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  #1  
Old 07-19-2016, 11:16 AM
Barkis is Willin' Barkis is Willin' is offline
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What are the odds of rain?

So the weather app tells me the chance of rain is:

1PM: 50%
2PM: 50%
3PM: 50%

What are the odds it will rain somewhere in the 1:00, 2:00 or 3:00 hours? The outcome of rain is an independent event, so one could calculate the chance of rain within any of these 3 hours is 87.5%. Or should I read the weather forecast to mean there is a 50% chance throughout that entire three hour timeframe?
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  #2  
Old 07-19-2016, 11:17 AM
Chronos Chronos is offline
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Rain is not an independent event, and I'm not sure why you would think it is. There is not enough information to calculate the total probability from that information.
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Old 07-19-2016, 11:18 AM
bob++ bob++ is offline
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The latter. These forecasts are for joe public, not professors of mathematics.

50% means that it is a coin toss as to whether it will rain or not.

Last edited by bob++; 07-19-2016 at 11:19 AM.
  #4  
Old 07-19-2016, 12:21 PM
Barkis is Willin' Barkis is Willin' is offline
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Originally Posted by Chronos View Post
Rain is not an independent event, and I'm not sure why you would think it is. There is not enough information to calculate the total probability from that information.
The probability of rain in the 1PM hour doesn't effect the probability of rain in the 3PM hour, does it? Or does it? They're certainly not mutually exclusive, meaning it could rain in each of the 3 hours.

What more info do you want from the weather app?
  #5  
Old 07-19-2016, 12:24 PM
Dead Cat Dead Cat is offline
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I think if it rains at 1pm, that is likely to make it either more likely or less likely that it will then rain at 3pm, but I don't know which. Nor, apparently, do professional meteorologists, much of the time. In other words, I think there are too many factors to say.

I personally don't pay much attention to the probabilities. Where I live (SW England), they are rarely accurate in my experience. The other day it said 0% chance of rain at 7pm, but there was some (with me looking at that forecast only a few hours before). So they're basically useless for any kind of forward planning.
  #6  
Old 07-19-2016, 12:26 PM
watchwolf49 watchwolf49 is offline
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As The Master explains it "What does it mean when 'X percent chance of rain' is predicted"?:

Quote:
The best forecasters can do is to give the probabilities, which they do by having the computer compare present conditions with historical data. When you hear there's a 10 percent chance of rain, that means that out of the last 100 times the weather conditions were just like they are now, it rained 10 times. (More or less — I'm obliged to oversimplify a bit.)
So in to OP ... at 1 pm, half the time it rained, half the time it didn't when the weather was the same. At 2 pm the same thing; half it did, half it didn't; etc etc etc ... ad nausium

Last edited by watchwolf49; 07-19-2016 at 12:29 PM.
  #7  
Old 07-19-2016, 01:46 PM
Chronos Chronos is offline
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Maybe it means that there's some big storm coming, and it might miss us, but if it doesn't, it'll rain for three hours. In that case, if it's still dry at 1:00, then it probably will be all day, because it meant the storm missed. On the other hand, maybe they're sure the storm is coming, but they're not sure precisely when it'll hit. In that case, if it hasn't started yet by 1:00, it's even more likely that it'll be raining later. Either case is plausible, as is any combination of the two.
  #8  
Old 07-19-2016, 02:20 PM
ftg ftg is offline
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The hourly estimates aren't to be taken as actual probabilities. They start with the probability for the day, actually half day in most circumstances. If all times of day are equally likely, then every hour is assigned the same probability. But often certain hours are more likely to get rain due to predicted changes in weather conditions so the odds are moved up or down accordingly. So if it's like to be dry in the morning, the odds are low while if it's going to be rainy in the after noon, the odds go up quite a bit (with most of the percentages being alloted there).

And then they fudge the numbers some more since they still don't make a lot of sense.

It can get pretty far from real statistics.

I just checked this with my local weather.com forecast comparing today's chance with the upcoming hourly chances. Yeah, it doesn't make any sense at all unless you see how they're fudging things.
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Old 07-19-2016, 02:40 PM
carnivorousplant carnivorousplant is offline
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Weather prediction is not a science. It is a Black Art.
  #10  
Old 07-19-2016, 03:37 PM
Barkis is Willin' Barkis is Willin' is offline
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Quote:
Originally Posted by watchwolf49 View Post
As The Master explains it "What does it mean when 'X percent chance of rain' is predicted"?:



So in to OP ... at 1 pm, half the time it rained, half the time it didn't when the weather was the same. At 2 pm the same thing; half it did, half it didn't; etc etc etc ... ad nausium
Interesting.
I'm inclined to say that if asked what are the chances of rain between 1PM - 3PM, the best answer seems to be 50%.
  #11  
Old 07-19-2016, 03:49 PM
watchwolf49 watchwolf49 is offline
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Predicting rain is chancy stuff ... for rain to form in 5șC air, the relative humidity must be 100% ... but if that same air is 5.5șC, then RH will be 95% (abouts) and it won't rain. Hell, clouds won't even form so if the forecast is a 90% chance of rain, there's a 10% chance it'll be sunny and warm ... and it's all about a half a degree higher or lower ... tricky stuff if you don't sell your soul to the Weather Demon.
  #12  
Old 07-19-2016, 11:23 PM
jtur88 jtur88 is online now
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Calcualte the negative, to get the simple probability of all being met The chance that it will rain in one of those periods equals one minus the chance it will not rain in any of them. So, the chance of no rain is 1pm-0.5, 2pm-0.5 and 3pm-o.5. Multiply those and get 0.125 as the chance of an absence of rain in all three, or 0.875 as the chance at least one of them will have rain.

As a better illustration, say the chance is 20% this evening, 50% overnight and 30% tomorrow morning. The chance there will be rain at least once by tomorrow noon is 1-(0.8x0.5x0.7) = 1-0.28 = 0.72. or 72%. We've calculated the chance it will NOT rain (80%, 50% and 70%) is 28%, so the chance it WILL rain is 72%.

Last edited by jtur88; 07-19-2016 at 11:26 PM.
  #13  
Old 07-20-2016, 05:46 AM
Arrogance Ex Machina Arrogance Ex Machina is offline
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Taking a look at weather radar and weather radar predictions tells usually a lot more about rain than just looking at the hourly rain possibilities. If you see a bunch of high intensity small rain areas wandering around there's a chance of either no rain or a lot of it, but if you see a wide rain front approaching then it is more of a question when it arrives than whether it will arrive at all.
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Old 07-20-2016, 08:37 AM
Chronos Chronos is offline
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jtur88, that assumes that all the probabilities are independent, which we've already pointed out probably isn't true.
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Old 07-20-2016, 10:30 AM
markn+ markn+ is offline
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You can't take each of those predictions as an independent event. To take it to an extreme, suppose the forecaster gave predictions every minute during those three hours instead of every hour. Almost certainly all those predictions would be identical (if you think otherwise, what do you think they would be?).

1:00 50%
1:01 50%
1:02 50%
...
2:59 50%
3:00 50%

Using jtur88's reasoning, there are 181 independent events with P=0.5 for each, so the probability of no rain is (0.5)^181, or 3 x 10^-55. So rain is essentially guaranteed, simply because more predictions were made, which is an absurd conclusion.

--Mark

Last edited by markn+; 07-20-2016 at 10:33 AM.
  #16  
Old 07-20-2016, 11:04 AM
Channing Idaho Banks Channing Idaho Banks is offline
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A lot of times when they say 50% chance of rain accumulation is only .001 inches. That's not very much rain.
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Old 07-20-2016, 11:12 AM
watchwolf49 watchwolf49 is offline
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Strictly speaking, these rain probabilities are only generated in 6 hour time intervals. We can of course interpolate these probabilities every hour or every minute, but the output of the numerical models are every six hours.

Quote:
The GFS (Global Forecast System) model produces forecasts out to 16 days, four times per day. The loop time steps are 6 hours from analysis time to 180 hours (7.5 days), then change to 12-hour time steps out to 384 hours (16 days).
"Weather Models" from NOAA.
  #18  
Old 07-20-2016, 11:35 AM
Thudlow Boink Thudlow Boink is offline
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Originally Posted by Barkis is Willin' View Post
The probability of rain in the 1PM hour doesn't effect the probability of rain in the 3PM hour, does it? Or does it?
If I pick two days at random, one of which had rain at 1:00 and the other of which didn't, and asked you to bet on which day had rain at 3:00, which day would you bet on?
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Old 07-20-2016, 01:52 PM
Riemann Riemann is offline
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I've often wondered about this, and we don't yet seem to have a clear answer to the OP. As the OP and others have said, the stated probabilities for rain during different lengths of time interval in popularized weather forecasts are quite obviously mutually inconsistent under any assumptions of dependence between consecutive periods.

watchwolf49 gives a cite that forecasts are calculated in 6-hour intervals, but since meteoroligists can actually do math, it does not necessarily follow that the probabilities that they distribute from their forecasts apply to 6-hour periods.

I'd really like to know a few things:

(1) What exactly constitutes "rain" in a given period in the models?
(If the threshold for a "rain" event is higher for a longer period, this might go some way to explaining the apparently inconsistent probabilties.)

(2) What's the best primary source of weather forecast data, where the probability is actually correct - i.e. where if the probability for a given period is stated as 50%, there really is an expectation under the model that rain will occur half the time in the stated period?

(3) What kind of screwy calculation is done (and by whom) to produce the nonsensical hourly probabilities shown in popular forecasts?

Last edited by Riemann; 07-20-2016 at 01:56 PM.
  #20  
Old 07-20-2016, 03:30 PM
muttrox muttrox is offline
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Given the lack of independence, the best you can infer is that the probability is somewhere between 50% and 87.5%. Either that or you need a source of information "upstream" of the weather app - you need access to the information that led to the information in the app.
  #21  
Old 07-20-2016, 03:44 PM
watchwolf49 watchwolf49 is offline
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Quote:
Originally Posted by Riemann View Post
[snip] ... (1) What exactly constitutes "rain" in a given period in the models?
(If the threshold for a "rain" event is higher for a longer period, this might go some way to explaining the apparently inconsistent probabilties.)

(2) What's the best primary source of weather forecast data, where the probability is actually correct - i.e. where if the probability for a given period is stated as 50%, there really is an expectation under the model that rain will occur half the time in the stated period?

(3) What kind of screwy calculation is done (and by whom) to produce the nonsensical hourly probabilities shown in popular forecasts?
(1) We have a positive for rain if 0.01" or more of liquid water is measured in the rain gauge at the specific location, and we'd have to melt any snow to find this amount. A negative for rain is when our rain gauge remains dry for the time interval.

(2) Some of the best and most accurate weather forecasts come from voodoo witch doctors ... [giggle] ... yes, that's being sarcastic ... but seriously, let's not confuse "best source" with any source that's in anyway "good". We do the best we can and that's the best we'll get. For example, we take our current weather conditions and search our historical data and find the same conditions 138 times. Of those 138 times, it rained within 6 hours on 16 occasions. We would then forecast a 10% chance of rain in the six hours following our current time. Yes, 10% here actually means anywhere from 5% to 14.9%, so-called accurate to one significant digit.

So, as long as we're clear that "best" source is "not very good either", then really any are fine. One BIG difference comes in whether the source is commercial or non-commercial. The non-commercial sources tend to be more honest, more willing to say they don't know and so they're just guessing. So the National Weather Service or World Meteorological Service. When I lived in Iowa, we had one local station's weather guy always forecast exactly what the farmers wanted. If it was running dry, he'd forecast rain; if things were too wet, he'd forecast sunny ... it was awful. But you know, the guy had products to sell and he sold more if he said things would be great in a couple days, "brought to you by The Johnson City Seed Company, where all news are good news".

(3) They interpolate (see Wikipedia article). We find the inbetween result by weight-based averaging. So if 2 x 2 = 4 and 3 x 3 = 9, then 2.5 x 2.5 ≈ 6.5. Similarly, if rain is 40% probable in the first six hours, 60% probable in the next 6 hours, we can approximate that it will be 50% someplace inbetween.

≠≠++≠≠

Yes, meteorologists can do the math, here's the formula caste as partial differential equations, NSFH two-click rule applies (DO NOT let your teenage kid see you looking at this or you WILL be doing a shitload of algebra homework next school year)

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Old 07-20-2016, 04:01 PM
Riemann Riemann is offline
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Quote:
Originally Posted by watchwolf49 View Post
(1) We have a positive for rain if 0.01" or more of liquid water is measured in the rain gauge at the specific location, and we'd have to melt any snow to find this amount. A negative for rain is when our rain gauge remains dry for the time interval.

(2) Some of the best and most accurate weather forecasts come from voodoo witch doctors ... [giggle] ... yes, that's being sarcastic ... but seriously, let's not confuse "best source" with any source that's in anyway "good". We do the best we can and that's the best we'll get. For example, we take our current weather conditions and search our historical data and find the same conditions 138 times. Of those 138 times, it rained within 6 hours on 16 occasions. We would then forecast a 10% chance of rain in the six hours following our current time. Yes, 10% here actually means anywhere from 5% to 14.9%, so-called accurate to one significant digit.

So, as long as we're clear that "best" source is "not very good either", then really any are fine. One BIG difference comes in whether the source is commercial or non-commercial. The non-commercial sources tend to be more honest, more willing to say they don't know and so they're just guessing. So the National Weather Service or World Meteorological Service. When I lived in Iowa, we had one local station's weather guy always forecast exactly what the farmers wanted. If it was running dry, he'd forecast rain; if things were too wet, he'd forecast sunny ... it was awful. But you know, the guy had products to sell and he sold more if he said things would be great in a couple days, "brought to you by The Johnson City Seed Company, where all news are good news".

(3) They interpolate (see Wikipedia article). We find the inbetween result by weight-based averaging. So if 2 x 2 = 4 and 3 x 3 = 9, then 2.5 x 2.5 ≈ 6.5. Similarly, if rain is 40% probable in the first six hours, 60% probable in the next 6 hours, we can approximate that it will be 50% someplace inbetween.

≠≠++≠≠

Yes, meteorologists can do the math, here's the formula caste as partial differential equations, NSFH two-click rule applies (DO NOT let your teenage kid see you looking at this or you WILL be doing a shitload of algebra homework next school year)

Yes, I understand what meteorological models do (in principle, at least). And I realize that forecasts are probabilisitic.

By (2), I meanst a source for the unadulterated forecasts that the models are producing - i.e. what comes out of the NOAA or other models, before being screwed up and misrepresented for popular presentation. The NWS website is the most credible source that I'm aware of, but it doesn't show very much detail of a probabilistic nature that I can find.

Re (3) - so, ok, then so long as we know the time period for which the probability is actually a probability (rather than just an mathematically invalid manipulation), then at least we know where we stand. Can you direct me to a primary source for NOAA forecasts that shows 6-hour forecast blocks with associated probabilities, if that's the way the real probabilities are generated in the models?

many thanks

Last edited by Riemann; 07-20-2016 at 04:05 PM.
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Old 07-20-2016, 04:22 PM
watchwolf49 watchwolf49 is offline
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I have this link from the NHC "NHC Forecast Model Information". This page also gives links to regular forecast models. Be warned:

"The National Hurricane Center does not generate a graphic of the guidance models it uses to produce its forecasts. Such graphics have the potential to confuse users and to undermine the effectiveness of NHC official tropical cyclone forecasts and warnings."

Keep in mind that some of these models are copyrighted and leased to the NWS under the conditions the NWS doesn't publish the detailed results ... however I seem to remember a NOAA site that actual allowed the user to download some of the public domain models. I imagine you'll need a stack of MacMinis to get the flops you'll need to get a six hour forecast within six hours.

I don't know what you mean by "a primary source for NOAA forecasts that shows 6-hour forecast blocks with associated probabilities" if none of the links I've provided already serve that purpose.
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Old 07-20-2016, 04:50 PM
Riemann Riemann is offline
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Quote:
Originally Posted by watchwolf49 View Post
I don't know what you mean by "a primary source for NOAA forecasts that shows 6-hour forecast blocks with associated probabilities" if none of the links I've provided already serve that purpose.
You said that probabilities are manipulated by the news services by interpolation. That's plausible but obviously quite bizarre, since this is a completely invalid manipulation for the probability of a binary event.

So I'd be interested to know some place where I can see the true mathematically coherent forecast probability distribution that's generated by the NOAA model for a given location. Perhaps that's somewhere on the NOAA site that you linked, but I haven't been able to find it so far.

Where can I see a valid probability distribution for rain in some major city over some time period in the near future? Pick any place and time period that you like, I'd just like to see what a real forecast looks like. Then maybe we can map that to what the hell the news services are doing with that to produce what they feed to the public.
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Old 07-20-2016, 05:41 PM
watchwolf49 watchwolf49 is offline
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Originally Posted by Riemann View Post
You said that probabilities are manipulated by the news services by interpolation. That's plausible but obviously quite bizarre, since this is a completely invalid manipulation for the probability of a binary event.
Why do you find this unbelievable from commercial news sources? See below ...

Quote:
Originally Posted by Riemann View Post
So I'd be interested to know some place where I can see the true mathematically coherent forecast probability distribution that's generated by the NOAA model for a given location. Perhaps that's somewhere on the NOAA site that you linked, but I haven't been able to find it so far.
First you'll need to contact the copyright holders and pay the licensing fees. NOAA isn't allowed to publish this information in accordance with their user agreement. Best you have a couple years upper division Atmospheric Science classes, but you sound smart enough you could learn the trade with a few years apprenticeship and know how to interpret the spaghetti charts. I can't help you there, I'm the guy who knows the size of header you'll need over your front door.

Quote:
Originally Posted by Riemann View Post
Where can I see a valid probability distribution for rain in some major city over some time period in the near future? Pick any place and time period that you like, I'd just like to see what a real forecast looks like. Then maybe we can map that to what the hell the news services are doing with that to produce what they feed to the public.
I cherry-picked a location where there's a chance of rain which is Winslow, AZ. Here's the forecaster's discussion of these chances.

A commercial news source will flat lie to you if it sells more Ford F-150 4x4's with the snow plough attachment on the bumper. How do they come up with these probabilities ... they lie ... simple.

≥≤≥≤≥≤

Again, you seem to not understand probability ... We have 138 trials, and 16 are positive ... why don't you understand this is a 10% probability (accurate to one significant digit)?

Last edited by watchwolf49; 07-20-2016 at 05:43 PM.
  #26  
Old 07-20-2016, 06:28 PM
Riemann Riemann is offline
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Originally Posted by watchwolf49 View Post
Why do you find this unbelievable from commercial news sources? See below ...
I said I found it plausible, not implausible.

Quote:
Originally Posted by watchwolf49 View Post
First you'll need to contact the copyright holders and pay the licensing fees. NOAA isn't allowed to publish this information in accordance with their user agreement. Best you have a couple years upper division Atmospheric Science classes, but you sound smart enough you could learn the trade with a few years apprenticeship and know how to interpret the spaghetti charts. I can't help you there, I'm the guy who knows the size of header you'll need over your front door.
This is a little ridiculous. I'm not asking for the technical details of how the models work. I'm asking for the form in which the forecast data is published. You said, I think, that probabilities are generated for 6-hour windows, is that correct? Is that what goes from NOAA to the news services, before they screw with it?

It's a very simple question - do the NOAA forecasts in original form give a rain probability (something that really is a probability) for the binary event of >0.01" rain within a 6-hour window?


Quote:
Originally Posted by watchwolf49 View Post
I cherry-picked a location where there's a chance of rain which is Winslow, AZ. Here's the forecaster's discussion of these chances.
This is the NWS forecast that I usually look at. But, again, what the hell do these "probabilities" mean? Probabilities are given for "today" and "tonight". Are these then 12-hour blocks? Are they using valid methods to derive these from the 6-hour windows that NOAA produces, if that's what NOAA produces? Or is this the actual form in which the NOAA forecasts are released?

Quote:
Originally Posted by watchwolf49 View Post
Again, you seem to not understand probability ... We have 138 trials, and 16 are positive ... why don't you understand this is a 10% probability (accurate to one significant digit)?
Huh? Of course I understand this.

The issue under discussion is the time periods for which probabilities of binary events are forecast, and the obviously invalid methods that news services are using to convert these to probabilities for shorter or longer time periods.

Last edited by Riemann; 07-20-2016 at 06:33 PM.
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Old 07-20-2016, 08:08 PM
watchwolf49 watchwolf49 is offline
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Originally Posted by Riemann View Post
[snip] ... This is the NWS forecast that I usually look at. ... [snip]
Perhaps we should start over, which part of The Master's article on the subject 1) don't understand and wish to be explained, or 2) would like to be elaborated on?

The statistics here are simplistic, the big computers are needed to search huge databases. If they get 528 hits and it rained 374 times ... that's 70% probability.
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Old 07-20-2016, 08:33 PM
Riemann Riemann is offline
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Please, I understand The Master's article in its entirety. Although I am old and grumpy these days, I do have a degree in math and a lapsed commercial pilot's license. I'm not seeking to be educated in the principles of meteorological modeling and forecasting or how to divide one number into another and express the answer to one significant figure.

I laid out my questions quite clearly in my prior comment. Since you seem to be connected with NOAA, I thought you might know the answer.

Do you understand the problem with obtaining the probability of a binary event for differing time periods, as laid out by the OP and others such as markn+ above?

I'm asking, quite simply:

What form do the probabilistic elements of NOAA forecasts take before they are manipulated by the news services? What is the time period for which the probability of rain is given in a standard NOAA forecast? I gather that I would need to pay a lot of money to see an actual NOAA forecast, but perhaps you have an example of an old one to see the form of an NOAA forecast? I already know how to see the NWS forecasts and aviation forecasts.

Then, what are NWS and the news services doing to obtain probabilities for time periods of different lengths? The NWS forecasts just say a probability for "today" and "tonight", what exactly does that mean - a 12-hour window? Are the NWS probabilities at least derived by a valid methodology from the NOAA forecasts?

If you don't know the answer, that's fine, but please just say so. For Jeebus sake, stop linking to things like the Wiki article on interpolation.

Last edited by Riemann; 07-20-2016 at 08:38 PM.
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Old 07-20-2016, 09:20 PM
watchwolf49 watchwolf49 is offline
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Quote:
Originally Posted by Riemann View Post
[snip] ... I'm asking, quite simply:

What form do the probabilistic elements of NOAA forecasts take before they are manipulated by the news services? What is the time period for which the probability of rain is given in a standard NOAA forecast? I gather that I would need to pay a lot of money to see an actual NOAA forecast, but perhaps you have an example of an old one to see the form of an NOAA forecast? I already know how to see the NWS forecasts and aviation forecasts.
You misunderstand ... that page you use IS the official NWS forecast, there is no other product unless you want the teletype version. That's the only internet site the NWS publishes their forecast. The NWS is the part of NOAA that issues this information ... none other.

Quote:
Originally Posted by Riemann View Post
Then, what are NWS and the news services doing to obtain probabilities for time periods of different lengths? The NWS forecasts just say a probability for "today" and "tonight", what exactly does that mean - a 12-hour window? Are the NWS probabilities at least derived by a valid methodology from the NOAA forecasts?
What the news services do with this data is up to them. If NWS says "highly uncertain", I suppose the news services makes shit up. And again, NWS is a division of NOAA, such that in all cases NOAA = NWS.

Quote:
Originally Posted by Riemann View Post
If you don't know the answer, that's fine, but please just say so. For Jeebus sake, stop linking to things like the Wiki article on interpolation.
That kind of a link is for the general readership, many who read this may not be familiar with such mathimagical manipulations. NWS runs their models every six hours, and every six hours they issue a "package". This package include a number of products that the variety of users use in their trade or business. You seem familiar with this package and that's all there is.

What do the news services do with the data to get the one hour probabilities? I don't know. It's certainly not math, and I serious doubt it's science ... and I'm sure every news services does its own way. However it's made up, it's not coming from the NWS and should be regarded with caution.
  #30  
Old 07-20-2016, 10:29 PM
jtur88 jtur88 is online now
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jtur88, that assumes that all the probabilities are independent, which we've already pointed out probably isn't true.
It doesn't matter. All I did was explain how to mathematically calculate the probability of one event, based on given cumulative probabilities of other events. I did not and will not, venture an opinion on the accuracy of the given odds.


If the first thre batters in an inning are batting .330, .240 and .220, what is the chance they will go three up three down? 1 - (.67 x .76 x .78), or 1 - .397, or .603.

Last edited by jtur88; 07-20-2016 at 10:34 PM.
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Old 07-20-2016, 10:48 PM
Count Blucher Count Blucher is offline
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Back in Grad School, my very cool statics professor ( Professor Chen ) explained that statistically over time, the weather changes every fourth day.
The way he explained it, if it is sunny for 3 straight days, statistically the weather will be something other than sunny on the fourth day.
Yes, there were a lot of complex calculations behind forecasting the weather... but... if you followed that very simple rule of thumb you would be right most of the time.

As a rule, I found it so simple that I never forgot it... and the results of its application so close to always acurate that it was almost laughable.

I miss Professor Chen. Great Professor. Great Guy....
  #32  
Old 07-20-2016, 10:51 PM
Riemann Riemann is offline
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Quote:
Originally Posted by jtur88 View Post
It doesn't matter. All I did was explain how to mathematically calculate the probability of one event, based on given cumulative probabilities of other events. I did not and will not, venture an opinion on the accuracy of the given odds.


If the first thre batters in an inning are batting .330, .240 and .220, what is the chance they will go three up three down? 1 - (.67 x .76 x .78), or 1 - .397, or .603.
Listen to Chronos, he's knows what he's talking about. This result requires the assumption of independence. Even then, you've actually done it wrong, unless I misunderstand what "three up and three down" means in baseball. The probability is .397, not 0.603.

Last edited by Riemann; 07-20-2016 at 10:52 PM.
  #33  
Old 07-20-2016, 11:09 PM
Riemann Riemann is offline
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Originally Posted by watchwolf49 View Post
You misunderstand ... that page you use IS the official NWS forecast, there is no other product unless you want the teletype version. That's the only internet site the NWS publishes their forecast. The NWS is the part of NOAA that issues this information ... none other.
Hmm, ok, thanks - that is certainly helpful. So I hope we can safely assume that the probabilities that are generated for the NWS format (and obviously the aviation format) are real probabilities derived from the model by people who understand math. I still can't find any documentation for the forecasts, but I'll take a proper look tomorrow. In the general NWS format they are given for "today" or "tonight" - presumably that's likely to mean 12 hour blocks of time, something like 0600-1800 and 1800-0600.

And we have no clue what the hourly "probabilities" given in popular forecasts are even supposed to mean, except that in a qualitative sense they do indicate at what time of day any rain is more likely to occur.
  #34  
Old 07-21-2016, 10:12 AM
markn+ markn+ is offline
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Quote:
Originally Posted by jtur88 View Post
It doesn't matter. All I did was explain how to mathematically calculate the probability of one event, based on given cumulative probabilities of other events.
Yes, it certainly does matter. You can't multiply probabilities for events that are not independent. For example, suppose the probability of a person having blue eyes is 1/10. Then the probability of three randomly selected people all having blue eyes is 1/1000, since they are independent. But the probability of three siblings all having blue eyes is much higher than 1/1000, since the events are not independent.

--Mark
  #35  
Old 08-10-2016, 12:20 PM
muttrox muttrox is offline
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I have a friend who is a meteorology professor. (Sidenote: Never smalltalk about the weather with him. It does not work.)

He sent me this link which explains the meaning behind the forecasts very well.
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