Skip to main content
SpringerLink
Log in

Quantifying Organization of Atmospheric Turbulent Eddy Motion Using Nonlinear Time Series Analysis

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

Abstract

Using three methods from nonlinear dynamics, we contrast the level of organization inthe vertical wind velocity (w) time series collected in the atmospheric surface layer(ASL) and the canopy sublayer (CSL) for a wide range of atmospheric stability (ξ)conditions. The nonlinear methods applied include a modified Shannon entropy, waveletthresholding, and mutual information content. Time series measurements collected overa pine forest, a hardwood forest, a grass-covered forest clearing, and a bare soil, desertsurface were used for this purpose. The results from applying all three nonlinear timeseries measures suggest that w in the CSL is more organized than that in the ASL, and that as the flows in both layers evolve from near-neutral to near-convective conditions, the level of organization increases. Furthermore, we found that the degree of organization in w associated with changes in ξ is more significant than the transition from CSL to ASL.

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

Similar content being viewed by others

References

  • Albertson, J. D., Parlange, M. B., Katul, G. G., Chu, C-R., Stricker, H., and Tyler, S.: 1995, 'Sensible Heat Flux fromArid Regions: A Simple Flux-Variance Method',Water Resour. Res. 31, 969–973.

    Google Scholar 

  • Baldocchi, D. D., Falge, E, Gu, L. H., Olson, R., Hollinger, D., Running, S., Anthoni, P., Bernhofer, C., Davis, K., Evans, R., Fuentes, J., Goldstein, A., Katul, G., Law, B., Lee, X. H., Malhi, Y., Meyers, T., Munger, W., Oechel, W. U. K. T. P., Pilegaard, K., Schmid, H. P., Valentini, R., Verma, S., Vesala, T., Wilson, K., Wofsy, S.: 2001, 'FLUXNET: A New Tool to Study the Temporal and Spatial Variability of Ecosystem-Scale Carbon Dioxide, Water Vapor, and Energy Flux Densities', Bull. Amer. Meteorol. Soc. 82, 2415–2434.

    Google Scholar 

  • Conklin, P.: 1994, 'Turbulent Wind, Temperature, and Pressure in a Mature Hardwood Canopy', Ph.D. Dissertation, School of the Environment, Duke University, Durham, N.C., 105 pp.

    Google Scholar 

  • Farge, M., Goirand, E., Meyer, Y., Pascal, F., and Wickerhauser, M. V.: 1992, 'Improved Predictability of Two-Dimensional Turbulent Flows UsingWavelet Packet Compression', Fluid Dyn. Res. 10, 229–250.

    Google Scholar 

  • Finnigan, J.: 2000, 'Turbulence inside Plant Canopies', Annu. Rev. Fluid Mech. 32, 519–571.

    Google Scholar 

  • Finnigan, J. and Shaw, R. H.: 2000, 'A Wind-Tunnel Study of Airflow in Waving Wheat: An EOF Analysis of the Structure of the Large-Eddy Motion', Boundary-Layer Meteorol. 96, 211–255.

    Google Scholar 

  • Fraser, A.M.: 1989, Information and Entropy in Strange Attractors', IEEE Trans. Inform. Theory 35, 245–262.

    Google Scholar 

  • Fraser, A. M. and Swinney, H. L.: 1986, 'Independent Coordinates for Strange Attractors from Mutual Information', Phys. Rev. A 33, 1134–1140.

    Google Scholar 

  • Gallego, M. C., García, J. A., and Cancillo, M. L.: 2001, 'Characterization of Atmospheric Turbulence by Dynamical Systems Techniques', Boundary-Layer Meteorol. 100, 375–392.

    Google Scholar 

  • Grassberger, P. and Procaccia, I.: 1983, 'Measuring the Strangeness of Strange Attractors', Physica D 9, 189–208.

    Google Scholar 

  • Havstad, J. W. and Ehlers, C. L.: 1989, 'Attractor Dimension of Nonstationary Dynamical Systems from Small Data Sets', Phys. Rev. A 39, 845–853.

    Google Scholar 

  • Jaramillo, G. P. and Puente, C. E.: 1993, 'Strange Attractors in Atmospheric Boundary-Layer Turbulence', Boundary-Layer Meteorol. 64, 175–197.

    Google Scholar 

  • Kaiser, J.: 1998, 'Climate Change-New Network Aims to Take the World's CO2 Pulse Source', Science 281, 506–507.

    Google Scholar 

  • Katul, G. G.: 1994, 'A Model for Sensible Heat-Flux Probability Density-Function for Near-Neutral and Slightly-Stable Atmospheric Flows', Boundary-Layer Meteorol. 71, 1–20.

    Google Scholar 

  • Katul, G. G. and Albertson, J. D.: 1999, 'Modeling CO2 Sources, Sinks, and Fluxes within a Forest Canopy', J. Geophys. Res. 104, 6081–6091.

    Google Scholar 

  • Katul, G. G. and Vidakovic, B.: 1996, 'The Partitioning of the Attached and Detached Eddy Motion in the Atmospheric Surface Layer Using Lorentz Wavelet Filtering', Boundary-Layer Meteorol. 77, 153–172.

    Google Scholar 

  • Katul, G. G. and Vidakovic, B.: 1998, 'Identification of Low-Dimensional Energy Containing/Flux Transporting Eddy Motion in the Atmospheric Surface Layer Using Wavelet Thresholding Methods', J. Atmos. Sci. 55, 377–389.

    Google Scholar 

  • Katul, G. G., Goltz, S. M., Hsieh, C-I., Cheng, Y., Mowry, F., and Sigmon, J.: 1995, 'Estimation of Surface Heat and Momentum Fluxes Using the Flux-Variance Method above Uniform and Non-Uniform Terrain', Boundary-Layer Meteorol. 74, 237–260.

    Google Scholar 

  • Katul, G. G., Hsieh, C-I., Bowling, D., Clark, K., Shurpali, N., Turnipseed, A., Albertson, J., Tu, K., Hollinger, D., Evans, B., Offerle, B., Anderson, D., Ellsworth, D., Vogel, C., and Oren, R.: 1999, 'Spatial Variability of Turbulent Fluxes in the Roughness Sublayer of an Even-Aged Pine Forest', Boundary-Layer Meterol. 93, 1–28.

    Google Scholar 

  • Katul, G. G., Hsieh, C-I., Kuhn, G., and Ellsworth, D.: 1997, 'Turbulent Eddy Motion at the Forest-Atmosphere Interface', J. Geophys. Res. 102(D12), 13409–13421.

    Google Scholar 

  • Katul, G. G., Schieldge, J., Hsieh, C-I., and Vidakovic, B.: 1998, 'Skin Temperature Perturbations Induced by Surface Layer Turbulence above a Grass Surface', Water Resour. Res. 34, 1265–1274.

    Google Scholar 

  • Lai, C.-T., Katul, G. G., Ellsworth, D. S., and Oren, R.: 2000a, 'Modeling Vegetation-Atmosphere CO2 Exchange by a Coupled Eulerian-Lagrangian Approach', Boundary-Layer Meteorol. 95, 91–122.

    Google Scholar 

  • Lai, C.-T., Katul, G. G., Oren, R., Ellsworth, D. S., and Schäfer, K.: 2000b, 'Modeling CO2 and Water Vapor Turbulent Flow Distributions within a Forest Canopy', J. Geophys. Res. 105, 26333–26351.

    Google Scholar 

  • Lorenz, E. N.: 1991, 'Dimension of Weather and Climate Attractors', Nature 353, 241–244.

    Google Scholar 

  • Nerenberg, M. A. H. and Essex, C.: 1990, 'Correlation Dimension and Systematic Geometric Effects', Phys. Rev. A. 42, 7065–7074.

    Google Scholar 

  • Palus, M.: 1993, 'Identifying and Quantifying Chaos Using Information-Theoretic Functionals', in A. S. Weigend and N. A. Gershenfeld (eds.), Time-Series Prediction: Forecasting the Future and Understanding the Past, Addison-Wesley, Reading, MA, pp. 387–413.

    Google Scholar 

  • Pineda, F. J. and Sommerer, J. C.: 1993, 'Estimating Generalized Dimensions and Choosing Time Delays: A Fast Algorithm', in A. S. Weigend and N. A. Gershenfeld (eds.), Time-Series Prediction: Forecasting the Future and Understanding the Past, Addison-Wesley, Reading, MA, pp. 367–385.

    Google Scholar 

  • Pool, R.: 1989, 'Is Something Strange about the Weather?', Science 243, 1290–1293.

    Google Scholar 

  • Procaccia, I.: 1988, 'Complex or Just Complicated?', Nature 333, 498–499.

    Google Scholar 

  • Raupach, M. R. and Thom, A. S.: 1981, 'Turbulence in and above Canopies', Annu. Rev. Fluid Mech. 13, 97–129.

    Google Scholar 

  • Raupach, M. R., Finnigan, J. J., and Brunet, Y.: 1989, 'Coherent Eddies in Vegetation Canopies', in Australian Conference on Heat and Mass Transfer, Christchurch, New Zealand, pp. 75–90.

    Google Scholar 

  • Raupach, M. R., Finnigan, J. J., and Brunet, Y.: 1996, 'Coherent Eddies and Turbulence in Vegetation Canopies: The Mixing Layer Analogy', Boundary-Layer Meterol. 78, 351–382.

    Google Scholar 

  • Ruelle, D.: 1990, 'Deterministic Chaos: The Science and the Fiction', Proc. Roy. Soc. Lond. A. 427, 241–248.

    Google Scholar 

  • Shannon, C. E.: 1948, 'A Mathematical Theory of Communications', Bell Syst. Tech. J. 27, 379–623.

    Google Scholar 

  • Sivakumar, B.: 2000, 'Chaos Theory in Hydrology: Important Issues and Interpretations', J. Hydrol. 227, 1–20.

    Google Scholar 

  • Skilling, J. and Gull, S. F.: 1985, 'Algorithm and Applications', in C. R. Smyth and W. T. GrandyJr. (eds.), Maximum-Entropy and Bayesian Method in Inverse Problems, D. Reidel, Dordrecht, pp. 83–131.

    Google Scholar 

  • Smith, L. A.: 1988, 'Intrinsic Limits on Dimension Calculations', Phys. Lett. A 133, 283–288.

    Google Scholar 

  • Szilagyi, J., Katul, G. G., Parlange, M. B., Albertson, J. D., and Cahill, A. T.: 1996, 'The Local Effect of Intermittency on the Inertial Subrange Energy Spectrum of the Atmospheric Surface Layer', Boundary-Layer Meterol. 79, 35–50.

    Google Scholar 

  • Townsend, A. A.: 1976, The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, 429 pp.

    Google Scholar 

  • Tsonis, A. A. and Elsner, J. B.: 1988, 'The Weather Attractor over Very Short Timescales', Nature 333, 545–547.

    Google Scholar 

  • Vidakovic, B.: 1995, 'Unbalancing Data with Wavelet Transformations', Wavelet Applications in Signal and Image Processing III, Proc. SPIE 2569 2, 845–857.

    Google Scholar 

  • Wickerhauser, M. V., Farge, M., Goirand, E., Wesfried, E., and Cubillo, E.: 1994, 'Efficiency Comparison of Wavelet Packet and Adapted Local Cosine Bases for Compression of a Two-Dimensional Turbulent Flow', in C. K. Chui, L. Montefusco, and L. Puccio (eds.), Wavelets: Theory, Algorithms, and Applications, Academic Press, San Diego, pp. 509–531.

    Google Scholar 

  • Wijesekera, H. W. and Dillion, T. M.: 1997, 'Shannon Entropy as an Indicator of Age Turbulent Overturns in the Oceanic Thermocline', J. Geophys. Res. 102, 3279–3291.

    Google Scholar 

  • Williams, G. P.: 1997, Chaos Theory Tamed, Joseph Henry Press, Washington, DC, 499 pp.

    Google Scholar 

  • Xin, L., Fei, H., and Gang, L.: 2001, 'Characteristics of Chaotic Attractors', Boundary-Layer Meteorol. 99, 335–345.

    Google Scholar 

  • Zubair, L., Sreenivasan, K. R., and Wickerhauser, M. V.: 1992, 'Turbulent Signals and Images Using Wavelet-Packets', in T. Gatski, S. Sarkar, and C. G. Speziale (eds.), Studies in Turbulence, Springer-Verlag, New York, 602 pp.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of the Environment, Duke University, Box 90328, Durham, NC, 27708-0328

    Karen H. Wesson, Gabriel G. Katul & Mario Siqueira

  2. The Cadmus Group, Inc., 6330 Quadrangle Drive, Suite 180, Chapel Hill, NC

    Karen H. Wesson

  3. Department of Civil and Environmental Engineering, Duke University, Durham, NC, 27708, U.S.A

    Mario Siqueira

Authors
  1. Karen H. Wesson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gabriel G. Katul
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mario Siqueira
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wesson, K.H., Katul, G.G. & Siqueira, M. Quantifying Organization of Atmospheric Turbulent Eddy Motion Using Nonlinear Time Series Analysis. Boundary-Layer Meteorology 106, 507–525 (2003). https://doi.org/10.1023/A:1021226722588

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021226722588

Search

Navigation