Plant species can show considerable morphological and functional variation along environmental gradients. This intraspecific trait variation (ITV) can have important consequences for community assembly, biotic interactions, ecosystem functions and responses to global change. However, directly measuring ITV across many species and wide geographic areas is often infeasible. Thus, a method to predict spatial variation in a species’ functional traits could be valuable. We measured specific leaf area (SLA), height and leaf area (LA) of grasses across California, covering 59 species at 230 sampling locations. We asked how these traits change along climate gradients within each species and used machine learning to predict local trait values for any species at any location based on phylogenetic position, local climate and that species’ mean traits. We then examined how much these local predictions alter patterns of assemblage-level trait variation across the state. Most species exhibited higher SLA and grew taller at higher temperatures and produced larger leaves in drier conditions. The random forests predicted spatial variation in functional traits very accurately, with correlations up to 0.97. Because trait records were spatially biased towards warmer areas, and these areas tend to have higher SLA individuals within each species, species means of SLA were upwardly biased. As a result, using species means over-estimates SLA in the cooler regions of the state. Our results also suggest that height may be substantially under-predicted in the warmest areas. Synthesis. Using only species mean traits to characterize the functional composition of communities risks introducing substantial error into trait-based estimates of ecosystem properties including decomposition rates or NPP. The high performance of random forests in predicting local trait values provides a way forward for estimating high-resolution patterns of ITV without a massive data collection effort.