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Shu-Ping, Weng, and Jau-Ming, Chen Research and Development Center Central Weather Bureau

Shu-Ping, Weng, and Jau-Ming, Chen Research and Development Center Central Weather Bureau Bin, Wang School of Ocean and Earth Science and Technology International Pacific Research Center University of Hawaii

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Shu-Ping, Weng, and Jau-Ming, Chen Research and Development Center Central Weather Bureau

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  1. Shu-Ping, Weng, and Jau-Ming, Chen Research and Development Center Central Weather Bureau Bin, Wang School of Ocean and Earth Science and Technology International Pacific Research Center University of Hawaii International Workshop on Monthly-to-Seasonal Climate Prediction, National Taiwan Normal University Taipei, Taiwan 25-26 October 2003 The Development of Statistic Projection Model for the Prediction of Global Sea Surface Temperature Anomalies (GSSTA) at Central Weather Bureau

  2. Outlines • Methodology of a SVD-based statistic projection model • The prediction of global SSTA with a leading time up to six months －A two-tier procedure using Nino3.4 SSTA as the primary predictor a. sensitivity test on the progressive method of setting for predicted time window b. sensitivity test on the method of global domain aggregation c. issue of season-dependent forecast skill • The potential in using SLP anomalies over Southern Indian Ocean (SIO, Bin Wang et al. 2003) and Philippine Sea (PS, Bin Wang et al. 2000, 2003) as the secondary predictor to the seasonal prediction of local SSTA over tropical Indo-Pacific • Summary

  3. Methodology of SVD-based Projection Model for Statistic GSSTA Forecast • SVD analysis The arrays A and B, which store the temporal evolution of predictors (e.g., preceding Nino3.4 domain SST) and predictand (e.g., predicted global SST field) respectively, can be used to construct a covariance matrix C representing the relatedness between these two fields: C = A BT (1) The matrix C is then subjected to SVD analysis to produce a pair of orthogonal bases of fields A and B, namely U and V: C = U W VT (2) The degree of coupling between A and B is quantified in the column vector W which stores the singular values of matrix C.

  4. Methodology of SVD-based Projection Model for Statistic GSSTA Forecast The corresponding time series expansion coefficients of A and B, E and F, are obtained by projecting them onto the orthogonal bases U and V (i.e., left and right singular vectors): E = UT A, F = VT B(3) • SVD Projection Model The prediction scheme is constructed by first building the connection between the matrices E and F: F = X E, which means X = F E+ (4)

  5. Methodology of SVD-based Projection Model for Statistic GSSTA Forecast Since the aim is to build up the transfer function R connecting predictor A and predictand B, B = R A. Inserting Eq.(3) and utilizing Eq.(4), the transfer function R is given by R = V X UT. (5) • Making the Hindcast Experiment Once the transfer function R is determined from the historic data, for any current predictor column vector a, the predictand column vector bis given as b = R a. The calculation of R is based on ‘take-one-out’ cross-validation in the following hindcast experiments.

  6. GSSTA Prediction Using Nino3.4 SSTA as Predictors • A two-tier Procedure is adopted • Step 1 － use historic Nino3.4 SSTA (previous 6-month period) as its own predictor in the future (next 6-month period) • Step 2 － aggregate the predicted Nino 3.4 SSTA to the global SSTA utilizing the transfer function built from the concurrent relationship between them

  7. Predictand Predictor Predictand Use current Nino SSTA to forecast future Nino SSTA Aggregates the forecasted Nino SSTA to global SSTA mXk(t1) nYk(t2) lZk(t2) nCl mCn projection SVD projection projection SVD Sj Si North’s thumb of rule North’s thumb of rule rsv lsv lsv rsv nPj lQj mUi nVi T T jek=jPn nYk, jfk =jQl lZk T iEk=iUm mXk,iFk =iVn nYk T ＋ ＋ iFk =iLi iEk, iLi = iFk kEi jfk =jLj jek, jLj = jfk kej Pseudo inverse Spatial mapping lZk =lRn nYk nYk nYk =nrm mXk lRn =lQj jLj jPn T nrm =nVi iLi iUm T

  8. GSSTA Prediction Using Nino3.4 SSTA as Predictors • An operation scenario of seasonal forecast at CWB Suppose CWB needs to make seasonal prediction twice a year in both late May and late November. The AGCM then needs global SST field as boundary condition by 15 May or 15 November to perform ensemble runs. The SST data available will be the 6-month period of NDJFMA (or MJJASO) to predict SSTA in the following MJJASO (or NDJFMA).

  9. GSSTA Prediction Using Nino3.4 SSTA as Predictors • Approaches to make prediction up to 6-month lead • Express :NDJFMA－＞ M, J, J, A, S,O • Update: NDJFMA－＞ M DJFMAM －＞ J JFMAMJ －＞ J FMAMJJ －＞ A MAMJJA －＞ S AMJJAS －＞ O • Reserved Update : NDJFMA－＞ M NDJFMAM －＞ J NDJFMAMJ －＞ J NDJFMAMJJ －＞ A NDJFMAMJJA －＞ S NDJFMAMJJAS －＞ O • Block: NDJFMA－＞ MJJASO

  10. GSSTA Prediction Using Nino3.4 SSTA as Predictors Data 1. A blended SST dataset (1950 – 2002) is used Reynolds EOF-reconstructed : 30。S - 30。N<＝ERSST GISST2.3b : elsewhere<＝HADISST 2. GMSLP 2.1f (U.K. Met. Office, 1950 – 2002)

  11. Fig.1a: The RMSE (root-mean-square-error) of 6 months forecast starting from November (lead 1 month) to April (lead 6 months). Block approach is used. Contour interval = 0.1C. Shading area starting from 0.4C.

  12. Fig.1b: The ACSS (anomaly-correlation-skill-score) of 6 months forecast starting from November (lead 1 month) to April (lead 6 months). Block approach is used. Contour interval = 0.1. Shading area starting from 0.5.

  13. Fig.2a: The RMSE of 6 months forecast starting from May (lead 1 month) to October (lead 6 months). Block approach is used. Contour interval = 0.1C. Shading area starting from 0.4C.

  14. Fig.2b: The ACSS of 6 months forecast starting from May (lead 1 month) to October (lead 6 months). Block approach is used. Contour interval = 0.1. Shading area starting from 0.5.

  15. Fig.3a Comparisons of RMSE among different approaches over the mid-latitude of NH (30N-60N, upper panels), the tropical band (30S-30N,middle panels), and mid-latitude of SH (30S-60S, lower panels). November and May denote the 1-month lead, and so on.

  16. Fig.3b Comparisons of ACSS among different approaches over the mid-latitude of NH (30N-60N, upper panels), the tropical band (30S-30N,middle panels), and mid-latitude of SH (30S-60S, lower panels).

  17. Fig.4a: Time series of lag 1-season (NDJ) over 4 Nino domains. Observed SSTA is shown as dashed lines.

  18. Fig.4b: Time series of lag 2-season (FMA) over 4 Nino domains. Observed SSTA is shown as dashed lines.

  19. GSSTA Prediction Using Nino3.4 SSTA as Predictors • Sensitivity tests on the way of domain separation 1. individual ocean basin 2. 10。by 10。Gridded cells around the globe 3. SVD varimax rotation 4. global ocean as a whole

  20. Fig.5a: The ACSS of 6 months forecast starting from November (lead 1 month) to April (lead 6 months). Block-Cell approach is used. Contour interval = 0.1. Shading area starting from 0.5.

  21. Fig.5b: The ACSS of 6 months forecast starting from November (lead 1 month) to April (lead 6 months). Block-SVD rotation approach is used. Contour interval = 0.1. Shading area starting from 0.5.

  22. GSSTA Prediction Using Nino3.4 SSTA as Predictors Season-dependent forecast skill

  23. 10, 11, 12, 1, 2, 3 4, 5, 6, 7, 8, 9 11, 12, 1, 2, 3,4 5, 6, 7, 8, 9, 10 12, 1, 2, 3,4, 5 6, 7, 8, 9, 10,11 1, 2, 3,4, 5, 6 7, 8, 9, 10,11,12 2, 3,4, 5, 6, 7 8, 9, 10,11,12, 1 9, 10,11,12, 1, 2 3,4, 5, 6, 7, 8 4, 5, 6, 7, 8, 9 10,11,12, 1, 2, 3 5, 6, 7, 8, 9,10 11,12, 1, 2, 3, 4 12, 1, 2, 3, 4, 5 6, 7, 8, 9,10,11 7, 8, 9, 10,11,12 1, 2, 3, 4, 5, 6 8, 9,10, 11,12, 1 2, 3, 4, 5, 6, 7 9, 10,11, 12, 1, 2 3, 4, 5, 6, 7, 8

  24. Fig.6 The ACSS of forecasted monthly-mean SSTA at lead 6-month for 12 calendar month. Contour interval = 0.1, shading areas start from 0.5.

  25. Fig.6 (continued)

  26. Fig.7a: Seasonal dependence of the RMSE over Indo-Pacific tropical bands (10S-10N) for lead 1, 2, and 3 months. Contour interval = 0.1C, shading areas start from 0.5C.

  27. Fig.7b: Seasonal dependence of the RMSE over Indo-Pacific tropical bands (10S-10N) for lead 4,5, and 6 months. Contour interval = 0.1C, shading areas start from 0.5C.

  28. Fig.8a: Seasonal dependence of the ACSS over Indo-Pacific tropical bands (10S-10N) for lead 1, 2, and 3 months. Contour interval = 0.1, shading areas start from 0.7.

  29. Fig.8b: Seasonal dependence of the ACSS over Indo-Pacific tropical bands (10S-10N) for lead 4, 5, and 6 months. Contour interval = 0.1, shading areas start from 0.7.

  30. Fig.9a: Area-averaged ACSS of forecasted monthly-mean SSTA for lead 1-to-6 month at 12 calendar month

  31. Fig.9b: Area-averaged RMSE of forecasted monthly-mean SSTA for lead 1-to-6 month at 12 calendar month

  32. SSTA Predictability Using SIO and PS SLPA as Secondary Predictors • In addition to the influences of remote ENSO teleconnection,SSTA in a given location can also be affected by local air-sea interaction • Positive feedback between the anomalous anticyclone (cyclone) and the east-west SST gradient intensifies air-sea coupling over SIO during growing El Nino (La Nina) episodes and maintains this coupled mode in the WNP during decaying El Nino (La Nina) (Wang et al., 2003)

  33. Cluster 2 Cluster 7 Fig.10a: The composites of SLPA during the developing El Nino (left panels), and La Nina (right panels) events. Shading areas denote local significance greater than 5% confidence level based on normal-Z test.

  34. Cluster 4 Cluster 1 Fig.10b: The composites of SLPA during the decaying El Nino (left panels), and La Nina (right panels) events. Shading areas denote local significance greater than 5% confidence level based on normal-Z test.

  35. Fig.11a: Seasonal dependence of the RMSE over tropical Pacific (10S-10N) for lead 1,2, and 3 months. The predictor is PSLPA (120E-150E, Eq-20N). Contour interval = 0.1C, shading areas start from 0.6C.

  36. Fig.11b: Seasonal dependence of the ACSS over tropical Pacific (10S-10N) for lead 1,2, and 3 months. The predictor is PSLPA (120E-150E, Eq-20N). Contour interval = 0.1, shading areas start from 0.5.

  37. Fig.12a: ACSS of SSTA prediction at lead 3-month using SIO (75E-120E,Eq-20S) plus PS (120E-150E, Eq-20N) SLPA as predictor. Contour interval = 0.1, shading areas start from 0.5.

  38. Fig.12b: RMSE of SSTA prediction at lead 3-month using SIO (75E-120E,Eq-20S) plus PS (120E-150E, Eq-20N) SLPA as predictor. Contour interval = 0.1C, shading areas start from 0.4C.

  39. Fig.13: RMSE of SSTA prediction at lead 3-month using ENSO-related SIO (75E-120E,Eq-20S) plus PS (120E-150E, Eq-20N) SLPA as predictor. Contour interval = 0.1C, shading areas start from 0.4C.

  40. Summary 1. Reasonable skills with ACSS > 0.6 and RMSE < 0.5C at lag 6 months are found over central tropical Indo-Pacific and Caribbean Sea. 2. Skills are highly seasonal dependent. 3. Forecast barriers are located in Nino1+2 domain during boreal spring (ocean dynamics) and mid-latitude storm tracks during late summers (internal atmospheric forcing). 4. Using SLPA over PS domain as predictor alone does NOT improve SSTA prediction over Nino domain － skill still cannot penetrate spring barrier. 5. However, local SSTA prediction up to lag 3-month over eastern coast of Africa (SONDJ) and Kuroshio Extension (SONDJ and AM) (northwestern quarter of SLPA predictors) is improved when SLPA over PS and SIO domains are used as predictor.

  41. Fig.2: The 6-month SSTA forecast starting from 2003/10 to 2004/03. Contour interval = 0.25C.

  42. The End

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