InSAR closure errors: temporal signatures and impact on deformation time series estimation

Closure errors quantify the inconsistency of seemingly redundant interferograms. Systematic closure errors, associated with e.g. changes in soil moisture or vegetation, can bias estimated InSAR time series. Previous work has shown that the bias can be reduced by including interferograms spanning long temporal baselines. However, it is not clear how the bias reduction depends on the temporal signatures of the closure errors and in what circumstances including long-term interferograms improves or deteriorates the InSAR phase history and ultimately deformation estimates.

To identify how the temporal signatures relate to InSAR time series estimation, we introduce a mathematical framework that quantifies temporal closure signatures as a function of time and time scale. Technically speaking, we construct two complementary bases of the annihilator of the vector space of all temporally consistent phases, with each basis element extracting the closure error corresponding to the element's time and time scale. Applying this framework to Sentinel-1 observations, we find contrasting short-term, seasonal, and multi-annual closure signatures across land cover types. The inclusion of long-term interferograms is associated with characteristic changes in seasonal amplitudes and long-term trends in the InSAR phase history estimates. 

To determine when including long-term interferograms improves InSAR time series estimation, we formulate simple interferometric scattering models for seasonally variable soil moisture and vegetation conditions and sub-resolution deformation as is common in ice-rich permafrost. We find that including long-term interferograms improves the InSAR time series in simulation scenarios dominated by soil moisture wetting and dry down cycles. Conversely, including long-term interferograms can have a deleterious impact on InSAR time series estimates in scenarios with seasonal vegetation and sub-resolution deformation.

We conclude with simple diagnostics on how temporal closure signatures and expert knowledge can inform InSAR processing to maximize deformation time series quality for a range of geohazards, including lowland permafrost deformation, landslides, and sinkholes.