seasonal dependence of initial error growth for enso in zebiak-cane model
DESCRIPTION
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). - PowerPoint PPT PresentationTRANSCRIPT
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
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1 Motivation
Outline
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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.
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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
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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?
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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
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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
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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
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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.
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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
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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
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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
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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
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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?
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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
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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
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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
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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
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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
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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.
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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
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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.
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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
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Cluster analysis:2 categories
negative E-nino3
positive E-nino3
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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.
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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.
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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