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- Title: Spacetime
- Type: Notes
- School: Washington
- Course: STAT 518
- Term: Spring
Coursehero >> Washington >> Washington >> STAT 518
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time Space statistics STAT 518 Sp08 Space time processes Separable covariance structure: Cov(Z(x,t),Z(y,s))=C1(x,y)C2(s,t) Nonseparable alternatives Temporally varying spatial covariances Fourier approach Completely monotone functions SARMAP study Spatial correlation structure depends on hour of the day (non separable): A national health effects study Region 6: S Calif, all 94 sites, fitting and validation Fitting (63) Validation (31) Los Angeles County Trend model m (si ) = m (si ) + dkVik 1 0 where Vik are covariates, such as population density, proximity to roads, local topography, etc. 2 (si ,t) = r j (si )fj (t) (si ,t) = m (si ) + m (si ,t) 1 2 where the fj are smoothed versions of temporal singular vectors (EOFs) of the TxN data matrix. We will set 1(si) = 0(si) for now. SVD computation Singular values of T=2912 x S=545 observation matrix 800 600 400 Singular value 200 0 0 100 200 300 Index, 1:545 400 500 EOF 1 Annual Trend Component 1 0.04 0.02 0.0 Annual.svd$svd$u[1:1456, j] -0.04 01/01/1987 10/01/1987 07/01/1988 04/01/1989 dates87to94[1:1456] 01/01/1990 10/01/1990 0.04 0.02 0.0 -0.02 Annual.svd$svd$u[1457:2912, j] 01/01/1991 10/01/1991 07/01/1992 04/01/1993 01/01/1994 10/01/1994 dates87to94[1457:2912] EOF 2 Annual Trend Component 2 0.06 0.02 -0.02 Annual.svd$svd$u[1:1456, j] -0.06 01/01/1987 10/01/1987 07/01/1988 04/01/1989 dates87to94[1:1456] 01/01/1990 10/01/1990 0.06 0.02 -0.02 Annual.svd$svd$u[1457:2912, j] -0.06 01/01/1991 10/01/1991 07/01/1992 01/01/1994 04/01/1993 10/01/1994 dates87to94[1457:2912] Annual Trend Component 3 EOF 3 0.04 0.0 Annual.svd$svd$u[1:1456, j] -0.04 01/01/1987 10/01/1987 07/01/1988 04/01/1989 dates87to94[1:1456] 01/01/1990 10/01/1990 0.06 0.02 -0.02 Annual.svd$svd$u[1457:2912, j] -0.06 01/01/1991 10/01/1991 07/01/1992 04/01/1993 01/01/1994 10/01/1994 dates87to94[1457:2912] 60370113 0.4 0.2 sqrt(max 8hr O3) 0.0 01/01/1989 01/01/1990 01/01/1991 01/01/1992 1987-1994 01/01/1993 01/01/1994 61112003 0.4 0.2 sqrt(max 8hr O3) 0.0 01/01/1989 01/01/1990 01/01/1991 01/01/1992 1987-1994 01/01/1993 01/01/1994 61111003 0.4 0.2 sqrt(max 8hr O3) 0.0 01/01/1989 01/01/1990 01/01/1991 01/01/1992 1987-1994 01/01/1993 01/01/1994 Kriging of 0 Kriging of 2 Quality of trend fits Fitted trend (solid) vs Predicted (dashed): 060371002 0.4 0.2 sq rt Ozone 0.0 01/01/1989 01/01/1990 01/01/1991 01/01/1992 Date 01/01/1993 01/01/1994 Fitted trend (solid) vs Predicted (dashed): 060371301 0.4 0.2 sq rt Ozone 0.0 01/01/1989 01/01/1990 01/01/1991 01/01/1992 Date 01/01/1993 01/01/1994 Fitted trend (solid) vs Predicted (dashed): 060375001 0.4 0.2 sq rt Ozone 0.0 01/01/1989 01/01/1990 01/01/1991 01/01/1992 01/01/1993 01/01/1994 Observed vs. predicted Observed (points) vs Predicted (lines): 060371301 0.4 0.2 sq rt Ozone 0.0 01/01/1989 04/01/1989 07/01/1989 10/01/1989 01/01/1990 Date 04/01/1990 07/01/1990 10/01/1990 0.4 0.2 sq rt Ozone 0.0 01/01/1991 04/01/1991 07/01/1991 10/01/1991 01/01/1992 Date 04/01/1992 07/01/1992 10/01/1992 0.4 0.2 sq rt Ozone 0.0 01/01/1993 04/01/1993 07/01/1993 10/01/1993 01/01/1994 Date 04/01/1994 07/01/1994 10/01/1994
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111syllabus.pdfPath: Washington >> INDON >> 111 Fall, 2008
Description: ATM S 111 Global Warming: Understanding the Debate Fall 2008 Syllabus Course overview Human-induced climate change - popularly known as \"global warming\" - is emerging as one of the great challenges facing society in the 21st century. If we ignore ...