can be represented as two vectors in t-dimensional space. You get the cosine from dividing the dot product of the two series by the volatility of each series.

I'm not sure whether, with more than two instruments, you can still flatten it to a circle and still have it show anything useful. But restricting the plot to two series, we could take one series to be "North" –logical candidates for this might be an interest rate, or a "market portfolio", or a major market index. Then the other series could be examined in relation to North. Samples of the other series could be colour coded and assigned polar positions.

Alternatively, perhaps north could be a straight line representing a desired or hypothesized drift. The result would be somewhat related to the R-squared technical trend indicator.

Alex Castaldo quibbles:

A correlation is exactly like the cosine of an angle, as opposed to an angle.  Because cosine is an even function, there is an ambiguity as to the sign of the angle.  For example if Bonds represent North and Stocks are correlated 0.5 with Bonds, how should that be plotted? As +60 degrees (approx. W-N-W) or -60 degrees (approx E-N-E)?





Speak your mind

5 Comments so far

  1. Craig Bowles on October 30, 2008 1:00 pm

    It might be worth mentioning that the Pacific is in a cooling phase…Winter and Climate

    1. The Atlantic Ocean is in a warming trend and the Pacific is cooling due to a negative PDO (Pacific Decadal Oscillation) that began to shift in 1995 and lasts for 20-30 years, historically. A cooling Pacific coincides with drought in the west.

    2. A negative PDO gives rise to a negative NAO (North Atlantic Oscillation) or a reversal of the wind patterns in the Atlantic Ocean. Cold polar air masses surge south contributing to cold winters in the northeast and central areas of the U.S.

    3. Increased volcanic activity cools climate in the northern hemisphiere. We currently have 7 active volcanoes around the Bering Sea (3 in Alaska, 4 in Russia). Over 70 per year recently is off the charts in historic numbers.

    4. Sunspot activity appears to be picking up which will have a greater affect in the equatorial region. Cooler air coming down from the north hitting warming air coming up from the south normally whips the jet stream back and forth wildly.

    5. Climate extremes have been trending higher since 1970 overall and winter extremes have trended higher since 1940. There’s a 20 year cycle in winter extremes and we’re coming off a low, so 2008-2018 will see dramatic increases.

  2. Michel Olagnon on October 31, 2008 6:13 am

    Jim Sogi’s post on polar plots touches to an interesting feature of measuring ocean waves. If waves are measured only by the heave of a buoy, it is not possible to find out where they come from. If one has also access to the horizontal motions or to the tilt angles of the buoy, then the directions can be computed and those spectral polar plots come out. Furthermore, if a time-sequence of such plots is available, then the time and location of the storm that created them can be estimated. Yet, all those measurements only provide hindsight.

    In order to flip to the foresight side, one needs to consider the global ocean (remember that waves generated off Alaska can propagate all the way to New-Zealand). One can model it, using the wind fields meteorological forecasts, and then hopefully predict the arrival of swells far from the storms. Unfortunately, there are uncertainties in the process and the exact times can be eventually misforecast by a few hours, and the aleatory variability inside a wave train of several hours escapes prediction. If one soars to take a global view from a satellite however, it may become possible to detect the wave train at some point along its track.
    An example can be found at

    Yet from my experience, the satellite information arrives too late, the interesting points are overseen within the huge amounts of data that come for analysis, spaceborne sensors may even be directed to the wrong places, and surfers or mariners are left to rely on the far-from-perfect meteorological models. Not a very different case from markets.

  3. Ace on October 31, 2008 12:53 pm

    Jeff — with surf cameras mysto swells not so good any more. You
    show up at your break and within half an hour 30 other guys paddle out.
    How many market analogies to this can you think of?
    Another thing, at least here in So. Cal. — new swells always seem to arrive a day or two later than predicted by NOAA.

  4. Prudence Gently on October 31, 2008 3:15 pm

    Alex, correct my logic here if it’s faulty. It seems to me if you had 3 or more data sets you could determine the sign of the angle — or at least consistently assign it. Take datasets A, B, C. A is north. If AB cor by .85, AC by .75, and BC by .95 — then B and C must lie on the same side of A. But if BC corr by say, .5, C would be closer to A than to B. I’m not sure what use this would be. Also, to keep things consistent for more data sets you’d probably need more than 2 dimensions, at which point we probably lose more than we gain…

  5. Jeff Watson on October 31, 2008 8:15 pm

    Only 30 guys showing up for a mysto swell? That’s no problem, it’s when 300 guys show up that makes one pause to move down a few peaks to surf waves in solitude. Conditions force one to adapt or suffer.
    Surf cameras don’t exist at my home break…never have, never will, as the locals won’t stand for them. Despite the presence of those insufferable cameras in other places, surfers manage to adapt to those changing conditions. Frankly, I would never use a camera due to my aversion of on site technology applied to surfing, although I will use buoy data in swell prediction. My old fashioned habits are also manifested in the fact that I still only wear whites when I play tennis.

    How many market analogies to this could I think of? Probably a hundred or so.

    Substitute NOAA reports with USDA grain reports and you’ll see many similarities of government incompetence.



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