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 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.
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Arnold CL, Gibbons CJ (1996) Impervious surface coverage—the emergence of a key environmental indicator. J Am Plan Assoc 62(2):243–258. doi:10.1080/01944369608975688
Ayyub BM, McCuen RH (2011) Probability, statistics, and reliability for engineers and scientists, 3rd edn. CRC Press
Baker DB, Richards RP, Loftus TT, Kramer JW (2004) A new flashiness index: characteristics and applications to midwestern rivers and streams. J Am Water Resour Assoc 40(2):503–522. doi:10.1111/j.1752-1688.2004.tb01046.x
Bandt C, Pompe B (2002) Permutation entropy: a natural complexity measure for time series. Phys Rev Lett 88(17):174102. doi:10.1103/PhysRevLett.88.174102
Bandt C, Shiha F (2007) Order patterns in time series. J Time Ser Anal 28(5):646–665. doi:10.1111/j.1467-9892.2007.00528.x
Basu NB, Rao PSC, Winzeler HE, Kumar S, Owens P, Merwade V (2010) Parsimonious modeling of hydrologic responses in engineered watersheds: structural heterogeneity versus functional homogeneity. Water Resour Res 46:W04501. doi:10.1029/2009WR007803
Basu NB, Thompson SE, Rao PSC (2011) Hydrologic and biogeochemical functioning of intensively managed catchments: a synthesis of top-down analyses. Water Resour Res 47, W00J15. doi:10.1029/2011WR010800
Beighley RE (2001) GIS adjustment of measured streamflow data from urbanized watersheds. University of Maryland, Ph.D. dissertation, p 262
Brandes D, Cavallo GJ, Nilson ML (2005) Base flow trends in urbanizing watersheds of the Delaware River basin. J Am Water Resour Assoc 41:1377–1391. doi:10.1111/j.1752-1688.2005.tb03806.x
Brown LR, Cuffney TF, Coles JF, Fitzpatrick F, McMahon G, Steuer J, Bell AH, May JT (2009) Urban streams across the USA: lessons learned from studies in 9 metropolitan areas. J North Am Benthol Soc 28(4):1051–1069. doi:10.1899/08-153.1
Chou C-M (2014) Complexity analysis of rainfall and runoff time series based on sample entropy in different temporal scales. Stoch Env Res Risk Assess 28:1401–1408. doi:10.1007/s00477-014-0859-6
Dooge JCI (1986) Looking for hydrologic laws. Water Resour Res 22(9):S46–S58. doi:10.1029/WR022i09Sp0046S
Eliazar I, Klafter J (2010) Universal generation of 1/f noises. Phys Rev E 82:021109
Feldman DP, Crutchfield JP (1998) Measures of statistical complexity: why? Phys Lett A 238:244–252. doi:10.1016/S0375-9601(97)00855-4
Fleming SW (2007) Quantifying urbanization-associated changes in terrestrial hydrologic system memory. Acta Geophys 55(3):359–368. doi:10.2478/s11600-007-0016-4
Folke C, Carpenter S, Walker B, Scheffer M, Elmqvist T, Gunderson L, Holling CS (2004) Regime shifts, resilience, and biodiversity in ecosystem management. Annu Rev Ecol Evol Syst 35:557–581. doi:10.1146/annurev.ecolsys.35.021103.105711
Gall H, Park J, Harman CJ, Jawitz JW, Rao PSC (2013) Landscape filtering of hydrologic and biogeochemical responses in managed catchments. Landscape Ecol 28(4):651–664. doi:10.1007/s10980-012-9829-x
Grassberger P (1986) Toward a quantitative theory of self-generated complexity. Int J Theor Phys 25(9):907–938. doi:10.1007/BF00668821
Hopkins KG, Morse NB, Bain DJ, Bettez ND, Grimm NB, Morse JL, Palta MM, Shuster WD, Bratt AR, Suchy AK (2015) Assessment of regional variation in streamflow responses to urbanization and the persistence of physiography. Environ Sci Technol 49(5):2724–2732. doi:10.1021/es505389y
Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Am Soc Civ Eng 116:770–799
Jovanovic T, Mejía A, Gall H, Gironás J (2016) Effect of urbanization on the long-term persistence of streamflow records. Phys A 447:208–221. doi:10.1016/j.physa.2015.12.024
Kantelhardt JW, Koscielny-Bunde E, Rybski D, Braun P, Bunde A, Havlin S (2006) Long-term persistence and multifractality of precipitation and river runoff records. J Geophys Res Atmos 111(D1):D01106. doi:10.1029/2005JD005881
Konrad C, Booth D (2005) Hydrologic changes in urban streams and their ecological significance. In: Brown LR et al (eds) Effects of urbanization on stream ecosystems. Am. Fish. Soc., Symposium 47, Bethesda, MD, pp 157–177
Kowalski AM, Martin MT, Plastino A, Rosso OA, Casas M (2011) Distances in probability space and the statistical complexity setup. Entropy 13(6):1055–1075. doi:10.3390/e13061055
Lamberti PW, Martin MT, Plastino A, Rosso OA (2004) Intensive entropic non-triviality measure. Phys A 334(1–2):119–131. doi:10.1016/j.physa.2003.11.005
Lange H, Rosso OA, Hauhs M (2013) Ordinal pattern and statistical complexity analysis of daily stream flow time series. Eur Phys J 222(2):535–552. doi:10.1140/epjst/e2013-01858-3
Li Z, Zhang Y-K (2008) Multi-scale entropy analysis of Mississippi River flow. Stoch Env Res Risk Assess 22:507–512. doi:10.1007/s00477-007-0161-y
Lopez-Ruiz R, Mancini HL, Calbet X (1995) A statistical measure of complexity. Phys Lett A 209(5–6):321–326. doi:10.1016/0375-9601(95)00867-5
Mejía A, Daly E, Rossel F, Jovanovic T, Gironas J (2014) A stochastic model of streamflow for urbanized basins. Water Resour Res 50(3):1984–2001. doi:10.1002/2013WR014834
Mejía A, Rossel F, Gironás J, Jovanovic T (2015) Anthropogenic controls from urban growth on flow regimes. Adv Water Resour 84:125–135. doi:10.1016/j.advwatres.2015.08.010
Mihailović D, Mimić G, Drešković N, Arsenić I (2015) Kolmogorov complexity based information measures applied to the analysis of different river flow regimes. Entropy 17:2973
Morley SA, Karr JR (2002) Assessing and restoring the health of urban streams in the Puget Sound basin. Conserv Biol 16(6):1498–1509. doi:10.1046/j.1523-1739.2002.01067.x
NOAA (2015) National climatic data center, quality controlled local climatological data. http://cdo.ncdc.noaa.gov/qclcd/QCLCD?prior=N. Accessed on January 2015
Olden JD, Poff NL (2003) Redundancy and the choice of hydrologic indices for characterizing streamflow regimes. River Res Appl 19:101–121. doi:10.1002/rra.700
Poff NL, Richter BD, Arthington AH, Bunn SE, Naiman RJ, Kendy E, Acreman M, Apse C, Bledsoe BP, Freeman MC, Henriksen J, Jacobson RB, Kennen JG, Merritt DM, O’Keeffe JH, Olden JD, Rogers K, Tharme RE, Warner A (2010) The ecological limits of hydrologic alteration (ELOHA): a new framework for developing regional environmental flow standards. Freshw Biol 55:147–170. doi:10.1111/j.1365-2427.2009.02204.x
Postel S, Richter B (2003) Rivers for life: managing water for people and nature. Island Press
Ravirajan K (2007) Development and application of a stream flashiness index based on imperviousness and climate using GIS. University of Maryland, M.S. thesis, p 275
Ribeiro HV, Zunino L, Mendes RS, Lenzi EK (2012) Complexity–entropy causality plane: a useful approach for distinguishing songs. Phys A 391:2421–2428. doi:10.1016/j.physa.2011.12.009
Richter BD, Baumgartner JV, Powell J, Braun DP (1996) A method for assessing hydrologic alteration within ecosystems. Conserv Biol 10:1163–1174. doi:10.1046/j.1523-1739.1996.10041163.x
Riedl M, Muller A, Wessel N (2013) Practical considerations of permutation entropy. Eur Phys J 222(2):249–262. doi:10.1140/epjst/e2013-01862-7
Rodríguez-Iturbe I, Rinaldo A (2001) Fractal river basins: chance and self-organization. Cambridge Univ. Press, New York. 564 pp
Rosso OA, Larrondo HA, Martin MT, Plastino A, Fuentes MA (2007a) Distinguishing noise from chaos. Phys Rev Lett 99(15), 154102 1–4. doi:10.1103/PhysRevLett.99.154102
Rosso OA, Zunino L, Perez DG, Figliola A, Larrondo HA, Garavaglia M, Martin MT, Plastino A (2007b) Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach. Phys Rev E 76(6), 061114 1–6. doi:10.1103/PhysRevE.76.061114
Salas JD (1993) Analysis and modeling of hydrologic time series. In: Maidment DR (ed) Handbook of hydrology. McGraw-Hill, New York, pp 19.5–19.9
Sen AK (2008) Complexity analysis of riverflow time series. Stoch Env Res Risk Assess 23:361–366. doi:10.1007/s00477-008-0222-x
Serinaldi F, Zunino L, Rosso OA (2014) Complexity-entropy analysis of daily stream flow time series in the continental United States. Stoch Env Res Risk Assess 28(7):1685–1708. doi:10.1007/s00477-013-0825-8
Shannon CE (1948) A mathematical theory of communication. Bell System Technol. J 27(3):379–423
Singh VP (1997) The use of entropy in hydrology and water resources. Hydrol Process 11:587–626. doi:10.1002/(SICI)1099-1085(199705)11:6<587:AID-HYP479>3.0.CO;2-P
Singh V (2011) Hydrologic synthesis using entropy theory: review. J Hydrol Eng 16:421–433. doi:10.1061/(ASCE)HE.1943-5584.0000332
Sivakumar B (2008) Dominant processes concept, model simplification and classification framework in catchment hydrology. Stoch Env Res Risk Assess 22:737–748. doi:10.1007/s00477-007-0183-5
USGS (2015) National water information system: Web Interface, http://waterdata.usgs.gov/nwis. Accessed on January 2015
Walsh CJ, Fletcher TD, Burns MJ (2012) Urban stormwater runoff: a new class of environmental flow problem. PLoS ONE 7(9):1–10. doi:10.1371/journal.pone.0045814
Wenger SJ et al (2009) Twenty-six key research questions in urban stream ecology: an assessment of the state of the science. J North Am Benthol Soc 28(4):1080–1098. doi:10.1899/08-186.1
Yang GX, Bowling LC (2014) Detection of changes in hydrologic system memory associated with urbanization in the Great Lakes region. Water Resour Res 50(5):3750–3763. doi:10.1002/2014WR015339
Zanin M, Zunino L, Rosso OA, Papo D (2012) Permutation entropy and its main biomedical and econophysics applications: a review. Entropy 14(8):1553–1577. doi:10.3390/e14081553
Zunino L, Pérez DG, Martín MT, Garavaglia M, Plastino A, Rosso OA (2008) Permutation entropy of fractional Brownian motion and fractional Gaussian noise. Phys Lett A 372:4768–4774. doi:10.1016/j.physleta.2008.05.026
Zunino L, Zanin M, Tabak BM, Pérez DG, Rosso OA (2010) Complexity-entropy causality plane: a useful approach to quantify the stock market inefficiency. Phys A 389(9):1891–1901. doi:10.1016/j.physa.2010.01.007
Zunino L, Tabak BM, Serinaldi F, Zanin M, Pérez DG, Rosso OA (2011) Commodity predictability analysis with a permutation information theory approach. Phys A 390(5):876–890. doi:10.1016/j.physa.2010.11.020
Zunino L, Fernández Bariviera A, Guercio MB, Martinez LB, Rosso OA (2012a) On the efficiency of sovereign bond markets. Phys A 391(18):4342–4349. doi:10.1016/j.physa.2012.04.009
Zunino L, Soriano MC, Rosso OA (2012b) Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach. Phys Rev E 86(046210):1–10. doi:10.1103/PhysRevE.86.046210
Acknowledgments
We acknowledge the criticisms and suggestions, which helped improve the overall quality of the manuscript, made by the four anonymous reviewers. The first and last authors gratefully acknowledge the funding support provided by the Department of Civil and Environmental Engineering at the Pennsylvania State University. The third author is supported, in part, by the Penn State Institutes of Energy and the Environment. The present work was partially developed within the framework of the Panta Rhei Research Initiative of the International Association of Hydrological Sciences.
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Jovanovic, T., García, S., Gall, H. et al. Complexity as a streamflow metric of hydrologic alteration. Stoch Environ Res Risk Assess 31, 2107–2119 (2017). https://doi.org/10.1007/s00477-016-1315-6
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DOI: https://doi.org/10.1007/s00477-016-1315-6