“May or may not rain… might be 4-10 inches of accumulation…might possibly be snow, might be a chance of be freezing rain.”
Why all the waffling?
With all the computing power at our disposal in 2005 why can’t we project with greater accuracy how much snow will fall, and when it will begin and end? It really seems that short term weather forecasts have not gotten that much more accurate in the past 10 years or so even though computer modeling power has increased exponentially.
What’s the hang up? Are meteorologists not making new advances in predicition accuracy? Is the accuracy available but only at a high cost, and the current non-specific forecasts are “good enough”? Is PC modeling of weather patterns more a software than hardware problem? Is it lack of sufficient data points?
Because the relevant equations are highly chaotic. It’s not a software or a hardware problem, it’s a reality problem.
Small errors in measurement very quickly become magnified into huge errors in prediction. A very conservative estimate shows that just in terms of air pressure, one loses five orders of magnitude in two weeks. That means an error of 0.0001 mbar in measurement becomes a 10 mbar error in prediction two weeks later: a full percent of atmospheric pressure! The air pressure equation on its own is among the best behaved of the relevant equations, and combining them together just complicates things even more.
I don’t know that they can or can’t be more accurate, and before someone who does know comes along, I’ll offer that television and radio stations broadcast over entire cities and their suburbs which makes more specific predictions problematic simply because not everyone within the broadcast range will experience the exact same weather at the exact same time. If you think about it, “A chance of rain,” is probably more accurate for a broadcast area on average than, “It will rain from 6:06 AM, to 4:12 PM, with an intermission from 8:27 AM to 9:16 AM, and 2:54 PM to 2:56 PM.” Clouds move, and I don’t think media outlets want to take the time to tell you in which sections of which towns rain will fall at what times. The broadcasts could run for hours.
There’s a previous thread or column about the inaccuracy of weather reports, at least in terms of what they mean. Essentially, when they say there’s a 40% chance of rain, it means that out of all the times the conditions have been what they are currently, it has rained 40% of the time.
But why so unscertain?
I recommend Chaos by James Gleick, which details the work of Edward Lorenz in 1960, when he created a computer model weather system, which printed out numbers representing various conditions. Wanting to see a sequence over again, he retyped in some results from a prior printout. However, the printout was trucated to 3 decimal places, whereas the internal calculations were not. His model deviated wildly from it previous behavior. Changes in conditions of one part in ten thousand can throw off resuts. No model since then has done any better.
I’m not talking about weeks. I’m talking about 2-4 days. From my layman’s perspective prediction accuracy doesn’t seem to have increased (real world) a whit in the last 10 years in what is being delivered to me as a consumer of weather projections.
Why aren’t mathematicans going after this prediction accuracy problem the way they did in the 70’s and 80’s, are they all going to Wall Street? It seems to have fallen off the radar screen of interesting problems. You don’t hear much anymore about research meterologists and math/physics types hailing some new piece of big iron that will revolutionize weather forecasting.
It’s not that more data points would make it work, it’s that NO amount of extra data points will be sufficient. The weather system is simply too sensitive to minute change.
So in 40 years we haven’t been able to improve this modeling paradigm? Amazing. So even for short term stuff it’s all just brute force calculation of chaotic data points? You’d think there would be some averaging effect that would mitigate the impact of chaotic fluctations.
Well, no. That’s the very nature of a chaotic system–it fluctuates, and there’s nothing to mitigate that.
One of the big issues is floating point error. The only rationals that have a terminating binary representation are of the form k/2[sup]n[/sup]. Anything else is repeating, and necessarily truncated. A lot of little truncations passed through non-linear functions again and again leads pretty quickly to large errors.
But even if that weren’t an issue, we would still need extremely precise measurements of the current conditions all over the globe to be able to predict what’ll happen in the near future.
Oh, come on. They can’t even figure out what’s happening right now, much less what’s going to be happening. I pulled up Yahoo weather for my town one day last week, and it said that the current temperature was -12 degrees, and that the daily low temperature was going to be 7 degrees. The -12 was pretty close. I’m sure that it was -12 somewhere in town at that time. But I found it really amusing that the daily low would be 19 degrees higher than the current temperature they were reporting.
Similarly, I’ve heard radio weather forecasts call for “partly cloudy skies” when it was snowing at that time. What? Nobody looked out the window?
If that’s the state of our weather reporting for right now, how can you expect them to get tomorrow right?
2 days is 48 hours. 4 days is 96 hours. On average the upper atmosphere, the part that drives the weather, moves at about 40mph. So you’re talking about predicting what chunk of air will be overhead Astroville, when that chunk is presently some 48 * 40 = 1920 miles away, or for 4 days, some 4000 miles away. That’s a tough request.
Further, even knowing exactly which chunk will be overhead in 48-96 hours tells us nothing about how it may have changed over the time as it interacts with the adjacent chunk. Any time lapse satellite photos or radar animation loops you’ve seen will clearly show the swirly, flame-like behavior of clouds & precip.
Flames are always the same, and never the same. Big picture they’re consistent from minute to minute, but pick a spot on a log near the top of a fireplace fire and note how often, and at what intervals, a flame licks the spot. Your data points will be all over the place. Weather’s the exact same phenomenon, just on a much larger & hence slower-moving scale.
Finally, what does “it’s going to rain” mean? It’s common where we live for it to rain like heck at my office and not a drop at my wife’s 20 miles away. From the perspective of the local NWS office, did it rain here today or not? Whether they say yes, or say no, a lot of people will conclude they were wrong, and that’s for a “prediction” made after the fact!. Imagine how much harder a prediction before the fact would be.
I will note that several of your complaints are “borderline” situations. The difference between snow and freezing rain is the result of changes in temperature at multiple altitudes over a rather large area. Those temperatures can be affected by pressure fronts either increasing the speed of the passage of the local conditions or stalling it in place. No weather is isoalted from any other weather; it is all contiguous with arbitrary human map lines attepting to make sense of “local” conditions.
Chaos indicates that we may never have a perfect handle on the situation (thus the reference to butterflies periodic call to “End the chaos. Kill the butterflies.”), but even with increased computer power to establish more data points in an effort to reduce the level of chaos, ther whole notion of storm systems require far more data collection and computer power than we are anywhere near managing.
I’m currently looking at my dad’s state of the art home weather station thingey. It reads our outside temp by a smaller unit on the porch, and gets the rest of its weather by radio from the National Weather Service, I think. Outside it’s cloudy and cool. The thing has the “cool” part right, as that’s directly from the porch (49.1 degrees), but it’s absolutely certain that it’s pouring down rain. (Even has an unhappy smiley face that says WET.) A quick look at the doppler station we get in the high cable channels suggests it’s not raining anywhere around us. At least the clock is right.
A weather station cannot tell you if it’s raining, only what the relative humidity is. So the unhappy face says that the humidity is at or near 100%, which means (if it’s not raining) that it’s overcast and/or foggy. Radar will not pick up any rain that’s very light, so even tho the radar may not show any rain, it could, in fact, be drizzling. In addition, and conversely, sometimes rain will evaporate before it hits the ground. The radar will then show rain when it’s not.
In one very important aspect, computers have really helped: hurricanes. Altho the exact location of the landing of a hurricane still is not known until a few hours before it hits, the general location can be predicted with much more accuracy within a few days. Still, different computer models will plot different paths since they are programed with different parameters. The six models all can show six different projected paths and it’s up to the expertise and experience, along with the computer’s past history as to accuracy, of the meteorologist. On a rare occasion, all models may be in agreement, but that’s rare.
It often thinks it’s sunny when it’s raining buckets, too.
Our local “good” weatherman, Jim Gandy, has it set for life because when Hurricane Hugo came in in, what, 89? he was the only local weather guy who predicted it would make landfall in South Carolina and possibly come inland. And of course it did, so we won’t get our weather from anybody else. Now, sure, maybe he was just a really good meteorologist, but you know he really just got lucky and erred on the safe side. He was probably wrong within a perfectly normal margin of error during the course of his career to that point, but he got the big one right, so people think he’s “better”.
Another example of “forecasting depends greatly on where you live”. In Key West, FL, in the summer, they ALWAYS forecast 20% chance of rain. The rain storms are so localized, I have seen it raining in the backyard but not the front yard. Then a few hours later, see it raining in the front yard, but not the backyard.
One buddy of mine said, “I’ve seen it rain on the highway here where you only need one windshield wiper”.
That’s funny. All of our meteorlogists in Charleston thought it would land in SC, near Beaufort was the original prediction, which is why I left town a day before it hit on Sept. 21, 1989.
Five orders of magnitude in a week is just the first example off the top of my head. There are similar problems in the shorter term, partially because the longer term is made up of the shorter term…
Basically, mathematicians have done all they really can do with it. The problem is as solved as it’s going to get.
Now, sure, maybe he was just a really good meteorologist, but you know he really just got lucky and erred on the safe side. He was probably wrong within a perfectly normal margin of error during the course of his career to that point, but he got the big one right, so people think he’s “better”.