Tomoko Matsuo s collaborators

Transcription

1 Tomoko Matsuo s collaborators Thermosphere-Ionosphere GCM Modeling A. Richmond (NCAR-HAO) T. Fuller-Rowell and M. Codrescu (NOAA) Polar Ionosphere Data Assimilation A. Richmond, G. Lu, and B. Emery (NCAR-HAO) D. Lummerzheim (U of Alaska) M. Hairston (U of Texas, Dallas) Spatial Statistics D. Nychka (NCAR-IMAGe) D. Paul (U of California, Davis) Middle Atmosphere Data Assimilation J. Anderson (NCAR-IMAGe) D. Marsh and A. Smith (NCAR-ACD) Advisory Panel Meeting, Apr 27, 26

2 Sun-Earth Connection GRL 98 Cover Page

3 Multi-resolution Based Nonstationary Covariance Modeling: Monte-Carlo EM approach Tomoko Matsuo in collaboration with Doug Nychka & Debashis Paul (UC, Davis) Advisory Panel Meeting, Apr 27, 26

4 Surface Ozone standard deviation latitude standard deviation longitude O 3 is one of six common pollutants EPA s national air quality standards (8 ppb) 1997 Data Set 364 locations on grid 184 days from May to Oct

5 Motivation and Goal Motivation: Flexible Nonstationary Covariance Model Gaussian Model in Spatial Statistics Kriging (geostatistics) [e.g., Higdon et al., 1999; Fuentes, 21; Fuentes and Smith, 21; Nychka et al., 23; Sampson and Guttorp, 1992; Anderes and Stein, 25] Variational and OI methods (data assimilation) [e.g., Purser et al., 25; Gaspari et al., 26] Goal and Challenges: Computational efficiency Irregularly distributed observational data Large data set

6 Nonparametric Model Σ = WH 2 W T [Nychka, Wikle, and Royle, 23] [ ] [ ] H H 1 H H = H 1 H 11 H1 where H is thresholded and H 1 = diag(h 11 ) Enforced sparsity in H wavelet coefficient wavelet coefficient wavelet coefficient wavelet coefficient

7 Covariance Estimator Gaussian Model: f = ( f 1 f 2 ) N (, Σ θ ) where Σ θ = W H 2 (θ)w T.

8 Covariance Estimator Gaussian Model: f = ( f 1 f 2 ) N (, Σ θ ) where Σ θ = W H 2 (θ)w T. Monte-Carlo EM [e.g., Wei and Tanner, 199]: Q(θ, θ ) = E[L(f, θ) f 1, θ ] 1 N L 1 N n=1 f (n) 2, θ MC sampling: f (n) 2 [ f 2 f 1, W H 2 (θ )W T ]

9 Covariance Estimator Gaussian Model: f = ( f 1 f 2 ) N (, Σ θ ) where Σ θ = W H 2 (θ)w T. Monte-Carlo EM [e.g., Wei and Tanner, 199]: Q(θ, θ ) = E[L(f, θ) f 1, θ ] 1 N L 1 N n=1 f (n) 2, θ MC sampling: f (n) 2 [ f 2 f 1, W H 2 (θ )W T ] Smoothed MC EM [e.g., Silverman et al., 199]: Q(θ, θ ) + p(θ)

10 Different thresholding in H Lev 2, 86.8% (545) Lev 3, 98% (8363) (a) (b) (a) (b) (c) (d) (c) (d)

11 Validation Sample v.s. Modeled Correlation.5..5 sample correlation modeled correlation.5.5. modeled correlation.5..5 modeled correlation (c) lev 3 98% (2 iteration) 1. (b) lev 2 86%, smoothed 1. (a) Stationary.5..5 sample correlation sample correlation 1.

12 Summary and Future Work To be submitted to JASA or JRSS-B Flexible nonstationary covariance model W H 2 W T Theory to support sparsity in H Practical estimator (Monte-Carlo EM) to handle the incomplete data Examples using surface ozone data

13 Summary and Future Work To be submitted to JASA or JRSS-B Flexible nonstationary covariance model W H 2 W T Theory to support sparsity in H Practical estimator (Monte-Carlo EM) to handle the incomplete data Examples using surface ozone data Another ozone application in collaboration with Eric Gilleland (NCAR-RAL)

14 Summary and Future Work To be submitted to JASA or JRSS-B Flexible nonstationary covariance model W H 2 W T Theory to support sparsity in H Practical estimator (Monte-Carlo EM) to handle the incomplete data Examples using surface ozone data Another ozone application in collaboration with Eric Gilleland (NCAR-RAL) Application to the Polar Ionosphere Aurora image data ( 1K) Prior covariance for ionospheric data assimilation