Global Ocean Tripole and Climate Variability

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1 Global Ocean Tripole and Climate Variability Peter C. Chu Naval Postgraduate School EAPS, MIT June 2, 2010

2 Outline (1) Recent Development in Short-term Climate Variability (2) Data Analysis: (T, S) Profiles Synoptic Gridded Data with Monthly Increment (3) Synoptic Upper Ocean (0-300 m) Heat Content (4) Global Tripole Canonical El Nino, El Nino Modoki, Indian Ocean Dipole,

3 (1) Recent Development in Climate Variability Indian Ocean Dipole El Nino Modoki

4 Indian Ocean Dipole (Saji et al. 1999)

5 Indian Ocean Dipole (Saji et al. 1999)

6 El Nino and El Nino Modoki (Weng et al. 2007, Ashok et al. 2007) (Images courtesy Karumuri Ashok, APEC Climate Center)

7 (2). Data Analysis Global Temperature and Salinity Profile Program (GTSPP)

improved access to Intergovernmental Oceanographic

It went into operation in November 1990.

(IODE) Steering Group on the Global Temperature Salinity

8 GTSPP GTSPP = Global Temperature Salinity Profile Program GTSPP is a joint WMO-IOC program designed to provide improved access to Intergovernmental Oceanographic Commission the highest resolution, (IOC) highest quality data as quickly as possible. GTSPP began as an official IODE pilot project in It went into operation in November Committee on International Oceanographic Data Exchange (IODE) Steering Group on the Global Temperature Salinity Profile Program (GTSPP) World Meteorological Organization (WMO) Joint Commission on Oceanography and Marine Meteorology (JCOMM)

11 Example GTSPP Data

12 Ocean Data Analysis Classical Method Fourier Series Expansion

Joseph Fourier 1768-1830 Fourier was obsessed with the physics of heat

13 Joseph Fourier Fourier was obsessed with the physics of heat and developed the Fourier series and transform to model heat-flow problems.

14 Fourier Series Expansion For a rectangular region (L x, L y ), the basis functions are sinusoidal functions. i x f ( x, y) aij sin sin L b i j x y cos i x cos j y ij i j Lx Ly j y L

15 For the Dirichret boundary condition : f = 0 at the boundaries i x f ( x, y) aij sin sin L j y L i j x y The dots represent the Observations.

16 Linear Algebraic Equations for the Coefficients a ij ob ob i x f ( x1, y1 ) aij sin sin L j y L ob ob 1 1 i j x y ob ob i x f ( x2, y2 ) aij sin sin L... j y L ob ob 2 2 i j x y ob i x f ( xm, ym ) aij sin sin L j y L ob ob ob M M i j x y

17 Determination of Spectral Coefficients (Ill-Posed Algebraic Equation)

18 Known a ij Analyzed Field i x f ( x, y) a sin sin L j y ij L i j x y

19 For the Neumann boundary condition at the boundaries n f 0 i x j y f ( x, y) bij cos cos L L i j x y The dots represent the Observations.

20 Linear Algebraic Equations for the Coefficients a ij ob ob i x f ( x1, y1 ) bij cos cos L j y L ob ob 1 1 i j x y ob ob i x f ( x2, y2 ) bij cos cos L... j y L ob ob 2 2 i j x y ob i x f ( xm, ym ) bij cos cos L j y L ob ob ob M M i j x y

21 Known b ij Analyzed Field i x f ( x, y) b cos cos L j y ij L i j x y

22 For General Ocean Basin Generalized Fourier Series Expansion

23 Spectral Representation Fourier Series Expansion m Basis functions (not sinusoidal) c any ocean variable

24 Determination of Basis Functions (1) Eigen Functions of the Laplace Operator (Data and Model Independent) (2) Empirical Orthogonal Functions (Data or Model Dependent)

25 Eigen Functions of Laplace Operator Basis Functions (Closed Basin) Ψ k Streamfunction Φ m T, S, Velocity Potential

26 Basis Functions (Open Boundaries)

27 Boundary Conditions

28 Spectral Decomposition M 0 m m m 1 T( x, t) T ( x) c ( t) ( x) M 0 m m m 1 S( x, t) S ( x) d ( t) ( x)

29 Benefits of Using OSD (1) Don t need first guess field (2) Don t need autocorrelation functions (3) Don t require high signal-to-noise ratio (4) Basis functions are pre-determined before the data analysis. They are independent on the data.

30 Optimal Mode Truncation

31 Vapnik (1983) Cost Function

32 Optimal Truncation Gulf of Mexico, Monterey Bay, Louisiana-Texas Shelf, North Atlantic Kopt = 40, Mopt = 30

33 Determination of Spectral Coefficients (Ill-Posed Algebraic Equation) This is caused by the features of the matrix A.

34 Rotation Method (Chu et al., 2004) Well-Posed The matrix S is determined by

35 Errors 0 48 l 1 Tˆ T ( x) T D ( x) T ( x) l l uˆ 24 0 n n n 1 u( x, t) C A k ( x) u( x) u ( x) T, u errors

36 Noise-to-Signal Ratio Error Estimation αβ, α β ( P) ( P) ( T, T T ') ~ 0.1

37 (3) Upper Ocean Heat Content

38 Upper Ocean (0-300 m) Heat Content HC 0 h ctdz HC = HC mean + HC seasonal + HC anomaly EOF Analysis HC anomaly Global Ocean Dipole Modes

Trend of Upper Ocean (0-700 m) Heat 0.4 X 10 22 J/yr (1958-2008) (Levitus et al.

39 Trend of Upper Ocean (0-700 m) Heat 0.4 X J/yr ( ) (Levitus et al.,grl, 2009) Without Argo data Content 1.3 X J/yr ( ) With Argo data

40 Upper Ocean (0-300 m) Mean Heat Content (J/m 2 ) ( )

41 Seasonal Variability of Upper Ocean (0-300 m) Heat Content (J/m 2 ) ( ) January April July October

42 EOF Analysis Heat Content Anomaly Relative to Seasonal Variation

43 EOF-1 (in 10 8 J/m 2 )

44 EOF-1 (in 10 8 J/m 2 )

45 PC1

46 Lag Correlation between PC 1 and SOI Positive Month PC 1 advancing SOI

47 EOF-2 (in 10 8 J/m 2 )

48 EOF-2 (in 10 8 J/m 2 )

49 PC2

50 Lag Correlation between PC 2 and SOI Positive Month PC 2 advancing SOI

51 (4) Global Ocean Tripole

52 Canonical La Nina More and Stronger Hurricanes in Atlantic (Pielke and Landsea, 1999 BAMS)

53 Canonical El Nino

55 El Nino Modoki More and Stronger Hurricanes in Atlantic

56 Trajectory in Phase Space (PC 1, PC 2 ) Blue Curve La Nina Red Curve Two Types of El Nino

57 Conclusions (1) Upper ocean heat content contains the signal for climate change (interannual) Global Ocean Tripole. (2) El Nino, El Nino Modoki, and Indian Ocean Dipole can be unified by Global Ocean Tripole.

58 Future Improvement Upper ocean heat content should not be calculated to a fixed depth such as 300 m in this study. Heat content in ocean mixed layer should be most important for the climate change. There is no simple, objective and effective method to determine mixed layer depth from profile data. My near future work is to develop such a method.

Optimal Spectral Decomposition (OSD) for GTSPP Data Analysis

Optimal Spectral Decomposition (OSD) for GTSPP Data Analysis Peter C Chu (1),Charles Sun (2), & Chenwu Fan (1) (1) Naval Postgraduate School, Monterey, CA 93943 pcchu@nps.edu, http://faculty.nps.edu/pcchu/