Abstract
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.
Highlights
The eddy-covariance technique has become the most commonly used method for measuring the ecosystem exchange of mass and energy with the atmosphere
While the Kaimal correction is only one of three priors tested in our Bayesian model, it is perhaps the most accepted algorithm currently available to correct transducer shadowing in the CSAT3
We provide the Markov chain Monte Carlo (MCMC) chain for the final posterior correction in the Supplement as a tool for researchers to evaluate in other sonic anemometer studies, to examine the uncertainty in ecosystem flux measurements, and to investigate surface energy balance closure
Summary
The eddy-covariance technique has become the most commonly used method for measuring the ecosystem exchange of mass and energy with the atmosphere. Frank et al.: A Bayesian model to correct underestimated 3-D wind speeds crometeorology and ecosystem flux communities that many sonic anemometers, the core instrument for all modern eddycovariance systems, systematically underestimate the vertical wind component (Frank et al, 2016; Horst et al, 2015; Kochendorfer et al, 2012). The ramifications for this are that all vertical fluxes (i.e., carbon dioxide, water vapor, latent heat, sensible heat, momentum) are underestimated for any ecosystem. This underestimate is roughly consistent with the persistent energy balance closure problem across flux sites (Leuning et al, 2012; Stoy et al, 2013; Wilson et al, 2002), where a vast majority are assumed to be systematic biased towards low turbulent fluxes of sensible and latent heat
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