Comments on Chaos, Uncertainty and Forecasts...

[RU848789]

Thought it was worth a comment on the high degree of uncertainty in the forecast for the 2/13/14 storm and what that means, practically speaking, and I also thought it would get buried in a model or obs thread, so figured I'd start a new thread (if the mods think this should go elsewhere, that's fine, as I rarely start threads around here).  Anyway, unless you've really studied chaos theory and done some numerical modeling of chaotic systems, I think it's hard to understand the high degree of uncertainty in this forecast and weather forecasting, in general.  I have, albeit in computational fluid dynamics (CFD), not weather, but they share a lot of similarities in terms of the fundamental science involved, as well as the numerical modeling component. 

 

As most here likely know, weather modeling (and CFD modeling) consists, basically, of selecting initial conditions and then moving the clock forward and trying to predict future states across 3-D space using the best fundamental science one can, i.e., equations of state for momentum, heat and mass transfer, physical chemistry models for phase transitions/precip, thermodynamics, etc.  As time goes by, the conditions at x hours out become the new initial conditions fed into the deterministic models and the model moves forward in time again to the next state, and so on until the end of the run. 

In chaotic systems, as time goes by, the variability (error bars) in each new set of initial conditions widens such that, for weather forecasting, the error bars become huge by 7-8 days out, which is why the NWS doesn't do predictions beyond 7 days.  As an aside, for those unfamiliar with it, chaos theory is often best understood by referring to the "butterfly effect," coined by Lorenz, one of the pioneers in the field, who essentially showed, by theory, that a butterfly fluttering its wings in Africa could result in a hurricane in the Atlantic weeks later.  The wiki description, at the bottom of this post, is excellent. 

So, even in setups like the coming storm, the uncertainty around precip amounts over time, when/where the rain snow line starts and moves to, how much snow before any possible changeover, and how much snow the back end might deliver are all incredibly complex and all have significant uncertainties associated with them.  Let me illustrate with an example, using New Brunswick, since this I first posted this on a Rutgers football board, oddly enough, where I'm kind of the resident weather geek/poster, lol.  The current NWS forecast for NB is for about 6" of snow, followed by 0.4" of rain in the early/mid afternoon (4" of snow equivalent), then 2" of snow on the backend, for 8" total, as per the NWS map.  Also, keep in mind that this is an illustration, not an exact analysis of the exact uncertainties, so please don't focus on "hey, the Euro says it's going to be X inches on the front end." 

What the NWS and any pro met will tell you, but can't really describe for every location, is that the error bars around this particular forecast (as opposed to storms without a rain/snow line, for example, where it's more about getting the precip amount correct, which is much simpler) are fairly large.  For example, for the first part of the storm, NB could probably get anywhere from 4-8" before a changeover (midpoint is 6") at 1 pm and 0.2-0.6" (midpoint is 0.4") of rain after a changeover at 1 pm (2-6" snow equivalent), then could get 0-4" of snow on the backend (midpoint is 2" and backend snows are difficult to rely on, hence the 0" potential; I would say, however that the upside is likely more than 4", but won't include that in this example).  So, if the changeover occurs at 1 pm, the actual range of snowfall in this uncertainty analysis is 4-12", with a midpoint of 8". 

But that's if the changeover is at 1 pm!  What if the changeover is at 11 am and lasts longer?  Or what if the changeover occurs at 3 pm and is very short?  For the first case, one would have to subtract about 2" from the snowfall range, so the range moves from 4-12" to 2-10"; similarly, for the second case, adding 2" of snow moves the range from 4-12" to 6-14".  However, there's simply no way any forecaster is going to try to explain an overall range of 2-14" for one point, let alone a region, which is why they usually will pick a reasonably "safe" midpoint, like 8" in this case and hope that if it underperforms or overperforms, it's only by 2-3", so that if 5" falls or 11" falls, people expecting 8" won't think it's that far off. And this analysis doesn't even factor in the variability amongst the multiple models, so it's easy to see how difficult forecasting is. 

This kind of variability happens in the summer all the time, but nobody cares when one town gets 1" of rain in a t-storm and the next town over gets 1/4" of rain - in winter that would be an incredible difference of 12" snow vs. 2.5" of snow and people would absolutely freak out.  But rain is kind of just rain and very few freak out.  Good thing, since the inherent uncertainty in mesoscale events like thunderstorms is about 8X that of winter storms, since the energy in a 30C atmosphere in the summer is about 8x more energetic (and holds about 8x more moisture) than a 0C atmosphere in the winter, using the Arrhenius relationship, in which a reaction rate (or system energy, if applied to weather) doubles for every 10C rise in temp.  So, now you really know why weather forecasts in situations like this contain fairly wide ranges and why, even then, they're regularly adjusted as one approaches an event, and why even the final forecasts are often incorrect - it's really, really hard to overcome the inherent uncertainty in chaotic systems like the weather. 

 

Hopefully people will find this of interest.  Comments/corrections (I'm not a met, so I may have not captured everything correctly) welcome...

 

 

Chaos theory is a field of study in mathematics, with applications in several disciplines including meteorology, physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions—an effect which is popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general.^[1] This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved.^[2] In other words, the deterministic nature of these systems does not make them predictable.^[3][4] This behavior is known as deterministic chaos, or simply chaos. This was summarised by Edward Lorenz as follows:^[5]

 

http://en.wikipedia.org/wiki/Chaos_theory

[AmyB]

I did find  this interesting, thanks for taking the time to explain it so well

[yl715]

This a must read. Wonderful writing. 

[RU848789]

amy/yl - thanks, I appreciate the kind words.  It's a concept that's not easy to explain in a sentence or two, which is probably why most of the public gets so easily frustrated with meteorologists and their forecasts.  I hear Joe/Jane Public getting so upset about the forecasts not being perfect, but the truth is they're being ignorant - but I'm not sure how to change that.  It was interesting to me that I posted this on a Rutgers football board, where I post a lot of weather info/forecasts for fun and in relation to gameday weather during the season and while there are tons of ignorant folks on that board, it's been kind of nice to see more than a few folks starting to get it.  I'm guessing most people on these boards are much more knowledgable about these concepts, so perhaps discussion will be limited, but then again, I sitll see some fairly ill-informed opinions being bandied about.