Statistical Properties of Closure Phases in SAR Interferometry

Abstract

The concept of closure phases is introduced in Inter-ferometric Synthetic Aperture Radar (InSAR) as a circular summation of three multilooked interferometric phases. Traditionally considered conservative, recent studies have shown real data examples exhibiting non-conservative closure phases resulting from phase noise and geophysical signals. Current literature attributes geophysical closure phases to dielectric variation in media, volumetric scattering in combination with perpendicular baseline, and skewed differential motion. While non-zero closure phases have been studied at local scales, a comprehensive and systematic statistical characterization of closure phases across broader spatial and temporal scales remains lacking. In this study, we present extensive analyses of closure phases across the diverse Iberian Peninsula to provide a general perspective on their occurrence, underscore the limitations of current understanding in explaining the observed signals, and qualitatively explore potential unexplained origins. Our results confirm that statistically significant closure phases are common rather than exceptional, show that their signatures vary across sub-regions depending on local geophysical conditions, and quantify that for the geophysical component, approximately five-sixths of the variance remains unexplained by existing models.