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Monin Obukhov Similarity Theory (MOST) is one of the cornerstones of surface layer meteorology and as such it is widely applied in models and for data analysis. One major disadvantage of using MOST for describing land-atmosphere interactions is that all turbulence properties are described as a function of the same limited set of key parameters. Therefore, MOST is in particular not valid over heterogeneous terrain (Andreas et al., 1998). To study the limits of MOST, deviations of similarity functions from their homogeneous versions need to be linked to the degree of heterogeneity (which may be different for different scalars, i.e. water vapor, CO2 and heat (Moene and Schüttemeyer, 2008)). In particular, the degree to which observations at a given point are influenced by different sources should be known. Footprint models can be used to partition EC (eddy covariance) measurements in scalar fluctuations originating from the different land use types in the measurement area. Calculations are made within footprint models to estimate the contribution of each unit element of the upwind surface area to a measured vertical flux. However, validations of footprint models with natural tracer experiments using several EC-stations and land use types are still needed. We will therefore present validation results of two analytical footprint models, using two different validation methods and several eddy covariance stations in two different landscapes. The first landscape is flat, with very small spatial variability in roughness lengths and soil properties. This mosaic-like land use pattern, together with entrainment, are expected to be the only challenge to MOST-based footprint models. The second landscape, in contrast, additionally includes slight slopes, spatial patterns in soil moisture, and some tree groups. The two sites should thus enable a characterization of the importance of different types of MOST violation. The analytical model of Kormann and Meixner (2001) and the approximately analytical model of Hsieh et al. (2000) were validated first using flux data from the Transregio experiment in Merken in August 2009. The eddy covariance observations were obtained in three adjacent fields with contrasting fluxes, a wheat, barley and a sugar beet field, as well as close to the edge between two of the fields. Two validation methods were applied: forward validation and validation by inversion. For the forward method, fluxes from the wheat, barley and sugar beet field were used together with the footprint model to estimate the flux measured at an EC-station in the barley field near the border with the sugar beet field. The inverted validation method is based on decomposed fluxes of seven eddy covariance stations in the three fields, to estimate the surface fluxes of the three underlying land use types and therewith perform a cross validation with left-out eddy covariance measurements. We secondly used EC-measurements from a more heterogeneous and complex campaign called BLLAST (in southern France in June 2011) to validate both footprint models using flux measurements from a wheat and a grass field, and from measurements at the border between these fields. Validation results will be shown and compared for both models, validation methods and datasets. Using the validated footprint models in a later stage of our study, the degree of heterogeneity at the point of observation can be quantified. Subsequently, deviations from published MOST relationships can be linked to the degree of heterogeneity.

Eddy covariance measurements are the method of choice to determine net land surface – atmosphere fluxes of energy and matter, but in some cases cannot be applied in a representative way. In particular, requirements on the measurement height and the principles underlying the fetch or footprint of the sensor inhibit straightforward application in small (

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 (sT and sq) 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 (rTq) which decreases from 0.75 to 0.5 in the course of the experiment (rTq 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 sT/¿* > sq/q* (equivalent to a relative transport efficiency ¿=rwT/rwq less than 1). This is indeed what is observed. Midday values for ¿ gradually decrease from 0.9 to 0.7. Apart from the similarity relationships for sT and sq, the relationships for CO2 standard deviation will also be discussed briefly.