The rapid growth of data center electricity demand, accelerated by AI, makes carbon-only accounting an incomplete measure of computing's environmental impact: low-carbon electricity mixes are often water-intensive, and the resulting harm depends on local, seasonal scarcity rather than on the volume of water consumed. We propose the Environmental Score (ES), a unified, dimensionless index in $[0, 100]$ that jointly captures the carbon footprint and the spatial-temporal, scarcity-weighted water impact of the electricity a workload consumes. It combines real-time, cross-border electricity flow tracing with monthly AWARE2.0 water-scarcity characterization factors, weighting global greenhouse-gas emissions together with the local, seasonal severity of water stress. Building on it, we define the Green Score (GS), a scheduling metric proportional to the useful computational work delivered per unit of real environmental impact, which also accounts for data center power and hardware efficiency. We add both metrics as a green-affinity feature to the GreenDirector schedulers of two production federated infrastructures, the AI4EOSC scientific cloud and the DIRAC workload management system. In AI4EOSC, a cluster-filling experiment over four pan-European providers shows that greener sites are filled first without degrading scheduling latency or end-user experience. In DIRAC, a trace-driven simulation of 133,631 jobs and a preliminary production deployment for the KM3NeT community reduce carbon emissions and improve carbon efficiency by about 40\%, while making the carbon-water trade-off explicit when the lowest-carbon site also carries higher water stress. The results show that hydrological stress can be dynamically weighted into workload placement in live, multi-tenant systems

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