Non-perennial streams comprise over half of the global stream network and impact downstream water quality. Although aridity is a primary driver of stream drying globally, surface flow permanence varies spatially and temporally within many headwater streams, suggesting that these complex drying patterns may be driven by topographic and subsurface factors. Indeed, these factors affect shallow groundwater flows in perennial systems, but there has been only limited characterisation of shallow groundwater residence times and groundwater contributions to intermittent streams.Here, we asked how groundwater residence times, shallow groundwater contributions to streamflow, and topography interact to control stream drying in headwater streams. We evaluated this overarching question in eight semi-arid headwater catchments based on surface flow observations during the low-flow period, coupled with tracer-based groundwater residence times. For one headwater catchment, we analysed stream drying during the seasonal flow recession and rewetting period using a sensor network that was interspersed between groundwater monitoring locations, and linked drying patterns to groundwater inputs and topography. We found a poor relationship between groundwater residence times and flowing network extent (R 2 < 0.24). Although groundwater residence times indicated that old groundwater was present in all headwater streams, surface drying also occurred in each of them, suggesting old, deep flowpaths are insufficient to sustain surface flows. Indeed, the timing of stream drying at any given point typically coincided with a decrease in the contribution from near-surface sources and an increased relative contribution of groundwater to streamflow at that location, whereas the spatial pattern of drying within the stream network typically correlated with locations where groundwater inputs were most seasonally variable. Topographic metrics only explained $30% of the variability in seasonal flow permanence, and surprisingly, we found no correlation with seasonal drying and down-valley subsurface storage area. Because we found complex spatial patterns, future studies should pair dense spatial observations of subsurface properties, such as hydraulic conductivity and transmissivity, to observations of seasonal flow permanence.

Many conventional stream network metrics are time-invariant and/or do not consider the importance of individual stream locations to network functionality. As a result, they are not well-suited to non-perennial streams, in which hydrologic status (flowing vs. pooled vs. dry) can vary substantially in space and time. To help address this issue, we consider non-perennial streams as directed acyclic graphs (DAGs). DAG metrics allow: 1) summarization of important network characteristics (e.g., centrality, complexity, connectedness, and nestedness) of both particular (local) stream network locations and entire (global) stream networks, and 2) tracking of these characteristics as non-perennial stream networks expand and shrink. We review a large number of graph-theoretic procedures for their utility in the analysis of non-perennial stream DAGs. Approaches we find useful are codified in a new publicly available R-package, streamDAG, which allows straightforward igraph representations of stream networks and easy modification of non-perennial stream DAG topologies based on water presence/absence data. The streamDAG package includes a wide variety of local and global measures for both unweighted and weighted stream digraphs, and provides procedures for generating Bayesian posterior distributions of the probability and the reciprocal probability of surface water presence. We demonstrate streamDAG algorithms using two North American non-perennial streams: Murphy Creek, a simple drainage system in the Owyhee Mountains of southwestern Idaho, and Konza Prairie, a relatively complex stream network in central Kansas.

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