A Robust and Multi-Weighted Approach to Estimating Topographically Correlated Tropospheric Delays in Radar Interferograms

Abstract

Spatial and temporal variations in the vertical stratification of the troposphere introduce significant propagation delays in interferometric synthetic aperture radar (InSAR) observations. Observations of small amplitude surface deformations and regional subsidence rates are plagued by tropospheric delays, and strongly correlated with topographic height variations. Phase-based tropospheric correction techniques assuming a linear relationship between interferometric phase and topography have been exploited and developed, with mixed success. Producing robust estimates of tropospheric phase delay however plays a critical role in increasing the accuracy of InSAR measurements. Meanwhile, few phase-based correction methods account for the spatially variable tropospheric delay over lager study regions. Here, we present a robust and multi-weighted approach to estimate the correlation between phase and topography that is relatively insensitive to confounding processes such as regional subsidence over larger regions as well as under varying tropospheric conditions. An expanded form of robust least squares is introduced to estimate the spatially variable correlation between phase and topography by splitting the interferograms into multiple blocks. Within each block, correlation is robustly estimated from the band-filtered phase and topography. Phase-elevation ratios are multiply- weighted and extrapolated to each persistent scatter (PS) pixel. We applied the proposed method to Envisat ASAR images over the Southern California area, USA, and found that our method mitigated the atmospheric noise better than the conventional phase-based method. The corrected ground surface deformation agreed better with those measured from GPS.

Tropospheric Delay Correction Based on a Three-Dimensional Joint Model for InSAR

“…Then, separate strategies are adopted to estimate the topography-correlated and long-scale tropospheric delays. To obtain the global transfer factor K k ∆φ , linear regression can be adopted directly, while for the local slope factors A k i and C k i , a block processing method [20,25] is applied first. The studied area is divided into multiple blocks by moving a small window from the left bottom to the right up corner of the full interferogram.…”

“…Thus, the strategy of simply using the XY-correlated method [26] and the T-correlated method [29] one by one to correct corresponding components may cause a less robust results. Therefore, a joint estimation method is proposed in next by considering that different tropospheric delay components have different spatial wavelength scales [25].…”

“…The phase-based methods, which do not require external data sets, can estimate tropospheric delays from the interferogram itself [25]. Since the long-scale component has spatial correlation characteristics, interferometric phase of the long-scale tropospheric delay, obtained by the Permanent Scatters technique [26], can be modeled linearly along azimuth and slant range directions.…”

Correcting InSAR Topographically Correlated Tropospheric Delays Using a Power Law Model Based on ERA-Interim Reanalysis

“…w ii is the corresponding weight factor calculated by the function of IGGIII [47]. The parametersX can be robustly and reliably estimated by an expanded robust estimation [46] given that the initial value of the equivalent weight matrix was set. When the parameters are estimated, the covariance matrix of the estimates can be obtained through variance propagation in Equation (12) as follows:…”

“…The local robust estimation of K l plays a critical role in increasing the accuracy of tropospheric delays. An expanded robust technique was used to estimate K l in each window, which can reduce the sensitivity to outliers (e.g., due to residual deformation signal or other measurement error sources) [46]. The error equation can be constructed based on Equation (9) as follows:…”