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Table 8 Cross-spectral analysis results among the orbital forcings (Laskar et al. 1993) and the orbitally driven δ18O and SST components for three time intervals. Data standardized (mean = 0, standard deviation = 1) and, where necessary, inverted to have the same paleoclimatic polarity (positive values for positive forcing and warming)

From: δ18O and SST signal decomposition and dynamic of the Pliocene-Pleistocene climate system: new insights on orbital nonlinear behavior vs. long-term trend

Time interval

Orbital forcing

Response component

Cross-spectrum freq. (kyr−1)

Cross-spectrum period (kyr)

Coherency

Phase shift

Post-MPT start

Eccentricity

LR04 comp-2 subcomp-1-4, 9-15

0.010742

93

0.72

− 16.65°

− 4.31 kyr

δ18O component lags eccentricity

SST comp-2 subcomp-1-4

0.010742

93

0.70

− 01.70°

− 0.44 kyr

SST component lags eccentricity

Obliquity

LR04 comp-3-4

0.024414

41

0.93

− 65.20°

− 7.42 kyr

δ18O component lags obliquity

SST comp-3-4

0.024414

41

0.68

− 23.78°

− 2.71 kyr

SST component lags obliquity

Precession

LR04 comp-5-7

0.041992

24

0.78

− 74.50°

− 4.93 kyr

δ18O component lags precession

SST comp-5-7

0.041992

24

0.72

− 53.24°

− 3.52 kyr

SST component lags precession

ONHG-MPT start

Eccentricity

LR04 comp-2 subcomp-1-4, 9-15

0.010742

93

0.47

− 27.57°

− 7.13 kyr

δ18O component lags eccentricity

SST comp-2 subcomp-1-4

0.010742

93

0.45

− 21.37°

− 5.53 kyr

SST component lags eccentricity

Obliquity

LR04 comp-3-4

0.024414

41

0.98

− 50.79°

− 5.78 kyr

δ18O component lags obliquity

SST comp-3-4

0.024658

41

0.95

− 46.85°

− 5.28 kyr

SST component lags obliquity

Precession

LR04 comp-5-7

0.044678

22

0.89

− 57.37°

− 3.57 kyr

δ18O component lags precession

SST comp-5-7

0.042236

24

0.28

− 119.35

− 7.85 kyr

SST component lags precession

Pre-ONHG

Eccentricity

LR04 comp-2 subcomp-1-4, 9-15

0.009766

102

0.32

− 01.48°

− 0.42 kyr

δ18O component lags eccentricity

SST comp-2 subcomp-1-4

0.010742

93

0.13

+ 07.06°

1.83 kyr

SST component leads eccentricity

Obliquity

LR04 comp-3-4

0.024414

41

0.95

− 36.02°

− 4.10 kyr

δ18O component lags obliquity

SST comp-3-4

0.024414

41

0.81

− 30.42°

− 3.46 kyr

SST component lags obliquity

Precession

LR04 comp-5-7

0.042480

24

0.42

− 88.11°

− 5.76 kyr

δ18O component lags precession

SST comp-5-7

0.042480

24

0.59

− 87.60°

− 5.73 kyr

SST component lags precession