粒子フィルタ法を利用した日本沿岸部
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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). 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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2653180

粒子フィルタ法を利用した日本沿岸部

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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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State Space Model for JapanMultivariate 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


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State Space Model for JapanMultivariate 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


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10/21 Japan

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


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Unknown Parameters to be Optimized Japan

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


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Comparison between Multivariate & JapanUnivariate 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


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Long-Term Trend in Tide Gauge Data Japan

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


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State Space Model for JapanMultivariate 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


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Unknown Parameters to be Optimized Japan

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


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Sea Level Change due to the 1923 Great Kanto Earthquake Japan

Gauss distribution:

Cauchy distribution:

第1回 データ同化ワークショップ Apr. 22, 2011


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Sea Level Changes due to Off-Miyagi Earthquakes Japan

Cauchy分布

第1回 データ同化ワークショップ Apr. 22, 2011


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SSH Anomalies JapanEstimated 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


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Summary Japan

  • 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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