Mitigation of tropospheric turbulent delays in InSAR time series by incorporating a stochastic process

Tropospheric delays present a significant challenge to accurately mapping the Earth’s surface movements using interferometric synthetic aperture radar (InSAR). These delays are typically divided into stratified and turbulent components. While efforts have been made to address the stratified component, effectively mitigating turbulence remains an ongoing challenge. In response, this study proposes a joint model that compasses both the deterministic components and stochastic elements to account for the phases raised by turbulent delays in full InSAR time series. In the joint model, the deformation phases are parameterized by time-domain polynomial, while the turbulent delays are treated as spatially correlated stochastic variables, defined by spatial variance–covariance functions. Least Squares Collocation (LSC) and Variance-Covariance Estimation (VCE) are employed to solve this joint model, enabling simultaneous estimation of modelled deformation and turbulent mixing from full InSAR time series. The rationale is rooted in the distinct temporal dependencies of deformation and turbulent delay. Its efficacy and versatility are demonstrated using simulated and Sentinel-1 data from Hong Kong International Airport (China) and the Southern Valley of California (USA). In simulations, the root mean square error (RMSE) of the differential delays decreased from 2.4 to 0.8 cm. In the Southern Valley, comparison with 70 GPS measurements showed a 73.7 % reduction in mean RMSE, from 1.9 to 0.5 cm. These results confirm the effectiveness of this approach in mitigating tropospheric turbulence delays in the time domain.