Skip to main content
SpringerLink
Log in

Turbulent Schmidt Numbers Above a Wheat Crop

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

Abstract

Measurements of vertical fluxes and concentration differences above a spring wheat crop (height \(h=0.9\)–\(0.95\) m, row spacing 0.25 m, displacement height \(d=0.5\)–\(0.6\) m) were analyzed to determine the Schmidt numbers for water vapour (\(S^\mathrm{v}\)) and carbon dioxide (\(S^\mathrm{c}\)) based on concentration differences between intakes 2.55 and 3.54 m above the ground. During nearly-neutral stratification \(S^\mathrm{v}(0) = 0.68 \pm 0.1\) while \(S^\mathrm{c} = 0.78 \pm 0.2\), implying that the roughness sublayer extended above \(2.5 h\).

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

Similar content being viewed by others

Notes

  1. The assumption that \(S\approx 1\) is rather common in general. For example, reviewing the matter in the context of their own measurements of the Schmidt number in a laboratory free shear layer, Huq and Stewart (2008) regard \(S \approx 1\) as being expected “in the absence of density stratification.”

  2. Might these offsets reflect a temporal trend in \(\mathrm{{CO}}_2\) concentration, in combination with the delay (\(t_1+t_2\)) between samples in the two intake polarities? A (large) trend of order \(10 \, \upmu \mathrm{{mol}}\,\mathrm{{ mol}}^{-1}\, \mathrm{{h}}^{-1}\), coupled with \(t_1+t_2=45\) s, would produce an offset \(\Delta \rho _\mathrm{c} \sim 0.1 \, \upmu \mathrm{{mol}}\,\mathrm{{ mol}}^{-1}\), i.e. too small to explain the observed values.

  3. To better than 1 %, computed fluxes and Schmidt numbers were indifferent to whether this correction was applied before or after the WPL correction.

  4. It is pertinent to recall the rather uncertain bias correction for the \(\Delta \overline{\rho }_\mathrm{c}\) measurements underlying \(S^\mathrm{c}\): no plausible assumption regarding that bias yielded a tidy pattern for \(S^\mathrm{v}/S^\mathrm{c}\).

References

  • Arya SP (2001) Introduction to micrometeorology, Second edition. Academic Press, New York, 420 pp

  • De Ridder K (2010) Bulk transfer relations for the roughness sublayer. Boundary-Layer Meteorol 134:257–267

    Article  Google Scholar 

  • Delaunay D (1996) Numerical simulation of atmospheric dispersion in an urban site: comparison with field data. J Wind Eng Ind Aerodyn 64:221–231

    Google Scholar 

  • Denmead O, Bradley E (1985) Flux–gradient relationships in a forest canopy. In: Hutchison B, Hicks B (eds) The forest–atmosphere interaction. D. Reidel Pub. Co., Boston (pp 421–442), 708 pp

  • Dyer A (1974) A review of flux-profile relationships. Boundary-Layer Meteorol 7:363–372

    Article  Google Scholar 

  • Dyer A, Bradley E (1982) An alternative analysis of flux–gradient relationships at the 1976 ITCE. Boundary-Layer Meteorol 22:3–19

    Article  Google Scholar 

  • Dyer A, Hicks B (1970) Flux–gradient relationships in the constant flux layer. Q J R Meteorol Soc 96:715–721

    Article  Google Scholar 

  • Finnigan J (1985) Turbulent transport in flexible plant canopies. In: Hutchison B, Hicks B (eds) The forest–atmosphere interaction. D. Reidel Pub. Co., Boston, pp 443–480

    Chapter  Google Scholar 

  • Foken T (2006) 50 years of the Monin–Obukhov similarity theory. Boundary-Layer Meteorol 119:431–447

    Article  Google Scholar 

  • Francey R, Garratt JR (1981) Interpretation of flux-profile observations at ITCE (1976). J Appl Meteorol 20:603–618

    Article  Google Scholar 

  • Garratt JR (1978) Flux profile relations above tall vegetation. Q J R Meteorol Soc 104:199–211

    Article  Google Scholar 

  • Glenn A, Amiro B, Tenuta M, Stewart S, Wagner-Riddle C (2010) Carbon dioxide exchange in a northern Prairie cropping system over three years. Agric For Meteorol 150:908–918

    Article  Google Scholar 

  • Harman I, Finnigan J (2008) Scalar concentration profiles in the canopy and roughness sublayer. Boundary-Layer Meteorol 129:323–351

    Article  Google Scholar 

  • Hassid S (1983) Turbulent Schmidt number for diffusion models in the neutral boundary layer. Atmos Environ 17:523–527

    Article  Google Scholar 

  • Huq P, Stewart E (2008) Measurements and analysis of the turbulent Schmidt number in density stratified turbulence. Geophys Res Lett 35:L23604. doi:10.1029/2008GL036056

    Article  Google Scholar 

  • Iwata H, Harazono Y, Ueyama M (2010) Influence of source/sink distributions on flux–gradient relationships in the roughness sublayer over an open forest canopy under unstable conditions. Boundary-Layer Meteorol 136:391–405

    Article  Google Scholar 

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

  • Kaimal J, Wyngaard J, Izumi Y, Coté O (1972) Spectral characteristics of surface-layer turbulence. Q J R Meteorol Soc 98:563–589

    Article  Google Scholar 

  • Lemon E, Stewart D, Shawcroft R (1971) The sun’s work in a cornfield. Science 174:371–378

    Article  Google Scholar 

  • Moore C (1986) Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol 37:17–36

    Article  Google Scholar 

  • Ohtaki E (1980) Turbulent transport of carbon dioxide over a paddy field. Boundary-Layer Meteorol 19:315–336

    Article  Google Scholar 

  • Ohtaki E (1984) The budget of carbon dioxide variance in the surface layer over vegetated fields. Boundary-Layer Meteorol 29:251–261

    Article  Google Scholar 

  • Pruitt W, Morgan D, Lourence F (1973) Momentum and mass transfers in the surface boundary layer. Q J R Meteorol Soc 99:370–386

    Article  Google Scholar 

  • Raupach MR (1979) Anomalies in flux–gradient relationships over forest. Boundary-Layer Meteorol 16:467–486

    Article  Google Scholar 

  • Raupach M (1987) A Lagrangian analysis of scalar transfer in vegetation canopies. Q J R Meteorol Soc 113:107–120

    Article  Google Scholar 

  • Raupach M, Antonia R, Rajagopalan S (1991) Rough-wall turbulent boundary layers. Appl Mech Rev 44:1–25

    Article  Google Scholar 

  • Raupach M, Finnigan J, Brunet Y (1996) Coherent eddies and turbulence in vegetation canopies: the mixing layer analogy. Boundary-Layer Meteorol 78:351–382

    Article  Google Scholar 

  • Sawford BL (2001) Project Prairie Grass—a classic atmospheric dispersion experiment revisited. In: 14th Australian fluid mechanics conference, Adelaide

  • Schotanus P, Nieuwstadt FTM, DeBruin HAR (1983) Temperature measurement with a sonic anemometer and its application to heat and moisture fluctuations. Boundary-Layer Meteorol 26:81–93

    Article  Google Scholar 

  • Taylor G (1921) Diffusion by Continuous Movements. Proc Lond Math Soc Ser 2 A20:196–211

    Google Scholar 

  • Thom A, Stewart J, Oliver H, Gash J (1975) Comparison of aerodynamic and energy budget estimates of fluxes over a pine forest. Q J R Meteorol Soc 101:93–105

    Article  Google Scholar 

  • Tominaga Y, Stathopoulos T (2007) Turbulent Schmidt numbers for CFD analysis with various types of flowfield. Atmos Environ 41:8091–8099

    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 

  • Wilczak J, Oncley S, Stage S (2001) Sonic anemometer tilt correction algorithms. Boundary-Layer Meteorol 99:127–150

    Article  Google Scholar 

  • Wilson J (1982) Turbulent dispersion in the atmospheric surface-layer. Boundary-Layer Meteorol 22:399–420

    Article  Google Scholar 

  • Wilson J (1989) Turbulent transport within the plant canopy. In: Estimation of areal evapotranspiration. International Association of Hydrological Sciences, Gothenburg, pp 43–80

  • Wilson J, Yee E (2007) A critical examination of the random displacement model of turbulent dispersion. Boundary-Layer Meteorol 125:399–416

    Article  Google Scholar 

  • Wilson J, Clarkson T, Hadfield M (1984) Observations of wind flow and tracer-gas dispersion over sand dunes. N Z J Sci 27:237–242

    Google Scholar 

  • Xu L, Matista A, Hsiao T (1999) A technique for measuring \({\rm {CO}}_{2}\) and water vapor profiles within and above plant canopies over short periods. Agric For Meteorol 94:1–12

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Natural Sciences and Engineering Research Council of Canada. Peter Carlson (Earth & Atmospheric Sciences, University of Alberta) helped with design of the air intake switching apparatus. The author is grateful to three unknown reviewers who provided incisive and constructive suggestions.

Author information

Authors and Affiliations

  1. Department of Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB, T6G 2E3, Canada

    J. D. Wilson

Authors
  1. J. D. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. D. Wilson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wilson, J.D. Turbulent Schmidt Numbers Above a Wheat Crop. Boundary-Layer Meteorol 148, 255–268 (2013). https://doi.org/10.1007/s10546-013-9819-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10546-013-9819-9

Keywords

Search

Navigation