How is the small scale variability of the atmosphere represented in the database ?

Mean fields are stored in the database once a season. Although the main variability, which is due to the diurnal cycle, is captured by storing the fields 12 times a day, there may still be significant variation about the mean due to, for example, motions of baroclinic weather systems.

• Large scale variability in the database is represented using a novel approach based on a technique that is widely used in meteorological data analysis as well as in other subject areas, using Empirical Orthogonal Functions (EOFs). Let $D(z)$ be the database mean vertical profile of a meteorological variable. We add a series of functions to the mean vertical profile,
  

  $$D(z)~=\overline{D}(z)~+~\sum_{n=1}^N~p_i e_i(z)$$ (2)

  
  
  where the functions ${e_i}$ are eigenvectors of the covariance matrix of the modelled profiles (the EOFs) and $p_i$ are the amplitudes of the functions (the Principal Components). The ${e_i}$ form an optimal linear basis such that the variance captured is high even when the truncation limit is low. In order to retain cross-correlations in altitude between different variables we combine all the variables together and form a set of multivariate functions. In practice the series (2) is truncated to 6 EOFs which, on average, capture around 80-90% of the variance.

• A small scale variability model, simulating perturbations of density, temperature and wind due to the upward propagation of small scale gravity waves have been included in the database system. The model is based on the parametrization scheme used the numerical models that simulated the data in the database.

Further details on the variability models can be found in Lewis et al. (2001b) .