Click to enlarge view of sunplumeA number of news sources reported yesterday that scientists had predicted more intense activity in the coming cycle of sun spots, solar flares, and other solar phenomena. This prediction was accompanied by another prediction on timing - the solar activity would be somewhat “delayed.“These statements naturally got me wondering about a number of issues - how is solar activity modeled? How accurate are the predictions? Is the underlying physics that causes the upsurge in activity understood?First, it’s clear why accurate predictions are needed: increased solar activity can really do a number on communication and navigation electronics, causing satellites to go awry - and in some cases causing delays of planned rocket launches.Now to the “delayed” issue - the basic lore is that the sun goes through an 11-year cycle of low-to-high activity, culminating in a significant number of sunspots appearing on the sun’s surface. In reality, there is a spread in this: cycles run from 9 to 14 years, with 11-years being the mode of the distribution of solar cycle lengths. (Solar cycles and their lenghts have been tabulated since approx. 1760. We are currently in Cycle 23, which started in May 1996. Click here for a histogram of cycle lengths .) Most solar cycles are near the 11-year length, so any delay is with respect to 11 years (i.e. the next cycle is expected to start sometime in 2008). The delay, then, is nothing out of the ordinary.Even with this spread in cycle lengths, the regularity is amazing, given the incredibly non-linear processes at work in the stellar interior - a hellish cauldron of gas and plasma, fission and fusion, in a tug-of-war between gravitational collapse and outward radiation pressure, a tussle that ends up with the solar dynamo switching its magnetic field direction every cycle.What is it that leads to this regularity? Models are of two types: empirical/statistical ones that use some serious regression techniques, and first-principles differential equation models.For a thorough description of the empirical models and a successful way to combine the positive features of these models, see A synthesis of Solar Cycle Prediction Techniques by Hathaway, Wilson, and Reichmann. Their synthesis works very well, i.e. parameters were adjusted so that past sunspot activity was correlated with current activity. The authors’ model demonstrates a very high degree of precision, and therefore there is a certain level of trust in using the model to predict future solar activity.To some, this regression-type modeling doesn’t seem quite right - as the authors themselves state, some view their modeling technique as only “slightly better than astrology.” This is certainly unfair - if the goal is prediction, then the nature of the model is immaterial - let the best predictor win. At a functional, pragmatic level, it doesn’t matter whether the model for prediction leads to any understanding of the underlying physics. The connection with the Chaos Game couldn’t be more dramatic. Predicting the resulting shapes in the Chaos Game for any shape figure can be handled easily by treating it as a tiling problem, without ever considering the random jumps that are happening on the “microlevel”.In the Chaos Game, however, the rules are known, and unchanging at the microlevel. Therefore it is possible to explain the resulting shapes that occur with a first-principles analysis of the microlevel process. What about the solar dynamo? Can’t fundamental physics be used to create a differential equation model (or model system) that can then be solved for an assumed set of initial conditions? Unfortunately, the state of understanding of the physics of the solar dynamo is still murky - how could it not be, given that turbulent stellar interior?For a thorough review of the status of understanding (or lack thereof) of the solar dyamo as of mid-2005, see the excellent Dynamo Models of the Solar Cycle by Paul Charbonneau. This article contains a very detailed non-linear magnetohydronamic model of the dynamo, and includes a section on the chaotic behavior of the model (warning: not for the squeamish - a lot of nasty Navier-Stokes equations here), but the overall message is that there is still a long way to go before true predictions of the solar cycle will come from this route.

So where do the 11-year cycles come from? Click to enlargeJust when it seemed that understanding was still way off, a new model of solar activity was announced earlier this week by Mausumi Dikpati et.al. (from the National Center for Atmospheric Research in Boulder.) The authors claim an astonishing accuracy rate of 98% in their model predictions! It was this model that predicted the delay in the onset of Solar Cycle 24. Note that the newspaper accounts described in the first paragraph of this post focused on the predictions, not the excitement of the new model. What the news accounts don’t say is that Hathaway, lead author of the statistical prediction paper, disputes the predictions of this new model. According to the empirical model, there will be no delay in the onset of Solar Cycle 24.So who’s right? The beauty of modeling, and the cruelty, is that the next piece of data can either further cement the model’s reputation, or crush it. We won’t have to wait too long to find out.I’m guessing that for the forseable future, solar cycles will be predicted using the statistical method that works so well - and most will worry about avoiding potential problems with satellite communication based on the prediction without worrying at all about understanding the phenomena from a basic physical level.A good website for an account of solar activity and plenty of informative links is NASA’s Solar Physics site, although there is a very disturbing message at the sight claiming that “funding stopped as of october 2005.“An even better site is the Australian Space Weather Agency , which has a large number of constantly updated space weather data, including solar wind speed and x-ray flux. Be sure to visit their Educational area for a very readable overview of solar cycle issues.