9. Recurrence Probabilites of Weather Events
What does this "40 percent" mean? ...will it rain 40 percent of of the time? ...will it rain over 40 percent of the area?
The "Probability of Precipitation" (PoP) describes the chance of precipitation occurring at any point you select in the area.
How do forecasters arrive at this value?
Mathematically, PoP is defined as follows:
PoP = C x A where "C" = the confidence that precipitation will occur somewhere in the forecast area, and where "A" = the percent of the area that will receive measureable precipitation, if it occurs at all.
So... in the case of the forecast above, if the forecaster knows precipitation is sure to occur ( confidence is 100% ), he/she is expressing how much of the area will receive measurable rain. ( PoP = "C" x "A" or "1" times ".4" which equals .4 or 40%.)
But, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that, if it does occur, it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )
In either event, the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area.
Recurrence Probabilites of Weather Events

10. Estimating other items like... Wave Heights, Storm Surge & Swells
Snow amounts & drifts
Climate Change...

11. In particular the development of so-called "ensemble forecasts" allows us to estimate many uncertainties automatically and provide extra information to customers in routine forecast products.  In an ensemble forecast, instead of running our computer forecast model just once, we run it many times from slightly different starting conditions to assess how certain or uncertain the forecast is. We can estimate the risk or probability of a given weather event from the proportion of these forecasts which predict the event to occur.
Ensemble forecasts available at the current time are best-suited to estimating uncertainty in forecasts between 3 and 10 days ahead.