Stream networks expand and contract through time, impacting chemical export, aquatic habitat, and water quality. Although recent advances improve prediction of the extent of the wetted channel network (L) based on discharge at the catchment outlet (Q), controls on the temporal variability of L remain poorly understood and unquantified. Here we develop a quantitative, conceptual framework to explore how flow regime and stream network hydraulic scaling factors co-determine the relative temporal variability in L (denoted here as the total wetted channel drainage density). Network hydraulic scaling determines how much L changes for a change in Q, while the flow regime describes how Q changes in time. We compiled datasets of co-located dynamic stream extent mapping and discharge to analyze all globally available empirical data using the presented framework. We found that although variability in L is universally damped relative to variability in Q (i.e., streamflow is relatively more variable in time than network extent), the relationship is elastic, meaning that for a given increase in the variability in Q, headwater catchments will experience greater-than-proportional increases in the variability of L. Thus, under anticipated climatic shifts towards more volatile precipitation, relative variability in headwater stream network extents can be expected to increase even more than the relative variability of discharge itself. Comparison between network extents inferred from the L-Q relationship and blue lines on USGS topographic maps shows widespread underestimation of the wetted channel network by the blue line network.