No matter how accurate a forecast is, a forecast is valuable only until it is correctly understood and used by an end-user to make a decision and take a necessary action upon it (Murphy, 1985). Therefore, the way to effectively and accurately communicate a forecast to end-users is critical since it determines what kind of information a user might get. This is particularly true and important for a forecast in probabilistic form. A same piece of probability information can lead one to take very different actions based on ways of expression. For example, a psychological experiment shows that given two jars, one with 1 red and 9 white balls and another with 10 red and 90 white balls in it respectively, if one can randomly pick one ball (only once) out of any one of the two jars of his own choice and wins an award if the ball he picks is red, it’s found that one is more likely to go to the jar with 100 balls to play the gamble hoping more chance (10 instead of 1 red balls!) to pick a red ball although the probability is exactly the same 10% mathematically. In general, what a user gets is often less than what we tell and what we tell is often less than what we know, which indicates rooms for improvement in communicating weather information. How to better convey probabilistic forecast information to end-users is still new to meteorological community and needs to be carefully studied together with scientists in behavioral sciences.

How to apply probabilistic information to decision-making is often most confusing to many people. One might complain what should I do with it if a probability says 50%, half right half wrong? As discussed in the Part 6, given a reliable ensemble system, a 50% forecast means that in 50 times out of 100 such “50%” forecasts of the event will actually occur and 50 times not occur. Thus, this information has significant economical value to a specific business based on its dependence on weather. Table 1 lists possible economic losses and costs involved in a damage-causing weather event under various decisions, where Lu is the loss that cannot be protected against, Lp the loss that can be protected against and C the cost of protection. The benefit of taking action if the event does occur is the difference between L and (Lu + C), while the risk of taking action is wasting the cost C if the event doesn’t occur. Therefore, for a reliable P% forecast, the possible benefit and risk are, respectively,

                                 Benefit = P% x [L – (Lu + C)] = P% (Lp - C)                                 (6)

                                 Risk = (1-P%) x C                                                                      (7)

Table 1: Potential economic loss and cost involved in a weather forecast by decisions.