1. Applying Ensemble Probabilistic Forecasts in Risk-Based Decision Making Hui-Ling Chang 1, Shu-Chih Yang 2, Huiling Yuan 3,4, Pay-Liam Lin 2, and Yu-Chieng Liou 2 1. Meteorological Satellite Center, Central Weather Bureau, Taipei, Taiwan; 2. Department of Atmospheric Sciences, National Central University, Jhong-Li, Taiwan 3. School of Atmospheric Sciences, and Key Laboratory of Mesoscale Severe Weather / Ministry of Education, Nanjing University, Nanjing, Jiangsu, China; 4. Jiangsu Collaborative Innovation Center for Climate Change, China

2. Deterministic forecasts vs. probabilistic forecasts Deterministic forecasts: −“The forecast rainfall tomorrow is 80 mm.” −It does not indicate the reliability of forecasts, but users assume that it’s completely correct. Probabilistic forecasts: −“The chance of heavy rainfall (rain > 80 mm/24 h) tomorrow is 70%.” −Users are not sure whether a probability of 70% indicates the event will happen or not.

3. Q : Can an optimal probability threshold (Pt) be provided so that users know whether they should take preventive action or not? Q : How to best use the ensemble probabilistic forecasts (EPFs) for decision making ?

4. Should the flight controller change the runway of incoming flight based on the forecast of severe weather ？

5. Pomelos Pomelos are vulnerable to strong winds.

6. Chinese dates Should the farmers harvest dates in advance to minimize their losses?

7. Analysis of economic value  Economic value (EV) for a forecast system (Richardson 2000) E climate : Expected expense (E) using climatological information. E forecast : E using a forecast system. E perfect : E using a perfect forecast system. Range of EV : -∞ ~ 1 EV max = 1: perfect value EV > 0 if E forecast < E climate

8. C : cost of protective action L = Lp + Lu : total loss Lp : protectable loss Lu : unprotectable loss h, m, f, and c are the relative frequencies (< 0) of four possible conditions (h + m + f + c = 1). Analysis of economic value Assume a decision maker takes action totally depending on forecast information. r = C / Lp : cost-loss ratio (o C )

9. Analysis of Economic Value  Economic value (EV) of a forecast system (Zhu et al. 2002) h, f and m : forecast performance parameters o : climatological frequency r : cost-loss ratio ( r = C/Lp ； o < r < 1 ) C : cost of protection Lp : protectable loss h + f m

10. LAPS ensemble prediction system (EPS) and Data  LAPS EPS - adopts time-lagged multimodel ensemble configuration (12 members)  Data : 0-6 h PQPFs of Typhoon cases in 2008 and 2009 * PQPF: probabilistic quantitative precipitation forecast 2008: 5 typhoons (total 90 samples ) 2009: 3 typhoons (total 58 samples )

11. Economic value of LAPS 0-6 h PQPFs Probability threshold (Pt) = 1/12 r= missing rate r= hit rate Pt = 2/12 Pt = 3/12 Pt = 4/12 Pt = 12/12

12. Economic value of LAPS 0-6 h PQPFs For users with r=0.25 EV obtained by users depends crucially on the choice of Pt. EV < 0 EV=52% EV=11%

13. EV max For a perfectly reliable forecast system, the optimal Pt to maximize the EV for a specific user is equal to his/her r (Murphy 1977). Economic value of LAPS 0-6 h PQPFs (o = 0.28)

14. Economic value of LAPS 0-6 h PQPFs For users with r = 0.5 optimal Pt = 0.5 EV max

15. Q: Can weather forecasters provide a general optimal Pt to all users? A : Users with different cost-loss ratio (r) have different optimal Pt, and should choose the optimal Pt based on their r.

16. Without an explicitly known cost-loss ratio, can users still optimize their decision-making to obtain the EV max ?

17. Chinese dates Two conditions are considered for price drop: premature harvest and being affected by heavy rainfall. The ratios between the reduced and original prices for these two conditions are denoted as R 1 and R 2. Should the date farmers harvest in advance to minimize their losses?

18. 2 weeks before T 0 4 weeks before T 0 T 0 (maturity time) R 1 =100% R 1 = 80% R 1 = 60% Assume Pf=50%, R 2 =40%, the total price of ripe dates is A. (2) C + Lu = (1-80%)A (1) C = (1-80%)A (3) L = Lp + Lu = (1 - 40%)A (4) N = 0  Case1 (two weeks before T 0 ) : R 1 = 80% time r= C/ L p = (1-80%)/(1-40%) ~ 0.33 1)P f =50%  P f > C/L p  take action 2)P f = 10%  P f < C/L p  need not take action

19. (2) C + Lu = (1-60%)A (1) C = (1-60%)A (3) L = Lp + Lu = (1 – 40%)A (4) N = 0  Case2 (four weeks before T 0 ) : R 1 = 60% 2 weeks before T 0 4 weeks before T 0 T 0 (maturity time) R 1 =100% R 1 = 80% R 1 = 60% Assume R 2 =40%, the total price of ripe dates is A time r= C/ L p = (1-60%)/(1-40%) ~ 0.67  Premature harvest is required only when Pf ≧ 67%.

20. What percentage of dates (F, 0 ＜ F ≦ 1 ) should be harvested to minimize the farmers’ losses ? Full harvest!! Chang, H. L., S.-C. Yang, H. Yuan, P. L. Lin, and Y. C. Liou, 2015: Analysis of relative operating characteristic and economic value using the LAPS ensemble prediction system in Taiwan area. Mon. Wea. Rev., 143, 1833–1848.