Biogeosciences, 14, 389–401, 2017www.biogeosciences.net/14/389/2017/doi:10.5194/bg-14-389-2017© Author(s) 2017. CC Attribution 3.0 License.

Dynamics of canopy stomatal conductance, transpiration, andevaporation in a temperate deciduous forest, validated bycarbonyl sulfide uptakeRichard Wehr1, Róisín Commane2, J. William Munger2, J. Barry McManus3, David D. Nelson3, Mark S. Zahniser3,Scott R. Saleska1, and Steven C. Wofsy2

1Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721, USA2John A. Paulson School of Engineering and Applied Sciences and Department of Earth and Planetary Sciences,Harvard University, Cambridge, MA 02138, USA3Aerodyne Research Inc., Billerica, MA 01821, USA

Correspondence to: Richard Wehr (rawehr@email.arizona.edu)

Received: 30 August 2016 – Published in Biogeosciences Discuss.: 2 September 2016Revised: 3 January 2017 – Accepted: 3 January 2017 – Published: 26 January 2017

Abstract. Stomatal conductance influences both photosyn-thesis and transpiration, thereby coupling the carbon andwater cycles and affecting surface–atmosphere energy ex-change. The environmental response of stomatal conduc-tance has been measured mainly on the leaf scale, and theo-retical canopy models are relied on to upscale stomatal con-ductance for application in terrestrial ecosystem models andclimate prediction. Here we estimate stomatal conductanceand associated transpiration in a temperate deciduous forestdirectly on the canopy scale via two independent approaches:(i) from heat and water vapor exchange and (ii) from car-bonyl sulfide (OCS) uptake. We use the eddy covariancemethod to measure the net ecosystem–atmosphere exchangeof OCS, and we use a flux-gradient approach to separatecanopy OCS uptake from soil OCS uptake. We find that theseasonal and diurnal patterns of canopy stomatal conduc-tance obtained by the two approaches agree (to within ±6 %diurnally), validating both methods. Canopy stomatal con-ductance increases linearly with above-canopy light inten-sity (in contrast to the leaf scale, where stomatal conductanceshows declining marginal increases) and otherwise dependsonly on the diffuse light fraction, the canopy-average leaf-to-air water vapor gradient, and the total leaf area. Based onstomatal conductance, we partition evapotranspiration (ET)and find that evaporation increases from 0 to 40 % of ET asthe growing season progresses, driven primarily by rising soiltemperature and secondarily by rainfall. Counterintuitively,

evaporation peaks at the time of year when the soil is dryand the air is moist. Our method of ET partitioning avoidsconcerns about mismatched scales or measurement types be-cause both ET and transpiration are derived from eddy co-variance data. Neither of the two ecosystem models testedpredicts the observed dynamics of evaporation or transpira-tion, indicating that ET partitioning such as that providedhere is needed to further model development and improveour understanding of carbon and water cycling.

1 Introduction

Stomata are the adjustable pores through which carbon diox-ide (CO2) enters and water vapor exits leaves. Stomatastrongly influence both carbon and water cycling and are akey point of coupling between them (Lin et al., 2015). Stom-ata also influence surface–atmosphere energy exchange viathe latent heat of water vaporization. How readily a leaf’s ora canopy’s stomata conduct gas is determined by their num-ber and degree of opening and is quantified by stomatal con-ductance. At the leaf level, stomatal conductance has beenextensively modeled both empirically and theoretically, withboth approaches describing it as proportional to net photo-synthesis, given fixed CO2 and water vapor concentrations inthe air (Collatz et al., 1991; Medlyn et al., 2011). However,scaling leaf-level stomatal conductance up to the canopy is

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

390 R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation

problematic because of the complex heterogeneity of thecanopy and its light environment (Bonan et al., 2011). Someempirical evidence suggests that on the canopy scale, stom-atal conductance is not proportional to photosynthesis: asphotosynthetically active radiation (PAR) increases, canopy-integrated stomatal conductance (estimated from eddy co-variance measurements of ecosystem–atmosphere heat andwater vapor exchange) responds linearly while photosynthe-sis responds nonlinearly (Wehr and Saleska, 2015). A linearresponse of canopy stomatal conductance to PAR has alsobeen inferred from sap flux measurements (Schäfer, 2011).However, estimates of stomatal conductance based on sapor water vapor flux measurements involve assumptions (e.g.about evaporation, leaf temperature, and plant internal stor-age) that have contributed substantial uncertainty (Schäfer,2011; Wehr and Saleska, 2015). Our objective here is to testWehr and Saleska’s (2015) method for estimating canopystomatal conductance from the water vapor flux against anew, independent method based on carbonyl sulfide (OCS)– and then to use stomatal conductance to partition evapo-transpiration.

OCS is currently a focus of ground- and satellite-basedmeasurements (Kuai et al., 2014; Montzka et al., 2007) andmodel development (Berry et al., 2013), owing mainly to itspotential as a large-scale proxy for gross primary production(GPP) (Blonquist et al., 2011). That potential stems from thefact that OCS is taken up by leaves (Sandoval-Soto et al.,2005), somewhat analogously to CO2. However, while hy-drolysis of both OCS and CO2 is catalyzed by the enzymecarbonic anhydrase (CA), the net rate of CO2 hydrolysis de-pends on downstream reactions involving light while the rateof OCS hydrolysis does not (Berry et al., 2013). Thus, theleaf OCS uptake is directly related not to GPP but to CAactivity and to the conductance of the diffusive pathway be-tween the air and the chloroplast (Commane et al., 2015).That pathway consists of the leaf boundary layer (i.e. thethin layer of stagnant air on the surface of the leaf), stomata,and mesophyll, with stomata typically being the most influ-ential component (Wehr and Saleska, 2015). On the ecosys-tem scale, the uptake of OCS by the canopy leaves should begiven by

F = gCn; g =(g−1

b + g−1s + g

−1m + g

−1CA

)−1, (1)

where F is the flux of OCS into the leaves (pmol m−2 s−1);Cn is the molar mixing ratio of OCS (to air) in thecanopy airspace (pmol mol−1); gb, gs, and gm are thecanopy-integrated conductances to OCS diffusion throughthe leaf boundary layer, stomata, and mesophyll, respectively(mol m−2 s−1); and gCA is the reaction rate coefficient forOCS destruction by CA, expressed as a “biochemical con-ductance” (mol m−2 s−1). Equation (1) approximates the dif-fusive pathway as being linear, thereby neglecting possibledifferences between the parallel pathways associated with in-dividual leaves, as well as the three-dimensionality of diffu-

sion through the mesophyll. This approximation will be jus-tified a posteriori.

In addition to being taken up by the canopy, OCS is alsotaken up or emitted by soils, with the direction and mag-nitude of the flux depending on soil type, temperature, andmoisture (Ogée et al., 2016; Sun et al., 2016; Whelan etal., 2016). The interpretation of large-scale OCS concen-trations or fluxes therefore requires understanding of howboth canopy and soil processes contribute to the overallecosystem–atmosphere OCS exchange.

Here we compare canopy stomatal conductance derivedfrom ecosystem–atmosphere heat and water vapor exchange(Wehr and Saleska, 2015) to that derived from canopy OCSuptake via Eq. (1), validating both methods by their agree-ment. The canopy OCS uptake is measured by using a sub-canopy flux-gradient approach to partition eddy covariancemeasurements of net ecosystem–atmosphere OCS exchangeinto canopy and soil components. Mesophyll conductance isestimated using an empirical temperature-dependent func-tion, and boundary layer conductance is estimated using atheoretical model; we are not able to test these estimatesbecause the gas exchange is not sensitive to them. For thebiochemical conductance, we test two simple assumptions:(i) that it is constant and (ii) that it depends on temperature.

Based on the validated canopy stomatal conductance, wepartition eddy covariance measurements of total ecosystem–atmosphere water vapor exchange (that is, evapotranspira-tion, or ET) into transpiration and evaporation, and exam-ine their diurnal and seasonal patterns. Various empirical andtheoretical methods have been used to estimate these waterfluxes in other ecosystems (Kool et al., 2014), but the presentmethod is advantageous because all fluxes are derived fromecosystem-scale eddy covariance data, minimizing concernsabout mismatched scales or measurement types. Finally, wecompare the estimated water fluxes to predictions by twoecosystem models.

2 Methods

2.1 Site description

The data presented here were collected from May throughOctober of 2012 and 2013 at the Harvard Forest Environ-mental Measurements Site (HF-EMS) in Petersham, Mas-sachusetts, USA. The site is located in a temperate decidu-ous forest dominated by red oak and red maple (with somehemlock, white pine, and red pine) and has been describedin detail previously (Urbanski et al., 2007). Leaf area index(LAI) at the site is steady at about 5 after leaf expansion andbefore autumnal abscission, although there are interannualdifferences of up to 10 % (Wehr and Saleska, 2015).

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R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation 391

2.2 OCS measurements

The ecosystem–atmosphere exchange of OCS was mea-sured by eddy covariance using a closed-path quantum cas-cade laser spectrometer (QCLS) manufactured by Aero-dyne Research Inc. and deployed at the site. This QCLS isan improved version of the one described in Commane etal. (2015). The QCLS recorded the OCS concentration in airat 4 Hz with a 1σ precision of 12 parts per trillion (ppt).

The QCLS was added to the existing air-conditioned in-strument shack, about 10 m from the base of the eddy fluxtower, and sampled air in series after a separate QCLS thatmeasured CO2 isotopologue fluxes (Wehr et al., 2013). Airwas sampled sequentially from seven heights on the tower(0.2, 1.0, 7.5, 12.7, 18.3, 24.1, and 29.0 m) through 1/4′′

(outside diameter) Eaton Synflex 1300 tubing with Teflon fil-ters at the inlets to keep out particles. The system’s 3 h dutycycle included three eddy covariance measurements (30 mineach) separated by profile measurements (seven inlets at1 min per inlet), as well as eight soil chamber measurements(5 min per chamber; Sect. 2.3) and two QCLS calibrationsusing gas cylinders (one calibration every 90 min).

The eddy covariance measurements used the 29 m in-let (about 4 m above the top of the canopy), which wason the same boom as the Applied Technologies Inc. sonicanemometer used to measure the wind (this anemometer ispart of the site’s long-running eddy covariance system; Ur-banski et al., 2007). The eddy covariance calculations fol-lowed the procedure described previously for CO2 isotopo-logues (Wehr et al., 2013). As the CO2 isotopologue andOCS spectrometers shared the same gas flow system, theco-spectral correction for high-frequency signal attenuationfor CO2 was applied also to OCS (the CO2 measurement ismuch less noisy and so gives a much more precise correc-tion). This approach assumes that OCS and CO2 suffer fromthe same attenuation, which would not be true for a “sticky”molecule like H2O. Fluxes for periods with a friction velocityof less than 0.17 m s−1 were not used (Urbanski et al., 2007).Storage of OCS in the canopy airspace was accounted for bythe profile measurements, which were also used for the flux-gradient approach used to partition canopy uptake from soiluptake (Sect. 2.4).

The gas cylinders contained known amounts of CO2 andnegligible OCS; they were used to calibrate the CO2 isotopo-logue QCLS (Wehr et al., 2013) and to simultaneously cali-brate the zero offset of the OCS QCLS. Drift in the zero off-set (caused by changes in the QCLS’s spectral baseline) wasby far the dominant source of error in the raw OCS measure-ments. To correct for such drift, the zero offset calibrations(one every 90 min) were linearly interpolated in time in post-processing.

2.3 Soil chamber CO2 measurements

Of the eight automated soil chambers sampled, only fourwere used here; these four were situated in a 5× 5 m plotabout 50 m to the south of the flux tower. The other fourwere in an adjacent plot that had been trenched to ex-clude live roots for another study. Each chamber consistedof a polyvinyl chloride (PVC) collar extending 5 cm intothe ground and covering a surface area of 0.07 m2. Aboveground, chamber heights were approximately 20 cm. ThePVC lid opened pneumatically under the control of a Camp-bell Scientific CR1000 data logger. An airtight seal betweenthe lid and collar was achieved by a neoprene gasket on thecollar. The chamber design is described in further detail else-where (Savage et al., 2014).

The chambers could not be used to measure the OCS effluxfrom the ground because materials used in the chamber flowsystem (particularly in the diaphragm pump and the chamberneoprene seal) emitted large amounts of OCS. The systemwas built for CO2 measurements as part of a separate studyand could not practicably be replaced. Thus, the chamberswere used instead to determine the CO2 efflux for the flux-gradient method described in Sect. 2.4.

Each chamber was sampled for 5 min once every hour. Forthe first 1.5 min, the chamber remained open (as it did whennot being sampled). For the following 3.5 min, the cham-ber was closed so that CO2 accumulated in the chamber. Astraight line was fit to the rise in the CO2 concentration overtime, and the slope of the fit line was used to calculate theCO2 flux into the chamber. Chamber closures for which thecoefficient of determination (r2) for the line fit was less than0.9 were rejected. The CO2 efflux from the soil was calcu-lated as the average of the valid fluxes from the four cham-bers.

2.4 Partitioning canopy uptake from soil uptake

A sub-canopy flux-gradient approach was used to parti-tion the net OCS flux into ground and canopy components.This approach assumed that OCS and CO2 were transportedto/from the ground by the same turbulent eddies and that theeddy transport could be treated as gradient-driven, so that theratio of the gradients of OCS and CO2 just above the groundwould be equal to the ratio of their fluxes into the ground:

FOCSground = F

CO2ground(C

OCS1.0 −C

OCS0.2 )/(C

CO21.0 −C

CO20.2 ), (2)

where the F are fluxes into the ground (the CO2 flux is neg-ative) and the C are molar mixing ratios of OCS or CO2 toair, measured at 0.2 m or 1.0 m above the ground, on the fluxtower. FOCS

ground calculated from Eq. (2) was smoothed versustime using a Loess filter, with a time window of about 12 hused for each local second-order regression. The canopy up-take of OCS was then calculated as the difference betweenthe total ecosystem uptake and the smoothed FOCS

ground. The as-sumption that the eddy transport near the ground could be

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392 R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation

treated as gradient-driven is questionable, as turbulent trans-port in forest canopies is dominated by large, quasiperiodiceddy motions (Raupach et al., 1996). Nonetheless, the con-sistency of the calculated soil OCS uptake over the diel cycleand over the growing season (Sect. 3.1) suggests that the as-sumption is sufficient for our purposes. Moreover, the calcu-lated soil OCS uptake varied by less than 0.2 pmol m−2 s−1

between low- and high-turbulence conditions as quantifiedby the friction velocity (results not shown).

This approach neglects horizontal heterogeneity in thefluxes. In reality, respiration rates vary spatially, and the au-tomated soil chambers used to measure FCO2

ground were locatedin an area where belowground respiration was on averageabout 50 % higher than in the typical eddy covariance sam-pling footprint, based on comparison to a multiyear synthesis(Giasson et al., 2013) of over 100 000 soil chamber measure-ments in that footprint. For this reason, we scaled the mea-sured CO2 efflux from the ground by a factor of 0.7 to ob-tain FCO2

ground. The flux tower itself, where the gradients weremeasured, was located about 20 m to the north of the cham-bers, and the effective footprint of the near-ground concen-tration measurements is unclear. These spatial mismatches inthe sampling footprints introduce additional uncertainty intothe mean magnitude of the soil OCS uptake but should haveat most a minor effect on its temporal patterns.

2.5 Estimating the diffusive conductances

The leaf boundary layer, stomatal, and mesophyll resistancesto CO2 or water vapor transport were estimated (along withleaf temperature) as described for the same forest site in Ap-pendix B of Wehr and Saleska (2015). Each resistance r(s m−1) was converted into a conductance g (mol m−2 s−1)

as follows:

g =P

RTL

1r, (3)

where P is air pressure (Pa), R is the universal gas constant(8.314 J mol−1 K−1), and TL is leaf temperature (K). The re-sulting conductances for CO2 or water vapor transport werethen converted into conductances for OCS transport as fol-lows (Stimler et al., 2010):

gb = gH2Ob /1.56, (4)

gs = gH2Os /1.94, (5)

gm = gCO2m , (6)

where the subscripts b, s, and m refer to the boundary layer,stomata, and mesophyll, respectively.

For the reader’s convenience, we now summarize the equa-tions used to calculate the resistances to CO2 or water vaportransport in Wehr and Saleska (2015). The boundary layer

resistance to water vapor transport was calculated as

rH2Ob = 2

(ScPr

) 23 150

LAI

√L

uh

1∫0

e0.5α(1−ζ )φ (ζ )dζ, (7)

where Sc is the Schmidt number for water vapor (0.67), Pr isthe Prandtl number for air (0.71), LAI is the leaf area in-dex (i.e. single-sided leaf area per unit ground area, mea-sured as described previously; Wehr and Saleska, 2015), Lis the characteristic leaf dimension (0.1 m), uh is the windspeed at the top of the canopy (m s−1), ζ is height as afraction of canopy top height, ϕ(ζ ) is the vertical profileof light absorption normalized such that

∫ 10 φ (ζ )dζ = 1, and

α = 4.39− 3.97e−0.258×LAI is the extinction coefficient forthe assumed exponential wind profile. The light absorptionprofile ϕ(ζ ) is used here as a proxy for the heat source pro-file.

Using the leaf boundary layer resistance to heat (rheatb =

rH2Ob /0.92), the leaf temperature was calculated as

TL =Hrheat

bρaCp

+ Tn, (8)

whereH is the measured eddy flux of sensible heat (W m−2),ρa is the density of air (kg m−3), Cp is the specific heat ca-pacity of air (J kg−1 K−1), and Tn is the canopy airspacetemperature (K). Surface temperatures estimated based onheat flux in this way have been termed “aerodynamic tem-peratures” to contrast them with radiometric temperatures(Kustas et al., 2007). The canopy airspace temperature Tnwas derived from the above-canopy air temperature using aturbulent eddy conductance derived in turn from the corre-sponding CO2 gradient and net ecosystem exchange (NEE).The above-canopy CO2 value was measured at 29 m and thewithin-canopy CO2 value was the average of measurementsat 12.7 and 18.3 m (canopy top height is about 25 m). The12.7 and 18.3 m measurements were generally indistinguish-able during the day due to efficient turbulent mixing.

The mesophyll resistance to CO2 transport was calculatedas

rCO2m =

P

RTL

(LAI× 0.188

× exp(−

12

( ln((TL− 273.15)/28.8)0.610

)2))−1

, (9)

following the empirical temperature response for Quercuscanariensis measured by Warren and Dreyer (Warren andDreyer, 2006), which agrees with the value determined byManter and Kerrigan (Manter and Kerrigan, 2004) at 25 ◦Cfor Quercus rubra (red oak), which dominates our site (Wehrand Saleska, 2015). There is debate in the literature as towhether mesophyll conductance varies also in response tolight, humidity, and other rapidly changing environmental

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R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation 393

variables (Flexas et al., 2012, 2008; Tholen et al., 2012).Some studies have argued that mesophyll conductance co-varies with stomatal conductance on a timescale of minutes(Flexas et al., 2008), whereas others have argued that an ap-parent correlation between the two conductances results fromfailing to account for diffusion of CO2 from the mitochondriato the chloroplasts (Tholen et al., 2012). Because the stom-atal and biochemical conductances limit OCS uptake at oursite, changing the mesophyll conductance to be perfectly cor-related with the stomatal conductance (but with a mean valuegiven by Eq. 9) has a negligible effect on the predicted OCSuptake from Eq. (1). We thus were unable to use OCS fluxesto directly address debates about controls on mesophyll con-ductance.

The stomatal resistance to water vapor transport was cal-culated (in the water-flux method) as

rH2Os =

1LAI

(b0eb1VPGeb2χ

)PAR

, (10)

where PAR is incident photosynthetically active radiation(µE m−2 s−1), VPG is the water vapor pressure gradient (Pa)between the canopy airspace and the sub-stomatal cavity, andχ is the clear-sky index (i.e. the ratio of observed PAR to thePAR that would have been observed for the same solar zenithangle under clear skies). The coefficients b0, b1, and b2 areempirically determined by fitting Eq. (10) to the followingwater vapor flux-gradient equation during times when wa-ter vapor flux was dominated by transpiration (i.e. evapora-tion was minimal, typically several days after rain, excludingmornings with possible dew evaporation):

rH2Os =

VPGRTnE

− rH2Ob , (11)

where E is the eddy flux of water vapor (i.e. ET,mol m−2 s−1) measured by the long-running HF-EMS eddycovariance system. In Eqs. (10) and (11), the vapor pressuregradient is calculated as

VPG= eSAT (TL)− en, (12)

where eSAT(TL) is the saturation vapor pressure (Pa) at tem-perature TL and en is the vapor pressure (Pa) in the canopyairspace. With b0 = 1.442×10−4, b1 =−4.035×10−4, andb2 =−0.8473, Eq. (10) was able to explain 92 % of the vari-ability (r2

= 0.92) in hourly evapotranspiration over threeentire growing seasons, during periods when evaporationwas minimal (Wehr and Saleska, 2015). It was necessary,however, to use wind-direction-dependent LAI because ofecosystem heterogeneity surrounding the HF-EMS site, asdescribed in Wehr and Saleska (2015). The clear-sky indexis used as a convenient proxy for diffuse light fraction inEq. (10); when available, measurements of the diffuse lightfraction can be used instead.

Equations (8), (11), and (12) can be combined to obtainthe Penman–Monteith (PM) equation (Monteith et al., 1965),

which is commonly used to calculate stomatal conductance.In principle, the two approaches are equivalent. However, thePM equation expresses H as the residual of the other termsin the energy budget (i.e. net radiation Rn, latent heat fluxλE, conductance to ground G, and energy storage S) be-cause measurements of H were not available when the PMequation was derived. As H is measured at all eddy fluxsites, using the PM equation to calculate stomatal conduc-tance from eddy flux measurements ofE is unnecessarily cir-cuitous. Moreover, it yields a different result in practice be-cause the measured energy budget is incomplete at most eddyflux sites, including ours, with the radiative input exceedingthe turbulent output by about 20 %. This energy balance clo-sure problem has been repeatedly investigated but the cul-prit remains unclear and might vary between sites (Wilson etal., 2002; Foken, 2008; Lindroth et al., 2010). If the closureproblem were known to be due to low bias in the eddy covari-ance method, as suggested by Foken (2008), then it wouldbe appropriate to adjust H and E to satisfy energy balancewhile maintaining the measured Bowen ratio (H/λE), eitherby modifying the PM equation as in Wohlfahrt et al. (2009)or by multiplying H and E by (Rn−G− S)/(H + λE) inEqs. (8) and (11); however, recent evidence suggests that theproblem is due to energy storage in the soil and biomass in-stead (Lindroth et al., 2010). At our site, the original PMequation underestimates stomatal conductance by 20 % com-pared to Eqs. (8), (11), and (12).

Equations (10)–(11) constitute the water-flux method forestimating stomatal conductance. To obtain stomatal conduc-tance from our OCS measurements, we rearranged Eq. (1) tosolve for gs and inserted the measured canopy OCS uptakeF along with the boundary layer, mesophyll, and biochem-ical conductance estimates described in this section and inSect. 2.6. As mentioned above (and see Sect. 3.2), the stom-atal and biochemical conductances were limiting to OCS up-take at our site, and so the calculated stomatal conductancewas not sensitive to the boundary layer and mesophyll con-ductances used.

At night, the leaf–air water vapor gradient was too smallto drive measurable transpiration, and so Eqs. (10) and (11)could not be used to determine nighttime rs. Instead, we setnighttime rs so as to obtain agreement between predicted andobserved nighttime canopy OCS uptake (Sect. 3.2). Night-time stomatal conductance turned out to be small enoughthat the canopy OCS uptake was completely insensitive toall other parameters within their plausible bounds.

The OCS- and water-flux methods for estimating stomatalconductance are illustrated as a flow chart in Fig. 1.

2.6 Modeling the carbonic anhydrase activity

The one term in Eq. (1) that is not constrained by measure-ments, empirical models, or established theory is the bio-chemical conductance associated with carbonic anhydraseactivity, gCA. Apparent CA activity depends on the amount

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394 R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation

Figure 1. Flowchart of the OCS- and water-flux methods for es-timating stomatal conductance. Note that the assumed CA activityand the empirical models for gb, gm, and gs also depend on leafarea index (not shown).

of CA enzyme and on where it is located relative to the inter-cellular air spaces, but little is presently known about eitherof those things (Berry et al., 2013). We therefore tested twosimple assumptions for gCA that allow us to solve Eq. (1).First, we assumed CA activity to be constant on the leaf scale,with the value 0.055 mol m−2 s−1 chosen to give the closestagreement with the observations; thus,

gCA = 0.055×LAI. (13)

Second, we assumed gCA to follow an Arrhenius function ofleaf temperature:

gCA = 0.8(0.055×LAI)eE0R

(1Tref−

1TL

), (14)

where E0 (40 J mol−1) is the activation energy and the ad-ditional factor of 0.8 was chosen to maintain agreement withthe observations at noon given the arbitrary reference temper-ature Tref = 20 ◦C. The magnitude of E0 controls the mag-nitude of the temperature dependence, but the choice of E0does not impact our findings; the value 40 J mol−1 was cho-sen merely to be large enough to distinguish the predictionsbased on Eqs. (13) and (14).

2.7 Partitioning evapotranspiration

We calculated transpiration for the whole data record by in-verting Eq. (11) to solve for the water-flux E and insert-ing the stomatal resistance calculated from Eq. (10). Evap-oration was then calculated as the difference between tran-spiration and total measured water flux (that is, ET). Thismethod of partitioning ET is advantageous because both ETand transpiration are derived from eddy covariance data, min-imizing concerns about mismatched scales or measurementtypes. Such concerns arise when using sap flux sensors orgas exchange chambers to estimate transpiration, for exam-ple (Kool et al., 2014).

Figure 2. Composite diel cycles (including May through October of2012 and 2013) of soil uptake, canopy uptake, and predicted canopyuptake from Eq. (1), along with the differences between predictedand observed canopy uptake and PAR for reference. Lines connectthe mean values of each 2 h bin. Pale bands depict standard errorsin the means as estimated from the variability within each bin.

3 Results and discussion

3.1 Soil–atmosphere exchange of OCS

The soil was a consistent sink of OCS at this site (Figs. 2and 3). OCS uptake by soil was highly stable, with a meanof 2.2 pmol m−2 s−1 and no discernable diel or seasonal pat-terns (for May through October). That value is roughly inthe middle of the range reported for temperate forest soils(−1.45 to +8 pmol m−2 s−1) (Whelan et al., 2016). Labora-tory incubations of soy field soil have shown OCS uptake todepend strongly on soil temperature and water content (Whe-lan et al., 2016), but we see no indication of those dependen-cies in the field at our site. It may be that the dependenciesare difficult to detect because the ranges of soil temperature(∼ 9–18 ◦C) and volumetric water content (∼ 22–37 %) aretoo small. It may also be that the dependencies on tempera-ture and water offset one another: OCS production increasedwith temperature in the incubations (Whelan et al., 2015) andmight therefore be expected to be highest mid-season, whileOCS consumption peaked at roughly 20 % water content inthe incubations (Whelan et al., 2015) and might thereforealso be expected to be highest mid-season at our site.

3.2 Canopy stomatal conductance and OCS uptake

Nighttime uptake of OCS by the canopy averaged2.4 pmol m−2 s−1, consistent with a nighttime stomatal con-

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R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation 395

Figure 3. Composite seasonal cycles (including the years 2012 and2013) of daytime soil uptake, canopy uptake, and predicted canopyuptake from Eq. (1), along with the differences between predictedand observed canopy uptake. Lines connect the mean values of each2-week bin. Pale bands depict standard errors in the means as esti-mated from the variability within each bin.

ductance to OCS transport of 0.0016 mol m−2 s−1 on a leafarea basis (about 1/40 of the mean midday value). We usedthis value to generate the nighttime points on the predicteduptake curve in Fig. 2. The corresponding conductanceto water vapor transport is 0.0031 mol m−2 s−1. Nighttimestomatal conductance to water vapor transport in individ-ual red oak and red maple leaves at this site was previouslyreported to be no more than 0.05 mol m−2 s−1 (Daley andPhillips, 2006), in agreement with our result. At another site,measured values ranged from 0 to 0.039 mol m−2 s−1 with anaverage of 0.011 mol m−2 s−1 (Barbour et al., 2005), whichis about 4 times larger than found here using OCS. Previ-ous estimates of nighttime ecosystem OCS uptake at this siteaveraged about 4 pmol m−2 s−1 between April and Novem-ber (Commane et al., 2015), similar to the 4.6 pmol m−2 s−1

(= 2.2 soil+ 2.4 canopy) found here.During the day, Eq. (1) successfully predicted the diurnal

and seasonal patterns of canopy OCS uptake when CA activ-ity was assumed constant at 0.055 mol m−2 s−1 on a leaf areabasis (Figs. 2 and 3, dotted lines), except at dawn (see be-low). Apart from dawn, the agreement with observations waswithin ±3 % for the diurnal pattern and ±10 % for the sea-sonal pattern (1 standard deviation). Assuming CA activity tobe a function of temperature did not improve the agreement(Figs. 2 and 3, dashed lines). Rearranging Eq. (1) to solvefor gs using the measured canopy OCS uptake gave a diurnalcycle of stomatal conductance that agreed with that obtainedfrom Eq. (10) to within ±6 % (1 standard deviation), againapart from dawn (Fig. 4).

Figure 4. Composite diel cycles (including May through Octoberof 2012 and 2013) of the expected leaf boundary layer, stomatal,mesophyll, biochemical, and total conductances to OCS transportand chemical destruction, along with the stomatal and total conduc-tances derived from OCS uptake. Lower panels show air tempera-ture and PAR for context. Lines connect the mean values of each2 h bin. Pale bands depict standard errors in the means as estimatedfrom the variability within each bin. The boundary layer conduc-tance is likely overestimated at night (see text).

At dawn, no value of CA activity or mesophyll conduc-tance or boundary layer conductance was capable of bringingthe predicted canopy uptake into agreement with the observa-tions because the stomatal conductance was strongly limitingat that time of day (Fig. 4). To obtain agreement, the stom-atal conductance would have had to be 5 times larger thanestimated from the measured heat and water fluxes, whichis implausible. We therefore suspect that the apparent surgein canopy OCS uptake at dawn is a measurement artifact re-sulting from a failure of the vertical profile measurements onthe flux tower to adequately capture changes in OCS stor-age within the canopy and sub-canopy airspaces in the eddycovariance footprint (which is tens to hundreds of meters up-wind of the tower). Such a failure could occur because ofdifferences in storage between the eddy covariance footprintand the profile footprint and/or because of hidden OCS stor-age in unsampled airspaces, such as in the leaf litter layer orwithin tree crowns. Specifically, we speculate that our ver-tical profile measurements on the tower do not adequatelycapture the depletion of the OCS concentration in the canopyand sub-canopy airspaces overnight and – more importantlyhere – the replenishing of that concentration with increasedturbulence at dawn. Thus, eddy flux that is in reality serving

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396 R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation

to replenish the OCS concentration is misinterpreted as be-ing taken up by the leaves. We have sometimes observed asimilar phenomenon in CO2, but with reversed sign: CO2 ac-cumulates in the canopy and sub-canopy airspaces overnightand is flushed out at dawn, so that if the changes in canopyand sub-canopy CO2 concentration are not adequately mea-sured, there appears to be a dawn pulse in respiration and inthe net ecosystem–atmosphere CO2 exchange.

The total conductance g, which controls the OCS uptake,is limited by gs early and late in the day but co-limited bygs and gCA through the middle of the day, so that g has amuch flatter diurnal peak than gs (Fig. 4; note the log scale).Equation (1) must therefore include the correct diurnal pat-terns and magnitudes of both stomatal conductance and CAactivity in order to reproduce the observed diurnal patternof canopy OCS uptake. Notwithstanding the dawn artifact,then, the close agreement between the temporal patterns ofobserved and predicted stomatal conductance in Fig. 4 (ortotal conductance in Fig. 4 or OCS uptake in Fig. 2) consti-tutes a strong validation of the simple empirical descriptionof canopy stomatal conductance in Eq. (10), which shouldprovide a reliable means to partition ET at this mesic forestsite.

Equation (10) was distilled from a more general equationallowing for direct temperature and soil moisture effects ongs and for a saturating response of gs to PAR, but those ef-fects were found to be negligible (Wehr and Saleska, 2015).The linear response of (canopy-scale) gs to PAR in Eq. (10)contrasts with the saturating response generally observed onthe leaf scale and implies that leaf-level stomatal models likethe Ball–Berry model (Collatz et al., 1991) or models basedon optimality theory (Medlyn et al., 2011) should not be ap-plied directly on the canopy scale (as in a “big leaf” canopymodel; De Pury and Farquhar, 1997), at least at this site. Notethat even though canopy gs responds linearly to PAR, it willappear to show a saturating response when the vapor pressuregradient is not controlled for, as PAR and the vapor gradienttend to be positively correlated (because clouds and moisturego together), while gs and the vapor gradient are negativelycorrelated (because stomata close to limit plant water loss).The insensitivity of gs to soil moisture is somewhat surpris-ing, but as the Harvard Forest is a mesic site, it might bethat soil water does not become limiting to the large treeseven in a dry year such as 2012. The insensitivity to temper-ature, on the other hand, is not surprising: it has been argued(Lloyd and Farquhar, 2008) that photosynthesis declines athigh temperature almost entirely due to the indirect effect oftemperature on stomatal conductance via the leaf-to-air wa-ter vapor pressure gradient, and Eq. (10) is consistent withthat view.

The boundary layer conductance gb is likely overestimatedat night in Fig. 4 because the value from Eq. (7) is weightedvertically according to the profile of light absorption calcu-lated from the leaf area density profile and the solar zenithangle – a method appropriate to sunlight-driven heat and CO2

fluxes during the day but not to any flux at night. Because thestomatal conductance is strongly limiting at night, this over-estimation of gb is inconsequential here.

While treating CA activity as constant on a leaf area ba-sis was sufficient to reproduce the observed canopy OCSuptake at this site, seasonal variations in CA activity at the±15 % level could also be consistent with our observations,and might be important for some studies.

We did not observe during 2012–2013 any repeat of theanomalous OCS emission previously reported at this site forJuly 2011 (Commane et al., 2015), despite similar environ-mental conditions. The cause of that apparent emission re-mains unknown.

3.3 Gross primary productivity and leaf relativeuptake

The success of Eq. (1) in predicting canopy OCS uptake sup-ports the theoretical expectation that canopy OCS uptake isdependent on the atmospheric OCS mixing ratio, the diffu-sive conductance, and CA activity – and is therefore not di-rectly related to GPP, which depends also on the enzyme Ru-bisco and on light. There is nonetheless widespread interestin using OCS uptake as a proxy for GPP. So for interestedreaders, we show how GPP and OCS uptake compare overthe diel cycle and over the growing season in Figs. 5 and 6,using both isotopic and standard partitioning methods for es-timating GPP as described in Wehr et al. (2016). We includea common metric for comparison, the leaf relative uptake(LRU): LRU is defined as the ratio of the canopy OCS uptaketo GPP, divided by the ratio of the atmospheric OCS concen-tration to the atmospheric CO2 concentration. Figures 5 and6 show that, as expected, LRU is inversely correlated withPAR, as PAR can directly limit uptake of CO2 but not ofOCS.

3.4 Transpiration and evaporation

On average over the growing season, evaporation accountedfor 16 % of ET; however, the proportion increased stronglythrough the growing season, from 0 % in May to 40 % in Oc-tober (Fig. 7). This trend was mostly due to increasing evapo-ration rather than decreasing transpiration, except in October,when leaves began to fall. Perhaps counter to intuition, evap-oration peaked at the time of year when the soil was dry (lowvolumetric soil moisture) and the air was moist (low vaporpressure deficit). There are two reasons. First, rainwater thatcollects on the leaf litter layer (Wilson et al., 2000), exposedsoil surfaces, and canopy surfaces contributes to evapora-tion but is not affected by transpiration, which draws downthe volumetric soil moisture in summer. Second, evaporationfrom the ground is driven by the water vapor pressure gradi-ent between the ground and the atmosphere, which dependsnot only on the available liquid water and the relative hu-midity but also on the temperatures of the ground and atmo-

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R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation 397

Figure 5. Composite diel cycles (including May through October of2012 and 2013) of canopy OCS uptake and GPP, along with LRUand PAR. GPP from the isotopic and standard partitioning meth-ods described in Wehr et al. (2016) are shown. Lines connect themean values of each 2 h bin. Pale bands depict standard errors inthe means as estimated from the variability within each bin.

sphere. For a given amount of liquid water or relative humid-ity, the vapor pressure increases with temperature.

In light of the above, we can identify different controlson the ratio of evaporation to ET in different seasons (color-coded in the lower panels of Fig. 7): in spring, despite plentyof rain and soil moisture, evaporation was suppressed by thenegative soil-to-air vapor pressure gradient that resulted fromthe lagged rise in soil temperature relative to the atmosphere(red); in summer, evaporation was mostly limited by rain-fall (blue); and in autumn, evaporation remained steady butthe ratio of evaporation to ET increased because transpira-tion declined with LAI (yellow). There was also a periodin September when the ratio of evaporation to ET remainedconstant despite declining rainfall, due again to the laggedrise in soil temperature (red). The overall increasing trendin evaporation through the season was driven primarily bysoil temperature rather than by rain, soil moisture, or atmo-spheric vapor pressure deficit (VPD). A similar pattern inevaporation was observed from the ground surface of anothertemperate deciduous forest via sub-canopy eddy covariancemeasurements (Wilson et al., 2000), but soil temperature wasnot discussed as a driver of that pattern.

On average, evaporation and the ratio of evaporation to ETwere highest immediately following rain and then declined(Fig. 8). ET, on the other hand, increased with time since rain,likely because of drier air, increased sunlight, and associatedwarmer surface temperatures.

Figure 6. Composite seasonal cycles (including the years 2012 and2013) of canopy OCS uptake and GPP, along with LRU and PAR.GPP from the isotopic and standard partitioning methods describedin Wehr et al. (2016) is shown. Lines connect the mean values ofeach 2-week bin. Pale bands depict standard errors in the means asestimated from the variability within each bin.

Although our transpiration and evaporation estimates arenot direct measurements, only three sets of assumptions arecommon to both of the methods by which we derived thoseestimates from our measurements: (1) the assumptions in-volved in the eddy covariance method, which seem to fail atdawn as discussed in Sect. 3.2; (2) the boundary layer resis-tance model described in Sect. 2.5, to which our estimates areinsensitive (within plausible bounds); and (3) the applicationof stoma-scale gas transport equations on the canopy scale,which neglects biological and environmental heterogeneitywithin the canopy but is a sufficiently good approximationto allow the observed temporal patterns of canopy OCS up-take to be precisely predicted from the observed heat and wa-ter vapor exchange, as shown in Sect. 3.2. Given the closeagreement between the two otherwise independent methods,our estimates of transpiration and evaporation should be ac-curate.

The stomatal and evaporative dynamics found here cantherefore be used to evaluate and improve the representationof carbon and water cycling in biosphere models. For exam-ple, Fig. 7 compares our empirical water-flux estimates topredictions by the Ecosystem Demography 2 (ED2) (Med-vigy et al., 2009) and Simple Biosphere 3 (SiB3) (Baker etal., 2008) models for the same site and exactly the same setof hourly measurement intervals. (The ED2 and SiB3 param-eters were optimized for the site using standard data that in-cluded NEE and ET but not our partitioned water fluxes orOCS measurements.) ED2 reproduces the seasonal variationof measured ET well but for the wrong reasons: it underesti-mates transpiration by a factor of 2 and greatly exaggerates

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398 R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation

Figure 7. Composite seasonal cycles (including the years 2012 and2013) of daytime evapotranspiration (ET), transpiration, and evap-oration, as estimated here and as predicted by the ED2 and SiB3models, along with the ratio of evaporation (Evap) to ET, the at-mospheric vapor pressure deficit (VPD), the soil–atmosphere vaporpressure difference, rainfall, the leaf area index (LAI), and the vol-umetric soil moisture content between 0 and 30 cm depth (VSM).Lines connect the mean values of each 2-week bin. Pale bands de-pict standard errors in the means as estimated from the variabilitywithin each bin. The soil–air vapor pressure difference is based onthe assumption of saturated air at the soil surface and therefore re-flects the maximum possible difference. Color-coding in the lowerpanels highlights which environmental control is dominating the be-havior of the Evap /ET ratio. Model output was filtered to includeonly times when measurements were made.

evaporation, particularly in spring. Moreover, ED2 predictstranspiration to fall off too rapidly in spring and autumn.SiB3 underestimates transpiration by just 20 % and evapo-ration by just 25 %, on average, but does not predict the earlysummer peak in transpiration or its persistence in autumn.Neither model predicts the observed increase in evaporationthrough the growing season, the magnitude of which is equalto 25 % of summertime ET. We do not troubleshoot the bio-sphere models here; suffice it to say that the stomatal and

Figure 8. Daytime evapotranspiration, transpiration, evaporation,and the ratio of evaporation to evapotranspiration versus time sincethe cessation of rain.

evaporative dynamics in this ecosystem are not accuratelyrepresented and that our findings and methods provide newmeans to diagnose and improve those aspects of the models.

4 Conclusion

Partitioning the net ecosystem–atmosphere exchange of OCSinto canopy and soil components revealed that the soil wasa consistent sink of OCS at this mesic, temperate deciduousforest site, while the canopy took up OCS according to a sim-ple prediction based on the OCS concentration in the air, theestimated diffusive conductance from the air to the chloro-plast, and the assumption of constant carbonic anhydrase ac-tivity on a leaf area basis.

Our findings validate (i) a simple empirical function forcanopy stomatal conductance at this site, which depends lin-early on PAR (in contrast to the leaf scale) and otherwise de-pends only on the leaf-to-air water vapor gradient, the diffuselight fraction, and the leaf area index; (ii) the approach usedto derive that function from eddy covariance measurementsof heat and water vapor exchange (Wehr and Saleska, 2015);and (iii) the assumption that CA activity can be treated asconstant over time in this ecosystem. Our findings also sug-gest that OCS-flux measurements could serve as a generaltool for probing stomatal conductance in other ecosystemsand possibly in leaf-level and laboratory studies.

Using the empirical function for stomatal conductance,we partitioned evapotranspiration and found that evaporationpeaked in late summer when the soil was dry and VPD waslow, mostly due to the strong influence of soil temperatureon the evaporation rate. From May to October, evaporationincreased from 0 to 40 % of evapotranspiration, with a meanof 16 %. Neither of the two ecosystem models that we testedpredicted the observed increase in evaporation through thegrowing season, and neither accurately predicted the sea-

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R. Wehr et al.: Dynamics of canopy stomatal conductance, transpiration, and evaporation 399

sonal dynamics of transpiration. Through empirical quan-tification of canopy stomatal conductance, transpiration, andevaporation, the methods described here enable more strin-gent evaluations of model performance and improve our abil-ity to predict carbon and water cycling.

5 Data availability

The OCS data are available from the Harvard For-est Data Archive (http://harvardforest.fas.harvard.edu/harvard-forest-data-archive) under record HF214(doi:10.6073/pasta/7ed7b4d1fc7ad303998e76143a3b279a;Commane et al., 2014). The other flux and site data areavailable from the same archive under record HF004(doi:10.6073/pasta/1580a910a8a1a154cb59c941b252613a;Munger and Wofsy, 1999).

Author contributions. J. Barry McManus, David D. Nelson,Mark S. Zahniser, Róisín Commane, and Steven C. Wofsy de-veloped the OCS spectrometer. Róisín Commane deployed andmanaged the spectrometer at the forest with the assistance ofRichard Wehr and J. William Munger. Richard Wehr wrote thedata processing and analysis algorithms and analyzed the re-sults with input from Róisín Commane, J. William Munger, andScott R. Saleska. Richard Wehr prepared the manuscript with con-tributions from all coauthors.

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

Acknowledgements. This research was supported by the US De-partment Of Energy (DOE)’s Office of Science’s TerrestrialEcosystem Science program (award DE-SC0006741) and the Ag-nese Nelms Haury Program in Environment and Social Justice atthe University of Arizona. Design of the OCS spectrometer wassupported by the DOE’s Small Business Innovation Research pro-gram (award DE-SC0001801). Operation of the HFEMS flux toweris supported by the DOE via the Ameriflux network, and the toweris a component of the Harvard Forest Long-Term EnvironmentalResearch (LTER) site supported by the US National Science Foun-dation (NSF). Soil chamber CO2 flux data were provided by Kath-leen Savage at the Woods Hole Research Center and Eric Davidsonat the University of Maryland Center for Environmental Science,also supported by award DE-SC0006741. Soil temperature and soilmoisture data were provided by E. Nicoll at the Harvard Forest, sup-ported by the NSF LTER program. ED2 model output was providedby Daniel Scott and Paul Moorcroft at Harvard University, also sup-ported by award DE-SC0006741. SiB3 model output was providedby Ian Baker at Colorado State University, supported by the USNational Oceanic and Atmospheric Administration’s AtmosphericChemistry, Carbon Cycle and Climate program, the US NationalAeronautics and Space Administration’s Carbon Cycle Science pro-gram, and the NSF’s Science and Technology Center for MultiscaleModeling of Atmospheric Processes, managed by Colorado StateUniversity.

Edited by: G. WohlfahrtReviewed by: two anonymous referees

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