Temporal Closure Signatures in Radar Interferometry

Systematic phase errors induced by processes such as soil and vegetation moisture dynamics impair interferometric synthetic aperture radar (InSAR) displacement measurements. They can manifest as closure errors and as discrepancies between phase history estimates obtained with contrasting algorithms. To advance InSAR deformation estimation algorithms and understand the biases, we need to quantify the temporal characteristics of closure errors. Here, we introduce temporal closure signatures, complete and nonredundant descriptions of the closure errors as a function of time and timescale. Temporal closure signatures are extracted using a suitable basis of the closure covector space, the annihilator of the vector space of consistent phases. Observed Sentinel-1 signatures from two such bases exhibited contrasting seasonal and long-timescale characteristics that covaried with land and vegetation cover. Strong spatial associations of closure signatures with secular and seasonal discrepancies in phase histories estimated from a subset or all interferograms were observed. To interpret these observations, we made predictions using simple interferometric scattering models. Model predictions for seasonally changing vegetation with a long-term drying trend resembled observed closure signatures over scrublands. The model further captured the observed subsidence in the nearest-neighbor relative to the all-interferogram estimate. The simulated deformation estimate deteriorated with the inclusion of long-term interferograms, as was also predicted for subresolution differential motion, but these predictions require validation with empirical data. The observations and simulations illustrate the potential of closure signatures for identifying sources of systematic closure errors, informing algorithm selection, and enabling model-driven bias correction.