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.

Seawater carbonate chemistry and shell weights of Laternula elliptica, Yoldia eightsi, Nacella concinna and Liothyrella uva during experiments, 2009

Antarctic calcified macroorganisms are particularly vulnerable to ocean acidification because many are weakly calcified, the dissolution rates of calcium carbonate are inversely related to temperature, and high latitude seas are predicted to become undersaturated in aragonite by the year 2100. We examined the post-mortem dissolution rates of aragonitic and calcitic shells from four species of Antarctic benthic marine invertebrates (two bivalves, one limpet, one brachiopod) and the thallus of a limpet shell-encrusting coralline alga exposed to acidified pH (7.4) or non-acidified pH (8.2) seawater at a constant temperature of 4 C. Within a period of only 14-35 days, shells of all four species held in pH 7.4 seawater had suffered significant dissolution. Despite calcite being 35% less soluble in seawater than aragonite, there was surprisingly, no consistent pattern of calcitic shells having slower dissolution rates than aragonitic shells. Outer surfaces of shells held in pH 7.4 seawater exhibited deterioration by day 35, and by day 56 there was exposure of aragonitic or calcitic prisms within the shell architecture of three of the macroinvertebrate species. Dissolution of coralline algae was confirmed by differences in weight loss in limpet shells with and without coralline algae. By day 56, thalli of the coralline alga held in pH 7.4 displayed a loss of definition of the conceptacle pores and cracking was evident at the zone of interface with limpet shells. Experimental studies are needed to evaluate whether there are adequate compensatory mechanisms in these and other calcified Antarctic benthic macroorganisms to cope with anticipated ocean acidification. In their absence, these organisms, and the communities they comprise, are likely to be among the first to experience the cascading impacts of ocean acidification.