Toward capturing hydrologically significant connectivity in spatial patterns

Many spatial fields exhibit connectivity features that have an important in fluence on hydrologic behavior. Examples include high-conductivity preferre d flow paths in aquifers and saturated source areas in drainage lines. Conn ected features can be considered as arbitrarily shaped bands or pathways of connected pixels having similar (e.g., high) values. Connectivity is a pro perty that is not captured by standard geostatistical approaches, which ass ume that spatial variation occurs in the most random possible way that is c onsistent with the spatial correlation, nor is it captured by indicator geo statistics. An alternative approach is to use connectivity functions. In th is paper we apply connectivity functions to 13 observed soil moisture patte rns from the Tarrawarra catchment and two synthetic aquifer conductivity pa tterns. It is shown that the connectivity functions are able to distinguish between connected and disconnected patterns. The importance of the connect ivity in determining hydrologic behavior is explored using rainfall-runoff simulations and groundwater transport simulations. We propose the integral connectivity scale as a measure of the presence of hydrologic connectivity. Links between the connectivity functions and integral connectivity scale a nd simulated hydrologic behavior are demonstrated and explained from a hydr ologic process perspective. Connectivity functions and the integral connect ivity scale provide promising means for characterizing features that exist in observed spatial fields and that have an important influence on hydrolog ic behavior. Previously, this has not been possible within a statistical fr amework.