In this study the Leonard (<<a><b>>-<a><b>, where < > is a commonly adopted running mean filter) and the Cross (<<a>b'>) terms have been estimated for the first time using atmospheric data. These terms represent part of the subgrid scale (SGS) contribution obtained when a running mean is used to average the atmospheric conservation equations or data adopting the Reynolds decomposition. An estimate of these terms allows us to quantify the error that one makes when, using a running mean filter, only the Reynolds terms (<a'b'>) are considered as subgrid scale contribution.
Datasets with various spectral characteristics have been used to calculate the terms. The latter have been obtained for both variance and co-variances of atmospheric variables (velocity components, temperature, moisture and chemical compounds). Long term data of the concentration of atmospheric constituents have also been used (ozone and nitrogen dioxide).
The SGS term including the Leonard and Cross components, have been calculated using averaging intervals typically used in boundary layer meteorology for averaging purposes.
The results reveal that the Leonard and the Cross term can have large values and costitute a large contribution to the determination
of the SGS term. Furthermore interesting features are shown by the terms such as a constant anticorrelation that, under certain circumstances, reduces their overall impact on the SGS value.
A relation is shown to exists between the behaviour of these terms and the shape of the power spectrum of the data.
The Leonard and Cross terms have been estimated in the past only for engineering flows and despite for atmospheric data no evidence has been collected, they are considered negligible by assumunig the validity of the Reynolds averaging rules and the existence of a Spectral Gap. The study conducted reveals that, in particular for scalar variables, the absence of a well defined scale separation does not allow to neglect these terms and that they can be comparable in order of magnitude to the usual Reynolds terms