Supplementary Materials to Alternating southern and northern Hemisphere Climate Response during the past 35 Million Years.

Transcription

1 GSA Data Repository Supplementary Materials to Alternating southern and northern Hemisphere Climate Response during the past 35 Million Years. David De Vleeschouwer 1, Maximilian Vahlenkamp 1, Michel Crucifix and Heiko Pälike 1 1 MARUM Center for Marine Environmental Science, Universität Bremen, Germany. ddevleeschouwer@marum.de Georges Lemaître Centre for Earth and Climate Research, Earth and Life Institute, Université catholique de Louvain, Belgium. CONSTRUCTION OF THE MEGASPLICE The nine δ18o benthic records that are used in the megasplice (Fig. 1) were selected with the aim of maximizing time-resolution throughout. All of the individual records have been originally published with an astronomically calibrated age-depth model (Suppl. Table DR1). We adopted all of those original age-depth models, except for Site 98. At that site, Hodell et al. (001) used an older astronomical solution (La90[1,1]; Laskar, 1990) to astronomically tune their δ 18 O benthic data, and Andersson and Jansen (003) employed a biostratigraphic age model. We revised the original site 98 age-depth models by tuning the δ 18 O benthic data to La004 obliquity (Laskar et al., 004; Suppl. Tables DR-DR3). With this revision, we ensure that all δ 18 O benthic records utilize the La004 astronomical solution for the development of their respective astronomically calibrated chronologies. The astronomical targets that the respective authors used in the tuning process of each record are provided in Suppl. Table DR1. The disadvantage of the megasplice, compared to δ 18 O benthic compilations or stacks (see main article for definitions), is that data from single sites do not only reflect whole-ocean conditions, but also contain a regional and local component. To account for this regional component, we take different isotope trends in individual ocean

2 basins into account (Suppl. Table DR1), using the largest basin -the Pacific Ocean- as the reference. For the North and South Atlantic basins, we consider the isotope trends as shown in Fig. 6 of Cramer et al. (009). For the Walvis Ridge Sites 164 and 167, however, we use the site-specific corrections calculated by Bell et al. (014). The final step in the construction of the megasplice consists of the establishment of the most suitable positions to transition between records (Suppl. Figure DR, Suppl. Table DR1), so as to ensure smooth transitions and to maximize temporal resolution. The switch from Site 98 to Site 164, for example, is put in the older portion of their overlapping interval, so to maximize the use of the higher-resolution Site 164 record. Between 0.3 and 0.0 Ma, two switches occur in a relatively short time interval. These switches do not influence the overall million-year-scale features of the megasplice, as the Site 1090 record does not exhibit major offsets with Site 1337 in its younger part, nor with Site 96 in its older part (Suppl. Fig. DR). This implies that the rapid decrease in δ18o benthic around 0. Ma in the megasplice is a real reflection of paleoclimate change, rather than an artifact of the construction of the megasplice. The same goes for the rapid increase in δ18o benthic in the megasplice between 0.0 and 19.8 Ma. In that same interval, however, one can observe highfrequency offsets between the Site 1090 and Site 1337 records. These offsets are examples of differences in δ18o benthic variability between records from different basins on short (10 4 yr) timescales. This high-frequency variability is not corrected for by the smooth isotopic trends between ocean basins by Cramer et al. (009) and Bell et al. (014). The result, the megasplice, contains 1114 δ 18 O benthic measurements with an average temporal resolution of.89 kyr. 55 GAUSSIAN PROCESS

3 We use the La004 astronomical solution (Laskar et al., 004) to seek the astronomical configuration (obliquity, sin, cos that corresponds to each δ 18 O benthic measurement in the megasplice, with being the eccentricity of the Earth s orbit and being the geocentric longitude of the perihelion. This definition implies that the longitude of the perihelion is measured from the vernal equinox, and the Earth thus reaches perihelion during the northern hemisphere (NH) summer half year when sin 0 and vice versa. Perihelion is reached in March when cos 1 and in September when cos 1. It should be noted that various astronomical solutions (Berger, 1978; Laskar et al., 004) use a heliocentric definition of, which differs 180 from the geocentric definition. Data points are considered as noisy observations in a 4-dimensional space, spanning time (t), climatic precession ( sin and cos ), and obliquity (). Variations of benthic oxygen isotopic ratios are supposed to vary smoothly within this space. One approach consists in modeling this dependency as a Gaussian process (Rasmussen and Williams, 005). Gaussian processes are routinely used for geospatial interpolation (this is kriging; Cressie, 1993) but they are also used for the analysis of computer experiments (Kennedy and O'Hagan, 000). The formalism used here is largely inspired from Oakley and O Hagan (00). Calibration. Domain axes are standardized as follows:,..,..,.,

4 with, the age of the middle of the time-window to be considered, in Ma. The denominator values in these equations have been chosen, such that the four dimensions vary approximately between - and. The array,,, is the observation taken a point in the time-astronomical space. The smoothness of the latent Gaussian process is determined by a correlation function, between two points of the time-orbital space. Rasmussen and Williams (005) enumerate different correlation functions, for simplicity we adopt the squared-exponential decay, which is infinitely differentiable:, exp, where T is the transpose operator,, and is a diagonal metric. The inverse of the diagonal elements are the length scales,,,. The prior mean of the process is a linear regression of the position in the time-astronomical space, i.e., 1,, and have the same number of components. The posterior mean and variance, assuming uniform priors for and log σ are known and given, e.g., in Oakley and O Hagan (00):, where A is the matrix of correlation functions calculated between data points, is the vector of correlation functions computed between the position of the data point and the position of the observations in the phase space, is the generalized least squares solution of the regression problem, accounting for the correlation function, and the vector of residuals of this regression. If we assume that the errors due to the measurement process are independent and identically Gaussian-distributed, then the

5 formalism above can be applied, except that a quantity has to be added to the diagonal elements of the matrix A. The parameter is commonly termed the jitter or nugget (Cressie, 1993). The likelihood of the process, given observations, and marginalized over the priors of and σ is given, e.g., in Andrianikis and Challenor (01). Different strategies exist to estimate the length scales and nugget. One simple approach is to maximize the likelihood of the process. With this method, however, length-scales may vary largely between subsections of the record, which may cause interpretation difficulties (maximum likelihood values for the length scales of,, are reported in Suppl. Figures DR5-DR8). We found by trial and error that length scales of, along with the maximum-likelihood estimate of work well. It also reflects our hypothesis that the dependency of the latent process across time and orbital elements has to be smooth enough. We report the standard deviation on Gaussian predictions of δ 18 O benthic for the four time-windows discussed in this paper (Suppl. Fig. DR4) to allow for a visual evaluation of the significance of the reported patterns of δ 18 O benthic to astronomical forcing. Model assessment. Models are assessed by inspection of the residues at the calibration points (checking for Gaussian distribution and independence on inputs) and following a leave-one-out approach, by which observations are being omitted from the calibration phase, and then predicted based on the remaining points. Relevant figures are available in Suppl. Figures DR5-DR8. 1

6 Supplementary Figure DR1: δ 18 O benthic megasplice without labels. The megasplice consists of nine globally distributed benthic oxygen isotope records: IODP/ODP Site 167 and 164 (Bell et al., 014), 98 (Andersson and Jansen, 003; Hodell et al., 001), 1146 (Holbourn et al., 013), 1338 (Holbourn et al., 014), 1337 (Holbourn et al., 015), 1090 (Billups et al., 004), 96 (Pälike et al., 006a) and 118 (Pälike et al., 006b). Supplementary Figure DR: Correlation between the different records used in the megasplice. Red triangles indicate the stratigraphic positions at which the megasplice passes from one record to another. Supplementary Figure DR3: Benthic 18 O response to astronomical forcing between Ma (left panels; 100-kyr world ), and between Ma (right panels; obliquity world ). The highest 18 O benthic gradient in the 100-kyr world occurs along the eccentricity axis (circle s radius on Suppl. Fig. DR3C), whereas the highest 18 O benthic gradient in the obliquity world occurs along the obliquity axis (x-axis on Suppl. Fig. DR3E). Supplementary Figure DR4: Variance analysis applied to the four time-windows discussed in this study. All panels show the standard deviation (1σ) on Gaussian predictions of δ 18 O benthic at cos 0 (upper panels) and 3.5 (lower panels), after subtraction of the observational error. All panels show that the Gaussian model is better constrained for astronomical configurations that occur more frequently than for astronomical configurations that occur sporadically. These panels can be compared to Figures and 3, showing the response of δ 18 O benthic to astronomical forcing, to evaluate the significance of the patterns shown in these figures. Supplementary Figure DR5: Assessment of the Gaussian model applied to the Ma time window, following a leave-one-out approach. Panels on the left side correspond to the roughness lengths setting adopted in the study. Panels on the right

7 side correspond to optimized roughness lengths. (A-G) Scatter plot showing the predicted δ 18 O benthic value for each individual datapoint in the considered timewindow after it has been eliminated from the dataset. (B-H) QQplot and Kolmogorov- Smirnov test to assess the equality between the distribution of residues and a Gaussian distribution. (C-I) Residues between predicted and measured δ 18 O benthic, following a leave-one-out approach, plotted in function of predicted δ 18 O benthic. (D-E-F-J-K-L) Residues between predicted and measured δ 18 O benthic, following a leave-one-out approach, plotted in function of obliquity, e 1 and e. These plots are used to ascertain residues are independent from the input parameters. Supplementary Figure DR6: Assessment of the Gaussian model applied to the Ma time window, following a leave-one-out approach. For a description of individual panels, see the caption of Supplementary Figure DR5. Supplementary Figure DR7: Assessment of the Gaussian model applied to the Ma time window, following a leave-one-out approach. For a description of individual panels, see the caption of Supplementary Figure DR5. Supplementary Figure DR8: Assessment of the Gaussian model applied to the Ma time window, following a leave-one-out approach. For a description of individual panels, see the caption of Supplementary Figure DR5.

8 Fig. DR kyr 41 kyr 100 kyr 405 kyr A Eccentricity - Tilt - Precession B C Megasplice 0 kyr 41 kyr 100 kyr 405 kyr 0 1 Benthic d Plt Pliocene 3 4 Miocene Oligocene Age (Ma) Eo

9 Fig. DR Benthic d 18 O Benthic d 18 O Benthic d 18 O Site 167 Site Site 164 Site Site 98 Site 98 Site Benthic d 18 O.4 Site 1146 Site 1338 Benthic d 18 O Benthic d 18 O Site 1337 Site 1338 Site 1337 Site 1090 Site Benthic d 18 O Site 96 Site Benthic d 18 O Site 1090 Site Age (Ma)

10 Fig. DR3 δ 18 O ( ) A Age (Ma) B perihelion during NH summer δ 18 O ( ) D Age (Ma) E perihelion during NH summer perihelion during SH summer perihelion during SH summer obliquity ( ) obliquity ( ) δ 18 O ( ) δ 18 O ( ) C Feb Mar Apr F Feb Mar Apr 0.0 Jan May 0.0 Jan May e cos(ω) Dec Jun e cos(ω) Dec Jun 0.0 Nov Jul 0.0 Nov Jul Oct Aug Sep Oct Aug Sep

11 Fig. DR Ma Ma Ma Ma obliquity ( ) obliquity ( ) obliquity ( ) obliquity ( ) Mar Mar Mar Mar Feb Apr Feb Apr Feb Apr Feb Apr Jan May Jan May Jan May Jan May e cos(ω) Dec Jun e cos(ω) Dec Jun e cos(ω) Dec Jun e cos(ω) Dec Jun Nov Jul Nov Jul Nov Jul Nov Jul Oct Aug Oct Aug Oct Aug Oct Aug Sep Sep Sep Sep σ uncertainty on

12 Fig. DR δ 18 O benthic ( ) Standard setting of roughness lenghts λ A Sample Quantiles Model Assessment for Ma window: Leave-one-out approach Kolmogorov Sirnov test p-value = Normal Q Q Plot Theoretical Quantiles B δ 18 O benthic ( ) Reoptimized roughness lenghts λ G Sample Quantiles Kolmogorov Sirnov test p-value = Normal Q Q Plot Theoretical Quantiles H C λ = D ε ( ) I λ = 1.5 J ε ( ) λ = E λ = e e F e λ = 1.69 K λ = 1.97 e L

13 Fig. DR Standard setting of roughness lenghts λ A Sample Quantiles Model Assessment for Ma window: Leave-one-out approach Kolmogorov Sirnov test p-value = Normal Q Q Plot B Reoptimized roughness lenghts λ G Sample Quantiles Kolmogorov Sirnov test p-value = Normal Q Q Plot H δ 18 O benthic ( ) Theoretical Quantiles δ 18 O benthic ( ) Theoretical Quantiles C λ = D ε ( ) I λ = 5.84 J ε ( ) λ = E λ = e e F e λ = 1.46 K λ = 1.50 e L

14 Fig. DR δ 18 O benthic ( ) Standard setting of roughness lenghts λ A Sample Quantiles Model Assessment for Ma window: Leave-one-out approach Kolmogorov Sirnov test p-value = Normal Q Q Plot Theoretical Quantiles B δ 18 O benthic ( ) Reoptimized roughness lenghts λ G Sample Quantiles Kolmogorov Sirnov test p-value = 0.66 Normal Q Q Plot Theoretical Quantiles H C λ = D ε ( ) I λ = 45.1 J ε ( ) λ = E λ = e e F e λ = 4.87 K λ = 5.60 e L

15 Fig. DR Standard setting of roughness lenghts λ A Sample Quantiles Model Assessment for Ma window: Leave-one-out approach Kolmogorov Sirnov test p-value = Normal Q Q Plot B Reoptimized roughness lenghts λ G Sample Quantiles Kolmogorov Sirnov test p-value = Normal Q Q Plot H δ 18 O benthic ( ) Theoretical Quantiles δ 18 O benthic ( ) Theoretical Quantiles C λ = D ε ( ) I λ = J ε ( ) λ = E λ = e e F e λ = 1.47 K λ = 1.75 e L

16 Site Lat. Lon. Source Ocean Basin correction Tuning target for age model construction Start (Ma) Stop (Ma) S 1.7 E utions_by_author/bell014/bell txt S.6 E utions_by_author/bell014/bell txt N 15.9 W an/sediment_files/complete/odp98dh-tab.txt South Atlantic Fig. 5c in Bell et al. (014) Alignment to LR04 stack South Atlantic Fig. 5d in Bell et al. (014) Alignment to LR04 stack North Atlantic Fig. 6 in Cramer et al. (009) Retuned to obliquity (La004) in this study (Suppl. Table DR) N 15.9 W North Atlantic Fig. 6 in Cramer et al. (009) Retuned to obliquity (La004) in this study (Suppl. Table DR3) N E Pacific None Tuned to ET target (La004) N W Pacific None Tuned to ET+0.3P target (La004) N 13. W Pacific None Tuned to ET+0.P target (La004) S 8.9 E South Atlantic Fig. 6 in Cramer et al. (009) Tuned to obliquity (La004), with a 7. kyr time lag S 4.9 W North Atlantic Fig. 6 in Cramer et al. (009) Tuned to ETP (La004), with a 6.4 kyr time lagged obliquity component S 8.9 E South Atlantic Fig. 6 in Cramer et al. (009) Tuned to obliquity (La004), with a 7. kyr time lag N E Pacific None Tuned to E+0.5T-0.4P (La004) Supplementary Table DR1: Individual records used in this study to construct the megasplice from IODP/ODP Site 167 (Bell et al., 014), 164 (Bell et al., 014), 98 (Andersson and Jansen, 003; Hodell et al., 001), 1146 (Holbourn et al., 013), 1338 (Holbourn et al., 014), 1337 (Holbourn et al., 015), 1090 (Billups et al., 004), 96 (Pälike et al., 006a), 118 (Pälike et al., 006b). La004 refers to the astronomical solution by Laskar et al. (004); LR04 refers to the benthic oxygen isotope stack by Lisiecki and Raymo (005).

17 Original Age (Ma) Revised Age (Ma) Supplementary Table DR: Update of the age model for Site 98, as published by Hodell et al. (001). The updated age model reflects an astronomical tuning approach to the La004 solution (Laskar et al., 004). The original benthic oxygen isotope time-series was converted to the new age model through linear interpolation between the listed tie-points.

18 Original Age (Ma) Revised Age (Ma) Supplementary Table DR3: Update of the age model for Site 98, as published by Andersson and Jansen (003). The updated age model reflects an astronomical tuning approach to the La004 solution (Laskar et al., 004). The original benthic oxygen isotope time-series was converted to the new age model through linear interpolation between the listed tie-points.

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20 Pälike, H., Norris, R. D., Herrle, J. O., Wilson, P. A., Coxall, H. K., Lear, C. H., Shackleton, N. J., Tripati, A. K., and Wade, B. S., 006b, The Heartbeat of the Oligocene Climate System: Science, v. 314, no. 5807, p Rasmussen, C., and Williams, C., 005, Gaussian Processes for Machine Learning., Cambridge, MA, University Press Group Limited, Adaptive Computation and Machine Learning, 48 p.: