PyReX: A Recursion Based Crossover Detection Algorithm in Python for Along-Track Geophysical Measurements

Abstract

A crossover point is the location of intersection of any two ground tracks charted by multiple platforms (ships, satellite radar and laser altimeters etc.). Detection of crossovers is of prime importance to estimate the discrepancies in the geophysical measurements at the crossover points. Usual approach of crossover detection considers consecutive data points in tracks as segments and checks for intersections between all combinations of these segments. We present a Recursion based crossover detection algorithm in Python (PyReX) for rapid detection of crossovers by avoiding redundant intersection checks. We test the performance of this algorithm using along-track sea surface height measurements from satellite altimeters. We observe that the time taken for flagging a crossover between pair of tracks with N segments each varies as $\log N$ vis-a-vis the $N^2$ dependency associated with the traditional methods. We further demonstrate that PyReX significantly improves the computation speed for high frequency along-track measurements from satellite altimeters and ship-borne gravity data compared to existing algorithms. PyReX is a flexible, open-source code that could be easily customized for variety of applications involving large-scale track-line data sets.