Abstract
Geophysical variables are orthogonally decomposed by averaging timeseries using different averaging lengths, referred to as a (Haar)multiresolution decomposition. This simple and economic decomposition isassociated with cospectra that formally satisfy Reynolds averaging rules foreach averaging length. The multiresolution decomposition provides a naturalestimate of the random error in estimating a mean turbulent flux. The Fourierand multiresolution decompositions are compared using aircraft data fromBOREAS.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahmed, N., Natarajan, T., and Rao, K. R.: 1973, ‘Cooley-Tukey Type Algorithm for the Haar Transform’, Electron. Lett. 9, 276–278.
Bendat, J. S. and Piersol, A. G.: 1986, Measurement and Analysis of Random Data, John Wiley and Sons, New York, 330 pp.
Beylkin, G., Coifman, R., and Rokhlin, V.: 1991, ‘Fast Wavelet Transforms and Numerical Algorithms I’, Comm. Pure Appl. Math. 44, 141–183.
Burt, P. J.: 1984, ‘The Pyramid as a Structure for Efficient Computation’, in A. Rosenfeld (ed.), Multiresolution Image Processing and Analysis, Springer-Verlag, pp. 6–35.
Daubechies, I.: 1988, ‘Orthonormal Bases of Compactly Supported Wavelets’, Comm. Pure Appl. Math. 41, 909–996.
Daubechies, I.: 1990, ‘The Wavelet Transform, Time-frequency Localization and Signal Analysis’, IEEE Trans. Inform. Theory 36, 961–1005.
Daubechies, I.: 1992, Ten Lectures on Wavelets, SIAM Press, Philadelphia, 357 pp.
Desjardin, R. L., MacPherson, J. I., Mahrt, L., Schuepp, P., Pattey, E., Neumann, H., Baldocchi, D., Wofsy, S., Fitzjarrald, D., and McCaughey, H.: 1996, ‘Scaling up Flux Measurements for the Boreal Forest using Aircraft-tower Combinations', Submitted to J. Geophys. Res.
Elliot, D. F. and Rao, K. R.: 1982, Fast Transforms: Algorithms, Analyses, Applications, Academic Press, New York, 488 pp.
Gabor, D.: 1946, ‘Theory of Communications’, J. Inst. Elec. Eng. (London) 93, 429–457.
Haar, A.: 1910, ‘Zur Theorie der orthogonalen Funktionensysteme’, Mathematische Annalen 69, 331–371.
Hagelberg, C. R. and Gamage, N. K. K.: 1994, ‘Structure-preserving Wavelet Decompositions of Intermittent Turbulence’, Boundary-Layer Meteorol. 70, 217–246.
Howell, J. F. and Mahrt, L.: 1994a, ‘An Adaptive Multiresolution Data Filter: Applications to Turbulence and Climatic Time Series’, J. Atmos. Sci. 51, 2165–2178.
Howell, J. F. and Mahrt, L.: 1994b, ‘An Adaptive Decomposition: Application to Turbulence’, in E. Foufoula-Georgiou and P. Kumar (eds.), Wavelets in Geophysics, Academic Press, pp. 107–128.
Howell, J. F.: 1995, ‘Identifying Sudden Changes in Data’, Mon. Wea. Rev. 123, 1207–1212.
Katul, G. and Parlange, M.: 1995, ‘The Spatial Structure of Turbulence at Production Wavenumbers using Orthonormal Wavelets’, Boundary-Layer Meteorol. 75, 81–108.
Katul, G. and Vidakovic, B.: 1996, ‘The Partitioning of Attached and Detached Eddy Motion in the Atmospheric Surface Layer using Lorentz Wavelet Filtering’, Boundary-Layer Meteorol. 77, 153–172.
Lenschow, D. H. and Stankov, B. B.: 1986, ‘Length Scales in the Convective Boundary Layer’, J. Atmos. Sci. 43, 1198–1209.
Lumley, J. L. and Panofsky, H. A.: 1964, The Structure of Atmospheric Turbulence, Wiley Interscience, New York, 239 pp.
Mahrt, L.: 1991, ‘Eddy Asymmetry in the Sheared Heated Boundary Layer’, J. Atmos. Sci. 48, 472–492.
Mahrt, L. and Gibson, W.: 1992, ‘Flux Decomposition into Coherent Structures’, Boundary-Layer Meteorol. 60, 143–168.
Mahrt, L. and Howell, J. F.: 1994, ‘The Influence of Coherent Structures and Microfronts on Scaling Laws Using Global and Local Transforms’, J. Fluid Mech. 260, 247–270.
Mahrt, L., Desjardin, R., and MacPherson, J.: 1994, ‘Observations of Fluxes over Heterogeneous Surfaces’, Boundary-Layer Meteorol. 67, 345–367.
Mallat, S. G.: 1989, ‘The Theory of Multiresolution Signal Decomposition: The Wavelet Representation’, IEEE Trans. Pattern Anal. Machine Intell. 7, 674–693.
Mann, J. and Lenschow, D. H.: 1994, ‘Errors in Airborne Flux Measurements’, J. Geophys. Res. 99, 519–526.
Meneveau, C.: 1991a, ‘Analysis of Turbulence in the Orthonormal Wavelet Representation’, J. Fluid Mech. 232, 469–520.
Meneveau, C.: 1991b, ‘Dual Spectra and Mixed Energy Cascade of Turbulence in the Wavelet Representation’, Phys. Rev. Lett. 11, 1450–1453, 232, 469-520.
Meyer, Y.: 1993, Wavelets: Algorithms and Applications, SIAM Press, Philadelphia, 133 pp.
Priestley, C. H. B.: 1959, Turbulent Transfer in the Lower Atmosphere, The University of Chicago Press, 130 pp.
Rao, K. R., Revuluri, J., Narasimhan, M. A., and Ahmed, N.: 1976, ‘Complex Haar Transform’,IEEE Trans. Acoust. Speech Signal Process. 24, 102–104.
Sellers, P., Hall, F., Margolis, H., Kelly, B., Baldocchi, D., den Hartog, G., Cihlar, F., Ryan, M.G., Goodison, B., Crill, P., Ranson, K. J., Lettenmaier, D., and Wickland, D. E.: 1995, ‘The Boreal Ecosystem-Atmosphere Study (BOREAS): An Overview and Early Results from the 1994 Field Year’, Bull. Amer. Meteor. Soc. 76, 1549–1577.
Shore, J. E.: 1973, ‘On the Application of Haar Functions’, IEEE Trans. Commun. 21, 209–216.
Sun, J., Howell, J., Esbensen, S. K., Mahrt, L., Greb, C. M., Grossman, R., and LeMone, M. A.: 1996, ‘Scale Dependence of Air-sea Fluxes over the Western Equatorial Pacific’, J. Atmos. Sci. 53, 2997–3012.
Tennekes, H.: 1976, ‘Fourier-transform Ambiguity in Turbulence Dynamics’, J. Atmos. Sci. 33, 1660–1663.
Weng, H. and Lau, K.-M.: 1994, ‘Wavelets, Period Doubling, and Time-frequency Localization with Application to Organization of Convection over the Tropical Western Pacific’, J. Atmos. Sci. 51, 2523–2541.
Wyngaard, J. C.: 1974, ‘On Surface Layer Turbulence’, in D. A. Haugen (ed.), Workshop on Micrometeorology, American Meteorological Society, pp. 101–149.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Howell, J.F., Mahrt, L. Multiresolution Flux Decomposition. Boundary-Layer Meteorology 83, 117–137 (1997). https://doi.org/10.1023/A:1000210427798
Issue Date:
DOI: https://doi.org/10.1023/A:1000210427798