Time-scale turbulent transport extraction and high time resolution flux estimation using wavelet analysis

Flux estimation from eddy-covariance flux tower measurements faces the problem of integrating fluxes only in the case of fully developed turbulence and in non-stationary environments with advective components. The standard eddy-covariance method operates on fixed-length signals, requiring the knowledge of a maximum correlation time-length as well as post-processing steps assessing the suitability and quality of the data. Statistical tests are carried out to assess if flux estimates were performed during sufficiently developed turbulence and if they were corrupted by advective components. Tests with friction velocity u* or σ_w, steady-state tests, and flux variance similarity are now standard during and after flux calculations. More elaborate methods such as ogive optimisation are used to deal with advection. An important disadvantage of all these statistical tests is that they discard the whole time interval such as half an hour if they detect failure.

Time-scale (time-frequency) analyses have been used as an alternative to the standard time-analysis approach to estimate ecosystem fluxes. In particular, wavelet analysis, which is well adapted to the study of non-stationary and scale invariant processes such as turbulence, has been used in previous works. It presents the ability of separating the different components of the flux in time-scale space and as such could be an efficient alternative for flux estimation avoiding the above statistical tests.

To address this problem, we propose a general framework for analysing fluxes in time-scale space, and propose a new method for identifying and extracting turbulent transport that avoids advective components and does not need statistical tests after the flux calculations. The new method is based on the analysis in time-scale domain of the amplitude of the vertical component of the Reynold stress tensor and can be seen as a time-scale transposition of standard tests mentioned above. As a direct consequence, we are able to estimate fluxes at high time resolution over times and scales with sufficiently developed turbulence. We show application of the framework at the beech forest site FR-Hes and demonstrate its relation with standard eddy covariance calculations. Our methodology is implemented in the Julia package TurbulenceFlux.jl and is readily available. The proposed framework and its code implementation is fully differentiable and hints to further investigations, such as the study of flux ecosystem response times, or sensitivity analysis against wavelet and averaging window parameters.