Underground karst drainage systems can be studied by the input‐output relations of rivers that flow through them. First, tracers enable the quantity of water at a sink that flows to a specific spring, and the fraction of a given spring derived from a sink, to be calculated. Second, when these methods are not applicable, cross‐covariance and cross‐spectral transfer function analysis can be used to examine input‐output stage records. These give information about the vadose and/or phreatic nature of the system. An inaccessible karst drainage system in western Alberta has a tracer flow‐through time of +80 to +130 hours and a positively skewed cross covariance of +70 to +124 hours; therefore the cave is not completely water filled. Additional unknown inputs are substantiated by a negatively peaking cross covariance.