Complexity as a streamflow metric of hydrologic alteration

We explore the potential of using a complexity measure from statistical physics as a streamflow metric of basin-scale hydrologic alteration. The complexity measure that we employ is a non-trivial function of entropy. To determine entropy, we use the so-called permutation entropy (PE) approach. The PE approach is desirable in this case since it accounts for temporal streamflow information and it only requires a weak form of stationarity to be satisfied. To compute the complexity measure and assess hydrologic alteration, we employ daily streamflow records from 22 urban basins, located in the metropolitan areas of the cities of Baltimore, Philadelphia, and Washington DC, in the United States. We use urbanization to represent hydrologic alteration since urban basins are characterized by varied and often pronounced human impacts. Based on our application of the complexity measure to urban basins, we find that complexity tends to decline with increasing hydrologic alteration while entropy rises. According to this evidence, heavily urbanized basins tend to be temporally less complex (less ordered or structured) and more random than basins with low urbanization. This complexity loss may have important implications for stream ecosystems whose ability to provide ecosystem services depend on the flow regime. We also find that the complexity measure performs better in detecting alteration to the streamflow than more conventional metrics (e.g., variance and median of streamflow). We conclude that complexity is a useful streamflow metric for assessing basin-scale hydrologic alteration.