WAVELET PROJECT

These are beautiful figures from Wavelet Project. The second is a graph of Paraguay River's level, and the first graph is its Continuous Wavelet Transform using the Morlet Wavelet. On the horizontal axis is the time-variable (year), on the vertical axis is the scale (year) and the colour shows the intensity of the fluctuation.

More informations about the Wavelet Project

INTRODUCTION

The main objective of this research is investigating the penetration mechanisms which couple the stable flow existing in the vegetal cover's interior to that which exists above the trees.

Many are the questions which have motivated researchers to intensify their studies concerning Amazon Forest-Atmosphere interaction. One of them, perhaps the most important, consists in the role the biggest forest area in the planet carries out in the energy liberation to the tropical atmosphere. As known, this energy, captured from the incident solar energy, later to be transported through the atmosphere towards the poles, in trying to decrease the thermal contrast between the equator and the polar regions. In this energy liberation the atmosphere the evapotranspiration phenomenon performs adominant role, since it consumes approximately 90% of the available solar energy. This elevated percentage expresses the relevant role performed by thevegetal cover in the surface energy budget. It is from this perspective that the deforestation problem comes in, with the crucial question: If the energy associated to the evapotranspiration is altered, what alterations may the planetary scale climate go through?

A relevant second problem concerns the role the Amazon Forest performs in the global budget of atmosphere residual gaseous components like ozone, carbonic gas, hidrocarbonets and others.

All this relevant questions will be able to be well answered only from measurements of the different involved physical quantities vertical fluxes of forest-atmosphere exchange processes. However, if on the one hand these measurements are important for the canopy's performed role understanding, on the other they are difficult to be executed particularly due to the exchange process essentially turbulent character. This puts forward the problem of understanding the physical nature of such complex process, still not well understood nowadays.

A probably complicating factor in the study of the turbulent process is its clearly intermittent character. This does not permit it to berigorously regarded as stationary or homogeneous. Nevertheless the largest part ofavailable flux estimation methods admit turbulence is stationary (homogeneous):Correlation Method (reference method), Flux-Profile Method, Dissipative-Inertial Method, among others. This problem becomes particularly critic when one studies the flow in the vegetal canopy's interior since most of its exchange processes with the atmospheric region immediately above it occur through "bursts"extremely localized in space and time.

This challenges the traditional spectral decomposition methods for the turbulence's study and the fluxes' estimation (Fitzjarrald et al,1990). Using the Wavelet Transform one expects to better understand such intermittencies, determining with greater precision its spectral characteristics. This will eventually allow the formulation of a method for estimation of fluxin well `localized' regions. It will equally be possible to better discernthe nature of the `low-pass filter' represented by the forest canopy in the turbulent process.

THEORETICAL ELEMENTS

In mathematical analysis, pure and applied, one of the most important and well consolidated topics is Fourier analysis. The Fourier integral and series are fundamental in many areas of Science and Technology, suggest significant physical interpretations and possess particularly interesting computational aspects. Recently another theme, the `wavelet analysis', has greatly attracted the attention of physics, mathematicians and engineers. Like in Fourier analysis, there are two important entities in `wavelet analysis':the continuous wavelet transform (WT) and the wavelet series. The continuous WT is the operator of convolution with basis functions F (x) = a F(a (x-b)) obtained through translations and dilations of a sole functionF(x), the mother- wavelet (Meyer, 1990). In wavelet series these basis functions exist only for a discrete set of translation and dilation parameters. The WT makes possible a local multiresolution analysis both in space (or time) and frequency domains (Mallat, 1989). In each basis function F (x) space localization is determined by translation parameter `b' and frequency localization by parameter `a'. Consider, for example, a time function presenting a frequency band during only a small time interval. The double-localization property implies that in this function's wavelet series such information is not distributed over all coefficients. It stays concentrated only in those coefficients of the basis functions whose parameters `a' and `b' interfere with such time and frequency intervals. This does not happen in Fourier analysis which permits only frequency localization. Henceforth, this double-localization property combined with efficient decomposition algorithms (calculation of a specific function's wavelet series coefficients) and synthesis (reconstruction of this function from the coefficients), allows a very extensive list of wavelet analysis' possible applications (Farge, 1992). The mechanism through which the surface boundary layer (SBL) and the forest canopy are thermodynamically coupled is still superficially understood, even though the sensible heat, mass and momentum exchanges are of great practical importance (Gao et al, 1989). Most studies on turbulent flow inside and immediately above the canopy have been based on the theory of diffusion associated to vertical gradients, what has been refuted by experimental results (Denmead and Bradley,1985). Although high-order closure lagrange methods have been developed to describe more precisely the turbulence in such conditions (Wilson and Shaw, 1977;Raupach, 1987), these were based on statistical turbulence descriptions and employed semi-empirical relations of arguable efficiency. One must, therefore, keep in mind that significant advances in the canopy's microclimate simulation will only be able to occur with correct understanding and description of the physics of the turbulent processes responsible for the diffusion of quantities in and above the canopy. One of the crucial aspects still badly understood is the nature of `structures' organized in the form of `ramps' which were identified in various turbulent flows (Schols, 1984). They are linked to `bursts' in the flow, also called `microfonts', `intermittencies' or `gusts' (Shaw and Schumann,1992). These elements, the bursts, that have a central role in the coupling process, are extremely localized in space and time. They seem to occur principally in the wind velocity field which `forces' similar events, though less significative, in the temperature fields, specific humidity and carbon gas (Fitzjarrald et al, 1988; Fitzjarrald et al, 1990; Fitzjarrald and Moore, 1990). Although such phenomena are `rare' from the perspective of time occurrence and possess marginal statistical significance, they are the main responsible for the exchange of physical quantities between what is and under the canopy.

OBJECTIVES

  1. Implementing an algorithm which permits a multiresolution decomposition of the signal through the WT.
  2. Studying the specific characteristics of turbulent exchange immediately above and inside the Amazon Forest. Better understanding the nature of the low-pass filter characterizing the forest canopy in interaction with the turbulent flow, and investigating the dissipation of kinetic energy linked to bursts and other `fast' phenomena.
  3. Determining with better precision the errors in the turbulent fluxes' estimation through the correlation and dissipative-inertial methods, specially emphasizing the study of spatially `localized' intermittent exchange processes.
  4. Better understanding the nature of the statistical distributions of the diverse turbulent parameters of the atmospheric surface boundary layer above the forest canopy.
  5. Studying the relationship between the object under analysis (the turbulent signal) and the analysis instrument (the WT: trying to choose the most convenient mother-wavelet function to study the intermittent signal).
  6. Exposing results in magazines and scientific meetings.

    AVAILABLE DATA

    We already have the data below and intend to make new turbulence measurements at Amazonia in the future using fast response sensors (with sampling rate equal to or above 10 Hz). Data obtained in Reserva Florestal "Ducke" (Ducke Forest Reserve), Manaus, during "GTE-ABLE 2B" experiment.
    Data specification:
    1. Sampling Rate: 10 Hz;
    2. Quantities : wind speed, temperature, specific humidity, carbon gas;
    3. Heights: inside canopy, upper level of canopy, above canopy;
    4. Sampling duration: approximately 6 h (day time and night time);
    5. Instruments used: sonic anemometer, resistance thermometer and infrared hygrometer.

    BIBLIOGRAPHY

    • Denmead, O. T., Bradley, E. F., 1985. `Flux-gradient Relationshipsin a Forest Canopy' in: The Forest-Atmosphere Interaction, Hutchison, A., and Hicks, B. B. Eds., Reidel, Dordrecht: 421-442.
    • Farge, M., 1992. `The Wavelet Transforms and their Applications to Turbulence'. Annual Review of Fluid Mechanics, 24: 395-457.
    • Fitzjarrald, D. R., Moore, K. E., Cabral, O. M. R., Scolar, J.Manzi, A. O., Sa, L. D. A., 1990. `Daytime turbulent exchange between the Amazon Forest and the Atmosphere'. Journal of Geophysical Research, 95 (D10):16825-16838.
    • Fitzjarrald, D. R., Stormwind, B. L., Fisch, G., Cabral, O. M. R.,1988. `Turbulent Transport Observed Just Above the Amazon Forest'.Journal of Geophysical Research, 93 (D2): 1551-1563.
    • Gao, W., Shaw, R. H., Paw, U. K. T., 1989. `Observation of Organized Structure in Turbulent flow within and above a Forest Canopy'. Boundary-Layer Meteor., 47: 349-377.
    • Mallat, S. G., 1989. `A Theory for Multiresolution Signal Decomposition: The Wavelet Representation'. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7): 674-693.
    • Meyer, Y., 1990. `Ondelettes et Operateurs I'. Hermann, Paris.
    • Raupach, M. R., 1987. `Lagrangian Analysis of Scalar Transfer in Vegetation Canopies'. Quart. J. R. Meteorol. Soc., 113: 107-120. in the Atmospheric Surface layer'. Boundary-Layer Meteor., 29:39-58.
    • Shaw, R. H., Schumann, U., 1992. `Large-Eddy Simulation of Turbulent Flow above and within a Forest'. Boundary-Layer Meteor., 61 (1-2): 47-4.
    • Wilson, N. R., Shaw, R. H., 1977. `A Higher Order Model Closure Model for Canopy Flow'. J. Appl. Meteorol., 16: 1197-1205.

    Comments, suggestions, research propositions and open discussion

    Last updated: 06/12/97
    Li Weigang (wei@met.inpe.br) Sabrina Sambatti (sabrina@met.inpe.br) Mauricio Bolzan (mauricio@met.inpe.br)