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Detrended fluctuation analysis and entropy-complexity causality analysis of temperatures in an urbanized mountain stream

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Abstract

We present the results of applying detrended fluctuation analysis (DFA) to study correlations in mountain stream temperatures over a 9-year period for impacted and unimpacted conditions. Permutation entropy and complexity are also computed for stream temperature time series at various locations characterized by varying degrees of human impact, and a graphical representation of the “complexity-entropy causality plane” is used to examine the degree of disturbance caused by human activities. Urban development such as canopy removal and urban infrastructure can lead to a higher degree of anti-persistent correlations indicated by lower values of DFA exponents. This effect is more pronounced downstream due to cumulative urbanization effects with downstream distance. Seasonal variations also influence stream temperature dynamics: less anti-persistent behavior is observed in winter months, and stronger anti-persistent correlations during summer. The position in the complexity-entropy plane, reflecting distribution of short term temperature patterns, is also affected, where most sites experience a shift towards higher entropy values after restoration, and only for one site entropy is reduced. Our results indicate the important role urbanization plays on stream evolution greatly influenced by human activities. This information may provide valuable insights for watershed management and water resources management.

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References

  • Anderson WP Jr, Babyak CM, Thaxton CS (2007) Baseline monitoring case study of a high-gradient urbanized stream: Boone Creek, Boone, NC. In: 2nd national low impact development conference, March 12–14, 2007, Wilmington, NC. ASCE

  • Anderson WP Jr, Anderson JL, Thaxton CS, Babyak CM (2010) Changes in stream temperatures in response to restoration of groundwater discharge and solar heating in a culverted, urban stream. J Hydrol 393:309–320. doi:10.1016/j.jhydrol.2010.08.030

    Article  Google Scholar 

  • Anderson WP Jr, Storniolo RE, Rice JS (2011) Bank thermal storage as a sink of temperature surges in urbanized streams. J Hydrol 409:525–537. doi:10.1016/j.jhydrol.2011.08.059

    Article  Google Scholar 

  • Bandt C, Pompe B (2002) Permutation entropy: a natural complexity measure for time series. Phys Rev Lett 88:174102:1–174102:4

    Article  Google Scholar 

  • Bariviera AF, Zunino L, Guercio MB, Martinez LB, Rosso OA (2013) Efficiency and credit ratings: a permutation-information-theory analysis. J Stat Mech Theory Exp 08:P08007

    Article  Google Scholar 

  • Barreiro M, Marti AC, Masoller C (2011) Inferring long memory processes in the climate network via ordinal pattern analysis. Chaos 21:013101

    Article  Google Scholar 

  • Benyahya L, Caissie D, St-Hilaire A, Ouarda TBMJ, Bobee B (2007) A review of statistical water temperature models. Can Water Resour J 32(3):179–192

    Article  Google Scholar 

  • Caissie D (2006) The thermal regime of rivers: a review. Freshwater Biol 51(8):1389–1406

    Article  Google Scholar 

  • Chou CM (2014) Complexity analysis of rainfall and runoff time series based on sample entropy in different temporal scales. Stoch Environ Res Risk Assess 28(6):1401–1408

    Article  Google Scholar 

  • Cockerill K, Anderson WP Jr (2014a) Creating false images: stream restoration in an urban setting. J Am Water Resour Assoc 50(2):468–482. doi:10.1111/jawr.12131

    Article  Google Scholar 

  • Cockerill K, Anderson WP Jr (2014b) Reply to discussion—“creating false images: streamrestoration in an urban setting” by David L. Rosgen. J Am Water Resour Assoc (JAWRA). doi:10.1111/jawr.12241

    Google Scholar 

  • Consolini G, DeMichelis P (2014) Permutation entropy analysis of complex magnetospheric dynamics. J Atmos Sol Terr Phys 115–116:25–31

    Article  Google Scholar 

  • Do Nascimento RS, de Araujo LHG, Moraes RB, Barbosa CT, Guedes RC, Nogueira RA, Stošić T (2010) Analysis of signal fluctuations of cortical spreading depression: preliminary findings. Phys A 389:1869–1873

    Article  Google Scholar 

  • dosAnjos PS, da Silva ASA, Stošić B, Stošić T (2015) Long-term correlations and cross-correlations in wind speed and solar radiation temporal series from Fernando de Noronha Island, Brazil. Phys A 424:90–96

    Article  Google Scholar 

  • Eke A, Herman P, Kocsis L, Kozak LR (2002a) Fractal characterization of complexity in temporal physiological signals. Physiol Meas 2002(23):R1–R38. doi:10.1088/0967-3334/23/1/201

    Article  Google Scholar 

  • Eke A, Herman P, Kocsis L, Kozak LR (2002b) Fractal characterization of complexity in temporal physiological signals. Physiol Meas 23(1):R1–38

    Article  CAS  Google Scholar 

  • Erickson TR, Stefan HG (2000) Linear air/water temperature correlations for streams during open water periods. J Hydrol Eng 5(3):317–321

    Article  Google Scholar 

  • Goldberger AL, Amaral LA, Hausdorff JM, Ivanov PCh, Peng C-K, Stanley HE (2002) Fractal dynamics in physiology: alterations with disease and aging. Proc Natl Acad Sci USA 99(Suppl. 1):2466–2472

    Article  Google Scholar 

  • Graff G, Graff B, Kaczkowska A, Makowiec D, Amigó JM, Piskorski J, Narkiewicz K, Guzik P (2013) Ordinal pattern statistics for the assessment of heart rate variability. Eur Phys J Spec Top 222(2):525–534

    Article  Google Scholar 

  • Gu C, Anderson WP Jr, Colby JD, Coffey CL (2014) Air-stream temperature correlation in forested and urbanheadwater streams in the Southern Appalachians. Hydrol Process. doi:10.1002/hyp.10225

    Google Scholar 

  • Gupta VK, Messa OJ, Dawdy DR (1994) Multi scaling theory of floodpeaks: regional quantile analysis. Water Resour Res 30:3405–3421

    Article  Google Scholar 

  • Hatch CE, Fisher AT, Revenaugh JS, Constantz J, Ruehl C (2006) Quantifying surface water-groundwater interactions using time series analysis of streambed thermal records: method development. Water Resour Res 42:W10410. doi:10.1029/2005WR004787

    Article  Google Scholar 

  • Hauhs M, Lange H (2008) Classification of runoff in headwater catchments: a physical problem. Geogr Compass 2(1):235–254

    Article  Google Scholar 

  • Huang F, Xia Z, Zhang N, Zhang Y, Li J (2011) Flow-complexity analysis of the upper reaches of the Yangtze River, China. J Hydrol Eng 16:914–919

    Article  Google Scholar 

  • Jovanovic T, Mejía A, Gall H, Gironás J (2016a) Effect of urbanization on the long-term persistence of streamflow records. Phys A 447:208–221

    Article  Google Scholar 

  • Jovanovic T, García S, Gall H, Mejía A (2016b) Complexity as a streamflow metric of hydrologic alteration. Stoch Environ Res Risk Assess. doi:10.1007/s00477-016-1315-6

    Google Scholar 

  • Kantelhardt JW, Konccielny-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 111:D011106

    Article  Google Scholar 

  • Keery J, Binley A, Crook N, Smith JWN (2007) Temporal and spatial variability of groundwater-surface water fluxes: development and application of an analytical method using temperature time series. J Hydrol 336:1–16. doi:10.1016/j.jhydrol.2006.12.003

    Article  Google Scholar 

  • Kelly GM, Perry LB, Taubman BF, Soule PT (2012) Synoptic classification of 2009–2010 precipitationevents in the southern Appalachian Mountains, USA. Clim Res 55:1–15

    Article  Google Scholar 

  • Kelly GM, Taubman BF, Perry LB, Sherman JP, Soule´ PT, Sheridan PJ (2013) Relationships between aerosols and precipitation in thesouthern Appalachian Mountains. Int J Climatol 33:3016–3028

    Article  Google Scholar 

  • Király A, Jánosi IM (2005) Detrended fluctuation analysis of daily temperature records: geographic dependence over Australia. Meteorol Atmos Phys 88:119–128

    Article  Google Scholar 

  • Labat D, Masbou J, Beaulieu E, Mangin A (2011) Scaling behavior of the fluctuations in stream flow at the outlet of karstic watersheds, France. J Hydrol 410(3–4, 22):162–168

    Article  Google Scholar 

  • Labat D, Sivakumar B, Mangin A (2016) Evidence for deterministic chaos in long-term high-resolution karstic streamflow time series. Stoch Environ Res Risk Assess 30(8):2189–2196

    Article  Google Scholar 

  • LeBlanc RT, Brown RD, FitzGibbon JE (1997) Modeling the effects of land use change on the water temperature in unregulated urban streams. J Environ Manage 49:445–469

    Article  Google Scholar 

  • Li Z, Zhang Y-K (2008) Multi-scale entropy analysis of Mississippi River flow. Stoch Environ Res Risk Assess 22:507–512

    Article  Google Scholar 

  • Li Q, Zuntao F (2014) Permutation entropy and statistical complexity quantifier of nonstationarity effect in the vertical velocity records. Phys Rev E 89(1):012905

    Article  Google Scholar 

  • Martin MT, Plastino A, Rosso OA (2006) Generalized statistical complexity measures: geometrical and analytical properties. Phys A 369:439–462

    Article  Google Scholar 

  • Maruyama T, Kawachi T, Singh VP (2005) Entropy-based assessment and clustering of potential water resources availability. J Hydrol 309(1–4):104–113

    Article  Google Scholar 

  • Matsoukas C, Islam S, Rodriguez-Iturbe I (2000) Detrended fluctuation analysis of rainfall and streamflow time series. J Geophys Res Atmos 105(D23):29165–29172

    Article  Google Scholar 

  • Mihailović DT, Nikolić-Djorić E, Drešković N, Mimić G (2014) Complexity analysis of the turbulent environmental fluid flow time series. Phys A 395:96–104

    Article  Google Scholar 

  • Mishra AK, Özger M, Singh VP (2009) An entropy-based investigation into the variability of precipitation. J Hydrol 370(1–4):139–154

    Article  Google Scholar 

  • Mohseni O, Stefan HG (1999) Stream temperature/air temperature relationship: a physical interpretation. J Hydrol 218:128–141

    Article  Google Scholar 

  • Mohseni O, Stefan HG, Erickson TR (1998) A nonlinear regression model for weekly stream temperatures. Water Resour Res 34(10):2685–2692

    Article  Google Scholar 

  • Montani F, Rosso OA (2014) Entropy-complexity characterization of brain development in chickens. Entropy 16(8):4677–4692

    Article  Google Scholar 

  • Morrill JC, Bales RC, Conklin MH (2005) Estimating stream temperature from air temperatures: implication for future water use. J Environ Eng 131(1):139. doi:10.1061/(ASCE)0733-9372

    Article  CAS  Google Scholar 

  • Neumann DW, Rajagopalan B, Zagona EA (2003) Regression model for daily maximum stream temperature. J Environ Eng 129(7):667–674

    Article  CAS  Google Scholar 

  • O’driscoll MA, DeWalle DR (2006) Stream-air temperature relations to classify stream-ground water interactions in a karst setting, central Pennsylvania, USA. J Hydrol 329:140–153

    Article  Google Scholar 

  • Olofsen E, Sleigh JW, Dahan A (2008) Permutation entropy of the electroencephalogram: a measure of anaesthetic drug effect. Br J Anaesth 101(6):810–821

    Article  CAS  Google Scholar 

  • Pan F, Pachepsky YA, Guber AK, McPherson BJ, Hill RL (2012) Scale effects on information theory-based measures applied to streamflow patterns in two rural watersheds. J Hydrol 414–415:99–107

    Article  Google Scholar 

  • Pandey G, Lovejoy S, Schertzer D (1998) Multifractal analysis of daily river flows including extremes for basins of five to million square kilometers, one day to 75 years. J Hydrol 208:62–81

    Article  Google Scholar 

  • Peng C-K, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mozaic organization of DNA nucleotides. Phys Rev E 49:1685–1689

    Article  CAS  Google Scholar 

  • Poole GC, Berman CH (2001) An ecological perspective on in-stream temperature: natural heat dynamics and mechanisms of human-caused thermal degradation. Environ Manage 27:787–802

    Article  CAS  Google Scholar 

  • Porporato A, Ridolfi L (1996) Clues to the existence of deterministic chaos in river flow. Int J Mod Phys 10:1821

    Article  Google Scholar 

  • Ribeiro HV, Zunino L, Mendes RS, Lenzi EK (2012) Complexity–entropy causality plane: a useful approach for distinguishing songs. Phys A 391(7):2421–2428

    Article  Google Scholar 

  • Rice JS, Anderson WP Jr, Thaxton CS (2011) Urbanization influences on stream temperature behavior within low-discharge headwater streams. Hydrol Res Lett 5:27–31

    Article  Google Scholar 

  • Rosgen DL (2014) Discussion—“Creating false images: stream restoration in an urban setting” by Kristan Cockerill and William P. Anderson, Jr. J Am Water Resour Assoc (JAWRA). doi:10.1111/jawr.12242

    Google Scholar 

  • Rosso OA, Larrondo HA, Martin MT, Plastino A, Fuentes MA (2007) Distinguishing noise from Chaos. PRL 99:154102

    Article  CAS  Google Scholar 

  • Serinaldi F, Zunino L, Rosso OA (2014) Complexity–entropy analysis of daily stream flow time series in the continental United States. Stoch Environ Res Risk Assess 28(7):1685–1708

    Article  Google Scholar 

  • Siqueira EL Jr, Stošić T, Bejan L, Stošić B (2010) Correlations and cross-correlations in the Brazilian agrarian commodities and stocks. Phys A 389:2739–2743

    Article  CAS  Google Scholar 

  • Sivakumar B (2009) Nonlinear dynamics and chaos in hydrological systems: latest developments and a look forward. Stoch Environ Res Risk Assess 23:1027–1036

    Article  Google Scholar 

  • Sivakumar B, Singh VP (2012) Hydrologic system complexity and nonlinear dynamics concepts for a catchment classification framework. Hydrol Earth Syst Sci 16:4119–4131

    Article  Google Scholar 

  • Telesca L, Lovallo M (2011) Revealing commpetitivebehaviours in music by means of the multifractaldetrended fluctuation analysis: application to Bach’s Sinfonias. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences

  • Telesca L, Lasaponara R, Lanorte A (2006) 1/f a fluctuations in the time dynamics of Mediterranean forest ecosystems by using normalized difference vegetation index satellite data. Phys A 361:699–706

    Article  Google Scholar 

  • Wang F, Shieh SJ, Havlin S, Stanley HE (2009) Statistical analysis of the overnight and daytime return. Phys Rev E 79(5):056109

    Article  Google Scholar 

  • Webb BW, Nobilis F (1997) Long-term perspective on the nature of the air-water temperature relationship: a case study. Hydrol Process 11:137–147

    Article  Google Scholar 

  • Webb BW, Clack PD, Walling DE (2003) Water-air temperaturerelationships in a Devon river system and the role of flow. Hydrol Process 17(15):3069–3084

    Article  Google Scholar 

  • Weck PJ, Schaffner DA, Brown MR, Wicks RT (2015) Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind. Phys Rev E 91(2):023101

    Article  CAS  Google Scholar 

  • Zhang Q, Xu CY, Yang T (2009) Scaling properties of the runoff variations in the arid and semi-arid regions of China: a case study of the Yellow River basin. Stoch Environ Res Risk Assess 23(8):1103–1111

    Article  Google Scholar 

  • Zhang Q, Zhou Y, Singh VP, Chen X (2012) The influence of dams and lakes on the Yangtze River streamflow: long-range correlations and complexity analysis. Hydrol Process 26:436–444

    Article  Google Scholar 

  • Zheng Z, Yamasaki K, Tenenbaum J, Podobnik B, Tamura Y, Stanley HE (2012) Scaling of seismic memory with earthquake size. Phys Rev E 86(1):011107

    Article  Google Scholar 

  • Zhou Y, Zhang Q, Singh VP (2014) Fractal-based evaluation of the effect of water reservoirs on hydrological processes: the dams in the Yangtze River as a case study. Stoch Environ Res Risk Assess 28:263–279

    Article  Google Scholar 

  • Zunino L, Zanin M, Tabak BM, Pérez DG, Rosso OA (2009) Forbidden patterns, permutation entropy and stock market inefficiency. Phys A 388(14):2854–2864

    Article  Google Scholar 

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Acknowledgements

Real-time stream data at the VG site is available at http://www.appstate.edu/~hydro/. All historical stream data is available upon request to Dr. William Anderson (andersonwp@appstate.edu). Air temperature data may be obtained from the State Climate Office of North Carolina, NC CRONOS database, for the site KTNB located in Boone, NC (NC CRONOS 2016, http://climate.ncsu.edu/cronos).

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Authors and Affiliations

  1. Department of Physics and Astronomy, Appalachian State University, Boone, NC, USA

    Christopher S. Thaxton

  2. Department of Geology, Appalachian State University, Boone, NC, USA

    W. P. Anderson Jr. & Chuanhui Gu

  3. Departmento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Recife, Brazil

    Borko Stosic & Tatijana Stosic

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  1. Christopher S. Thaxton
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  2. W. P. Anderson Jr.
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Correspondence to Christopher S. Thaxton.

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Thaxton, C.S., Anderson, W.P., Gu, C. et al. Detrended fluctuation analysis and entropy-complexity causality analysis of temperatures in an urbanized mountain stream. Stoch Environ Res Risk Assess 32, 843–858 (2018). https://doi.org/10.1007/s00477-017-1434-8

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