weather prognosis show min/max temperatures; but do they know distribution by hour?

it seems to me that knowing the minimum and maximum numbers out of a set of 24 temperatures for the respective hours of the day is kind of insufficient. Can the meteorologists also predict (and tell us) average temperatures by time interval, e.g. that from 2pm to 4pm it would be approximately 83F but 4pm - 6pm it will drop to 80F and so forth?

yes they can make predictions like that and weather data sites will give you those expected values.

Absolutely. Here, for example, is the National Weather Service’s hour-by-hour predictions for my town:

http://forecast.weather.gov/MapClick.php?CityName=Brookfield&state=IL&site=LOT&textField1=41.8243&textField2=-87.8478&e=0&FcstType=graphical

This is slightly different, but is there any weather forecaster that will give you some estimate of the error in their forecast? I’d love to see those “10-day” forecasts with 95% confidence intervals for each day. Or, alternatively, if meteorologist know a particular front will roll past and bring some specific condition, some sort of estimate (with error) on when that particular weather will arrive. Something like “this Saturday will have a high of 80°±4° and be sunny all day, and there will be a cold front that passes next Tuesday (±1.5 days).” I’d be a hell of a lot happier knowing when I could actually depend on a forecast…

And here they are for mine.

Of course they can. And do.

This is a totally off-topic, but the way TWC shows their hourly forecasts annoys me (far more than it should, admittedly). They apply a completely bogus-looking smoothing algorithm to connect the hourly forecast points. The points themselves are given with a reasonable sort of accuracy, only to the nearest degree. But the curve connecting them wiggles around all over the place, implying that (in this case) they precisely forecast that today’s high of 89.1° will occur at 1:50 pm, and there will be an uptick from 88° to 88.2° back to 88° at 3:42.

Gah. I blame this pet peeve on the time-traveling ghost of Edward Tufte.

As a general rule, modern short-term weather forecasts (i.e., for the next couple of days) are pretty accurate. Note that “pretty accurate” is not “100% accurate”. They may get the passage of that cold front off by a few hours. It may make it to 95 today when they only predicted a high of 90. You may get poured on when they only predicted “a chance of showers”. But, generally, you don’t get big surprises. If they say it’ll be hot, it’s almost always hot. If they say it’ll storm, it almost always storms. That said, some sorts of weather (such as summer thunderstorms) are often very very localized, and thus, very hard to predict with perfect accuracy.

The NWS, and various private services, create forecasts out to 7 to 10 days, but the error range will increase as you go out in time (i.e., the NWS currently has a forecast for next Tuesday, but that’s 5 days from now, and a lot of things could happen between then and now).

The mathematical models which drive modern forecasting are extremely complex, and take into account hundreds of factors, but they are still imperfect models of how weather works.

I know I’ve seen web pages in which the general accuracy level of short-term and long-term forecasts is discussed, but I’m not finding it at the moment. I’ll keep looking.