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

Abstract. We introduce a novel framework for estimating eddy fluxes using cross-scalogram smoothing, addressing key limitations of the standard eddy-covariance method. The standard approach suffers from fixed averaging times (typically 30 min) and limited frequency resolution, which can lead to biases and an inability to capture fast dynamics. Our method, based on wavelet transforms, allows for high-resolution analysis of fluxes in both time and frequency domains. It adaptively localises turbulent scales using a metric derived from the vertical component of the Reynolds stress tensor, enabling more accurate flux estimation under varying turbulence conditions. The proposed metric is similar to the u* and σw tests, but it is adapted to the time–frequency setting. By decoupling the filtering of perturbative scales from flux calculations, our approach allows for flexible averaging times. This adaptability makes it particularly suitable for studying rapid ecosystem responses to environmental changes, such as those occurring on timescales shorter than 1 h. We show application of the framework at the beech forest site Hesse (code FR-Hes) and demonstrate its relation with standard eddy-covariance calculations. The proposed method allows for varying the averaging time without impacting the filtering of the perturbative scales. It thus allows for producing estimates of CO2, latent heat, and sensible heat fluxes with faster dynamics (e.g. with 1, 10, and 30 min averaging time). We present statistics of the 10 min averaged fluxes and show that they align well with estimates of the 30 min standard eddy-covariance method. The improved localisation of turbulent scales results in higher estimates of carbon uptake during summer (+2 ± 1 µmolm-2s-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, making it readily accessible for practical applications.