Sampling error in aircraft flux measurements based on a high-resolution large eddy simulation of the marine boundary layer

A high-resolution (1.25 m) large eddy simulation (LES) of the nocturnal cloud-topped marine boundary layer is used to evaluate random error as a function of continuous track length inline-formulaL for virtual aircraft measurements of turbulent fluxes of sensible heat, latent heat, and horizontal momentum. Results are compared with the widely used formula of citxref_text.1#bib1.bibx15Lenschow and Stankov (#bib1.bibx151986). In support of these comparisons, the relevant integral length scales and correlations are evaluated and documented. It is shown that for heights up to approximately 100 m (inline-formula $M2inlinescrollmathmlz/z_i=\mathrm{normal\; 0.12}$ 57pt14ptsvg-formulamathimg6f8a3ca2e443c5beb97da180fec0bd1c amt-14-1959-2021-ie00001.svg57pt14ptamt-14-1959-2021-ie00001.png ), the length scales are accurately predicted by empirical expressions of the form inline-formulaI_f=Az^b. The Lenschow and Stankov expression is found to be remarkably accurate at predicting the random error for shorter (7–10 km) flight tracks, but the empirically determined errors decay more rapidly with inline-formulaL than the inline-formula $M5inlinescrollmathml{L}^{-\mathrm{normal\; 1}/\mathrm{normal\; 2}}$ 28pt14ptsvg-formulamathimg4ddac4ef7aef725aa9035c853cd60130 amt-14-1959-2021-ie00002.svg28pt14ptamt-14-1959-2021-ie00002.png relationship predicted from theory. Consistent with earlier findings, required track lengths to obtain useful precision increase sharply with altitude. In addition, an examination is undertaken of the role of uncertainties in empirically determined integral length scales and correlations in flux uncertainties as well as of the flux errors associated with crosswind and along-wind flight tracks. It is found that for 7.2 km flight tracks, flux errors are improved by factor of approximately 1.5 to 2 for most variables by making measurements in the crosswind direction.