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.

Stress-tolerant corals of Florida Bay are vulnerable to ocean acidification

In situ calcification measurements tested the hypothesis that corals from environments (Florida Bay, USA) that naturally experience large swings in pCO2 and pH will be tolerant or less sensitive to ocean acidification than species from laboratory experiments with less variable carbonate chemistry. The pCO2 in Florida Bay varies from summer to winter by several hundred ppm roughly comparable to the increase predicted by the end of the century. Rates of net photosynthesis and calcification of two stress-tolerant coral species, Siderastrea radians and Solenastrea hyades, were measured under the prevailing ambient chemical conditions and under conditions amended to simulate a pH drop of 0.1-0.2 units at bimonthly intervals over a 2-yr period. Net photosynthesis was not changed by the elevation in pCO2 and drop in pH; however, calcification declined by 52 and 50 % per unit decrease in saturation state, respectively. These results indicate that the calcification rates of S. radians and S. hyades are just as sensitive to a reduction in saturation state as coral species that have been previously studied. In other words, stress tolerance to temperature and salinity extremes as well as regular exposure to large swings in pCO2 and pH did not make them any less sensitive to ocean acidification. These two species likely survive in Florida Bay in part because they devote proportionately less energy to calcification than most other species and the average saturation state is elevated relative to that of nearby offshore water due to high rates of primary production by seagrasses.