Biogeosciences, 16, 1111–1132, 2019https://doi.org/10.5194/bg-16-1111-2019© Author(s) 2019. This work is distributed underthe Creative Commons Attribution 4.0 License.

Source partitioning of H2O and CO2 fluxes based on high-frequencyeddy covariance data: a comparison between study sitesAnne Klosterhalfen1, Alexander Graf1, Nicolas Brüggemann1, Clemens Drüe2, Odilia Esser1,María P. González-Dugo3, Günther Heinemann2, Cor M. J. Jacobs4, Matthias Mauder5, Arnold F. Moene6,Patrizia Ney1, Thomas Pütz1, Corinna Rebmann7, Mario Ramos Rodríguez3, Todd M. Scanlon8, Marius Schmidt1,Rainer Steinbrecher5, Christoph K. Thomas9, Veronika Valler1, Matthias J. Zeeman5, and Harry Vereecken1

1Agrosphere Institute, IBG-3, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany2Department of Environmental Meteorology, University of Trier, 54296 Trier, Germany3IFAPA – Consejería de Agricultura, Pesca y Desarrollo Rural, Centro Alameda del Obispo, 14080 Córdoba, Spain4Wageningen Environmental Research, Wageningen University and Research, 6708 PB Wageningen, the Netherlands5Institute of Meteorology and Climate Research, IMK-IFU, Karlsruhe Institute of Technology (KIT),82467 Garmisch-Partenkirchen, Germany6Meteorology and Air Quality Group, Wageningen University and Research, 6708 PB Wageningen, the Netherlands7Department Computational Hydrosystems, Helmholtz Centre for Environmental Research (UFZ),04318 Leipzig, Germany8Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22904, USA9Micrometeorology Group, University of Bayreuth, 95447 Bayreuth, Germany

Correspondence: Anne Klosterhalfen (a.klosterhalfen@fz-juelich.de)

Received: 24 October 2018 – Discussion started: 5 November 2018Revised: 11 February 2019 – Accepted: 22 February 2019 – Published: 19 March 2019

Abstract. For an assessment of the roles of soil and vegeta-tion in the climate system, a further understanding of the fluxcomponents of H2O and CO2 (e.g., transpiration, soil res-piration) and their interaction with physical conditions andphysiological functioning of plants and ecosystems is neces-sary. To obtain magnitudes of these flux components, we ap-plied source partitioning approaches after Scanlon and Kus-tas (2010; SK10) and after Thomas et al. (2008; TH08) tohigh-frequency eddy covariance measurements of 12 studysites covering different ecosystems (croplands, grasslands,and forests) in different climatic regions. Both partitioningmethods are based on higher-order statistics of the H2O andCO2 fluctuations, but proceed differently to estimate transpi-ration, evaporation, net primary production, and soil respira-tion. We compared and evaluated the partitioning results ob-tained with SK10 and TH08, including slight modificationsof both approaches. Further, we analyzed the interrelationsamong the performance of the partitioning methods, turbu-lence characteristics, and site characteristics (such as plantcover type, canopy height, canopy density, and measurement

height). We were able to identify characteristics of a data setthat are prerequisites for adequate performance of the parti-tioning methods.

SK10 had the tendency to overestimate and TH08 to un-derestimate soil flux components. For both methods, the par-titioning of CO2 fluxes was less robust than for H2O fluxes.Results derived with SK10 showed relatively large depen-dencies on estimated water use efficiency (WUE) at the leaflevel, which is a required input. Measurements of outgoinglongwave radiation used for the estimation of foliage tem-perature (used in WUE) could slightly increase the qualityof the partitioning results. A modification of the TH08 ap-proach, by applying a cluster analysis for the conditionalsampling of respiration–evaporation events, performed sat-isfactorily, but did not result in significant advantages com-pared to the original method versions developed by Thomaset al. (2008). The performance of each partitioning approachwas dependent on meteorological conditions, plant devel-opment, canopy height, canopy density, and measurementheight. Foremost, the performance of SK10 correlated nega-

Published by Copernicus Publications on behalf of the European Geosciences Union.

1112 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

tively with the ratio between measurement height and canopyheight. The performance of TH08 was more dependent oncanopy height and leaf area index. In general, all site char-acteristics that increase dissimilarities between scalars ap-peared to enhance partitioning performance for SK10 andTH08.

1 Introduction

The eddy covariance (EC) method is a micrometeorologi-cal technique commonly used to measure the energy, wa-ter vapor, and carbon dioxide exchange between biosphereand atmosphere across a large range of scales in time andspace (Baldocchi et al., 2001; Reichstein et al., 2012). Themeasurements help us to understand the temporal and spatialvariations of these fluxes at the land–atmosphere interface.However, the EC method quantifies only net fluxes of watervapor, i.e., evapotranspiration (ET), and the net ecosystemexchange of CO2 (NEE). Thus, for a better assessment of therole of soil and vegetation in the climate system, a furtherunderstanding of the flux components of H2O and CO2 andtheir interaction with physical conditions and physiologicalfunctioning of plants and ecosystems is necessary (Baldocchiet al., 2001). To obtain magnitudes of transpiration, evapora-tion, photosynthesis, and respiration by soil and vegetation,certain measurements with additional instrumentation inde-pendent of the EC technique can be conducted. Alternativelyor additionally, so-called source partitioning approaches canbe applied to the net fluxes obtained with the EC method.For instance, with the notion that during night no CO2 is as-similated by plants (and hence observed NEE equals respi-ration), respiratory fluxes are often estimated based on semi-empirical models describing the relationship between a phys-ical driver (e.g., temperature) and respiration (Lloyd and Tay-lor, 1994; Reichstein et al., 2005, 2012). To estimate soilsurface fluxes of both H2O and CO2 directly from high-frequency EC data without assumptions on such drivers, twodistinct partitioning approaches were developed by Scanlonand coauthors (Scanlon and Sahu, 2008; Scanlon and Kus-tas, 2010) and Thomas et al. (2008). Both approaches relyon the assumption that the presence of multiple sources andsinks in and below the canopy will lead to decorrelation ofthe high-frequency scalar concentrations measured by the ECmethod above the canopy. This decorrelation contains infor-mation about the strength of these sinks and sources, whichcan be quantified by applying the flux–variance similaritytheory or conditional sampling strategies. The scalar–scalarcorrelations of H2O and CO2 are, however, not only influ-enced by the sink–source distribution, but also by height (at-mospheric surface layer, roughness sublayer), surface hetero-geneity (Williams et al., 2007), canopy density, and coherentstructures (Edburg et al., 2012; Huang et al., 2013).

The source partitioning approach after Scanlon andSahu (2008) and Scanlon and Kustas (2010) has already beenapplied to data acquired above a cornfield (eastern USA;Scanlon and Kustas, 2012), compared to an isotopic H2Oflux partitioning method (Good et al., 2014) and to the NoahLand Surface Model (Wang et al., 2016) for grasslands, andevaluated for a forest site on a decadal timescale (Sulmanet al., 2016). Zeeman et al. (2013) further investigated thepartitioning approach after Thomas et al. (2008) in associa-tion with coherent structures. To better assess these two ap-proaches and their theoretical background, an intercompari-son at a variety of study sites is necessary (Anderson et al.,2018).

The objective of this study is to compare and evalu-ate source partitioning approaches after Scanlon and Kus-tas (2010) and after Thomas et al. (2008) by applying themto high-frequency scalar measurements of various study sitesin different ecosystems. In addition to testing slight mod-ifications of both partitioning methods, the conditions andcharacteristics of study sites are identified under which themethods perform best. Based on the findings of the above-mentioned authors and a large eddy simulation (LES) study(Klosterhalfen et al., 2019), we hypothesize that the meth-ods’ performance is dependent on the canopy height (hc),which should represent the vertical separation of sinks andsources of H2O and CO2 between canopy top and soil sur-face, on the canopy density (leaf area index, LAI, or ex-pressed as the ratio LAI h−1

c ), and on the ratio between mea-surement height (z) and hc. All these factors affect the de-gree of mixing of the scalars detected by the EC sensors.With a high and sparse canopy and a low z h−1

c , we hypoth-esize a larger dissimilarity between scalar fluctuations and amore precise partitioning result for both source partitioningapproaches. To summarize, goals of this study are the follow-ing.

– The comparison and evaluation of the partitioning re-sults obtained with the approaches after Scanlon andKustas (2010) and after Thomas et al. (2008) for var-ious ecosystems and testing slight modifications of theapproaches.

– An analysis of the two approaches with respect to theirdependence on their underlying assumptions.

– The description of the interrelations among the perfor-mance of the partitioning methods, turbulence charac-teristics, and site characteristics (such as canopy type,hc, z h−1

c , LAI, and LAI h−1c ).

– The identification of the characteristics of a data set (i.e.,of study site and period properties) that lead to a satis-factory performance of the partitioning methods if suchcharacteristics exist.

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1113

2 Material and methods

2.1 Source partitioning after Scanlon andKustas (2010) – SK10

To estimate the contributions of transpiration (T ), evapora-tion (E), photosynthesis as net primary production (NPP),and soil respiration (Rsoil, autotrophic and heterotrophicsources) to the measured net fluxes, Scanlon and Sahu (2008)and Scanlon and Kustas (2010) proposed a source partition-ing method using high-frequency time series from a typicalEC station. This method (SK10 in the following) is basedon the spatial separation and relative strength of sinks andsources of water vapor and CO2 below the canopy (sourceof both water vapor and CO2), in the canopy (source of wa-ter vapor and sink of CO2 during daylight), and in the at-mosphere. Assuming that air from those sinks and sourcesis not yet perfectly mixed before reaching the EC sensors,partitioning is estimated based on the separate application ofthe flux–variance similarity theory to the stomatal and non-stomatal components of the scalars, as well as an estimationof canopy water use efficiency (WUE). The slope of the rela-tionship between water vapor fluctuations (q ′) and CO2 fluc-tuations (c′) originating from stomatal and non-stomatal pro-cesses usually differs from the WUE at the leaf level and thecorrelation between the two scalars (ρq ′c′ ) usually deviatesfrom −1 during daytime. This deviation of the slope of theq ′ versus c′ relationship from WUE at leaf level and the re-duction of correlation are used to estimate the composition ofthe measured fluxes (Scanlon and Kustas, 2010; Scanlon andSahu, 2008). For a detailed analytical description of SK10see Scanlon and Albertson (2001), Scanlon and Sahu (2008),Scanlon and Kustas (2010, 2012), and Palatella et al. (2014).Furthermore, Skaggs et al. (2018) implemented SK10 in theopen-source Python 3 module FLUXPART. In the presentstudy, SK10 was applied to high-frequency EC data and theflux components were estimated using the implementation ofSK10 as described by Klosterhalfen et al. (2019).

As mentioned before, the WUE at the leaf level has tobe estimated for the application of SK10. WUE at the leaflevel describes the relation between the amount of CO2 up-take through stomata (photosynthesis) and the correspondingamount of H2O loss (T ). One way to derive WUE (withoutadditional measurements at leaf level) is to relate the differ-ence in mean CO2 concentration between air outside and in-side the leaf to the difference in mean water vapor concentra-tion between air outside and inside the leaf, including a fac-tor that accounts for the difference in diffusion rate betweenH2O and CO2 through the stomatal aperture (Campbell andNorman, 1998; Scanlon and Sahu, 2008). The mean H2O andCO2 concentrations just outside the leaf can be inferred fromEC measurements by considering logarithmic mean concen-tration profiles implementing the Monin–Obukhov similar-ity theory (MOST; Scanlon and Kustas, 2010, 2012; Scan-lon and Sahu, 2008). For the internal CO2 concentration,

a constant value of 270 or 130 ppm was presumed, typicalfor C3 or C4 plants, respectively (Campbell and Norman,1998; Špunda et al., 2005; Williams et al., 1996; Xue etal., 2004). Values for the internal water vapor concentrationwere estimated based on 100 % relative humidity at foliagetemperature. Measurements of foliage temperature were notavailable at the study sites, so for the source partitioning fo-liage temperature was set equal to measured air temperature(WUEmeanT; Scanlon and Sahu, 2008). Additionally, to in-vestigate the sensitivity of WUE, foliage temperature wasalso derived by means of measured outgoing longwave radi-ation (WUEOLR; with a surface emissivity of 0.98) or calcu-lated similar to the external concentrations by considering amean profile based on MOST (WUEMOST). Thus, three dif-ferent approaches of SK10 with differing inputs for WUEwere applied to all study sites.

2.2 Source partitioning after Thomas et al. (2008) –TH08

Thomas et al. (2008) presented a new method (TH08 in thefollowing) to estimate the daytime sub-canopy respiration offorests directly from EC raw data by conditional sampling. Inan analogous way, evaporation can be quantified by exchang-ing c′ with q ′ in the equations given by Thomas et al. (2008;Eqs. 1–11, pp. 1212–1215). The method assumes that occa-sionally air parcels moving upward (vertical wind fluctua-tions w′ > 0) carry unaltered H2O/CO2 concentration com-binations of the sub-canopy. Looking at the fluctuations q ′

and c′, both normalized with the corresponding standard de-viation, respiration–evaporation signals should occur withinthe part of the joint probability distribution where w′, q ′, andc′ are positive, i.e., in the first quadrant in the q ′–c′ plane(where q ′ > 0 and c′ > 0). Additionally, Thomas et al. (2008)introduced a hyperbolic threshold criterion within quadrant 1in order to only sample all data points above this hyper-bola. Thomas et al. (2008) found realistic respiration esti-mates with a hyperbolic threshold of 0.25, which was alsoapplied here. Subsequently, daytime evaporation and respi-ration can be determined from the conditionally sampled w′,q ′, and c′ time series within quadrant 1 (Q1) or using thehyperbola threshold criterion (H). For the determination ofthe turbulent H2O and CO2 fluxes either the covariance be-tween w′ and the corresponding scalar (CV) can be used orthe relaxed eddy accumulation (REA) technique (Busingerand Oncley, 1990) using the coefficient β (as described inEq. 4, p. 1213 and statements on p. 1215 in Thomas etal., 2008). Hence, Thomas et al. (2008) applied four differ-ent approaches to quantify respiration–evaporation events bycombining the two conditional sampling criteria (Q1 or H)and the two calculation strategies (CV or REA technique).

For some averaging periods in our data, a potentialrespiration–evaporation “cloud” was evident but did not oc-cur (completely) within quadrant 1 (Fig. 1). As a modifica-tion of the conditional sampling strategy and a more tolerant

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1114 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

detection of respiration–evaporation events, a distribution-based cluster analysis was conducted (fifth approach, GMM).With the Gaussian mixture model (Canty, 2010) using theexpectation–maximization algorithm, two clusters were de-fined for each averaging period: the respiration–evaporationcloud and all further points associated with T and photosyn-thesis independent of the sign of w′. Soil surface fluxes werecalculated by CV from data in the respiration–evaporationcloud, for which the deviations from the averages of all sam-pled cluster data points (instead of all data points) were usedfor q ′ and c′ (w′ kept unchanged). Because the sampledrespiration–evaporation cloud by GMM would not always liewithin quadrant 1 (often in quadrant 1 and 4 or in 1 and 2),and q ′ and/or c′ of the defined cloud could correlate nega-tively with w′, the corresponding surface flux would often benegative (Fig. 1). If this was the case for H2O and/or CO2soil fluxes, the corresponding flux was recalculated consider-ing the deviations from the averages of all data points for w′,q ′, and c′ and only including data points within quadrant 1of the original q ′–c′ plane and with w′ > 0. This recalculatedflux represented only a minimal fraction of the correspond-ing flux component in the considered averaging period. Also,as a result of this procedure the number of data points coulddiffer between H2O and CO2 for TH08 CV GMM dependingon the calculation step used.

2.3 Study sites and data processing

For the application and evaluation of the source partitioningmethods, various study sites in a number of countries withdiffering cover types, canopy densities (represented by LAI),and measurement heights were chosen (Table 1). Almost allstudy sites are part of the FLUXNET network (Baldocchi etal., 2001). Detailed site and measurement descriptions canbe found in the listed references. Besides coniferous and de-ciduous forests with closed canopy cover, grasslands, andcroplands, some sites represent special canopy types: in For-est_SC (for site abbreviations see Table 1) EC measurementshave been conducted above a Mediterranean oak savanna(dehesa; Andreu et al., 2018); in Wüstebach an area of about9 ha was deforested in 2013, so measurements were obtainedabove the still-present spruce forest (Forest_WU) and the de-forested area (Grass_WU) (Graf et al., 2014; Wiekenkamp etal., 2016), where grass, shrubs, and young deciduous treeshave been regrowing swiftly; and in Forest_LA a conifer-ous forest has been regrowing gradually after a non-clearedwindthrow in 2007 (Matiu et al., 2017). These three studysites represent the most heterogeneous land cover types inthis study.

For each study site, measurements from days with a highlyproductive state of the vegetation and fair-weather conditionswere selected to exclude factors interfering with the perfor-mance of the partitioning method. Time periods with pre-cipitation events were excluded. Furthermore, the quality as-sessment scheme after Mauder et al. (2013) was applied to

each data set and source partitioning was only conducted fortime periods with the highest or intermediate quality flag lev-els assigned by this scheme. We only considered partitioningresults from daytime data because both methods require thepresence of photosynthesis. Here, daytime was determinedby calculating sunrise and sunset times by means of localtime. Additionally, the TH08 method was only applied totime periods with a negative ρq ′c′ , and if less than 1 % ofthe total data points in one 30 min time period were sampledas the respiration–evaporation “event”, the partitioning resultwas disregarded.

The high-frequency H2O and CO2 time series of all studysites were preprocessed and prepared for the application ofthe source partitioning approaches as described by Kloster-halfen et al. (2019). For each study site, physically impossi-ble values and spikes were excluded in the high-frequencyEC data on vertical wind, total H2O, and CO2 concentra-tions. The time delay was corrected, missing raw data withina 30 min period were gap-filled by linear interpolation, anda planar-fit rotation was conducted, whereby the rotationmatrix was calculated for only a maximum time period of2 weeks. Further, the EC data were corrected for density fluc-tuations after Detto and Katul (2007). Then, the source par-titioning approaches were applied to half-hourly time seriesof these preprocessed high-frequency data; partitioning frac-tions (E /ET or Rsoil /NEE) were calculated and applied tothe post-processed half-hourly EC data.

2.4 Evaluation of source partitioning results

The evaluation of the source partitioning performance wasconducted in multiple ways for the various study sites de-pending on data availability. At some study sites, Rsoil wasmeasured additionally with closed-chamber measurementsindependently of the EC measurements. In Grass_RO andthe cropland in Selhausen (Wheat_SE, Barley_SE, Inter-crop_SE, SugarBeet_SE), continuous measurements of mul-tiple long-term chambers were available for the consideredtime periods (half-hourly at Selhausen and hourly interpo-lated to half-hourly at Grass_RO). In Maize_DI, Forest_WU,and Grass_WU, Rsoil was measured with survey chambersat several measurement points on one day during the con-sidered time periods, so spatial and temporal averages forthe hours in question could be calculated. For all studysites, soil evaporation (Esoil) was estimated as a fractionof measured ET based on Beer’s law depending on LAI(Esoil =ET exp(−0.6 LAI)); Campbell and Norman, 1998;Denmead et al., 1996). Thus, the root mean square error(RMSE) and the bias could be calculated between the par-titioning results for E or Rsoil and the estimated Esoil orchamber measurements. RMSE was sensitive to bias and out-liers, and the distribution of errors was skewed. The pos-itive outliers and errors (overestimations) were larger thannegative errors (underestimations). An overestimation of theflux component magnitude may result in a larger RMSE than

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1115

Tabl

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tion

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opy

type

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opy

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ence

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tude

heig

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alan

nual

win

dhe

ight

Tem

pP

sum

dire

ctio

n(m

a.s.

l.)(m

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2 )(m

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st_L

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oobo

s52

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625

FR(p

ine)

8–14

Jul2

003

1.9

18.6

24.0

10.0

966

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WD

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anet

al.(

2002

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ethe

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ds5.

7436

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etal

.(20

11)

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bach

(for

est)

50.5

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–24

May

2015

3.9

25.0

38.0

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1116 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

Figure 1. Exemplary scatterplots of w′, q ′, and c′ from the Wüstebach study site (forest), 18 May 2015, 12:00–12:30 LT (local time),including results of the cluster analysis by Gaussian mixture model (orange data points) for the conditional sampling. Also shown arethe hyperbolic threshold (H = 0.25, green line) after Thomas et al. (2008), the averages of q and c only considering data points of therespiration–evaporation “cloud” (red lines), and reduced major axis regression lines after Webster (1997) for all data points (blue dashedlines) and only cloud data points (red dashed lines). In this example, calculating the covariance for w and c considering the CO2 average ofthe cloud yielded a negative soil flux (negative correlation). Thus, only cloud data points within quadrant 1 in the original q ′–c′ plane wereconsidered for flux calculation using averages of all data points.

an underestimation. Therefore, we also calculated a versionof the RMSE based on log-transformed data (RMSEln; datatransformed with ln(x+1)) before computing differences be-tween estimated and reference E or Rsoil. Furthermore, onehas to keep in mind that the measurements of Rsoil and LAIcan also contain errors and that Esoil is only a rough modelapproximation that can only give an order of magnitude toexpect.

In addition, partitioned CO2 fluxes were evaluated in ref-erence to results from the established partitioning approachafter Reichstein et al. (2005) if available, even though thisapproach targets other flux components (total ecosystem res-piration, TER, and gross primary production, GPP). For For-est_MMP and Forest_WA, results from this partitioning ap-proach were not available, and thus we chose for these sitesmaximal margins for GPP and TER based on partitioning re-sults from previous years and experience. For all sites, theestimated NPP and Rsoil for every time step were classifiedas reasonable if their magnitudes were smaller than the de-termined GPP or TER, respectively. Since all data sets werefrom the main growing season and for weather conditionsfavorable to high respiration, we assumed that Rsoil shouldadditionally be larger than 1 µmol m−2 s−1. In the follow-ing, NPP and Rsoil estimates meeting these criteria (“hitsin range”) will be counted as HiR GPP (magnitude of NPPsmaller than magnitude of GPP) and HiR TER (Rsoil smallerthan TER and larger than 1 µmol m−2 s−1). We calculated thepercent fraction of HiR GPP and HiR TER in relation to thecount of time steps with valid partitioning solutions. Withinthis evaluation step two source partitioning approaches (ap-proach after Reichstein et al., 2005, versus SK10 or TH08)were examined and compared, including their different as-sumptions and uncertainties, and the results have to be han-dled with care. An evaluation of the estimated flux magni-

tudes was also possible for some study sites by means ofprior publications.

2.5 Analysis of source partitioning approaches

To compare the strengths and limitations of SK10 and TH08and to gain better insight into their functionality and depen-dencies on turbulence and site characteristics, a correlationanalysis was conducted between HiR GPP or HiR TER andthe variables z, hc, z h−1

c , LAI, or LAI h−1c . Here, we have

chosen HiR GPP and HiR TER as the criteria for partitioningperformance because these could be calculated for all consid-ered study sites, unlike the error metrics (RMSE, bias, etc.)regarding Rsoil. Different subsets of sites were considered forthe calculation of the correlations: all study sites, only forestsites, or only cropland and grassland sites.

SK10 was already thoroughly analyzed by means of syn-thetic high-frequency data derived by LES (Klosterhalfen etal., 2019). To obtain a better understanding of the strengthsand limitations of TH08, we constructed a conceptual modelto generate simple, synthetic data sets of w′, q ′, and c′ (withsample sizes of N = 100) with different degrees of mixingbetween scalar sinks and sources from the soil, canopy, andboundary layer (Fig. 7a). We considered no mixing, com-plete mixing, and partial mixing between scalars originat-ing from the soil and canopy (with positive w′). For allthree sets, mixing with scalars originating from the boundarylayer (with negative w′) was excluded. Averages of fluctua-tions were all specified as zero, and each scalar sink–sourcestrength was determined such that the net H2O flux equals1 mmol m−2 s−1 and the net CO2 flux −1 µmol m−2 s−1. Toeach generated data point of w′, q ′, and c′ a random number,sampled from a standard normal distribution and rescaled toa standard deviation of 5 % of the magnitude of the variable,was added to simulate additional sources of variance not re-

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1117

lated to the degree of mixing. TH08 was applied to these syn-thetic data sets and could be validated with the true knownpartitioning fractions.

3 Results and discussion

For each study site, the number of half-hourly time stepsduring daylight per considered time period is shown in Ta-ble A1 in the Appendix. Also, the fraction of daylight timesteps of high-quality (HQ) data that were used in the appli-cation of SK10 and TH08 are shown; for SK10 only a goodor intermediate quality flag (after Mauder et al., 2013) andno precipitation were required, and for TH08 additionally anegative ρq ′c′ . Furthermore, the fraction of these HQ timesteps, for which partitioning solutions were found, is shownfor each method version. Thus, from the original data, only apart remained for the partitioning, and for only a part of theremaining data could a partitioning result be obtained.

3.1 Evaluation of source partitioning results

3.1.1 Flux components magnitudes

In the following, figures are shown for some selected sites,which were deemed most representative for all study sites,and/or for some selected method versions of SK10 andTH08, which usually exhibited the best partitioning perfor-mance. In Fig. 2 the source partitioning results for H2O andCO2 fluxes for Forest_LO are shown in half-hourly timesteps as an example. The partitioning results for all sites andall method versions are shown in the Supplement, includ-ing Esoil estimations based on Beer’s law, chamber measure-ments of Rsoil, and/or partitioning results after Reichstein etal. (2005), depending on data availability. Figures 3 and 4show the mean diurnal variation in H2O and CO2 fluxes andtheir components. Figure 3 shows data from one site (For-est_WA) and all method versions, whereas Fig. 4 shows re-sults for all study sites and just two method versions: SK10with WUEOLR and TH08 with REA H. In Fig. 5 the totalaverages of the flux components over the available time pe-riods are shown. Figure 5a compares all method versions fora single site (Forest_MMP), whereas Fig. 5b and c compareall sites for two method versions (SK10 with WUEOLR andTH08 with REA H). For the calculation of these mean di-urnal variations as well as the total averages, large spikes inthe estimated flux components (deviation from the mean bymore than 10 times the standard deviation) were excluded.Figure 6 shows the error quantities, RMSEln, and bias rel-ative to Rsoil chamber measurements, HiR GPP, HiR TER,and Esoil estimation for each site and method version. In allfigures, time stamps are in local time.

In general, the partitioned CO2 fluxes showed a highervariability and more spikes than the partitioned H2O fluxesfor all sites (e.g., at Forest_HH; Fig. S2 in Supplement). Fur-thermore, SK10 and TH08 gave differing results for each

study site and performed disparately between method ver-sions. In Figs. 2–5, it is apparent that TH08 mostly resultedin lower magnitudes of the flux components originating fromthe soil surface or sub-canopy than SK10. The source parti-tioning results for Forest_LO (Figs. 2, 4, 5) were an excep-tion to this rule. For this study site, the partitioning fractionsof SK10 and TH08 were very similar and thus suggest a lowuncertainty of the results. For the other study sites, larger dis-crepancies were observed between SK10 and TH08. Further-more, the partitioning fractions E /ET and NPP /NEE var-ied much less between sites for TH08 than for SK10 (Fig. 5).Good et al. (2015) determined a global estimate for T /ETof 0.65 and Schlesinger and Jasechko (2014) an estimate of0.61. Li et al. (2019) deduced mean annual partitioning frac-tions of 0.75, 0.62, and 0.56 for evergreen coniferous forests,croplands, and grasslands, respectively. Our derived parti-tioning fractions had approximately the same magnitudes orassigned a larger fraction to transpiration, most likely due tothe seasons chosen. We could not observe a clear differencein partitioning fractions between ecosystem types as in Li etal. (2019).

For a number of our sites, information on componentfluxes is available from the literature. For Forest_LO in 1997,Dolman et al. (2002) reported a peak respiration measure-ment of 12 µmol m−2 s−1, and Falge et al. (2002) reporteda seasonal maximum GPP of −24 µmol m−2 s−1 and sea-sonal maximum TER of 5.3 µmol m−2 s−1; chamber mea-surements in June 2003 revealed a maximum soil respirationrate of 17.3 µmol m−2 s−1. Our partitioning results for For-est_LO based on SK10, TH08, and the approach after Re-ichstein et al. (2005) were within the range of these reportedflux magnitudes (Figs. 2, S1). For Forest_WA, SK10-derivedpartitioning fractions, with T /ET > 0.5 and NPP /NEE > 2,were relatively large. On 8 July 2016, however, the CO2flux components were smaller, with NPP /NEE < 1.4 andRsoil < 10 µmol m−2 s−1 (Fig. S4). On this day no significantdifferences in weather conditions or scalar statistics wereapparent in contrast to the other days. For Forest_MMP,Thomas et al. (2009) derived a T /ET ratio of 50 % from sapflow measurements, which agrees well with the partitioningresults obtained with the SK10 approach (Figs. 5, S6). Re-sults from the TH08 approach and estimated Esoil imply arelatively larger fraction of T . At Forest_SC, the results fromthe different source partitioning methods were impacted bywater stress. For a very dry period in August 2016, both parti-tioning approaches were not applicable because transpirationand photosynthesis almost ceased due to water stress, and thecorrelations between H2O and CO2 fluxes were almost al-ways positive (not shown). In April 2017, partitioning resultswere obtained showing an increase in Rsoil estimated withSK10 and a decrease in estimated E (Fig. S7). Spring 2017was considered relatively dry in this region, and the last pre-cipitation event was 5 days before the respective time period,so it can be assumed that water stress increased steadily inApril 2017. No respiration–evaporation events were apparent

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1118 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

Figure 2. Source partitioning results for (a) H2O and (b) CO2 fluxes in half-hourly time steps for the Loobos study site (forest) in theNetherlands. The figure shows 4 days of the considered time period and selected method versions (see text for description). Results for alldays and for every method version are shown in the Supplement. Grey areas show the measured water and CO2 fluxes. Soil evaporationestimates derived based on Beer’s law and CO2 flux estimates by Reichstein et al. (2005; RE05) are also included (LE: latent heat flux;E: evaporation; Esoil: estimated soil evaporation; GPP: gross primary production; NPP: net primary production; TER: total ecosystemrespiration; Rsoil: soil respiration; z: measurement height; hc: canopy height; LAI: leaf area index).

in the q ′–c′ planes, which could be caused by the sub-canopyin the oak savanna, and thus TH08 probably underestimatedsoil fluxes substantially.

In Grass_RO the continuous chamber measurements ofRsoil and TER estimated with the approach after Reichsteinet al. (2005) did not agree well. TER decreased steadily over

the 7 days (this could also be observed for Grass_FE) andwas mostly lower than measured Rsoil (Fig. S8). In compar-ison to measured Rsoil, SK10 still overestimated and TH08underestimated Rsoil fluxes. For Forest_WU and Grass_WU,TH08 yielded results matching comparatively well with themodeled estimate Esoil and the gap-filling approach after Re-

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1119

Figure 3. Diurnal dynamics of source partitioning results for (a) H2O and (b) CO2 fluxes and (c) water use efficiency (WUE) for theWaldstein study site (forest) in Germany for 4–10 July 2016 and for selected method versions (see text for description; LE: latent heat flux;E: evaporation; NPP: net primary production; Rsoil: soil respiration; z: measurement height; hc: canopy height; LAI: leaf area index). Errorbars indicate the 95 % confidence intervals of the mean values.

ichstein et al. (2005) (Figs. S3, S9). As mentioned before,Grass_WU is a very heterogeneous site with regrowing veg-etation of grasses, shrubs, and trees on dry and wet areas.Thus, the measured signals might display fluxes originat-ing from different sinks and sources distributed horizontallyrather than vertically. The present variety of plant types in-creased the uncertainty in the estimation of WUE. Usage ofWUEOLR improved the partitioning by SK10 significantly,but could not avoid overestimation of Rsoil (in reference tochamber measurements and TER). For Forest_LA, we ob-served a behavior similar to Grass_WU (Fig. S5). Here, the

forest is also regrowing, but spruce trees are already moreabundant and larger.

For Maize_DI in 2007, Jans et al. (2010) reported amean Rsoil flux of 3.16 µmol m−2 s−1 and a peak Rsoil of23 µmol m−2 s−1. Rsoil estimates by SK10 were often aslarge as this peak, but the maximum observed by Jans etal. (2010) was triggered by precipitation, which does notapply in our case (Fig. S11). The partitioning results forthe cropland in Selhausen (Wheat_SE, Barley_SE, Inter-crop_SE, SugarBeet_SE) showed large differences betweencrops and were more robust for H2O fluxes than CO2 fluxes.

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1120 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

Figure 4. Diurnal dynamics of source partitioning results for (a) H2O and (b) CO2 fluxes for all study sites and for the approach after Scanlonand Kustas (2010; SK10) with WUEOLR and after Thomas et al. (2008; TH08) with REA H (see text for description; LE: latent heat flux;E: evaporation; NPP: net primary production; Rsoil: soil respiration). Error bars indicate the 95 % confidence intervals of the mean values.

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1121

Figure 5. Averages of source partitioning results for the following: (a) H2O and CO2 fluxes for the Metolius Mature Pine study site (forest)in the US and for all method versions; (b) CO2 fluxes for all study sites and for the approaches after Scanlon and Kustas (2010; SK10) withWUEOLR and after Thomas et al. (2008; TH08) with REA H; and (c) H2O fluxes and the partitioning fraction E /ET for all study sitesand for the approaches SK10 WUEOLR and TH08 REA H (see text for description; LE: latent heat flux; E: evaporation; NPP: net primaryproduction; Rsoil: soil respiration; z: measurement height; hc: canopy height; LAI: leaf area index). Error bars indicate the 95 % confidenceintervals of the mean values. For each study site, net fluxes (evapotranspiration and net ecosystem exchange) differ between method versionsbecause each method version found a different number of partitioning solutions, and thus the averages were taken from different subsets ofthe original data.

3.1.2 Error metrics

Figure 6 shows the error metrics RMSEln and bias relativeto chamber measurements of Rsoil, HiR GPP, HiR TER, andRMSEln and bias relative to Esoil estimation for each site andmethod version. A clear pattern in the performance of thesource partitioning depending on method version or on studysite characteristics could not be identified in the error metrics(Fig. 6). However, the following general statements can bemade.

1. The RMSE in Rsoil was usually larger for SK10 thanfor TH08 (not shown). Considering RMSEln in Rsoil,

SK10 performed better at forest sites than TH08 andslightly worse for croplands and grasslands (Fig. 6a).The bias in Rsoil was always positive for SK10 (exceptfor Forest_WU) and often negative for TH08 (except forTH08 REA H; Fig. 6b); SK10 has the tendency to over-estimate and TH08 to underestimate Rsoil compared torespiration chamber measurements. The lowest RMSE,RMSEln, and bias were found for the SK10 methodversions in Forest_WU and for TH08 in Forest_WU,Grass_WU, and SugarBeet_SE_09.

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1122 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

2. When using the gap-filling model after Reichstein etal. (2005) as a reference, high HiR GPP values wererelatively frequent for TH08, with a minimum of 66.7 %for SugarBeet_SE_06, while HiR GPP values for SK10were considerably lower (Fig. 6c). For HiR TER, sucha clear difference in performance could not be observed(Fig. 6d). While SK10 mostly overestimated TER,TH08 often estimated soil fluxes smaller than the min-imum Rsoil threshold of 1 µmol m−2 s−1. TH08 REA Husually gave the best results for HiR TER and the worstfor HiR GPP within the method versions of TH08.Also, the performance of SK10 improved for CO2 inMaize_DI with increasing crop height and lower LAI(Figs. 4, 6).

3. The RMSE (not shown), RMSEln, and bias of E (in ref-erence to Esoil estimated using Beer’s law) were mostlysimilar or slightly larger for SK10 than for TH08 exceptfor the low crop canopies, Forest_LO, Forest_MMP,and Forest_SC (Fig. 6e, f). These sites also had a rel-atively low LAI. The error metrics were low in For-est_WU and Grass_WU for SK10 and TH08. The worstperformance regarding E could be found in Forest_HHfor SK10 and in Forest_SC, Maize_DI_06, and Inter-crop_SE for TH08. The bias indicated that SK10 un-derestimated E for all canopies with an LAI lowerthan 2.3 (Forest_LO, Forest_SC, Maize_DI_06, Sugar-Beet_SE_06, Intercrop_SE; the latter three have rela-tively short canopies). This could also be explained bythe larger Esoil estimates based on Beer’s law due tothe smaller LAIs, thus preventing an overestimation bySK10.

To summarize, for TH08 the calculation of the fluxes viaREA yielded larger fluxes than via CV (Figs. 2, 3, 5). Be-cause averaging in the flux calculation is performed dif-ferently for CV and REA (i.e., Eq. 1, p. 1212 and Eq. 8,p. 1214 in Thomas et al., 2008) and fewer data points aresampled with the hyperbolic threshold than using data fromthe entire Q1, the largest magnitudes were obtained by us-ing REA with the hyperbolic threshold (REA H). In sometime steps, no respiration–evaporation cloud was apparentin the q ′–c′ plane, and thus the applied conditional sam-pling strategies were not as effective as intended, and anassessment of a correct sampling was not possible. UsingGPP and TER estimated with the gap-filling model after Re-ichstein et al. (2005) as a reference, components estimatedby TH08 were almost always within this prescribed range(i.e., magnitude of NPP smaller than magnitude of GPP,and Rsoil smaller than TER) because of their small result-ing fluxes, whereby Rsoil was often below the assumed min-imum threshold of 1 µmol m−2 s−1; thus, we assume thesevalues to be underestimated (Figs. 6, S1–S13). Regardingthe error metrics in Fig. 6, TH08 REA H, among all TH08method versions, yielded the best result for the largest num-ber of sites and error metrics. Partitioning results obtained by

TH08 CV GMM were not systematically different from theother method versions, but showed no extreme spikes in thesoil flux components.

The SK10 approach had the tendency to produce very highvalues for the soil flux components. Considering the diurnaldynamics and averages (Figs. 3–5), results for SK10 weresatisfactory, but still relatively large. For most of the studysites, the magnitudes and variability in the half-hourly re-sults for the soil flux components were decreased by usingWUEMOST or WUEOLR instead of WUEmeanT. The differ-ing WUE inputs had a larger effect on the CO2 flux com-ponents than on H2O. The magnitudes of the estimated leaf-level WUEs agreed well with magnitudes stated by Good etal. (2014), Linderson et al. (2012), and Sulman et al. (2016).Considering the error metrics in Fig. 6, SK10 with WUEOLRvery often gave the best results.

3.2 Analysis of source partitioning approaches

3.2.1 Analysis by means of correlation analysis

We studied the interrelations between partitioning perfor-mance (expressed in HiR GPP and HiR TER) and site charac-teristics such as canopy height hc, LAI, canopy density (us-ing LAI h−1

c as proxy), measurement height z, and the posi-tion of the measurements relative to the roughness sublayer(using z h−1

c as a proxy) by means of a correlation analysis(Tables 2, 3). Here, hc represents the vertical separation ofsinks and sources of passive scalars between the canopy topand soil surface. For the chosen study sites, LAI correlatedwith hc when considering a specific ecosystem type (forest,cropland, or grassland). Thus, LAI h−1

c was also consideredto distinguish between their impacts on partitioning perfor-mance. The ecosystem type “cropland” included only twodifferent sites, Maize_DI and Selhausen (Wheat_SE, Bar-ley_SE, Intercrop_SE, SugarBeet_SE), and thus only twodifferent measurement heights z, but a total of nine data setsresulting from the considered time periods and various crops(Table 1). Therefore, the correlation coefficients with z in-cluding this ecosystem type have to be handled with care.All these site characteristics contain some information aboutthe characteristics of the observed turbulence and also affectthe degree of mixing of the scalars when they reach the ECsensor. Furthermore, we assume that with increasing LAI,LAI h−1

c and z h−1c , and with decreasing hc the dissimilarity

between q ′ and c′ decreases and EC measurements containless information for the partitioning approaches (Edburg etal., 2012; Huang et al., 2013; Williams et al., 2007). The re-sults of Klosterhalfen et al. (2019) suggest a decreasing per-formance of SK10 with increasing z h−1

c .Correlation coefficients between the partitioning perfor-

mance and site characteristics were calculated for all sites to-gether, for forests only, or for croplands and grasslands only(Tables 2, 3). For the SK10 method versions, the correlationcoefficients showed similar relations between variables and

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1123

Figure 6. Error metrics for source partitioning results for each study site and method version (see text for description). (a–b) Root meansquare error in log-transformed data (RMSEln) and bias considering soil respiration (Rsoil) chamber measurements, (c–d) percent fractionof time steps with partitioning results in the range (HiR) of estimated gross primary production (GPP) and total ecosystem respiration (TER)by the approach after Reichstein et al. (2005), and (e–f) RMSEln and bias considering soil evaporation (Esoil) estimated based on Beer’s law.

partitioning results for both HiR GPP and HiR TER becauseSK10 had the tendency to overestimate both NPP and Rsoil.For the TH08 method versions, relations slightly differ be-tween HiR GPP and HiR TER because TH08 had the ten-dency to underestimate Rsoil fluxes (< 1 µmol m−2 s−1), andthus HiR TER values were smaller than HiR GPP. For the for-est sites, the correlations were relatively high between vari-ables and partitioning performance, even though they weremostly not significantly different from zero.

The performance of all SK10 method versions correlatednegatively with LAI h−1

c and z h−1c , and positively with

hc and z; the correlation with z h−1c was often significant.

The correlation coefficients regarding LAI, despite also be-ing positive, were the smallest. Therefore, the partitioningperformance of SK10 was mostly enhanced with a sparsecanopy and measurements obtained close to the canopy(close to or within the roughness sublayer). For the TH08method versions, LAI had larger effects on partitioning per-formance than for SK10 method versions, and hc, z h−1

c , andLAI h−1

c had smaller effects. Correlation coefficients of LAIand LAI h−1

c were mostly positive with a few exceptions(e.g., regarding HiR TER for croplands and grasslands). Forthe TH08 method versions, all site characteristics correlatedpositively with HiR GPP, except for z h−1

c , considering allstudy sites. The correlations between site characteristics andHiR TER were weak while considering all study sites. Forforest sites, HiR TER correlated negatively with LAI h−1

c and

z h−1c and positively with hc, LAI, and z. For croplands and

grasslands, similar results were obtained, except for the neg-ative correlation between HiR TER and LAI. Also, the corre-lations with hc and z increased in significance. Apparently, adense canopy yielded too-low sub-canopy fluxes derived byTH08, but more reasonable canopy fluxes.

The variable LAI mostly correlated positively with par-titioning performance for TH08 method versions and veryweak with partitioning performance for SK10 method ver-sions, which contradicted our initial hypotheses. Also, thecorrelation between partitioning performance by TH08 andLAI h−1

c at forest sites contradicted our assumption that ahigher plant density would have a strong negative effect.Next to canopy density, LAI could also be connected tolarger sinks and sources of canopy fluxes (T and photosyn-thesis) relative to soil surface fluxes due to larger biomassand to the appearance and frequency of coherent structures.A dense canopy prevents frequent ejections of air parcelsfrom the sub-canopy, but provokes higher scalar concentra-tions in such air parcels because of a longer accumulationunder the canopy. Respiration–evaporation events could oc-cur less frequently but be of higher magnitude. Also, smallgaps in an otherwise dense canopy can play an importantrole regarding ejection events. Thus, how canopy density af-fects scalar–scalar correlation measured above the canopy(and that associated with the partitioning performance) can-not be easily assessed. In this study, canopy density (LAI and

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1124 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

Figure 7. (a) Setup of the conceptual model for synthetic fluctuations (q ′ and c′) originating from the soil, canopy, or boundary layerwith differing degrees of mixing (no, complete, or partial mixing between soil and canopy sink–source) including water use efficiency(WUE=−1.444 µmol mmol−1

=−3.53 mg g−1; blue line), reduced major axis regression (red line) after Webster (1997), hyperbolic thresh-old criterion after Thomas et al. (2008; TH08) (H = 0.25; green dashed line), and correlation coefficient between q ′ and c′ (ρq ′c′ ). (b) Trueknown partitioning ratios (dashed line) and source partitioning results from all TH08 method versions (see text for description) for eachdegree of mixing.

LAI h−1c ) and partitioning performance (especially regarding

HiR TER) correlated negatively at cropland and grasslandsites and mostly positively at the forest sites for TH08. As-suming gaps in the canopy can be more frequent in foreststhan in croplands or grasslands, these results support theabovementioned aspects. Zeeman et al. (2013) found a clearconnection between the appearance of coherent structuresand the detection of respiration–evaporation events followingthe TH08 approach, in which the best results were obtainedfor an open canopy (Forest_MMP). They found a temporalseparation of 10–20 s among sub-, mid-, and above-canopymeasurements. In order to assess to what extent these ef-fects play a role in the current data sets, an estimate of the(large-scale) heterogeneity and density of the vegetation atall study sites (gap fraction, canopy openness) would be nec-essary, which is beyond the scope of this paper.

3.2.2 Analysis by means of a conceptual model

SK10 was already thoroughly analyzed by means of the syn-thetic high-frequency data derived by LES (Klosterhalfen etal., 2019). In the present study, TH08 was applied to varioussynthetic w′, q ′, and c′ data sets including soil, canopy, andboundary layer scalar sink–sources derived by a simple con-ceptual model as described above (Fig. 7a). Defined by theconditional sampling concept, we hypothesized that TH08

would work perfectly with no mixing of the scalars fromthe three different origins, would not obtain any partitioningfractions in the case of complete mixing, and would underes-timate the soil fluxes in the case of partial mixing.

TH08 behaved as hypothesized except for TH08 REA H(see below; Fig. 7b). For partial mixing, a small differencein TH08-derived partitioning fractions (especially for H2O)was observed between the sampling in Q1 and with H be-cause one data point was not sampled with the hyperbolicthreshold, but was located within Q1. TH08 REA H didnot yield any partitioning results in the case of no or par-tial mixing. This is due to the different definitions of β inthe application of REA with the sampling in Q1 or with H(Thomas et al., 2008, Eq. 4, p. 1213 and statement on page1215). β is an empirical constant and can be approximatedby the ratio between the standard deviation of w′ (σ ′w) andthe difference between the mean vertical velocities in up-drafts and downdrafts (w+−w−). For the conditional sam-pling approach within Q1, β is derived including all datapoints (disregarding the sign of q ′ or c′). For the approach in-cluding the hyperbolic threshold criterion, β is derived fromw′ data points that satisfy the hyperbolic threshold criterionfor positive q ′ and c′. In the case of our conceptual modelfor partial mixing, no data point with negative w′ satisfiedthis criterion, so without w−, β and a partitioning fraction

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1125

Table 2. Correlation coefficients between the partitioning performances of each method version regarding HiR GPP (see text for description)and study site characteristics (hc: canopy height; LAI: leaf area index; z: measurement height) considering different sets of sites: all, onlyforest, or only cropland and grassland sites. Bold lettering indicates highest positive and highest negative correlation. Underlined letter-ing indicates highest magnitude of correlation and italic lettering lowest magnitude of correlation. Also, the statistical significance of thecorrelations is indicated with ∗ p ≤ 0.1 and ∗∗ p ≤ 0.05.

Variable SK10 SK10 SK10 TH08 TH08 TH08 TH08 TH08WUEmeanT WUEMOST WUEOLR CV Q1 CV H REA Q1 REA H CV GMM

All

hc 0.52 ∗∗ 0.56∗∗ 0.44∗ 0.21 0.27 0.28 0.45∗ 0.23LAI 0.04 0.01 −0.08 0.44 ∗ 0.25 0.45 ∗ 0.17 0.30z 0.48∗∗ 0.52∗∗ 0.40∗ 0.23 0.27 0.31 0.48 ∗∗ 0.25z h−1

c −0.51∗∗ − 0.60 ∗∗ − 0.45 ∗ − 0.11 −0.15 −0.13 −0.15 −0.10LAI h−1

c −0.38 −0.47∗∗ −0.41∗ 0.18 0.03 0.09 −0.13 0.09

Forests

hc 0.64 0.63 0.56 0.20 0.21 0.21 0.27 0.11LAI −0.03 −0.07 −0.10 0.61 0.77 ∗∗ 0.68 ∗ 0.69 ∗ 0.69 ∗z 0.62 0.60 0.55 0.37 0.31 0.36 0.41 0.27z h−1

c − 0.74 ∗ − 0.75 ∗ − 0.68 ∗ 0.27 0.25 0.28 0.20 0.37LAI h−1

c −0.59 −0.61 −0.59 0.19 0.38 0.26 0.22 0.36

Croplands, grasslands

hc 0.54∗ 0.64∗∗ 0.33 0.07 0.23 0.12 0.31 0.16LAI 0.07 0.05 −0.10 0.40 0.10 0.37 − 0.03 0.15z 0.02 0.07 −0.29 − 0.44 −0.11 −0.17 0.37 −0.23z h−1

c − 0.58 ∗∗ − 0.71 ∗∗ − 0.51 ∗ −0.01 −0.01 0.03 0.17 0.03LAI h−1

c −0.37 −0.49 −0.46 0.37 0.21 0.32 0.16 0.28

could not be calculated. Figure 7 shows the partitioning frac-tions for TH08 REA H while applying β as calculated inTH08 REA Q1 (non-filled markers). TH08 CV GMM per-formed similarly to the other method versions: it sampled thecorrect respiration–evaporation cloud in the case of no mix-ing and no cloud in the case of complete mixing. However,in the case of partial mixing all data points with q ′ > 0 weresampled by TH08 CV GMM, thus also considering the frac-tion originating from the canopy. For the latter, the covari-ances applying the averages of q or c of the sampled cluster,and considering only data points with w′ > 0, were negativefor H2O and CO2 (not shown). Thus, E and Rsoil were re-calculated, with the covariance taking the deviations of theaverage of q or c considering all data points and includingonly data points with w′ > 0, within quadrant 1, and withinthe sampled cluster. This way of correcting the sampling byGMM resulted in a similar partitioning fraction as the othermethod versions.

4 Summary and conclusions

For all sites and all applied method versions, the partitionedCO2 fluxes generally showed a higher variability and morespikes than the partitioned H2O fluxes. Mean diurnal cy-

cles averaged over each site’s specific time period yieldedsatisfactory results. The partitioning approaches after Scan-lon and Kustas (2010; SK10) and after Thomas et al. (2008;TH08) gave differing results and performed disparately be-tween method versions. TH08 mostly resulted in lower mag-nitudes of the flux components originating from the soil sur-face than SK10. In addition, TH08 had the tendency to un-derestimate these flux components in reference to soil res-piration flux measurements and estimates of Esoil based onBeer’s law. SK10 usually had the tendency to overestimatesoil flux components and yielded larger error metrics (RMSEand bias). The RMSE depends on the bias, and the error dis-tribution was asymmetric. The positive errors (overestima-tions) were larger than negative errors (underestimations).Decreasing the weight of outliers by log-transforming Rsoildata from chamber observations and partitioning estimationsrevealed a lower RMSEln for SK10 at forest sites than forTH08.

SK10 was used with a variety of estimates of WUE. Es-timating input WUE using foliage temperature derived fromthe observed outgoing longwave radiation often improved thepartitioning performance. For TH08, various options weretested regarding the conditional sampling and flux calcula-tion. Applying a Gaussian mixture model for the conditional

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1126 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

Table 3. Correlation coefficients between the partitioning performances of each method version regarding HiR TER (see text for descrip-tion) and study site characteristics (hc: canopy height; LAI: leaf area index; z: measurement height) considering different sets of sites: all,only forest, or only cropland and grassland sites. Bold lettering indicates highest positive and highest negative correlation. Underlined let-tering indicates highest magnitude of correlation and italic lettering lowest magnitude of correlation. Also, the statistical significance of thecorrelations is indicated with ∗ p ≤ 0.1 and ∗∗ p ≤ 0.05.

Variable SK10 SK10 SK10 TH08 TH08 TH08 TH08 TH08WUEmeanT WUEMOST WUEOLR CV Q1 CV H REA Q1 REA H CV GMM

All

hc 0.52 ∗∗ 0.52∗∗ 0.47 ∗∗ −0.12 −0.18 0.17 0.01 −0.23LAI 0.01 0.06 −0.03 − 0.20 0.04 −0.01 0.24 −0.12z 0.48∗∗ 0.47∗∗ 0.44∗ −0.17 − 0.24 0.12 −0.06 −0.27z h−1

c −0.47∗∗ − 0.57 ∗∗ −0.42∗ 0.08 −0.01 −0.14 −0.15 0.30LAI h−1

c −0.37 −0.44∗ −0.41∗ −0.06 0.06 − 0.21 −0.04 0.18

Forests

hc 0.63 0.63 0.63 0.59 0.68 ∗ 0.56 0.76 ∗∗ 0.43LAI −0.02 0.02 0.05 0.43 0.31 0.61 0.65 0.28z 0.60 0.59 0.64 0.46 0.60 0.41 0.72∗ 0.30z h−1

c − 0.72 ∗ − 0.73 ∗ − 0.66 −0.48 −0.52 −0.39 −0.47 −0.35LAI h−1

c −0.56 −0.54 −0.53 −0.07 −0.26 0.09 −0.13 0.01

Croplands, grasslands

hc 0.54 ∗ 0.59∗∗ 0.34 0.42 0.61 ∗∗ 0.50∗ 0.85 ∗∗ −0.25LAI 0.01 0.06 −0.13 −0.49 −0.04 −0.33 0.03 − 0.32z 0.04 0.01 −0.23 0.64 ∗∗ 0.59∗∗ 0.70 ∗∗ 0.48 −0.03z h−1

c −0.48 − 0.66 ∗∗ −0.47 −0.16 −0.45 −0.20 −0.59∗∗ 0.12LAI h−1

c −0.34 −0.47 − 0.47 −0.36 −0.30 −0.31 −0.37 −0.06

sampling approach in TH08 did not improve partitioning per-formance significantly because obtaining a positive and cor-rect flux estimation was difficult for data points outside quad-rant 1 in the q ′–c′ plane. For TH08, conditional samplingincluding a hyperbolic threshold and calculating flux com-ponents based on the relaxed eddy accumulation techniqueyielded the best partitioning results.

The dependencies of the partitioning performance on tur-bulence and site characteristics were analyzed based on a cor-relation analysis and the application of TH08 to synthetic,conceptual data sets of scalar fluctuations. Foremost, the per-formance of SK10 was improved for sparse canopies and es-pecially with a low ratio between measurement height andcanopy height. The performance of TH08 was more depen-dent on canopy height and leaf area index. The partitioningperformance of TH08 improved with increasing canopy den-sity for forests, whereas the opposite was observed for grassand crops. In general, site characteristics that increase dis-similarities between scalars (due to less mixing, large sink–source separation, coherent structures, ejections, etc.) ap-peared to enhance partitioning performance for SK10 andTH08.

For the forest site Loobos in the Netherlands, SK10 andTH08 obtained similar partitioning results and sufficient er-

ror metrics, suggesting a low uncertainty. At this site witha relatively low leaf area index, high canopy, and low ratiobetween measurement and canopy height, the conditions forboth partitioning approaches seemed to be appropriate.

Data availability. The data sets generated and/or analyzed duringthe current study are available from the corresponding author or therespective site PI on reasonable request.

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A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1127

Appendix A

In Table A1 the number of half-hourly time steps during day-light per considered time period is shown for each study site.Also, the fraction of daylight time steps of high quality (HQ)that were used in the application of SK10 and TH08 areshown; for SK10 only a good or intermediate quality flag (af-ter Mauder et al., 2013) and no precipitation were required,and for TH08 additionally a negative ρq ′c′ . Furthermore, thefraction of these HQ time steps for which partitioning so-lutions were found is shown for each method version. WithTH08 by sampling in the first quadrant (Q1) a partitioningresult could be obtained for almost every time step (mini-mum of 98.2 %). With the hyperbolic threshold criterion andwith GMM fewer solutions could be found because quiteoften the number of sampled data points was less than 1 %of the total number in one 30 min time period. SK10 some-times could not find a partitioning solution, when the mea-sured and estimated ρq ′c′ were not equal and removing large-scale processes by Wavelet transform could not help to solvethe system of equations. The most solutions were found forForest_MMP and the least for Grass_RO, suggesting a de-pendence on vegetation height. For crop sites Maize_DI andSugarBeet_SE, the number of solutions with SK10 increasedwith development stage of the maize or sugar beet, respec-tively, while the ratio between measurement height and hcdecreased. At the same sites the number of solutions forTH08 with a hyperbolic threshold and GMM decreased (theconditional sampling in Q1 was not affected). Generally, forthe grasslands and the lower crop canopies more solutionswere obtained with TH08 than SK10. An exception was thelow intercrop in Selhausen (Intercrop_SE).

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1128 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

TableA

1.Countof

half-hourlytim

esteps

duringdaylight(C

oD)

perconsidered

time

periodfor

eachstudy

site,correspondingpercentfractions

ofC

oDof

highquality

(HQ

),andpercentfractions

ofthese

HQ

time

stepsw

itha

foundpartitioning

solutionfor

eachm

ethodversion.B

old(italic)

letteringindicates

thehighest(low

est)fraction

ofsolutions

foreach

site.Plus(m

inus)indicatesthe

highest(lowest)fraction

foreachm

ethodversion.

Method

SiteC

oDR

elCoD

RelH

Qw

ithSite

CoD

RelC

oDR

elHQ

with

Time

periodused

(HQ

)partitioning

Time

periodused

(HQ

)partitioning

solutionsolution

SK10

WU

Em

eanT

231

91.884.4

99

84.826.2

SK10

WU

EM

OST

82.134.5

SK10

WU

EO

LR

Forest_LO

65.6M

aize_DI_06

23.8−

TH

08C

VQ

1,RE

AQ

18–14

Jul200368.0

99.414–16

Jun2007

63.698.4

TH

08C

VH

,RE

AH

86.082.5

TH

08C

VG

MM

59.257.1

SK10

WU

Em

eanT

231

89.275.7

96

97.990.4

SK10

WU

EM

OST

76.288.3

SK10

WU

EO

LR

Forest_HH

74.8M

aize_DI_07

77.7

TH

08C

VQ

1,RE

AQ

13–9

Jul201659.7

100.0+

14–16Jul2007

78.198.7

TH

08C

VH

,RE

AH

55.850.7

TH

08C

VG

MM

51.452.0

SK10

WU

Em

eanT

218

78.080.6

91

94.595.3+

SK10

WU

EM

OST

78.894.2

SK10

WU

EO

LR

Forest_WU

70.6M

aize_DI_08

89.5

TH

08C

VQ

1,RE

AQ

118–24

May

201555.5

100.0+

4–6A

ug2007

80.2100.0

+

TH

08C

VH

,RE

AH

74.445.2

TH

08C

VG

MM

51.257.5

SK10

WU

Em

eanT

222

92.888.3

96

92.757.3

SK10

WU

EM

OST

91.757.3

SK10

WU

EO

LR

Forest_WA

89.3SugarB

eet_SE_06

52.8

TH

08C

VQ

1,RE

AQ

14–10

Jul201675.2

100.0+

20–22Jun

201776.0

98.6T

H08

CV

H,R

EA

H65.9

58.9T

H08

CV

GM

M50.3

47.9

SK10

WU

Em

eanT

164

84.133.3

90

77.872.9

SK10

WU

EM

OST

38.471.4

SK10

WU

EO

LR

Forest_LA

56.5SugarB

eet_SE_08

72.9

TH

08C

VQ

1,RE

AQ

124–30

Sep2017

54.9100.0

+2–4

Aug

201762.2

100.0+

TH

08C

VH

,RE

AH

93.3+

37.5T

H08

CV

GM

M58.9

41.1

Biogeosciences, 16, 1111–1132, 2019 www.biogeosciences.net/16/1111/2019/

A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1129

Tabl

eA

1.C

ontin

ued.

Met

hod

Site

CoD

Rel

CoD

Rel

HQ

with

Site

CoD

Rel

CoD

Rel

HQ

with

Tim

epe

riod

used

(HQ

)pa

rtiti

onin

gTi

me

peri

odus

ed(H

Q)

part

ition

ing

solu

tion

solu

tion

SK10

WU

Em

eanT

211

84.8

95.0

78

92.3

80.6

SK10

WU

EM

OST

95.0+

81.9

SK10

WU

EO

LR

Fore

st_M

MP

93.3+

Suga

rBee

t_SE

_09

81.9

TH

08C

VQ

1,R

EA

Q1

6–12

Jun

2014

73.0

100.

0+4–

6Se

p20

1776

.998

.3T

H08

CV

H,R

EA

H70

.825

.0−

TH

08C

VG

MM

60.4

16.7−

SK10

WU

Em

eanT

175

87.4

73.9

96

93.8

56.7

SK10

WU

EM

OST

75.2

52.2

SK10

WU

EO

LR

Fore

st_S

C77

.1W

heat

_SE

46.7

TH

08C

VQ

1,R

EA

Q1

1–7

Apr

2017

77.7

99.3

3–5

Jun

2015

77.1

98.6

TH

08C

VH

,RE

AH

47.1

25.7

TH

08C

VG

MM

40.4

32.4

SK10

WU

Em

eanT

217

91.7

21.1−

96

82.3

50.6

SK10

WU

EM

OST

32.7−

51.9

SK10

WU

EO

LR

Gra

ss_R

O28

.6B

arle

y_SE

58.2

TH

08C

VQ

1,R

EA

Q1

15–2

1Ju

l201

373

.310

0.0+

27–2

9M

ay20

1667

.798

.5T

H08

CV

H,R

EA

H53

.526

.2T

H08

CV

GM

M53

.527

.7

SK10

WU

Em

eanT

218

82.1

31.3

71

91.5

64.6

SK10

WU

EM

OST

38.0

70.8

SK10

WU

EO

LR

Gra

ss_W

U40

.8In

terc

rop_

SE73

.8

TH

08C

VQ

1,R

EA

Q1

18–2

4M

ay20

1558

.710

0.0+

23–2

5Se

p20

1680

.398

.2−

TH

08C

VH

,RE

AH

90.6

35.1

TH

08C

VG

MM

88.3+

28.1

SK10

WU

Em

eanT

217

82.0

34.8

SK10

WU

EM

OST

36.0

SK10

WU

EO

LR

Gra

ss_F

E39

.9

TH

08C

VQ

1,R

EA

Q1

11–1

7Ju

l201

558

.510

0.0+

TH

08C

VH

,RE

AH

46.5

TH

08C

VG

MM

65.4

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1130 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

Supplement. The supplement related to this article is availableonline at: https://doi.org/10.5194/bg-16-1111-2019-supplement.

Author contributions. AK and AG designed the work and con-ducted the main analyses. All authors provided measurements oftheir study sites (including obtaining and processing data), docu-mented their site and its methodology, and aided its interpretation.AK primarily wrote the paper with input from all coauthors.

Competing interests. The authors declare that they have no conflictof interest.

Acknowledgements. This research was supported by the GermanFederal Ministry of Education and Research BMBF, projectIDAS-GHG (grant number 01LN1313A). The measurement infras-tructure providing observational data was supported by the GermanResearch Foundation DFG through the Transregional CollaborativeResearch Centre 32 (TR 32) and Terrestrial Environmental Obser-vatories (TERENO). The authors thank all technicians, engineers,and laboratory assistances in TR32, TERENO, and elsewhere forproviding measurements from the test sites. Finally, we thankthe editor and the reviewers for their helpful and constructivecomments that improved the quality of this paper.

The article processing charges for this open-accesspublication were covered by a ResearchCentre of the Helmholtz Association.

Edited by: Trevor KeenanReviewed by: two anonymous referees

References

Anderson, R.G., Zhang, X., and Skaggs, T. H.: Measure-ment and partitioning of evapotranspiration for applica-tion to vadose zone studies, Vadose Zone J., 16, 1–9,https://doi.org/10.2136/vzj2017.08.0155, 2018.

Andreu, A., Kustas, W. P., Polo, M. J., Carrara, A., and González-Dugo, M. P.: Modeling surface energy fluxes over a dehesa(oak savanna) ecosystem using a thermal based two-sourceenergy balance model (TSEB) I, Remote Sens., 10, 1–27,https://doi.org/10.3390/rs10040567, 2018.

Babel, W., Lüers, J., Hübner, J., Rebmann, C., Wichura, B.,Thomas, C. K., Serafimovich, A., and Foken, T.: Long-termcarbon and water vapour fluxes, in: Energy and matter fluxesof a spruce forest ecosystem, edited by: Foken, T., Ecologi-cal Studies (Analysis and Synthesis), Vol. 229, Springer, 73–96,https://doi.org/10.1007/978-3-319-49389-3_4, 2017.

Baldocchi, D., Falge, E., Gu, L., Olson, R., Hollinger, D., Running,S., Anthoni, P., Bernhofer, C., Davis, K., Evans, R., Fuentes, J.,Goldstein, A., Katul, G., Law, B., Lee, X., Malhi, Y., Meyers, T.,Munger, W., Oechel, W., Paw, U. K. T., Pilegaard, K., Schmid, H.P., Valentini, R., Verma, S., Vesala, T., Wilson, K., and Wofsy, S.:FLUXNET: A new tool to study the temporal and spatial variabil-

ity of ecosystem-scale carbon dioxide, water vapor, and energyflux densities, Bull. Am. Meteorol. Soc., 82, 2415–2434, 2001.

Borchard, N., Schirrmann, M., von Hebel, C., Schmidt, M., Baatz,R., Firbank, L., Vereecken, H., and Herbst, M.: Spatio-temporaldrivers of soil and ecosystem carbon fluxes at field scale in anupland grassland in Germany, Agr. Ecosyst. Environ., 211, 84–93, https://doi.org/10.1016/j.agee.2015.05.008, 2015.

Businger, J. A. and Oncley, S. P.: Flux measurement with condi-tional sampling, J. Atmos. Ocean. Technol., 7, 349–352, 1990.

Campbell, G. S. and Norman, J. M.: An introduction to environ-mental biophysics, New York, Springer, 286 pp., 1998.

Canty, M. J.: Image analysis, classification and change detectionin remote sensing, with algorithms for ENVI/IDL, CRC Press,Boca Raton, FL, 441 pp., 2010.

Denmead, O. T., Dunin, F. X., Leuning, R., and Raupach, M.R.: Measuring and modelling soil evaporation in wheat crops,Phys. Chem. Earth, 21, 97–100, https://doi.org/10.1016/S0079-1946(97)85567-X, 1996.

Detto, M. and Katul, G. G.: Simplified expressions for ad-justing higher-order turbulent statistics obtained from openpath gas analyzers, Bound.-Lay. Meteorol., 122, 205–216,https://doi.org/10.1007/s10546-006-9105-1, 2007.

Dolman, A. J., Moors, E. J., and Elbers, J. A.: The carbon up-take of a mid latitude pine forest growing on sandy soil, Agr.Forest Meteorol., 111, 157–170, https://doi.org/10.1016/S0168-1923(02)00024-2, 2002.

Edburg, S. L., Stock, D., Lamb, B. K., and Patton, E. G.: The effectof the vertical source distribution on scalar statistics within andabove a forest canopy, Bound.-Lay. Meteorol., 142, 365–382,https://doi.org/10.1007/s10546-011-9686-1, 2012.

Eder, F., Schmidt, M., Damian, T., Träumer, K., and Mauder, M.:Mesoscale eddies affect near-surface turbulent exchange: ev-idence from Lidar and tower measurements, J. Appl. Mete-orol. Clim., 54, 189–206, https://doi.org/10.1175/JAMC-D-14-0140.1, 2015.

Elbers, J. A., Jacobs, C. M. J., Kruijt, B., Jans, W. W. P., and Moors,E. J.: Assessing the uncertainty of estimated annual totals of netecosystem productivity: A practical approach applied to a midlatitude temperate pine forest, Agr. Forest Meteorol., 151, 1823–1830, https://doi.org/10.1016/j.agrformet.2011.07.020, 2011.

Falge, E., Baldocchi, D., Tenhunen, J., Aubinet, M., Bakwin, P.,Berbigier, P., Bernhofer, C., Burba, G., Clement, R., Davis, K.J., Elbers, J. A., Goldstein, A. H., Grelle, A., Granier, A., Guð-mundsson, J., Hollinger, D., Kowalski, A. S., Katul, G., Law,B. E., Malhi, Y., Meyers, T., Monson, R. K., Munger, J. W.,Oechel, W., Paw, U. K. T., Pilegaard, K., Rannik, Ü., Rebmann,C., Suyker, A., Valentini, R., Wilson, K., and Wofsy, S.: Sea-sonality of ecosystem respiration and gross primary productionas derived from FLUXNET measurements, Agr. Forest Meteo-rol., 113, 53–74, https://doi.org/10.1016/S0168-1923(02)00102-8, 2002.

Foken, T., Gerstberger, P., Köck, K., Siebicke, L., Serafimovich, A.,and Lüers, J.: Description of the Waldstein measuring site, in:Energy and matter fluxes of a spruce forest ecosystem, editedby: Foken, T., Ecological Studies (Analysis and Synthesis), Vol.229, Springer, 19–38, https://doi.org/10.1007/978-3-319-49389-3_2, 2017.

Gebler, S., Hendricks Franssen, H.-J., Pütz, T., Post, H., Schmidt,M., and Vereecken, H.: Actual evapotranspiration and precipi-

Biogeosciences, 16, 1111–1132, 2019 www.biogeosciences.net/16/1111/2019/

A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes 1131

tation measured by lysimeters: a comparison with eddy covari-ance and tipping bucket, Hydrol. Earth Syst. Sci., 19, 2145–2161,https://doi.org/10.5194/hess-19-2145-2015, 2015.

Good, S. P., Soderberg, K., Guan, K., King, E. G., Scanlon,T. M., and Caylor, K. K.: δ2H isotopic flux partitioning ofevapotranspiration over a grass field following a water pulseand subsequent dry down, Water Resour. Res., 50, 1410–1432,https://doi.org/10.1002/2013WR014333, 2014.

Good, S. P., Noone, D., and Bowen, G.: Hydrologic connectiv-ity constrains partitioning of global terrestrial water fluxes, Sci-ences, 349, 175–177, https://doi.org/10.1126/science.aaa5931,2015.

Graf, A., Bogena, H. R., Drüe, C., Hardelauf, H., Pütz, T., Heine-mann, G., and Vereecken, H.: Spatiotemporal relations be-tween water budget components and soil water content in aforested tributary catchment, Water Resour. Res., 50, 4837–4857,https://doi.org/10.1002/2013WR014516, 2014.

Huang, J., Katul, G., and Albertson, J.: The role of coherentturbulent structures in explaining scalar dissimilarity withinthe canopy sublayer, Environ. Fluid Mech., 13, 571–599,https://doi.org/10.1007/s10652-013-9280-9, 2013.

Jans, W. W. P., Jacobs, C. M. J., Kruijt, B., Elbers, J. A., Barendse,S., and Moors, E. J.: Carbon exchange of a maize (Zea mays L.)crop: Influence of phenology, Agr. Ecosyst. Environ., 139, 316–324, https://doi.org/10.1016/j.agee.2010.06.008, 2010.

Jin, H. and Eklundh, L.: A physically based vegetation index forimproved monitoring of plant phenology, Remote Sens. Environ.,152, 512–525, https://doi.org/10.1016/j.rse.2014.07.010, 2014.

Klosterhalfen, A., Moene, A. F., Schmidt, M., Scanlon, T. M.,Vereecken, H., and Graf, A.: Sensitivity Analysis of a sourcepartitioning method for H2O and CO2 fluxes based on highfrequency eddy covariance data: findings from field data andlarge eddy simulations, Agr. Forest Meteorol., 265, 152–170,https://doi.org/10.1016/j.agrformet.2018.11.003, 2019.

Li, X., Gentine, P., Lin, C., Zhou, S., Sun, Z., Zheng, Y., Liu,J., and Zheng, C.: A simple and objective method to par-tition evapotranspiration into transpiration and evaporation ateddy-covariance sites, Agr. Forest Meteorol., 265, 171–182,https://doi.org/10.1016/j.agrformet.2018.11.017, 2019.

Lindauer, M., Schmid, H. P., Grote, R., Mauder, M., Steinbrecher,R., and Wolpert, B.: Net ecosystem exchange over a non-cleared wind-throw-disturbed upland spruce forest – Measure-ments and simulations, Agr. Forest Meteorol., 197, 219–234,https://doi.org/10.1016/j.agrformet.2014.07.005, 2014.

Linderson, M.-L., Mikkelsen, T. N., Ibrom, A., Lindroth, A.,Ro-Poulsen, H., and Pilegaard, K.: Up-scaling of wa-ter use efficiency from leaf to canopy as based on leafgas exchange relationships and the modeled in-canopylight distribution, Agr. Forest Meteorol., 152, 201–211,https://doi.org/10.1016/j.agrformet.2011.09.019, 2012.

Lloyd, J. and Taylor, A.: On the temperature depen-dence of soil respiration, Funct. Ecol., 8, 315–323,https://doi.org/10.2307/2389824, 1994.

Matiu, M., Bothmann, L., Steinbrecher, R., and Men-zel, A.: Monitoring succession after a non-clearedwindthrow in a Norway spruce mountain forest us-ing webcam, satellite vegetation indices and turbulentCO2 exchange, Agr. Forest Meteorol., 244/245, 72–81,https://doi.org/10.1016/j.agrformet.2017.05.020, 2017.

Mauder, M., Cuntz, M., Drüe, C., Graf, A., Rebmann, C.,Schmid, H. P., Schmidt, M., and Steinbrecher, R.: A strat-egy for quality and uncertainty assessment of long-term eddy-covariance measurements, Agr. Forest Meteorol., 169, 122–135,https://doi.org/10.1016/j.agrformet.2012.09.006, 2013.

Ney, P. and Graf, A.: High-resolution vertical profiles measure-ments for carbon dioxide and water vapour concentrations withinand above crop canopies, Bound.-Lay. Meteorol., 166, 449–473,https://doi.org/10.1007/s10546-017-0316-4, 2018.

Ney, P., Graf, A., Bogena, H., Diekkrüger, B., Drüe, C., Esser, O.,Heinemann, G., Klosterhalfen, A., Pick, K., Pütz, T., Schmidt,M., Valler, V., and Vereecken, H.: CO2 fluxes before and afterpartially deforestation of a Central European spruce forest, Agr.Forest Meteorol., in review, 2019.

Palatella, L., Rana, G., and Vitale, D.: Towards a flux-partitioning procedure based on the direct use of high-frequencyeddy-covariance data, Bound.-Lay. Meteorol., 153, 327–337,https://doi.org/10.1007/s10546-014-9947-x, 2014.

Reichstein, M., Falge, E., Baldocchi, D., Papale, D., Aubinet,M., Berbigier, P., Bernhofer, C., Buchmann, N., Gilmanov, T.,Granier, A., Grünwald, T., Havránková, K., Ilvesniemi, H.,Janous, D., Knohl, A., Laurila, T., Lohila, A., Loustau, D., Mat-teucci, G., Meyers, T., Miglietta, F., Ourcival, J.-M., Pumpanen,J., Rambal, S., Rotenberg, E., Sanz, M., Tenhunen, J., Seufert,G., Vaccari, F., Vesala, T., Yakir, D., and Valentini, R.: Onthe separation of net ecosystem exchange into assimilation andecosystem respiration: review and improved algorithm, Glob.Change Biol., 11, 1424–1439, https://doi.org/10.1111/j.1365-2486.2005.001002.x, 2005.

Reichstein, M., Stoy, P. C., Desai, A. R., Lasslop, G., and Richard-son, A. D.: Partitioning of net fluxes, in: Eddy covariance. Apractical guide to measurement and data analysis, edited by:Aubinet, M., Vesala, T., and Papale, D., Dordrecht, Heidelberg,London, New York, Springer, 263–289, 2012.

Scanlon, T. M. and Albertson, J. D.: Turbulent transport ofcarbon dioxide and water vapor within a vegetation canopyduring unstable conditions: Identification of episodes us-ing wavelet analysis, J. Geophys. Res., 106, 7251–7262,https://doi.org/10.1029/2000JD900662, 2001.

Scanlon, T. M. and Kustas, W. P.: Partitioning car-bon dioxide and water vapor fluxes using correla-tion analysis, Agr. Forest Meteorol., 150, 89–99,https://doi.org/10.1016/j.agrformet.2009.09.005, 2010.

Scanlon, T. M. and Kustas, W. P.: Partitioning evapotranspirationusing an eddy covariance-based technique: Improved assessmentof soil moisture and land-atmosphere exchange dynamics, Va-dose Zone J., 11, 12 pp., https://doi.org/10.2136/vzj2012.0025,2012.

Scanlon, T. M. and Sahu, P.: On the correlation structure of wa-ter vapor and carbon dioxide in the atmospheric surface layer:A basis for flux partitioning, Water Resour. Res., 44, W10418,https://doi.org/10.1029/2008WR006932, 2008.

Schlesinger, W. H. and Jasechko, S.: Transpiration in theglobal water cycle, Agr. Forest Meteorol., 189/190, 115–117,https://doi.org/10.1016/j.agrformet.2014.01.011, 2014.

Skaggs, T. H., Anderson, R. G., Alfieri, J. G., Scan-lon, T. M., and Kustas, W. P.: Fluxpart: Open sourcesoftware for partitioning carbon dioxide and water va-

www.biogeosciences.net/16/1111/2019/ Biogeosciences, 16, 1111–1132, 2019

1132 A. Klosterhalfen et al.: Source partitioning of H2O and CO2 fluxes

por fluxes, Agr. Forest Meteorol., 253/254, 218–224,https://doi.org/10.1016/j.agrformet.2018.02.019, 2018.

Špunda, V., Kalina, J., Urban, O., Luis, V. C., Sibisse, I., Puér-tolas, J., Šprtová, M., and Marek, M. V.: Diurnal dynamicsof photosynthetic parameters of Norway spruce trees culti-vated under ambient and elevated CO2: the reasons of mid-day depression in CO2 assimilation, Plant Sci., 168, 1371–1381,https://doi.org/10.1016/j.plantsci.2005.02.002, 2005.

Sulman, B. N., Roman, D. T., Scanlon, T. M., Wang, L.,and Novick, K. A.: Comparing methods for partitioninga decade of carbon dioxide and water vapor fluxes in atemperate forest, Agr. Forest Meteorol., 226/227, 229–245,https://doi.org/10.1016/j.agrformet.2016.06.002, 2016.

Thomas, C., Martin, J. G., Goeckede, M., Siqueira, M. B., Fo-ken, T., Law, B. E., Loescher, H. W., and Katul, G.: Esti-mating daytime subcanopy respiration from conditional sam-pling methods applied to multi-scalar high frequency turbu-lence time series, Agr. Forest Meteorol., 148, 1210–1229,https://doi.org/10.1016/j.agrformet.2008.03.002, 2008.

Thomas, C. K., Law, B. E., Irvine, J., Martin, J. G., Pet-tijohn, J. C., and Davis, K. J.: Seasonal hydrology ex-plains interannual and seasonal variation in carbon and wa-ter exchange in a semiarid mature ponderosa pine for-est in central Oregon, J. Geophys. Res., 114, G04006,https://doi.org/10.1029/2009JG001010, 2009.

Vickers, D., Thomas, C. K., Pettijohn, C., Martin, J. G., and Law, B.E.: Five years of carbon fluxes and inherent water-use efficiencyat two semi-arid pine forests with different disturbance histories,Tellus B, 64, 17159, https://doi.org/10.3402/tellusb.v64i0.17159,2012.

Wang, W., Smith, J. A., Ramamurthy, P., Baeck, M. L.,Bou-Zeid, E., and Scanlon, T. M.: On the correlationof water vapor and CO2: application to flux partitioningof evapotranspiration, Water Resour. Res., 52, 9452–9469,https://doi.org/10.1002/2015WR018161, 2016.

Webster, R.: Regression and functional relations, Eur. J.Soil. Sci., 48, 557–566, https://doi.org/10.1111/j.1365-2389.1997.tb00222.x, 1997.

Wiekenkamp, I., Huisman, J. A., Bogena, H. R., Graf, A., Lin,H. S., Drüe, C., and Vereecken, H.: Changes in measured spa-tiotemporal patterns of hydrological response after partial de-forestation in a headwater catchment, J. Hydrol., 542, 648–661,https://doi.org/10.1016/j.jhydrol.2016.09.037, 2016.

Williams, M., Rastetter, E. B., Fernandes, D. N. Goulden, M. L.,Wofsy, S. C., Shaver, G. R., Melillo, J. M., Munger, J. W.,Fan, S.-M., and Nadelhoffer, K. J.: Modelling the soil-plant-atmosphere continuum in a Quercus-Acer stand at Harvard For-est: the regulation of stomatal conductance by light, nitrogen andsoil/plant hydraulic properties, Plant Cell Environ., 19, 911–927,https://doi.org/10.1111/j.1365-3040.1996.tb00456.x, 1996.

Williams, C. A., Scanlon, T. M., and Albertson, J. D.: Influ-ence of surface heterogeneity on scalar dissimilarity in theroughness sublayer, Bound.-Lay. Meteorol., 122, 149–165,https://doi.org/10.1007/s10546-006-9097-x, 2007.

Wollschläger, U., Attinger, S., Borchardt, D., Brauns, M., Cuntz,M., Dietrich, P., Fleckenstein, J. H., Friese, K., Friesen, J.,Harpke, A., Hildebrandt, A., Jäckel, G., Kamjunke, N., Knöller,K., Kögler, S., Kolditz, O., Krieg, R., Kumar, R., Lausch, A.,Liess, M., Marx, A., Merz, R., Mueller, C., Musolff, A., Norf,H., Oswald, S.E., Rebmann, C., Reinstorf, F., Rode, M., Rink,K., Rinke, K., Samaniego, L., Vieweg, M., Vogel, H.-J., Weitere,M., Werban, U., Zink, M., and Zacharias, S.: The Bode hydro-logical observatory: a platform for integrated, interdisciplinaryhydro-ecological research within the TERENO Harz/CentralGerman Lowland Observatory, Environ. Earth Sci., 76, 25 pp.,https://doi.org/10.1007/s12665-016-6327-5, 2017.

Xue, Q., Weiss, A., Arkebauer, T. J., and Baenziger, P. S.: Influenceof soil water status and atmospheric vapor pressure deficit on leafgas exchange in field-grown winter wheat, Environ. Exp. Bot.,51, 167–179, https://doi.org/10.1016/j.envexpbot.2003.09.003,2004.

Zeeman, M. J., Eugster, W., and Thomas, C. K.: Concur-rency of coherent structures and conditionally sampled day-time sub-canopy respiration, Bound.-Lay. Meteorol., 146, 1–15,https://doi.org/10.1007/s10546-012-9745-2, 2013.

Zeeman, M. J., Mauder, M., Steinbrecher, R., Heidbach, K. Eckart,E., and Schmid, H. P.: Reduced snow cover affects productivityof upland temperate grasslands, Agr. Forest Meteorol., 232, 514–526, https://doi.org/10.1016/j.agrformet.2016.09.002, 2017.

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