Multiscale analysis of vegetation surface fluxes: from seconds to years

The variability in land surface heat (H), water vapor (LE), and CO₂ (or net ecosystem exchange, NEE) fluxes was investigated at scales ranging from fractions of seconds to years using eddy-covariance flux measurements above a pine forest. Because these fluxes significantly vary at all these time scales and because large gaps in the record are unavoidable in such experiments, standard Fourier expansion methods for computing the spectral and cospectral statistical properties were not possible. Instead, orthonormal wavelet transformations are proposed and used. The are ideal at resolving process variability with respect to both scale and time and are able to isolate and remove the effects of missing data (or gaps) from spectral and cospectral calculations. Using the spectra, we demonstrated unique aspects in three appropriate ranges of time scales: turbulent time scales (fractions of seconds to minutes), meteorological time scales (hour to weeks), and seasonal to interannual time scales corresponding to climate and vegetation dynamics. We have shown that: (1) existing turbulence theories describe the short time scales well, (2) coupled physiological and transport models (e.g. CANVEG) reproduce the wavelet spectral characteristics of all three land surface fluxes for meteorological time scales, and (3) seasonal dynamics in vegetation physiology and structure inject strong correlations between land surface fluxes and forcing variables at monthly to seasonal time scales. The broad implications of this study center on the possibility of developing low-dimensional models of land surface water, energy, and carbon exchange. If the bulk of the flux variability is dominated by a narrow band or bands of modes, and these modes “resonate” with key state and forcing variables, then low-dimensional models may relate these forcing and state variables to NEE and LE.     

The Role of Wake Production on the Scaling Laws of Scalar Concentration Fluctuation Spectra Inside Dense Canopies

The scalar concentration fluctuations within a plane parallel-to-the-ground surface were measured inside a model canopy composed of densely arrayed rods using the laser-induced fluorescence technique. Two-dimensional scalar concentration spectra were computed and were shown to exhibit an approximate ?3 power-law scaling at wavenumbers larger than those associated with wake production during quiescent instances when von Karman vortex streets dominated the flow. However, during instances when sweeps disrupted the flow, the spectral exponents increased above ?3. The ?3 power-law for these concentration fluctuation spectra measurements was shown to be consistent with a simplified spectral budget for locally homogeneous and isotropic turbulence augmented with a relaxation time scale similarity argument that assumed a constant enstrophy injection rate and wake generation mechanism. Hence, the origin of this ?3 power-law scaling here differs from the well-known ?3 power-law result for the so-called inertial diffusive range derived for the scalar concentration spectrum at small Prandtl numbers.     

The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering

Townsend's attached eddy hypothesis states that the turbulent structure in the constant stress layer can be decomposed into attached and detached eddy motion. This paper proposes and tests a methodology for separating the attached and detached eddy motion from time series measurements of velocity and temperature. The proposed methodology is based on the time-frequency localization and filtering capabilities of the orthonormal wavelet transforms. Using a relative entropy statistical measure, the optimal wavelet basis is identified first. The turbulence time series measurements are then transformed into the wavelet domain where the contribution of specific events in the time-frequency domain is identified. The filtering scheme utilizes a recently constructed Lorentz thresholding methodology that successfully eliminates all wavelet coefficients associated with the detached eddy motion. While this filtering scheme lacks the compression efficiency of the classical Donoho and Johnstone's universal thresholding model, it conserves the higher-order statistics and important turbulence interactions related to the Reynolds stresses. Following the filtering scheme, the attached eddy motion time series is re-constructed by an inverse wavelet transform of the non-zero wavelet coefficients. The proposed partitioning methodology for attached and detached eddy motion is tested using 56 Hz triaxial sonic anemometer velocity and temperature measurements above a uniform dry lake bed in Owens valley, California, for a wide range of atmospheric stability conditions. Validation that the wavelet filtered time series represents the attached eddy motion is also discussed in the context of conservation of turbulence energy and surface fluxes.