Assessment of Radial Distortion Parameter Variability in Airborne Photogrammetry: Implications for Atmospheric Refraction

Abstract. The Valpelline Valley, located in the northern Aosta Valley (Italy) along the Swiss border, is a typical Alpine valley shaped by glacial and fluvial processes. Characterized by a large altitudinal range (900-4000 m a.s.l.) and hosting glaciers feeding the Place Moulin reservoir, the area plays a key role in regional hydroelectric production. Since 2020, GlacierLAB has been conducting glacier monitoring activities through biannual aerial photogrammetric surveys, overcoming the logistical constraints imposed by the steep and inaccessible morphology of the valley.
The surveys were performed using a medium-format camera mounted under an aircraft wing and equipped with GNSS and IMU systems. Due to the lack of synchronization between the camera shutter and GNSS receiver, georeferencing relied on Ground Control Points (GCPs), whose spatial distribution is often limited in high-mountain environments. This condition makes camera calibration a critical factor for ensuring reliable multi-temporal analysis.
This study investigates the behavior of the radial distortion parameter k₁ using images previously corrected for optical distortion. A multi-run bundle adjustment strategy was applied in Agisoft Metashape, including baseline configurations, global and image-wise estimation of k₁, and robustness tests under different GCP setups. Statistical analyses reveal a systematic and significant dependence of k₁ on the vertical camera–terrain distance.
However, comparison with a theoretical atmospheric model based on the Saastamoinen formulation shows weak correlation, indicating that the observed effect cannot be attributed solely to atmospheric refraction. Instead, k₁ acts as a compensatory parameter absorbing depth-dependent systematic effects related to block geometry and acquisition conditions.