Scalar similarity functions: the influence of surface heterogeneity and entrainment

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 (the analysis of) 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 rather limited, which is both its strength and its weakness. The main assumptions needed to limit the number of relevant variables are stationarity and horizontal homogeneity. Furthermore the analysis should be restricted to the lower part of the boundary layer where the only relevant height is the height above the ground, not the distance to the top of the boundary layer.

This study presents a detailed analysis of two data sets of surface layer observations over drying terrain (Bowen ratio increasing from 0.5-1 to 4 in a month time). One data set was obtained over savannah vegetation in Ghana (West Africa). The vegetation consisted of a mixture of grass, bushes and trees (approx. 25 trees/ha). Data were gathered directly following the rainy season. In that period the grass died, whereas the trees went on transpiring, yielding an increasingly heterogeneous distribution of sources and sinks for humidity sources, heat and carbondioxide: a first violation of the MOST assumptions. The other data set was collected during CASES-99, over relatively flat and homogeneous terrain in Kansas (US). Both data sets have in common that the surface flux of humidity decreased over time. Provided that the entrainment flux of humidity remains relatively constant, this could lead to an increasing importance of processes outside the surface layer, thus violating the assumptions underlying MOST.

For the present study only high-quality data (based wind direction and on the statistical error in the dimensionless groups under consideration) were utilized for the derivation of MOST-relationships for the variances. A general conclusion is that the dimensionless variances of humidity (and carbondioxide in the Ghana data) are higher (statistically significant) than those of temperature. It turns out that for the savannah data the dimensionless variances of humidity and carbondioxide increase over time. From a deeper analysis there are indications that both the surface heterogeneity and the entrainment processes play an important role. The role of the surface heterogeneity can be inferred from the fact that also during night-time the dimensionless variances increase during the dry season. The role of entrainment is indicated by a large increase in the dominant timescale of the humidity fluctuations. The dimensionless variances in the CASES-99 data do not show a trend in time, despite the decrease in the surface humidity flux. One reason for the absence of a clear effect of entrainment may be that the entrainment flux of humidity is more variable over time in mid-latitudes compared to tropical regions.