A Bayesian model to correct underestimated 3-D wind speeds from sonic anemometers increases turbulent components of the surface energy balance

Abstract. Sonic anemometers are the principal instruments in micrometeorological studies of turbulence and ecosystem fluxes. Common designs underestimate vertical wind measurements because they lack a correction for transducer shadowing, with no consensus on a suitable correction. We reanalyze a subset of data collected during field experiments in 2011 and 2013 featuring two or four CSAT3 sonic anemometers. We introduce a Bayesian analysis to resolve the three-dimensional correction by optimizing differences between anemometers mounted both vertically and horizontally. A grid of 512 points (∼ ±5° resolution in wind location) is defined on a sphere around the sonic anemometer, from which the shadow correction for each transducer pair is derived from a set of 138 unique state variables describing the quadrants and borders. Using the Markov chain Monte Carlo (MCMC) method, the Bayesian model proposes new values for each state variable, recalculates the fast-response data set, summarizes the 5 min wind statistics, and accepts the proposed new values based on the probability that they make measurements from vertical and horizontal anemometers more equivalent. MCMC chains were constructed for three different prior distributions describing the state variables: no shadow correction, the Kaimal correction for transducer shadowing, and double the Kaimal correction, all initialized with 10 % uncertainty. The final posterior correction did not depend on the prior distribution and revealed both self- and cross-shadowing effects from all transducers. After correction, the vertical wind velocity and sensible heat flux increased  ∼ 10 % with  ∼ 2 % uncertainty, which was significantly higher than the Kaimal correction. We applied the posterior correction to eddy-covariance data from various sites across North America and found that the turbulent components of the energy balance (sensible plus latent heat flux) increased on average between 8 and 12 %, with an average 95 % credible interval between 6 and 14 %. Considering this is the most common sonic anemometer in the AmeriFlux network and is found widely within FLUXNET, these results provide a mechanistic explanation for much of the energy imbalance at these sites where all terrestrial/atmospheric fluxes of mass and energy are likely underestimated.