We modeled ground- and surface-water exchange and hyporheic water flux on ~2km² of the Umatilla River Floodplain, Oregon, USA, based on a continuous representation of water stage and floodplain elevation derived from LIDAR data. Without calibration, our model explained 99.4% of the variation in water table elevation (range = 397.7m to 410.1m) observed in 45 monitoring wells, suggesting that the spatial distribution of surface water stage is the predominant driver of hyporheic flux in the floodplain aquifer. Model results document a spatially explicit, nested hierarchy of hyporheic flow path lengths, yielding a complex, intermingled mosaic of residence times for hyporheic water reentering the channel. Short flow paths (1s to 10s of m) outnumber long flow paths (100s to 1000s of m) by ~3 orders of magnitude. Our analysis illustrates the utility of "hydrologic spiraling" as a conceptual hydrologic basis for understanding alluvial river ecosystems. Hydrologic spiraling length is the downstream distance a water molecule travels during the cycle of downwelling, flux through the aquifer, upwelling, and flow in the channel to a new point of downwelling. Water temperature and nutrient cycling provide contrasting examples of how the frequency distribution of hydrologic spiraling lengths influence lotic ecosystems.