欧陽 懋

Abstract. Controlling weather is an outstanding and pioneering challenge for researchers around the world, due to the chaotic features of the complexatmosphere. A control simulation experiment (CSE) on the Lorenz-63 model, which consists of positive and negative regimes represented by the statesof variable x, demonstrated that the variables can be controlled to stay in the target regime by adding perturbations with a constant magnitude toan independent model run (Miyoshi and Sun, 2022). The current study tries to reduce the input manipulation of the CSE, including the total controltimes and magnitudes of perturbations, by investigating how controls affect the instability of systems. For that purpose, we first explored theinstability properties of Lorenz-63 models without and under control. Experiments show that the maximum growth rate of the singular vector (SV) reduceswhen the variable x was controlled in the target regime. Subsequently, this research proposes to update the magnitude of perturbationsadaptively based on the maximum growth rate of SV; consequently, the times to control will also change. The proposed method successfully reducesaround 40 % of total control times and around 20 % of total magnitudes of perturbations compared to the case with a constant magnitude.Results of this research suggest that investigating the impacts of control on instability would be beneficial for designing methods to control thecomplex atmosphere with feasible manipulations.

Internal erosion has been frequently reported and has caused failures and instabilities of geotechnical structures. A plane strain erosion apparatus is developed in this study to allow the subsequent conduction of drained compression test after seepage test and the microscopic observation of particle movement through a transparent window. A drained compression test preceded by a seepage test is performed on specimens containing the same initial fines contents to investigate the mechanical consequence impacts of seepage-induced internal erosion. Experimental results reveal that, compared with uneroded soils, internally eroded soils show a larger secant stiffness at a small strain level (-1 %). At medium strain level (-15 %), the soils with erosion show smaller deviator stress comparing with soils without erosion. The analysis of images recorded by the microscope proves that the fines contacted with coarse particles possibly transferring the load are distinct between the soils with and without internal erosion at both small and medium strain levels during the drained compression test, which indicates that the soil fabric could affect the mechanical behaviors of soils subjected to internal erosion. Our designed equipment and microscopic observation could throw some light on the research of internal erosion from the view of particle scale.

数値気象予測において，観測情報は予報誤差低減に重要な役割を果たす一方，観測位置を最適化する手法は未確立である．近年，PODモードと観測値を用いて場を復元する方法や，復元される場のスパース性に着目し，フィッシャー情報行列Fを最大化するスパースセンサ位置最適化(SSP)手法が提案されている．本論文では大次元力学系に適したSSP手法を検討し，SSTを用いた数値実験により提案手法の妥当性を考察した．場の復元にデータ同化を新たに応用し，精度改善に成功した．更にSSPにモードのみを用いた場合と，モードと特異値を考慮した場合を比較し，特異値を考慮した観測位置決定では上位モードが優先されることを示した．Fの最大化の解釈として，Fの行列式最大化とFの逆行列対角和の最小化を検討し，後者が適することを示した．

雨量計は降水量の時空間分布推定に大きな役割を果たし，効率的に雨量計を配置することが重要である．本研究では，情報科学分野で提案されているスパースセンサ位置最適化手法（SSP）を雨量計配置の問題に適用し，時空間分布推定に有効な位置を推定する．更に少ない観測情報から全体の場を復元する手法として，新たに局所アンサンブル変換カルマンフィルタ（LETKF）を適用する．気象庁の解析雨量を使用して，雨量計配置と場の復元を北海道を対象に行った．AMeDASの観測位置情報から場の復元手法をLETKFと最近傍法とで行い，LETKFがより高精度であることを確認した．更にSSPによる雨量計配置とAMeDASの観測位置からLETKFによる場の復元をそれぞれ行い，SSPによる雨量計配置が有効に機能することを確認した．