Precipitation Probability Myths
A common error made by TV weathermen comes while making precipitation probability statements. For example; he may say that the probability for rain this afternoon is 30% or the probability is 30% for the period between noon and 6pm. Then, in his graphics, he will indicate or say that the probability is 30% between noon and 3pm and 30% between 3pm and 6pm. That is absurd. If the probability for precipitation is 30% from noon to 3pm and 30% from 3pm to 6pm, then the probability for precipitation from noon to 6pm is not 60%.
In order to compute the probability of precipitation between noon and 6pm when the probability for precipitation between noon and 3pm is 30 percent and between 3pm and 6pm is 30 percent, one has to avoid counting the occurrence precipitation during the first three hours and the occurrence of precipitation during the second three hours twice. The fact that precipitation may occur twice or more during the 6 hour period should not be counted more than once. Therefore, the possibility that precipitation may occur during both 3 hour periods should not be counted twice. How is this done? This is done by computing the probability that it will not rain during the 6 hours period and subtract that number from one. In the example given above, the probability that there will be no precipitation during both of the three hour periods is 70% or .7. The probability that there will be no precipitation during the 6 hour period is .7 X .7 = .49 or 49%. Thus, the probability that precipitation may occur during the 6 hour period is 1-.49 = .51 or 51%. The principal is the same even if the probabilities of the 3 hour periods are not equal. For example, if during the first 3 hours the rain probability is 60% and the second 3 hours is 30%, then the probability it won’t rain is .4 X .7 = .28 =.28 or 28%. The probability that it will rain is 72% not 90%.
That is not the only error. Some people believe that the precipitation probability is the chance that one will see precipitation falling when a door is opened or when one looks out of a window. If one looks out of the window enough times and counts the number of times during an interval of time that precipitation is observed. The number is divided by the total number of times that one looks out of the window gives approximately the fraction of time precipitation falls. For example, if during a three hour interval of time, precipitation is observed 1/3rd of the total number of observations, it is likely that precipitation fell 1/3rd of the time. This is not the probability precipitation may fall. Instead this is the percentage of time that precipitation falls. Another example is a narrow, solid, and fast moving band of precipitation may bring a high probability that precipitation may fall during an interval of time, but it may last only a tiny fraction of the same interval.
The probabilities for precipitation issued by the National Weather Service are point probabilities. Point probabilities are probabilities that precipitation may occur during an interval of time at some airport. It is not the percentage of time precipitation may occur; nor is it the percentage of some area precipitation may occur.
Fredmet.
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