Random uncertainties of flux measurements by the eddy covariance technique

Abstract

Abstract. Large variability is inherent to turbulent flux observations. We review different methods used to estimate the flux random errors. Flux errors are calculated using measured turbulent and simulated artificial records. We recommend two flux errors with clear physical meaning: the flux error of the covariance, defining the error of the measured flux as 1 standard deviation of the random uncertainty of turbulent flux observed over an averaging period of typically 30 min to 1 h duration; and the error of the flux due to the instrumental noise. We suggest that the numerical approximation by Finkelstein and Sims (2001) is a robust and accurate method for calculation of the first error estimate. The method appeared insensitive to the integration period and the value 200 s sufficient to obtain the estimate without significant bias for variety of sites and wide range of observation conditions. The filtering method proposed by Salesky et al. (2012) is an alternative to the method by Finkelstein and Sims (2001) producing consistent, but somewhat lower, estimates. The method proposed by Wienhold et al. (1995) provides a good approximation to the total flux random uncertainty provided that independent cross-covariance values far from the maximum are used in estimation as suggested in this study. For the error due to instrumental noise the method by Lenschow et al. (2000) is useful in evaluation of the respective uncertainty. The method was found to be reliable for signal-to-noise ratio, defined by the ratio of the standard deviation of the signal to that of the noise in this study, less than three. Finally, the random uncertainty of the error estimates was determined to be in the order of 10 to 30 % for the total flux error, depending on the conditions and method of estimation.

Shifted energy fluxes, increased Bowen ratios, and reduced thaw depths linked with drainage-induced changes in permafrost ecosystem structure

“…Random errors in time series of eddy-covariance fluxes are mostly linked to turbulence sampling errors, instrument errors, and uncertainties of the footprint (Rannik et al, 2016). We ignored the footprint errors in this context, since both towers are exposed to the same wind climatology.…”

“…Uncertainty assessments for the gap-filled flux values were taken from the output of the marginal distribution sampling routine (Reichstein et al, 2005) employed for this purpose. The random errors of the ensemble averaged fluxes were computed following Rannik et al (2016) Regarding the accuracy of radiation measurements, the Kipp & Zonen CNR4 radiation sensors employed here at both observation sites are officially classified as "first class" instruments (for shortwave radiation, e.g., a resolution of ±5 W m −2 and a stability of ±2 %). However, based on the direct comparison of data from both instruments, we find cumulative differences below 1 % of the total incoming radiation; therefore, our sensors would even qualify for the next highest quality rating (secondary standard, e.g., a resolution of ±1 W m −2 and a stability of ±1 %).…”

The NASA Carbon Airborne Flux Experiment (CARAFE): instrumentation and methodology

“…When extrapolating airborne fluxes to the surface, uncertainties in vertical flux divergence must also be considered. Methods to quantify flux errors are reviewed elsewhere (Langford et al, 2015;Mauder et al, 2013;Rannik et al, 2016). Here we leverage a combination of these methods and suggest a new technique to quantify the total random error in wavelet fluxes.…”

The NASA Carbon Airborne Flux Experiment (CARAFE): Instrumentation and Methodology

“…Methods to quantify flux errors are reviewed elsewhere (Langford et al, 2015;Mauder et al, 2013;Rannik et al, 2016). Here we leverage a combination of these methods and suggest a new technique to quantify the total random error in wavelet fluxes.…”