Abstract. Data assimilation (DA) of time-variable satellite gravity observations, such as those from the Gravity Recovery and Climate Experiment (GRACE), GRACE Follow-On (GRACE-FO), and future gravity missions, can be used to constrain simulations of the vertical sum of water storage in Global Hydrological Models (GHMs). However, current DA implementations of these Terrestrial Water Storage (TWS) changes are often performed at regional scales or, if applied globally, at low spatial resolutions. This limitation is primarily due to the high computational demands of DA and numerical challenges, such as instabilities in covariance matrix inversion. To fully exploit the potential of satellite gravity observations and the high spatial resolution of GHMs, we developed PyGLDA, an open-source Python-based system that enables fine-scale and computationally efficient global DA. The key innovations of PyGLDA include (1) a global patch-wise DA approach using domain localization and neighboring-weighted global aggregation and (2) seamless compatibility between basin-scale and grid-scale DA implementations. PyGLDA represents a significant functional improvement over previous DA systems, offering wide-ranging and flexible options for user-specific applications. The modular structure of the system allows users to customize water storage compartments, modify observation representations, and potentially select different GHMs. This paper provides a comprehensive description of PyGLDA and its application in a case study of the Danube River Basin, along with a demonstration of global DA, where experiments involve integrating monthly GRACE TWS fields (2002–2010) with the daily W3RA water balance model at 0.1° spatial resolution.
Yang et al. (2025) studied this question.