Run down of model biases.....

[Pebbles]

FANTASTIC post Dan... hope you do post more soon!

P.S. Is most of the research on these equations derived from the chaos mathematical theory? If you don't know that's ok. Just know that mathematicians were working on that theory for use in complex systems such as weather.

[tropicsgal]

Which of these models are best for predicting the path of storms?

[Wthrman13]

P.S. Is most of the research on these equations derived from the chaos mathematical theory? If you don't know that's ok. Just know that mathematicians were working on that theory for use in complex systems such as weather.

No, not really, at least not in the sense that I think you are driving at. The equations that describe basic atmospheric motions have been known in most of their details for quite a long time, as have the various techniques for discretizing them. However, it has only been in the last 50 years or so that we have had the capability of practically using the numerical discretized version of the governing equations to forecast the weather, due to the development of high-speed computers. L.F. Richardson in the early part of this century was well ahead of his time in that he was the first to actually attempt a numerical forecast, doing all the calculations for all the grid points BY HAND. Unfortunately, his forecast failed utterly because the numerical scheme he chose was unstable (he used too large of a time step). He envisioned a veritable army of people with pencils and paper doing all the numerical calculations for all the various grid points, and passing the answers back and forth among each other as needed. If you replace the people by CPU's in a supercomputer, he wasn't really very far off the mark .

As far as chaos theory goes, it is a relatively recent development, and it was a big buzz for a while. People thought it would revolutionize how we do math, but it seems to have died a quiet death in that regard, but don't quote me on that . However, it IS relevant to weather prediction, because it's central conclusion is that the solution to many nonlinear equations or systems of nonlinear equations (which is what the governing equations of the atmosphere are) are very sensitive to the initial conditions. Two initial conditions that are arbitrarily close together will eventually diverge until the solution to the equations starting from the two different initial conditions will eventually look nothing like each other. This means that if I'm even 1 degree off in my measurement of the temperature at a given station, and this ob gets into a model, eventually the model forecast will diverge from reality. Furthermore, even if I'm only a tenth of a degree off, or a hundredth of a degree off, this still will inevitably happen. This is even assuming that the model is perfect (which none of them are even close). The pioneer of chaos theory was a meteorologist named Ed Lorenz, and he has been widely quoted as estimating the limit of predictability for weather, again even assuming perfect models, at about 2 weeks, due to this "sensitive dependence on initial conditions". Believe it or not, we are actually approaching that limit with our current models, and even exceeding it in some rare instances using ensemble forecasts.

[Wthrman13]

To answer a question posted previously, yes, most of the simpler hurricane track models, such as the LBAR and the BAM models, do indeed use the dynamical model output as either the boundary conditions or as the background wind field for their calculations. The BAM models simply use a vertically averaged horizontal wind from the output of the GFS model, and assume (with some other minor corrections), the the storm will move with this average wind. The LBAR is actually a dynamical model, but an incredibly simplified one that treats the atmosphere as a single 2d layer, and assumes it's frictionless and barotropic. These kind of simplifications were needed back in the day because of limited computing power, but nowadays we can use the full set of equations at reasonable resolutions with little difficulty. Thus, I suspect that many of these simplified models will go the way of the dodo in the coming years.

The fact of the matter, however, is that there are still many issues with hurricane track and intensity forecasting that even our best dynamical models have trouble with. Intensity forecasting, which of course has feedbacks into the track forecasting, and vice versa, is virtually useless and a total crapshoot at this time. The best intensity forecasting model to my knowledge is still the SHIPS, which is a statistical model based on past tropical cyclone behavior. The fact that it still outperforms the much more complex dynamical models in intensity forecasting is a telling reflection on just how far we need to go.

The GFDL model to me is a huge disappointment. It has the potential to be a great track and intensity forecasting model (and it is pretty good on track forecasting, actually), but suffers from what I believe to be fundamental problems in its design, which contribute to it's absolutely awful intensity predictions. I think it was OtherHD who first started calling it the Goofdl, and it certainly fits. I still think that high-resolution, explicit convection (that is, the model is able to resolve the individual convective clouds), nested grid runs centered on a tropical cyclone are the way to go in the future for better intensity forecasting, but a great deal of work needs to be done in this area. I have full confidence that one day we will be able to demonstrate much higher skill in forecasting intensity changes, especially rapid ones which we currently have virtually no skill in.

P.S. I am taking a graduate Tropical Meteorology course this semester. For my term project I am considering running high-resolution ARPS runs of Hurricane Charley to see if the model can even come close to forecasting it's intensity changes, etc. I'll let the board know what I find (I'll probably set a website up) once I get this going.

[Pebbles]

Excellent. I wasn't aware that the pioneer for chaos was actually a meteorologist. And both your explainations draw a clearer picture on the foundations of model extrapulation in more 'laymen' terms. Thanks again! I would like to encourage you to maybe make a web page or keep the link to this thread handy and any other discussions along this line. The question that started this thread seems to pop up at least a couple times a season.

[Wthrman13]

Hmmm.. a web page.

Not a bad idea, I'll think about doing that.

I suppose I could put up a sort of Storm2k faq page on tropical cyclones, but I would still continue to refer people to Chris Landsea's excellent FAQ on the NHC web site.