Investigations of structure parameters and their similarity relationships in the convective boundary layer by means of large-eddy simulations and comparison with measurement data

Turbulent fluctuations of the refractive index (n) in the atmospheric boundary layer are related to local fluctuations in the air density, which can be expressed by the refractive-index structure parameter (C_n²). Since these fluctuations depend mainly on temperature and humidity, it is possible to relate C_n² to the structure parameters for temperature (C_T²) and humidity (C_q²). Recently, large-aperature scintillometers (LAS) have been increasingly used to measure C_T² over path lengths of several kilometers in the surface layer. By means of Monin-Obukhov similarity theory, the surface fluxes of sensible and latent heat can be estimated from measurements of C_T² and C_q². However, a validation of these measurements is challenging.

We derive C_T² and C_q² from high-resolution (grid spacing of 2-4 m) large-eddy simulations (LES) of a homogeneously-heated convective boundary layer, driven by measurements at Cabauw (The Netherlands). Three different methods to obtain the structure parameters from LES are investigated. Among others, it is found that the shape of the vertical profiles of the structure parameters compares well with former experimental and modelling results. Depending on the method, deviations in the magnitude up to a factor of two are found and traced back to effects of subgrid-scale modeling in LES.

In the presentation we compare the structure parameter profiles with data from an LAS ranging over a distance of 9.8km as well as aircraft measurements along the LAS path in different heights during RECAB 2002 (courtesy of Fred Bosveld at KNMI and courtesy of Beniamino Gioli at Ibimet). In the mixed layer we find that C_q² compares well between LES and aircraft data, whereas C_T², derived from aircraft data, underestimates the proposed decrease with height. In the surface layer we find a good agreement with the LAS data. Virtual scintillometer measurements are employed in the LES in order to investigate the statistical error in LAS measurements due to the temporal and spatial variability of the path-averaged C_T² as well as its variability along the path.

Furthermore we present results from investigations of the similarity relationships for structure parameters in the surface layer. Universal functions, relating the structure parameters to the surface fluxes of sensible and latent heat, by means of Monin-Obkhukov similarity and local free convection similarity are calculated from the LES data and compared with the proposed formulations in literature.