Abstract. To quantify water flows between groundwater (GW) and surface water (SW) as well as the impact of capillary rise on evapotranspiration by global hydrological models (GHMs), it is necessary to replace the bucket-like linear GW reservoir model typical for hydrological models with a fully integrated gradient-based GW flow model. Linear reservoir models can only simulate GW discharge to SW bodies, provide no information on the location of the GW table and assume that there is no GW flow among grid cells. A gradient-based GW model simulates not only GW storage but also hydraulic head, which together with information on SW table elevation enables the quantification of water flows from GW to SW and vice versa. In addition, hydraulic heads are the basis for calculating lateral GW flow among grid cells and capillary rise. G3M is a new global gradient-based GW model with a spatial resolution of 5' that will replace the current linear GW reservoir in the 0.5° WaterGAP Global Hydrology Model (WGHM). The newly developed model framework enables in-memory coupling to WGHM while keeping overall runtime relatively low, allowing sensitivity analyses and data assimilation. This paper presents the G3M concept and specific model design decisions together with results under steady-state naturalized conditions, i.e. neglecting GW abstractions. Cell-specific conductances of river beds, which govern GW-SW interaction, were determined based on the 30'' steady-state water table computed by Fan et al. (2013). Together with an appropriate choice for the effective elevation of the SW table within each grid cell, this enables a reasonable simulation of drainage from GW to SW such that, in contrast to the GW model of de Graaf et al. (2015, 2017), no additional drainage based on externally provided values for GW storage above the floodplain is required in G3M. Comparison of simulated hydraulic heads to observations around the world shows better agreement than de Graaf et al. (2015). In addition, G3M output is compared to the output of two established macro-scale models for the Central Valley, California, and the continental United States, respectively. As expected, depth to GW table is highest in mountainous and lowest in flat regions. A first analysis of losing and gaining rivers and lakes/wetlands indicates that GW discharge to rivers is by far the dominant flow, draining diffuse GW recharge, such that lateral flows only become a large fraction of total diffuse and focused recharge in case of losing rivers and some areas with very low GW recharge. G3M does not represent losing rivers in some dry regions. This study presents the first steps towards replacing the linear GW reservoir model in a GHM while improving on recent efforts, demonstrating the feasibility of the approach and the robustness of the newly developed framework.
A graph-based model framework for steady-state load flow problems of general multi-carrier energy systems
