MILLS: MItigation Leakage through Least Square -- A new method to estimate regional mass variations from GRACE/-FO

Variations in water mass redistribution are a critical indicator of climate change, revealing processes such as global continental desertification and cryosphere melting. The Gravity Recovery and Climate Experiment (GRACE) and Follow-On (GRACE-FO) satellite missions have provided over 20-yrs of essential records of Earth's mass variations, significantly advancing our understanding of climate-driven processes.

However, GRACE/-FO spherical harmonic solutions suffer from aliasing errors, as well as measurement uncertainty, manifesting as North/South striping due to propagation of correction model errors and temporal averaging of the signal. While filtering is necessary to reveal meaningful geophysical signals, it introduces leakage and bias by causing signals to smear beyond their location, which impacts the accuracy of regional mass estimates. To overcome these limitations, we introduce MILLS (MItigation Leakage through Least Square), a new method for estimating regional mass variations from GRACE/-FO Level-3 solutions. MILLS leverages knowledge on solution-specific spherical harmonic filters to correct signal leakage and bias. It computes the least square affine regression between a filtered artificial uniform unit source signal over the region of interest and the similarly filtered GRACE/-FO solution for each time step. The affine models are then applied to non-filtered unit source signal, effectively mitigating leakage and bias, thus improving time-dependent regional mass estimates.

We validate MILLS over the Caspian Sea, an ideal test case due to its large size, significant mass depletion signal, and minimal contamination by external geophysical signals. Comparison of MILLS-derived mass estimate with independent estimates from altimetry and in situ tide gauges demonstrates the method's effectiveness in isolating sources and resolving the phase of the annual variations, which is usually uncertain in other methods due to the disturbance caused by regional signals. We then apply MILLS to glacial regions to evaluate its capability for monitoring glacier mass change. Although glacier regions present greater challenges than the Caspian Sea due to more complex external geophysical signals to account for, preliminary results of MILLS-derived glacier mass change show good agreement with independent estimates from optical imagery.