Boundary-Layer Meteorology

, Volume 169, Issue 2, pp 163–184 | Cite as

Ejective and Sweeping Motions Above a Peatland and Their Role in Relaxed-Eddy-Accumulation Measurements and Turbulent Transport Modelling

  • Gabriel Katul
  • Olli PeltolaEmail author
  • Tiia Grönholm
  • Samuli Launiainen
  • Ivan Mammarella
  • Timo Vesala
Research Article


The three turbulent velocity components, water vapour (\(\text {H}_2\text {O}\)), carbon dioxide (\(\text {CO}_{2}\)), and methane (\(\text {CH}_{4}\)) concentration fluctuations are measured above a boreal peatland and analyzed using conditional sampling and quadrant analysis. The overarching question to be addressed is to what degree lower-order cumulant expansion methods describe transport efficiency and the relative importance of ejections and sweeps to momentum, \(\text {CH}_{4}\), \(\text {CO}_{2}\) and \(\text {H}_2\text {O}\) fluxes across a range of atmospheric flow regimes. The patchy peatland surface creates distinctly different source and sink distributions for the three scalars in space and time thereby adding to the uniqueness of the set-up. The measured and modelled fractional contributions to the momentum flux show that sweep events dominate over ejections in agreement with prior studies conducted in the roughness sublayer. For scalar fluxes, ejections dominate the turbulent fluxes over sweeps. While ejective motions persist longer for momentum transport, sweeping events persist longer for all three scalars. Third-order cumulant expansions describe many of the results detailed above, and the results are surprising given the highly non-Gaussian distribution of \(\text {CH}_{4}\) turbulent fluctuations. Connections between the asymmetric contributions of sweeps and ejections and the flux-transport term arising in scalar turbulent-flux-budget closure are derived and shown to agree reasonably well with measurements. The proposed model derived here is much simpler than prior structural models used to describe laboratory experiments. Implications of such asymmetric contributions on, (i) the usage of the now proliferating relaxed-eddy-accumulation method in turbulent flux measurements, (ii) the constant-flux assumption, and (iii) gradient-diffusion closure models are presented.


Closure models Cumulant expansion Ejections and sweeps Methane flux Relaxed eddy accumulation 



G.K. acknowledges support from the National Science Foundation (NSF-EAR-1344703, NSF-DGE-1068871), and the U.S. Department of Energy (DOE) through the office of Biological and Environmental Research (BER) Terrestrial Ecosystem Science (TES) Program (DE-SC0011461). T.V., O.P., and T.G. acknowledge support from the Academy of Finland Center of Excellence (Project Nos. 272041 and 118780) and Academy Professor projects (Nos. 1284701 and 1282842), ICOS-Finland (Project No. 281255) and CARB-ARC (Project No. 286190) funded by the Academy of Finland and the AtMath project funded by University of Helsinki. S.L. acknowledges support from the Academy of Finland Academy Research Fellow Project (Nos. 296116 and 307192).


  1. Ammann C, Meixner F (2002) Stability dependence of the relaxed eddy accumulation coefficient for various scalar quantities. J Geophys Res Atmos 107(D8):ACL7-1–ACL7-9CrossRefGoogle Scholar
  2. Andreas EL, Hill RJ, Gosz JR, Moore DI, Otto WD, Sarma AD (1998) Stability dependence of the eddy-accumulation coefficients for momentum and scalars. Boundary-Layer Meteorol 86(3):409–420CrossRefGoogle Scholar
  3. Antonia R (1981) Conditional sampling in turbulence measurement. Annu Rev Fluid Mech 13(1):131–156CrossRefGoogle Scholar
  4. Antonia R, Atkinson J (1973) High-order moments of Reynolds shear stress fluctuations in a turbulent boundary layer. J Fluid Mech 58(03):581–593CrossRefGoogle Scholar
  5. Baker J, Norman J, Bland W (1992) Field-scale application of flux measurement by conditional sampling. Agric For Meteorol 62(1–2):31–52CrossRefGoogle Scholar
  6. Baldocchi DD, Meyers TP (1988) Turbulence structure in a deciduous forest. Boundary-Layer Meteorol 43(4):345–364CrossRefGoogle Scholar
  7. Bash JO, Miller DR (2008) A relaxed eddy accumulation system for measuring surface fluxes of total gaseous mercury. J Atmos Ocean Technol 25(2):244–257CrossRefGoogle Scholar
  8. Beverland I, Moncrieff J, Oneill D, Hargreaves K, Milne R (1996) Measurement of methane and carbon dioxide fluxes from peatland ecosystems by the conditional-sampling technique. Q J R Meteorol Soc 122(532):819–838CrossRefGoogle Scholar
  9. Bowling D, Turnipseed A, Delany A, Baldocchi D, Greenberg J, Monson R (1998) The use of relaxed eddy accumulation to measure biosphere-atmosphere exchange of isoprene and other biological trace gases. Oecologia 116(3):306–315CrossRefGoogle Scholar
  10. Bowling DR, Baldocchi DD, Monson RK (1999) Dynamics of isotopic exchange of carbon dioxide in a tennessee deciduous forest. Global Biogeochem Cycles 13(4):903–922. CrossRefGoogle Scholar
  11. Businger JA, Oncley SP (1990) Flux measurement with conditional sampling. J Atmos Ocean Technol 7(2):349–352CrossRefGoogle Scholar
  12. Cantwell BJ (1981) Organized motion in turbulent flow. Annu Rev Fluid Mech 13(1):457–515CrossRefGoogle Scholar
  13. Cava D, Katul G, Scrimieri A, Poggi D, Cescatti A, Giostra U (2006) Buoyancy and the sensible heat flux budget within dense canopies. Boundary-Layer Meteorol 118(1):217–240CrossRefGoogle Scholar
  14. Christensen C, Hummelshøj P, Jensen N, Larsen B, Lohse C, Pilegaard K, Skov H (2000) Determination of the terpene flux from orange species and Norway spruce by relaxed eddy accumulation. Atmos Environ 34(19):3057–3067CrossRefGoogle Scholar
  15. Ciccioli P, Brancaleoni E, Frattoni M, Marta S, Brachetti A, Vitullo M, Tirone G, Valentini R (2003) Relaxed eddy accumulation, a new technique for measuring emission and deposition fluxes of volatile organic compounds by capillary gas chromatography and mass spectrometry. J Chromatogr A 985(1):283–296CrossRefGoogle Scholar
  16. Cobos DR, Baker JM, Nater EA (2002) Conditional sampling for measuring mercury vapor fluxes. Atmos Environ 36(27):4309–4321CrossRefGoogle Scholar
  17. Corrsin S (1975) Limitations of gradient transport models in random walks and in turbulence. Adv Geophys 18:25–60CrossRefGoogle Scholar
  18. Deardorff J (1978) Closure of second-and third-moment rate equations for diffusion in homogeneous turbulence. Phys Fluids 21(4):525–530CrossRefGoogle Scholar
  19. Fer I, McPhee MG, Sirevaag A (2004) Conditional statistics of the Reynolds stress in the under-ice boundary layer. Geophys Res Lett. CrossRefGoogle Scholar
  20. Finnigan J (1979) Turbulence in waving wheat II. Structure of momentum transfer. Boundary-Layer Meteorol 16:213–236Google Scholar
  21. Finnigan J (2000) Turbulence in plant canopies. Annu Rev Fluid Mech 32(1):519–571CrossRefGoogle Scholar
  22. Foken T (2006) 50 years of the Monin–Obukhov similarity theory. Boundary-Layer Meteorol 119(3):431–447CrossRefGoogle Scholar
  23. Foken T, Wichura B (1996) Tools for quality assessment of surface-based flux measurements. Agric For Meteorol 78(1–2):83–105CrossRefGoogle Scholar
  24. Francone C, Katul GG, Cassardo C, Richiardone R (2012) Turbulent transport efficiency and the ejection-sweep motion for momentum and heat on sloping terrain covered with vineyards. Agric For Meteorol 162:98–107CrossRefGoogle Scholar
  25. Frenkiel FN, Klebanoff PS (1967) Higher-order correlations in a turbulent field. Phys Fluids 10(3):507–520CrossRefGoogle Scholar
  26. Frenkiel FN, Klebanoff PS (1973) Probability distributions and correlations in a turbulent boundary layer. Phys Fluids 16(6):725–737CrossRefGoogle Scholar
  27. Gallagher M, Clayborough R, Beswick K, Hewitt C, Owen S, Moncrieff J, Pilegaard K (2000) Assessment of a relaxed eddy accumulation for measurements of fluxes of biogenic volatile organic compounds: study over arable crops and a mature beech forest. Atmos Environ 34(18):2887–2899CrossRefGoogle Scholar
  28. Gaman A, Rannik Ü, Aalto P, Pohja T, Siivola E, Kulmala M, Vesala T (2004) Relaxed eddy accumulation system for size-resolved aerosol particle flux measurements. J Atmos Ocean Technol 21(6):933–943CrossRefGoogle Scholar
  29. Gao W (1995) The vertical change of coefficient b, used in the relaxed eddy accumulation method for flux measurement above and within a forest canopy. Atmos Environ 29(17):2339–2347CrossRefGoogle Scholar
  30. Ghannam K, Duman T, Salesky ST, Chamecki M, Katul G (2017) The non-local character of turbulence asymmetry in the convective atmospheric boundary layer. Q J R Meteorol Soc 143(702):494–507CrossRefGoogle Scholar
  31. Graus M, Hansel A, Wisthaler A, Lindinger C, Forkel R, Hauff K, Klauer M, Pfichner A, Rappenglück B, Steigner D et al (2006) A relaxed-eddy-accumulation method for the measurement of isoprenoid canopy-fluxes using an online gas-chromatographic technique and PTR-MS simultaneously. Atmos Environ 40:43–54CrossRefGoogle Scholar
  32. Grönholm T, Aalto PP, Hiltunen V, Rannik Ü, Rinne J, Laakso L, Hyvönen S, Vesala T, Kulmala M (2007) Measurements of aerosol particle dry deposition velocity using the relaxed eddy accumulation technique. Tellus B 59(3):381–386CrossRefGoogle Scholar
  33. Held A, Patton E, Rizzo L, Smith J, Turnipseed A, Guenther A (2008) Relaxed eddy accumulation simulations of aerosol number fluxes and potential proxy scalars. Boundary-Layer Meteorol 129(3):451–468CrossRefGoogle Scholar
  34. Hensen A, Nemitz E, Flynn M, Blatter A, Jones S, Sørensen LL, Hensen B, Pryor S, Jensen B, Otjes R et al (2009) Inter-comparison of ammonia fluxes obtained using the relaxed eddy accumulation technique. Biogeosciences 6(11):2575–2588CrossRefGoogle Scholar
  35. Katsouvas GD, Helmis CG, Wang Q (2007) Quadrant analysis of the scalar and momentum fluxes in the stable marine atmospheric surface layer. Boundary-Layer Meteorol 124(3):335–360CrossRefGoogle Scholar
  36. Katul G, Albertson J (1998) An investigation of higher-order closure models for a forested canopy. Boundary-Layer Meteorol 89(1):47–74CrossRefGoogle Scholar
  37. Katul GG, Finkelstein PL, Clarke JF, Ellestad TG (1996) An investigation of the conditional sampling method used to estimate fluxes of active, reactive, and passive scalars. J Appl Meteorol 35(10):1835–1845CrossRefGoogle Scholar
  38. Katul G, Hsieh CI, Kuhn G, Ellsworth D, Nie D (1997a) Turbulent eddy motion at the forest-atmosphere interface. J Geophys Res Atmos 102(D12):13,409–13,421CrossRefGoogle Scholar
  39. Katul G, Kuhn G, Schieldge J, Hsieh CI (1997b) The ejection-sweep character of scalar fluxes in the unstable surface layer. Boundary-Layer Meteorol 83(1):1–26CrossRefGoogle Scholar
  40. Katul G, Poggi D, Cava D, Finnigan J (2006) The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer. Boundary-Layer Meteorol 120(3):367–375CrossRefGoogle Scholar
  41. Katul GG, Porporato A, Manes C, Meneveau C (2013) Co-spectrum and mean velocity in turbulent boundary layers. Phys Fluids 25(9):091,702CrossRefGoogle Scholar
  42. Katul GG, Li D, Liu H, Assouline S (2016) Deviations from unity of the ratio of the turbulent Schmidt to Prandtl numbers in stratified atmospheric flows over water surfaces. Phys Rev Fluids 1(3):034,401CrossRefGoogle Scholar
  43. Lamb B, Pierce T, Baldocchi D, Allwine E, Dilts S, Westberg H, Geron C, Guenther A, Klinger L, Harley P et al (1996) Evaluation of forest canopy models for estimating isoprene emissions. J Geophys Res Atmos 101(17):22,787–22,797CrossRefGoogle Scholar
  44. Launder B, Reece GJ, Rodi W (1975) Progress in the development of a Reynolds-stress turbulence closure. J Fluid Mech 68(03):537–566CrossRefGoogle Scholar
  45. Li D, Bou-Zeid E (2011) Coherent structures and the dissimilarity of turbulent transport of momentum and scalars in the unstable atmospheric surface layer. Boundary-Layer Meteorol 140(2):243–262CrossRefGoogle Scholar
  46. Li D, Katul GG, Zilitinkevich SS (2015) Revisiting the turbulent Prandtl number in an idealized atmospheric surface layer. J Atmos Sci 72(6):2394–2410CrossRefGoogle Scholar
  47. Lu S, Willmarth W (1973) Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J Fluid Mech 60(03):481–511CrossRefGoogle Scholar
  48. Maitani T, Ohtaki E (1987) Turbulent transport processes of momentum and sensible heat in the surface layer over a paddy field. Boundary-Layer Meteorol 40(3):283–293CrossRefGoogle Scholar
  49. Mammarella I, Peltola O, Nordbo A, Järvi L, Rannik Ü (2016) Quantifying the uncertainty of eddy covariance fluxes due to the use of different software packages and combinations of processing steps in two contrasting ecosystems. Atmos Meas Tech 9(10):4915CrossRefGoogle Scholar
  50. Mattson MD, Likens GE (1990) Air pressure and methane fluxes. Nature 347:718–719CrossRefGoogle Scholar
  51. Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys 20(4):851–875CrossRefGoogle Scholar
  52. Milne R, Mennim A, Hargreaves K (2001) The value of the \(\beta \) coefficient in the relaxed eddy accumulation method in terms of fourth-order moments. Boundary-Layer Meteorol 101(3):359–373CrossRefGoogle Scholar
  53. Mochizuki T, Tani A, Takahashi Y, Saigusa N, Ueyama M (2014) Long-term measurement of terpenoid flux above a Larix kaempferi forest using a relaxed eddy accumulation method. Atmos Environ 83:53–61CrossRefGoogle Scholar
  54. Moriwaki R, Kanda M (2006) Local and global similarity in turbulent transfer of heat, water vapour, and CO\(\rm{_2}\) in the dynamic convective sublayer over a suburban area. Boundary-Layer Meteorol 120(1):163–179CrossRefGoogle Scholar
  55. Nagano Y, Tagawa M (1990) A structural turbulence model for triple products of velocity and scalar. J Fluid Mech 215:639–657CrossRefGoogle Scholar
  56. Nakagawa H, Nezu I (1977) Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows. J Fluid Mech 80(01):99–128CrossRefGoogle Scholar
  57. Nemitz E, Flynn M, Williams P, Milford C, Theobald M, Blatter A, Gallagher M, Sutton M (2001) A relaxed eddy accumulation system for the automated measurement of atmospheric ammonia fluxes. Water Air Soil Pollut: Focus 1(5):189–202CrossRefGoogle Scholar
  58. Nie D, Kleindienst T, Arnts R, Sickles J (1995) The design and testing of a relaxed eddy accumulation system. J Geophys Res Atmos 100(D6):11,415–11,423CrossRefGoogle Scholar
  59. Nordbo A, Katul G (2013) A wavelet-based correction method for eddy-covariance high-frequency losses in scalar concentration measurements. Boundary-Layer Meteorol 146(1):81–102. CrossRefGoogle Scholar
  60. Obukhov A (1971) Turbulence in an atmosphere with a non-uniform temperature. Boundary-Layer Meteorol 2(1):7–29CrossRefGoogle Scholar
  61. Park C, Schade GW, Boedeker I (2010) Flux measurements of volatile organic compounds by the relaxed eddy accumulation method combined with a GC-FID system in urban Houston, Texas. Atmos Environ 44(21):2605–2614CrossRefGoogle Scholar
  62. Pattey E, Desjardins R, Rochette P (1993) Accuracy of the relaxed eddy-accumulation technique evaluated using CO\(\rm{_2}\) flux measurements. Boundary-Layer Meteorol 66(4):341–355CrossRefGoogle Scholar
  63. Peltola O, Mammarella I, Haapanala S, Burba G, Vesala T (2013) Field intercomparison of four methane gas analyzers suitable for eddy covariance flux measurements. Biogeosciences 10(6):3749–3765. CrossRefGoogle Scholar
  64. Poggi D, Katul G (2007) The ejection-sweep cycle over gentle hills covered with bare and forested surfaces. Boundary-Layer Meteorol 122:493–515CrossRefGoogle Scholar
  65. Poggi D, Katul G, Albertson J (2004a) Momentum transfer and turbulent kinetic energy budgets within a dense model canopy. Boundary-Layer Meteorol 111:589–614CrossRefGoogle Scholar
  66. Poggi D, Porporato A, Ridolfi L, Katul G, Albertson J (2004b) The effect of vegetation density on canopy sublayer turbulence. Boundary-Layer Meteorol 111:565–587CrossRefGoogle Scholar
  67. Priyadarshana P, Klewicki J (2004) Study of the motions contributing to the Reynolds stress in high and low Reynolds number turbulent boundary layers. Phys Fluids 16(12):4586–4600CrossRefGoogle Scholar
  68. Raupach M (1981) Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers. J Fluid Mech 108:363–382CrossRefGoogle Scholar
  69. Ren X, Sanders J, Rajendran A, Weber R, Goldstein A, Pusede S, Browne E, Min KE, Cohen R (2011) A relaxed eddy accumulation system for measuring vertical fluxes of nitrous acid. Atmos Meas Tech 4(10):2093–2103CrossRefGoogle Scholar
  70. Rinne J, Riutta T, Pihlatie M, Aurela M, Haapanala S, Tuovinen JP, Tuittila ES, Vesala T (2007) Annual cycle of methane emission from a boreal fen measured by the eddy covariance technique. Tellus B 59(3):449–457CrossRefGoogle Scholar
  71. Robinson SK (1991) Coherent motions in the turbulent boundary layer. Annu Rev Fluid Mech 23(1):601–639CrossRefGoogle Scholar
  72. Rotach MW (1993) Turbulence close to a rough urban surface part I: Reynolds stress. Boundary-Layer Meteorol 65(1):1–28CrossRefGoogle Scholar
  73. Ruppert J, Thomas C, Foken T (2006) Scalar similarity for relaxed eddy accumulation methods. Boundary-Layer Meteorol 120(1):39–63CrossRefGoogle Scholar
  74. Salesky ST, Chamecki M, Bou-Zeid E (2017) On the nature of the transition between roll and cellular organization in the convective boundary layer. Boundary-Layer Meteorol 163(1):41–68. CrossRefGoogle Scholar
  75. Schade GW, Goldstein AH (2001) Fluxes of oxygenated volatile organic compounds from a Ponderosa pine plantation. J Geophys Res Atmos 106(D3):3111–3123CrossRefGoogle Scholar
  76. Shaw RH, Tavangar J, Ward DP (1983) Structure of the Reynolds stress in a canopy layer. J Clim Appl Meteorol 22(11):1922–1931CrossRefGoogle Scholar
  77. Skov H, Brooks SB, Goodsite ME, Lindberg SE, Meyers TP, Landis MS, Larsen MR, Jensen B, McConville G, Christensen J (2006) Fluxes of reactive gaseous mercury measured with a newly developed method using relaxed eddy accumulation. Atmos Environ 40(28):5452–5463CrossRefGoogle Scholar
  78. Su HB, Shaw RH, Paw KT, Moeng CH, Sullivan PP (1998) Turbulent statistics of neutrally stratified flow within and above a sparse forest from large-eddy simulation and field observations. Boundary-Layer Meteorol 88(3):363–397CrossRefGoogle Scholar
  79. Thomas C, Foken T (2007) Flux contribution of coherent structures and its implications for the exchange of energy and matter in a tall spruce canopy. Boundary-Layer Meteorol 123(2):317–337CrossRefGoogle Scholar
  80. Thomas C, Martin J, Goeckede M, Siqueira M, Foken T, Law B, Loescher H, Katul G (2008) Estimating daytime subcanopy respiration from conditional sampling methods applied to multi-scalar high frequency turbulence time series. Agric For Meteorol 148(8):1210–1229CrossRefGoogle Scholar
  81. Tsai JL, Tsuang BJ, Kuo PH, Tu CY, Chen CL, Hsueh MT, Lee CS, Yao MH, Hsueh ML (2012) Evaluation of the relaxed eddy accumulation coefficient at various wetland ecosystems. Atmos Environ 60:336–347CrossRefGoogle Scholar
  82. Variano EA, Cowen EA (2013) Turbulent transport of a high-Schmidt-number scalar near an air-water interface. J Fluid Mech 731:259–287CrossRefGoogle Scholar
  83. Wallace JM (2016) Quadrant analysis in turbulence research: history and evolution. Annu Rev Fluid Mech 48:131–158CrossRefGoogle Scholar
  84. Wallace JM, Eckelmann H, Brodkey RS (1972) The wall region in turbulent shear flow. J Fluid Mech 54(01):39–48CrossRefGoogle Scholar
  85. Walter BP, Heimann M (2000) A process-based, climate-sensitive model to derive methane emissions from natural wetlands: application to five wetland sites, sensitivity to model parameters, and climate. Global Biogeochem Cycles 14(3):745–765CrossRefGoogle Scholar
  86. Wang L, Li D, Gao Z, Sun T, Guo X, Bou-Zeid E (2014) Turbulent transport of momentum and scalars above an urban canopy. Boundary-Layer Meteorol 150(3):485–511CrossRefGoogle Scholar
  87. Watanabe T (2004) Large-eddy simulation of coherent turbulence structures associated with scalar ramps over plant canopies. Boundary-Layer Meteorol 112(2):307–341CrossRefGoogle Scholar
  88. Whalen SC (2005) Biogeochemistry of methane exchange between natural wetlands and the atmosphere. Environ Eng Sci 22(1):73–94. CrossRefGoogle Scholar
  89. Willmarth W, Lu S (1972) Structure of the Reynolds stress near the wall. J Fluid Mech 55(01):65–92CrossRefGoogle Scholar
  90. Wyngaard JC, Moeng CH (1992) Parameterizing turbulent diffusion through the joint probability density. Boundary-Layer Meteorol 60(1):1–13CrossRefGoogle Scholar
  91. Yue W, Meneveau C, Parlange MB, Zhu W, van Hout R, Katz J (2007) A comparative quadrant analysis of turbulence in a plant canopy. Water Resour Res 43:W05422. CrossRefGoogle Scholar
  92. Zahn E, Dias NL, Araújo A, Sá LD, Sörgel M, Trebs I, Wolff S, Manzi A (2016) Scalar turbulent behavior in the roughness sublayer of an amazonian forest. Atmos Chem Phys 16(17):11,349–11,366CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Nicholas School of the EnvironmentDuke UniversityDurhamUSA
  2. 2.Department of Civil and Environmental EngineeringDuke UniversityDurhamUSA
  3. 3.Institute for Atmospheric and Earth System Research/Physics, Faculty of ScienceUniversity of HelsinkiHelsinkiFinland
  4. 4.Natural Resources Institute FinlandEnvironmental Impacts of ProductionHelsinkiFinland
  5. 5.Institute for Atmospheric and Earth System Research/Forest Sciences, Faculty of Agriculture and ForestryUniversity of HelsinkiHelsinkiFinland

Personalised recommendations