A Bayesian model to estimate the true 3-D shadowing correction in sonic anemometers

Abstract:

Sonic anemometers are the principal instruments used in micrometeorological studies of turbulence and ecosystem fluxes. Recent studies have shown the most common designs underestimate vertical wind measurements because they lack a correction for transducer and structural shadowing; there is no consensus describing a true correction. We introduce a novel Bayesian analysis with the potential to resolve the three-dimensional (3-D) correction by optimizing differences between anemometers mounted simultaneously vertical and horizontal. The analysis creates a geodesic grid around the sonic anemometer, defines a state variable for the 3-D correction at each point, and assigns each a prior distribution based on literature with ±10% uncertainty. We use the Markov chain Monte Carlo (MCMC) method to update and apply the 3-D correction to a dataset of 20-Hz sonic anemometer measurements, calculate five-minute standard deviations of the Cartesian wind components, and compare these statistics between vertical and horizontal anemometers. We present preliminary analysis of the CSAT3 anemometer using 642 grid points (±4.5° resolution) from 423 five-minute periods (8,964,000 samples) collected during field experiments in 2011 and 2013. The 20-Hz data was not equally distributed around the grid; half of the samples occurred in just 8% of the grid points. For populous grid points (weighted by the abundance of samples) the average correction increased from prior to posterior (+5.4±10.0% to +9.1±9.5%) while for desolate grid points (weighted by the sparseness of samples) there was minimal change (+6.4±10.0% versus +6.6±9.8%), demonstrating that with a sufficient number of samples the model can determine the true correction is ~67% higher than proposed in recent literature. Future adaptions will increase the grid resolution and sample size to reduce the uncertainty in the posterior distributions and more precisely quantify the 3-D correction.