Translating the Words and Numbers of Official Forecasts into Predictions of Amount and Probability of Precipitation

Australian Bureau of Meteorology day-to-day weather forecasts are presented in a format that comprises an extended worded description of the expected weather, a brief précis which summarises that description, estimates of the anticipated minimum temperature, maximum temperature, probability of precipitation, and amount of precipitation (the latter expressed as a range - for example, 5 - 10 mm, unless no precipitation is considered possible, in which case, 0 mm. 

Using an Aug-05 to Jul-16 data base of official précis forecasts for Melbourne, and a Sep-11 to Jul-16 data base of official estimates of the anticipated probability and amount of precipitation, statistical relationships are established between the words and numbers contained in the official forecasts and what eventuates in terms of the likelihood and amount of precipitation.

The image on the left hand side illustrates the multiple linear relationship between the words used, and what eventuated in terms of the amount of precipitation (expressed as the square root of the precipitation amount). The first column lists the words, placed in order of the corresponding t statistic. It may be seen that the most positively related words (in order) are RAIN, SHOWER, SHOWER, HEAVY and THUNDER. The most negatively related words (in order) are LITTLE, FEW, CHANCE, CLEARING and LATE. The second column lists the probabilities that the sign of the corresponding t statistic (whether the sign was positive or negative) was not of the direction indicated. These probabilities are rounded to three decimal places, and those significant at the 1% level or better (most of them) are highlighted with a reddish-pink color. The third column lists the corresponding regression coefficients.

The relationship between what eventuated in terms of the amount of precipitation and what was suggested by the LOWER and UPPER official estimates and the WORDS is:

AMOUNT = -0.024 + 0.220*LOWER + 0.459*UPPER + 0.262*WORDS

The image on the right hand side illustrates the multiple linear relationship between the words used, and what eventuated in terms of the likelihood of precipitation. The first column lists the words, placed in order of the corresponding t statistic. It may be seen that the most positively related words (in order) are RAIN, SHOWER, SHOWER, DRIZZLE and THUNDER. The most negatively related words (in order) are LITTLE, CHANCE, CLEARING, LATE and FINE. The second column lists the probabilities that the sign of the corresponding t statistic (whether the sign was positive or negative) was not of the direction indicated. These probabilities are rounded to three decimal places, and those significant at the 1% level or better (most of them) are highlighted with a reddish-pink color. The third column lists the corresponding regression coefficients.

The relationship between what eventuated in terms of the likelihood of precipitation and what was suggested by the OFFICIAL estimates and the WORDS is:

LIKELIHOOD = -6.634 + 0.765*OFFICIAL + 0.437*WORDS