The complexity of the atmosphere renders the modelling of the atmospheric delay in multi temporal InSAR difficult. This limits the potential of achieving millimetre accuracy of InSAR-derived deformation measurements. In this paper we review advances in tropospheric delay modelling in InSAR, tropospheric correction methods and integration of the correction methods within existing multi temporal algorithms. Furthermore, we investigate ingestion of the correction techniques by different InSAR applications, accuracy performance metrics and uncertainties of InSAR derived measurements attributed to tropospheric delay. Spatiotemporal modelling of atmospheric delay has evolved and can now be regarded as a spatially correlated turbulent delay with varying degree of anisotropy random in time and topographically correlated seasonal stratified delay. Tropospheric corrections methods performance is restricted to a case by case basis and ingestion of these methods by different applications remains limited due to lack of their integration into existing algorithms. Accuracy and uncertainty assessments remain challenging with most studies adopting simple statistical metrics. While advances have been made in tropospheric modelling, challenges remain for the calibration of atmospheric delay due to lack of data or limited resolution and fusion of multiple techniques for optimal performance.
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