Carbonyl sulfide (COS) as a tracer for canopy photosynthesis, transpiration and stomatal conductance: potential and limitations

The theoretical basis for the link between the leaf exchange of carbonyl sulfide (COS), carbon dioxide (CO2) and water vapour (H2O) and the assumptions that need to be made in order to use COS as a tracer for canopy net photosynthesis, transpiration and stomatal conductance, are reviewed. The ratios of COS to CO2 and H2O deposition velocities used to this end are shown to vary with the ratio of the internal to ambient CO2 and H2O mole fractions and the relative limitations by boundary layer, stomatal and internal conductance for COS. It is suggested that these deposition velocity ratios exhibit considerable variability, a finding that challenges current parameterizations, which treat these as vegetation-specific constants. COS is shown to represent a better tracer for CO2 than H2O. Using COS as a tracer for stomatal conductance is hampered by our present poor understanding of the leaf internal conductance to COS. Estimating canopy level CO2 and H2O fluxes requires disentangling leaf COS exchange from other ecosystem sources/sinks of COS. We conclude that future priorities for COS research should be to improve the quantitative understanding of the variability in the ratios of COS to CO2 and H2O deposition velocities and the controlling factors, and to develop operational methods for disentangling ecosystem COS exchange into contributions by leaves and other sources/sinks. To this end, integrated studies, which concurrently quantify the ecosystem-scale CO2, H2O and COS exchange and the corresponding component fluxes, are urgently needed. We investigate the potential of carbonyl sulfide (COS) for being used as a tracer for canopy net photosynthesis, transpiration and stomatal conductance by examining the theoretical basis of the link between leaf COS, carbon dioxide (CO2) and water vapour (H2O) exchange. Our analysis identifies several limitations that need to be overcome to this end, however at present we lack appropriate ecosystem-scale field measurements for assessing their practical significance. It however appears that COS represents a better tracer for CO2 than H2O. Concurrent measurements of ecosystem scale COS, CO2 and H2O exchange are advocated.


INTRODUCTION
Canopy net photosynthesis, transpiration and stomatal conductance are key conceptual terms in most contemporary models of ecosystem carbon and water cycling (Sitch et al. 2008). While net photosynthesis, transpiration and stomatal conductance can be quantified accurately with enclosures at the leaf scale [e.g. von Caemmerer & Farquhar (1981), but see Rodeghiero, Niinemets & Cescatti (2007)], obtaining reliable estimates at the canopy scale is much more difficult. Scaling up net photosynthesis, transpiration and stomatal conductance measured in leaf enclosures to the canopy scale requires minimum knowledge on (1) the response of leaf gas exchange rates to environmental drivers; (2) how this response changes with depth in the canopy; (3) the vertical variation of environmental drivers within the plant canopy; and (4) the vertical distribution of the assimilating/ transpiring plant area (Kruijt, Ongeri & Jarvis 1997;Wohlfahrt et al. 2010). Transpiration of individual trees can be directly quantified by sap flux methods; however, up-scaling methods are again needed to turn these measurements into canopy transpiration (Wilson et al. 2001). Enclosures that include entire ecosystem are prone to artefacts due to modifications of the environmental conditions (Dore et al. 2003). In addition, ecosystem enclosures yield the net ecosystem CO2 and H2O exchange, that is, they are unable to partition between canopy net photosynthesis/transpiration and CO2/H2O fluxes from/to the soil and other ecosystem components. This drawback also holds for micrometeorological techniques such as the eddy covariance method, which, however has the advantage of being unobtrusive and able to provide near-continuous long-term flux data (Baldocchi, Hicks & Meyers 1988;Baldocchi 2003). In order to recover canopy net photosynthesis and transpiration from net ecosystem fluxes of CO2 and H2O, it is necessary to concurrently quantify/estimate the confounding CO2 and H2O fluxes -a non-trivial task in particular for CO2, which has multiple sources in an ecosystem. Converting estimates of canopy transpiration to stomatal conductance in turn is fraught with problems due to difficulties with the correct specification of the vapour gradient between the transpiring surface and ambient air (Magnani et al. 1998). As a consequence, available estimates of canopy net photosynthesis, transpiration and stomatal conductance are inherently uncertain, which in turn translates into uncertain model parameterizations and predictions.
Recently, several authors have advocated measurements of COS exchange to provide independent constraints on canopy net photosynthesis in particular (Sandoval-Soto et al. 2005; Montzka et al. 2007;Campbell et al. 2008;Brugnoli & Calfapietra 2010;Seibt et al. 2010;Stimler et al. 2010aStimler et al. , 2011, as well as on canopy transpiration and stomatal conductance (Seibt et al. 2010). The rationale for these proposals derives from both leaf and (very few) ecosystem flux measurements, which show a high degree of co-variation between the net exchange rates of CO2, H2O and COS (Xu, Bingemer & Schmidt 2002;Sandoval-Soto et al. 2005;Stimler et al. 2010a).
Given the promising possibility of quantifying ecosystem-scale COS exchange by using the eddy covariance method in combination with new analytical techniques (Graus, Müller & Hansel 2010;Stimler, Nelson & Yakir 2010b), in order to better constrain canopy photosynthesis, transpiration and stomatal conductance, the objective of the present paper is: (1) to review the mechanistic link between leaf-and ecosystem-scale CO2, H2O and COS fluxes; (2) to critically evaluate the assumptions required for estimating canopy net photosynthesis, transpiration and stomatal conductance from COS exchange measurements; and finally (3) to indicate areas of future research.

THE LINK BETWEEN LEAF CO2, H2O AND COS EXCHANGE
We begin our assessment with a review of the equations describing the diffusive flux of CO2, H2O and COS in/out of leaves, as sketched in Fig. 1. Leaf net photosynthesis (Fl C ) is given as Figure 1. Schematic illustration of the diffusion pathways of CO2, H2O and COS into/out of a leaf. Blue panels represent mole fractions; red panels are conductances using abbreviations introduced in the text. Additional abbreviations include: ggp C and ggp S referring to gas phase conductances for CO2 and COS in the intercellular space; gw C and gw S (including cell wall, plasma membrane and cytosol) and cw C and cw S referring to cell wall conductances and mole fractions of CO2 and COS, respectively; ccs C and ccs S referring to chloroplast surface mole fractions of CO2 and COS; gch C referring to the chloroplast conductance to CO2 and cc C referring to the chloroplast CO2 mole fraction. Following Stimler et al. (2010a), who concluded CA to be effectively located at the chloroplast surface, the end point for diffusion of COS is placed at the inside of the chloroplast surface.
and the leaf net flux of COS (Fl S ) as Here, c refers to mole fractions (subscripts: a . . . ambient air, i . . . intercellular space, c . . . chloroplast) and g to conductances (subscripts: b . . . boundary layer, s . . . stomata, i . . . internal). Note that we employ a sign convention by which fluxes directed into the leaf have a negative sign. The boundary layer and stomatal conductances may be interconverted between COS, CO2 and H2O based on their diffusivity (D) ratios, that is, where the exponent 'a' takes a value of 1 for gs (i.e. molecular diffusion) and 0.67 for gb (i.e. forced convection which typically applies in well-ventilated leaf enclosures) (Campbell & Norman 1998). gs S and gb S may thus be converted to their CO2 (H2O) counterparts by multiplication with ca. 1.21 (2.00) and 1.14 (1.59), respectively (Seibt et al. 2010;Stimler et al. 2010a). While Eqns 1 and 2 are well established (von Caemmerer & Farquhar 1981), Eqn 3 merits further explanation: the endpoint of the diffusion gradient for COS is the location of the enzyme CA, which appears to be available throughout the plasma membrane, cytosol, chloroplast envelope and stroma (Evans et al. 2009). Stimler et al. (2010a), following Gillon & Yakir (2000), concluded CA to be effectively located at the chloroplast surface, an assumption we graphically followed in Fig. 1. CA, which has an extremely high sensitivity to COS [larger by a factor of 1000 compared with CO2; Protoschill-Krebs, Wilhelm & Kesselmeier (1996)], is responsible for the hydration of COS, as nicely demonstrated by Stimler et al. (2011) with CA-deficient antisense lines of C3 and C4 plants.The hydration of COS is essentially a one-way reaction whereby one molecule H2S and CO2 are generated for each hydrated molecule COS (Protoschill-Krebs et al. 1996). As emissions of COS out of leaves have not been reported even at very low ambient COS concentrations (Seibt et al. 2010), it is reasonable to assume that the COS mole fraction at the CA reaction site (ci S ) is much smaller than its ambient concentration. We therefore follow others (Seibt et al. 2010;Stimler et al. 2010a) in assuming that c i S can be neglected, as has been done on the right-hand side of Eqn 3. As depicted in Fig. 1, the similarity in diffusion pathways of CO2 and COS depends on where actually most of COS becomes hydrated by CA, which is somewhere between the plasma membrane and the chloroplast stroma. Additional differences in gi S and gi C arise from differing biochemical reaction rates of CA and Rubisco, respectively, which are implicit in their numerical values.
In summary, the diffusion pathway of COS is not identical to, but more similar for CO2 than H2O (Fig. 1). In the following, we will discuss the implications of these differences for using COS as a tracer for canopy CO2 and H2O exchange.As previous studies were almost exclusively interested in linking photosynthesis to COS exchange, we first develop the procedure for estimating CO2 from COS fluxes and then turn to the subject of water vapour fluxes. We would like to note that the approach outlined below, in contrast to what several studies have suggested (Stimler et al. 2010a), allows the quantification of canopy net, but not gross photosynthesis. Gross photosynthesis equals net photosynthesis minus any autotrophic respiration that continues in the light (Larcher 2001), a dissimilatory process with no apparent link to leaf COS uptake.

Linking leaf-level COS and CO2 exchange
In order to provide independent estimates of net photosynthesis, leaf COS exchange measurements have to allow eliminating the unknowns in Eqn 1. Given that Eqn 3 contains three unknowns (gb S , gs S and gi S assuming Fl S and ca S to be known) and inserting Eqn 3 into Eqn 1, making use of Eqn 4, would add two new unknowns for the one removed, this is however not possible. This problem has been overcome by parameterization of the relationship between COS and CO2 fluxes through the ratio of their deposition velocities, that is, the flux, normalized with the ambient concentration, of COS relative to CO2 (for negative values of Fl C ), that is Based on an estimate of l C and measurements of ca C , ca S and Fl S , Fl C (negative values only) may then be simply calculated as (Campbell et al. 2008 Up to now, parameterizations of l C have treated it as a vegetation-type specific constant (Sandoval-Soto et al. 2005;Campbell et al. 2008;Seibt et al. 2010), but how constant is l C expected to be? In order to answer this question, we rearrange Eqns 1 and 3 to yield the respective deposition velocities, that is COS as a tracer for canopy gas exchange 659 Making use of the diffusivity ratios (Eqn 4), we now introduce a non-dimensional coefficient b C as which when combined with Eqn 5 yields the following expression: A similar, albeit less general, expression was derived by Seibt et al. (2010). It functionally relates the deposition velocities for CO2 and COS and shows that the CO2 deposition velocity will, for any given COS deposition velocity, vary with four unknowns: the ratio of intercellular to ambient CO2 concentration [cf. fig. 3 in Seibt et al. (2010)], gb S , gs S and gi S , which have been incorporated into our coefficient b C for convenience. By expressing these three conductances in a mutual fashion as ratios, that is, R g g Two limits of Eqn 11 are useful to explore: the first one relates to the case when Rbs approaches infinity, as might be observed in a well-ventilated leaf enclosure where gb >> gs.
In this case, it can be shown that b c ≡ 1.21 (1 + Rsi), that is, b C increases in a linear fashion with the ratio of stomatal to mesophyll conductance with the slope and y-intercept equal to 1.21, that is, the gs S /gs C ratio. The second limit relates to the case of an infinite gi s , that is, Rsi approaches zero. In this case, Eqn 11 reduces to β C bs bs ≡ + + 1 1 1 1 14 . which corresponds to an asymptotic increase from 1.14, that is, the gb S /gb C ratio, when Rbs is very small to the previously found limit of 1.21 when Rbs becomes very large. Assuming physically/physiologically plausible values of 1-100 and 0.001-2 for R bs and Rsi, respectively, yields b C values in the range of 1.2-3.6 ( Fig. 2). Combining these values with ci C / ca C ratios typical for C3 plants of 0.5-0.8 (Larcher 2001) yields a range of 0.6-4.3 for l C , broadly in correspondence with the spread of 0.4-10.3 reported by Sandoval-Soto et al. (2005) in a recent literature survey. Lower ci C /ca C ratios of C4 plants result in correspondingly lower l C values (Stimler et al. 2011). An example of the actual variability of l C as a function of the intercellular to ambient CO2 concentration and b C is shown in Fig. 3 using data digitized from fig. 6 of Stimler et al. (2010a). While part of the variability in l C relates to changes in the intercellular to ambient CO2 concentration ratio (leading to the asymptotic decrease as ci C / ca C decreases), it is also clear that part of the between-and within-species variability has to be ascribed to variability in b C and associated changes in Rbs and Rsi. An example of how diurnal variability in gb S and gs S may affect b C , and thus in turn l C , under field conditions, is given in Fig. 4 using boundary layer and stomatal conductance values measured over the course of 1 d in a temperate mountain grassland (Wohlfahrt et al. 2010). In this particular case, differences in b C values between the upper and lower canopies (1.4-1.8 and 1.2-1.3, respectively) were driven mainly by differences in stomatal conductance (assuming a constant gi S of 0.3 mol m -2 s -1 ), as Rbs values (6-21) were in a similar range in the upper and lower canopies. Assuming a ci C /ca C ratio of 0.7 (Larcher 2001) results in l C values of 1.8-2.3 and 2.5-2.6 in the upper and lower canopies, respectively. On the other hand, assuming a constant gi S is likely to be incorrect because experimental evidence suggests CA activity, which is implicit in gi S , to be dependent on leaf cellular pH (Sültemeyer 1998), light intensity (Moskvin et al. 2000), as well as to be under circadian control (Eriksson et al. 1998).
Another complicating issue, that up to now has not received appropriate attention, is whether l C determined from measurements in well-ventilated leaf enclosures is applicable to real-world, within-canopy transfer processes. Firstly, within plant canopies boundary layer conductances are not necessarily large as opposed to stomatal conductances (Baldocchi 1988), for example, combination of low wind speeds and vigorous transpiration. Secondly, transfer mechanisms across the boundary layer may be dominated by free instead of forced convection with light winds and strong leaf-to-air temperature gradients (Finnigan & Raupach 1987), which would change the exponent in Eqn 4 to 0.75 (Campbell & Norman 1998).
Both the variability in l C inferred from theoretical considerations (Fig. 2) and experimental evidence shown in Figs 3 and 4 suggest l C to differ between plant species and vary dynamically in response to changing environmental conditions.This conclusion seems to be inconsistent with constant l C values in the range of 2-3 reported in previous studies (Sandoval-Soto et al. 2005;Seibt et al. 2010). On the basis of Eqns 10 and 11, we suggest l C values on the order of 2-3 to reflect similar experimental conditions rather than an underlying universal principle. Most of the studies to date have been performed at leaf level under laboratory conditions by using enclosure systems [see review by Sandoval-Soto et al. (2005)] and thus tend to be biased towards high boundary layer (due to leaf enclosures usually being well ventilated) and relatively low stomatal conductances (due to limitations resulting from pot size and growth under relatively low light conditions). For example, for an infinite Rbs and a ci C /ca C ratio of 0.7, l C values between 2 and 3 are observed for Rsi < 0.4. Limited support for this hypothesis derives from the recent work of Sandoval-Soto et al. (2005), where field as opposed to laboratory studies tended to yield higher l C values. If true, the reliability of available l C values for estimating canopy net photosynthesis under field conditions may be seriously questioned.

Transferring the leaf-level COS-CO2 relationship to the canopy level
The ecosystem level net exchange of COS (Fe S ) comprises, in addition to the leaf exchange, flux contributions by above-and below-ground sources/sinks, that is Here, Fnl S represents above-ground COS flux contributions other than from leaves (i.e. woody organs, flowers, attached dead plant matter, etc.), and Fs S represents COS fluxes from/to the soil surface.Both COS emission from and uptake by soils have been reported, although COS emissions from soils in some older studies appear to be due to experimental artefacts caused by the use of COS-free instead of ambient air in soil enclosures (Watts 2000). Recent studies, where soil chambers were flushed with ambient air, have reported soil COS uptake rates relative to deposition to vegetation that ranged from negligible (Xu et al. 2002;White et al. 2010) to dominant (Kuhn et al. 1999). Velmeke (1993), cited in Xu et al. (2002), investigated COS exchange in branches with and without leaves and found deposition and emission of COS, respectively. Given the scarcity of ecosystem-scale COS flux measurements (Xu et al. 2002), the significance of soil and non-leaf COS exchange is thus unclear and Fnl S + Fs S in Eqn 12 should not be neglected a priori. Ideally, Fnl S + Fs S would be quantified concurrently with Fe S in order to derive

COS as a tracer for canopy gas exchange 661
canopy-scale Fl S by difference. Such an approach may however be problematic in practice, as there is a mismatch in footprint of soil/branch enclosure as opposed to abovecanopy micrometeorological flux measurements, which may be aggravated by the presence of spatial heterogeneity in COS sources/sinks. In addition, concurrent measurements of Fnl S + Fs S and Fe S would significantly increase the experimental effort.As an alternative, night-time measurements of Fe S might be used for estimating daytime Fnl S + Fs S , similar to the current practice of estimating daytime ecosystem respiration from night-time CO2 flux measurements (Wohlfahrt et al. 2005). For this approach to work, night-time leaf COS exchange should be negligible, as confirmed by Sandoval-Soto et al. (2005), who found COS uptake during darkness to virtually cease when stomata are closed. In contrast, White et al. (2010) reported significant COS uptake by loblolly pine during darkness. Micrometeorological night-time COS flux measurements may however be problematic due to methodological limitations during calm and stable atmospheric conditions (Aubinet 2008). It remains to be determined whether approaches for dealing with unreliable night-time measurements developed for CO2, for example, filtering of data according to the magnitude of turbulence and imputation of resulting gaps based on empirical regression models (Goulden et al. 1996;Gu et al. 2005) are applicable to COS as well.
As mentioned earlier, only a handful of concurrent ecosystem-scale COS and CO2 flux measurements have been published so far (Hofmann, Hofmann & Kesselmeier 1992;Bartell et al. 1993;Xu et al. 2002). In order to explore the magnitude and variability of ecosystem-scale l C and differences to leaf-scale values, we re-analysed COS, CO2 and H2O flux data collected by Xu et al. (2002) over a Norway Spruce forest in Germany using the relaxed eddy accumulation (REA) method. Due to the lack of concurrent measurements of Fnl S + Fs S and reliable night-time REA estimates of Fe S , we have assumed Fe S = Fl S . This simplification is supported by soil COS exchange measured at the same site by Steinbacher, Bingemer & Schmidt (2004) showing an average deposition of -0.81 Ϯ 0.03 pmol m -2 s -1 to the soil as opposed to an average ecosystem deposition of -93 Ϯ 11.7 pmol m -2 s -1 (Xu et al. 2002). Ecosystem COS flux measurements of Xu et al. (2002), however, were on average positive during the morning and the   evening when the NEE was positive (i.e. net loss of CO2 to the atmosphere), suggesting that other COS sources (e.g. woody plant material) may be playing an important role. Disentangling canopy net photosynthesis from NEE measured above the canopy would require estimates of soil and woody respiration, which were not available for this study. However, by following a common practice (Wohlfahrt et al. 2005), we used night-time NEE measurements under windy conditions for parameterizing RECO as a function of air temperature. RECO was then extrapolated to daytime temperature conditions to derive GPP as GPP = NEE -RECO. We have used GPP as a proxy for canopy net photosynthesis, recognizing that canopy net photosynthesis is larger (i.e. less negative) than GPP by the amount of CO2 respired from autotrophic tissues during daylight (Larcher 2001). l C was then calculated separately for NEE and GPP by dividing the measured ecosystem-scale COS fluxes normalized with ambient COS mole fractions with the measured NEE (inferred GPP) normalized with ambient CO2 concentrations in analogy to Eqn 5.
Values of l C calculated by considering NEE and GPP averaged 10.3 and 5.8 (Fig. 5), respectively. Considering that GPP overestimates canopy net photosynthesis, l C values resulted to be at least by a factor of 2 larger than the range of 2-3 reported by Sandoval-Soto et al. (2005) and Seibt et al. (2010) based on leaf-level laboratory enclosure studies. On a diurnal timescale, l C varied from 9 to 12.4 (38%) and from 4.4 to 7.1 (59%) for NEE and GPP, respectively. The range of l C variability is comparable in magnitude to the one deduced from diurnal changes in gb S and gs S (31%; Fig. 3), directly supporting our idea that changes in gb S , gs S (and most likely gi S ) cause diurnal variability in b C and thus in l C . With known l C values, Eqn 10 can be used to explore possible values for b C and ci C /ca C . Commonly observed ci C /ca C ratios between 0.5 and 0.8 resulted in b C values of 0.35-0.87, well below the theoretical limit of 1.14 calculated from Eqn 9. In order to reach b C values within the theoretical range (Fig. 2), ci C /ca C values of at least 0.85 are required. While ci C /ca C values > 0.8 are higher than the usual range (Larcher 2001), Huber (1993, cited in Seibt et al. (2010), indeed determined ci C /ca C values of 0.91-0.93 for Norway Spruce, resulting in b C of 1.9-2.5 (Fig. 5), that is, clearly within the range shown in Fig. 2.

ESTIMATING CANOPY TRANSPIRATION FROM COS EXCHANGE MEASUREMENTS
Although several authors have linked ecosystem H2O and COS flux measurements (Hofmann et al. 1992;Xu et al. 2002), to our knowledge only one study (Seibt et al. 2010)   explicitly mentioned the potential of COS as a tracer for estimating canopy transpiration. This may be due to the fact that the diffusion pathway of COS has less in common with H2O than CO2 (Fig. 1) and COS may thus be anticipated to be less suitable as a tracer for H2O.
In analogy to Eqn 10, the following link can be established between transpiration and the COS deposition velocity: The coefficient b V can be calculated in analogy to Eqn 9 but does not equal b C because of differences in the COS to CO 2 and H2O diffusivity ratios. The ratio of b V /b C varies between ca. 1.4 and 1.7, depending on Rbs.
Provided leaf temperature and atmospheric pressure (required to estimate the saturation water vapour mole fraction ci V ) are available and assuming a known value for b V (our previous discussion on b C applies here as well), Eqn 13 can in principle be used to infer transpiration on the basis of a measured COS deposition velocity. While leaf temperature is usually known with enough precision in leaf enclosures [but see Sharkey, Wiberley & Donohue (2008)], this is not granted at canopy scale under field conditions. Therefore, we further develop Eqn 13 according to Penman (1948) by introducing T1 = Ta + DT, where Ta represents air temperature and DT the difference between Tl and Ta. As a consequence, ci V /ca V in Eqn 13 can now be reformulated as: which holds for small values of DT and where e represents the vapour pressure and s the slope of the saturation vapour pressure function (Campbell & Norman 1998). Combining Eqns 13 and 14 yields, after some re-arrangement, the following expression: where VPD refers to the vapour pressure deficit of air, that is, es(Ta)-ea. Equation 15 clearly addresses the relationship between transpiration and COS deposition velocity showing how that relationship may be sensibly affected by changes in DT, Ta and ea, independently of b V . If DT = 0 (isothermal case), the right-hand side of Eqn 15 reduces to ((RH -1 -1) b V ) -1 , scaling positively with RH. When DT 0, additional nonlinear variability proportional to DT arises because s increases exponentially with temperature (Campbell & Norman 1998).
In contrast to the ci C /ca C ratio, which appears relatively conservative under a wide range of environmental conditions (Larcher 2001), the ratio of the saturation vapour pressure (at leaf temperature) to ambient vapour pressure may be expected to be much more variable, causing larger variability in l V as compared with l C . Radiometric leaf temperature measurements would greatly reduce this problem in principle, may though be difficult in practice due to contributions by non-transpiring components such as the soil surface and/or woody plant tissue (Sánchez et al. 2009). In addition, radiometric measurements of leaf temperature may not necessarily represent a good estimate to be used for calculating the intercellular saturation vapour pressure due to within-canopy differences in the sources of thermal radiation and latent heat (Campbell & Norman 1998).
Because to our knowledge no data regarding l V have been published so far, we again make use of the study of Xu et al. (2002) to investigate the magnitude and diurnal variability of l V at ecosystem scale.As shown in Fig. 5, l V results re-calculated from bin-averaged CO2, H2O and COS flux measurements over Norway Spruce (Xu et al. (2002); note that periods with average net COS emission were excluded). GPP was calculated by parameterizing RECO, derived from night-time NEE measurements under windy conditions (horizontal wind speed > 3 m s -1 ), as a function of air temperature which was then extrapolated to daytime conditions as GPP = NEE -RECO. b C values in (a) were calculated from measured l C values (based on GPP) and an ci C /ca C ratio of 0.92 [Huber (1993) cited in Seibt et al. (2010)]. Dashed lines in (b) refer to l V at various RHs calculated from b C shown in (a) and an average b V /b C ratio of 1.5.
to have an average value of 1.64 (ranging from 1.2 to 2.2), exhibiting higher and lower values in the morning/evening and noon, respectively, as expected from the positive relationship with RH and the typically lower RH values around noon. Assuming a constant b V /b C ratio, the additional variability in l V (81%) as opposed to GPP-based l C (59%) is due to diurnal variability in the ci V /ca V ratio, supporting our arguments raised previously.

ESTIMATING CANOPY STOMATAL CONDUCTANCE FROM COS EXCHANGE MEASUREMENTS
By re-arranging Eqn 3, leaf stomatal conductance to COS, which may be converted to CO2 or H2O via Eqn 4, may be calculated as: Equation (16) differs from the equations developed above for canopy net photosynthesis and transpiration in three different aspects: (1) the COS to CO2 (l C ) and H2O (l V ) deposition velocity ratios are not included; (2) instead, Eqn 16 contains two unknowns as absolute numbers -the Gb S and the Gi S ; (3) Gb S and Gi S represent bulk quantities: Gb S includes both the aerodynamic and the quasi-laminar boundary layer conductance (Monteith & Unsworth 1990), while Gi S is the integral of the internal conductance over the canopy leaf area -in order to emphasize this difference to the leaf-scale conductances used in Eqns 1-4, 7-11, we have used uppercase letters in Eqn 16.While models for the combined aerodynamic and quasi-laminar boundary layer conductance are available [but see Liu et al. (2007) for systematic uncertainties], little a priori knowledge is usually available on the magnitude of gi S , which is inter alia why l C and l V were introduced earlier, prohibiting a reliable up-scaling to Gi S . A better quantitative understanding of gi S (cf. Stimler et al. 2011) needs to be achieved to employ COS as a practical tool for estimating canopy stomatal conductance.

CONCLUSIONS
The theoretical basis for the observed co-variation of leaf net photosynthesis, transpiration and COS uptake was reviewed. In addition, the assumptions which are required to use COS as a tracer for canopy net photosynthesis, transpiration and stomatal conductance, were discussed. Based on our analysis, we identified the following two priorities for future research: 1 We showed that l C and l V are not constants, but vary as a function of ci C /ca C and ci V /ca V , respectively, and the ratios of boundary layer to stomatal and stomatal to internal conductance (Eqns 9-10 & 13). Due to the comparably more conservative nature of ci C /ca C and the more similar diffusion pathway, our theoretical analysis suggests COS to represent a better tracer for CO 2 than H2O. For routine application of Eqn 6 in field conditions, it will be necessary to develop a better understanding of the in situ variability and the factors controlling l C and l V , which may result to be quite different from what has been observed under laboratory conditions by using leaf enclosures. To this end, it will be more important to study the four component processes controlling l C and l V in greater detail than limiting the investigation to the deposition velocities ratios. A particularly important step into this direction, which is prerequisite to improving the potential of COS as a tracer for canopy conductance, is to better understand and quantify variability in gi S between species and on diurnal and seasonal time scales. A promising approach for independently characterizing l C under field conditions has already been put forward by Seibt et al. (2010), who showed that l C is related to the 13 C discrimination during photosynthesis and that for example d 13 C of leaf samples could be used as timeintegrated estimates for l C . 2 The potential of COS as a tracer for canopy-scale exchange processes hinges upon our ability to operationally disentangle leaf from any other ecosystem COS exchange. While progress has been made in understanding the factors which drive soil COS exchange (Kuhn et al. 1999;Van Diest & Kesselmeier 2008), we definitely need a better quantitative understanding of the contribution of soil and other non-leaf ecosystem components to the overall ecosystem-scale COS exchange. Here it appears that advantage can be taken from the vast amount of experience gathered in recent years in disentangling ecosystem CO2 flux components (Reichstein et al. 2005).
In summary, our study confirmed previous pioneering work highlighting the potential of COS as a tracer for canopy net photosynthesis; however, we have also indicated a number of limitations. For the first time, we have assessed the link between leaf COS and H2O exchange, addressing the potential and the limitations of COS as a tracer for canopy transpiration and stomatal conductance. At present, we face a serious lack of ecosystem-scale field measurements (Brühl et al. 2011) that represent an essential requirement for assessing the practical significance of these limitations and whether or not ecosystem COS flux measurements will be able to provide sensible constraints on canopy net CO2 and H2O exchanges. Such measurements will be of great value also for studies at larger scales (e.g. regional or global), which aim at inverting concurrent COS and CO2 concentration measurements to disentangle the components of the net ecosystem CO2 exchange (Campbell et al. 2008). We thus advocate concurrent measurements of ecosystem-scale COS, CO2 and H2O exchange and the corresponding component fluxes to allow testing and validation of our theoretical COS exchange models and their relation to canopy CO2 and H2O fluxes under field conditions. Here, great advancements can be expected from recent developments in analytical instrumentation (Graus et al. 2010; Stimler COS as a tracer for canopy gas exchange 665 et al. 2010b) that will allow quantifying ecosystem-scale COS exchange by using the eddy covariance method in the near future.