系集預報系統除了可以針對預報之不確定性與機率進行評估以外，由其產生的預報也通常優於任一 成員的決定性預報。對於連續性的變數，系集平均或中位數等簡單的統計方法通常可做為其單一預報的 基準。對於定量降水預報(Quantitative Precipitation Forecast, QPF)的問題，系集平均雖然對於中小雨之預 報技術亦常優於決定性預報，但因極端降雨常與中尺度之對流過程相關，其分布在時間、空間及系集等 維度上並非連續的變數，因此簡單的平均易將各成員之雨量預報平滑而低估較大雨量之預報。Ebert (2001) 首先針對澳大利亞地區的QPF 提出機率擬合平均(Probability-matched ensemble Mean, PM)的概念，這個 方法採取系集平均的空間相對分布，其降雨頻率則以所有系集成員之總降雨頻率取代系集平均之降雨頻 率。但PM 用於氣象局發展的區域高解析系集預報系統(WEPS)，常過度預報較大雨量。主要是因為系集 預報系統之總降雨頻率，容易因為某些成員的明顯過度預報偏差，導致極端雨量之過度預報。 本研究嘗試由系集預報系統之設計概念，探討理想上系集預報系統對於產生最佳定量降水預報的原 理，並應用於氣象局WEPS 在一般的作業或統計上之特性，基於PM 方法，提出修正的NPM 方法(New Probability-matched ensemble Mean, NPM)，此方法亦使用系集平均之空間相對分布，但降雨頻率修正為 各系集成員降雨頻率分布之平均，因此可以改善PM 過度預報較大雨量的缺點，減少個別成員導致之偏 差。針對2013 蘇力颱風個案與2015 年梅雨季檢測系集平均、PM 與NPM 系統性統計分析，發現系集 平均對於中小雨的預報能力（TS 或ETS）的確能明顯提升，但對於大雨或極端雨量之預報技術卻可能低於決定性預報，因此系集平均並不適合做為系集預報系統之最佳QPF，而PM與NPM可明顯改善系 集平均過度預報小雨及大雨低估的情形，同時也提升對於豪大雨事件的預報能力；PM與NPM相比， PM較能預報到極端降水的發生，但相對的也容易高估極端降水面積。NPM可保留系集成員預報極值的 能力，並且改善PM容易過度預報的問題，是最中性的系集預報方法，最適合做為系集預報系統的最佳 解。

A complete ensemble prediction system is interpreted by 3 factors, i.e. deterministic solution, spread, and probability. For a continuous variable, ensemble mean is usually the best solution. It is not, however, for Quantitative Precipitation Forecast (QPF) because ensemble mean gets only higher scores for small to medium precipitation but not for the heavy or extreme precipitation. A effect makes a smoothing QPF when averaging among the ensemble dimension. Ebert (2001) thus proposed a solution, probability matched mean (PM), for this problem. PM takes the relative special pattern of ensemble mean, but resamples the mean frequency as the frequency of the ensemble itself regardless of the special and ensemble dimension. Using PM on the WEPS in CWB, we found it over-predicts heavy to extreme QPF a lot because the nature of PM tends to match the maximum value of the ensemble system. The authors thus propose a NPM (new PM) method modified from PM. As the way to make PM, NPM takes the relative special pattern as ensemble mean, and resamples the mean frequency as frequency averaging from members' frequency. We make this assumption because the truth for a well-defined ensemble system is usually covered in the ensemble dimension. We thus assume the maximum precipitation is covered in members' maximum QPF as well. In this study, threat score (TS), equitable threat score (ETS) and bias score (BS) are introduced to verify the ensemble system. Both for case study during Typhoon Soulik (2013) and for statistics of May and June 2015 which is defined as meiyu season in Taiwan, it is found both TS and ETS of ensemble mean QPF are slightly better for light to medium threshold on QPF as compared to PM, NPM and deterministic WRFD as well.owever, it loses its skill or has no skill for heavy to extreme QPF threshold. PM gets both the highest TS and ETS for heavy or extreme rainfall, but its BS increases to 4 or higher for extreme rainfall forecast as well, which means PM overestimates heavy to extreme rainfall threshold for 4 times over above to observation. The performance of NPM has similar characteristics to PM except for the extreme cases. NPM keeps a higher performance on heavy rainfall and reduces the weakness of overestimating extreme rainfall as compared to PM. Based on this result, we would suggest NPM but not ensemble mean or PM as the best solution on QPF for the ensemble system.