Nonlinear-Constrained Geographically Weighted Regression: Enabling Multidimensional Dynamics Analysis Using Monostatic Terrestrial Radar Interferometry at Helheim Glacier

Abstract. Monostatic Terrestrial Radar Interferometry (TRI) provides an alternative approach for glacier one-dimensional velocity mapping when bistatic configurations are unavailable. However, existing monostatic methods typically rely on a single source of auxiliary information, limiting error suppression and reducing the accuracy of velocity retrieval. Here, we propose a nonlinear-constrained Geographically Weighted Regression (NL-GWR) framework that integrates TRI interferometric and amplitude-derived displacement observations with external velocity constraints under prior physical assumptions including short-term velocity-direction invariance and parallel flow to retrieve glacier velocity over Helheim Glacier in August, 2016. Validated against synchronous bistatic TRI measurements, NL-GWR achieves superior consistency metric between monostatic and bistatic measurements by mitigating quality deficiencies in amplitude-derived observations and alleviating the ill-conditioning inherent in conventional approaches. Leveraging this capability, we derive a 16-day velocity sequence at the Helheim Glacier terminus, where we identify short-term periodic variations in glacier velocity and strain rate potentially driven by both tidal forcing and meltwater processes. In addition, our analysis reveals a transition zone between the dominant controls on glacier motion located approximately 1–3 km upstream of the calving front. The proposed framework provides a practical pathway for overcoming the inherent information limitations of monostatic TRI in resource-constrained glacier kinematic studies and offers new opportunities for capturing and inferring the external forcing mechanisms driving changes at glacier terminus.