• Banta, R., , Newsom R. , , Lundquist J. , , Pichugina Y. L. , , Coulter R. L. , , and Mahrt L. , 2002: Nocturnal low-level jet characteristics over Kansas during CASES-99. Bound.-Layer Meteor., 105 , 221252.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Businger, J. A., , Wyngaard J. C. , , zumi Y. , , and Bradley E. F. , 1971: Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28 , 181189.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dyer, A., 1974: A review of flux-profile relationships. Bound.-Layer Meteor., 7 , 363372.

  • Haar, A., 1910: Zur theorie der orthogonalen funktionensysteme. Math. Ann., 69 , 331371.

  • Howell, J. F., , and Mahrt L. , 1997: Multiresolution flux decomposition. Bound.-Layer Meteor., 83 , 117137.

  • Howell, J. F., , and Sun J. , 1999: Surface-layer fluxes in stable conditions. Bound.- Layer Meteor., 90 , 495520.

  • Kaimal, J. C., , and Finnigan J. J. , 1994: Atmospheric Boundary Layer Flows: Their Structure and Measurements. Oxford University Press, 289 pp.

    • Search Google Scholar
    • Export Citation
  • Katul, G., , and Vidakovic B. , 1996: The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering. Bound.-Layer Meteor., 77 , 153172.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mahrt, L., 1998: Flux sampling strategy for aircraft and tower observations. J. Atmos. and Oceanic Technol., 15 , 416429.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mahrt, L., , and Vickers D. , 2002: Contrasting vertical structures of nocturnal boundary layers. Bound.-Layer Meteor., 105 , 351363.

  • Mahrt, L., , Lee X. , , Black A. , , Neumann H. , , and Staebler R. M. , 2000: Nocturnal mixing in a forest subcanopy. Agric. For. Meteor., 101 , 6778.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mahrt, L., , Moore E. , , Vickers D. , , and Jensen N. O. , 2001: Dependence of turbulent and mesoscale velocity variances on scale and stability. J. Appl. Meteor., 40 , 628641.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mallat, S. G., 1989: The theory of multiresolution signal decomposition: The wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell., 7 , 674693.

    • Search Google Scholar
    • Export Citation
  • Paulson, C. A., 1970: The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J. Appl. Meteor., 9 , 857861.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Poulos, G. S., ,and Coauthors. 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull. Amer. Meteor. Soc., 83 , 555581.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sakai, R. K., , Fitzjarrald D. R. , , and Moore K. E. , 2001: Importance of low-frequency contributions to the eddy fluxes observed over rough surfaces. J. Appl. Meteor., 40 , 21782192.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smedman, A. S., 1988: Observations of multi-level turbulence structure in a very stable atmospheric boundary layer. Bound.-Layer Meteor., 44 , 231253.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smedman, A. S., , and Högström U. , 1975: Spectral gap in surface-layer measurements. J. Atmos. Sci., 32 , 340350.

  • Stull, R. B., 1990: An Introduction to Boundary Layer Meteorology. Kluwer Academic, 666 pp.

  • Sun, J., ,and Coauthors. 2002: Intermittent turbulence associated with a density current passage in the stable boundary layer. Bound.-Layer Meteor., 105 , 199219.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Taylor, G., 1938: The spectrum of turbulence. Proc. Roy. Soc. London, A164 , 476490.

  • Vickers, D., , and Mahrt L. , 1997: Quality control and flux sampling problems for tower and aircraft data. J. Atmos. Oceanic Technol., 14 , 512526.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 220 220 27
PDF Downloads 107 107 26

The Cospectral Gap and Turbulent Flux Calculations

View More View Less
  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
© Get Permissions
Restricted access

Abstract

An alternative method to Fourier analysis is discussed for studying the scale dependence of variances and covariances in atmospheric boundary layer time series. Unlike Fourier decomposition, the scale dependence based on multiresolution decomposition depends on the scale of the fluctuations and not the periodicity. An example calculation is presented in detail.

Multiresolution decomposition is applied to tower datasets to study the cospectral gap scale, which is the timescale that separates turbulent and mesoscale fluxes of heat, moisture, and momentum between the atmosphere and the surface. It is desirable to partition the flux because turbulent fluxes are related to the local wind shear and temperature stratification through similarity theory, while mesoscale fluxes are not. Use of the gap timescale to calculate the eddy correlation flux removes contamination by mesoscale motions, and therefore improves similarity relationships compared to the usual approach of using a constant averaging timescale.

A simple model is developed to predict the gap scale. The goal here is to develop a practical formulation based on readily available variables rather than a theory for the transporting eddy scales. The gap scale increases with height, increases with instability, and decreases sharply with increasing stability. With strong stratification and weak winds, the gap scale is on the order of a few minutes or less. Implementation of the gap approach involves calculating an eddy correlation flux using the modeled gap timescale to define the turbulent fluctuations (e.g., w′ and T′). The turbulent fluxes (e.g., wT′) are then averaged over 1 h to reduce random sampling errors.

Corresponding author address: Dean Vickers, College of Oceanic and Atmospheric Sciences, Oceanography Administration Bldg. 104, Oregon State University, Corvallis, OR 97331-5503. Email: vickers@coas.oregonstate.edu

Abstract

An alternative method to Fourier analysis is discussed for studying the scale dependence of variances and covariances in atmospheric boundary layer time series. Unlike Fourier decomposition, the scale dependence based on multiresolution decomposition depends on the scale of the fluctuations and not the periodicity. An example calculation is presented in detail.

Multiresolution decomposition is applied to tower datasets to study the cospectral gap scale, which is the timescale that separates turbulent and mesoscale fluxes of heat, moisture, and momentum between the atmosphere and the surface. It is desirable to partition the flux because turbulent fluxes are related to the local wind shear and temperature stratification through similarity theory, while mesoscale fluxes are not. Use of the gap timescale to calculate the eddy correlation flux removes contamination by mesoscale motions, and therefore improves similarity relationships compared to the usual approach of using a constant averaging timescale.

A simple model is developed to predict the gap scale. The goal here is to develop a practical formulation based on readily available variables rather than a theory for the transporting eddy scales. The gap scale increases with height, increases with instability, and decreases sharply with increasing stability. With strong stratification and weak winds, the gap scale is on the order of a few minutes or less. Implementation of the gap approach involves calculating an eddy correlation flux using the modeled gap timescale to define the turbulent fluctuations (e.g., w′ and T′). The turbulent fluxes (e.g., wT′) are then averaged over 1 h to reduce random sampling errors.

Corresponding author address: Dean Vickers, College of Oceanic and Atmospheric Sciences, Oceanography Administration Bldg. 104, Oregon State University, Corvallis, OR 97331-5503. Email: vickers@coas.oregonstate.edu

Save