GNSS coordinate series noise modeling is essential for reliable geophysical signal estimation and uncertainty assessment. The generalized Gauss–Markov (GGM) noise model and the Matérn process (MP) noise model are widely used to describe low-frequency spectral flattening in GNSS coordinate series, but they differ in their definition domains, parameterizations and autocovariance function (ACF) structures. These differences may lead to misconceptions, complicate noise model comparison and practical implementation. Building on a systematic review of the theories of GGM and MP, this study proposes a generalized Matérn process (GMP) noise model. By introducing a fractional step size hyperparameter μ into the differencing operator, GMP provides a unified framework that continuously connects the two models: when μ = 1, GMP reduces to GGM; as μ → 0, the spectrum of GMP approaches that of MP. The preferred range of μ is investigated using 420 GNSS coordinate series from 140 global GNSS sites, considering differences in geographical region, coordinate component and length of observations. The results show that the preferred values of μ are robustly concentrated within the interval [0.7, 1]. Large-scale validation is then conducted using 846 GNSS coordinate series from 282 global GNSS sites. The experimental results show that under AIC, BIC and BIC_tp, the proposed WN + GMP family consistently accounts for a large proportion of the optimal models. These results demonstrate that GMP provides a more general noise model family for GNSS coordinate series noise modeling and can improve the fidelity and flexibility of stochastic noise modeling.

To mitigate the impact of north–south strip errors inherent in Gravity Recovery and Climate Experiment (GRACE) spherical harmonic coefficient solutions, this research develops a state-space model to generate a more robust solution. The efficacy of the state-space model is demonstrated by comparing its performance with that of conventional filtering methods and hydrological modeling schemes. The method is subsequently applied to estimate the GRACE Groundwater Drought Index in the California Central Valley basin, a region significantly affected by drought during the GRACE observation period. This analysis quantifies the severity of droughts and floods while investigating the direct influences of precipitation, runoff, evaporation, and anthropogenic activities. By incorporating the El Niño–Southern Oscillation (ENSO) and the Pacific Decadal Oscillation, the study offers a detailed causal analysis and proposes a novel methodology for water resource management and disaster early warning. The results indicate that a moderate-duration flood event in 2006 resulted in a recharge of 19.81 km³ of water resources in the California Central Valley basin, whereas prolonged droughts in 2008 and 2013, lasting over 15 months, led to groundwater depletion of 41.53 km³ and 91.45 km³, respectively. Precipitation and runoff are identified as the primary determinants of local drought and flood conditions. The occurrence of ENSO events correlates with sustained precipitation variations over the subsequent 2–3 months, resulting in corresponding changes in groundwater storage.