Code and readme of a MATLAB-based graphical user interface program for computing functionals of the geopotential

We present a novel graphical user interface program GrafLab (GRAvity Field LABoratory) for spherical harmonic synthesis (SHS) created in MATLAB®. This program allows to comfortably compute 38 various functionals of the geopotential up to ultra-high degrees and orders of spherical harmonic expansion. For the most difficult part of the SHS, namely the evaluation of the fully normalized associated Legendre functions (fnALFs), we used three different approaches according to required maximum degree: (i) the standard forward column method (up to maximum degree 1800, in some cases up to degree 2190); (ii) the modified forward column method combined with Horner's scheme (up to maximum degree 2700); (iii) the extended-range arithmetic (up to an arbitrary maximum degree). For the maximum degree 2190, the SHS with fnALFs evaluated using the extended-range arithmetic approach takes only approximately 2-3 times longer than its standard arithmetic counterpart, i.e. the standard forward column method. In the GrafLab, the functionals of the geopotential can be evaluated on a regular grid or point-wise, while the input coordinates can either be read from a data file or entered manually. For the computation on a regular grid we decided to apply the lumped coefficients approach due to significant time-efficiency of this method. Furthermore, if a full variance-covariance matrix of spherical harmonic coefficients is available, it is possible to compute the commission errors of the functionals. When computing on a regular grid, the output functionals or their commission errors may be depicted on a map using automatically selected cartographic projection.

Stable oxygen isotope ratios, calcium carbonate and opal content in late Pliocene sediments of DSDP Hole 75-532 in the Southeast Atlantic (Table 1)

Site 532 on the Walvis Ridge was sampled at 4000- to 800-year intervals from 2.24 to 2.60 Ma, spanning the three large glacial advances of the late Pliocene. An age model was created by correlating the oxygen isotope record to Site 607 with linear interpolations between tie-lines. The resultant age model differs from that in the site reports by more than 800,000 years, due to misidentification of a magnetic boundary. Sedimentation rates varied by an order of magnitude at this site, with minimum accumulation during glacial events. Interglacial intervals were charactrized by high marine production and high summer precipitation on land, while glacials had very low production and arid continental climate. During the large glacial events (Stages 96-100) conditions of low production and continental aridity reached their greatest intensity, but there is no evidence of a permanent mode shift in either marine or terrestrial records. Calcite concentration has a strong variation at obliquity frequencies, with maxima during interglacials, but occasionally shows a large amplitude at precessional frequencies as well, so that high concentrations occur in a few glacial intervals. As a result, color variation is not a reliable guide to glacial-scale cycles at this site. Composition of the phytoplankton assemblage is diverse and highly variable, and we have not been able to distinguish a clear indicator of upwelling-related production. Spectral analysis reveals obliquity and precessional signals in the pollen data, while several diatom records contain combination tones, indicating that these data represent a complicated response to both local and high-latitude forcing.