Estimation of the statistical error in large eddy simulation results

In the study of the atmospheric boundary layer, Large Eddy Simulation (LES) results are nearly considered to be experimental data. However, where experimental results on turbulent quantities are occasionally accompanied by an estimation of the statistical error in the result, this is not the case for LES results. From the statistical literature methods are available to estimate the statistical error in central moments of arbitrary order of one and two variables based on higher moments of those variables. For statistics other than central moments (e.g. terms in a flux budget) resampling algorithms are available such as the jackknife method and bootstrap method. All these methods rely on the assumption that samples are independent. Statistics are derived from atmospheric LES results by averaging in all homogeneous dimensions (usually time and both horizontal directions) and the total number of samples equals the product of the number of samples in each direction. The number of independent samples, however, depends on the spatial and temporal correlation. For discretely sampled data the effect of the correlation between samples can either be determined using the integral scale or using the number of zero-crossings of the variable under consideration (after subtraction of the mean). An LES of a convective boundary layer will be used to demonstrate the use and results of the estimation of statistical errors in central moments and flux budget