Iterative Mathematical Optimization Approach for Monsoonal Temperate Glacier Velocity Time Series Inversion Using Optical Flow Offset Estimation

The Optical Flow (OF) algorithm is applied to glacier velocity field extraction due to its highly efficient data processing capability. However， the presence of outliers in OF-driven offset stacks poses significant challenges to the accuracy and reliability of glacier velocity time series inversion. In this study， we formulate a temporal model to represent recurrent seasonal variability in glacier flow. Based on this formulation， we develop an iterative refinement method for OF-derived offset stacks and a multi-constrained optimisation framework for glacier velocity time-series inversion. To evaluate the proposed framework， Hailuogou Glacier， a monsoonal temperate glacier in the southeastern Tibetan Plateau， was selected as the study area. Using 90 Synthetic Aperture Radar (SAR) images acquired by Sentinel-1 between 2018 and 2020， we analyzed the distribution patterns of unreliable observations in OF-derived offset stacks and identified systematic baseline-dependent attenuation in the OF-derived motion estimates， particularly over rapidly moving glacier surfaces. The results demonstrate that the proposed iterative refinement method effectively reduces unreliable observations in the offset stacks. Based on the refined offset stacks， the multi-constrained iterative least-squares inversion improves the stability of glacier velocity time-series reconstruction and reduces the influence of residual observational errors and underdetermined solutions associated with observation-matrix rank deficiency. Overall， the proposed framework improves the reliability of OF-based glacier velocity time-series reconstruction and provides a methodological reference for glaciers exhibiting recurrent seasonal velocity variability.