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粒子フィルタ法を利用した日本沿岸部 に おける 潮位の長期変動解析 長尾大道　樋口知之（統計数理研究所） 三浦 哲　稲津大祐（東北大学理学研究科）

粒子フィルタ法を利用した日本沿岸部 に おける 潮位の長期変動解析 長尾大道　樋口知之（統計数理研究所） 三浦 哲　稲津大祐（東北大学理学研究科）. Outline Time-series a nalysis of tide g auge r ecords using the PF Univariate a nalysis Multivariate a nalysis Event detection using a non-Gaussian distribution Future plans Summary.

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粒子フィルタ法を利用した日本沿岸部 に おける 潮位の長期変動解析 長尾大道　樋口知之（統計数理研究所） 三浦 哲　稲津大祐（東北大学理学研究科）

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  1. 粒子フィルタ法を利用した日本沿岸部に おける潮位の長期変動解析 長尾大道　樋口知之（統計数理研究所） 三浦 哲　稲津大祐（東北大学理学研究科） • Outline • Time-series analysis of tide gauge records using the PF • Univariateanalysis • Multivariate analysis • Event detection using a non-Gaussian distribution • Future plans • Summary 第1回 データ同化ワークショップ　Apr. 22, 2011

  2. Tidal Data along the Coastline of Japan • Continuous observation since 1884 • ~ 150 observatories • Monthly means from 1966 to 2008(i.e., 43years) corrected to the 1000hPa constant-pressure surface by using atmospheric pressure data Distribution of tidal observatories 第1回 データ同化ワークショップ　Apr. 22, 2011

  3. Example of Application (black) (blue) (red) ±std. err 第1回 データ同化ワークショップ　Apr. 22, 2011

  4. Long-Term Trend in Tide Gauge Data Crustal deformation Crust uplift~2m when Great Kanto EQ (GSI website) monthly means at Aburatsubo observatory 第1回 データ同化ワークショップ　Apr. 22, 2011

  5. Several Years to Decadal Variations in Tide Gauge Data Oceanic Variations Kato and Tsumura (1979) Residual obtained by subtract of trend & seasonal variations from original data 第1回 データ同化ワークショップ　Apr. 22, 2011

  6. Clustering of AR components (Ward’s method) Kobayashi (2008) 第1回 データ同化ワークショップ　Apr. 22, 2011

  7. State Space Model for Univariate Analysis Observation model observation noise data trend (long-term variation) seasonal (annual variation) AR (several-years variation) cf. Kato & Tsumura method (1979) • We are going to improve this to • detect a sudden baseline jump such as due to an earthquake • take time-varying annual variations into consideration • deal with missing values as easy as possible 第1回 データ同化ワークショップ　Apr. 22, 2011

  8. State Space Model for Univariate Analysis System model Trend component Seasonal component AR component (long-term variation) (annual variation) (several-years variation) (follows a Gaussian distribution) System noise v1 expresses slight changes from a linear trend System noise v2 expresses small temporal changes of amplitude and phase AR model extracts several- years variation Observation noise component 第1回 データ同化ワークショップ　Apr. 22, 2011

  9. Unknown Parameters to be Optimized in Univariate Analysis • variance of • observation • noise • initial state vector • variances of • system noises • AR coefficients 第1回 データ同化ワークショップ　Apr. 22, 2011

  10. State Space Model Linear form cf. Non-linear form State vector 第1回 データ同化ワークショップ　Apr. 22, 2011

  11. Successive Estimation of the States Step 1: One-step ahead prediction Step 2: Filtering : state at time t when that at time at t-1 is given : observation data at times 1 to t Each distribution is approximated as an ensemble of particles 第1回 データ同化ワークショップ　Apr. 22, 2011

  12. Flowchart of Model Parameter Estimation Sample a parameter vector from an appropriate prior Sample N initial state vectors from an appropriate prior Calculate one-step ahead prediction by Resample N particles on the basis of likelihood No End of time series? Yes Calculate likelihood of the time series No Enough number of parameter vectors? Yes Optimum parameters 第1回 データ同化ワークショップ　Apr. 22, 2011

  13. PC Cluster of Data Assimilation Group DELL Precision T5400 x 24nodes(192 cores in total)for data assimilation (theoretical performance >2TFlops) ・CPU: Intel Xeon 2.83GHz Quad core×2 ・Memory: 32GB/node ・Intel Fortran+ MPI 第1回 データ同化ワークショップ　Apr. 22, 2011

  14. Land Sinking & Sea Level Changes along the coastline of Japan Pacific Ocean Sea of Japan Sea of Japan View from North 50cm Pacific Ocean Oceanic Current “Kuroshio” View from South 第1回 データ同化ワークショップ　Apr. 22, 2011

  15. State Space Model for Multivariate Analysis State Space Model for Univariate Analysis Observation model vector form Observatory # 第1回 データ同化ワークショップ　Apr. 22, 2011

  16. State Space Model for Multivariate Analysis System model Trend component Seasonal component AR component (linear trend) (annual variation) (several years variation) System noise v1 expresses slight changes from a linear trend System noise v2 expresses small temporal changes of amplitude and phase Multivariate AR model extracts spatial correlation between observatories Observation noise component 第1回 データ同化ワークショップ　Apr. 22, 2011

  17. 10/21 Multivariate AR model AR coefficient matrix All roots of are enforced to be outside the unit circle in the complex plane using the Lehman-Schur method. 1 -1 1 indicates cross-correlation between each observation degree -1 ERCIM’10 @ University of London, December 10, 2010

  18. Unknown Parameters to be Optimized in Multivariate Analysis • variance of • observation • noise • initial state vector • variances of • system noises • AR coefficients 第1回 データ同化ワークショップ　Apr. 22, 2011

  19. Comparison between Multivariate & Univariate Analyses Multivariate Analysis Univariate Analysis Noise level is drastically reduced !! 第1回 データ同化ワークショップ　Apr. 22, 2011

  20. Long-Term Trend in Tide Gauge Data Crustal deformation Crust uplift~2m when Great Kanto EQ (GSI website) monthly means at Aburatsubo observatory 第1回 データ同化ワークショップ　Apr. 22, 2011

  21. State Space Model for Multivariate Analysis with event detection System model Trend component Seasonal component AR component (linear trend) (annual variation) (several years variation) (follows Cauchy distribution) System noise v1 expresses slight changes from a linear trend System noise v2 expresses small temporal changes of amplitude and phase Multivariate AR model extracts spatial correlation between observatories Observation noise component 第1回 データ同化ワークショップ　Apr. 22, 2011

  22. Unknown Parameters to be Optimized in Multivariate Analysis with Event Detection • variance of • observation • noise • initial state vector • variances of • system noises • AR coefficients Scale factor of Cauchy distribution 第1回 データ同化ワークショップ　Apr. 22, 2011

  23. Sea Level Change due to the 1923 Great Kanto Earthquake Gauss distribution: Cauchy distribution: 第1回 データ同化ワークショップ　Apr. 22, 2011

  24. Sea Level Changes due to Off-Miyagi Earthquakes Cauchy分布 第1回 データ同化ワークショップ　Apr. 22, 2011

  25. SSH Anomalies Estimated by MRI.COM Yasuda and Sakurai (2006) temporal & spatial resolution? 第1回 データ同化ワークショップ　Apr. 22, 2011

  26. Summary • We develop a particle filter code of univariate/multivariate time series analysis, which is applicable to any time series data in various field of science. • The particle filter algorithm is effective such as a sudden event detection, i.e., situations that non-Gaussian distributions are required in the model. • Does a modeling of several-years oceanic variations by using MRI.COM help to detect coseismic/post-seismicdeformations? 第1回 データ同化ワークショップ　Apr. 22, 2011

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