What do the probabilities of precipitation mean in weather forecasts? I
THINK that, say, 60% means the probability of 0.1 inch of precipitation
is 0.6.

If so, this leads to some fairly obvious contradictions. At
http://www.wunderground.com/cgi-bin/...?query=seattle
right now the probability of precipitation on New Year's Day is 70%. But
clicking on the "Details" link for that day shows the day broken up into
4 6-hour periods, for all of which the probability is also 70%. See
http://www.wunderground.com/cgi-bin/...st?query=98101
&hourly=1&yday=1&weekday=Monday

Another example is Friday, Dec. 30. Probability for the day is 90%; the
details page for Friday shows it broken into 8 3-hour periods, for which
the probabilities are 70%, 70%, 90%, 90%, 90%, 90%, 80% and 80%,
respectively.

Now for the first example, the probability of less than 0.1 inch of rain
during the day would be 30% (1 - 70%). The same for each of the 4 6-hour
periods. And .3*.3*.3*.3 is 0.0089, the probablity of less than 0.1 inch
in all of the 4 periods together. Therefore the probablilty that at least
one of the 4 periods having more than 0.1 inch is 1 - 0.0089 = 0.991. And
yet the probability of precipitation for the whole day is supposed to be
only 70%.

For the second example the analagous probabilities are 0.9999 vs. 0.9.

Something seems to be wrong here. Am I correct?

It's 0.01" (measurable precipitation), not 0.10" (a tenth of an inch).

Also, you can't simply multiple the chances as you have done below. Each
time segment is a unique and independent set. The chance of precipitation
listed in a forecast is typically the highest probability that is found in
any subset of the day. Smart forecasts will even provide detail such as
"Chance of rain 30% this morning, increasing to 70% this afternoon".

"Jack Crane" wrote in message
.. .
What do the probabilities of precipitation mean in weather forecasts? I
THINK that, say, 60% means the probability of 0.1 inch of precipitation
is 0.6.

If so, this leads to some fairly obvious contradictions. At
http://www.wunderground.com/cgi-bin/...?query=seattle
right now the probability of precipitation on New Year's Day is 70%. But
clicking on the "Details" link for that day shows the day broken up into
4 6-hour periods, for all of which the probability is also 70%. See
http://www.wunderground.com/cgi-bin/...st?query=98101
&hourly=1&yday=1&weekday=Monday

Another example is Friday, Dec. 30. Probability for the day is 90%; the
details page for Friday shows it broken into 8 3-hour periods, for which
the probabilities are 70%, 70%, 90%, 90%, 90%, 90%, 80% and 80%,
respectively.

Now for the first example, the probability of less than 0.1 inch of rain
during the day would be 30% (1 - 70%). The same for each of the 4 6-hour
periods. And .3*.3*.3*.3 is 0.0089, the probablity of less than 0.1 inch
in all of the 4 periods together. Therefore the probablilty that at least
one of the 4 periods having more than 0.1 inch is 1 - 0.0089 = 0.991. And
yet the probability of precipitation for the whole day is supposed to be
only 70%.

For the second example the analagous probabilities are 0.9999 vs. 0.9.

Something seems to be wrong here. Am I correct?

Jack Crane mentioned in passing :

What do the probabilities of precipitation mean in weather forecasts?
I THINK that, say, 60% means ...

"out of one hundred times we have had conditions similar to these, we
have had rain sixty times"

--
Bill DeWitt
Even if you're on the right track, you'll get run over if you just sit
there. - Will Rogers

"wxforecaster" wrote in
:

Also, you can't simply multiple the chances as you have done below.
Each time segment is a unique and independent set.

Surely the chance of rain during one segment in a day depends to some
extent on the chances of rain during other segments. If there are 4
segments in a day, and the chances in order are 80%, 90%, X% and 70%,
it's a good bet that X is much closer to 100 than 0.

But in what I described, independence is irrelevant.

I've heard that the probability of getting cancer at least once in one's
lifetime is about one-third. Let's call it 30%. Then what's the chance
that no one in a group of 4 people (chosen at random -- independent of
each other) will get cancer? (1 - .3) to the fourth power, or .240,
right? So the probability that at least one will get cancer is (1 -
..240), or .760 .

Similarly, if a forecast says the chance of rain in each of 4 6-hour
periods is 30%, then the chance of at least some rain that day is .760 .

The chance of
precipitation listed in a forecast is typically the highest
probability that is found in any subset of the day. Smart forecasts
will even provide detail such as "Chance of rain 30% this morning,
increasing to 70% this afternoon".

"Bill DeWitt" wrote in message
...
Jack Crane mentioned in passing :

What do the probabilities of precipitation mean in weather forecasts?
I THINK that, say, 60% means ...

"out of one hundred times we have had conditions similar to these, we
have had rain sixty times"


When conditions were 'similar' within the numerical forecast model's
developmental data set , measureable precipitation (= 0.01") was observed
60% of the time.

TQ mentioned in passing :

"out of one hundred times we have had conditions similar to
these, we have had rain sixty times"

When conditions were 'similar' within the numerical forecast model's...

Hmmm... I suggest that a pretty girl is like a spring morning, you
respond that the temperature and humidity of a human female body is not even
near the recorded average for spring mornings.

I'm OK with that.

--
Bill DeWitt
Just as a solid rock is not shaken by the storm, even so the wise are
not affected by praise or blame.