A Bayesian approach to estimating surface fluxes with the eddy covariance method

Abstract. Eddy covariance is the state-of-the-art technique for measuring fluxes of energy and gases between the land surface and the atmosphere. However, many processing steps sit between the data that are actually measured and the calculated flux. In practice, the data processing constitutes a modelling exercise, requiring a model of the measurement system and of the surface layer of the atmosphere. In conventional data processing, we treat the parameters of this model as known constants, and this inevitably fails to propagate the true uncertainties. In a Bayesian approach, we treat the parameters of a model (representing the biological system, measurement system and atmosphere) as uncertain parameters, which we characterise with probability distributions. We use our knowledge of the system and previous data to specify prior probability distributions for these parameters. We then update these with the data we actually observe (a high-frequency time series of turbulence components, temperature, pressure, and mixing ratios) to yield the posterior distributions for these parameters. In this way, we can produce estimates of the fluxes of interest, such as the long-term net carbon balance of an ecosystem, in the form of posterior probability distributions, in which the uncertainty is correctly represented following the axioms of conditional probability.