Fig. 1
Schematic of the two-season model. Note that represents the temperature anomaly at the start of winter in year i−1.
Table 1. Variables and parameters in the two-season model
T Si Temperature anomaly at the end of summer iT Wi Temperature anomaly at the end of winter iQ Si Summer atmospheric forcing anomaly in year iQ Wi Winter atmospheric forcing anomaly in year iσ QW Winter forcing standard deviation20Wm−2σ QS Summer forcing standard deviation10Wm−2κ S Summer atmospheric damping rate10Wm−2K−1κ W Winter atmospheric damping rate25Wm−2K−1h S Summer mixed layer depth25mh W Winter mixed layer depth250mf S Summer attenuation0.22f W Winter attenuation0.68rh S/ h W 0.1γFraction of sequestered winter anomaly1ηFraction of winter anomaly influencing summer layer1ρ0Ocean density1027 Kg m−3c p Specific heat4028 JKg−1K−1
Fig. 2
(a) Dependence of the summer attenuation factor f S on the damping rate κ S , with h S =25 m; (b) dependence of the winter attenuation factor f W on damping rate κ W and depth h W .
Fig. 3
Winter-to-winter correlation Corr(T W , T W−1): (a) dependence on summer damping rate κ S and winter depth h W , (b) dependence on winter damping rate κ W and depth h W .
Table 2. Statistics for standard values in the two-season model
Corr(T W , T W−1)0.63Corr(T W , T S )0.21σ R 0.26 W2m−4σ TW 0.33 K2σ TS 0.79 K2α2.4P W (0)0.49 K2P W (0.5)0.03 K2G W (0)7.3G W (0.5)0.38
Fig. 4
Dependence of rf W on the damping rate κ W and depth h W . The thick line indicates where, for each κ W , rf W =f W1.
Fig. 5
Dependence of rf S /(1−r) on summer damping rate κ S and winter depth h W .
Fig. 6
Dependence of the winter variance on damping rate κ W and depth h W .
Fig. 7
Winter variance components associated with the random forcing. (a) dependence of on winter damping rate κ W and depth h W , (b) likewise for .
Fig. 8
Dependence of the predictable component of winter variance on winter damping rate κ W and depth h W : (a) process flags γ=1, η=0, (b) γ=0, η=1.
Fig. 9
Winter variance (a) dependence on summer damping κ S and winter depth h W , (b) dependence on winter random forcing and depth h W .
Fig. 10
Power spectrum P W (ω) of winter temperature anomalies for standard parameter values and various combinations of process flags. Solid line γ=0, η=0; dashed line γ=0, η=1; thick line γ=1, η=0. Note that the thin solid and dashed lines nearly coincide.
Fig. 11
Power spectrum P W (ω) of winter temperature anomalies. In each case the thin line is P W (ω) for standard values, the thick line for parameter variations. (a) winter damping κ W increased to 40 Wm−2K−1, (b) summer damping κ S increased to 40 Wm−2K−1, (c) winter depth h W doubled to 500 m, (d) winter random forcing σ QW doubled to 40 Wm−2.
Fig. 12
Dependence of summer and winter relations on the winter damping rate κ W and depth h W (a) the summer-to-winter correlation Corr(T W , T S ), (b) the ratio α=σ TS/ σ TW , (c) the component f W rα of Corr(T W , T S ), (d) the component f W f S (1−r)/α of Corr(T W , T S ).
Fig. 13
Dependence of summer and winter relations on the summer damping rate κ S and winter depth h W (a) the summer-to-winter correlation Corr(T W , T S ), (b) the ratio α=σ TS /σ TW , (c) the component f W rα of Corr(T W , T S ), (d) the component f W f S (1−r)/α of Corr(T W , T S ).
Fig. 14
Dependence of summer and winter relations on the winter forcing σ QW and depth h W (a) the summer-to-winter correlation Corr(T W , T S ), (b) the ratio α=σ TS/ σ TW , (c) the component f W rα of Corr(T W , T S ), (d) the component f W f S (1−r)/α of Corr(T W , T S ).
Fig. 15
Parameter dependence of the correlation ratios and . (a) R and (b) R * dependence on κ W and h W ; (c) R and (d) R * dependence on κ S and h W ; (e) R and (f) R * dependence on σ QW and h W .
Fig. 16
Summer-to-summer correlation Corr(T S ,T S−1). (a) dependence on winter damping rate κ W and depth h W , (b) dependence on summer damping rate κ S and winter depth h W , (c) dependence on winter forcing σ QW and depth h W .
Fig. 17
Power spectrum P S (ω) of summer temperature anomalies. In each case the thin line is P S (ω) for standard values, the thick line for parameter variations. (a) winter damping k W increased to 40 Wm−2K−1, (b) summer damping κ S increased to 40 Wm−2K−1, (c) winter depth h W doubled to 500 m, (d) winter random forcing σ QW doubled to 40 Wm−2.