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We analyze 36 years of global, hourly weather data (1980–2015) to quantify the covariability of solar and wind resources as a function of time and location, over multi-decadal time scales and up to continental length scales. Assuming minimal excess generation, lossless transmission, and no other generation sources, the analysis indicates that wind-heavy or solar-heavy U.S.-scale power generation portfolios could in principle provide ∼80% of recent total annual U.S. electricity demand. However, to reliably meet 100% of total annual electricity demand, seasonal cycles and unpredictable weather events require several weeks’ worth of energy storage and/or the installation of much more capacity of solar and wind power than is routinely necessary to meet peak demand. To obtain ∼80% reliability, solar-heavy wind/solar generation mixes require sufficient energy storage to overcome the daily solar cycle, whereas wind-heavy wind/solar generation mixes require continental-scale transmission to exploit the geographic diversity of wind. Policy and planning aimed at providing a reliable electricity supply must therefore rigorously consider constraints associated with the geophysical variability of the solar and wind resource—even over continental scales.