Non-perennial stream networks as directed acyclic graphs: The R-package streamDAG

Ken Aho, Cathy Kriloff, Sarah E Godsey, Robert Ramos , Chris Wheeler, Yaqi You, Sara Warix, DeWayne Derryberry, Sam Zipper , Rebecca L Hale

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.