## 4 Applications of InSAR in Landslide Monitoring
### Recent Advances in Landslide Monitoring with InSAR  
#### 4.2.1 Enhancements in Atmospheric Delay Correction  
Atmospheric delays, particularly those caused by the troposphere, significantly affect the accuracy of InSAR measurements. These delays occur because the radar signal travels through the atmosphere, which is influenced by factors such as temperature, pressure, and water vapor. The troposphere, being the lowest layer of the atmosphere, is especially impactful due to its highly variable conditions, manifesting as phase delays in the radar signal and leading to misinterpretation of deformation monitoring. The tropospheric delay can be divided into two main components: stratified delay and turbulent delay. To enhance the reliability of InSAR measurements, various methods have been developed to correct these delays.  
A commonly used correction approach involves supplementary datasets, such as GNSS data [52; 53], spectrometer observations [54; 55], and numerical weather models (NWM) [56; 57; 58; 59]. Although methods based on external data have demonstrated strong performance in numerous studies, they are typically constrained by the distribution density of stations and inconsistency with the spatial and temporal resolutions of SAR images.  
Another approach involves the use of phase-elevation models, which exploit the relationships between phase delays and elevation to estimate the stratified tropospheric delay [60; 61]. The conventional linear phase-elevation model posits a linear relationship between the unwrapped phase and the elevation, implying a uniform increase in delay with altitude [62]. While this model is easy to implement and its results are straightforward to interpret, it presumes atmospheric homogeneity and fails to account for the complexities of atmospheric variability. One recent solution is the power-law phase-elevation model [63], which introduces greater flexibility by allowing the phase delay to vary across multiple moving windows based on a power function of elevation. Another recent advancement is optimizing the traditional linear model by incorporating spatial variability in atmospheric conditions. For instance, ref. [64] developed a multi-temporal moving-window linear model (MMLM) that effectively addresses tropospheric delay in wide-area landslide investigations by modeling phases within a dynamic sliding window.  
In addition, atmospheric delay correction benefits from the increasing application of deep learning models, which can learn complex atmospheric patterns from large datasets, offering efficient and accurate corrections. For example, [PERSON] et al. [65] introduced a deep learning approach, AtmNet, which leverages NWM without external data to correct spatial heterogeneity in tropospheric delays, particularly in mountainous regions. This method showed superior performance compared to traditional linear models and generic atmospheric correction models (GACOS).  
Notably, although a considerable number of methods for InSAR atmospheric correction have been accumulated, it is necessary to judiciously select the appropriate atmospheric delay correction techniques tailored to specific geographical environments in order to enhance the accuracy of InSAR deformation monitoring [66].