Skip to main content
SpringerLink
Log in

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

  • Research Article
  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • 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 160:12–21

    Article  Google Scholar 

  • Andreas EL, Geiger C, Trevĩno G, Claffey K (2008) Identifying non-stationarity in turbulence series. Boundary-Layer Meteorol 127:37–56

    Article  Google Scholar 

  • Aubinet M (2008) Eddy covariance \(\text{ CO }_{2}\) flux measurements in nocturnal conditions: an analysis of the problem. Ecol Appl 18:1368–1378

    Article  Google Scholar 

  • Baldocchi D (2003) Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of ecosystems: past, present and future. Glob Change Biol 9:479–492

    Article  Google Scholar 

  • 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 82:2415–2435

    Article  Google Scholar 

  • Barnhart BL, Eichinger WE, Prueger JH (2012) A new eddy-covariance method using empirical mode decomposition. Boundary-Layer Meteorol 145:369–382

    Article  Google Scholar 

  • 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 15:1783–1794

    Article  Google Scholar 

  • Bendat JS, Piersol AG (1958) Measurement and analysis of random data. Wiley, New York

    Google Scholar 

  • 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 105:19905–19916

    Article  Google Scholar 

  • Camarori P, Schuepp P, Desjardins R, MacPherson I (1994) Structural analysis of airborne flux estimates over a region. J Clim 7:627–640

    Article  Google Scholar 

  • 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 112:129–157

    Article  Google Scholar 

  • 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 194:88–103

    Article  Google Scholar 

  • Cava D, Giostra U, Katul G (2015) Characteristics of gravity waves over an Antarctic ice sheet during an austral summer. Atmosphere 6:1271–1289

    Article  Google Scholar 

  • Christen A (2014) Atmospheric measurement techniques to quantify greenhouse gas emissions from cities. Urban Clim 10:241–260

    Article  Google Scholar 

  • 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 6:942–959

    Article  Google Scholar 

  • 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:D16202

    Article  Google Scholar 

  • 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 46:25–35

    Article  Google Scholar 

  • 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 40:1050–1058

    Article  Google Scholar 

  • 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 151:1312–1324

    Article  Google Scholar 

  • 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 214–215:328–340

    Article  Google Scholar 

  • Deventer MJ, El-Mandany T, Griessbaum F, Klemm O (2015b) One-year measurement of size-resolved particle fluxes in an urban area. Tellus 67B:25531

    Article  Google Scholar 

  • 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

  • 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 21:385–398

    Article  Google Scholar 

  • 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 36:791–800

    Article  Google Scholar 

  • Fairall CW (1984) Interpretation of eddy correlation measurements of particulate deposition and aerosol flux. Atmos Environ 18:1329–1337

    Article  Google Scholar 

  • 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 150:786–793

    Article  Google Scholar 

  • 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 4:1275–1289

    Article  Google Scholar 

  • 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 47:818–830

    Article  Google Scholar 

  • 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 158–159:30–42

    Article  Google Scholar 

  • 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 107:1–48

    Article  Google Scholar 

  • 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 85–132

  • 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:AAC8-10

    Article  Google Scholar 

  • Gash JHC, Culf AD (1996) Applying a linear detrend to eddy correlation data in real time. Boundary-Layer Meteorol 79:301–306

    Article  Google Scholar 

  • 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 35:355–361

    Article  Google Scholar 

  • Held A (2014) Spectral analysis of turbulent aerosol fluxes by Fourier transform, wavelet analysis, and multiresolution decomposition. Boundary-Layer Meteorol 151:79–94

    Article  Google Scholar 

  • Horst TW (1997) A simple formula for attenuation of eddy fluxes measured with first-order-response scalar sensor. Boundary-Layer Meteorol 82:219–233

    Article  Google Scholar 

  • 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 9:7847–7856

    Article  Google Scholar 

  • Jenkins GM, Watts DG (1968) Spectral analysis and its applications. Holden-Day, Oakland, 525 pp

  • Kaimal and Finnigan (1994) Atmospheric boundary layer flows. Oxford University Press, Oxford, 289 pp

  • 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 5:1053–1123

    Article  Google Scholar 

  • Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl Akad Nauk 30:9–13

    Google Scholar 

  • Legates DR, McCabe GJ (1999) Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241

    Article  Google Scholar 

  • Mahrt L (1998) Flux sampling errors for aircraft and towers. J Atmos Ocean Technol 15:416–429

    Article  Google Scholar 

  • Mahrt L (2010) Variability and maintenance of turbulence in the very stable boundary layer. Boundary-Layer Meteorol 135:1–18

    Article  Google Scholar 

  • Mahrt L (2014) Stably stratified atmospheric boundary layers. Annu Rev Fluid Mech 46:23–45

    Article  Google Scholar 

  • 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 6:769–785

    Article  Google Scholar 

  • Massman WJ (2000) A simple method for estimating frequency response corrections for eddy covariance systems. Agric For Meteorol 104:185–198

    Article  Google Scholar 

  • 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 123:29–54

    Article  Google Scholar 

  • 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 169:122–135

    Article  Google Scholar 

  • McMillen RT (1988) An eddy correlation technique with extended applicability to non-simple terrain. Boundary-Layer Meteorol 43:231–245

    Article  Google Scholar 

  • 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 pp

  • Monin AS, Yaglom AM (1971) Statistics fluid mechanics. The MIT Press, Cambridge, 769 pp

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models: part 1. A discussion of principles. J Hydrol 10(3):282–290

    Article  Google Scholar 

  • 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 42:636–657

    Article  Google Scholar 

  • Nilsson ED, Rannik Ü (2001) Turbulent aerosol fluxes over the Arctic Ocean 1. Dry deposition over sea and pack ice. J Geophys Res Atmos 106:32125–32137

    Article  Google Scholar 

  • Rannik Ü (1998) On the surface layer similarity at a complex forest site. J Geophys Res 103:8685–8697

    Article  Google Scholar 

  • Rannik Ü, Vesala T (1999) Autoregressive filtering versus linear detrending in estimation of fluxes by the eddy covariance method. Boundary-Layer Meteorol 91:259–280

    Article  Google Scholar 

  • 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 15:19367–19403

    Article  Google Scholar 

  • 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 8:7405–7417

    Article  Google Scholar 

  • Seinfeld JH, Pandis SN (2006) Atmospheric chemistry and physics: from air pollution to climate change. Wiley, New York

    Google Scholar 

  • Singh J, Knapp HV, Demissie M (2004) Hydrologic modelling of the Iroquois River watershed using HSPF and SWAT. Illinois State Water Survey. www.sws.uiuc.edu/pubdoc/CR/ISWSCR2004-08.pdf

  • Stull RB (1988) An introduction to boundary layer meteorology. Kluwer Academic Publishers, Dordrecht, 666 pp

  • 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 213:193–202

    Article  Google Scholar 

  • 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:729–742

    Article  Google Scholar 

  • 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 6:1777–1813

    Article  Google Scholar 

  • 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 7:959–977

    Article  Google Scholar 

  • 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 404:861–865

    Article  Google Scholar 

  • 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 59:942–958

    Article  Google Scholar 

  • Vickers D, Mahrt L (2003) The cospectral gap and turbulent flux calculations. J Atmos Ocean Technol 20:660–672

    Article  Google Scholar 

  • 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 106:85–100

    Article  Google Scholar 

  • Wesely ML, Hicks BB (2000) A review of the current status of knowledge on dry deposition. Atmos Environ 34:2261–2282

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Scienze dell’Atmosfera e del Clima (ISAC), Consiglio Nazionale delle Ricerche, 73100, Lecce, Italy

    Antonio Donateo, Daniela Cava & Daniele Contini

Authors
  1. Antonio Donateo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniela Cava
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniele Contini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Donateo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Donateo, A., Cava, D. & Contini, D. A Case Study of the Performance of Different Detrending Methods in Turbulent-Flux Estimation. Boundary-Layer Meteorol 164, 19–37 (2017). https://doi.org/10.1007/s10546-017-0243-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-017-0243-4

Keywords

Search

Navigation