Abstract
The related concepts of stationarity and the existence and values of integral timescales are central to the ability of analyzing micrometeorological data within theframework of Monin–Obukhov similarity theory. Not only does the theory strongly hinge on the stationarity assumption, the estimation of turbulence moments and their accuracies are dependent on the values of the correspondent integral time scales. In spite of the general importance of these concepts, there are relatively few studiesconcerned with them. Moreover, although each turbulence variable has its ownintegral scale, this fact is often overlooked when numerical values are estimated.In this work we study three daytime events of surface inversion formation, that is,events where a nonstationary period is clearly present. Our analysis reveals alow-frequency component in the temperature data that is not totally removed bya simple (but often used in turbulence data analysis) first-order recursive filter.This component has to be filtered out in the frequency domain, after which we areable to recover similarity between temperature and humidity statistical descriptors(in this case, the structure function). After applying a simple criterion to estimatenumerical values of the integral time scales, we are able to assess the relationshipsbetween the existence of integral scales and the stationarity of the correspondingprocess. Finally, we find out that in the case of second-order moments the Sarmanovtheorem does not always apply. The implications for accuracy estimates of thesemoments are then briefly discussed.
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Asanuma, J. and Brutsaert, W.: 1999, 'Turbulence Variance Characteristics of Temperature and Humidity in the Unstable Atmospheric Surface Layer above a Variable Pine Forest', Water Resour. Res. 35, 515-521.
Bendat, J. S. and Piersol, A. G.: 1986, Random Data, 2nd edn., John Wiley &; Sons, New York, 566 pp.
Bradley, J. V.: 1968, Distribution-Free Statistical Tests, Prentice-Hall, New Jersey, 388 pp.
Dias, N. L. and Brutsaert, W.: 1996, 'Similarity of Scalars under Stable Conditions', Boundary-Layer Meteorol. 80, 355-373.
Gluhovsky, A. and Agee, E.: 1994, 'A Definitive Approach to Turbulence Statistical Studies in Planetary Boundary Layers', J. Atmos. Sci. 51, 1682-1690.
Haugen, D. A.: 1978, 'Effects of Sampling Rates and Averaging Periods on Meteorological Measurements', in Proceedings of the Fourth Symposium on Meteorological Observations and Instruments, American Meteorological Society Denver, CO, pp. 15-18.
Hinze, J. O.: 1975, Turbulence, McGraw-Hill Publishing Company, New York, 790 pp.
Howell, J. F. and Mahrt, L.: 1997, 'Multiresolution Flux Decomposition', Boundary-Layer Meteorol. 83, 117-137.
Jenkins, G. M.: 1968, Spectral Analysis, Holden-Day, San Francisco, 525 pp.
Kaimal, J. C. and Finnigan, J. J.: 1994, Atmospheric Boundary Layer Flows: Their Structure and Measurement, Oxford University Press, New York, 289 pp.
Katul, G. G. and Parlange, M. B.: 1995, 'Analysis of Land Surface Heat Fluxes Using the Orthonormal Wavelet Approach', Water Resour. Res. 31, 2743-2749.
Koprov, B. M., Zubkovsky, S. L., Koprov, V. M., Fortus, M. I., and Makarova, T. I.: 1998, 'Statistics of Air Temperature Spatial Variability in the Atmospheric Surface Layer', Boundary-Layer Meteorol. 88, 399-423.
Lumley, J. L.: 1970, Stochastic Tools in Turbulence, Academic Press, New York, 194 pp.
Lumley, J. L. and Panofksy, H. A.: 1964, The Structure of Atmospheric Turbulence, Interscience, New York, 239 pp.
McNaughton, K. G. and Brunet, Y.: 2002, 'Townsend's Hypothesis, Coherent Structures and Monin-Obukhov Similarity', Boundary-Layer Meteorol. 101, 161-175.
McNaughton, K. G. and Laubach, J.: 1998, 'Unsteadiness as a Cause of Non-Equality of Eddy Diffusivities for Heat and Vapour at the Base of an Advective Inversion', Boundary-Layer Meteorol. 88, 479-504.
McNaughton, K. G. and Laubach, J.: 2000, 'Power Spectra and Cospectra for Wind and Scalars in a Disturbed Surface Layer at the Base of an Advective Inversion', Boundary-Layer Meteorol. 96, 143-185.
Okawa, C. M. P.: 1998, Medição Contínua do Fluxo de Calor Sensível Para a Atmosfera, Tese de mestrado, Universidade Federal do Paraná, Curitiba, PR.
Orlanski, I.: 1975, 'A Rational Subdivision of Scales for Atmospheric Processes', Bull. Amer. Meteorol. Soc. 56, 529-530.
Rannik, U. and Vesala, T.: 1999, 'Autoregressive Filtering versus Linear Detrending in Estimation of Fluxes by the Eddy Covariance Method', Boundary-Layer Meteorol. 91, 259-280.
Smith, S. W.: 1997, The Scientist and Engineer's Guide to Digital Signal Processing, 2nd edn., California Technical Publishing, San Diego, 650 pp.
Stull, R.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, 666 pp.
Tennekes, H. and Lumley, J. L.: 1972, A First Course in Turbulence, The MIT Press, Cambridge, MA, 300 pp.
Tritton, D. J.: 1988, Physical Fluid Dynamics, Oxford University Press, New York, 519 pp.
Watanabe, T., Yamanoi, K., and Yasuda, Y.: 2000, 'Testing of the Bandpass Eddy Covariance Method for a Long-Term Measurement of Water Vapour Flux over a Forest', Boundary-Layer Meteorol. 96, 473-491.
Wyngaard, J. C.: 1973, 'On Surface-Layer Turbulence', in D. A. Haugen (ed.), Workshop on Micrometeorology, American Meteorological Society, Boston, MA, 392 pp.
Yaglom, A. M.: 1987, Correlation Theory of Stationary and Related Random Functions I: Basic Results, Springer-Verlag, New York, 526 pp.
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Dias, N.L., Chamecki, M., Kan, A. et al. A Study of Spectra, Structure and Correlation Functions and Their Implications for the Stationarity of Surface-Layer Turbulence. Boundary-Layer Meteorology 110, 165–189 (2004). https://doi.org/10.1023/A:1026067224894
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DOI: https://doi.org/10.1023/A:1026067224894