系集轉換卡爾曼漸進式平滑器在資料同化之應用

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林哲暉(Zhe-Hui Lin) 查詢紙本館藏

畢業系所

大氣科學學系

論文名稱

系集轉換卡爾曼漸進式平滑器在資料同化之應用
(The application of Ensemble Transform Kalman Incremental Smoother on Data Assimilation)

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摘要(中)

漸進式分析增量更新(IAU)透過逐漸更新步驟減緩因資料同化修正而產生的高頻波動或不平衡量。而其可減緩模式衝擊(model shock)並具備低通濾波效果已廣泛地被應用於大氣或海洋資料同化系統中。但因IAU直接將單一時間點得之分析增量等量套用於同化窗區上，在變化較快的動力系統上，可能反而造成負面修正效果。本研究基於系集轉換濾波器演算法(ETKF)，將系集轉換平滑器(no-cost smoother)與IAU進行整合與重新推導，提出系集轉換漸進式平滑器(ETKIS)。主要概念為將ETKF所得之系集最佳權重漸進式應用於不同時間之系集，以獲得隨時間變化之分析場增量。
為了驗證ETKIS是否能達到預期的效果，本研究分別以淺水波模式及Lorenz 63 model進行多組實驗。前者用於驗證新方法是否能減緩因系集卡爾曼濾波器使用局地化而產生的非地轉風及同化所造成的濾波效果。後者利用強烈非線性動力誤差成長與變化快速的特徵，驗證新方法是否能估計出理想的隨時間變化的分析增量及其所能帶來的改善。
淺水波的實驗結果顯示，ETKIS能成功平滑因系集卡爾曼濾波器中使用局地化而產生的非地轉風，但有不會因此平滑掉分析增量之特徵優點。Lorenz 63 model的實驗顯示，相較原本的IAU，ETKIS可有隨時間變化的分析增量，可成功修正強烈非線性下的修正誤差的效果。且此改善不只限於平均場，對系集擾動場亦有效果，進而能夠改進下個同化時間之背景及分析場。此外，更新窗區策略的敏感性測試結果顯示，較早進行更新修正能有較好的修正誤差效果，但不同窗區長度的影響則較不明顯。並且在非完美模式下，ETKIS避免了系集轉換平滑器分析結果會表現大幅劣化的問題。
本研究結果顯示，ETKIS達到了藉由估計出隨時間變化之分析增量以改善漸進式更新方法的目的。此方法不僅能保有著漸進式更新方法提供的減緩模式衝擊及低通濾波的效果，能夠改善分析場的穩定度。並且此方法所估計出的隨時間變化之分析增量能夠在較強非線性，或模式誤差的情況下亦保持有良好的修正效果。

摘要(英)

The analysis correction made by data assimilation (DA) can improve the accuracy of the initial condition of the model forecast, but it may also lead to model shock or artificial signal if the correction cannot be well taken by the model. Incremental Analysis Update (IAU) divides the correction into constant increments and gradually add them to the model state to eliminate the negative impact induced by DA. However, the performance of IAU can be seriously degraded when dealing with a fast weather system, with rapid development or fast movement. In this study, we propose an Ensemble Transform Kalman Incremental Smoother (ETKIS) based on Local Ensemble Transform Kalman Filter and no-cost Ensemble Transform Kalman Smoother as a refined IAU solution for ETKF-based algorithms. ETKIS is designed to improve effectiveness of the correction by providing well estimated time-varying increment.
To evaluate the performance of ETKIS, we conducted experiments with shallow water model and Lorenz 63 model. The shallow water model is used to investigate whether the ETKIS can reduce the imbalanced component induced by covariance localization and how much signals can be retained with the filtering property of ETKIS. The Lorenz 63 model, in which the error can grow fast due to strong nonlinearity, is used to verify whether ETKIS can improve the effectiveness of the correction with its time-varying analysis increment.
Results of the experiments with the shallow water model show that ETKIS still can smooth out the imbalance associated with the presence of the ageostrophic wind. More importantly, ETKIS does not smooth out correction that is valid to remove background error and thus it allows preserving the real signal better. Results from the offline-cycling experiments with Lorenz 63 model show that the ETKIS’ time-varying increment improves the effectiveness of the correction. Furthermore, positive impact from ETKIS is amplified through the accumulated effect during the online DA cycles. The result of sensitivity experiment shows both longer and earlier beginning update window have positive effect on error correction, while the influence of beginning time is more significant than length of the update window. With imperfect model experiments, the performance of ETKIS is not downgraded, but the RMSE is kept to a similar level of ETKF.
In summary, ETKIS has a great potential in real applications. Mainly, it takes the advantages from the IAU schemes to improve the balance in the analysis and can provide effective gradual correction especially under a strong nonlinear scenario.

關鍵字(中)

★ 資料同化
★ 系集轉換卡爾曼漸進式平滑器

關鍵字(英)

★ Data Assimilation
★ Ensemble Transform Kalman Incremental Smoother

論文目次

摘要 i
Abstract ii
致謝 iii
Index iv
List of figures and tables vi
Explanation of symbols viii
1. Introduction 1
2. Methodology 5
2.1. Local Ensemble Transform Kalman Filter (LETKF) 5
2.2. No-cost Ensemble Transform Kalman Smoother (ETKS) 7
2.3. Incremental Analysis Update (IAU) 8
2.4. Four-Dimensional Incremental Analysis Update (4DIAU) 9
2.5. Ensemble Transform Kalman Incremental Smoother (ETKIS) 10
2.6. How ETKIS consist with original ETKF in a linear model 12
2.7. The filtering property of ETKIS 13
3. Experiments with the shallow water model 15
3.1. Shallow water model 15
3.2. Experiments and initial conditions 16
3.3. Observation and Data Assimilation 17
4. Results with the shallow water model 18
4.1. Experiment with the balanced initial condition 18
4.2. Experiment with the imbalanced initial condition 19
5. Experiments with the Lorenz 3-variable model 21
5.1. Lorenz 63 model 21
5.2. Experiments 22
5.3. Observation, Data Assimilation and judgement 23
6. Results with the Lorenz 3-variable model 24
6.1. Offline-cycling experiment 24
6.2. Online cycling experiment 27
6.3. Sensitivity experiments 28
6.4. Imperfect model experiment 29
7. Conclusion 31
Appendix 34
A.1. The accuracy of calculation for root of matrix 34
A.2. The increased computational cost for gradual update schemes 35
Reference 37
Figures 40
Tables 69

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指導教授

楊舒芝(Shu-Chih Yang)

審核日期

2018-1-30

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