Analysis of temporal variation and scaling of hydrological variables based on a numerical model of the Sagehen Creek watershed

Original Paper


Temporal variations of the main hydrological variables over 16 years were systematically investigated based on the results from an integrated hydrological modeling at the Sagehen Creek watershed in northern Sierra Nevada. Temporal scaling of these variables and damping effects of the hydrological system as well as its subsystems, i.e., the land surface, unsaturated zone, and saturated zone, were analyzed with spectral analyses. It was found that the hydrological system may act as a cascade of hierarchical fractal filters which sequentially transfer a non-fractal or less correlated fractal hydrological signal to a more correlated fractal signal. The temporal scaling of simulated infiltration (SI), simulated actual evapotranspiration (SET), simulated recharge (SR), measured baseflow (MBF), measured streamflow (MSF) exist and the temporal autocorrelation of these variables increase as water moves through the system. The degree of the damping effect of the subsystems is different and is strongest in the unsaturated zone compared with that of the land surface and saturated zone. The temporal scaling of the simulated groundwater levels (Sh) also exists and is strongly affected by the river: the temporal autocorrelation of Sh near the river is similar to that of the river stage fluctuations and increases away from the river. There is a break in the temporal scaling of Sh near the river at low frequencies due to the effect of the river. Temporal variations of the simulated soil moisture (Sθ) is more complicated: the value of the scaling exponent (β) for Sθ increases with depth as water moves downwards and its high-frequency fluctuations are damped by the unsaturated zone. The temporal fluctuations of measured precipitation and SI are fractional Gaussian noise, those of SET, SR, MBF, and MSF are fractional Brownian motion (fBm), and those of Sh away from the river are 2nd-order fBm based on the values of β obtained in this study.


Temporal variations Scaling Damping effect Hydrological system 



This study was partially supported with research grants from the National Nature Science Foundation of China (NSFC-41272260, NSFC-41330314, and NSFC-41302180), the Natural Science Foundation of Jiangsu Province (BK20130571), the program “The Social Development-Sicence & Technology Demostration Projects” sponsored by Department of Science and Technology of Jiangsu Province (BE2015708). The data used in this study can be accessed by contacting the corresponding author directly.


  1. Amenu GG, Kumar P, Liang XZ (2005) Interannual variability of deep-layer hydrologic memory and mechanisms of its influence on surface energy fluxes. J Clim 18:5024–5045. doi: 10.1175/Jcli3590.1 CrossRefGoogle Scholar
  2. Aubert AH, Kirchner JW, Gascuel-Odoux C, Faucheux M, Gruau G, Merot P (2014) Fractal water quality fluctuations spanning the periodic table in an intensively farmed watershed. Environ Sci Technol 48:930–937. doi: 10.1021/Es403723r CrossRefGoogle Scholar
  3. Bierkens MFP, van den Hurk BJJM (2007) Groundwater convergence as a possible mechanism for multi-year persistence in rainfall. Geophys Res Lett. doi: 10.1029/2006gl028396 Google Scholar
  4. Changnon SA (1987) Detecting drought conditions in Illinois. Illinois State Water Survey Circular, Champaign, Circular 169Google Scholar
  5. Das S, Pan I (2012) Fractional order signal processing: introductory concepts and applications. SpringerBriefs in applied sciences and technology. Springer, HeidelbergCrossRefGoogle Scholar
  6. Delworth TL, Manabe S (1988) The influence of potential evaporation on the variabilities of simulated soil wetness and climate. J Clim 1:523–547CrossRefGoogle Scholar
  7. Entin JK, Robock A, Vinnikov KY, Hollinger SE, Liu SX, Namkhai A (2000) Temporal and spatial scales of observed soil moisture variations in the extratropics. J Geophys Res Atmos 105:11865–11877. doi: 10.1029/2000jd900051 CrossRefGoogle Scholar
  8. Essaid HI, Hill BR (2014) Watershed-scale modeling of streamflow change in incised montane meadows. Water Resour Res 50:2657–2678. doi: 10.1002/2013wr014420 CrossRefGoogle Scholar
  9. Feder J (1988) Fractals. Physics of solids and liquids. Plenum Press, New YorkGoogle Scholar
  10. Godsey SE et al (2010) Generality of fractal 1/f scaling in catchment tracer time series, and its implications for catchment travel time distributions. Hydrol Process 24:1660–1671. doi: 10.1002/hyp.7677 CrossRefGoogle Scholar
  11. Guan K et al (2011) Spatiotemporal scaling of hydrological and agrochemical export dynamics in a tile-drained Midwestern watershed. Water Resour Res. doi: 10.1029/2010wr009997 Google Scholar
  12. Harbaugh AW (2005) MODFLOW-2005, The U.S. Geological Survey modular ground-watermodel—the Ground-Water Flow Process, U.S. Geological Survey Techniques and Methods 6-A16, variously pGoogle Scholar
  13. Hassan SMT, Lubczynski MW, Niswonger RG, Su ZB (2014) Surface-groundwater interactions in hard rocks in Sardon Catchment of western Spain: an integrated modeling approach. J Hydrol 517:390–410. doi: 10.1016/j.jhydrol.2014.05.026 CrossRefGoogle Scholar
  14. Huntington JL, Niswonger RG (2012) Role of surface-water and groundwater interactions on projected summertime streamflow in snow dominated regions: an integrated modeling approach. Water Resour Res. doi: 10.1029/2012wr012319 Google Scholar
  15. Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Am Soc Civ Eng 116:770–799Google Scholar
  16. 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. doi: 10.1029/2005jd005881 Google Scholar
  17. Katul GG et al (2007) On the spectrum of soil moisture from hourly to interannual scales. Water Resour Res. doi: 10.1029/2006wr005356 Google Scholar
  18. Kirchner JW, Neal C (2013) Universal fractal scaling in stream chemistry and its implications for solute transport and water quality trend detection. Proc Natl Acad Sci USA 110:12213–12218. doi: 10.1073/pnas.1304328110 CrossRefGoogle Scholar
  19. Kirchner JW, Feng XH, Neal C (2000) Fractal stream chemistry and its implications for contaminant transport in catchments. Nature 403:524–527. doi: 10.1038/35000537 CrossRefGoogle Scholar
  20. Kirchner JW, Feng X, Neal C (2001) Catchment-scale advection and dispersion as a mechanism for fractal scaling in stream tracer concentrations. J Hydrol 254:82–101. doi: 10.1016/S0022-1694(01)00487-5 CrossRefGoogle Scholar
  21. Labat D, Ababou R, Mangin A (2000) Rainfall runoff relations for karstic springs:convolution and spectral analysis. J Hydrol 238:123–148CrossRefGoogle Scholar
  22. Leavesley GH, Lichty RW, Troutman BM, Saindon LG (1983) Precipitation-runoff modeling system—User’s manual: U.S. Geological Survey Water-Resources Investigations Report 83-4238Google Scholar
  23. Lévy P (1953) Random functions: general theory with special references to Laplacian random functions. Univ Calif Publ Stat 1:331–390Google Scholar
  24. Li M (2010) Fractal time series—a tutorial review. Math Probl Eng. doi: 10.1155/2010/157264 Google Scholar
  25. Li ZW, Zhang YK (2007) Quantifying fractal dynamics of groundwater systems with detrended fluctuation analysis. J Hydrol 336:139–146. doi: 10.1016/j.jhydrol.2006.12.017 CrossRefGoogle Scholar
  26. Liang XY, Zhang YK (2013) Temporal and spatial variation and scaling of groundwater levels in a bounded unconfined aquifer. J Hydrol 479:139–145. doi: 10.1016/j.jhydrol.2012.11.044 CrossRefGoogle Scholar
  27. Liang XY, Zhang YK (2015) Analyses of uncertainties and scaling of groundwater level fluctuations. Hydrol Earth Syst Sci 19:2971–2979. doi: 10.5194/hess-19-2971-2015 CrossRefGoogle Scholar
  28. Lim KJ, Engel BA, Tang Z, Choi J, Kim KS, Muthukrishnan S, Tripathy D (2005) Automated web GIS based hydrograph analysis tool, WHAT. J Am Water Res Assoc 41(6):1407–1416CrossRefGoogle Scholar
  29. Little MA, Bloomfield JP (2010) Robust evidence for random fractal scaling of groundwater levels in unconfined aquifers. J Hydrol 393:362–369. doi: 10.1016/j.jhydrol.2010.08.031 CrossRefGoogle Scholar
  30. Lovejoy S, Schertzer D (2013) The weather and climate: emergent laws and multifractal cascades. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  31. Malamud BD, Turcotte DL (1999) Self-affine time series: measures of weak and strong persistence. J Stat Plan Inference 80:173–196. doi: 10.1016/S0378-3758(98)00249-3 CrossRefGoogle Scholar
  32. Mandelbr BB, Vanness JW (1968) Fractional brownian motions fractional noises and applications. Siam Rev 10:422–437. doi: 10.1137/1010093 CrossRefGoogle Scholar
  33. Mandelbrot BB, Wallis JR (1968) Noah, Joseph, and operational hydrology. Water Resour Res 4(5):909–918CrossRefGoogle Scholar
  34. Markstrom SL, Niswonger RG, Regan RS, Prudic DE, Barlow PM (2008) GSFLOW—Coupled ground-water and surface-water flow model based on the integration of the Precipitation-Runoff Modeling System (PRMS) and the Modular Ground-Water Flow Model (MODFLOW-2005), U.S. Geological Survey Techniques and Methods 6-D1Google Scholar
  35. Matsoukas C, Islam S, Rodriguez-Iturbe I (2000) Detrended fluctuation analysis of rainfall and streamflow time series. J Geophys Res Atmos 105:29165–29172. doi: 10.1029/2000jd900419 CrossRefGoogle Scholar
  36. Neal C et al (2013) High-frequency precipitation and stream water quality time series from Plynlimon, Wales: an openly accessible data resource spanning the periodic table. Hydrol Process 27:2531–2539. doi: 10.1002/hyp.9814 CrossRefGoogle Scholar
  37. Niswonger RG, Allander KK, Jeton AE (2014) Collaborative modelling and integrated decision support system analysis of a developed terminal lake basin. J Hydrol 517:521–537. doi: 10.1016/j.jhydrol.2014.05.043 CrossRefGoogle Scholar
  38. Olsson J, Niemczynowicz J, Berndtsson R (1993) Fractal analysis of high-resolution rainfall time-series. J Geophys Res Atmos 98:23265–23274. doi: 10.1029/93jd02658 CrossRefGoogle Scholar
  39. Ozger M, Mishra AK, Singh VP (2013) Seasonal and spatial variations in the scaling and correlation structure of streamflow data. Hydrol Process 27:1681–1690. doi: 10.1002/Hyp.9314 CrossRefGoogle Scholar
  40. Pandey G, Lovejoy S, Schertzer D (1998) Multifractal analysis of daily river flows including extremes for basins of five to two million square kilometres, one day to 75 years. J Hydrol 208:62–81. doi: 10.1016/S0022-1694(98)00148-6 CrossRefGoogle Scholar
  41. Rakhshandehroo GR, Amiri SM (2012) Evaluating fractal behavior in groundwater level fluctuations time series. J Hydrol 464:550–556. doi: 10.1016/j.jhydrol.2012.07.030 CrossRefGoogle Scholar
  42. Romero-Melendez G, Ojeda-Suarez R, Nava-Huerta A, Garcia-Valdez CA (2008) Fractal time series and a prediction method. Trimest Econ 75:179–189CrossRefGoogle Scholar
  43. Schilling KE (2002) Chemical transport from paired agricultural and restored prairie watersheds. J Environ Qual 31:1184–1193CrossRefGoogle Scholar
  44. Schilling KE, Zhang YK (2012) Temporal scaling of groundwater level fluctuations near a stream. Ground Water 50:59–67. doi: 10.1111/j.1745-6584.2011.00804.x CrossRefGoogle Scholar
  45. Skoien JO, Bloschl G, Western AW (2003) Characteristic space scales and timescales in hydrology. Water Resour Res. doi: 10.1029/2002wr001736 Google Scholar
  46. Tessier Y, Lovejoy S, Hubert P, Schertzer D, Pecknold S (1996) Multifractal analysis and modeling of rainfall and river flows and scaling, causal transfer functions. J Geophys Res Atmos 101:26427–26440. doi: 10.1029/96jd01799 CrossRefGoogle Scholar
  47. Turcotte DL (1992) Fractals and chaos in geology and geophysics. Cambridge University Press, CambridgeGoogle Scholar
  48. Wu WR, Geller MA, Dickinson RE (2002) The response of soil moisture to long-term variability of precipitation. J Hydrometeorol 3:604–613. doi: 10.1175/1525-7541(2002)003<0604:Trosmt>2.0.Co;2 CrossRefGoogle Scholar
  49. Yang C, Zhang Y-K, Liang X (2015) Effects of temporally correlated infiltration on water flow in an unsaturated–saturated system. Stoch Environ Res Risk Aaaess. doi: 10.1007/s00477-015-1119-0 Google Scholar
  50. Zhang YK, Li ZW (2005) Temporal scaling of hydraulic head fluctuations: nonstationary spectral analyses and numerical simulations. Water Resour Res. doi: 10.1029/2004wr003797 Google Scholar
  51. Zhang YK, Li ZW (2006) Effect of temporally correlated recharge on fluctuations of groundwater levels. Water Resour Res. doi: 10.1029/2005wr004828 Google Scholar
  52. Zhang YK, Schilling K (2004) Temporal scaling of hydraulic head and river base flow and its implication for groundwater recharge. Water Resour Res. doi: 10.1029/2003wr002094 Google Scholar
  53. Zhang YK, Schilling K (2005) Temporal variations and scaling of streamflow and baseflow and their nitrate-nitrogen concentrations and loads. Adv Water Resour 28:701–710. doi: 10.1016/j.adwatres.2004.12.014 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Environmental StudiesChina University of GeosciensesWuhanPeople’s Republic of China
  2. 2.School of Earth Sciences and EngineeringNanjing UniversityNanjingPeople’s Republic of China
  3. 3.School of Environment Science and EngineeringSouthern University of Science and TechnologyShenzhenPeople’s Republic of China

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