Abstract Basin‐wide snow depth (SD) maps can support operational water supply assessments, but their availability is limited by measurement costs (airborne) or sampling constraints (satellite and drone). We present Swath‐random forest (RF), a methodology that trains random forests on SD measured within a narrow swath (<10% of a basin) to extrapolate basin‐wide depths. Using 68 LiDAR surveys from eight basins in Colorado and California, we evaluate two predictor cases: (a) physiography plus prior full‐basin snow‐depth maps and (b) physiography alone. For the first case, Swath‐RF with 2‐km‐wide swaths reproduces basin‐wide depth with low extrapolation absolute bias (0.019 m) and RMSE (0.21 m), and represents snow volume across topographic gradients and across dissimilar years. Errors are 2–3 times larger when using physiography alone. Swath‐RF enables basin‐wide mapping more frequently or across more basins, but at the cost of accuracy; applicability to other regions will depend on snow climate, physiography, and data availability.