When probabilities are not required

If an end-user does not appreciate forecasts in probabilistic terms and, instead, asks for categorical “rain” or “no rain” statements, the forecaster must make the decisions for him. Unless the relevant cost-loss ratio is known, this restriction puts forecasters in a difficult position.

If, on the other hand, they have a fair understanding of the end-user’s needs, forecasters can simply convert their probabilistic forecast into a categorical one, depending on whether the end-user’s particular probability threshold is exceeded or not. The forecasters are, in other words, doing what the end-user should have done. So, for example, to an end-user with a 40% threshold weather service A would issue categorical forecasts which during a 100 day period would verify like this:    

Table 8

Note that for this particular end-user the rain has been over-forecast: 40 forecasts against 30 occurrences. For an end-user with a threshold of 60% the contingency table would look like

 Table 9 below.

Table 9

In the example in Table 9, the rain is under-forecast: 18 forecasts against 30 occurrences. Generally, categorical forecasts have to be biased, either positively i.e. over-forecasting the event, for end-users with low cost-loss ratios or negatively, i.e. under-forecasting, for end-users with high cost-loss ratios [5].