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.

Shipborne ocean color remote sensing

In this paper, modernized shipborne procedures are presented to collect and process above-water radiometry for remote sensing applications. A setup of five radiometers and a bidirectional camera system, which provides panoramic sea surface and sky images, is proposed for the collection of high-resolution radiometric quantities. Images from the camera system can be used to determine sky state and potential glint, whitecaps, or foam contamination. A peak in the observed remote sensing reflectance RRS spectra between 750-780 nm was typically found in spectra with relatively high surface reflected glint (SRG), which suggests this waveband could be a useful SRG indicator. Simplified steps for computing uncertainties in SRG corrected RRS are proposed and discussed. The potential of utilizing "unweighted multimodel averaging," which is the average of four or more common SRG correction models, is examined to determine the best approximation RRS. This best approximation RRS provides an estimate of RRS based on various SRG correction models established using radiative transfer simulations and field investigations. Applying the average RRS provides a measure of the inherent uncertainties or biases that result from a user subjectively choosing any one SRG correction model. Comparisons between inherent and apparent optical property derived observations were used to assess the robustness of the SRG multimodel averaging ap- proach. Correlations among the standard SRG models were completed to determine the degree of association or similarities between the SRG models. Results suggest that the choice of glint models strongly affects derived RRS values and can also influence the blue to green band ratios used for modeling biogeochemical parameters such as for chlorophyll a. The objective here is to present a uniform and traceable methodology for determining ship- borne RRS measurements and its associated errors due to glint correction and to ensure the direct comparability of these measurements in future investigations. We encourage the ocean color community to publish radiometric field measurements with matching and complete metadata in open access repositories.