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Abstract. Earth and other terrestrial and icy planetary bodies deform viscoelastically under various forces. Numerical modeling plays a critical role in understanding the nature of various dynamic deformation processes. This article introduces a newly developed open-source package, CitcomSVE-3.0, which efficiently solves the viscoelastic deformation of planetary bodies. Based on its predecessor, CitcomSVE-2.1, CitcomSVE-3.0 is updated to account for three-dimensional elastic compressibility and depth-dependent density, which are particularly important in modeling horizontal displacement for viscoelastic deformation. We benchmark CitcomSVE-3.0 against a semi-analytical code for two types of loading problems: (1) single harmonic loads on the surface or as a tidal force and (2) the glacial isostatic adjustment (GIA) problem with a realistic ice sheet loading history (ICE-6G_D) and an updated version of sea level equations. The benchmark results presented here demonstrate the accuracy and efficiency of this package. CitcomSVE-3.0 shows second-order accuracy in terms of spatial resolution. For typical GIA modeling with a 122 kyr glaciation–deglaciation history, a surface horizontal resolution of ∼50 km, and a time increment of 125 years, this takes ∼3 h on 384 CPU cores to complete, with displacement rate errors of less than 5 %. 

Abstract. Root-zone water storage capacity (Sr) – the maximum water volume available for vegetation uptake – bolsters ecosystem resilience to droughts and heatwaves, influences land–atmosphere exchange, and controls runoff and groundwater recharge. In land models, Sr serves as a critical parameter to simulate water availability for vegetation and its impact on processes like transpiration and soil moisture dynamics. However, Sr is difficult to measure, especially at large spatial scales, hindering an accurate understanding of many biophysical processes, such as photosynthesis, evapotranspiration, tree mortality, and wildfire risk. Here, we present a global estimate of Sr using measurements of total water storage (TWS) anomalies from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On satellite missions. We find that the median Sr value for global vegetated regions is at least 220±40 mm, which is over 50 % larger than the latest estimate derived from tracking storage change via water fluxes and 380 % larger than that calculated using a typical soil and rooting-depth parameterization. These findings reveal that plant-available water stores exceed the storage capacity of 2 m deep soil in nearly half of Earth's vegetated surface, representing a notably larger extent than previous estimates. Applying our Sr estimates in a global hydrological model improves evapotranspiration simulations compared to other Sr estimates across much of the globe, particularly during droughts, highlighting the robustness of our approach. Our study highlights the importance of continued refinement and validation of Sr estimates and provides a new observational approach for further exploring the impacts of Sr on water resource management and ecosystem sustainability. 

Abstract This article presents a comprehensive benchmark study for the newly updated and publicly available finite element code CitcomSVE for modeling dynamic deformation of a viscoelastic and incompressible planetary mantle in response to surface and tidal loading. A complete description of CitcomSVE’s finite element formulation including calculations of the sea‐level change, polar wander, apparent center of mass motion, and removal of mantle net rotation is presented. The 3‐D displacements and displacement rates and the gravitational potential anomalies are solved with CitcomSVE for three benchmark problems using different spatial and temporal resolutions: (a) surface loading of single harmonics, (b) degree‐2 tidal loading, and (c) the ICE‐6G GIA model. The solutions are compared with semi‐analytical solutions for error analyses. The benchmark calculations demonstrate the accuracy and efficiency of CitcomSVE. For example, for a typical ICE‐6G GIA calculation with a 122‐ky glaciation‐deglaciation history, time increment of 100 years, and ∼50 km (or ∼0.5°) surface horizontal resolution, it takes ∼4.5 hr on 96 CPU cores to complete with about 1% and 5% errors for displacements and displacement rates, respectively. Error analyses shows that CitcomSVE achieves a second order accuracy, but the errors are insensitive to temporal resolution. CitcomSVE achieves the parallel computational efficiency >75% for using up to 6,144 CPU cores on a parallel supercomputer. With its accuracy, computational efficiency and its open‐source public availability, CitcomSVE provides a powerful tool for modeling viscoelastic deformation of a planetary mantle with 3‐D mantle viscous and elastic structures in response to surface and tidal loading problems.