Boundary-Layer Meteorology

, Volume 164, Issue 1, pp 19–37 | Cite as

A Case Study of the Performance of Different Detrending Methods in Turbulent-Flux Estimation

Research Article


The performance of different detrending methods in removing the low-frequency contribution to the calculation of turbulent fluxes is investigated. The detrending methods are applied to the calculation of turbulent fluxes of different scalars (temperature, ultrafine particle number concentration, carbon dioxide and water vapour concentration), collected at two different measurement sites: one urban and one suburban. We test and compare the performance of filtering methodologies frequently used in real-time and automated procedures (mean removal, linear detrending, running mean, autoregressive filter) with the results obtained from a reference method, which is a spectral filter based on the Fourier decomposition of the time series. In general, the largest differences are found in the comparison between the reference and the mean-removal procedures. The linear detrending and running-mean procedures produce comparable results, and turbulent-flux estimations in better agreement with the reference procedure than those obtained with the mean-removal procedure. The best agreement between the running mean and the spectral filter is achieved with a time window of 15 min at both sites. For all the variables studied, average fluxes calculated using the autoregressive filter are increasingly overestimated for a time constant \(\tau \) compared with that obtained using the spectral filter. The minimization of the difference between the two detrending methods is achieved with a time constant of 120 s, with similar behaviour observed at both sites.


Aerosol flux Detrending Eddy covariance Stationarity Turbulent fluxes 


  1. Alberto MCR, Wassmann R, Buresh RJ, Quilty JR, Correa TQ Jr, Sandro JM, Arloo C, Centeno R (2014) Measuring methane flux from irrigated rice fields by eddy covariance method using open-path gas analyzer. Field Crop Res 160:12–21CrossRefGoogle Scholar
  2. Andreas EL, Geiger C, Trevĩno G, Claffey K (2008) Identifying non-stationarity in turbulence series. Boundary-Layer Meteorol 127:37–56CrossRefGoogle Scholar
  3. Aubinet M (2008) Eddy covariance \(\text{ CO }_{2}\) flux measurements in nocturnal conditions: an analysis of the problem. Ecol Appl 18:1368–1378CrossRefGoogle Scholar
  4. Baldocchi D (2003) Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future. Glob Change Biol 9:479–492CrossRefGoogle Scholar
  5. Baldocchi DD, Falge E, Gu L, Olson R, Hollinger D, Running S, Anthoni P, Bernhofer C, Davis K, Evans R, Fuentes J, Goldstein A, Katul G, Law B, Lee X, Malhi Y, Meyers T, Munger W, Oechel W, Paw UKT, Pilegaard K, Schmid HP, Valentini R, Verma S, Vesala T, Wilson K, Wofsy S (2001) FLUXNET: a new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapour and energy flux densities. Bull Am Meteorol Soc 82:2415–2435CrossRefGoogle Scholar
  6. Barnhart BL, Eichinger WE, Prueger JH (2012) A new eddy-covariance method using empirical mode decomposition. Boundary-Layer Meteorol 145:369–382CrossRefGoogle Scholar
  7. Bell TG, De Bruyn W, Marandino CA, Miller SD, Law CS, Smith MJ, Saltzman ES (2015) Dimethylsulfide gas transfer coefficients from algal blooms in the Southern Ocean. Atmos Chem Phys 15:1783–1794CrossRefGoogle Scholar
  8. Bendat JS, Piersol AG (1958) Measurement and analysis of random data. Wiley, New YorkGoogle Scholar
  9. Buzorius G, Rannik Ü, Mäkelä JM, Keronen P, Vesala T, Kulmala M (2000) Vertical aerosol fluxes measured by the eddy covariance method and deposition of nucleation mode particles above a Scots pine forest in southern Finland. J Geophys Res 105:19905–19916CrossRefGoogle Scholar
  10. Camarori P, Schuepp P, Desjardins R, MacPherson I (1994) Structural analysis of airborne flux estimates over a region. J Clim 7:627–640CrossRefGoogle Scholar
  11. Cava D, Giostra U, Siqueira M, Katul G (2004) Organised motion and radiative perturbations in the nocturnal canopy sublayer above an even-aged pine forest. Boundary-Layer Meteorol 112:129–157CrossRefGoogle Scholar
  12. Cava D, Donateo A, Contini D (2014) Combined stationarity index for the estimation of turbulent fluxes of scalars and particles in the atmospheric surface layer. Agric For Meteorol 194:88–103CrossRefGoogle Scholar
  13. Cava D, Giostra U, Katul G (2015) Characteristics of gravity waves over an Antarctic ice sheet during an austral summer. Atmosphere 6:1271–1289CrossRefGoogle Scholar
  14. Christen A (2014) Atmospheric measurement techniques to quantify greenhouse gas emissions from cities. Urban Clim 10:241–260CrossRefGoogle Scholar
  15. Conte M, Donateo A, Dinoi A, Belosi F, Contini D (2015) Influence of nucleation events on number particles fluxes and size distributions in south-eastern Italy during summer season. Atmosphere 6:942–959CrossRefGoogle Scholar
  16. Contini D, Donateo A, Belosi F, Grasso FM, Santachiara G, Prodi F (2010) Deposition velocity of ultrafine particles measured with the eddy-correlation method over the Nansen Ice Sheet (Antarctica). J Geophys Res Atmos 115:D16202CrossRefGoogle Scholar
  17. Contini D, Donateo A, Elefante C, Grasso FM (2012) Analysis of particles and carbon dioxide concentrations and fluxes in an urban area: correlation with traffic rate and local micrometeorology. Atmos Environ 46:25–35CrossRefGoogle Scholar
  18. Damay PE, Maro D, Coppalle A, Lamaud E, Connan O, Hebert D, Talbaut M, Irvine M (2009) Size-resolved eddy covariance measurements of fine particle vertical fluxes. J Aerosol Sci 40:1050–1058CrossRefGoogle Scholar
  19. Detto M, Verfaillie J, Anderson F, Xu L, Baldocchi D (2011) Comparing laser-based open- and closed-path gas analyzers to measure methane fluxes using the eddy covariance method. Agric For Meteorol 151:1312–1324CrossRefGoogle Scholar
  20. Deventer MJ, Held A, El-Madanya TS, Klemm O (2015a) Size-resolved eddy covariance fluxes of nucleation to accumulation mode aerosol particles over a coniferous forest. Agric For Meteorol 214–215:328–340CrossRefGoogle Scholar
  21. Deventer MJ, El-Mandany T, Griessbaum F, Klemm O (2015b) One-year measurement of size-resolved particle fluxes in an urban area. Tellus 67B:25531CrossRefGoogle Scholar
  22. Donateo A, Contini D (2014) Correlation of dry deposition velocity and friction velocity over different surfaces for PM2.5 and particle number concentrations. Adv Meteorol. doi: 10.1155/2014/760393
  23. Donateo A, Contini D, Belosi F, Gambaro A, Santachiara G, Cesari D, Prodi F (2012) Characterization of PM2.5 concentrations and turbulent fluxes on an island in the Venice lagoon using high temporal resolution measurements. Meteorol Z 21:385–398CrossRefGoogle Scholar
  24. Dorsey JR, Nemitz E, Gallagher MW, Fowler D, Williams PI, Bower KN, Beswick KM (2002) Direct measurements and parameterisation of aerosol flux, concentration and emission velocity above a city. Atmos Environ 36:791–800CrossRefGoogle Scholar
  25. Fairall CW (1984) Interpretation of eddy correlation measurements of particulate deposition and aerosol flux. Atmos Environ 18:1329–1337CrossRefGoogle Scholar
  26. Famulari D, Nemitz E, Di Marco C, Phillips GJ, Thomas R, House E, Fowler D (2010) Eddy-covariance measurements of nitrous oxide fluxes above a city. Agric For Meteorol 150:786–793CrossRefGoogle Scholar
  27. Farmer DK, Kimmel JR, Phillips G, Docherty KS, Worsnop DR, Sueper D, Nemitz E, Jimenez JL (2011) Eddy covariance measurements with high-resolution time-of-flight aerosol mass spectrometry: a new approach to chemically resolved aerosol fluxes. Atmos Meas Tech 4:1275–1289CrossRefGoogle Scholar
  28. Farmer DK, Chen Q, Kimmel JR, Docherty KS, Nemitz E, Artaxo PA, Cappa CD, Martin ST, Jimenez JL (2013) Chemically resolved particle fluxes over tropical and temperate forests. Aerosol Sci Technol 47:818–830CrossRefGoogle Scholar
  29. Ferrara RM, Loubet B, Di Tommasi P, Bertolini T, Magliulo V, Cellier P, Eugster W, Rana G (2012) Eddy covariance measurement of ammonia fluxes: comparison of high frequency correction methodologies. Agric For Meteorol 158–159:30–42CrossRefGoogle Scholar
  30. Finnigan JJ, Clement R, Malhi Y, Leuning R, Cleugh HA (2003) A re-evaluation of long-term flux measurement techniques. Part 1: Averaging and coordinate rotation. Boundary-Layer Meteorol 107:1–48CrossRefGoogle Scholar
  31. Foken T, Leuning R, Oncley SP, Mauder M, Aubinet M (2012) Corrections and data quality control. In: Aubinet M, Vesala T, Papale D (eds) Eddy covariance: a practical guide to measurement and data analysis. Springer, Dordrecht, pp 85–132Google Scholar
  32. Gallagher MW, Nemitz E, Dorsey JR, Fowler D, Sutton MA, Flynn M, Duyzer J (2002) Measurements and parameterisations of small aerosol deposition velocities to grassland, arable crops, and forest: influence of surface roughness length on deposition. J Geophys Res 107:AAC8-10CrossRefGoogle Scholar
  33. Gash JHC, Culf AD (1996) Applying a linear detrend to eddy correlation data in real time. Boundary-Layer Meteorol 79:301–306CrossRefGoogle Scholar
  34. Grönlund A, Nilsson ED, Koponen IK, Virkkula A, Hansson ME (2002) Aerosol dry deposition measured with eddy covariance technique at Wasa and Aboa, Dronning Maud Land, Antarctica. Ann Glaciol 35:355–361CrossRefGoogle Scholar
  35. Held A (2014) Spectral analysis of turbulent aerosol fluxes by Fourier transform, wavelet analysis, and multiresolution decomposition. Boundary-Layer Meteorol 151:79–94CrossRefGoogle Scholar
  36. Horst TW (1997) A simple formula for attenuation of eddy fluxes measured with first-order-response scalar sensor. Boundary-Layer Meteorol 82:219–233CrossRefGoogle Scholar
  37. Jarvi L, Rannik Ü, Mammarella I, Sogachev A, Aalto PP, Keronen P, Siivola E, Kulmala M, Vesala T (2009) Annual particle flux observations over a heterogeneous urban area. Atmos Chem Phys 9:7847–7856CrossRefGoogle Scholar
  38. Jenkins GM, Watts DG (1968) Spectral analysis and its applications. Holden-Day, Oakland, 525 ppGoogle Scholar
  39. Kaimal and Finnigan (1994) Atmospheric boundary layer flows. Oxford University Press, Oxford, 289 ppGoogle Scholar
  40. Kanakidou M, Seinfeld JH, Pandis SN, Barnes I, Dentener FJ, Facchini MC, Van Dingenen R, Ervens B, Nenes A, Nielsen CJ, Swietlicki E, Putaud JP, Balkanski Y, Fuzzi S, Horth J, Moortgat GK, Winterhalter R, Myhre CEL, Tsigaridis K, Vignati E, Stephanou EG, Wilson J (2005) Organic aerosol and global climate modelling: a review. Atmos Chem Phys 5:1053–1123CrossRefGoogle Scholar
  41. Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl Akad Nauk 30:9–13Google Scholar
  42. Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241CrossRefGoogle Scholar
  43. Mahrt L (1998) Flux sampling errors for aircraft and towers. J Atmos Ocean Technol 15:416–429CrossRefGoogle Scholar
  44. Mahrt L (2010) Variability and maintenance of turbulence in the very stable boundary layer. Boundary-Layer Meteorol 135:1–18CrossRefGoogle Scholar
  45. Mahrt L (2014) Stably stratified atmospheric boundary layers. Annu Rev Fluid Mech 46:23–45CrossRefGoogle Scholar
  46. Mårtensson EM, Nilsson ED, Buzorius G, Johansson C (2006) Eddy covariance measurements and parameterisation of traffic related particle emissions in an urban environment. Atmos Chem Phys 6:769–785CrossRefGoogle Scholar
  47. Massman WJ (2000) A simple method for estimating frequency response corrections for eddy covariance systems. Agric For Meteorol 104:185–198CrossRefGoogle Scholar
  48. Mauder M, Oncley SP, Vogt R, Weidinger T, Ribeiro L, Bernhofer C, Foken T, Kohsiek W, De Bruin HAR, Liu H (2007) The energy balance experiment EBEX-2000. Part II: intercomparison of eddy-covariance sensors and post-field data processing methods. Boundary-Layer Meteorol 123:29–54CrossRefGoogle Scholar
  49. Mauder M, Cuntz M, Drüe C, Graf A, Rebmann C, Schmid HP, Schmidt M, Steinbrecher R (2013) A strategy for quality and uncertainty assessment of long-term eddy-covariance measurements. Agric For Meteorol 169:122–135CrossRefGoogle Scholar
  50. McMillen RT (1988) An eddy correlation technique with extended applicability to non-simple terrain. Boundary-Layer Meteorol 43:231–245CrossRefGoogle Scholar
  51. Moncrieff J, Clement R, Finnigan J, Meyers T (2004) Averaging, detrending, and filtering of eddy covariance time series. In: Lee X, Massman WJ, Law B (eds) Handbook of micrometeorology: a guide for surface flux measurement and analysis. Kluwer Academic Publishers, Dordrecht, 250 ppGoogle Scholar
  52. Monin AS, Yaglom AM (1971) Statistics fluid mechanics. The MIT Press, Cambridge, 769 ppGoogle Scholar
  53. Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models: part 1. A discussion of principles. J Hydrol 10(3):282–290CrossRefGoogle Scholar
  54. Nemitz E, Jimenez JL, Huffman JA, Ulbrich IM, Canagaratna MR, Worsnop DR, Guenther AB (2008) An eddy-covariance system for the measurement of surface/atmosphere exchange fluxes of submicron aerosol chemical species—first application above an urban area. Aerosol Sci Technol 42:636–657CrossRefGoogle Scholar
  55. Nilsson ED, Rannik Ü (2001) Turbulent aerosol fluxes over the Arctic Ocean 1. Dry deposition over sea and pack ice. J Geophys Res Atmos 106:32125–32137CrossRefGoogle Scholar
  56. Rannik Ü (1998) On the surface layer similarity at a complex forest site. J Geophys Res 103:8685–8697CrossRefGoogle Scholar
  57. Rannik Ü, Vesala T (1999) Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method. Boundary-Layer Meteorol 91:259–280CrossRefGoogle Scholar
  58. Rannik Ü, Zhou L, Zhou P, Gierens R, Mammarella I, Sogachev A, Boy M (2015) Aerosol dynamics within and above forest in relation to turbulent transport and dry deposition. Atmos Chem Phys Discuss 15:19367–19403CrossRefGoogle Scholar
  59. Schmidt A, Klemm O (2008) Direct determination of highly size-resolved turbulent particle fluxes with the disjunct eddy covariance method and a 12 stage electrical low pressure impactor. Atmos Chem Phys 8:7405–7417CrossRefGoogle Scholar
  60. Seinfeld JH, Pandis SN (2006) Atmospheric chemistry and physics: from air pollution to climate change. Wiley, New YorkGoogle Scholar
  61. Singh J, Knapp HV, Demissie M (2004) Hydrologic modelling of the Iroquois River watershed using HSPF and SWAT. Illinois State Water Survey.
  62. Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht, 666 ppGoogle Scholar
  63. Sun K, Tao L, Miller DJ, Zondlo MA, Shonkwiler KB, Nash C, Ham JM (2015) Open-path eddy covariance measurements of ammonia fluxes from a beef cattle feedlot. Agric For Meteorol 213:193–202CrossRefGoogle Scholar
  64. Suzuki T, Ichii K (2010) Evaluation of a terrestrial carbon cycle submodel in an earth system model using networks of eddy covariance observations. Tellus 62B:729–742CrossRefGoogle Scholar
  65. Textor C, Schulz M, Guibert S, Kinne S, Balkanski Y, Bauer S, Berntsen T, Berglen T, Boucher O, Chin M, Dentener F, Diehl T, Easter R, Feichter H, Fillmore D, Ghan S, Ginoux P, Gong S, Grini A, Hendricks J, Horowitz L, Huang P, Isaksen I, Iversen I, Kloster S, Koch D, Kirkeväg A, Kristjansson JE, Krol M, Lauer A, Lamarque JF, Liu X, Montanaro V, Myhre G, Penner J, Pitari G, Reddy S, Seland Ø, Stier P, Takemura T, Tie X (2006) Analysis and quantification of the diversities of aerosol life cycles within AeroCom. Atmos Chem Phys 6:1777–1813CrossRefGoogle Scholar
  66. Ueyama M, Ichii K, Hirata R, Takagi K, Asanuma J, Machimura T, Nakai Y, Saigusa N, Takahashi Y, Hirano T (2010) Simulating carbon and water cycles of larch forests in East Asia by the Biome-BGC model with AsiaFlux data. Biogeosciences 7:959–977CrossRefGoogle Scholar
  67. Valentini R, Matteucci G, Dolman AJ, Schulze ED, Rebmann C, Moors EJ, Granier A, Gross P, Jensen NO, Pilegaard K, Lindroth A, Grelle A, Bern-Hofer C, Grunwald T, Aubinet M, Ceulemans R, Kowalski AS, Vesala T, Rannik Ü, Berbigier P, Loustau D, Guomundsson J, Thorgeirsson H, Ibrom A, Morgenstern K, Clement R, Moncrieff J, Montagnani L, Minerbi S, Jarvis PG (2000) Respiration as the main determinant of carbon balance in European forests. Nature 404:861–865CrossRefGoogle Scholar
  68. Van de Wiel BJH, Ronda RJ, Moene AF, de Bruin HAR, Holtslag AAM (2002) Intermittent turbulence and oscillations in the stable boundary layer over land. Part I: bulk model. J Atmos Sci 59:942–958CrossRefGoogle Scholar
  69. Vickers D, Mahrt L (2003) The cospectral gap and turbulent flux calculations. J Atmos Ocean Technol 20:660–672CrossRefGoogle Scholar
  70. Webb EK, Pearman GI, Leuning R (1980) Correction of flux measurements for density effects due to heat and water-vapour transfer. Q J R Meteorol Soc 106:85–100CrossRefGoogle Scholar
  71. Wesely ML, Hicks BB (2000) A review of the current status of knowledge on dry deposition. Atmos Environ 34:2261–2282CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Istituto di Scienze dell’Atmosfera e del Clima (ISAC)Consiglio Nazionale delle RicercheLecceItaly

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