4.7.12 Correlation Coefficient (COCO)

This function addresses two fundamental issues in cyclostratigraphy and paleoclimatology: identification of astronomical forcing in sequences of stratigraphic cycles, and accurate evaluation of sedimentation rates.

The technique considers these issues part of an inverse problem and estimates the product-moment correlation coefficient between the power spectra of astronomical solutions and paleoclimate proxy series across a range of test sedimentation rates. The number of contributing astronomical parameters in the estimate is also considered.

Our estimation procedure tests the hypothesis that astronomical forcing had a significant impact on proxy records. The null hypothesis of no astronomical forcing is evaluated using a Monte Carlo simulation approach.

Details are included in (Li et al., 2018c).

Step 1: settings for generating a target power spectrum

Select a depth series (interpolated, detrended), select Timeseries --> Correlation Coefficient menu

Note: the data series must have a unit in meter.

Type the approximate middle age for the depth series, the unit is million years ago (Ma).

Target frequency ranges from 0 cycle/kyr to the given “MAX frequency”. Default values are recommended for the depth series with age less than 250 Ma.

For the depth series older than 250 Ma, the MAX frequency may be set to 0.08. This is because the precession cycle can be very short than 16 kyr.

Step 2: astronomical solution [optional]

If the age of the data in Ma is larger than 249 Ma, users need to select which astronomical solution should be used.

• 1 = Berger89 solution (Berger et al., 1989),

• 2 = Laskar 2004 solution (Laskar et al., 2004),

• 3 = user-defined solution and the second box should be filled by 7 astronomical periods.

Online resource for user-defined astronomical parameters may be found at http://nm2.rhul.ac.uk/wp-content/uploads/2015/01/Milankovitch.html (Waltham, 2015).

Step 3: settings for generating data power spectrum

• MIN sedimentation rate (cm/kyr): This default value may represent the detection limit of COCO.
• MAX sedimentation rate (cm/kyr): This default value may represent the detection limit of COCO.
• STEP sedimentation rate (cm/kyr): tested sedimentation rates range from MIN to MAX, with a step of STEP cm/kyr.

In the following example, the tested sed. rates are 1, 1.5, 2, 2.5, 3, …, 29.5, and 30 cm/kyr.

• Number of simulations: 200-600 simulations are suggested for an initial run. And 2000 simulations generate publication-quality results, however, 5000, or 10000 simulations are even better.

• Remove red noise: 0 = no removing (recommended if the power spectrum is not “red”); else, removing red noise:

1 = power spectrum / AR(1) series and those less than AR(1) series are set to 0;

2 = power spectrum - AR(1) series and those less than 0 are set to 0 (Default, the best option for the time series with a “red” spectrum).

3 = power spectrum – robust AR(1) series and those less than 0 are set to 0.

• Split series: 1 (default), 2, 3. If a number of “2” is used, the series will be split into 2 slices.

Click the OK button, Monte Carlo simulation steps can be displayed in the Command Window of MatLab.

A log file will be generated recording all parameters used in the correlation coefficient analysis.