Supporting Information
Giannakis and Majda 10.1073/pnas.1118984109
Movie S1. Spatio-temporal patterns ∑k x~ kt of the upper 300 m temperature anomaly field (annual mean subtracted at each gridpoint, color-coded in °C)
evaluated using [9] and [1] for a 100-y portion of the dataset. (A) Raw data. (B) The PDO mode from SSA. (C–F) NLSA patterns using (C) the annual modes,
k ∈ f1;2g (see Figs. 1 and 2); (D) The leading-low-frequency (PDO) mode, k ¼ 3; (E) The semiannual modes, k ∈ f6;7g; (F) The leading two intermittent (Kuroshio) modes, k ∈ f9;10g. The starting time of this animation is the same as in Fig. 2. PDO, Pacific Decadal Oscillation; SSA, singular spectrum analysis.
Movie S1 (MP4)
A
B
C
D
Movie S2. 1,000-d trajectories for the zonal modes fx 1 ;x 4 g in (A) the full model (Table S1); (B–D) reduced models constructed by projection onto the NLSA
modes uk from [9].
Movie S2 (MP4)
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Table S1. Governing equations and parameter values of the sixmode low-order atmospheric model; after Crommelin and Majda
(1)
x 1 ¼ 0.95
b ¼ 0.5
β ¼ 1.25
pffiffi
2
2
x_ 1 ¼ γ 1 x 3 − Cðx 1 − x 1 Þ
x_ 2 ¼ −ðα1 x 1 − β1 Þx 3 − Cx 2 − δ1 x 4 x 6
x_ 3 ¼ ðα1 x 1 − β1 Þx 2 − γ 1 x 1 − Cx 3 þ δ1 x 4 x 5
x_ 4 ¼ γ 2 x 6 − Cðx 4 − x 4 Þ þ ϵðx 2 x 6 − x 3 x 5 Þ
x_ 5 ¼ −ðα2 x 1 − β2 Þx 6 − Cx 5 − δ2 x 4 x 3
x_ 6 ¼ ðα2 x 1 − β2 Þx 5 − γ 2 x 4 − Cx 6 þ δ2 x 4 x 2
2
−1
αm ¼ 8 π 2 4mm2 −1 bbþm
2
þm2
pffiffi
2
2
þ1
δm ¼ 6415π2 bb−m
2
2
pffiffi þm
ϵ ¼ 165π 2
x 4 ¼ −0.76095
C ¼ 0.1
γ ¼ 0.2
2
βm ¼ b2βb
2
þmp
ffiffi
2b
γ m ¼ γ 4m4m
2 −1 π
pffiffi
2b
4m3
γ m ¼ γ 4m2 −1 πðb2 þm
2Þ
1 Crommelin DT, Majda AJ (2004) Strategies for model reduction: Comparing dierent optimal bases. J Atmos Sci 61:2206–2217.
Other Supporting Information Files
SI Appendix (PDF)
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