Since CM4 has zero core field coefficients above degree 13, we supplement the model with synthetic coefficients at those degrees.
For the computation of the synthetic coefficients, we use with after Pais and Jault (2008), as suggested by Lesur et al. (2008), and randomly set for each coefficient.
This formulation of synthetic coefficients is such that they vary around zero mean with a time constant of (S l))-1/2 year.
For LMF = 18, three results are plotted in accordance with different sets of the synthetic coefficients and (14 = l = 18) generated using Eqs.
Figures 10(a) and 11(a) show three results of non-advective SV obtained using three different sets of MF and SV consisting of CM4 and synthetic coefficients up to degree LMF= 18.
The definitions of R(l) and S l) are consistent with the synthetic coefficients averaged in time; their time-averaged squares,, give statistical expected variances of in accordance with the power spectrum R(l) (they are assumed to be uncorrelated to one another).
The northern gravity gradient changes are evaluated from the derivative of the associate Legendre function according to the spherical harmonic expansion of Earth's gravity field (e.g., Li and Shen 2011), based on the model and GRACE-synthetic SH coefficients, respectively.
The path was generated using Morgan fingerprint, Tanimoto coefficient, and synthetic accessibility filter turned on.
Black dots and red vertical lines represent maximum cross-correlation coefficients and synthetic lag times, τ syn, respectively.
The 1-D simulations were conducted without recourse to synthetic algorithms utilizing coupling coefficients under very large temperature gradients leading to results that differ somewhat from some theories including that of RLL for harmonic potentials, that feature single particle thermostats with coupling coefficients.
