Diurnal cycles of streamflow in snow-fed rivers can be used to infer the average time a water parcel spends in transit from the top of the snowpack to a stream gauge in the river channel. This travel time, which is measured as the difference between the hour of peak snowmelt in the afternoon and the hour of maximum discharge each day, ranges from a few hours to almost a full day later. Travel times increase with longer percolation times through deeper snowpacks, and prior studies of small basins have related the timing of a stream's diurnal peak to the amount of snow stored in a basin. However, in many larger basins the time of peak flow is nearly constant during the first half of the melt season, with little or no variation between years. This apparent self-organization at larger scales can be reproduced by employing heterogeneous observations of snow depths and melt rates in a model that couples porous medium flow through an evolving snowpack with free surface flow in a channel.