Quantification of the effect of surface heterogeneity on scalar variance similarity

To study turbulent flows in the atmospheric boundary layer dimensional analysis is widely applied. For flows in the lower part of the atmospheric boundary layer the cornerstone of analysing experiments and modelling is Monin-Obukhov Similarity Theory (MOST). The central assumption is that once all relevant variables are identified, the number of dimensionless groups can be determined. Those dimensionless groups should be related in a universal way, irrespective of the magnitude of the individual (dimensional) variables. For MOST the list of relevant variables is limited, which is both its strength and its weakness. The main assumptions needed to limit the number of relevant variables are stationarity, horizontal homogeneity and irrelevance of processes outside the atmospheric surface layer. These conditions are easily violated in realistic situations. Although violations of MOST conditions in relation to non-universality of the MOST relationships are widely discussed in literature, this is nearly always done in a qualitative sense only.

 

Here we will focus on the similarity relationships for standard deviations of temperature and humidity (σ_T and σ_q) and study how they deviate from universal behaviour due to heterogeneity of the underlying surface. The spatial scale of the heterogeneity we address is the scale of contrasts between individual fields (order of 100 meter). In the analysis we will use the framework presented in Moene and Schüttemeyer (2008).

 

This study presents a detailed analysis of a dataset gathered during the BLLAST field campaign near Lannemezan (Southern France) in the summer of 2011. Three eddy-covariance systems were set up: one in a meadow (green throughout the campaign), one in a field with a mixture of cereals and peas (ripening during the campaign) and one right at the edge between the two fields ('edge station'). This setup enables us to obtain surface fluxes and other turbulence statistics both for two contrasting landuse types with homogeneous fetch as well as for a station with a heterogeneous fetch.

 

The objective is to quantify the impact of surface heterogeneity on the dissimilarity between the similarity relationships of different scalars. The degree to which the edge station experiences a heterogeneous fetch depends on two aspects. 

• The potential heterogeneity is determined by the contrast in surface fluxes between the two fields: the mid-day Bowen ratio of the meadow is approximately constant at 0.3, whereas the Bowen ratio of the cereal field increases from 1 to 1.5 over the course of the experiment. The midday CO₂ flux is -7·10^-7 kg m^-2s^-1 for the meadow, whereas for the cereals it increases from -2·10^-7 kg m^-2s^-1 to +0.6·10^-7 kg m^-2s^-1.
• The actual heterogeneity is determined by the wind direction, or more exactly, the location of the source area. Only if the source area of the observations is located in different fields, then the contrast in fluxes between fields will be actually relevant and lead to non-universal behaviour of MOST relationships. In order to quantify the relative contribution of the two fields in the signal of the edge station the footprint model of Hsieh et al. (2000), augmented with the crosswind distribution of Kormann and Meixner (2001), is used.

 

The development of the fluxes of both surfaces indicates that the potential heterogeneity indeed increases in time. Furthermore, it turns out that for a significant part of the time footprint contributions come from both fields. Hence, the actual heterogeneity increases in time as well. This we express in a new heterogeneity parameter that combines the flux contrast between the fields and the heterogeneity of the land use in the footprint.

 

The actual heterogeneity is clearly visible in the midday correlation coefficient between temperature and humidity (r_Tq) which decreases from 0.75 to 0.5 in the course of the experiment (r_Tq is of the order of 0.8 for both homogeneous fields). The mean Bowen ratio measured at the edge station is generally below 0.5, which implies that, according to Moene and Schüttemeyer (2008), one would expect that σ_T/θ_* > σ_q/q_*  (equivalent to a relative transport efficiency λ=r_wT/r_wq  less than 1). This is indeed what is observed. Midday values for λ gradually decrease from 0.9 to 0.7. Apart from the similarity relationships for σ_T and σ_q, the relationships for CO₂ standard deviation will also be discussed briefly.

 

 

References

            Hsieh, C., Katul, G., Chi, T., 2000. An approximate analytical model for footprint estimation of scalar fluxes in thermally stratified atmospheric flows. Adv. Water Resour. 23, 765–772.

            Kormann, R., Meixner, F.X., 2001. An analytical footprint model for non-neutral stratification. Boundary Layer Meteorol. 99, 207–224.

            Moene AF, Schüttemeyer D , 2008. The effect of surface heterogeneity on the temperature-humidity correlation and the relative transport efficiency. Boundary-Layer Meteorol 129, 99–113