Weather With Weird Odds

Weather With Weird Odds

Oh shit, the internet says it’s gonna rain today. Or does it really? There are actually different ways to present the possibility of rain. The usual way is the one shown below: an hourly resolution of the day’s rain probability. But some other websites take these probabilites and calculate the arithmetic mean value to show the probability of rain for the whole day. Is this acceptable? I’ll show you that it is not.

BBC's weather forecast
BBC’s weather forecast

Mean value is not equal to the real rain probability

Let’s check the two ways to calculate the probabilites:

  • Mean value is the sum of all individual hourly percentages, divided by the number of hours taken into account. For this example: Mean = (0.65 + 0.34 + … + 0.05) / 12 = 0.314 = 31.4%. To set this into context: The mean value (which some data providers take as the real rain probability) of 31% is smaller that the rain probability of 12.00 – 13.00. So this is not the way to calculate!
  • In fact, the real one has do be worked out step by step. The prob. of rain between 12.00 and 14.00 is 0.65 plus the prob. of not raining in the first hour but raining in the second one – which is: (1 – 0.65) * 0.34 = 0.119. This sums up to 0.65 + 0.119 = 0.769 = 76.9%. If all 12 hours are considered, the overall percentage of a single drop of rain at this afternoon is over 99%!

So to be safe, take an umbrella with you – even if the forecasted rain probability für the next three hours is only 20% [20% + 80%*20% + 80%*80%*20% = 48,8%!].

But be careful: To be more clear and to make it more complex, all figures are calculated for the case where the individual probabilities of occurrence are independent of each other.

May the RNG be with you.

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