ORIGINAL PAPER Complexity as a streamflow metric of hydrologic alteration Tijana Jovanovic 1 • Susana Garcı ´a 1 • Heather Gall 2 • Alfonso Mejı ´a 1 Ó Springer-Verlag Berlin Heidelberg 2016 Abstract 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 sat- isfied. 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. Keywords Complexity-entropy causality plane  Permutation entropy  Hydrologic change  Land-use change  Urbanization  Environmental flows 1 Introduction Hydrologic alteration, i.e. anthropogenically driven chan- ges in the hydrologic behavior of a river basin, can be used to indirectly assess the condition of stream, riparian, and floodplain ecosystems (Morley and Karr 2002; Konrad and Booth 2005; Brown et al. 2009; Wenger et al. 2009). This is the case since riverine ecosystems depend strongly on hydrologic conditions, and direct information about river- ine ecosystems are usually less available than hydrologic observations. Specifically, streamflow metrics derived directly from streamflow records are often used to char- acterize and quantify basin-scale hydrologic alteration (Baker et al. 2004; Walsh et al., 2012; Gall et al. 2013; Mejı ´a et al. 2014; Hopkins et al. 2015). Streamflow metrics are typically derived from streamflow magnitudes, i.e. they are based on different statistical properties obtained from the probability density function (pdf) of streamflow (Mejı ´a et al. 2014, 2015). This means that streamflow metrics do not tend to explicitly consider hydrologic alterations to the temporal structure of streamflow (Fleming 2007; Yang and Bowling 2014; Jovanovic et al. 2016). One of the most common and prevalent applications of streamflow metrics is in the assessment of environmental flows (Richter et al. 1996; Olden and Poff 2003; Postel and Richter 2003; Poff et al. 2010). The metrics used in these & Alfonso Mejı ´a amejia@engr.psu.edu 1 Department of Civil and Environmental Engineering, The Pennsylvania State University, 215B Sacket Building, University Park, PA 16802-1408, USA 2 Department of Agricultural and Biological Engineering, The Pennsylvania State University, University Park, PA, USA 123 Stoch Environ Res Risk Assess DOI 10.1007/s00477-016-1315-6