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.

Point clouds of measurements in the Dechen Cave near Iserlohn, Germany

Modeling natural phenomena from 3D information enhances our understanding of the environment. Dense 3D point clouds are increasingly used as highly detailed input datasets. In addition to the capturing techniques of point clouds with LiDAR, low-cost sensors have been released in the last few years providing access to new research fields and facilitating 3D data acquisition for a broader range of applications. This letter presents an analysis of different speleothem features using 3D point clouds acquired with the gaming device Microsoft® Kinect. We compare the Kinect sensor with terrestrial LiDAR reference measurements using the KinFu pipeline for capturing complete 3D objects (< 4m**3). The results demonstrate the suitability of the Kinect to capture flowstone walls and to derive morphometric parameters of cave features. Although the chosen capturing strategy (KinFu) reveals a high correlation (R2=0.92) of stalagmite morphometry along the vertical object axis, a systematic overestimation (22% for radii and 44% for volume) is found. The comparison of flowstone wall datasets predominantly shows low differences (mean of 1 mm with 7 mm standard deviation) of the order of the Kinect depth precision. For both objects the major differences occur at strongly varying and curved surface structures (e.g. with fine concave parts).