The Cospectral Gap and Turbulent Flux Calculations

An alternative method to Fourier analysis is discussed for studying the scale dependence of variances and covariances in atmospheric boundary layer time series. Unlike Fourier decomposition, the scale dependence based on multiresolution decomposition depends on the scale of the fluctuations and not the periodicity. An example calculation is presented in detail. Multiresolution decomposition is applied to tower datasets to study the cospectral gap scale, which is the timescale that separates turbulent and mesoscale fluxes of heat, moisture, and momentum between the atmosphere and the surface. It is desirable to partition the flux because turbulent fluxes are related to the local wind shear and temperature stratification through similarity theory, while mesoscale fluxes are not. Use of the gap timescale to calculate the eddy correlation flux removes contamination by mesoscale motions, and therefore improves similarity relationships compared to the usual approach of using a constant averaging timescale. A simple model is developed to predict the gap scale. The goal here is to develop a practical formulation based on readily available variables rather than a theory for the transporting eddy scales. The gap scale increases with height, increases with instability, and decreases sharply with increasing stability. With strong stratification and weak winds, the gap scale is on the order of a few minutes or less. Implementation of the gap approach involves calculating an eddy correlation flux using the modeled gap timescale to define the turbulent fluctuations (e.g., w′ and T′). The turbulent fluxes (e.g., w′T′) are then averaged over 1 h to reduce random sampling errors.