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Interferometric synthetic aperture radar (InSAR) allows for mapping of crustal deformation on land with high spatial resolution and precision in areas with high signal-to-noise ratios. Efforts to obtain precise displacement time series globally, however, are severely limited by radar path delays within the troposphere. The tropospheric delay is integrated along the full path length between the ground and the satellite, resulting in correlations between the interferometric phase and elevation that can vary dramatically in both space and time. We evaluate the performance of spatially variable, empirical removal of phase-elevation dependence within SAR interferograms through the use of the $K$ -means clustering algorithm. We apply this method to both synthetic test data, as well as to C-band Sentinel-1a/b time series acquired over a large area in south-central Mexico along the Pacific coast and inland—an area with a large elevation gradient that is of particular interest to researchers studying tectonic- and anthropogenic-related deformation. We show that the clustering algorithm is able to identify cases where tropospheric properties vary across topographic divides, reducing total root mean square (rms) by an average of 50%, as opposed to a spatially constant phase-elevation correction, which has insignificant error reduction. Our approach also reduces tropospheric noise while preserving test signals in synthetic examples. Finally, we show the average standard deviation of the residuals from the best-fit linear rate decreases from approximately 3 to 1.5 cm, which corresponds to a change in the error on the best-fit linear rate from 0.94 to 0.63 cm/yr. [ABSTRACT FROM AUTHOR]

The rapid expansion of SAR data availability and advancements in InSAR processing methods has enabled the formation of ground displacement time series for many parts of the world where such research was previously hindered by decorrelation due to sparse temporal sampling and SAR operating frequency. In particular, free and open data access from the European Sentinel-1 constellation and the future NASA-ISRO SAR (NISAR) mission is encouraging the global community to move towards automated, cloud-based processing that can accommodate these rapidly growing data volumes and facilitate the use of a suite of corrections to the data. A key challenge is related to path delays introduced when the radar signal propagates through the troposphere. Tropospheric corrections estimated from empirical, phase-based methods and those using independent data from weather models, GPS, and radiometers have been included in open-source packages such as TRAIN, PyAPS and GACOS. Users within the InSAR community have reported varying degrees of success using these methods in a range of areas around the world. However, the various statistical metrics used to evaluate the reliability of tropospheric corrections are not consistently applied and often depend on the area and the spatial scale over which they are evaluated. Examination of a simple metric such as the overall reduction in phase variability within an interferogram does not allow the user to determine whether the improvement was at large or short length scales. We present a review of existing tropospheric correction methods and statistical performance metrics, providing guidelines for global assessment and verification of the efficacy of tropospheric correction methods. We summarize the assumptions and limitations for each correction method as well as each statistical performance metric. We examine two regions with different atmospheric characteristics - one Sentinel-1 swath covering the central United States and one swath covering south central Mexico, including part of the Pacific coast. As the SAR community moves towards reliance on global and automated InSAR processing platforms that incorporate tropospheric corrections, approaches such as those examined here can aid researchers in their efforts to evaluate such corrections and include their uncertainties in derived products such as surface displacement time series, coseismic offsets, processes that correlate with topography, and signals with smaller magnitude or larger spatial scales such as those associated with small earthquakes, aseismic creep and slow slip events. We found that the GACOS products (leveraging the operational high resolution ECMWF weather model) outperform the other correction methods explored here on average, but this result is highly dependent on location, acquisition time, and data availability. We found spatial structure functions to be most useful for performance assessment because of their ability to convey information about performance at discrete spatial scales. • We examine tropospheric corrections in two regions with very different tropospheric characteristics. • We compare three different metrics for assessment of the efficacy of the corrections. • Spatial structure functions are the most informative assessment approach. [ABSTRACT FROM AUTHOR]