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A Wavelet-Based Correction Method for Eddy-Covariance High-Frequency Losses in Scalar Concentration Measurements

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Abstract

Eddy-covariance (EC) scalar-flux measurements suffer from unavoidable biases introduced by high-frequency losses in the sampled scalar concentration fluctuations. This bias alone leads to an underestimation of scalar fluxes by as much as 20% in some cases, especially when a closed-path gas analyzer is used to sample concentration far from the inlet location. A novel method that directly corrects for these high-frequency losses using only the sampled scalar-concentration time series is proposed and tested. The sampled concentration fluctuation time series is adjusted, point-by-point, in the wavelet half-plane for each EC averaging interval (≈30 min). Similarity between scalars (and temperature) is not necessary and a pre-defined theoretical shape of the cospectrum is not required, making this method attractive at meteorologically non-ideal sites. When closed-path gas analyzers are used to measure H2O concentration fluctuations, the method is shown to reproduce the dependence of the attenuation on air relative humidity. Nevertheless, the method is not able to account for excessively large spectral attenuation that occurs close to the spectral peak, as might be the case with long tubes and high relative humidity. Since the method corrects the original scalar concentration time series and not the cospectrum, other flow statistics—such as variances and integral time scales—are also adjusted. The proposed method can be used synergistically with conventional high-frequency cospectral correction methods given the differences in assumptions and approaches among these methods. When the conventional and the proposed methods agree, added confidence to the estimate of the high frequency correction is gained, and vice versa.

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References

  • Ammann C, Brunner A, Spirig C, Neftel A (2006) Technical note: water vapour concentration and flux measurements with PTR-MS. Atmos Chem Phys 6: 4643–4651

    Article  Google Scholar 

  • Aubinet M, Grelle A, Ibrom A, Moncrieff J, Moncrieff J, Foken T, Kowalski AS, Martin PH, Berbigier P, Bernhofer C, Clement R, Elbers J, Granier A, Grunwald T, Morgenstern K, Pilegaard K, Rebmann C, Snijders W, Valentini R, Vesala T (2000) Estimates of the annual net carbon and water exchange of forests: the EUROFLUX methodology. Adv Ecol Res 30: 113–175

    Article  Google Scholar 

  • Baldocchi D, Hicks B, Meyers T (1988) Measuring biosphere-atmosphere exchanges of biologically related gases with micrometeorological methods rid A-1625-2009. Ecology 69: 1331–1340. doi:10.2307/1941631

    Article  Google Scholar 

  • Bos WJT, Touil H, Shao L, Bertoglio J-P (2004) On the behavior of the velocity-scalar cross correlation spectrum in the inertial range. Phys Fluids 16(10): 3818–3822

    Article  Google Scholar 

  • Burba GG, Mcdermitt DK, Anderson DJ, Furtaw MD, Eckles RD (2010) Novel design of an enclosed CO2/H2O gas analyser for eddy covariance flux measurements. Tellus Ser B 62: 743–748. doi:10.1111/j.1600-0889.2010.00468.x

    Article  Google Scholar 

  • Cava D, Katul GG (2012) On the scaling laws of the velocity-scalar cospectra in the canopy sublayer above tall forests. Boundary-Layer Meteorol. doi:10.1007/s10546-012-9737-2

  • Daubechies I (1993) Orthonormal bases of compactly supported wavelets II, variations on a theme. SIAM J Math Anal 24: 499–519. doi:10.1137/0524031

    Article  Google Scholar 

  • De Ligne A, Heinesch B, Aubinet M (2010) New transfer functions for correcting turbulent water vapour fluxes. Boundary-Layer Meteorol 137: 205–221. doi:10.1007/s10546-010-9525-9

    Article  Google Scholar 

  • Eugster W, Senn W (1995) A cospectral correction model for measurement of turbulent NO2 flux. Boundary-Layer Meteorol 74: 321–340

    Article  Google Scholar 

  • Farge M (1992) Wavelet transforms and their applications to turbulence. Annu Rev Fluid Mech 24: 395–457. doi:10.1146/annurev.fl.24.010192.002143

    Article  Google Scholar 

  • Foken T (2008) Micrometeorology. Springer, Berlin, 308 pp

  • Foken T, Aubinet M, Leuning R (2012) The eddy covariance method. In: Aubinet M, Vesala T, Papale D (eds) Eddy covariance—a practical guide to measurement and data analysis. Springer, Dordrecht, pp 1–19

  • Grinsted A, Moore JC, Jevrejeva S (2004) Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Proc Geophys 11: 561–566

    Article  Google Scholar 

  • Haar A (1909) Zur theorie der orthogonalen funktionensysteme (erste mitteilung). Mathe Ann 69: 331–371. doi:10.1007/BF01456326

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ibrom A, Dellwik E, Flyvbjerg H, Jensen NO, Pilegaard K (2007) Strong low-pass filtering effects on water vapour flux measurements with closed-path eddy correlation systems. Agric For Meteorol 147: 140–156. doi:10.1016/j.agrformet.2007.07.007

    Article  Google Scholar 

  • Ibrom A, Dellwik E, Larsen SE, Pilegaard K (2007b) On the use of Webb–Perman–Leuning theory for closed-path eddy correlation measurements. Tellus Ser B (59):937–946. doi:10.1111/j.1600-0889.2007.00311.x

  • Järvi L, Hannuniemi H, Hussein T, Junninen H, Aalto PP, Hillamo R, Mäkelä T, Keronen P, Siivola E, Vesala T, Kulmala M (2009) The urban measurement station SMEAR III: continuous monitoring of air pollution and surface-atmosphere interactions in Helsinki, Finland. Boreal Environ Res 14: 86–109

    Google Scholar 

  • Katul GG, Parlange MB (1994) On the active role of temperature in surface-layer turbulence. J Atmos Sci 51: 2181–2195

    Article  Google Scholar 

  • Katul G, Vidakovic B (1998) Identification of low-dimensional energy containing/flux transporting eddy motion in the atmospheric surface layer using wavelet thresholding methods. J Atmos Sci 55: 377–389. doi:10.1175/1520-0469(1998)055<0377:IOLDEC>2.0.CO;2

    Article  Google Scholar 

  • Katul G, Hsieh CI, Sigmon J (1997) Energy-inertial scale interactions for velocity and temperature in the unstable atmospheric surface layer. Boundary-Layer Meteorol 82: 49–80

    Article  Google Scholar 

  • Katul G, Lai C, Schafer K, Vidakovic B, Albertson J, Ellsworth D, Oren R (2001) Multiscale analysis of vegetation surface fluxes: from seconds to years. Adv Water Resour 24: 1119–1132. doi:10.1016/S0309-1708(01)00029-X

    Article  Google Scholar 

  • Katul G, Porporato A, Cava D, Siqueira M (2006) An analysis of intermittency, scaling, and surface renewal in atmospheric surface layer turbulence. Phys D 215: 117–126. doi:10.1016/j.physd.2006.02.004

    Article  Google Scholar 

  • Lee X, Massman W, Law B (2004) Handbook of micrometeorology—a guide for surface flux measurement and analysis—introduction. Kluwer, Dordrecht, 250 pp

  • Lenschow DH, Mann J, Kristensen L (1994) How long is long enough when measuring fluxes and other turbulence statistics. J Atmos Ocean Technol 11: 661–673

    Article  Google Scholar 

  • Leuning R, Judd MJ (1996) The relative merits of open- and closed-path analyzers for measurements of eddy fluxes. Glob Chang Biol 2: 241–253

    Article  Google Scholar 

  • Licor Biosciences (2009) Licor 7200 CO2/H2O analyzer instruction manual. 3-7-3-9

  • Mahrt L (1991) Eddy asymmetry in the sheared heated boundary-layer. J Atmos Sci 48: 472–492

    Article  Google Scholar 

  • Mallat S (1999) A wavelet tour of signal processing. Academic Press, New York, 637 pp

  • Mammarella I, Launiainen S, Gronholm T, Keronen P, Pumpanen J, Vesala T, Vesala T (2009) Relative humidity effect on the high-frequency attenuation of water vapor flux measured by a closed-path eddy covariance system. J Atmos Ocean Technol 26: 1856–1866. doi:10.1175/2009JTECHA1179.1ER

    Article  Google Scholar 

  • Massman WJ, Ibrom A (2008) Attenuation of concentration fluctuations of water vapor and other trace gases in turbulent tube flow. Atmos Chem Phys 8: 6245–6259

    Article  Google Scholar 

  • Moncrieff J, Massheder JM, de Bruin H, Elbers J, Friborg T, Heusinkveld B, Kabat P, Scott S, Soegaard H, Verhoef A (1997) A system to measure surface fluxes of momentum, sensible heat, water vapour and carbon dioxide. J Hyrdrol 188–189: 589–611

    Article  Google Scholar 

  • Monin AS, Yaglom AM (1975) Statistical fluid mechanics. MIT Press, Cambridge, 875 pp

  • Moore CJ (1986) Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol 37: 17–35

    Article  Google Scholar 

  • Moriwaki R, Kanda M (2006) Local and global similarity in turbulent transfer of heat, water vapour, and CO2 in the dynamic convective sublayer over a suburban area. Boundary-Layer Meteorol 120: 163–179. doi:10.1007/s10546-005-9034-4

    Article  Google Scholar 

  • Nordbo A, Launiainen S, Mammarella I, Leppäranta M, Huotari J, Ojala A, Vesala T (2011) Long-term energy flux measurements and energy balance over a small boreal lake using eddy covariance technique. J Geophys Res 116: 1–17. doi:10.1029/2010JD014542

    Article  Google Scholar 

  • Nordbo A, Järvi L, Vesala T (2012) Revised eddy covariance flux calculation methodologies—effect on urban energy balance. Tellus Ser B 64:18184. http://dx.doi.org/10.3402/tellusb.v64i0.18184

  • Panofsky HA, Tennekes H, Lenschow DH, Wyngaard JC (1977) The characteristics of turbulent velocity components in the surface layer under convective conditions. Boundary-Layer Meteorol 11: 355–361

    Article  Google Scholar 

  • Peltola O (2011) Field intercomparison of four methane gas analyzers suitable for eddy covariance flux measurements, 80 pp. http://urn.fi/URN:NBN:fi-fe201110275747

  • Poggi D, Katul GG, Vidakovic B (2011) The role of wake production on the scaling laws of scalar concentration fluctuation spectra inside dense canopies. Boundary-Layer Meteorol 139: 83–95

    Article  Google Scholar 

  • Qin Z, Ouyang Y, Su G, Yu Q, Li J, Zhang J, Wu Z (2008) Characterization of CO2 and water vapor fluxes in a summer maize field with wavelet analysis. Ecol Inform 3: 397–409. doi:10.1016/j.ecoinf.2008.09.002

    Article  Google Scholar 

  • Stoy P, Katul G, Siqueira M, Juang J, McCarthy H, Kim H, Oishi A, Oren R (2005) Variability in net ecosystem exchange from hourly to inter-annual time scales at adjacent pine and hardwood forests: a wavelet analysis. Tree Physiol 25: 887–902

    Article  Google Scholar 

  • Su HB, Schmid HP, Grimmond CSB et al (2004) Spectral characteristics and correction of long-term eddy covariance measurements over two mixed hardwood forests in non-flat terrain. Boundary-Layer Meteorol 110(2): 213–253

    Article  Google Scholar 

  • Thomas C, Foken T (2005) Detection of long-term coherent exchange over spruce forest using wavelet analysis. Theor Appl Climatol 80: 91–104. doi:10.1007/s00704-004-0093-0

    Article  Google Scholar 

  • Thomas C, Mayer J, Meixner FX, Foken T (2006) Analysis of low-frequency turbulence above tall vegetation using a doppler sodar. Boundary-Layer Meteorol 119: 563–587. doi:10.1007/s10546-005-9038-0

    Article  Google Scholar 

  • Vesala T, Järvi L, Launiainen S, Sogachev A, Mammarella I, Mammarella I, Siivola E, Keronen P, Rinne J, Riikonen A, Nikinmaa E (2008) Surface-atmosphere interactions over complex urban terrain in Helsinki, Finland. Tellus Ser B 60: 188–199. doi:10.1111/j.1600-0889.2007.00312.x

    Article  Google Scholar 

  • Yamada M, Ohkitani K (1990) Orthonormal wavelet expansion and its application to turbulence. Prog Theor Phys 83: 819–823. doi:10.1143/PTP.83.819

    Article  Google Scholar 

  • Yamada M, Ohkitani K (1991) An identification of energy cascade in turbulence by orthonormal wavelet analysis. Prog Theor Phys 86: 799–815. doi:10.1143/PTP.86.799

    Article  Google Scholar 

  • Yamada M, Ohkitani K (1991) Orthonormal wavelet analysis of turbulence. Fluid Dyn Res 8: 101–115. doi:10.1016/0169-5983(91)90034-G

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Division of Atmospheric Sciences, University of Helsinki, P.O. Box 48, 00014, Helsinki, Finland

    Annika Nordbo

  2. Nicholas School of the Environment, Duke University, Box 90328, Durham, NC, 27708-0328, USA

    Gabriel Katul

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  1. Annika Nordbo
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  2. Gabriel Katul
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Correspondence to Annika Nordbo.

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Nordbo, A., Katul, G. A Wavelet-Based Correction Method for Eddy-Covariance High-Frequency Losses in Scalar Concentration Measurements. Boundary-Layer Meteorol 146, 81–102 (2013). https://doi.org/10.1007/s10546-012-9759-9

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  • DOI: https://doi.org/10.1007/s10546-012-9759-9

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