Exploration of hybrid gain data assimilation algorithm for numerical weather prediction

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張志謙(Chih-Chien Chang) 查詢紙本館藏

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大氣科學學系

論文名稱

(Exploration of hybrid gain data assimilation algorithm for numerical weather prediction)

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摘要(中)

此論文將透過觀測系統模擬實驗(Observing System Simulation Experiment, OSSE)探討兩個主題，一是提出一種新的混成同化方法改善混成增益矩陣(Hybrid gain)資料同化系統，以避免在混成資料同化方法中，使用需基於經驗或人為給定之權重係數以結合子同化系統資訊。二是探討於區域模式WRF (Weather Research and Forecasting)中，比較使用不同的資料同化方法同化福衛三號(FS-3)以及福衛七號(FS-7)掩星觀測資料(Radio Occultation, RO)之同化效益。

混成資料同化方法(Hybrid data assimilation)結合變分與系集資料同化方法之優勢，但傳統的混成資料同化方法皆需給定一個權重係數結合子同化系統的資訊，此係數對混成資料同化方法的表現有舉足輕重的影響。為客觀呈現混成資料同化方法的優勢，本文提出新的混成資料同化方法(QR-HGDA)，於變分子同化系統進行分析修正時，僅採用與系集正交之修正量(正交向量)更新，此更新方法可避免主觀決定權重係數。本論文所提出之混成資料同化方法已成功應用於準地轉模式中。透過一系列敏感性實驗的研究，我們建議使用混成增益矩陣資料同化系統時，應重新建立靜態(非流場相依)之背景誤差結構以優化混成同化系統表現，而非使用傳統變分系統之統計背景誤差結構。

本研究也利用WRF-3DVAR，WRF-LETKF同化系統將混成增益矩陣資料同化方法建構於WRF模式中(WRF-HGDA)，並比較分別同化福衛三號及福衛七號的表現。研究結果顯示，當觀測密度不足時，透過WRF-3DVAR所提供的第二階段修正，WRF-HGDA仍可在觀測密度較低的區域中有效地降低背景場的誤差，改善同化表現。即使已根據準地轉模式的經驗，調整WRF-3DVAR之靜態背景誤差矩陣的結構，但當觀測密度增加後，受限於WRF-3DVAR靜態的背景誤差矩陣結構，WRF-HGDA雖在水氣場與風場仍具優勢，但於溫度場的表現反而不如WRF-LETKF。區域模式實驗中獲得的結果同樣表示出重建背景誤差結構之重要性。除藉由調整權重係數改善WRF-HGDA的同化表現外，我們更建議直接將QR-HGDA應用於WRF模式，透過正交向量的更新，完整發揮WRF-3DVAR的同化效益。

雖然整體同化結果顯示，WRF-LETKF只在溫度場較WRF-HGDA佳。但當掩星觀測數量增加後，WRF-LETKF的改善量卻最為顯著。本研究因而採用WRF-LETKF同化系統進一步探討同化福衛七號掩星觀測對旋生發展的影響。此實驗將OSSE中真實場(Nature Run)的解析度提高至三公里，再利用WRF-LETKF系統同化這些來自高解析度真實場的觀測。相對於颶風Helene的高可預報度，即使提高解析度，颶風Gordon的旋生與增強過程仍不易掌握。研究結果顯示，利用WRF-LETKF系統同化福衛七號的掩星觀測資料比同化福衛三號的掩星觀測更能提供合適的大氣環境。從機率預報的角度，同化福衛七號掩星觀測有助於改善氣旋旋生的預報，且對於後續氣旋的增強和維持都有正面助益，並可進而改進降雨預報。

摘要(英)

This dissertation aims at exploring two major issues with an Observing System Simulation Experiment (OSSE) configuration:
(1) Exploring the feasibility to eliminate an artificial combination weighting parameter in hybrid data assimilation,
(2) Evaluating the benefits of assimilating the GPS RO (Radio Occultation) observation with hybrid gain data assimilation (HGDA).

Traditional hybrid data assimilation requires an empirically estimated parameter to combine information from its component data assimilation (DA) systems. The performance of the hybrid DA system highly relies on this parameter. We therefore motivated to develop a parameterless hybrid DA algorithm. By limiting the variational correction to the subspace orthogonal to the ensemble perturbation subspace, the modified algorithm (QR-HGDA) is attainable with a quasi-geostrophic model. Our results suggest that a well-tuned static background error covariance for pure 3DVAR is not necessarily the optimal candidate for the use in hybrid DA. It implies the imperative of evaluating the optimality of the static B matrix for hybrid algorithms.

The parameter-dependent HGDA algorithm was implemented in the regional WRF model (WRF-HGDA) with the WRF-3DVAR and WRF-LETKF systems. To evaluate the benefits of RO observation, the synthetic RO observations were generated based on the real observation location from FORMOSAT-3/COSMIC (FS-3) and the simulated observation location of FORMOSAT-7/COSMIC2 (FS-7). Results indicate that the WRF-HGDA is superior to its component systems as the observation is sparse. With a dense observation network, the WRF-HGDA has the smallest RMSE in moisture and wind field while the WRF-LETKF outperforms the other two systems in temperature field. Although the static B matrix used in WRF-3DVAR has been tuned, it is unable to further improve the WRF-HGDA, echoing the imperative of evaluating the optimality of the static B matrix for the hybrids. Adjusting the combination weight improves the performance of WRF-HGDA while applying the QR-HGDA might be recommended.

Besides, to evaluate the benefits of FS-7 observation, an experiment with a higher resolution nature run was conducted with the WRF-LETKF to focus on the TC genesis. In contrast to the high predictability of Hurricane Helene, it is challenging to simulate the generation of Hurricane Gordon. Results show that assimilating the FS-7 observation leads to an environment that favors the TC genesis while the assimilation of FS-3 exhibits a drier environment and Hurricane Gordon’s structure is less robust in the FS-3 analysis. From the probabilistic perspective, assimilating the FS-7 observation leads to a positive impact on predicting the TC genesis and the heavy rainfall.

關鍵字(中)

★ 資料同化
★ 混成增益矩陣資料同化
★ 福衛七號
★ 掩星觀測

關鍵字(英)

★ Data Assimilation
★ Hybrid Gain Data Assimilation
★ FORMOSAT-7/COSMIC2
★ Radio Occultation

論文目次

摘要 I
Abstract III
Table of Contents V
List of Figures VIII
List of Tables XVIII

CHAPTER 1 Introduction 1
1.1 Background 1
1.2 Approach 7
1.3 Objectives 8
1.4 Outline 10

CHAPTER 2 Hybrid gain data assimilation (HGDA) algorithms 11
2.1 Hybrid data assimilation 11
2.2 Hybrid Gain Data Assimilation (HGDA) 15
2.3 Modified HGDA with VAR update limited to the orthogonal subspace 19

CHAPTER 3 Investigations of QR-HGDA on QG-model 23
3.1 QG model 23
3.2 Experimental Setup 24
3.2.1 Default setup for DA systems 24
3.2.2 Setup of the sensitivity experiments 25
3.3 Results with Default DA setup 28
3.4 Results with Sensitivity Experiments 34
3.4.1 Sensitivity to model bias 34
3.4.2 Sensitivity to observation error estimation 35
3.4.3 Sensitivity to background error estimation 37
3.5 Discussion of Global orthogonality and local orthogonality 42
3.6 Short Summary 44

CHAPTER 4 An observation Simulation system Experiment (OSSE) with GPS RO observation 47
4.1 Introduction of RO observation 48
4.1.1 Radio Occultation technique 49
4.1.2 FORMOSAT-3/COSMIC (FS-3) and FORMOSAT-7/COSMIC2 (FS-7) missions 52
4.2 Experimental configuration 52
4.2.1 Configuration of numerical model 52
4.2.2 Configuration of Data assimilation systems 53
4.2.3 Experiment design 55
4.2.4 Synthetic observation generation 56
4.3 Results of DA systems w/o RO observation 58
4.3.1 Single point observation experiment 59
4.3.2 Cycling run experiments with conventional observations 62
4.4 Results of DA systems with conventional and RO observations 65
4.5 Discussion on the static B matrix used in WRF-3DVAR 70
4.6 Short summary 73

CHAPTER 5 Comparison of FS-3 and FS-7 observation on hurricane prediction 75
5.1 Experimental setup 76
5.1.1 Nature Run analysis 76
5.1.2 Synthetic Observation generation 77
5.2 Results of DA cycles 78
5.3 Results of ensemble forecast 79
5.4 Short summary 82

CHAPTER 6 Conclusion and future research 83

Glossary of Mathematical Quantities 88
Acronyms 90
Bibliography 92
Tables 107
Figures 117

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指導教授

楊舒芝(Shu-Chih Yang)

審核日期

2020-7-29

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