UAW Jul 2008

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

UAW Jul 2008

1 Motivation

Outline

UAW Jul 2008

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.

UAW Jul 2008

Causes:

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

CNOP-type errors

SPB

Some other errors

Different phases

of El Nino

UAW Jul 2008

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?

UAW Jul 2008

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

Outline

UAW Jul 2008

1 Introduction of CNOP

0 10 2

|| ||( ) max || '( ) ||

uJ u T

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 .

0u

' '0 1 0 2 0( , )u wT w h

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

is the constraint condition of initial errors 0 1|| ||u

UAW Jul 2008

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.

Spring in

growth phase

Spring in

decay phase

UAW Jul 2008

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.

UAW Jul 2008

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

  JAS OND JFM AMJ E-Nino3

R1Jan 1.77 1.21 3.46 6.54 -2.23

R2Jan 1.82 1.03 3.13 4.77 -1.79

R1Apr 1.05 0.32 1.54 5.32 -1.60

R2Apr 1.32 0.54 1.29 5.62 -1.64

R1Jul 1.89 2.60 3.57 5.00 -2.01

R2Jul 2.33 3.65 4.17 5.12 -2.44

R1Oct 1.63 1.45 1.77 4.05 -1.54

R2Oct 1.95 5.07 3.02 4.76 2.53

UAW Jul 2008

  OND JFM AMJ JAS E-Nino3

R1Jan 1.58 1.07 8.91 5.88 -2.99

R2Jan 1.53 2.02 8.19 5.18 -2.88

R1Apr 1.10 1.34 5.32 6.48 -2.69

R2Apr 2.03 1.47 7.61 4.89 -2.66

R1Jul 1.71 2.31 6.16 5.01 -2.63

R2Jul 1.78 2.80 7.04 2.83 -2.41

R1Oct 1.92 1.53 5.53 5.13 -2.31

R2Oct 1.96 2.66 8.34 8.00 -3.55

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

UAW Jul 2008

  JFM AMJ JAS OND E-Nino3

R1Jan 1.58 6.44 9.33 1.51 -3.38

R2Jan 1.30 5.74 8.72 1.80 -3.15

R1Apr 1.35 3.92 7.69 4.81 -3.32

R2Apr 1.50 6.00 10.03 1.66 -3.23

R1Jul 1.40 5.01 8.07 2.05 -2.98

R2Jul 0.65 2.36 3.57 2.14 1.71

R1Oct 1.97 4.52 7.24 0.84 -2.37

R2Oct 2.15 6.25 9.78 0.81 -3.21

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

UAW Jul 2008

  AMJ JAS OND JFM E-Nino3

R1Jan 2.91 6.23 6.11 -0.88 -2.24

R2Jan 1.93 5.08 8.87 -1.33 -2.18

R1Apr 2.48 5.64 6.61 1.23 -2.64

R2Apr 2.93 8.30 9.02 -3.94 -2.28

R1Jul 2.29 4.94 4.39 0.26 -1.97

R2Jul 1.65 3.62 2.89 -0.54 1.34

R1Oct 1.60 5.04 3.62 3.44 -2.53

R2Oct 1.66 3.83 0.59 -1.12 -0.41

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

UAW Jul 2008

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.

Growth Phase

Decay Phase?

UAW Jul 2008

  JAS OND JFM AMJ E-Nino3

R1Jan 2.52 2.37 1.42 5.66 -2.00

R2Jan 2.66 3.42 3.22 4.45 -2.37

R1Apr 2.53 2.79 1.28 5.11 -2.26

R2Apr 2.64 1.28 -0.95 2.34 1.10

R1Jul 2.28 2.68 1.89 4.35 -1.95

R2Jul 1.45 2.01 1.59 2.59 1.25

R1Oct 1.23 0.69 -0.24 2.41 -0.85

R2Oct 1.49 0.60 -0.21 2.30 -0.83

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

UAW Jul 2008

  OND JFM AMJ JAS E-Nino3

R1Jan 0.61 0.28 2.78 3.57 1.31

R2Jan 0.70 0.44 2.60 3.44 1.14

R1Apr 0.92 0.84 4.02 4.08 -1.69

R2Apr 0.67 -0.28 0.95 0.89 -0.20

R1Jul 0.66 0.33 2.59 3.35 1.36

R2Jul 1.07 1.45 3.98 -1.83 -0.54

R1Oct 0.43 0.00 1.24 2.11 0.80

R2Oct 0.54 0.09 1.45 0.33 0.36

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

UAW Jul 2008

  JFM AMJ JAS OND E-Nino3

R1Jan 0.64 2.08 3.34 -1.16 0.68

R2Jan 2.20 5.31 -1.99 0.09 1.10

R1Apr 0.21 1.08 3.31 1.06 0.63

R2Apr 0.59 1.34 1.01 0.24 0.10

R1Jul 0.40 1.99 3.12 0.06 0.84

R2Jul 2.21 3.71 -2.44 6.32 2.04

R1Oct 0.66 0.38 1.03 1.05 0.55

R2Oct 1.17 4.09 -0.30 -0.27 0.81

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

UAW Jul 2008

  AMJ JAS OND JFM E-Nino3

R1Jan 0.70 0.29 1.35 -0.72 -0.08

R2Jan 1.48 1.62 0.87 -0.06 0.41

R1Apr 0.95 2.88 2.15 -2.31 0.08

R2Apr 1.29 2.00 0.63 -0.24 -0.33

R1Jul 2.37 4.34 -0.40 -2.21 -0.36

R2Jul 1.90 0.57 0.87 0.19 0.15

R1Oct 2.10 3.18 -1.18 -0.63 0.23

R2Oct 1.95 2.26 1.17 -0.16 0.35

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

UAW Jul 2008

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

2 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

UAW Jul 2008

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.

UAW Jul 2008

  JAS OND JFM AMJ E-Nino3

R1Jan 1.33 0.30 -0.09 0.76 -0.423

R2Jan 1.04 0.29 0.05 -0.16 0.134

R1Apr 0.30 0.14 0.11 0.34 0.069

R2Apr 0.68 0.02 -0.32 0.05 -0.006

R1Jul 0.59 -0.04 -0.11 0.99 -0.302

R2Jul -0.05 0.22 0.06 0.40 -0.193

R1Oct 0.77 1.08 -0.34 -0.56 -0.138

R2Oct -0.21 -0.05 -0.07 0.02 0.008

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

Small

UAW Jul 2008

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.

UAW Jul 2008

4 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.

1 2

1 2

,

|| |||| ||

u uS

u u

1u

2u

UAW Jul 2008

Cluster analysis:2 categories

negative E-nino3

positive E-nino3

UAW Jul 2008

Cluster analysis:5 categories

category Samples in each category

1 4R1Jan, 4R2

Jan, 4R1Apr, 4R2

Apr, 4R1Jul, 4R1

Oct, 4R2Oct, 7R1

Jan

2 10R1Jan, 10R2

Jan, 10R2Apr, 10R1

Jul, 10R2Jul, 10R1

Oct, 10R2Oct

3 7R2Jan, 7R1

Apr, 7R2Apr, 7R1

Jul, 7R2Jul, 7R1

Oct

4 1R1Jan, 1R2

Jan, 1R1Apr, 1R2

Apr, 1R1Jul, 1R1

Oct, 1R2Oct, 10R1

Apr

5 1R2Jul, 4R2

Jul, 7R2Oct

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

UAW Jul 2008

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.

UAW Jul 2008

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.

UAW Jul 2008

4 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.

Summary

UAW Jul 2008

UAW Jul 2008

  JAS OND JFM AMJ E-Nino3

R1Jan 1.33 0.30 -0.09 0.76 -0.423

R2Jan 1.04 0.29 0.05 -0.16 0.134

R1Apr 0.30 0.14 0.11 0.34 0.069

R2Apr 0.68 0.02 -0.32 0.05 -0.006

R1Jul 0.59 -0.04 -0.11 0.99 -0.302

R2Jul -0.05 0.22 0.06 0.40 -0.193

R1Oct 0.77 1.08 -0.34 -0.56 -0.138

R2Oct -0.21 -0.05 -0.07 0.02 0.008

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

UAW Jul 2008

  OND JFM AMJ JAS E-Nino3

R1Jan 1.45 0.38 0.06 0.16 0.067

R2Jan 0.87 0.27 -0.01 -0.4 0.073

R1Apr 0.32 0.05 -0.2 0.08 0.098

R2Apr 0.54 -0.19 0.27 1.95 -0.455

R1Jul 0.4 -0.11 0.17 0.24 -0.158

R2Jul -0.12 0.06 0.58 0.45 -0.242

R1Oct 0.81 0.09 0.32 0.65 -0.260

R2Oct 0.76 0.17 1.52 1.58 -0.761

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

UAW Jul 2008

  JFM AMJ JAS OND E-Nino3

R1Jan 0.74 0.53 1.65 0.79 -0.670

R2Jan 0.49 0.53 1.24 0.44 -0.480

R1Apr 0.13 0.29 0.62 0.41 -0.299

R2Apr 0.37 0.03 0.68 1.71 -0.414

R1Jul 0.22 0.46 0.62 0.39 -0.352

R2Jul -0.16 0.53 0.83 0.88 -0.457

R1Oct 0.48 0.13 0.84 -0.53 0.094

R2Oct 0.51 0.30 1.01 -0.53 0.035

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

UAW Jul 2008

  AMJ JAS OND JFM E-Nino3

R1Jan 0.93 0.98 0.28 -0.75 -0.200

R2Jan 0.53 0.08 0.28 -0.15 -0.122

R1Apr 0.11 0.12 0.38 -0.18 -0.071

R2Apr 0.3 0.88 1.73 0.61 -0.545

R1Jul 0.3 0.74 0.25 -0.13 -0.263

R2Jul 0.11 0.99 1.34 0.75 -0.520

R1Oct 0.36 0.44 -0.23 -0.36 -0.001

R2Oct 0.34 0.38 -0.36 -0.24 0.025

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

UAW Jul 2008

  JAS OND JFM AMJ E-Nino3

R1Jan 0.51 -0.16 -0.22 0.44 0.106

R2Jan 0.47 0.46 0.12 1.26 -0.541

R1Apr 0.00 0.19 -0.19 -0.01 -0.048

R2Apr 0.46 1.34 0.66 2.02 -0.820

R1Jul 0.20 0.30 -0.38 -0.16 -0.015

R2Jul 0.21 0.88 0.75 -0.10 -0.286

R1Oct 0.30 0.06 -0.17 0.02 -0.093

R2Oct 0.44 0.04 -0.27 0.15 -0.109

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

UAW Jul 2008

  OND JFM AMJ 0.34 E-Nino3

R1Jan 0.48 -0.11 0.38 0.19 -0.251

R2Jan 0.45 0.24 0.59 1.16 -0.122

R1Apr 0.02 0.02 0.51 14.5 -0.410

R2Apr 0.4 0.45 2.85 0.31 -0.062

R1Jul 0.15 -0.04 0.08 -0.27 -0.165

R2Jul 0.23 0.18 0.29 0.75 0.026

R1Oct 0.22 0.09 0.49 0.69 -0.359

R2Oct 0.39 0.08 0.84 0.34 -0.380

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

UAW Jul 2008

  JFM AMJ JAS OND E-Nino3

R1Jan 0.51 0.49 1.13 -0.29 -0.281

R2Jan 0.43 0.82 0.46 -0.53 -0.199

R1Apr -0.05 0.87 1.50 -0.82 -0.216

R2Apr 0.36 2.53 15.27 -15.09 -0.300

R1Jul 0.20 1.13 1.86 -0.78 -0.437

R2Jul 0.34 0.38 -0.12 0.02 0.060

R1Oct 0.45 1.89 1.81 -0.53 -0.594

R2Oct 0.67 2.11 1.03 -0.25 0.555

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

UAW Jul 2008

  AMJ JAS OND JFM E-Nino3

R1Jan 0.77 1.57 0.94 -1.13 0.205

R2Jan 0.71 0.62 0.37 -0.43 0.139

R1Apr 0.47 1.74 -0.43 -1.15 -0.021

R2Apr 1.08 0.62 -0.39 -0.32 0.027

R1Jul 0.78 1.56 -0.03 -0.98 -0.114

R2Jul 0.7 0.02 0.09 -0.26 -0.018

R1Oct 1.02 1.13 -0.23 -0.53 -0.024

R2Oct 1.22 1.18 0.38 -1.48 0.097

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