Improved ensemble-mean forecast skills of ENSO events by a zero-mean stochastic model-error model

of an intermediate coupled model

Jiang Zhu and Fei Zheng

Institute of Atmospheric Physics

Chinese Academy of Sciences

Beijing, China

Outlines• The ENSO model: what it has and what it misses• Sampling the model errors• Building the model-error model stochastically• Improvement of ensemble-mean forecast skills• Ensemble-mean dynamics• Summary

The ENSO model: what it has and what it misses

An intermediate coupled model (Keenlyside and Kleeman, 2002; Zhang et al., 2005) is used for this study:

• Dynamical ocean model

Response of ocean currents and waves from wind forcing

• SSTA budget model

Horizontal and vertical transport/diffusion effects on SST, simple heat flux

• Subsurface temperature anomaly model

A regression from sea level anomaly

• Wind model

A regression from SST gradient

The model can describe the main/classic ENSO mechanism:

• Bjerknes’ positive feedback: positive correlation between SST zonal gradient and westerly wind anomaly;

• Delayed negative feedback: a westerly anomaly can trigger Rossby and Kalvin waves that will be bounced back later from the west and east boundaries and reduce the SST zonal gradient.

The model misses the following processes:

• explicit air-sea heat interactions,

• stochastic atmospheric forcing/MJO,

• extra-tropical cooling and warming,

• Indian Ocean Dipole mode,

• the feedback of cloud and the salinity effect,

• etc.

However the net effect of these missing processes on ENSO is less studied.

Sampling the model errors

• A EnKF data assimilation scheme is developed (a coupled

assimilation scheme, see Zheng and Zhu poster in this workshop);

• The SST data is assimilated into model (1963-1996);

• Lunch a 12-month forecast every month (1963-1996);

• Compare forecasted SST (ensemble mean) to SST observations (f-o);

• Obtain 408 f-o samples for each lead time (1-month, ..12-month);

• Perform EOF analysis for each set of 408 samples (12 sets).

By this method, we assume that the forecast errors are all due to model errors, or in another word, the initial errors are zero.

Results from model error sampling

• Over the multi-decade period, the model errors are of random, zero-mean

(or model is not biased over multi-decade period)

• The random model errors have spatial patterns

• The random model errors have time correlations (scale: several months)

(or the model is biased over interannual time scale)

Building the model-error model stochastically

• A first-order Markov stochastic model is used to modelling the mode error;

• The model error model is only acting on the time coefficients of EOF modes;

• 10 Modes are used;

• The model error model has only one variable: SST anomaly.

Original SSTa model

SSTa error

EOF mode White noise

i: mode index; j: lead time index

Cor

rela

tion

RM

SE

(o C

)

Lead time Lead time

Persistence Persistence

Exp1: Deterministic forecast no initial perturbation no model error

Exp2: Ensemble forecast with initial perturbation no model error

Exp3: Ensemble forecast no initial perturbation with model error

Exp4: Ensemble forecast with initial perturbation with model error

Nino 3.4 index of deterministic and ensemble-mean forecast skills with SST&SLA assimilation

Improvement of ensemble-mean forecast skills

Ensemble-mean dynamics

How does a zero-mean stochastic model-error interact with the nonlinear ENSO model and improve the ensemble-mean forecast?

Nino 3.4 index

Ensemble mean departure caused by 1st mode zero-mean perturbations: Nonlinear term contributions

T’ (+)

Rz

Tw

x

Tu

z

Tw

x

Tu

z

Tw

x

Tu

t

T

z

Tw

- +Wind

< 0

Linear terms (zero-mean) Nonlinear terms

Horizontal pattern induced by a 1st-mode positive perturbation

Wind

Rz

Tw

x

Tu

z

Tw

x

Tu

z

Tw

x

Tu

t

T

Linear terms (zero-mean) Nonlinear terms

z

Tw

+ -

< 0

Horizontal pattern induced by a 1st- mode negative negative perturbation

T’(-)

Forecast case starting at 1997.01

The difference between the ensemble-mean and deterministic forecasts

Summary

• A stochastic model is developed for modeling the model errors of an intermediate coupled model for ENSO prediction;

• The stochastic model-error perturbations have significant impacts on improving the ensemble-mean prediction skills;

• The nonlinear heating mechanism in the tropic air-sea couple system can sum a series of weather time scale random perturbations up to a positive “heating source” over a period of longer time scale;

• The nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which resembles the real world to some extend.

END

THANKS

18-year averaged difference(Ensemble Mean – Deterministic)

Prediction skills of ensemble mean forecast for Nino 3.4 index (1993-2007)