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

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The Development of Statistic Projection Model for the The Development of Statistic Projection Model for the Prediction of Global Sea Surface Temperature Prediction of Global Sea Surface Temperature

Anomalies (GSSTA) at Central Weather BureauAnomalies (GSSTA) at Central Weather Bureau

Shu-Ping, Weng, and Jau-Ming, ChenShu-Ping, Weng, and Jau-Ming, ChenResearch and Development CenterResearch and Development Center

Central Weather BureauCentral Weather Bureau

Bin, WangBin, WangSchool of Ocean and Earth Science and TechnologySchool of Ocean and Earth Science and Technology

International Pacific Research CenterInternational Pacific Research CenterUniversity of HawaiiUniversity of Hawaii

International Workshop on Monthly-to-Seasonal ClimatInternational Workshop on Monthly-to-Seasonal Climate Prediction, National Taiwan Normal Universitye Prediction, National Taiwan Normal University

Taipei, Taiwan 25-26 October 2003 Taipei, Taiwan 25-26 October 2003

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OutlinesOutlines

1.1. Methodology of a SVD-based statistic projection modelMethodology of a SVD-based statistic projection model

2.2. The prediction of global SSTA with a leading time up to six months The prediction of global SSTA with a leading time up to six months －－ A twA tw

o-tier procedure using Nino3.4 SSTA as the primary predictoro-tier procedure using Nino3.4 SSTA as the primary predictor

a. sensitivity test on the progressive method of setting for predicted time wia. sensitivity test on the progressive method of setting for predicted time wi

ndowndow

b. sensitivity test on the method of global domain aggregationb. sensitivity test on the method of global domain aggregation

c. issue of season-dependent forecast skillc. issue of season-dependent forecast skill

3.3. The potential in using SLP anomalies over Southern Indian Ocean (The potential in using SLP anomalies over Southern Indian Ocean (SIO, SIO, Bin Bin

Wang et al. 2003) and Philippine Sea (Wang et al. 2003) and Philippine Sea (PSPS, Bin Wang et al. 2000, 2003) as the , Bin Wang et al. 2000, 2003) as the

secondary predictor to the seasonal prediction of local SSTA over tropical Insecondary predictor to the seasonal prediction of local SSTA over tropical In

do-Pacificdo-Pacific

4.4. Summary Summary

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Methodology of SVD-based Projection Model for Methodology of SVD-based Projection Model for Statistic GSSTA ForecastStatistic GSSTA Forecast

SVD analysisSVD analysis

The arrays The arrays AA and and BB, which store the temporal evolution of predictors (e.g., p, which store the temporal evolution of predictors (e.g., preceding Nino3.4 domain SST) and predictand (e.g., predicted global SST fireceding Nino3.4 domain SST) and predictand (e.g., predicted global SST field) respectively, can be used to construct a covariance matrix eld) respectively, can be used to construct a covariance matrix CC representi representing the relatedness between these two fields:ng the relatedness between these two fields: C = A BC = A BTT (1)(1)

The matrix The matrix CC is then subjected to SVD analysis to produce a pair of orthogo is then subjected to SVD analysis to produce a pair of orthogonal bases of fields nal bases of fields A A and and BB, namely , namely UU and and VV::

C = U W VC = U W VTT (2)(2)

The degree of coupling between The degree of coupling between AA and and BB is quantified in the column vector is quantified in the column vector WW which stores the singular values of matrix which stores the singular values of matrix CC..

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The corresponding time series expansion coefficients of The corresponding time series expansion coefficients of AA and and BB, , EE and and FF, , are obtained by projecting them onto the orthogonal basesare obtained by projecting them onto the orthogonal bases U U and and V V (i.e., left (i.e., left and right singular vectors):and right singular vectors):

E = UE = UTT A A, , F = VF = VTT B B (3)(3)

SVD Projection ModelSVD Projection Model

The prediction scheme is constructed by first building the connection betweThe prediction scheme is constructed by first building the connection between the matrices en the matrices EE and and F F::

F = X EF = X E, which means , which means X = F EX = F E++ (4)(4)

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Since the aim is to build up the transfer function Since the aim is to build up the transfer function RR connecting predictor connecting predictor AA an an

d predictand d predictand BB, , B = R AB = R A. Inserting Eq.(3) and utilizing Eq.(4), the transfer fu. Inserting Eq.(3) and utilizing Eq.(4), the transfer functionnction R R is given by is given by

R = V X UR = V X UTT.. (5)(5)

Making the Hindcast ExperimentMaking the Hindcast Experiment

Once the transfer function Once the transfer function RR is determined from the historic data, for any cur is determined from the historic data, for any cur

rent predictor column vector rent predictor column vector aa, the predictand column vector , the predictand column vector bb is given as is given as

bb = R = R aa. . The calculation of The calculation of R R is based on ‘take-one-out’ cross-validation in is based on ‘take-one-out’ cross-validation in the following hindcast experiments. the following hindcast experiments.

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GSSTA Prediction Using Nino3.4 SSTA as GSSTA Prediction Using Nino3.4 SSTA as PredictorsPredictors

A two-tier Procedure is adoptedA two-tier Procedure is adopted

Step 1 Step 1 －－ use historic Nino3.4 SSTA (previous 6-use historic Nino3.4 SSTA (previous 6-month period) as its own predictor in the future (nmonth period) as its own predictor in the future (next 6-month period)ext 6-month period)

Step 2 Step 2 －－ aggregate the predicted Nino 3.4 SSTA aggregate the predicted Nino 3.4 SSTA to the global SSTA utilizing the transfer function bto the global SSTA utilizing the transfer function built from the concurrent relationship between theuilt from the concurrent relationship between the

mm

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mXk(t1) nYk(t2)lZk(t2)

mCn nCl

SiSj

mUi nVi nPj lQj

iEk=iUm mXk,iFk =iVn nYkT T

jek=jPn nYk, jfk =jQl lZkT T

iFk =iLi iEk, iLi = iFk kEi＋

jfk =jLj jek, jLj = jfk kej＋

nYk =nrm mXk

nrm =nVi iLi iUmT

lZk =lRn nYk

lRn =lQj jLj jPn

T

nYk

Use current Nino SSTA to forecast future Nino SSTA

Aggregates the forecasted Nino SSTA to global SSTA

North’s thumb of ruleNorth’s thumb of rule

Pseudo inverse

Predictor Predictand

SVDSVD

pro

ject

ion

pro

ject

ion

pro

ject

ion

Spatial mapping

lsv rsv rsvlsv

Predictand

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GSSTA Prediction Using Nino3.4 GSSTA Prediction Using Nino3.4 SSTA as PredictorsSSTA as Predictors

An operation scenario of seasonal forecast An operation scenario of seasonal forecast at CWBat CWB

Suppose CWB needs to make seasonal Suppose CWB needs to make seasonal prediction twice a year in both late May and late prediction twice a year in both late May and late November. The AGCM then needs global SST November. The AGCM then needs global SST field as boundary condition by 15 May or 15 field as boundary condition by 15 May or 15 November to perform ensemble runs. The SST November to perform ensemble runs. The SST data available will be the 6-month period of data available will be the 6-month period of NDJFMA (or MJJASO) to predict SSTA in the NDJFMA (or MJJASO) to predict SSTA in the following MJJASO (or NDJFMA).following MJJASO (or NDJFMA).

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Approaches to make prediction up to 6-month leadApproaches to make prediction up to 6-month lead

Express Express :: NDJFMANDJFMA －＞－＞ MM, , JJ, , JJ, , AA, , SS,,OO

UpdateUpdate :: NDJFMANDJFMA －＞－＞ MMDJFMADJFMAM M －＞－＞ JJJFMAJFMAMJ MJ －＞－＞ JJFMAFMAMJJ MJJ －＞－＞ AAMAMAMJJA MJJA －＞－＞ SSAAMJJAS MJJAS －＞－＞ OO

Reserved UpdateReserved Update : : NDJFMANDJFMA －＞－＞ MMNDJFMANDJFMAM M －＞－＞ JJNDJFMANDJFMAMJ MJ －＞－＞ JJNDJFMANDJFMAMJJ MJJ －＞－＞ AANDJFMANDJFMAMJJA MJJA －＞－＞ SSNDJFMANDJFMAMJJAS MJJAS －＞－＞ OO

BlockBlock :: NDJFMANDJFMA －＞－＞ MJJASOMJJASO

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DataData

11. . A blended SST dataset (1950 – 2002) is usedA blended SST dataset (1950 – 2002) is used

Reynolds EOF-reconstructed : 30Reynolds EOF-reconstructed : 30 。。 S - 30S - 30 。。 NN << ＝＝ ERSSERSSTT

GISST2.3b : elsewhereGISST2.3b : elsewhere << ＝＝ HADIHADISSTSST

2. GMSLP 2.1f (U.K. Met. Office, 1950 – 2002)2. GMSLP 2.1f (U.K. Met. Office, 1950 – 2002)

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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.

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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.

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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.

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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.

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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.

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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).

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

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

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Sensitivity tests on the way of domain separationSensitivity tests on the way of domain separation

1. individual ocean basin1. individual ocean basin

2. 102. 10 。。 by 10by 10 。。 Gridded cells around the globeGridded cells around the globe

3. SVD varimax rotation3. SVD varimax rotation

4. 4. global ocean as a wholeglobal ocean as a whole

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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.

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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.

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Season-dependent forecast skillSeason-dependent forecast skill

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11, 12, 1, 2, 3, 4

12, 1, 2, 3, 4, 5

1, 2, 3, 4, 5, 6

2, 3, 4, 5, 6, 7

8, 9,10, 11,12, 1

3, 4, 5, 6, 7, 8

10, 11, 12, 1, 2, 3

9, 10,11, 12, 1, 2

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9,10

6, 7, 8, 9,10,11

7, 8, 9, 10,11,12

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9, 10

6, 7, 8, 9, 10,11

7, 8, 9, 10,11,12

8, 9, 10,11,12, 1

9, 10,11,12, 1, 2

10,11,12, 1, 2, 3

11,12, 1, 2, 3, 4

12, 1, 2, 3, 4, 5

1, 2, 3, 4, 5, 6

2, 3, 4, 5, 6, 7

3, 4, 5, 6, 7, 8

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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.

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Fig.6 (continued)

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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.

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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.

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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.

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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.

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

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

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SSTA Predictability Using SIO and PS SLPA SSTA Predictability Using SIO and PS SLPA as Secondary Predictorsas Secondary Predictors

In addition to the influences of remote ENSO telecoIn addition to the influences of remote ENSO teleconnection,nnection, SSTA in a given location can also be affecSSTA in a given location can also be affected by local air-sea interactionted by local air-sea interaction

Positive feedback between the anomalous anticycloPositive feedback between the anomalous anticyclone (cyclone) and the east-west SST gradient intensifine (cyclone) and the east-west SST gradient intensifies air-sea coupling over SIO during growing El Nino es air-sea coupling over SIO during growing El Nino (La Nina) episodes and maintains this coupled mode (La Nina) episodes and maintains this coupled mode in the WNP during decaying El Nino (La Nina) (Wang in the WNP during decaying El Nino (La Nina) (Wang

et al., 2003et al., 2003) )

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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.

Cluster 2 Cluster 7

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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.

Cluster 4 Cluster 1

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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.

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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.

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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.

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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.

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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.

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SummarySummary

1. Reasonable skills with ACSS > 0.6 and RMSE < 0.5C at lag 6 mo1. Reasonable skills with ACSS > 0.6 and RMSE < 0.5C at lag 6 months are found over central tropical Indo-Pacific and Caribbean nths are found over central tropical Indo-Pacific and Caribbean Sea.Sea.

2. Skills are highly seasonal dependent.2. Skills are highly seasonal dependent.

3. Forecast barriers are located in Nino1+2 domain during boreal 3. Forecast barriers are located in Nino1+2 domain during boreal spring (spring (ocean dynamicsocean dynamics) and mid-latitude storm tracks during l) and mid-latitude storm tracks during l

ate summers (ate summers (internal atmospheric forcinginternal atmospheric forcing).). 4. Using SLPA over PS domain as predictor alone does 4. Using SLPA over PS domain as predictor alone does NOTNOT impro impro

ve SSTA prediction over Nino domain ve SSTA prediction over Nino domain －－ skill still cannot peneskill still cannot penetrate spring barriertrate spring barrier..

5. However, local SSTA prediction up to lag 3-month over eastern 5. However, local SSTA prediction up to lag 3-month over eastern coast of Africa (SONDJ) and Kuroshio Extension (SONDJ and Acoast of Africa (SONDJ) and Kuroshio Extension (SONDJ and AM) (M) (northwestern quarternorthwestern quarter of SLPA predictors) is improved when of SLPA predictors) is improved when SLPA over PS and SIO domains are used as predictor.SLPA over PS and SIO domains are used as predictor.

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

The EndThe End

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