本研究發展出一種全新的預報後處理方法來改進地表溫度在多模式系集平均的季節預報技術。簡要來說，此方法使用變數轉換、馬可夫模式(Markov model)和主成分分析引進觀測資料所提供的資訊來修正原始模式的預報值並改進多模式系集平均之預報技術。我們使用哥白尼氣候變遷系統(Copernicus Climate Change Service；C3S)的多模式季節預報計畫的月平均兩米溫度後報(hindcast)資料來進行方法的發展與評估。預報技術的評估指標是預報值和觀測值之間的相關係數和均方根誤差。參考的預報方法是持續性預報(Persistence forecast)和原始的模式預報。
首先我們在ENSO 指標區域利用k交叉驗證(K-fold cross-validation forecasts)來建立和測試此預報後處理方法。ENSO indices預報實驗的結果顯示，預報技術的修正幅度是由東向西增加的，而且這方法中僅保留1個經驗正交(empirical orthogonal function; EOF)模態所得到的修正預報值結果為最佳。方法建立後，我們接著進行全球1° x 1°經緯網格溫度場的預報實驗。一般而言，原始的多模式系集平均預報在陸地上的第1個月超前預報技術表現有比持續預報要好，而在海洋上除了Niño區域外則是在所有的超前預報都比持續預報要差。全球溫度場的預報實驗顯示，此方法不僅大幅度的提升原模式的預報技術，同時仍保有原模式在中太平洋的預報能力。比較修正後預報值與模式預報之結果亦指出，此方法的修正量可能會受到模式本身預報能力的影響而有所不同。在原模式表現不好之區域，其改善程度並不明顯甚至有變差的現象，反之在部分有預報能力之區域則會有明顯的改進。總體而言，在經過本文的方法修正後的預報大體保留了原始的多模式系集平均預報和持續預報的優點。

In this study, we develop a novel forecast post-processing method to improve multi-model mean (MME) seasonal forecast skill of surface temperature. Briefly speaking, this method uses variable transformation, Markov model, and principal components analysis to combine the information from observation to calibrate and improve MME forecast skill. We apply monthly mean 2m temperature hindcast data from the multi-system seasonal forecast service of the Copernicus Climate Change Service (C3S) to develop and evaluate this method. Forecast skills were evaluated using correlation coefficient and root-mean-square error (RMSE) between forecasts and observations. The performance of this method is evaluated by comparing forecast skills among this method, persistence forecasts, and original model MME forecasts.
We first used K-fold cross-validation forecasts to build and test the post-process of forecast method. Results from ENSO indices forecast experiments show that the forecast skill is increased from east to west and the use of only one EOF mode in this method yields the largest forecast skill improvement. After finishing the development of the method, we conduct the 1° x 1° global surface temperature forecast experiment. Generally speaking, original model MME forecasts of global surface temperature field have better skill in land area at lead one month and worse skill in ocean area except the Niño region at all lead months than persistence forecasts. The forecast experiment shows that the calibrated MME forecasts show notable improvement over the original model MME forecasts. Furthermore, the degree of improvement in skill depends on the original model skill. Overall speaking, the calibrated MME forecasts combine the advantages of both the persistence forecasts and the original model MME forecasts to yield better forecast skill than both methods.

王俊寓，2017：CMIP5多模式系集年代際預報實驗對熱帶地區的年際預報能力與偏差校正的探討。國立中央大學大氣物理所碩士論文，1–68。
許家華，2014：資料時空前置處理對主成份分析法的影響: 一個基於AO和NAO訊號之研究。國立中央大學大氣物理所碩士論文，1–89。
Christensen, J. H., Kjellström, E., Giorgi, F., Lenderink, G., and Rummukainen, M., 2010: Weight assignment in regional climate models, 44, 179–194.
Chen, D., and Yuan, X., 2004: A Markov model for seasonal forecast of Antarctic sea ice, J. Clim., 17, 3156– 3168.
Doblas-Reyes, F. J., M. Deque, and J.-P. Piedelievre, 2000: Multi model spread and probabilistic seasonal forecasts in PROVOST, Quart. J. Roy. Meteor. Soc., 126, 2069–2088.
Delsole, T., 2007: A Bayesian framework for multimodel regression, J. Climate, 20, 2810–2826.
Hagedorn, R., F. J. Doblas-Reyes, and T. N. Palmer, 2005: The rationale behind the success of multi-model ensembles in seasonal forecasting—I. Basic concept, Tellus, 57A, 219–233.
Hannachi, A., 2004: A primer for EOF analysis of climate data, Tech. rep. Reading, UK: Department of Meteorology, University of Reading.
Krishnamurti, T. N., and Coauthors, 1999: Improved weather and seasonal climate forecasts from multi-model superensemble, Science, 285, 1548–1550.
Krishnamurti, T. N., Kishtawal, C. M., Zhang, Z., LaRow, T. E., Bachiochi, D. R., Williford, C. E., Gadgil, S., and Surendran, S., 2000a:Improving tropical precipitation forecasts from a multianalysis superensemble, J. Climate, 13, 4217–4227.
Krishnamurti, T. N., Kishtawal, C. M., Zhang, Z., LaRow, T., Bachiochi, D., Williford, E., Gadgil, S., and Surendran, S., 2000b: Multimodel Ensemble Forecasts for Weather and Seasonal Climate, J. Climate, 13, 4196–4216.
Lee, D. Y., C.-Y. Tam, and C.-K. Park, 2008: Effects of multicumulus convective ensemble on East Asian summer monsoon rainfall simulation, J. Geophys. Res., 113, D24111.
Lee, K. Ashok, and J.-B. Ahn, 2011: Toward enhancement of prediction skills of multimodel ensemble seasonal prediction: A climate filter concept, J. Geophys. Res., 116, D06116.
Lee, Y.-A., and R.-Y. Tzeng, 2012: Persistence neutralization transformation: An effective way to improve short-lead forecast skill, J. Geophys. Res., 117, D23109.
Lee, D. Y., Ahn, J. B., and Ashok, K., 2013a: Improvement of multi‐model ensemble seasonal prediction skills over East Asian summer monsoon region using a climate filter concept, J. Appl. Meteorol. Climatol., 52, 1127– 1138.
Lambert S J , Boer G J.,2001: CMIP1 evaluation and intercomparison of coupled climate models, Clim. Dynam., 17, 83-106.
Palmer, T., and Coauthors, 2004: Development of a European Multimodel Ensemble System for Seasonal to Interannual Prediction (DEMETER), Bull. Amer. Meteor. Soc., 85, 853– 872.
Palmer, T., Shutts, G., Hagedorn, R., Doblas-Reyes, F., Jung, T. & Leutbecher, M., 2005a: Representing model uncertainty in weather and climate prediction, Annu. Rev. Earth Planet. Sci., 33, 163–193.
Palmer, T. N., Doblas-Reyes, F. J., Hagedorn, R. & Weisheimer, A., 2005b: Probabilistic prediction of climate using multi-model ensembles: from basics to applications, Phil. Trans. R. Soc. B, 360, 1991–1998.
Park, Y., R. Buizza, and M. Leutbeche, 2008: TIGGE: Preliminary results on comparing and combining ensembles, Quart.J. Roy. Meteor. Soc., 134, 2029–2050.
Roy Bhowmik, S. K. and Durai, V. R. , 2010: Application of multi-model ensemble techniques for real time district level rainfall forecasts in short range time scale over Indian region, Meteorol. Atmos. Phys., 106, 19–35.
Tebaldi C and Knutti R., 2007: The use of the multi-model ensemble in probabilistic climate projections, Phil. Trans. R. Soc. London A, 365 2053-2075.
Wang, B., and Coauthors, 2009: Advance and prospectus of seasonal prediction:Assessment of the APCC/CliPAS 14 model ensemble retrospective seasonal prediction (1980–2004), Climate Dyn., 33, 93–117.
Wu, Q., Yan, Y., and Chen, D., 2013: A Linear Markov Model for East Asian monsoon seasonal forecast, J. Clim., 26, 5183– 5195.
Xue, Y., A. Leetmaa, and M. Ji, 2000: ENSO prediction with Markov models: The impact of sea level, J. Climate, 13, 849–871.
Yuan, X., D. Chen, C. Li, L. Wang, and W. Wang, 2016: Arctic sea ice seasonal prediction by a linear Markov model, J. Clim., 29( 22), 8151– 8173.