How to Optimize the Decision-Making Using Ensemble Probabilistic Forecasts?

Different from the deterministic forecasts (DFs), the ensemble probabilistic forecasts (EPFs) consider uncertainties during the forecast process (e.g., initial errors, nonlinear dynamic errors, and model errors), and convey the uncertainty information to the users using probability. However, compared with the DFs with indication of "Yes" or "No" only, can such probabilities or uncertainties information really benefit the users or confuse them in decision-making? For example, the information provided by the EPFs is "the chance of heavy rainfall tomorrow is 70%". Users who are not familiar with the meaning of EPFs might have difficulty in making a decision, since they are not sure whether a probability of 70% indicates that the event will happen or not. Therefore, users wonder how to best use the EPFs for decision-making to lower the cost of preventive action or decrease the losses.

In this study, we take the 0-6 h probabilistic quantitative precipitation forecasts (PQPFs) as an example to illustrate how to evaluate the economic value (EV) of EPFs and offer an example for users to understand how to optimize their decision-making using EPFs. The PQPFs are generated from the ensemble prediction system (EPS) of the Local Analysis and Prediction System (LAPS) operated at the Central weather bureau (CWB) in Taiwan. With the cases of typhoon-associated rainfall prediction, the LAPS EPS has a good spread-skill relationship and good discrimination, and can provide skillful PQPFs. A total of 148 cases of 0-6-h PQPFs based on all typhoon cases in Taiwan during 2008 and 2009 were used to evaluate the EV of users.

It is commonly assumed that users' cost-loss ratio are explicitly known in the EV analysis. In addition, it has been shown that for a perfectly reliable forecast system (i.e., without forecast bias), the optimal probability threshold to maximize the EV for a particular user is equal to his or her cost-loss ratio. Unfortunately, information of users' cost or loss (and thus the cost-loss ratio) cannot be obtained explicitly in some cases. For example, farmers may wonder whether they should harvest their crops before the arrival of typhoon accompanied by heavy rainfall. Compared with normal harvesting, the action of harvesting in advance does not seem to need any cost; however, it may lead to a hidden loss since unripe crops are sold at a lower price. Furthermore, the farmers may also wonder what percentage of crops should be harvested in order to minimize losses if they harvest crops in advance. This example implies that the cost and loss of farmers can be derived based on the experience of preventive actions through the EV analysis. Although the farmers' expected expense based on the LAPS PQPFs will vary with the harvest percentage, the maximum EV provided by the LAPS remains the same regardless of the harvest percentage. In addition, the "full harvest" action yields minimum long-term average losses.