Boundary-Layer Meteorology

, Volume 110, Issue 2, pp 213–253

Spectral Characteristics and Correction of Long-Term Eddy-Covariance Measurements Over Two Mixed Hardwood Forests in Non-Flat Terrain


  • Hong-Bing Su
    • Indiana University
  • Hans Peter Schmid
    • Indiana University
  • C. S. B. Grimmond
    • Indiana University
  • Christoph S. Vogel
    • University of Michigan Biological Station
  • Andrew J. Oliphant
    • Indiana University
    • San Francisco State University

DOI: 10.1023/A:1026099523505

Cite this article as:
Su, H., Schmid, H.P., Grimmond, C.S.B. et al. Boundary-Layer Meteorology (2004) 110: 213. doi:10.1023/A:1026099523505


We present turbulence spectra and cospectra derived from long-term eddy-covariancemeasurements (nearly 40,000 hourly data over three to four years) and the transferfunctions of closed-path infrared gas analyzers over two mixed hardwood forests inthe mid-western U.S.A. The measurement heights ranged from 1.3 to 2.1 times themean tree height, and peak vegetation area index (VAI) was 3.5 to 4.7; the topographyat both sites deviates from ideal flat terrain. The analysis follows the approach ofKaimal et al. (Quart. J. Roy. Meteorol. Soc.98, 563–589, 1972) whose results were based upon 15 hours of measurements atthree heights in the Kansas experiment over flatter and smoother terrain. Both thespectral and cospectral constants and stability functions for normalizing and collapsingspectra and cospectra in the inertial subrange were found to be different from those ofKaimal et al. In unstable conditions, we found that an appropriate stabilityfunction for the non-dimensional dissipation of turbulent kinetic energy is of the form Φε(ζ) = (1 - b-ζ)-1/4 - c-ζ, where ζ representsthe non-dimensional stability parameter. In stable conditions, a non-linear functionGxy(ζ) = 1 + bxyζcxy (cxy < 1) was found to benecessary to collapse cospectra in the inertial subrange. The empirical cospectralmodels of Kaimal et al. were modified to fit the somewhat more (neutraland unstable) or less (stable) sharply peaked scalar cospectra observed over forestsusing the appropriate cospectral constants and non-linear stability functions. Theempirical coefficients in the stability functions and in the cospectral models varywith measurement height and seasonal changes in VAI. The seasonal differencesare generally larger at the Morgan Monroe State Forest site (greater peak VAI) andcloser to the canopy.

The characteristics of transfer functions of the closed-path infrared gas analysersthrough long-tubes for CO2 and water vapour fluxes were studied empirically. This was done by fitting the ratio between normalized cospectra of CO2 or watervapour fluxes and those of sensible heat to the transfer function of a first-order sensor.The characteristic time constant for CO2 is much smaller than that for water vapour. The time constant for water vapour increases greatly with aging tubes. Three methods were used to estimate the flux attenuations and corrections; from June through August, the attenuations of CO2 fluxes are about 3–4% during the daytime and 6–10% at night on average. For the daytime latent heat flux (QE), the attenuations are foundto vary from less than 10% for newer tubes to over 20% for aged tubes. Correctionsto QE led to increases in the ratio (QH + QE)/(Q* - QG) by about 0.05 to0.19 (QH is sensible heat flux, Q* is net radiation and QG is soil heat flux),and thus are expected to have an important impact on the assessment of energy balanceclosure.

Cospectral correctionCospectral modelEnergy balanceForesSpectral characteristicsTransfer function

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© Kluwer Academic Publishers 2004