Optimal Spectral Decomposition for ARGO Data Analysis

Transcription

1 IUGG 2007 PS010 New Insights into the Ocean and Its Circulation from ARGO and GODAE July 9-10, Perugia, Italy Optimal Spectral Decomposition for ARGO Data Analysis Peter C. Chu Naval Postgraduate School Charles Sun NOAA/NODC Oleg Melnichenko University of Hawaii

2 Part-1 Theory and Methodology

3 Observational Data (Sparse and Noisy)

4 Most Popular Method for Ocean Data Analysis: Optimum Interpolation (OI)

5 Three Necessary Conditions For the OI Method (1) First guess field (2) Autocorrelation functions (3) Low noise-to-signal ratio

6 Ocean velocity data (1) First guess field (?) (2) Unknown autocorrelation function (3) High noise-to-signal ratio

7 It is not likely to use the OI method to process ocean velocity data.

8 Spectral Representation - a Possible Alternative Method Theoretical Base: Fourier Series Expansion

9 Flow Decomposition

10 Basis Functions (Closed Basin) Eremeev et al. (1992 JGR)

11 Rectangular Domain with Flat Bottom Sinusoidal Basis Functions

12 Basis Functions for Rectangular Domain

13 Basis Functions for Rectangular Domain

14 Basis Functions (Open Boundaries) (Chu et al., 2003 a,b JTECH)

15 Boundary Conditions

16 Spectral Decomposition

17 Benefit of Using OSD Ocean Topographic Configuration Basis Functions (Pre-Determined)

18 Optimal Mode Truncation

19 Vapnik (1983) Cost Function Optimal Mode Truncation

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

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

22 Rotation Method (Chu et al., 2004)

23 Part-2 Applications

24 Are mid-depth (~1000 m) ocean circulations steady? If not, what mechanisms cause the change? (Rossby wave propagation)

25

26 ARGO Observations (Oct-Nov 2004) (a) Subsurface tracks (b) Float positions where (T,S) were measured 10 S (a) 70 W 0 W 30 W 10 W 10 S (b) 70 W 0 W 30 W 10 W

27 Circulations at 1000 m estimated from the original ARGO float tracks (bin method) April 2004 April W 60 W 0 W 40 W 30 W 20 W 10 W 40 cm/s 70 W 0 W 30 W 10 W It is difficult to use such noisy data into ocean numerical models.

28 Boundary Configuration Basis Functions for OSD Γ 2 Azores Islands Γ 1 10 S Γ 3 Γ 3 / 70 W 0 W 30 W 10 W

29 Basis Functions for Streamfunction Mode-1 and Mode S 70 W 0 W 30 W 10 W 10 S 70 W 0 W 30 W 10 W

30 May July 4 4 Temperature at 90 m depth W 60 W 0 W 40 W 30 W 20 W 10 W W 60 W 0 W 40 W 30 W 20 W 10 W September November W 60 W 0 W 40 W 30 W 20 W 10 W 70 W 60 W 0 W 40 W 30 W 20 W 10 W

31 8 4 January March 4 4 Temperature at 90 m depth W 60 W 0 W 40 W 30 W 20 W 10 W W 60 W 0 W 40 W 30 W 20 W 10 W May W 60 W 0 W 40 W 30 W 20 W 10 W

32 Statistical Features of Temperature at 90 m Depth p (%) p (%) t / ( C) Std=1.00 ( C) Kur=7.40 Sk=1.17 Me=0.08 ( C) Std=1.03 ( C) Kur=7.79 Sk=1.21 Me=0.07 ( C) 70 W 0 W 30 W 10 W t / ( C) 4 p (%) Std=0.97 ( C) Kur=8.31 Sk=1.31 Me=0.06 ( C) 3 p (%) Std=0.97 ( C) Kur=8.42 Sk=1.36 Me=0.08 ( C) t / ( C) t / ( C)

33 Circulations at 1000 m (March 04 to May 0) Bin Method OSD cm/s cm/s 70 W 0 W 30 W 10 W 70 W 0 W 30 W 10 W

34 Circulation at 100 m depth April 04 August 04 June 04 cm/s cm/s cm/s 70 W 0 W 30 W 10 W 70 W October 04 0 W 30 W 70 W 10 W 0 W 30 W 10 W February 0 December 04 cm/s cm/s cm/s 70 W 0 W 30 W 10 W 70 W 0 W 30 W 10 W 70 W 0 W 30 W 10 W

35 Statistical Features of Velocity h (%) 2 h (%) Std=4.86 Kur=7.00 Sk= u (cm/s) Std=6.63 Kur=.60 Sk= Std=4.6 Kur=6. Sk= v (cm/s) Std=.92 Kur=.40 Sk= W 0 W 30 W 10 W u (cm/s) v (cm/s) 4 h (%) Std=4.91 Kur=.44 Sk= Std=4.0 Kur=.62 Sk= Std=3.7 Kur=9.2 Sk= Std=3. Kur=9.20 Sk= u (cm/s) v (cm/s)

36 Conclusions OSD is an effective method to analyze noisy and sparse data. OSD has successfully demonstrated the feasibility of optimal estimations of the Atlantic ocean temperatures and currents at 90 m and 1000 m, using the Argo data. We will apply OSD to reanalyze the Pacific ocean temperature and salinity fields, using the Global Temperature-Salinity Profile Program (GTSPP) data maintained at NODC.