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Weakening t-storms…drying after noon

Hey bloggers:

We have a new camera over Lake of Ozarks…a beauty of a shot!

Like it?  This morning I showed it as a boat was cruising along and a thunderstorm rain shaft was approaching from the distance.  In this shot you can see some shafts of rain in the distance

T-storms were firing strong in the vicinity of KC this morning.  Sedalia reported some small hail…there was a lot of lightning with a band of t-storms approach from the west.  They weakened dramatically while approaching KC resulting in weak scattered showers.  These showers pass and we dry up afternoon and warm to the low-mid 60s.

This was our weekend weather trivia from today.  Can you pull your statistics from memory and figure this one out?

Yeah, you can draw a Venn Diagram, but I thought the easiest way to show the answer on air was with this graphic:

Since each day is a 50/50 shot, the possibility that we’d have rain at some point this weekend encompasses the top three out of four equally likely possibilities.  I should have drawn a table, right.  The point is you can’t add 50% to 50% and get a 100% chance for rain.  Fun?

And I just received an email from a local Meteorologist who will remain nameless about this subject:

George,

Just caught your trivia segment about rain chances and probabilities. Unfortunately, the correct answer to your question was not listed. It is *not* 75%.

If there’s a 50% chance of rain Saturday and a 50% chance of rain Sunday, the chance of rain over the weekend is still 50%. Each day’s forecast is an independent occurrence.

Let’s equate this to a coin flip. Let’s say that “heads” = rain and “tails” = no rain. An identical 50/50 proposition.

No matter how many times you flip a coin, there is still a 50% that you get heads on any individual flip. If there was a 75% chance that you would get heads on one or both of the two flips, casinos would not exist and I would be raking in billions at the Baccarrat or Roulette tables.

The confusion lies in the difference between unique event probability and possible outcomes. Yes, on two coin flips there are 4 possible outcomes of those two flips, 3 of which are favorable to heads (rain). However, the expectation at getting one of those possible outcomes not equal.

As an FYI, my mom has taught college statistics since before I was born, and so this sort of thing is second nature to me. I’m hoping that you will correct this graphic as this places an incorrect understanding of how weather forecasts work in the eye of the general public.

Respectfully,

XXXXXX

I replied with the following email:

I disagree 

The coin flip was the exact analogy I used to explain this to my coworkers

With the coin flip analogy, the question becomes “What are my chances to flip heads at least once if I am given two flips of the coin?”

This is not an “individual flip”…it’s two separate, independent flips.

 The answer is 75% and can be proved by constructing a simple Venn Diagram.

Why two coin flips?  Because they represent two SEPARATE storms, each with a 50% chance to rain on a SEPARATE days.  The probability of each dropping rain doesn’t change…but that wasn’t the question…the question (was) can rain fall AT LEAST ONCE given these two independent “flips”.

 As for your casino analogy, winning ONE TIME on the roulette wheel is more likely with a group of 38 spins as opposed to an individual spin.  However, the winning probability of each spin remains the same as it is independent of other spins.  Unfortunately, each time you spin, you must pay.   The house will always have the same advantage, remaining unchanged for each spin.

 We can talk about this more…call me at the station today after 2pm.

Ask for weather

Thanks!

-GW

I just received this reply from the same person:

It’s nice to finally have a discussion with a very intelligent person on this subject. George, your math is spot on and I concede that in the sense of “classical statistics” your answer is correct. I think my mistake in my argument was the example I chose, and seek to prove that we’re both right.
The deeper problem is that classical probabilities (like coins, Vegas, cards, lottery), etc… is that the known outcomes are provable. When we make a weather forecast, the forecast is not provable (in which case we’d both be in another line of work). The forecast is subjective. We forecast the chance of rain on a scale of 0 to 100%, when in reality the result is binary and furthermore skewed toward quasi-predictable factors. Thus, one cannot apply classical probability theory and the mathematical statistics in a case where the probabilities themselves are subjective. Probably better examples of this would be something like a 10% chance of rain Saturday and a 90% chance of rain Sunday, or 30/40, or 20/20. In a meteorological sense, the effective chance of rain over the span of the weekend would be likely closer to the greater of the two numbers due to the higher confidence both forecast period. The subjectivity/confidence of our forecast also varies with time. I could say there’s a 30% chance of rain every day this month, but what inherent value is that 30% chance at day 20 vs. day 1? Also, the chance that is rains once in that month is likely vastly different than an individual day’s forecast.
I totally get where you’re coming from, and the explanation is completely plausible in a classical sense. But again, my original argument (which I completely failed to convey) is that the forecast is subjective rather than objective. My choice of “independent events” was probably a poor way to broach the subject.
 
Enlightening stuff!

What do you think?

-GW

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27 comments to Weakening t-storms…drying after noon

  • Weatherfreak01

    I love this comment from NWS.. I think someone needs to proof read their script.

    “THE STRONGEST STORMS MAY BE ABLE TO PRODUCE SMALL AND BRIEFLY TORRENTIAL RAINFALL THIS MORNING.”

    What is a small and briefly torrential rainfall? Are the rain drops really tiny or is the rainfall limited to an area equal to one square foot? I know that they meant to say small hail… but it amuses me never the less. Have a great weekend everyone.

  • R-Dub

    Once again rain is looking meager on the south side…heavier stuff going north. Maybe I can match the 0.05″ I got earlier this week.

  • Skylar

    It seems like the opposite of the LLTI has been happening since Gary left. We have some sprinkles right now in southern OP, it’s kinda disappointing. I was looking forward to rain.

  • Brett Budach

    So, what are the chances that I am not going to get rained on at Wyandotte County Lake at 1pm?

  • calikufan

    So anyone notice the SPC outlooks? Seems like were rolling into the LRCs first severe weather setup next week. Are you seeing that George?

  • Henley

    My confidence in rain forecasts, whether it be short term or long term, is becoming very low.

  • RickMckc

    I was a math major in college (many, many years ago) and my first thought concerning your question was “hmmm … he doesn’t have the correct answer on the list” as the two days are independent and the chance through the whole weekend would be 50%. However, it’s been a long time since I lived in that world, so I will be curious to see how the debate resolves.

    My wife is a math teacher, too. I’ll see what she thinks!

  • RickMckc

    Upon further review, GW, I think you may be wrong. :)

    According to the chart you made, there is only a 25% chance of rain occuring on both Saturday and Sunday. That’s not what you meant to imply by your forecast is it (i.e “if it rains Sat it won’t rain Sun” or vice versa)? It’s 50% both days regardless of what happens on the other day.

    • Rick…no, the rain on each day has to be independent… and we get two “flips” here for a probability of rain at least once!

      I’m really digging that people are really thinking hard about this!

  • StormyWX

    Wait…you email the other mets in town? How interesting indeed…

  • kiper32

    People do not seem to be taking the fact that it is two days into consideration. GW is right in this. The other met brought vegas into the conversation. The odds of rolling a 7 are the same on every roll, but depending on how many rolls I watch my odds of seeing a 7 rolled are different. I did a quick check online on probability to make sure, and my initial reaction was correct. Lets sub in coin flips for rain and walk through this. First we have to lay out all possible outcomes:

    Saturday-heads
    Sunday-heads

    Saturday- heads
    sunday- tails

    saturday- tails
    sunday- tails

    saturday- tails
    sunday- heads

    Now then 50% of the time the coin flips were heads, adding up to the proper probability, but the question asked what the probability overall of it occurring at least once was. On 3 of 4 possible outcomes heads was flipped at least once thus giving it a 75% chance of occurring at least one time over the 2 days.

  • R-Dub

    People are way over thinking this…probability of something happening twice in a row is the square of the probability of it happening once. Simple. (1/2)^2 is 1/4. So the chance of getting either rain both days or no rain either day is 25%.

    A lot cleaner conceptually with coins or dice where you know the probability in advance…but if the forecast 50% is accurate than it is just like a coin flip.

  • R-Dub

    By extension to dice (more fun than coin flips) what are the chances of rolling boxcars (2 sixes)? (1/6)^2 or (1/36).

    • RickMckc

      Interesting … so the application to forecasting would be something like this?

      Forecast calls for 50% chance of rain each day for the next five days. Forecaster intends to communicate to the public that the chance that it rains at some point on each day in that five day stretch is 1/2^5?

      I get the math of it … I just am not sure that’s what the forecaster actually intends to communicate.

      • Rick…
        Rdub’s explanation would say there’s a 1/2^5 (one in 32) chance of it raining every day

        the chance it rain at some point on each day in the 5day stretch is 50%

        • RickMckc

          GW, I understand … but, when if you made a five day forecast like that, would you be meaning to communicate “folks, there’s a 50% chance of rain each day, but only a 3% chance that it will rain at some point on all five days?”

          What I’m getting at is that very few people would assume that is what you mean.

  • Jerry

    Good work, George. You nailed it.

    And you shouldn’t have redacted that other guy’s name.

  • calikufan

    So George nws discussions around the area and the hpc keep popping up about severe weather late in the week. Are you seeing this or is it too far to discuss yet?

    • jeff and I were talking about this yesterday…that severe weather Thursday is possible somewhere… our idea was that it’d be south or southwest of KC…as it’d be too cool in KC.

      Saturday will be a day to watch

      • calikufan

        Thanks bruddah. Haha. I’ve been waiting for a Chase day that’s on the weekend. Hopefully this one is west…much easier in Kansas to Chase than Missouri

  • OlatheMatt

    I have a question, If KSHB is voted the most accurate weather team in Kansas City, who on that list was the LEAST accurate? Where does this list come from and how can it all be verified?

    • The company that rates the weather is called WEATHERATE. They keep score of all the forecasts from all stations and compare them to the weather that verifies over the next 5 days…it’s a similar process to the way my forecasting class was graded at UCLA.

      We know which station is last, but it wouldn’t be gentlemanly to disclose that information… :)

  • Kole Christian

    I do like the Ozarks cam. Also, interesting tid bit with the trivia