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Sonic anemometers are the principal instruments inmicrometeorological studies of turbulence and ecosystem fluxes. Commondesigns underestimate vertical wind measurements because they lack acorrection for transducer shadowing, with no consensus on a suitablecorrection. We reanalyze a subset of data collected during field experimentsin 2011 and 2013 featuring two or four CSAT3 sonic anemometers. We introducea Bayesian analysis to resolve the three-dimensional correction by optimizingdifferences between anemometers mounted both vertically and horizontally. Agrid of 512 points (∼ ±5° resolution in wind location) isdefined on a sphere around the sonic anemometer, from which the shadowcorrection for each transducer pair is derived from a set of 138 unique statevariables describing the quadrants and borders. Using the Markov chain MonteCarlo (MCMC) method, the Bayesian model proposes new values for each statevariable, recalculates the fast-response data set, summarizes the 5 minwind statistics, and accepts the proposed new values based on the probabilitythat they make measurements from vertical and horizontal anemometers moreequivalent. MCMC chains were constructed for three different priordistributions describing the state variables: no shadow correction, theKaimal correction for transducer shadowing, and double the Kaimal correction,all initialized with 10 % uncertainty. The final posterior correction didnot depend on the prior distribution and revealed both self- andcross-shadowing effects from all transducers. After correction, the verticalwind velocity and sensible heat flux increased  ∼ 10 % with ∼ 2 % uncertainty, which was significantly higher than the Kaimalcorrection. We applied the posterior correction to eddy-covariance data fromvarious sites across North America and found that the turbulent components ofthe energy balance (sensible plus latent heat flux) increased on averagebetween 8 and 12 %, with an average 95 % credible interval between 6and 14 %. Considering this is the most common sonic anemometer in theAmeriFlux network and is found widely within FLUXNET, these results provide amechanistic explanation for much of the energy imbalance at these sites whereall terrestrial/atmospheric fluxes of mass and energy are likelyunderestimated

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