Regionalization of turbulent fluxes by combining aircraft measurements with footprint analysis

Regionalization of turbulent fluxes by combining aircraft measurements with footprint analysis T. El-Madany, H. Geiß, A. Schmidt, and O. Klemm University of Münster, Institute for Landscape Ecology, Robert-Koch-Straße 28, 48149 Münster, Germany Forschungszentrum Jülich GmbH, Institute of Chemistry and Dynamics of the Geosphere, ICG2 (Troposphere), 52425 Jülich, Germany Received: 19 May 2009 – Accepted: 26 June 2009 – Published: 14 July 2009 Correspondence to: T. El-Madany (tarek.elmadany@uni-muenster.de) Published by Copernicus Publications on behalf of the European Geosciences Union.


Introduction
Knowledge about nutrition and water cycles is of extraordinary importance for characterizing ecosystems and their role in the context of climate change.Especially sources and sinks of water vapor and carbon dioxide, the two single most important greenhouse gases, need to be quantified with high spatial and temporal resolution.A well developed understanding of these fluxes and the processes and parameters driving these fluxes will help to model the role of ecosystems and regions with respect to regional aspects of global change.
Cities are known to be sources of CO 2 as a result of human activity, as they concentrate traffic, power plants, industry and domestic heating.Their emission (and uptake) of green house gases including water vapor, is, however, difficult to model due to large variations in architecture, size, traffic, green belt and park areas, and the associated Figures positive and negative feedback mechanisms.Although urban regions in Europe are densely covered with buildings and streets, significant portions resemble rural areas which act as a sink of carbon dioxide and, at the same time, as a source of water vapor.These rural areas are responsible for a significant contribution to the budget of CO 2 and H 2 O even in the industrialized countries.
Eddy covariance is a method to estimate the turbulent exchange between surface and atmosphere.It is widely accepted and has been used since the early 1950's (Swinbank, 1951).Worldwide measurement networks have been established (Fluxnet; Wilson et al., 2002;Richardson et al., 2006, Ameriflux;Baldocchi et al., 2000;Falge et al., 2002, Carboeurop;Berbigier et al., 2001;Dolman et al., 2006, Asiaflux;Saigusa et al., 2002;Hirata et al., 2008 and Chinaflux;Fu et al., 2006;Yu et al., 2006) to quantify the energy and mass exchange between different vegetation types on the one hand and the atmosphere on the other.For various forest types (Yasuda et al., 2003;Li et al., 2005), agricultural crops (Kim et al., 2002;Moureaux et al., 2006), and natural vegetation (Nakai et al., 2008;Wohlfahrt et al., 2008) the carbon dioxide flux has been quantified by using tower-based applications of eddy covariance.Furthermore, flux measurements above cities (e.g.Grimmond et al., 2004;Schmidt et al., 2008) were employed to quantify the emission of carbon dioxide in urban areas.
Unfortunately, the areas captured by ground based flux towers only represent a limited section of an ecosystem or landscape.The respective measurement can be directly scaled up to larger areas only as long as the respective larger area is of identical vegetation type.To quantify the flux of CO 2 for a whole ecosystem or landscape, all aspects of the region have to be captured by the flux measurement.This is virtually impossible to be realized even with a large number of ground based experimental platforms.
One possibility to measure the CO 2 exchange of an entire ecosystem is to use a moving platform, as carried by a helicopter (Bange et al., 2006) or by an airplane (Graber et al., 1998;Gioli et al., 2006).
First attempts of airborne flux measurements have been made in the early 1980s Introduction

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Full Screen / Esc Printer-friendly Version Interactive Discussion (Lenschow et al., 1980;Alvo et al., 1984;Desjardins et al., 1982).Since then measurement problems arising from the use of aircraft have been discussed by many authors.Desjardins et al. (1989) showed that means of consecutive flight segments are similar to a single long segment and that the flight direction with respect to the wind direction is important for flux measurements sampling at heights over 50 m above ground.Furthermore, Mann and Lenschow (1994) analyzed sets of short flights at different altitudes, and high-pass filtered time series and found that flux gradient errors and systematic flux errors are potentially large.A ground-speed correction for the time average was introduced by Crawford (1993), taking into account the aerodynamic characteristics of the airplane that correlate with the vertical wind speed.As a result, a spatial average is used instead of a time average.A model that estimates if an aircraft is suited to fly with rigid altitude control in a boundary layer with strong convection was presented by Busch et al. (1996).Strategies for obtaining adequate flux sampling by the use of repeated aircraft passes and grid patterns was developed by Mahrt (1998).Isaac et al. (2004) and Gioli et al. (2004) demonstrated that comparison of aircraft and ground based data show best agreement if flight height and sensor height are equal and if the footprint areas are of similar composition (e.g.vegetation and surface characteristics).
In other words, great care must be taken if flux measurements from airborne platforms are interpreted in terms of surface fluxes.So-called footprint models were developed to determine the surface area that contributes to the measured turbulent exchange.For example, at tower based sites, the vegetation directly underneath the tower does not contribute to the flux at the tower top at all, but the "source area" or "footprint" (Schmid, 2002) is located in the upwind direction of the tower.The function that describes the relationship between the spatial distribution of surface exchange flux and the measured signal at a certain height is the "source weight function" or "footprint function" (Schmid, 1997).Thus the source area or footprint can be interpreted as the integral of the source weight function or footprint function.Size and shape of the footprint vary with meteorological conditions such as wind speed and stability and are therefore highly time dependent.Since the early 1990s, various footprint models were developed (Leclerc and Thurtell, 1990;Schuepp et al., 1990) to quantify the source areas contributing to experimentally determined fluxes (Schmid, 1997).There is a variety of models employing analytical forward (Horst, 2001;Kormann and Meixner, 2001) analytical backward (Kljun et al., 2002), and Lagrangian stochastical (Kurbanmuradov and Sabelfeld, 2000;Lee, 2003) approaches.They utilize different assumptions and approaches to model the respective footprint areas.Various meteorological data are used as input parameters to estimate the footprint function.The different models and their applications have been discussed and compared with each other by Schmid (2002) and Foken and Leclerc (2004) with the result that there is no optimum model.The model has to be chosen individually for each experimental site or instrumental approach.

Meteorology
Meteorological measurement flights were conducted between May 21st and 24th 2008 above the "M ünsterland" region in northwest Germany.The weather during the flight days was influenced by a moderately developed high pressure system with pressure between 1020 and 1015 hPa.The wind directions were from north to east.Cloud cover varied from 1/8 to 6/8 but it did not rain during the measurement period.Daily mean temperatures increased constantly from 12.6 to 16.7 • C. The sun shine duration varied between 10 and 14 h per day.Wind speed was constant on the first three days, from 3 to 6 m s −1 .On the 24th the wind speed increased to up to 10 m s −1 .

Flight pattern
During the four measurement days eight flights with a total duration of 14 h and 34 min were performed.The flight pattern was designed to gather information about the CO and H 2 O fluxes of the city of M ünster and its surrounding agricultural area.At the beginning and the end of each flight, vertical profiles were flown to analyze the height and vertical structure of the boundary layer, particularly with respect of the occurrence of temperature inversions and its turbulent mixing status.Due to federal restrictions and safety considerations, the flight height above the city was limited to a minimum of 300 m above ground.For the agricultural areas, a low-level flight permission allowed flight sections as deep as 50 m above ground.

Aircraft
A motor glider (ECO Dimona) endowed with fast response instruments for meteorological parameters and trace gases (Neininger et al., 2001;Schmitgen et al., 2004) was used to perform measurement flights around the city of M ünster.The average operational cruising speed is between 40 m s −1 and 50 m s −1 , with the scientific payload used and full gasoline tanks the maximum endurance is about 5 h.The instruments are installed inside, or attached to the pods, which are mounted under the wings of the motor glider.Others are located inside the cockpit.The three dimensional wind speed is measured with a sensitive fast response five hole pressure probe as described in Crawford and Dobosy (1992).The water vapor concentrations are calculated with a combination of dew point mirror (Meteolabor) and an open path infrared gas analyzer (IRGA) (LI-COR 7500).The slow response (1 s) dew point mirror is for the exact concentration measurement and the IRGA to catch the fluctuations at 10 Hz.Carbon dioxide concentrations and fluctuations are derived in a similar way by using a combination of a closed path IRGA (LI-COR 6262) for concentrations and an open path IRGA for fluctuations.Furthermore, CO is measured with a fast response vacuum UV resonance fluorescence instrument as described by Gerbig et al. (1999).NO 2 is detected with a NOxTOy 6 channel Luminol detector (Dommen et al., 1999)

Eddy covariance
The eddy covariance method was used to calculate the fluxes as measured with the airborne platform.
F is the flux of a scalar, w the vertical wind speed, ϕ the scalar of interest, the prime denotes a deviation from the mean and the overbar indicates a mean over that time period.Straight and leveled flight segments were extracted for the flux calculation.To reduce the risk of measuring artificial fluxes which evoke from height gradients of the scalar of interest (Vickers and Mahrt, 1997;Mahrt, 1998), leveled segments with a standard deviation of less than 6 m of the flight height above sea level were used.Straight flight segments also assure that the airplane flies at a constant angle to the mean wind direction along each segment.This is a requirement for correct measurement of atmospheric turbulent fluxes, according to Taylor's frozen turbulence hypothesis (1938).Therefore, when flying straight segments, the airplane flies through differently sized eddies and captures them as a whole.Another aspect is that the airplane is horizontally leveled while flying straight, thus all instruments inside the left and right wing pods measure at the same height.Kirby et al. (2008), Gioli et al. (2004), andLeMone et al. (2003) showed that an averaging length of four km is adequate to sample long enough wave components of the fluxes to represent the turbulent exchange.For this reason, the minimum length used for the flux calculation was set at 4 km.
Time series of temperature, H 2 O and CO 2 were linearly detrended to eliminate artificial flux contributions that may occur when concentrations increase or decrease constantly due to events like advection of differently polluted air masses.The vertical wind speed was not detrended to maintain the turbulent structures of vertical air motion.Crawford et al. (1993) showed that the use of a time average instead of a space average can lead to biases in the flux calculation of up to 20%.The space average is Introduction

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Full derived from a time series via: The square brackets indicate a space average of ϕ, where ϕ represents the vertical wind speed, temperature, water vapor, or carbon dioxide concentration.S is the speed of the aircraft, the overbar indicates an average over the time T (time of the flight segment), ∆t is the time step between two measurement points and the subscript i refers to an instantaneous value.Density fluctuations in the air result in apparent fluctuations of CO 2 and H 2 O and thus have an effect on the calculated flux.This issue has to be addressed when using open path instruments.To eliminate this effect, Webb et al. (1980) introduced a correction term which was used in here.

Footprint model/footprint tool
To relate the fluxes as measured on the aircraft to their source area on the ground, the footprint tool of Neftel et al. (2008) was used.It is based on the footprint model of Kormann and Meixner (2001) and features a function for calculating footprint fractions related to predefined areas.A footprint fraction is a percentile contribution of a certain predefined area (in this study 1 km by 1 km squares, see below) inside the footprint, to the respective footprint.The footprint is represented by the area of an ellipse that is an approximation of the total area within the 1% isopleths of the maximum of the integrated footprint function (Neftel et al., 2008).This ellipse is used for the determination of the total footprint and will from now on be referred to as the footprint.The footprint is characterized by the displacement, i.e. the smallest distance of the 1% isopleths from the measuring point.
The footprint tool needs different types of input data: meteorological parameters (average wind speed for the flight segment, wind direction, standard deviation of the cross wind, Obukhov length L and friction velocity u * ), parameters describing the position Introduction

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Full of the airplane (flight height above ground level and position of the airplane), and the coordinates of the predefined areas.The Monin-Obukhov length L was calculated via: where u * is the friction velocity, k the Von Karmann constant (0.4), g the acceleration due to gravity, θ v the virtual potential temperature, and w θ v buoyancy flux at ground level.
The friction velocity u * was calculated through the following formula: where u, v, and w are the three dimensional wind components, the primes refer to a deviation from the mean of the flight segment and the overbars denote a mean over the time of a flight segment.
One restriction for the footprint tool is that the value of z/L, which is an indicator for the atmospheric stratification, has to be between −3 and 3.This limitation is used in the footprint model because for a very unstable stratification (values of z/L<−3) the error of the velocity profile is unacceptably large (Kormann and Meixner, 2001).For values of z/L>3, the stability of the boundary layer is too high and turbulent exchange is inhibited thereby.In cases for which these conditions were not fulfilled, the respective footprint area was not calculated.
Usually, a footprint for fixed ground based flux measurements is calculated for the averaging period of the flux calculation (typically 30 min).For the aircraft, instead, for each time step of a flight segment, i.e. every 0.1 s, a footprint is generated and thus the footprints are overlapping each other (Fig. 1a).All input values for the footprint tool are averaged for the respective flight segment except for instantaneous wind direction and flight height.By adding up all contributions of the predefined areas from the individual footprints, a total footprint is obtained for each flight segment.The percentile contribution of each predefined area to the total footprint is then computed.The result is a total footprint with spatial information about the flux contribution as shown in Fig. 1b.
In cases when the meteorological conditions are constant the contribution to the total footprint increases from the marginal areas to the center of the total footprint as shown in Fig. 1b.In cases of changing meteorological conditions, especially wind speed and wind direction, the maximum of the contribution appears smeared or even two local maxima may occur.The spatial information, derived from the predefined areas (1 km×1 km), was spatially interpolated in Fig. 1b.To check the validity of the interpolation procedure above, the footprint contribution was calculated for a 250 m×250 m grid and compared to the 1 km×1 km grid results (Fig. 2).It can be seen that the major features of the footprint can be reproduced by the interpolation procedure.The approach for calculating the spatial information of the footprint was especially used for the evaluation of the footprint model for airborne flux measurements (Sect.2.6).

Suitability of the footprint model/footprint tool for airborne flux measurements
From the perspective of a fast moving platform, the surface characteristics (forests, lakes, agricultural areas, and urban areas) captured by a footprint change from one footprint to another.In order to evaluate the suitability and correctness of the applied footprint model, specific "flux events" were compared with each other.A flux event in this sense is a short section of a sible.Under these conditions, relative differences in the flux events can be attributed to different surface characteristics.Three major kinds of surfaces can be distinguished: vegetation surfaces that exhibit in an anti-correlation of w CO 2 and w H 2 O , urban areas where traffic emissions lead to a positive CO 2 and NO 2 flux even at flight level, and water surfaces that have a positive impact on the H 2 O flux.To illustrate this procedure an example is given in Sect.3.1.

Regionalization of fluxes
Regionalization describes an up-scaling process of data measured at a point or within a small area (e.g. a couple of field plots) to a larger region.Up-scaling can only be realized if the sample area has at least the same characteristics (e.g.vegetation, soil and surface structure) as the area to which the information is to be scaled up to.This was assured by analyzing the land use inside the total footprint of a flight segment, and comparing it with the area that is supposed to be scaled up to.

Extraction and comparison of land use data
To combine the information from the land use data and the footprint data, geo information software (ArcGIS Version 9.3, ESRI Geoinformatik GmbH) was used.The routine involves six consecutive steps.First, the ellipsis data from the footprint tool (length of the ellipsis axis, center coordinates, and rotation angle) are transformed into a geo referenced area by creating a shape file that contains all individual footprints that the total footprint of the respective

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Full flight segment consists of.This is done with a tool (military analyst) that comes with the ArcGIS software.
Secondly, the land use data that fall into the total footprint of a flight segment are extracted from the entire land use dataset.The result is a land use map reduced to the size of the total footprint.
Thirdly, the land use type statistics inside the total footprint is calculated as a number of pixels representative for each land use type.The area of each land use type is calculated by multiplying the number of pixels with the area each pixel represents (900 m 2 ).
Fourthly, when steps one to three are executed for all flight segments, the total land use that was captured by the flights is calculated.Therefore, land use data from all total footprints are added up and the percentile contribution for all land use types is calculated.
Fifthly, the percentile contribution of the land use types of the area that is supposed to be up-scaled, is calculated.This is done in the same manner as for the land use inside the total footprints.
Sixthly, the percentile contribution of the land use types is used to compare the composition of the sampled area and the area that is supposed to be scaled up.To the extent of which the compositions of the two areas are similar to each other up-scaling is considered possible.

Fluxes used for the regionalization
The flux data have to be of high quality to assure the accuracy for the regionalization.Therefore different criteria are more condensed than for simply applying the footprint model and additional criteria are introduced.Data are only used if a flight segment is longer than 4 km, the ratio of z/L is between −3 and 0.1 and the flight height is lower than 275 m above ground level.Analysis of segments longer than 4 km assure, that most of the flux contributing eddies are sampled (Sect.3.3).A value of z/L between −3 and 0.1 assures that the stratification of the atmosphere is not stable and thus the Introduction

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Full exchange between surface and atmosphere (in flight height) is not inhibited.The flight height limitation assures that the airplane is well inside the mixing layer and thus the surface-atmosphere exchange can be measured correctly.The average of all fluxes that fulfill the restrictions mentioned above is used for the regionalization.

Suitability of the footprint model for airborne flux measurements
The suitability of the footprint model for the interpretation of airborne flux measurements is of crucial importance.If the footprint model does not give a good representation of the source areas the regionalization of fluxes cannot be achieved.The source areas that influence turbulent exchange thus have to be characterized carefully in order to relate the measured, turbulent flux to land use types.In the following the flux events shown in Fig. 4 and Fig. 5 are discussed in combination with Fig. 3 to underline the differences in the flux events and the causes for these differences.this flux event was east.The colored squares represent the percentile contribution to the footprint of the flux event.The two areas that contribute together about 58% to the flux signal consist mainly of urban areas, a highly frequented autobahn, a bypass, and some major roads.Furthermore some green-and park areas are within this footprint area and many streets that are planted with trees can be found.
The second flux event occurs 15 s after the first one.The wind direction changed during this time from east to north north-east as shown in Fig. 3d.On the one hand the second flux event is characterized by high, positive NO 2 and H 2 O fluxes, and on the other hand it is characterized by a strong, negative CO 2 flux.As for the first flux event the positive flux of the w H 2 O and w NO 2 time series indicate that the air masses are transported from the ground into the atmosphere.The strong anti-correlation between w CO 2 and w H 2 O shows that the air masses are dominated by the photosynthesis of the vegetation that takes up carbon dioxide and releases water vapor at the same time.
Nevertheless the high values of the w NO 2 time series indicate, that the air mass was influenced by anthropogenic emissions too.
Figure 5 shows w H 2 O -values of the above described segment, including the second flux event shown in Fig. 3.The areas that contribute 72% (51%, 15%, 6%) to the footprint of the flux event are strongly influenced by green areas including a forest, crops, grassland, shrubs and a lake.These green areas account for the strong anti-correlation of w CO 2 and w H 2 O and the high values of w H 2 O for the flux event.
Urban areas that are also contained in the footprint contribute significant to the flux pattern.However, in contrast to the first event, the air was depleted of CO 2 by the vegetation, which results in a strong negative CO 2 flux.Applying this method, many flight segments where evaluated.A good agreement between the observed flux events and the composition of the footprint areas was found.Thus the footprint model is well suited for the determination of the footprint for airborne flux measurements under the premises used in this study.Introduction

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Footprint analysis and land use data
The total footprint areas from the 99 flight segments add up to an area of 6947 km 2 .The individual total footprint sizes vary between 13 km 2 and 268 km 2 .The large differences in the total footprint sizes result from the differences in the flight segments length and micrometeorological parameters.The footprint area grows from unstable over neutral to stable stratification and with flight height above ground.The mean total footprint size is 70 km 2 .The sample area is 1510 km 2 in size.Due to repetitive flight patterns the area of all total footprints is more than 4 times larger than the area of the "M ünsterland" and the sample area, respectively.The area of the "Westf älische Bucht" is 6054 km 2 .This is the regional landscape, in which the "M ünsterland" is integrated and that is to be up-scaled to.The major land use type in the "M ünsterland" region is arable land (over 50%).Meadows and grassland account for approximately 20%, forests (pine-, mixed-, and deciduous forests) for 15%, and the urban areas add up to 10% of the land use.The other land use types (water bodies, military training areas (land use is blacked out), lignite open pit mining, and gravel pit mining) add up to 1% of the land use.
The percentile land use contribution for all total footprint areas, the sample area of the "M ünsterland", and the "Westf älische Bucht" is very similar with differences of only a view percent (Fig. 6).Since the land use types, sampled by all total footprints, represent the composition of the "M ünsterland" very well (Fig. 6) it can be assumed that the flux average is a representative value for the turbulent exchange of the "M ünsterland".

Flux calculation from flight segments
Due to the restrictions mentioned in Sect.2.4 and 2.9, 99 out of a total of 244 flight segments could be used for the flux calculation The averaging length of a flight segment, which is essential for the computation of reliable flux magnitudes, results in a blurred flux signal that cannot be related to certain source area types inside the footprint.Exemplarily a high contribution of a forest (45%) in a total footprint does not result in a more negative CO 2 flux than a small forest contribution (5%) (Fig. 9).As a result, when comparing the fluxes from the various flight segments with respect to the land use inside the footprints, there is no significant correlation between a certain land use type and the magnitude of the fluxes (Fig. 9).Nevertheless, for short time scales the contributing features can be identified.Examples for this are the flux events that can be related to small scaled land use types.

Conclusions
In this study airborne measurements of turbulent exchange were regionalized by an analysis of footprint data and high resolution land use maps.We found that all requirements for a regionalization are fulfilled: the footprint model gives a good estimation of the source area; the land use type distribution inside the footprints and the up-scaled area are very similar to each other; the average period for the flux calculation was long enough to capture the relevant eddies.Thus, the measured values of the fluxes can be extrapolated to the area of the "Westf äliche Bucht" and give a quantitative estimate of the respective fluxes.The result is a mean carbon dioxide uptake by the different vegetation types of 4177 kg s −1 (± 2300 kg s −1 ) for the area of the "Westf älische Bucht" (6054 km 2 ).The water vapor transferred into the atmosphere through evapotranspiration is 1029000 kg s −1 (±544000 kg s −1 ).These average fluxes are representative for the growing period of late spring/early summer under day time conditions.Further investigations in this manner would certainly help to understand processes driving the turbulent fluxes on a regional scale.Moreover, quantification for the CO 2 uptake and the variance throughout the year would become feasible for a regional scale.
As the investigation of the footprint model showed, the footprint model by Kormann and Meixner (2001)  The footprint fraction contribution to the footprint is a very useful feature of the footprint tool by Neftel et al. (2008).The tool should be developed further so it can be used for larger areas or whole regions.
Furthermore, a connection to a mesoscale chemical transport model would help to evaluate and verify the results achieved in this project.
w ϕ time series, typically 2-4 s (about 100-200 m flight path) that has a high contribution to the averaged flux of the respective flight segment.During such time sections the landscape elements (lake, forest, urban area) that are accountable for the measured flux are represented by a few footprints (ca.20-40).Only flux events within the same flight segment are compared to each other to assure that the meteorological conditions are comparable to each other as well as pos- Fig. 3 shows two typical flux events (grey shaded areas) in a 60 s extraction of the same flight segment.The first flux event is characterized by positive contributions to the CO 2 , H 2 O, and NO 2 fluxes.NO 2 is primarily from ground based, anthropogenic sources, traffic and other combustion processes.Thus it can be argued that the observed strong positive flux originated from the ground.The positive flux of H 2 O is a result of evapotranspiration at vegetated areas.When looking at the concurrent positive NO 2 , CO 2 , and H 2 O fluxes one would assume a footprint area that is dominated by heavy traffic (w NO 2 time series) but also includes some vegetated areas, as well as water bodies which both result in a positive H 2 O flux too.In this example anthropogenic emissions dominate the total CO 2 flux, while the vegetated areas are not large enough to take up all the emitted CO 2 , but they influence the amplitude of the CO 2 flux.In Fig.4the footprint of the first flux event and a part of the w CO 2 time series including the flux event is shown.The wind direction for the time of . The mean measurement height from the flight segments used for the flux calculation varied between 98 m and 275 m above ground level.The mean, minimum, maximum and standard deviation of the fluxes of CO 2 , H 2 O and sensible heat are represented in Table1.The large standard deviation of the observed fluxes reflects the inhomogeneity of the surfaces with different compo-, water surfaces, and urban areas.The strong anti-correlation of CO 2 and H 2 O fluxes (Fig.7, top) is a result of the vegetated areas that were sampled mostly.Since sensible heat, H 2 O, and NO 2 have their sources on the ground their positive fluxes are indicators for the transport of air from the surface into the atmosphere.Thus a positive correlation can be observed between the fluxes of sensible heat and H 2 O (Fig.7, bottom) as well as for NO 2 (not shown).For all four measurement days the fluxes of CO 2 , H 2 O and sensible heat vary within the same range (Fig.8, right side) even though the concentrations of CO 2 , water vapor and the temperature change (Fig.8, left side).This indicates that the influence of advective fluxes can be excluded on a time scale corresponding to the length of a flight segment.In a heterogeneous landscape with high spatial variability, any measured flux signal is influenced by the combined influence of various surface types (e.g.vegetation, water bodies, and urban areas).
Furthermore, there is no significant correlation of the measured fluxes with wind speed, wind direction, flight height or time of the day on a time scale of the flight segments (Fig.10).This absence of significant correlation indicates that different combinations of the various parameters lead to the observed fluxes.The lack of correlation for the flight and meteorological parameters with the flux values shows that the turbulent exchange is not governed by any single parameter.The missing correlation between the flight segment distance and flux values indicates that the minimum length of 4 km is adequate for sampling the majority of the flux contributing eddies.This is Fig.11that shows the spectral analysis of the vertical wind speed for three flight segments of different length.The mostly sampled eddies are in a range of 20-40 s for all three flight segments.Thus the longer flights capture eddies of similar size as compared to the shorter segments.Consequently the shorter segments do not miss eddies of larger sizes.Considering the speed of the airplane the apparent eddies are of about 1000-2000 m horizontal extent.The averaging length of the flight segments used for the flux calculation is therefore adequate.
is well suited for estimating the source area of the airborne flux measurements under the conditions used in this study.More investigations with specific tracers like SF 6 or CO from open fire could help to quantify the use of this footprint conditions as used in this study.

Fig. 1 .Fig. 2 .
Fig. 1. (A) Land use map with all footprints (beige colored ellipses) of the flight segment.The black polygon represents the footprint of the right side, which was calculated from the ellipsis data of the left side.(B) A sketch of a footprint with interpolated, spatial information of the flux contribution.Colors represent the contribution of areas inside the footprint to the measured flux (from red (20%) to blue (1%) decreasing).The flight track of the aircraft is symbolized by a red line.

Fig. 3 .Fig. 5 .Fig. 6 .
Fig. 3.A section of 60 s of a flight segment on 22.05.08 from east towards urban area.(A) w CO 2 time series in mg m −2 s −1 (B) w H 2 O time series in g m −2 s −1 (C) w NO 2 time series in ppb m −2 s −1 .(D) Wind direction in • .Grey shaded areas show flux events which are used in Fig. 4 (first highlight) and Fig. 5 (second highlight).

Fig. 7 .
Fig. 7. Correlation between carbon dioxide fluxes and water vapor fluxes (top) and correlation of sensible heat fluxes and water vapor fluxes (bottom) from 99 flight segments.

Fig. 9 .
Fig. 9. Correlation of carbon dioxide flux (left) and sensible heat flux (right) to different land use type contributions.

Fig. 10 .
Fig. 10.Correlation of the carbon dioxide flux (left) and the sensible heat flux (right) to different meteorological and flight parameters.

Fig. 11 .
Fig. 11.Spectral analysis of three flight segments of different length.The duration of the flight segments is 189 seconds (top), 146 s (center), and 88 s (bottom).