Turbulent transport extraction in time and frequency and the estimation of eddy fluxes at high resolution

Abstract. We propose a framework for the estimation of eddy fluxes based on cross-scalogram smoothing. This is motivated by two main problems encountered with the standard eddy-covariance method: (1) limited temporal resolution leading to estimated fluxes unable to characterise fast dynamics (< 30 min) and with potentially large periods of data discarded after the application of quality tests; (2) limited frequency resolution leading to poor localisation of the turbulent scales and thus to potential biases in the estimations. We show that cross-scalogram smoothing can be viewed as an extension of the standard eddy-covariance approach where measurement signals are analysed in multiple frequency bands leading to a high resolution analysis of fluxes in time and frequency. A metric based on the vertical component of the Reynold's stress tensor is proposed to localise the turbulent scales in time and frequency. It conditions the estimation of any scalar flux decomposed in time and frequency. The proposed metric is similar to the u* and σ_w tests but it is adapted to the time-frequency setting. We also address practical issues encountered with cross-scalogram smoothing such as the choice of the wavelet family and the conservative property of the decomposition. We show application of the framework at the beech forest site FR-Hes and demonstrate its relation with standard eddy covariance calculations. The proposed method produces high temporal resolution (1 min) estimates of CO₂, latent and heat fluxes that align well with estimates from the standard 30-minute eddy-covariance method. The improved localisation of turbulent scales results in higher estimates of carbon uptake during summer (+2 ± 1 µmol m^-2 s^-1) and a more accurate assessment of nighttime respiration compared to standard eddy-covariance estimates. The methodology is implemented in the Julia package TurbulenceFlux.jl and is readily available for use.