Communication Distance and Bayesian Inference in Non‐Perennial Streams

Non‐perennial streams are receiving increased attention from researchers, however, suitable methods for measuring their hydrologic connectivity remain scarce. To address this deficiency, we developed Bayesian statistical approaches for measuring both average active stream length, and a new metric called average communication distance. Average communication distance is a theoretical increased effective distance that stream‐borne materials must travel, given non‐continuous streamflow. Because it is the product of the inverse probability of surface water presence and stream length, the average communication distance of a non‐perennial stream segment will be greater than its actual physical length. As an application we considered Murphy Creek, a simple non‐perennial stream network in southwestern Idaho, USA. We used surface water presence/absence data obtained in 2019, and priors for the probability of surface water, based on predictions from an existing regional United States Geological Survey model. Average communication distance posterior distributions revealed locations where effective stream lengths increased dramatically due to flow rarity. We also found strong seasonal (spring, summer, fall) differences in network‐level posterior distributions of both average stream length and average communication distance. Our work demonstrates the unique perspectives concerning network drying provided by communication distance, and demonstrates the general usefulness of Bayesian approaches in the analysis of non‐perennial streams. Plain Language Summary We developed a new metric, communication distance, appropriate for measuring connectivity in non‐perennial stream networks. Communication distance can be considered a theoretical potential distance that water borne material must travel in the absence of continuous surface flow. Communication distance will be in units of measured stream length. Nonetheless, the communication distance of a non‐perennial stream segment will be greater than the actual physical length of the segment, and this distance will increase further with increased intermittency. We developed Bayesian extensions for both communication distance, and an existing stream length model of network connectivity. The use of a Bayesian approach allowed: (a) explicit consideration of the variation and uncertainty in stream segment probabilities of surface water presence, and (b) the incorporation of preexisting US Geological Survey model predictions as a framew