Sc

Aa

b

c

a

ARR2A

KEFNF

1

detdaFEoflflme

hanpTse

v

0h

Agricultural and Forest Meteorology 169 (2013) 1– 11

Contents lists available at SciVerse ScienceDirect

Agricultural and Forest Meteorology

jou rn al h om epa g e: www.elsev ier .com/ locate /agr formet

ensitivity and uncertainty of analytical footprint models according to aombined natural tracer and ensemble approach

. van de Boera,b,∗, A.F. Moenea, D. Schüttemeyerb, A. Grafc

Meteorology and Air Quality Group, Wageningen University, PO Box 47, 6700 AA Wageningen, The NetherlandsMeteorological Institute University Bonn, Auf dem Hügel 20, 53121 Bonn, GermanyAgrosphere Institute, Forschungszentrum Jülich, IBG-3, 52428 Jülich, Germany

r t i c l e i n f o

rticle history:eceived 9 March 2012eceived in revised form0 September 2012ccepted 22 September 2012

a b s t r a c t

Evaluations of analytical footprint models using data from several stations located in different land usetypes are still scarce, but valuable for defining the spatial context of the measurements. Therefore, weevaluated two analytical footprint models by applying a ‘forward’ and an ‘inversion’ method. We usededdy covariance measurements from a flat agricultural landscape in western Germany in the summer of

eywords:ddy covarianceootprint modelatural tracer experiment

2009, with seven eddy covariance systems over three different land use types with contrasting sensibleheat fluxes. We found that the model of Hsieh et al. (2000. Adv. Water Resour. 23, 765–772) and of Kor-mann and Meixner (2001. Boundary Layer Meteorol. 99, 207–224) are both overestimating the distanceof the peak contribution of the footprint. In our evaluation, the former model performs slightly better,independent of whether the crosswind dispersion was used from the latter model, or from the proposed

6. W

ootprint inversion model by Detto et al. (200

. Introduction

The large horizontal variability of the energy and gas exchangeown to very smn scales, and especially the representation of gasxchange in land-surface models, still poses major problems. Longerm monitoring networks have been established during the lastecades to determine trace gas fluxes between terrestrial surfacesnd the atmosphere, e.g. FLUXNET (Baldocchi et al., 2001), AMERI-LUX and CARBOEUROPE. The eddy covariance (later referred to asC) method is widely used to quantify land–atmosphere exchangef carbon dioxide and water vapor. However, EC systems measureuxes at field to catchment scale, which implies that the measuredux often originates from a mixture of land use types. Footprintodels (Schmid, 2002) aim at predicting the contribution of differ-

nt parts of the surface to a measured flux or scalar concentration.Although footprint models are frequently used to determine the

omogeneity of the footprint of EC-measurements, little is knownbout their validity and accuracy. The use of artificial tracer gases,atural sources of scalars, and isolated heterogeneities for foot-rint model evaluation is discussed by Foken and Leclerc (2004).

hey point out that well designed experiments with natural tracershould be performed to investigate the application range for differ-nt footprint models, since those studies can often be included into

∗ Corresponding author at: Meteorology and Air Quality Group, Wageningen Uni-ersity, PO Box 47, 6700 AA Wageningen, The Netherlands.

E-mail address: anneke.vandeboer@wur.nl (A. van de Boer).

168-1923/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.agrformet.2012.09.016

ater Resour. Res. 42, 1–16).© 2012 Elsevier B.V. All rights reserved.

on-going flux field campaigns. This was done by Reth et al. (2005)and Göckede et al. (2005) among others, who tested the suitabilityof natural tracer experiments in the evaluation of footprint mod-els. Reth et al. (2005) attempted to use soil chamber measurementsand EC data to evaluate footprint models. Göckede et al. (2005)compared soil chamber measurements with EC and scintillometermeasurements with various footprints, using data from the samefield experiment as Reth et al. (2005). During the past decades,research on footprint modeling has increased significantly. Differ-ent types of methods have been developed by many researchers.Pasquill (1972) simulated the transfer between downwind obser-vations and two-dimensional upwind sources analytically. Theadvantage of an analytical footprint model is its ability to describethe horizontal distribution of source weight with one or two equa-tions and a manageable amount of parameters. The parameterscan typically be computed from measurement height, roughnesslength, atmospheric stability and crosswind variance.

Analytical footprint models in the strict sense are analyticalsolutions of the advection–diffusion equation (e.g. Gash, 1986;Schmid and Oke, 1990; Schuepp et al., 1990; Horst and Weil, 1992;Schmid, 1994; Stannard, 1997; Horst, 1999; Haenel and Grünhage,1999; Kormann and Meixner, 2001). The flow field in analyticalfootprint models is implicitly calculated using either (quasi) log-arithmic profiles from MOST (Monin–Obukhov similarity theory)

or power law profiles. The crosswind dispersion is described as aGaussian plume. As an improvement to such analytical models, anapproximate analytical model was developed by Hsieh et al. (2000).Their model is based on a combination of Lagrangian stochastic

2 and Forest Meteorology 169 (2013) 1– 11

dcrata

adppicc

atatpamdhmsot(solaibefbs

pitmdtcfob

matidowussa

1

Table 1Footprint model input for the original models and our implementations. HKC, KMand Det indicate our implementations of respectively the alongwind part of HKC00,the alongwind or crosswind part of KM01, and the crosswind function describedby Detto et al. (2006).

√indicates that the parameter is required for the given

implementation.

Input Original Our implementations

Longitudinal Crosswind HKC-KM KM-KM HKC-Det

HKC00 KM01 Det KM01

u* – –√

–√ √ √

z0√ √ √ √

– – –L

√ √ √ √ √ √ √zm

√ √ √ √ √ √ √�v – –

√ √ √ √ √√ √ √

els (after Eqs. (A.1) and (A.2)) for two different atmospheric stability

A. van de Boer et al. / Agricultural

ispersion model results and dimensional analysis. It does notontain a crosswind distribution in its original form, which is a pre-equisite for the kind of application and evaluation our study aimst. However, it can be combined with the crosswind distribution inhe frequently used model of Kormann and Meixner (2001) as wells with a crosswind distribution suggested by Detto et al. (2006).

Lagrangian stochastic dispersion models (e.g. Kljun et al., 2002)nd LES-based models (e.g. Steinfeld et al., 2008) have beeneveloped as well. However, computations in those types of foot-rint models are time consuming. The approximate analyticalarametrization by Kljun et al. (2004) would be interesting to

nclude in a comparison because of its ability to predict downwindontributions. However, the model does not yet include a publishedrosswind distribution for these downwind contributions.

Here, we test two frequently used analytical footprint modelsnd various ways to obtain their required input data on a set-uphat allows for extensive natural tracer experiments. We deliber-tely focus on sensible heat flux because it depends (apart fromhe Schotanus correction) on one sensor only, which is the sameroviding all other footprint-relevant turbulence data; the sonicnemometer. Other scalar fluxes are known to fail quality testsore often than sensible heat fluxes. Furthermore, we will use a

ataset from a landscape with different land use types, but withouteterogeneities in orography or roughness which would affect theean flow in a direct way and to a high degree. With the present

tudy, we hope to contribute to the proper use and further devel-pment of footprint models used over sites with several land useypes, for EC flux data quality control, validation of new instrumentse.g. scintillometers and chambers), or for dis-aggregation by inver-ion (Hutjes et al., 2010). In this study, we build on the suggestionf Foken and Leclerc (2004) to include a footprint evaluation in aarger field experiment. Seven EC sensor pairs (sonic anemometersnd gas analyzers) at locations implying footprints with differencesn the main land use type were operated in a landscape dominatedy a mosaic of three land use types. In this way, the natural tracervaluation concept can be extended to a dataset where differentootprint model properties (e.g. upwind and crosswind extension)ecome important in different situations (e.g. wind direction andtability).

Within the core of our study, a forward application of the foot-rint model of Hsieh et al. (2000), hereafter referred to as HKC00,

s used to predict fluxes at the border station, which is located inhe most heterogeneous surrounding. For this purpose, the HKC00

odel is combined with a land use map. EC data were used toetermine the representative fluxes of the three dominant land useypes in the measurement area. These fluxes were multiplied withontributions of the corresponding land use type in the calculatedootprint of the border station. The predicted fluxes at the borderf the two fields were evaluated with flux measurements from theorder station.

This evaluation method is repeated systematically using theodel of Kormann and Meixner (2001), hereafter referred to

s KM01. Furthermore, the sensitivity of the evaluation resultso different choices of parameterizations and input variables isnvestigated. These runs include the parametrization of crosswindistribution, surface roughness, and atmospheric stability. More-ver, we will give a brief example of solving the evaluation problemith an inversion approach, which estimates fluxes for each landse type from all measured fluxes and modeled footprints for eachtation, rather than assuming any of the stations to deliver ‘pure’urface fluxes of a single land use type. Together, these approachesim at answering the following questions:

. Can we identify, by reference to the natural tracer experi-ment, certain recommendations on the implementation of theapproaches presented by HKC00 and KM01? (Section 5.2)

U – – – –

2. Is the footprint model uncertainty related to• the crosswind distribution,• surface roughness of an area with different land use types,• atmospheric stability in an area with different land use types?(Sections 5.2 and 5.3)

3. Does an ensemble average derived from different model com-binations and input parameterizations improve our forwardevaluation results? (Section 5.4)

4. Is inversion, as suggested by Neftel et al. (2008) and Hutjes et al.(2010), robust enough to serve as an alternative way to deter-mine ‘pure’ land use fluxes? (Section 5.5)

We will first describe the two footprint models (HKC00 and KM01),our implementation of the models, and the method to obtain foot-print weights of each land use type in Section 2. In Section 3, wedescribe the evaluation methods and the sensitivity analyses. Adescription of the measurements, the data processing and the mea-surement area is given in Section 4. In Section 5, results will beshown characterizing the meteorological conditions, the modelevaluation, the sensitivity analysis, and the ensemble evaluation.Conclusions are given in the final Section 6. Equations used in thisstudy can be found in Appendix A (footprint models) and AppendixB (surface layer similarity).

2. Model description

2.1. HKC00 and KM01

The parameters in the models proposed by HKC00 and KM01are determined explicitly from micro-meteorological parameters(see Appendix A for equations used in the footprint models). Themodel by HKC00 requires roughness length (z0), Obukhov length (L)and aerodynamic measurement height (zm, height above displace-ment height) as input to determine its shape parameters (cf. Eq.(A.1)). A rougher surface, a more unstable atmosphere, and lowersensors all result in a smaller footprint. The model returns the cross-wind integrated source weight as a function of upwind distance (x).The crosswind distribution later added by Detto et al. (2006) addi-tionally requires the standard deviation of crosswind speed (�v, Eq.(A.5)) and the friction velocity (u*). The crosswind integrated partof KM01 (cf. Eq. (A.2)) also requires z0, L and zm (see Table 1). Thecrosswind distribution part of KM01 (Eq. (A.3)) only requires �v asextra input.

Fig. 1 shows crosswind integrated flux footprints for both mod-

cases. The input data chosen represent a daytime and night-timesituation which are inspired by our measurement data. The fig-ure clearly shows the main difference between the two models for

A. van de Boer et al. / Agricultural and Forest Meteorology 169 (2013) 1– 11 3

0 50 1000

0.01

0.02

0.03

0.04

0.05

Upwind distance from instrument (m)

Foo

tprin

t (m

−1 )

HKC00 unstableKM01 unstable

0 500 10000

0.5

1

1.5

2

2.5

3

3.5x 10

−3

Upwind distance from instrument (m)

Foo

tprin

t (m

−1 )

HKC00 stableKM01 stable

Fig. 1. Longitudinal distribution function of KM01 and HKC00 for a typical unstable situation (z/L = −0.44, z0 = 0.05 m, u = 0.22 m s−1, U = 1.8 m s−1), and a stable situation( s are d

uaooiftKae

atosfKszTpEpodbDf

Faa

z/L = 1.13, z0 = 0.05 m, u* = 0.05 m s−1, U = 1.2 m s−1). Note that the values on the axe

nstable conditions. For the unstable case, the peak contributionccording to HKC00 is located 12 m closer to the instrument, and isne and a half times higher than the peak modeled by the functionf KM01. When comparing the KM01 model with their backwardsn time Lagrangian stochastic dispersion model, Kljun et al. (2003)ound that the upwind tail of the KM01 footprint was heavier thanheir tail. We also included the parameterized footprint model byljun et al. (2004) (not shown). Although the model by HKC00 gives

lower tail than KM01, it is still relatively high compared to Kljunt al. (2004).

For the stable case, the peak contributions predicted by HKC00nd KM01 are very small and occur at less different locations, andails are much longer than for the unstable case. The peak locationsf both models differ less than 10% for this case. The dependence ontability within a stability regime (stable or unstable) is differentor both models. HKC00 shows a stronger dependence on z/L thanM01 (not shown). Also the dependence on surface roughness (nothown) is different. The KM01 model is more affected by a changing0. In Fig. 2a, a Gaussian crosswind dispersion function is shown.he second part of Fig. 2 shows the increase of the crosswind widtharameter �y (depending on crosswind standard deviation and u*,qs. (A.4) and (A.5)) with upwind distance for the crosswind dis-ersion functions of KM01 and Detto et al. (2006). The specificationf �y is the only difference between the two Gaussian crosswind

ispersion functions. Further away from the station, the differenceetween the two crosswind functions increases, and the function ofetto et al. (2006) results in more crosswind dispersion than KM01

or both the day and night time case.

−50 0 500

0.005

0.01

0.015

0.02

0.025

Crosswind distance (m)

Foo

tprin

t (m

−1 )

a

ig. 2. (a) Crosswind distribution function at upwind distance of the peak location. Peaknd HKC00 stable respectively. (b) Crosswind width, described by KM01 and Detto et al.

s in Fig. 1, with �v = 0.83 and 0.21 m s−1 respectively.

*

ifferent for both cases.

2.2. Our implementations

2.2.1. Determination of roughness lengthIn a widespread implementation of the KM01 model (Neftel

et al., 2008), the observed wind speed (U) together with the vari-ables zm/L and u* are used to determine z0 (Eq. (A.7)), rather thanusing a fixed estimate of z0. By doing so, the z0 value that wouldbe consistent with the observed combination of U, u*, and L can beused to detect violations of the assumptions underlying the model,in particular MOST. We calculate z0 using Eq. (A.7) (Neftel et al.,2008) in our three implementations of the models (see Table 1how the model input differs). Records yielding values outside therange 1 × 10−4 to 0.2 m were adapted to these limits. We analyzethe effect of z0 by also using fixed estimates of z0 for footprintcalculations in two members of our ensemble study.

2.2.2. DiscretizationTo assign the flux contributions to different land use types, the

source weight function (footprint), the position of the EC station,wind direction (Udir) and a land use map are required. Neftel et al.(2008) integrated the footprint density function over a defined sur-face area given as quadrangular polygons representing the fields. Incontrast, we used grid information of the land use types to compute

the integral footprint weight of each land use type. This grid infor-mation is more easily applicable to arbitrary field shapes. However,the resolution at which the source weight function is discretizedis imposed by the resolution of the land use map. Therewith, a

0 50 100 150 2000

50

100

Upwind distance (m)

σy (

m)

b KM01 stable KM01 unstable Detto stable Detto unstable

locations are 18, 93, 6 and 84 m for KM01 unstable, KM01 stable, HKC00 unstable(2006), depending on upwind distance, for the same unstable and stable situation

4 and Forest Meteorology 169 (2013) 1– 11

cd

cecotiu

2

wC(iwKrmiwcStob

3

tswst(lwe(

3

dtewS

F

ifu

2nitc

Table 2Configuration of the different model setups. The first three runs are used for themodel evaluation (results in Table 3), the other 7 are used in the sensitivity analyses(results in Table 4). The entire list of 10 runs is used in the ensemble average (resultsin Table 5).

Run Longit. model Crossw. model z/L source z0 source

RefHKC-KM HKC KM Border BorderKM-KM KM KM Border BorderHKC-Det HKC Det Border Border

AreaAvga HKC KM Average AverageMostStableb HKC KM Highest z/L BorderMostUnstabb HKC KM Lowest z/L BorderBorderZ0

c HKC KM Border 0.02 mSugBeetZ0

c HKC KM Border 0.07 mCorWDd HKC KM Border BorderHacte HKC KM Border Border

a Averages are taken of u*, Hv and U of the 7 EC-systems. From those, area averagez0 and z/L were determined.

b The quartiles and median for z/L for MostUnstab are −0.63, −0.15 and −0.01, andfor MostStable −0.05, 0.01 and 0.72 (without selection for heterogeneity).

c 0.02 m is the most frequently observed z0 at the border station in August 2009.0.07 m is the most different frequently observed z0, measured at the sugar beet fieldin August 2009.

d A correction of −6◦ , the deviation from the median of the 7 systems, was applied

A. van de Boer et al. / Agricultural

ertain minimum resolution is required to properly integrate theispersion function.

In a series of numerical experiments, we found that for ouronditions the footprint models need a spatial resolution roughlyqual to the measurement height for unstable atmospheric stratifi-ations. Using a coarser resolution will lead to a wrong descriptionf the sharp peak contribution close to the station. Furthermore,he integral of the discretized footprint function can differ signif-cantly from one (up to 10% for �x = 8zm) in case the function isnder-resolved.

.2.3. Construction of 2D footprint modelA combination of the longitudinal part of HKC00 and the cross-

ind part of KM01 was chosen for our reference footprint model.omparison results of Kljun et al. (2003) show a disadvantagementioned in Section 2) of using KM01. On the other hand, HKC00nitially did not include a crosswind distribution function; therefore

e use the one of KM01. The choice of the reference run RefHKC-M does not imply any appraisal at this point, but is owed to theequirement of one central combination from which only one ele-ent at a time is changed in the model runs, which is described

n more detail in Section 3.2. Detto et al. (2006) propose a cross-ind function for the HKC00 model, which is used in one of the

onfigurations of footprint model functions and input (given inection 3.2). Hereafter, HKC, KM and Det indicate our implementa-ions of respectively the alongwind part of HKC00, the alongwindr crosswind part of KM01, and the crosswind function describedy Detto et al. (2006).

. Research strategy

The core of our study is the evaluation of our implementa-ions of HKC00 and KM01 using a natural tracer experiment forensible heat flux. We use two different evaluation methods; a for-ard method and an inversion method (Section 3.1). We tested the

ensitivity (Section 3.2) to choices of model combinations (longi-udinal and crosswind distribution) and input parameterizationse.g. instantaneous estimates vs. long-term averages of roughnessength) using our forward method. In order to give the uncertainty

ith respect to the choice of model components and input param-ters we also evaluate the performance of an ensemble averageSection 3.3).

.1. Footprint model evaluation

We used HKC-KM, KM-KM, and HKC-Det (see Table 1) to pre-ict the measured flux at the border station, in order to evaluatehe models. This border station is the station with the most het-rogeneous surrounding, located in a barley field near the borderith a sugar beet field (a more detailed site description is given in

ection 4.2). We calculate H at the border station as:

border =I∑i=1

ciF̃i (1)

n which Fborder is the estimated flux at the border station, ci is theractional contribution of land use type i, I is the number of landse types, and F̃i is the ‘pure’ flux of land use type i.

These estimates are compared to the measured flux (question). The footprint of the border station may be rather homoge-

eous in case the flux is resulting from the field it was installed

n; barley regrowth. Therefore, we separately examined the 10% ofhe cases when the footprint contained the most sugar beet con-entration. We applied a forward (Section 3.1.1) and an inversion

to the wind direction measured at the border station.e The actual instead of the virtual sensible heat flux was taken for the footprint

calculations.

(Section 3.1.2) method to estimate the ‘pure’ fluxes F̃i of all land usetypes.

3.1.1. Forward methodTo estimate the ‘pure’ fluxes (F̃i) using this method, we first

applied RefHKC-KM to select those half-hours, where the lowerlevels of all three EC stations located in the middle of the fields hada flux contribution of more than 80% from their own target field:

F̃i = Fj|ci > 80% (2)

in which measured fluxes at station ‘j’ are indicated with Fj. It shouldbe noted that this filtering unavoidably depletes atmosphericallystable situations in the dataset, because these situations producelarger footprints.

To ensure that the model combinations are evaluated on thesame dataset, the 80% input criterion was always determinedaccording to the reference run ‘RefHKC-KM’ (see Table 2). The for-ward evaluation method was applied to each model combination,as well as to the other runs (described in Section 3.2).

3.1.2. Inversion methodThe fluxes measured at the stations are acknowledged to contain

contributions from different land use types. Hence, for the inversionmethod the ‘pure’ fluxes F̃i are defined implicitly:

Fj =I∑i=1

cijF̃i (3)

where the modeled contribution of each land use type to eachstation is given by matrix cij, and the measured fluxes at eachstation (except for the border station) are indicated with Fj (ques-tion 3). This system (Eq. (3)) was solved in a similar way assuggested by Neftel et al. (2008) for two ground-based stations,or by Ogunjemiyo (2003), Hutjes et al. (2010), and Metzger et al.(2012) for an arbitrary number of airborne measurement points.

Unlike in the Neftel et al. (2008) case, our system is overdeter-

mined, with six included stations and three considered land usetypes, requiring regression as the solution strategy. At the sametime, however, the relatively small degree of overdeterminednessas compared to the Hutjes et al. (2010) case does not allow for an

and Forest Meteorology 169 (2013) 1– 11 5

alflnpsa

3

fanoiifaurtTte

a(btuotico‘ta

eiwtflsiti(

3

naatmra

F

A. van de Boer et al. / Agricultural

pplication of robust statistics. Consequently, we used the ordinaryeast squares solution to determine the unknown ‘pure’ surfaceuxes. Different from the forward approach, this approach doesot require the 80% criterion for the input data. Hence, a largerart of the dataset can be used for the evaluation. However, inver-ion is more vulnerable to violations of the assumptions underlyingnalytical footprint models, as pointed out by Schmid (2006).

.2. Sensitivity analysis and specification of the ensemble

The model evaluation tests the dependence of the model per-ormance on the choice of model components: HKC or KM for thelongwind component, and KM or Det for the crosswind compo-ent. For our sensitivity analysis, we varied the input parametersne at a time (Table 2). Different values were used for L because ofts large variation between the different fields and because of itsmpact on footprint size. In the reference run we used L calculatedrom measurements at the border station. In the runs ‘MostStable’nd ‘MostUnstab’, we used the most stable (typically the leastnstable) and the most unstable (sometimes the least stable) z/Lespectively. Moreover, one model run is based on the determina-ion of z/L (and z0) from the area averaged u*, Hv and U (‘AreaAvg’).he effective area average of z/L (and of z0) was computed fromhe arithmetic averages of u*, Hv and U from all (7) EC-systems forvery half hour of data.

Since the roughness length is calculated for each intervals a function of observed thermal and aerodynamic parametersNeftel et al., 2008), unnecessary and unrealistic variability maye introduced. Because a change in the roughness length affectshe features of the footprint, other footprint models (e.g. HKC00)se the assumption that the roughness length has a fixed valuef for example 10% of the vegetation height. However, poten-ial real time-variability and direction dependence are not takennto account using this assumption. To quantify the effect of aonstant z0, we use two runs with two different constant mostlybserved values at the two most different stations (‘BorderZ0’ and

SugBeetZ0’, question 4). Furthermore, we use an area average z0 inhe run ‘AreaAvg’ (calculated from the arithmetic averages of u*, Hvnd U).

We also deal with the fact that the wind direction was notxactly the same for all the 7 EC-systems due to small differencesn alignment. We corrected the wind direction at the border station

ith −6◦, which is the mean deviation of the border station fromhe median of the 7 systems. The last run is related to the heatux used in the Obukhov length L (Appendix B). In principle, thishould be the virtual sensible heat flux. However, some past stud-es used the actual sensible heat flux, which might have affectedhe usual parameterization of universal functions. Therefore, wenclude a run ‘Hact’, in which we used the actual sensible heat fluxsee Table 2).

.3. Ensemble average

In the sensitivity analysis we perform a number of runs, but it isot a priori clear which permutation is correct. Therefore, we cre-ted an ensemble out of all members given in Table 2. An ensembleverage (and associated variances) was calculated from the con-ributions of the members. To see if an ensemble out of different

odel and input choices provides a better flux estimate than theeference run, the evaluation method mentioned in Section 3.1 waspplied to the ensemble average:

border = 1M

I∑i=1

M∑m=1

cimF̃i (4)

Fig. 3. Land use map of the study area with locations of the four EC stations inMerken (Germany), and a wind rose of daytime measurements with wind speedsbetween 0 (light gray) and 8 m s−1 (dark), both of August 2009.

where an average is taken over a number of M ensemble members(given in Table 2).

4. Data

4.1. Experiment

Eddy covariance data used in this study were collected withinthe Transregio 32 FLUXPAT campaign in summer 2009 nearMerken, Germany (6◦24′E, 50◦50′N, 114 m asl), see e.g. Graf et al.(2010). Three stations with EC sensors at 6.0 m and at 2.5 m wereinstalled in the middle of a field containing one of the three domi-nating crops: winter wheat, winter barley and sugar beet. Each ECsystem consisted of a fast response 3D sonic anemometer (CSAT3,Campbell Scientific, Logan, UT, USA), and an open-path infra-redgas analyzer (LI-7500, LI-COR). A border station was installed withsensors at 2.5 m height, in a barley field 50 m away from its borderwith a sugar beet field. As a result, this station has a more heteroge-neous footprint for certain wind directions. Fig. 3 gives an overviewof the locations of the EC-stations, and of the wind directions forthe daytime data. The study region was chosen, among other rea-sons, for the fact that spatial flux variability in the footprint of thestations is dominated by sharp contrasts between few land usetypes (Fig. 3), rather than gradual changes due to soil propertiesor other resources. At a radius of 700 m around the EC stations, theterrain is flat with a maximum slope of less than 0.7◦. No ditches andno plants higher than the mapped crops were found, and the soiltexture is uniform within this area (silt loam). Comparing cham-ber measurements between juvenile sugar beet and fully growingwheat in the spring of 2008 yielded differences in soil CO2 effluxbetween the fields twice as high as the 95% confidence interval ofspatial variability within each crop (Graf et al., 2011).

Data from all anemometers and gas analyzers were logged at20 Hz. The azimuth angle of the anemometers in the three fields was230◦, and the angle of the anemometer at 2.5 m close to the borderwas 135◦. Data from 4 to 27 August 2009 were used for this study.The barley field had already been harvested before August, howeveranother canopy from weeds and new barley seedlings, scatteredand with a maximum height of about 0.1 m, had developed inAugust. This field is therefore be called ‘barley regrowth’. The wheatfield was harvested at the 3rd of August and are called ‘wheat resid-ual’, and the sugar beet field was harvested after August. The height

of the sugar beet plants was 0.68 m throughout August. We useda displacement height of zero for the wheat residual and barleyregrowth, and a displacement height of d = 0.51 m for the sugarbeets.

6 and F

4

fltdn((owqlc

4

cbofcl7av1wAttbpftaf

5

5

thlobatfl>u

dda1wtfi

(e

A. van de Boer et al. / Agricultural

.2. Processing

The 20 Hz raw data were processed to yield 30-min averageuxes with the software ECpack (van Dijk et al., 2004). A planar fitilt correction (Wilczak et al., 2001) was performed with tilt anglesetermined over periods of 5–12 days, depending on the mainte-ance dates. Linear trends were removed, and the Webb-correctionWebb et al., 1980) was carried out. The Schotanus correctionSchotanus et al., 1983) was applied to correct for humidity effectsn the temperature. Raw data points flagged by the instrumentere eliminated, and 95% confidence intervals were estimated by

uantifying the sampling error for each scalar average and flux fol-owing van Dijk et al. (2004). Half-hours with sensible heat fluxonfidence intervals larger than 20 W m−2 were removed.

.3. Land use map

Depending on stability, either the coverage of a large area (stableonditions), or a high resolution near the stations (especially unsta-le conditions) may become critical (explained in Section 2.2.2). Inrder to satisfy both requirements, our land use map was mergedrom two different sources. The station locations, crop types andorner points of all fields surrounding the stations to a distance of ateast 300 m, were manually surveyed with a differential GPS (GPS-02/Propak V3,NovAtel, Calgary, Alberta, Canada), which assuresn accuracy in the cm range. The resulting vector dataset was con-erted to a 1 m resolution grid and amended to a distance of at least

km from the stations with a satellite based land use classificationith an effective resolution of 15 m. This classification was based onSTER and RapidEye data (see Waldhoff, 2010). Each grid point of

he combined dataset was assigned to one of the land use types win-er wheat, winter barley, sugar beet, maize, road, water, and other,ut only the first three crop types and the sum of weights from alloints assigned to any other land use type are important within theramework of this study. The combined map is shown together withhe location of the stations in Fig. 3. Domains of 2400 m × 2400 mround each EC-system were selected as square subsets of the mapor the actual calculation of the footprint.

. Results and discussion

.1. Meteorological conditions and eddy covariance fluxes

Fig. 4 shows the sensible and latent heat fluxes as observed overhe different fields during the experiment. Sensible heat fluxes wereighest at the harvested wheat field, with peaks of 300 W m−2, and

atent heat fluxes were highest at the sugar beet field, with peaksf 350 W m−2. From the flux differences between the wheat andarley field, we can derive that the young and new barley canopy islready contributing a significant amount of transpiration to evapo-ranspiration. Hence, the daytime Bowen ratios and sensible heatuxes can be put into the order wheat residual > barley regrowth

sugar beet, and three considerably different flux magnitudes aresed in the footprint model evaluation.

The four stations measured similar temperatures and windirections. The measurement area was characterized by relativelyry summer weather in August 2009, with a mean maximumir temperature of 26.9 ◦C, a mean minimum air temperature of4.8 ◦C, with only 5 days of rain, and with winds coming from theest mainly (see Figs. 3 and 4). This implies that the footprint of

he border station did not generally include the closest sugar beet

eld at the south east of the border station.

A period of fair weather can be found between day of the yearDOY) 216 and 219, when the winds mainly came from the south-ast during the day. The wind also came from the southeast at DOY

orest Meteorology 169 (2013) 1– 11

230–232 and 235–236, which implies that those days are character-ized by a heterogeneous footprint for the border station, containinga considerable sugar beet contribution. However, we can concludefrom Figs. 3 and 4 that the barley regrowth field acts as the mainsource in the footprint of the border station for most of the days.For those cases, the footprint of the border station can not be ide-ally heterogeneous, which confirms that the unpredictability of thewind direction is a disadvantage of natural tracer experiments.

Some light rain events occurred at DOY 214, 225, 233 and 238,and a heavy rain event occurred at DOY 220, which can be seen inFig. 4. Logically, latent heat fluxes increase after a rain event, whichdecreases the contrast between the wheat-residual and the sugarbeet fluxes significantly. Hence, using fluxes from periods after arain event (similar fluxes for all fields) for our evaluation mightlead to a trivial result for those data points.

5.2. Footprint model evaluation: forward method

Fig. 5 shows the evaluation of predicted fluxes of the two ana-lytical models (both combined with the KM crosswind dispersion)with measured sensible heat fluxes from the border station for thefull dataset. ‘Pure’ fluxes were estimated using the forward methoddescribed in Section 3.1.1. Most of the stable data do not meet the80% criterion and were therefore filtered out.

Using the full KM01 model (KM-KM) instead of HKC-KM, wefound a very slight degradation (from 0.95 to 0.94) of the slope.Also, R2 is slightly lower. The difference is however not significant(see Table 3 for regression results). We also see that it does notmatter much which of the two crosswind functions is chosen forHKC.

Next we applied regression analysis on the 10th percentile ofdata with the highest sugar beet contributions (explained in Sec-tion 3.1), which corresponds to a minimum contribution larger than16.2% in the reference run RefHKC-KM. We see that for KM-KM, thedata points for which the footprint model matters most show anunderestimation of the sensible heat flux. The slope of the regres-sion fit for only heterogeneous data, which is only shown in Table 3and not in the figure, increases for this sub-dataset to 0.96 ± 0.03for RefHKC-KM, but decreases to 0.87 ± 0.02 for KM-KM. The largeR2 values found for the heterogeneous sub-dataset might be causedby the fact that the selection for heterogeneity only includes datafrom similar days. Varying the minimum criterion for the sugarbeetcontribution and thus the size of the heterogeneous sub-dataset(not shown) yielded considerable differences in the overall perfor-mance (e.g. slopes and R2) of all runs, but the relative performanceof runs compared to each other remained conserved. This findingalso applies to most results presented in the following sections.

Since sensible heat fluxes were generally much lower at thesugar beet field compared to the barley-regrowth and the wheat-residual field, an underestimation of the border station sensibleheat flux indicates that a too large sugar beet contribution wasestimated by the footprint model. This is the case for all runs con-sidered so far, especially KM-KM. If we combine these results withthe land use map in Fig. 3, we can derive that this can be explainedby the extent of the footprint. The peak contribution is located fur-ther from the instrument according to KM01 compared to HKC00(Fig. 1). For winds from the south-east, KM-KM will therefore pre-dict larger contributions of sugar beet than the other runs. It shouldbe noted that the criteria of a considerable sugar beet contributionin the border station footprint, and of >80% target field contributionto each center station, are somewhat conflicting. Heterogeneous

footprints of the border station installed 50 m from the border, inthe barley field, should partly capture the sugar beet field, whereasthe footprints of the other stations should be small enough to bemostly located in one field. However, flux measurements from the

A. van de Boer et al. / Agricultural and Forest Meteorology 169 (2013) 1– 11 7

215 220 225 230 235

0100200300

Whe

at H LvE

0100200300

Sug

ar b

eet

0100200300

Bar

ley

0100200300

Bor

der

215 220 225 230 2350

90180270360

Bor

der

215 220 225 230 2350

102030

Time (DOY)

FZ

J

Hea

t flu

x (W

m−

2 )D

ir (ϒ

)P

rec

(mm

)

Fig. 4. From top to bottom: sensible (H) and latent (LvE) heat fluxes measured at the EC-station at 2.5 m in the wheat residual, sugar beet, barley regrowth, and at a stationclose to the border between the sugar beet and barley regrowth, respectively. The wind direction is measured at the border EC-station, and precipitation (shown cumulativeover 6 h) is measured at the Research Centre, close to Merken.

0 50 100 150 200

0

50

100

150

200

Observed sensible heat flux (Wm−2 )

Pre

dict

ed s

ensi

ble

heat

flux

(W

m−

2 )

KM−KM

0 50 100 150 200

0

50

100

150

200

Observed sensible heat flux (Wm−2 )

Pre

dict

ed s

ensi

ble

heat

flux

(W

m−

2 )

HKC−KM

Fi

TEf

ig. 5. Evaluation of sensible heat fluxes estimated using a combination of HKC00 and

ndicate heterogeneous data as identified by a minimum sugar beet contribution (see tex

able 3valuation of different model combinations, evaluated for different data selections (heteootprint).

Run Data Slope

RefHKC-KM All 0.95 ± 0.03

KM-KM All 0.94 ± 0.03

HKC-Det All 0.95 ± 0.03

RefHKC-KM Heterog. 0.96 ± 0.03

KM-KM Heterog. 0.87 ± 0.02

HKC-Det Heterog. 0.96 ± 0.03

KM01 and of KM01 only, with measurements from the border station. Black dotst). The 1:1 line is given dashed.

rog. indicates filtered data with a minimum sugar beet contribution to the border

Offset (W m−2) R2 N

3.1 ± 2.8 0.84 2672.5 ± 2.9 0.83 2673.1 ± 2.8 0.84 267

2.7 ± 1.6 0.98 272.6 ± 1.3 0.99 272.7 ± 1.6 0.98 27

8 A. van de Boer et al. / Agricultural and Forest Meteorology 169 (2013) 1– 11

Table 4Evaluation of different runs explained in Table 2, evaluated only for the heterogene-ity data selection.

Run Slope Offset (W m−2) R2 N

RefHKC-KM 0.96 ± 0.03 2.7 ± 1.6 0.98 27AreaAvg 0.96 ± 0.03 2.8 ± 1.6 0.98 27MostStable 0.94 ± 0.03 2.0 ± 1.6 0.98 27MostUnstab 0.97 ± 0.03 2.6 ± 1.5 0.98 27BorderZ0 0.97 ± 0.03 2.6 ± 1.6 0.98 27SugBeetZ0 0.99 ± 0.03 2.8 ± 1.7 0.98 27

bb

5

epbitndsr

saeaar(b(

iatufwrbhdspvs

5

diSdtbe

e

0 50 100 150 200 250

0

50

100

150

200

250

Observed sensible heat flux (Wm−2 )

Pre

dict

ed s

ensi

ble

heat

flux

(W

m−

2 )Fig. 6. Evaluation of sensible heat fluxes estimated using the average of the 10ensemble members given in Table 2, with measurements from the border station

CorWD 0.97 ± 0.03 2.8 ± 1.6 0.98 27Hact 0.95 ± 0.03 2.2 ± 1.5 0.98 27

order station which remain after this selection are equally spreadetween 0 and 200 W m−2.

.3. Footprint model sensitivity to input parameters

Regression results of the evaluation of different input param-ters (mentioned in Section 3.2) are given in Table 4. We onlyresent the sensitivity evaluations using the most heterogeneousorder footprints, since regression results without this heterogene-

ty selection are less different among the different runs. This is dueo the fact that for the full dataset, most points have a homoge-eous footprint which makes the evaluation insensitive to the exactetails of the footprint model. Even for the heterogeneity selection,lope differences are only significant between the most extremeesults.

Using the most stable stability parameter from the four EC-tations (measured over sugar beet) leads to larger footprints and

poorer fit (‘MostStable’), which is in agreement with the over-stimation of sugar beet contributions. We found that this resultlso applies for the model combination HKC-Det, but it does notpply for the model combination KM-KM (not shown). A fixedoughness length which corresponds with the sugar beet field‘SugBeetZ0’) instead of the area around the border station (mainlyarley-regrowth), results in a slope insignificantly different from 1see the regression slopes in Table 4).

The other changes in input parameterizations do not signif-cantly improve or decline the footprint model results; usingveraged stability and roughness parameters from the four sta-ions (‘AreaAvg’) does not change performance. Applying the mostnstable stability parameter does hardly change the model per-ormance. This is probably due to the fact that the border stationas among the most unstable stations. Furthermore, using a fixed

oughness length from the border station itself is not significantlyetter than calculating z0 after Neftel et al. (2008) for every halfour of data. Moreover, a small correction for the wind directionue to small alignment differences between the stations does notignificantly change the results using the more heterogeneous foot-rints (‘CorWD’). Using the actual sensible heat flux instead of theirtual sensible heat flux for L also does not significantly change thelope, and R2 (‘Hact’).

.4. Footprint model ensemble average

The evaluation of the ensemble average is shown for the fullataset in Fig. 6. Errorbars are given according to 95% confidence

ntervals; for the horizontal bars they are estimated by ECpack (seeection 4.2), and the vertical bars are calculated from the standardeviations within the ensemble. We see that errors in observa-ions and in predictions are both not negligible; predictions may

e expected to additionally be affected by the flux measurementrrors of the three stations in the field centers (not shown).

The ensemble average does not improve the outcome of thevaluation compared to the reference run RefHKC-KM, neither for

and without selection for heterogeneous data. Error bars show 95% confidence inter-vals from standard deviations within the ensemble (vertical), and from ECpack(horizontal). The 1:1 line is given dashed.

the full, nor for the reduced dataset (see Table 5). According toour dataset, the ensemble of models and input is therefore onlya helpful tool to indicate the uncertainty resulting from modelingdecisions, but not to reduce this uncertainty. This result is howeverdepending on the weight assigned to each ensemble member. In ourcase, all members account for 10% in the ensemble average, includ-ing the most deviating member (KM-KM). If the weights wouldhave been different among the members, the ensemble averagewould behave differently. An alternative distribution of the weightswould be: 25% for each of the three model variations discussed inSection 5.2, and 25% for the 7 runs with different input (mentionedin Section 5.3).

5.5. Footprint model evaluation: inversion method

Fig. 7 shows the evaluation of the HKC-KM combination usingthe inversion method. Unlike the forward method, near neutraland stable conditions remain, since no selection of ‘pure’ fluxes(measurements with homogeneous footprints) needs to be made.The regression line fits with R2 = 0.92, and its slope is very close toone when using homogeneous and heterogeneous data. The sameapplies when using exactly the same 267 data points as for thenon-heterogeneity filtered forward 80% criterion for reasons ofconsistency. When using the heterogeneous data (all data with asugar beet contribution larger than 16.2%, which is consistent withthe 10th percentile using the forward method), 364 points remainwith a slope slightly lower than one, but which is still larger thanfollows from the forward method. A slope of 1.04 ± 0.05 resultswhen using only the same heterogeneous data as for the referenceforward run.

Due to the interactions between filter criteria, dataset size andmodel performance on the dataset, it is not save to concludewhether the inversion method is better or worse for calculating

the fluxes from every land use type. The advantage of the inversionmethod is that more data remain, so that the evaluation of the foot-print model can be made with more confidence (note the smallererror in the slope for the inversion method on the full dataset, as

A. van de Boer et al. / Agricultural and Forest Meteorology 169 (2013) 1– 11 9

Table 5Evaluation of the ensemble average from all members explained in Table 2, evaluated for two different data selections (all data and only heterogeneous data).

Run Data Slope Offset (W m−2) R2 N

RefHKC-KM All 0.95 ± 0.03 3.1 ± 2.8 0.84 267EnsAvg All 0.95 ± 0.03 3.0 ± 2.8 0.84 267

RefHKC-KM Heterog. 0.96 ± 0.03 2.7 ± 1.6 0.98 27EnsAvg Heterog. 0.95 ± 0.03 2.6 ± 1.5 0.98 27

Table 6Evaluation of HKC-KM, where ‘pure’ fluxes are derived after the inversion method, for different data selections (all data and only heterogeneous data, with and without thenon-homogeneity filtering described in Eq. (2)).

Run Data Slope Offset (W m−2) R2 N

Ref forward All 0.95 ± 0.03 3.1 ± 2.8 0.84 267Ref invers. All 0.99 ± 0.03 2.0 ± 3.1 0.82 267Ref invers. All 1.01 ± 0.01 0.4 ± 0.7 0.92 867

Ref forward Heterog. 0.96 ± 0.03

Ref invers. Heterog. 1.04 ± 0.05

Ref invers. Heterog. 0.97 ± 0.01

−100 0 100 200 300−100

−50

0

50

100

150

200

250

300

Observed sensible heat flux (Wm−2 )

Pre

dict

ed s

ensi

ble

heat

flux

(W

m−

2 )

Fig. 7. Evaluation of HKC-KM, where ‘pure’ fluxes are derived with the inversionmd

cpteifl

6

mMaetf

w

a weaker dependence on stability than HKC00. Unfortunately we

ethod. Black dots indicate the heterogeneous sub-dataset). The 1:1 line is givenashed.

ompared to the forward method (Table 6). However, it has beenointed out that footprint models may be overcharged by effortso inversely determine fluxes (Schmid, 2002, 2006). The systematicrror introduced by the non-pure footprint is reduced, at the cost ofncreasing random errors (with respect to the originally measureduxes).

. Conclusion and outlook

This study presents a comparison of two-dimensional footprintodels based on HKC00 (Hsieh et al., 2000), KM01 (Kormann andeixner, 2001), and Detto et al. (2006). The main focus is the evalu-

tion of these models through a natural tracer (here sensible heat)xperiment over terrain with multiple land use types with con-

rasting sensible heat fluxes: Do the models predict the correct fluxor a station that is influenced by a combination of land use types?

Based on a forward approach and all available data points,e found a slight underestimation of the estimated sensible heat

2.7 ± 1.6 0.98 27−0.2 ± 2.7 0.95 27

0.1 ± 0.4 0.93 364

fluxes compared to measurements for all model combinations.Due to our set-up, this indicates an overestimation of the foot-print length. However, most data points did not contain significantcontributions from the most deviating land use type (sugar beet).Selecting only the most heterogeneous footprints of the border(evaluation) station resulted in a negligible overestimation by thereference model RefHKC-KM and a significant underestimation byKM-KM, which indicates an overestimation of the peak distance.The number of data points with such a heterogeneous footprintfor the border station was very limited. For the forward evaluationapproach and the encountered wind directions, a placement of theborder station closer than 50 m to the border would have increasedthis sample size.

Compared to the ‘forward’ method, a substantial part of the sys-tematic non-random deviations disappeared using the inversionmethod for HKC-KM. An additional advantage of the method isthat the footprints of the fluxes from the individual fields (usedas input) need not be homogeneous, so that more data remain.A disadvantage is that the footprint model has to be appliedtwice for this method. On the heterogeneity sub-dataset definedby a minimum sugar beet contribution to the border stationand simultaneous data availability for the forward approach, theinversion approach yielded a slight flux overestimation by HKC-KM. Inversion seems however a promising method for futurestudies.

In the application of footprint models over terrains with differ-ent land use types, there is some uncertainty what the ‘effective’values for stability and roughness should be. From our sensitiv-ity analysis, we can conclude that the performance of the HKC00model deteriorates if input parameters are chosen such that theyincrease the footprint length (e.g. a more stable z/L than observedat the station with the heterogeneous footprint). In contrast, themodel results improved after applying a fixed but too high rough-ness length. We did not find a significant impact of replacing Hv byH in the definition of L, of using area averaged values for z/L andz0, and of applying a small wind direction correction. Although wefound an impact of the choices for z/L and z0, it remains unclear ifthe choices made for the reference run were correct, or that theywere compensated by deficiencies in the footprint models them-selves. In general, the choice of the input parameters appears toaffect model results less than the choice of the model itself. Bothfootprint models depend on stability, but the model by KM01 has

do not have enough data to decompose the dataset into stabil-ity classes and evaluate the performance for each stability classseparately.

1 and F

trabrfiee

foHbedimcstmttar

A

gbittstwo

A

xmv

f

wdrOfld

f

waff

D

0 A. van de Boer et al. / Agricultural

For all evaluations, scatter might have been caused by a hypo-hetical imperfect homogeneity of the single fields and by theandom errors of the measured fluxes. For the forward approach,dditionally only relatively small footprints and mostly unsta-le situations remained after applying the 80% criterion that wasequired to confirm the purity of input fluxes measured by theeld center stations. Furthermore, the set-up of the natural tracerxperiment was not ideal concerning the wind direction during thexperiment.

Altogether, the HKC00 model combined with the crosswindunction from KM01 or Detto et al. (2006), form the best out ofur tested footprint modeling approaches in our site conditions.owever, to confirm the choice for the roughness length and sta-ility to be used in the determination of the footprint, natural tracerxperiments need to be repeated at more sites with different con-itions, including an even more balanced mix of land use types

n the footprint of at least one station. Our study is restricted toeasurements in the lower part of the surface layer, and to non-

omplex terrain conditions where scalar flux contrasts are the onlyource and type of major heterogeneity. Furthermore, the evalua-ion needs to be extended to other scalar fluxes, notably those of

oisture and CO2. Since these involve an additional instrument,ypically reducing the amount of high-quality data, it is importanto operate multi-station set-ups not only within campaigns, butlso on long-term sites, as has already been suggested for othereasons (Mahrt, 2010).

cknowledgements

This work was financed by the DFG (Deutsche Forschungs-emeinschaft), project GR2687/3-1 and SCHU 2350/2-1; “Linksetween local scale and catchment scale measurements and model-

ng of gas exchange processes over land surfaces”. We would like tohank Martin Lennefer and Bernhard Pospichal for additional assis-ance in the field experiment. Additional contributions to the fieldetup were made possible by the DFG collaborative research cen-er TR32 “Patterns in soil-plant-atmosphere systems”. Furthermoree would like to thank Miranda Braam for fruitful discussions, and

ur anonymous reviewers for their clear and helpful comments.

ppendix A. Footprint model equations

The crosswind integrated footprint function at upwind distance and height zm (zm = z − d, in which z is the height of the instru-ent above the surface, and d is the displacement height of 75% of

egetation height in our study) is in HKC00 described by:

HKC00(x) = c

x2e−c/x, c = RzPu |L|1−P

�2(A.1)

here � (=0.4) is the von Kármán constant, P and R are constantsepending on stability, zu is a length scale depending on z0 (theoughness length in meters, cf. Eq. (A.7)) and zm, and L is thebukhov length defined in Eq. (B.1). The crosswind integratedux footprint at the upwind distance x > 0 and at the height zm isescribed in KM01 by:

KM01(x) = 1�(�)

��

x1+� e−�/x (A.2)

here �(zm, z0, L) is the flux length scale, � the Gamma function,nd �(zm, L, z0) a constant (power law estimates are performedor these parameters, see KM01, p 211). The crosswind dispersion

unction depends on the crosswind distance y and is described by:

(x, y) = 1√2��y

e−y2/2�2

y (A.3)

orest Meteorology 169 (2013) 1– 11

in which �y is the crosswind width (m), described by Detto et al.(2006) as:

�yDetto = a1z0�v

u∗

(x

z0

)p1(A.4)

and by KM01 as:

�yKM ≈ �vx

Up(A.5)

where �v is the standard deviation of the crosswind speed in m s−1

(depending on wind speed and stability), Up is the effective plumevelocity in m s−1 (see Eq. (18) in Kormann and Meixner, 2001), u*is the friction velocity and a1 (=0.3) and p1 (=0.86) are empiricalparameters. The 2D footprint DF(x, y) is calculated as:

DF(x, y) = D(x, y)F(x) (A.6)

The roughness length z0 is estimated following Neftel et al. (2008)using:

z0 = zme�U/(u∗− (zm/L))

(A.7)

Where U is the observed wind speed in m s−1, and the stabilityparameter is described in Eq. (B.3).

Appendix B. Surface layer scaling

The Obukhov length L is defined by:

L = −cpTau3∗

�gHv(B.1)

In which is the air density in kg m−3, u* the friction velocityin m s−1, � the von Kàrmàn constant, Hv the virtual sensible heatflux in W m−2, cp the specific heat capacity at constant pressure inJ (kg K)−1 and Ta the air temperature in K. Logarithmic wind profilesfrom MOST are calculated using:

U = u∗�

(log

zmz0

+ (zmL

))(B.2)

in which is the integrated flux gradient relationship given inEq. (B.3) (which drops out for neutral conditions). The integratedflux-gradient relationship for momentum for unstable conditionsis given by:

(zmL

)= −2 log

1 +

2− log

1 + 2

2+ 2 atan

( − �

2

)(B.3)

where is given as:

=(

1 − 16zmL

)0.25(B.4)

For stable conditions, the integrated flux-gradient relationship formomentum can be described by:

(zmL

)= 5

zmL

(B.5)

References

Baldocchi, D., Falge, E., Gu, L., Olson, R., Hollinger, D., Running, S., Anthoni, P., Bern-hofer, C., Davis, K., Evans, R., Fuentes, J., Goldstein, A., Katul, G., Law, B., Lee, X.,Malhi, Y., Meyers, T., Munger, W., Oechel, W., Paw, K.T., Pilegaard, K., Schmid,H.P., Valentini, R., Verma, S., Vesala, T., Wilson, K., Wofsy, S., 2001. FLUXNET: anew tool to study the temporal and spatial variability of ecosystem-scale car-bon dioxide, water vapor, and energy flux densities. Bull. Am. Meteorol. Soc. 82,2415–2434.

Detto, M., Montaldo, N., Albertson, J.D., Mancini, M., Katul, G., 2006. Soil moisture andvegetation controls on evapotranspiration in a heterogeneous Mediterraneanecosystem on Sardinia, Italy. Water Resour. Res. 42, 1–16.

Foken, T., Leclerc, M., 2004. Methods and limitations in validation of footprint mod-els. Agric. For. Meteorol. 127, 223–234.

and F

G

G

G

G

H

H

H

H

H

K

K

K

K

M

M

A. van de Boer et al. / Agricultural

ash, J., 1986. A note on estimating the effect of a limited fetch on micrometeoro-logical evaporation measurements. Boundary Layer Meteorol. 35, 409–413.

öckede, M., Markkanen, T., Mauder, M., Arnold, K., Leps, J.P., Foken, T., 2005. Vali-dation of footprint models using natural tracer measurements from a fieldexperiment. Agric. For. Meteorol. 135, 314–325.

raf, A., Schüttemeyer, D., Geiß, H., Knaps, A., Möllmann-Coers, M., Schween,J.H., Kollet, S., Neininger, B., Herbst, M., Vereecken, H., 2010. Boundedness ofturbulent temperature probability distributions, and their relation to the ver-tical profile in the convective boundary layer. Boundary Layer Meteorol. 134,459–486.

raf, A., Prolingheuer, N., Schickling, A., Schmidt, M., Schneider, K., Schüttemeyer, D.,Herbst, M., Huisman, J.A., Weihermüller, L., Scharnagl, B., Steenpass, C., Harms,R., Vereecken, H., 2011. Temporal downscaling of soil carbon dioxide efflux mea-surements based on time-stable spatial patterns. Vadose Zone J. 10, 239–251.

aenel, H.D., Grünhage, L., 1999. Footprint analysis: a closed analytical solutionbased on height-dependent profiles of wind speed and eddy viscosity. BoundaryLayer Meteorol., 395–409.

orst, T.W., Weil, J.C., 1992. Footprint estimation for scalar flux measurements inthe atmospheric surface layer. Boundary Layer Meteorol., 279–296.

orst, T.W., 1999. The footprint for estimation of atmosphere-surface exchangefluxes by profile techniques. Boundary Layer Meteorol., 171–188.

sieh, C., Katul, G., Chi, T., 2000. An approximate analytical model for footprint esti-mation of scalar fluxes in thermally stratified atmospheric flows. Adv. WaterResour. 23, 765–772.

utjes, R., Vellinga, O., Gioli, B., Miglietta, F., 2010. Dis-aggregation of airborneflux measurements using footprint analysis. Agric. For. Meteorol. 150, 966–983.

ljun, N., Rotach, M.W., Schmid, H.P., 2002. A three-dimensional backwardLagrangian footprint model for a wide range of boundary-layer stratifications.Boundary Layer Meteorol. 103, 205–226.

ljun, N., Kormann, R., Rotach, M.W., Meixner, F.X., 2003. Comparison of the Lan-grangian footprint LPDM-B with an analytical footprint model. Boundary LayerMeteorol. 106, 349–355.

ljun, N., Calanca, P., Rotach, M.W., Schmid, H.P., 2004. A simple parameterisationfor flux footprint predictions. Boundary Layer Meteorol. 112, 503–523.

ormann, R., Meixner, F.X., 2001. An analytical footprint model for non-neutralstratification. Boundary Layer Meteorol., 207–224.

ahrt, L., 2010. Computing turbulent fluxes near the surface: needed improvements.Agric. For. Meteorol. 150, 501–509.

etzger, S., Junkermann, W., Mauder, M., Beyrich, F., Butterbach-Bahl, K., Schmid,H.P., Foken, T., 2012. Eddy Covariance flux measurements with a weight-shiftmicrolight aircraft. Atmos. Meas. Tech. Discus. 5, 2591–2643.

orest Meteorology 169 (2013) 1– 11 11

Neftel, A., Spirig, C., Ammann, C., 2008. Application and test of a simple tool foroperational footprint evaluations. Environ. Pollut. 152, 644–652.

Ogunjemiyo, S., 2003. Methods of estimating CO2, latent heat and sensible heatfluxes from estimates of land cover fractions in the flux footprint. Agric. For.Meteorol. 117, 125–144.

Pasquill, F., 1972. Some aspects of boundary layer description. Q. J. R. Meteorol. Soc.98, 469–494.

Reth, S., Göckede, M., Falge, E., 2005. CO2 efflux from agricultural soils in East-ern Germany – comparison of a closed chamber system with eddy covariancemeasurements. Theor. Appl. Climatol. 80, 105–120.

Schmid, H.P., 1994. Source areas for scalars and scalar fluxes. Boundary Layer Mete-orol. 67, 293–318.

Schmid, H.P., 2006. On the Do’s and Dont’s of footprint analysis in difficult conditions.In: Proceedings of the iLEAPS Specialist Workshop Flux Measurement in DifficultConditions, Boulder, CO, USA, January 2006.

Schmid, H.P., Oke, T.R., 1990. A model to estimate the source area contributing toturbulent exchange in the surface layer over patchy terrain. Q. J. R. Meteorol.Soc., 965–988.

Schmid, H.P., 2002. Footprint modeling for vegetation atmosphere exchange studies:a review and perspective. Agric. For. Meteorol. 113, 159–183.

Schotanus, P., Nieuwstadt, F., de Bruin, H., 1983. Temperature measurement witha sonic anemometer and its application to heat and moisture fluxes. BoundaryLayer Meteorol. 26, 81–93.

Schuepp, P., Leclerc, M., Macpherson, J., Desjardins, R., 1990. Footprint prediction ofscalar fluxes from analytical solutions of the diffusion equation. Boundary LayerMeteorol. 50, 355–373.

Stannard, D.I., 1997. A theoretically based determination of Bowen-ratio fetchrequirements. Boundary Layer Meteorol., 375–406.

Steinfeld, G., Raasch, S., Markkanen, T., 2008. Footprints in homogeneously andheterogeneously driven boundary layers derived from a Lagrangian stochasticparticle model embedded into large-eddy simulation. Boundary Layer Meteorol.129, 225–248.

van Dijk, A., Moene, A.F., de Bruin, H.A.R., 2004. The principles of surface fluxphysics: theory, practice and description of the ECPACK library. Internal ReportMeteorology and Air Quality Group, Wageningen University, Wageningen, TheNetherlands, 99 pp.

Waldhoff, G., 2010. Land use classification of 2009 for the Rur catchment.

http://dx.doi.org/10.1594/GFZ.TR32.1

Webb, E., Pearman, G., Leuning, R., 1980. Correction of flux measurements for densityeffects due to heat and water vapour transfer. Q. J. R. Meteorol. Soc. 106, 85–100.

Wilczak, J.M., Oncley, S.P., Stage, S.A., 2001. Sonic anemometer tilt correction algo-rithms. Boundary Layer Meteorol., 127–150.