以多變量貝氏系集處理器配合球面調和函數波段拆解進行展期極端低溫預報
Authors: 朱心宇 朱心宇 , Hsin-Yu, Chu 張惠玲 
Published: December 2022

<p>透過統計後處理(statistical post-processing, SPP)方法將原始模式進行偏差修正，並降尺度到高解析格點或特定點位，可提供使用者更具參考價值的預報資訊；但偏差修正往往需要大量的訓練樣本以估算預報偏差。由於展期系集重預報/後預報(reforecast/hindcast)需要大量計算資源，剛發展成熟之系集預報系統可能缺乏足夠之重(後)預報資料以進行偏差校正。本研究擬發展結合多變量貝氏系集處理器(Multi-Variate Bayesian Processor of Ensemble, BPE)與球面調和函數波段拆解(spherical harmonics decomposition, SHD)之先進SPP技術，目的在於探討以單一預報取代系集預報進行SPP之可行性，以解決上述系集預報系統缺乏大量訓練樣本，無法進行偏差校正之困境。</p>
<p>本研究將原始系集模式的控制模擬(Control Run)進行SHD，以拆解後的不同波段作為BPE預報因子，進行SPP以得到臺灣測站點上之展期極端低溫機率預報。BPE演算法利用預報因子及觀測值關聯結構產生的邊緣分布作為概似函數(likelihood)，並以觀測值的氣候分布作為先驗函數(prior)，再根據最新的預報資料予以結合成後驗函數(posterior, 即為預報機率函數)；因其完全貝氏的架構，BPE在重預報資料(Reforecast)較少的狀況下，依然可以充分利用觀測氣候資料建立先驗函數，得到可信的後驗分布函數。</p>
<p>本研究以美國國家環境預測中心第12版全球系集預報(NCEP GEFS v12)之 (1)2公尺最低溫系集平均作為單變量BPE預報因子 (實驗SP_BPE)、(2)控制模擬(Control Run)之標準化2公尺最低溫拆解後的波段作為多變量BPE預報因子(實驗MP_BPE_SH)，進行8至14天日極端低溫預報以及第三、四週之週極端溫度預報校正。多項指標顯示：SP_BPE與MP_BPE_SH兩種校正方式皆顯著提升原始模式的預報品質，但SP_BPE校正效果略優於MP_BPE_SH，特別是在第三、四週之週極端低溫預報。上述結果應與預報因子的可預報度有關，因此未來擬利用可預報度較高之大尺度指標做為多變量BPE的預報因子，以提升第三、四週預報之校正成效。</p>
<p>&nbsp;</p><p>To produce elaborate, location specific extended-range probabilistic forecasts, it is required to bias-correct and downscale raw model. If statistical methods are used, then the two processes can be collectively phrased as &ldquo;statistical post-processing (SPP)&rdquo;. To infer a representative estimate of the raw model&rsquo;s systematic bias, large hindcast sets have to be produced. However, creating hindcast for a recently operational, state-of the art ensemble that prolongs to extended-range is very computationally extensive. In practical operations, the size of hindcast are often limited, and far smaller than observations. In this research, we aim to evaluate if the forecast performance of filtering non-linear noise using ensemble mean, is achievable by wave decomposition of a single model with the best initial condition and post-processing the wavebands using state-of-art SPP method. We hope this will reduce the reliance on both ensemble and large hindcast in SPP, providing a solution to aforementioned issues. </p>
<p>The control run from raw ensemble model are waveband decomposed using spherical harmonics, and the wavebands are used as predictors. These predictors are then feed into a state-of-the-art, multi-variate Bayesian Processor of Ensemble (BPE), to produce post-processed extreme minimum temperature probabilistic forecasts located on specific meteorological stations in Taiwan. As a full Bayesian Method, BPE utilizes the copula of the predictors-predictand pair to generate a marginal distribution as the likelihood, and the climatological distribution constructed by the observational data as prior. The predictive distribution, or the posterior, are generated using fusion of likelihood and prior once receiving the latest run from the raw model. Due to its Bayesian structure, the advantage of BPE is the capability to derive well-calibrated posterior under limited reforecast data, from using a larger observation dataset to construct an informative prior.</p>
<p>This research uses (1) The ensemble mean of 2-meter minimum temperature (Experiment SP_BPE), and (2) The wavebands decomposed from the standardized 2-meter minimum temperature of the control run (Experiment MP_BPE) of NCEP GEFSv12 as the predictor(s) to calibrate daily minimum temperature for lead times of 8-14 days and weekly minimum temperature for lead times of week 3 and 4. We use various performance benchmarks to compare the different aspects of probabilistic forecast and found that both SP_BPE and MP_BPE could improve the quality of probability forecasts over raw ensemble model. It is worth noting the performance of SP_BPE is better than MP_BPE_SH, especially in the lead times of week 3 to week 4, but we think that the cause should be related to the selection of predictors, instead of a deficiency in the methodology. In the future, alternative variables can be decomposed, or use large scale indices as predictors to improve the calibration of week 3 and 4.</p>
<p>&nbsp;</p>