COMPUTATIONAL METHOD
The 15N secular variations are smoothed using a linear fitting where the significance of dots corresponds to the height of a Gaussian Kernel function (i.e. The kernel regression is a non- parametric technique in statistics to estimate the conditional expectation of a random variable,
Ruppert et al. 2003). The bandwidth (h) influences the amount of smoothing and this parameter might be chosen on the basis of the whole dataset structure (Jones et al. 1996).
However, because there is no uniform way to define it, several authors proposed to consider multiple smoothing curves with different h values (the “family approach” to smoothing,
Marron and Chaudhuri 1998). In order to identify which features (increases and/or decreases) are significant, they introduced the SiZer method. The first derivative of each curve is computed and when locally positive or negative at 95% confidence, it is symbolized in red or blue, respectively. When it does not significantly differ from zero, the segment is represented in purple. The resulting SiZer map therefore provides valuable insights about the significant variations recognized at different time-scales, and together with the original data time series can reveal significant evolution of a given parameter through time. It is noteworthy that such an approach has already been successfully used on Quaternary (Erästö and Holmström 2006) and Jurassic (Dera et al. 2011) d18O time series for paleoclimate reconstruction. In order to perform SiZer analyses, based on Kernel regressions, the SizerSM package (copyright, J.S.
Marron 2000-2004) running on the Matlab platform was used. This package is downloadable at: http://www.unc.edu/~marron/marron_software.html.
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