Seasonal dependence of initial error growth for enso in zebiak cane model
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Seasonal dependence of initial error growth for ENSO in Zebiak-Cane model. Yu Yanshan, Duan Wansuo, Xu Hui, Mu Mu LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China. Outline. 1 Motivation. 1 Motivation. Spring Predictability Barrier (SPB).

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Seasonal dependence of initial error growth for ENSO in Zebiak-Cane model

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Seasonal dependence of initial error growth for enso in zebiak cane model

Seasonal dependence of initial error growth for ENSO in Zebiak-Cane model

Yu Yanshan, Duan Wansuo, Xu Hui, Mu Mu

LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China


Outline

Outline

  • 1 Motivation


Seasonal dependence of initial error growth for enso in zebiak cane model

1 Motivation

Spring Predictability Barrier (SPB)

Luo, J.-J., S. Masson, S. Behera, and T. Yamagata 2008: Extended ENSO predictions using a fully coupled ocean-atmosphere model. J. Climate, 21(1), 84-93.


Seasonal dependence of initial error growth for enso in zebiak cane model

Causes:

Using the approach of Conditional Nonlinear Optimal Perturbation (CNOP) to study SPB (Mu et al., 2007)

Different phases

of El Nino

CNOP-type errors

SPB

Some other errors


Seasonal dependence of initial error growth for enso in zebiak cane model

Questions

1 In different phases of El Nino, is the strength of SPB different?

2 Can initial random error cause SPB?

3 What is the spatial pattern of CNOP-type error related to SPB?


Seasonal dependence of initial error growth for enso in zebiak cane model

Outline

  • 1 Motivation

  • 2 Introduction of the approach of Conditional Nonlinear Optimal Perturbation(CNOP)

  • 3 Seasonal dependence of CNOP-type error growth in different phases of El Niño

  • 4 Effect of initial random errors on Spring predictability barrier

  • 5 Spatial patterns and categories of CNOP-type errors

  • 6 Summary


Seasonal dependence of initial error growth for enso in zebiak cane model

1 Introduction of CNOP

Construct a cost function to measure the evolution of initial error at time . CNOP is the initial error that makes cost function maximal, denoted by .

is the non-dimensional initial errors of SSTA and thermocline depth anomaly.

is the constraint condition of initial errors


Seasonal dependence of initial error growth for enso in zebiak cane model

Spring in

growth phase

Spring in

decay phase

2 Seasonal dependence of CNOP-type

error growth in different phases of El Niño

Experiment design:8 El Niño reference states,

8 forecasts for each El Niño reference state.


Seasonal dependence of initial error growth for enso in zebiak cane model

JFM, AMJ, JAS, OND

Slope K of error growth at different seasons. The larger the absolute value of K, the faster the increase of error.


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of CNOP-type error evolution for start month July


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of CNOP-type error evolution for start month October


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of CNOP-type error evolution for start month January


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of CNOP-type error evolution for start month April


Seasonal dependence of initial error growth for enso in zebiak cane model

Growth Phase

When El Niño events are predicted from Jul, Oct and Jan ahead of spring in growth phase, the CNOP-type errors tend to grow aggressively during AMJ, and cause severe prediction errors. There is apparent seasonal dependence of CNOP-type error growth related to SPB.

Decay Phase?


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of CNOP-type error evolution for start month July


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of CNOP-type error evolution for start month October


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of CNOP-type error evolution for start month January


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of CNOP-type error evolution for start month April


Seasonal dependence of initial error growth for enso in zebiak cane model

Differences of CNOP-type error growth between in growth phase of El Niño and in decay phase

  • 1 Average of prediction errors(E-Nino3) caused by CNOP-type errors:

  • Growth phase : 2.4

  • Decay phase : 0.9

  • Seasonal dependence of CNOP-type error growth:

  • Growth phase : Obvious in any case

  • Decay phase : in the case of start month being Oct and Jan, less prominent


Seasonal dependence of initial error growth for enso in zebiak cane model

3 Effect of initial random errors on SPB

Generation of random errors:

Generating a sequence of random numbers satisfying normal distribution at each grid point. Picking up one random number at each grid point to construct a spatial field as a random error.


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of random error evolution for start month July

Small


Seasonal dependence of initial error growth for enso in zebiak cane model

Random error can not cause SPB in growth or decay phase of El Nino events. Spatial pattern of initial error plays an important role in SPB.


Seasonal dependence of initial error growth for enso in zebiak cane model

  • Spatial patterns and categories of CNOP-type errors

Similarity coefficient S is used to measure the similarity between different CNOP-type errors quantitatively, defined as follows:

where , are two CNOP-type errors.

Some CNOP-type errors are similar, and S reaches 0.93. On the other hand , some CNOP-type errors are almost opposite, and S reaches –0.87.


Seasonal dependence of initial error growth for enso in zebiak cane model

Cluster analysis:

2 categories

negative E-nino3

positive E-nino3


Seasonal dependence of initial error growth for enso in zebiak cane model

Cluster analysis:

5 categories

CNOP-type errors are denoted by start months and reference states. The first number is start month , and the latter is reference state.


Seasonal dependence of initial error growth for enso in zebiak cane model

Target observation

Area with large anomaly in CNOP field represents the ‘sensitive area’. Intensifying observations in such areas might be of importance to increase the ENSO prediction skill by the reduction of SPB.


Seasonal dependence of initial error growth for enso in zebiak cane model

Summary

1 In growth phase of El Niño,CNOP-type error could cause severe SPB.

2 In decay phase of El Niño,the seasonal dependence of CNOP-type error growth is less apparent than that in growth phase, and prediction errors are smaller. SPB in decay phase is not as severe as that in growth phase.

3 Initial random error could not cause SPB in growth or decay phase of El Nino.


Seasonal dependence of initial error growth for enso in zebiak cane model

Summary

  • We can classify CNOP-type errors into 2 categories according to their similarity coefficient. The CNOP-type errors have almost opposite spatial patterns between these 2 categories, and could cause predicted Nino3 Index larger or smaller than that of reference states.

  • 5 Spatial patterns of CNOP-type errors may be different when we forecast from different start months, but be less related to the reference states we chose.


Seasonal dependence of initial error growth for enso in zebiak cane model

Thanks


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of random error evolution for start month July


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of random error evolution for start month October


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of random error evolution for start month January


Seasonal dependence of initial error growth for enso in zebiak cane model

In growth phase of El Niño,Slope K of random error evolution for start month April


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of random error evolution for start month July


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of random error evolution for start month October


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of random error evolution for start month January


Seasonal dependence of initial error growth for enso in zebiak cane model

In decay phase of El Niño,Slope K of random error evolution for start month April


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