The San Luis Valley (SLV), Colorado, is challenged with implementing sustainable groundwater management in the face of increasing surface water scarcity due to climate change. Groundwater extraction in unconsolidated aquifers such as the SLV can cause cm-scale subsidence and rebound. This study utilizes Interferometric Synthetic Aperture Radar (InSAR) data, validated by Global Navigation Satellite System (GNSS) measurements, to measure subsidence and analyze the groundwater dynamics that cause it. Addressing the challenges of phase decorrelation and data gaps, notably from September 2018 to April 2019, we adopted a modified DS-interpolation algorithm, alongside a Singular Spectrum Analysis (SSA)-based gap filling technique. Furthermore, we enhanced the temporal resolution of groundwater level data through the Theis curve interpolation. These methodologies enabled the integration of observational well data with satellite measurements to calibrate a one-dimensional deformation model, capturing both the elastic and inelastic responses of the aquifer system. Our investigation, spanning 2015 to 2021, reveals both seasonal and long-term subsidence, with the confined aquifer section experiencing up to 1 cm/year of subsidence alongside notable seasonal fluctuations. The methodology presented here provides a path to model subsidence in regions with sparse groundwater level and noisy InSAR data. It also provides valuable insights for developing effective water management strategies in the SLV.