On Crop Growth and InSAR Closure Phases

The closure phase, which is a circular summation of the phases of the three multilooked interferograms, comprises a geophysical component and phase noise. In agricultural regions of southern Spain, encompassing both open crop fields and greenhouses, the closure phases constructed from Sentinel-1 acquisitions consistently exhibit positive signatures. The evolution of these observations appears to be related to the phenological stages of plants, as evidenced by crop calendars. Moreover, the signatures of closure phases stand out as a potential indicator of vegetation development under dense vegetation conditions when compared to coherence and normalized radar cross-section (NRCS). Two existing models, one based on dielectric variation in the sub-surface and another on volume scattering combined with perpendicular baselines, do not explain observed time series. Therefore, the presence of these positive closure phases implies the existence of supplementary factors contributing to closure phases associated with plant development. In this context, we explore two potential factors: variations in dielectric properties within crop canopies and the line-of-sight motion of crops. These factors are considered to establish connections between temporal changes in vegetation parameters and observed closure phase signatures. Regarding the first factor, we characterize the crop canopies using the dielectric constant of an equivalent medium, thereby capturing changes in wave propagation within the canopies due to leaves and vertical stalks development throughout the crop growth stages. We then model their contributions to closure phases in a manner analogous to an existing soil-moisture model. By using realistic vegetation parameters derived from in-situ measurements, this forward model generates synthetic data comparable in magnitude to the observations. As for the second factor, we propose an additional contributing mechanism to closure phases — skewed motion in the radar line-of-sight (LoS) direction induced by plant growth. This motion model is mathematically verified under a small-motion approximation. Both models offer valuable insights into the origins of geophysical closure phases.