Carbonyl sulfide (COS) follows the same diffusion pathway into the leaf chloroplasts as CO~2~ and is consumed by the enzyme carbonic anhydrase (CA) ([@r1], [@r2]). The hydrolysis of COS via CA is irreversible ([@r3]), such that no respiration-like COS flux is evident under ambient conditions. Consequently, the atmospheric drawdown of COS above an ecosystem reflects the uptake of COS by plants, provided that other sources and sinks in the ecosystem are negligible or known. The dominant vegetative sink of COS was therefore recognized as a way to separate net ecosystem exchange of CO~2~ (NEE) into gross primary productivity (GPP) and respiration ([@r4][@r5][@r6]--[@r7]). With a known ratio of COS to CO~2~ uptake at the leaf level, GPP can be determined from COS ecosystem fluxes (F~COS-E~) following ([@r5], [@r7]):$$\text{GPP}_{\text{COS}} = - \text{F}_{\text{COS} - \text{E}}\frac{\text{C}_{\text{a},\text{CO}2}}{\text{C}_{\text{a},\text{COS}}}\frac{1}{\text{LRU}},$$with atmospheric mole fractions C~a,COS~ and C~a,CO2~, and the leaf-scale relative uptake ratio (LRU) = F~COS~/F~CO2~·C~a,CO2~/C~a,COS~, with F~COS~ and F~CO2~ being the flux rates of COS and CO~2~ at the leaf level). LRU is also referred to as the ratio of deposition velocities of COS and CO~2~ ([@r8]). The accuracy of LRU is key in translating COS fluxes into GPP, and several studies have derived LRU for different plant species from chamber enclosure measurements ([@r8][@r9][@r10][@r11][@r12][@r13][@r14][@r15][@r16]--[@r17]). Those LRU values ranged from 0.4 to 9.5 with a median of 1.75 and with 50% of the values between 1.48 and 2.46 around the median (see ref. [@r18] for an overview).

Many of the laboratory studies measured LRU under constant conditions and few have investigated LRU response to environmental variations or under field conditions ([@r13], [@r17]). If effects of light, humidity, and temperature on dissolution, diffusion, and relevant enzyme reactions differ between COS and CO~2~, then LRU should be expected to vary ([@r13]). It has already been found that LRU changes with light intensity ([@r13], [@r14], [@r17], [@r19], [@r20]). This is due to the light independence of the CA enzyme that controls F~COS~ ([@r14], [@r21], [@r22]), whereas F~CO2~ depends on the light reactions in the photosystems.

LRU values are typically larger than 1.0, which implies that the deposition velocities of COS are typically higher than those of CO~2~. This is attributed to a lower reaction efficiency of ribulose-1,5-bisphosphate carboxylase/oxygenase with CO~2~ than that of CA with COS ([@r9], [@r12]), which can be expected because CA is known to be the enzyme with the highest molar activity ([@r2]). Therefore, COS uptake is not expected to be strongly limited by biochemical reactions, unlike CO~2~ uptake, which is limited by light reactions in the photosystems. As a result, the stomatal conductance should be a more limiting component for F~COS~ than for F~CO2~, which makes LRU dependent on stomatal conductance ([@r17]). In line with this hypothesis, it has been found that a further decrease of LRU at high radiation levels may occur under conditions of increasing vapor pressure deficit (VPD) and lower stomatal conductance in the afternoon ([@r17]). Furthermore, the fact that COS and CO~2~ do not share the photochemical reaction in the leaf, but only the diffusive pathway between air and the chloroplast, has recently motivated the use of COS as a tracer for diffusive conductance, of which the stomatal conductance is the dominant component ([@r20], [@r23]).

In this study, we aim to characterize F~COS~ at the branch level under field conditions and investigate if F~COS~ and F~CO2~ respond similarly to environmental changes. We performed continuous COS and CO~2~ branch chamber measurements over 5 mo during spring recovery and early summer in 2017 in a boreal forest in Finland, making this a study investigating F~COS~ at the branch level over different phenological stages. This dataset allows us to test the applicability of findings from previous studies---which were confined to laboratory conditions or field measurements over a short period of time---to different phenological stages and environmental conditions. With the different components of F~COS~ (ecosystem, soil, and branch fluxes) being characterized at the site, we are able to derive COS-based GPP estimates and test the effect of the variability of LRU on GPP.

Results and Discussion {#s1}
======================

Responses of F~COS~ and F~CO2~ to Light and Stomatal Conductance. {#s2}
-----------------------------------------------------------------

Both F~COS~ and F~CO2~ show a strong diurnal cycle with a sink during the daytime ([Fig. 1*A*](#fig01){ref-type="fig"}). The increase of COS uptake (more negative F~COS~) early in the morning coincides with the increase of stomatal conductance (g~s,COS~), whereas the increase of F~CO2~ lags behind due to its light dependence. The peak of F~COS~ is typically 1 h earlier than that of F~CO2~ ([Fig. 1*A*](#fig01){ref-type="fig"}), which was also observed by Geng and Mu ([@r24]) in a Chinese deciduous forest. Unlike F~CO2~, F~COS~ shows continued uptake during nighttime of −1.44 ± 0.95 pmol m^−2^⋅s^−1^ (median ± SD) in May--July ([Fig. 1*A*](#fig01){ref-type="fig"}). The different responses of F~COS~ and F~CO2~ to light is also evident from [Fig. 2 *A* and *B*](#fig02){ref-type="fig"}; F~CO2~ increases with the photosynthetically active radiation (PAR) up to ∼700 µmol m^−2^⋅s^−1^, whereas F~COS~ increases up to a PAR value of ∼200 µmol m^−2^⋅s^−1^. The light dependence of F~CO2~ is caused by two distinct processes: (*i*) carbon fixation depends on the light reactions in the photosystems ([@r25]) and (*ii*) stomatal aperture, which controls the intercellular CO~2~ available for fixation, increases with light as a strategy to optimize carbon gain against water loss ([@r26], [@r27]). In contrast to CO~2~, the COS biochemical reactions are light independent ([@r14], [@r21], [@r22]), but F~COS~ responds to light solely due to the light response of stomatal conductance.

![Average diurnal cycles of F~COS~ and F~CO2~ (*A*), LRU (*B*), and g~s,COS~ and VPD (*C*) between 18 May and 13 July 2017 (the peak season), for chambers 1 (solid) and 2 (dashed). g~s,COS~ is determined in two ways: daytime g~s,COS~ (solar elevation angle \> 0°) is determined from the Ball--Berry model, nighttime g~s,COS~ (solar elevation angle \< 0°, shaded) is determined from transpiration measurements ([*Methods*](#s8){ref-type="sec"})---both independent of F~COS~. We report stomatal conductance as that to COS (g~s,COS~), which relates to stomatal conductance to H~2~O (g~s,H2O~) through g~s,COS~ = g~s,H2O~/2.00, where the value 2.00 is the ratio of H~2~O and COS diffusivities ([@r12]). Time series of F~COS~, F~CO2~, LRU, and meteorological parameters can be found in [*SI Appendix*, Fig. S1](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental).](pnas.1807600116fig01){#fig01}

![Responses of F~COS~, F~CO2~, and LRU to light and of F~COS~ to g~s,COS~. Average F~COS,~ F~CO2~ (*A* and *B*) and LRU (*C* and *D*) versus PAR, and F~COS~ versus g~s,COS~ (*E* and *F*) from 18 May to 13 July for chambers 1 (*Left*) and 2 (*Right*). Data are plotted as the median of 15 equal-sized bins in the *x* range. The error bars represent the 25th and 75th percentiles of data in each bin. For the correlation of F~COS~ with g~s,COS~ (*E* and *F*) the different colors represent different light conditions: nighttime (blue); daytime with low light conditions (PAR \< 150 and 100 µmol m^−2^⋅s^−1^ for chambers 1 and 2, respectively; green); daytime with high light conditions (PAR \> 300 µmol m^−2^⋅s^−1^; orange). A transition phase between low and high PAR values is neglected. The coefficient of determination (R^2^), slope (sl), significance level (P), and number of data (n) are given for a linear regression through the median values (*E* and *F*).](pnas.1807600116fig02){#fig02}

F~COS~ and F~CO2~ peak early in the morning when VPD is still low and g~s,COS~ is high ([Fig. 1 *A* and *C*](#fig01){ref-type="fig"}), which confirms a shared stomatal control on both fluxes. We find strong correlations of F~COS~ with g~s,COS~ at all light levels and even during night ([Fig. 2 *E* and *F*](#fig02){ref-type="fig"}). This is strong evidence that F~COS~ could provide a means to constrain stomatal conductance---during both day and night---and therefore links to both the carbon and water cycles ([@r23]). However, we also find that, at high light levels, the increase of F~COS~ with g~s,COS~ is smaller than at low light levels ([Fig. 2 *E* and *F*](#fig02){ref-type="fig"}). This suggests that during the daytime F~COS~ is colimited by nonstomatal resistances, which will be further discussed in the next section.

In the correlation with PAR, we find a decrease of COS uptake (less negative F~COS~) toward higher light levels ([Fig. 2 *A* and *B*](#fig02){ref-type="fig"}) that is consistent with a decrease of g~s,COS~ ([*SI Appendix*, Fig. S2](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)), while on average F~CO2~ remains constant. This is in line with the hypothesis that the stomatal closure would affect F~COS~ more than it would affect F~CO2~ because the stomatal conductance is a more dominant component for F~COS~ than it is for F~CO2~ ([@r17]). This may also explain why the peak of F~COS~ occurs earlier than that of F~CO2~ ([Fig. 1*A*](#fig01){ref-type="fig"}); F~COS~ becomes more limited as VPD increases and g~s,COS~ is limited ([Fig. 1*C*](#fig01){ref-type="fig"}), whereas F~CO2~ can continue to increase due to increasing PAR.

LRU varies largely over a day, which reflects the fact that COS uptake is light independent, whereas CO~2~ uptake is restricted under low light conditions, e.g., around sunrise and sunset ([Fig. 1*B*](#fig01){ref-type="fig"}). Therefore, LRU decreases exponentially toward high PAR ([Fig. 2 *C* and *D*](#fig02){ref-type="fig"}), which is similar to the findings in Stimler et al. ([@r14]) and Sun et al. ([@r17]). The variation of LRU with PAR largely explains the variation of daytime LRU between days ([*SI Appendix*, Fig. S1](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)). Moreover, LRU does not become constant toward high light conditions ([Fig. 2 *C* and *D*](#fig02){ref-type="fig"}, *Insets*), which was also observed by Sun et al. ([@r17]) for vegetation in a freshwater marsh. At high light levels we find a correlation between LRU and VPD (*P* \< 0.01) and between LRU and g~s,COS~ (*P* \< 0.05) in the peak of the growing season ([*SI Appendix*, Fig. S3](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)), which is likely due to the different responses of F~COS~ and F~CO2~ to g~s,COS~. These findings support that differential stomatal limitations on F~COS~ and F~CO2~ drive LRU variation.

The light-saturated LRU (for PAR \> 700 µmol m^−2^⋅s^−1^) is on average 1.1, which is on the lower end of LRU values reported in previous studies (see ref. [@r18] for an overview). Note that previous LRU measurements could have been affected by the dependence of LRU to PAR. LRU values have not always been determined at high light levels, which would have led to overestimated LRU. For example, Kesselmeier and Merk ([@r9]) determined LRU at a light level of 300 µmol m^−2^⋅s^−1^ and Sandoval-Soto et al. ([@r8]) also measured LRU in Scots pine but at a light level of 600 µmol m^−2^⋅s^−1^ where F~CO2~ is not PAR saturated.

Internal Conductance of COS Limits F~COS~ During Daytime. {#s3}
---------------------------------------------------------

We estimated the internal conductance to COS (g~i,COS~), which is a combination of nonstomatal conductance terms, and find that during daytime g~i,COS~ is smaller than g~s,COS~ (see [*SI Appendix*, Fig. S4](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental) and the accompanying explanation). The ratio of g~s,COS~ over g~i,COS~ determines the relative importance of the two conductances on F~COS~ and thereby also on LRU (see equation 8 in ref. [@r12]). The fact that we find a relatively low g~i,COS~ compared with g~s,COS~ during the daytime implies that g~i,COS~ has a relatively large control on F~COS~. Wehr et al. ([@r23]) estimated that the biochemical conductance (the CA activity) was of similar magnitude as g~s,COS~ during the daytime. The fact that we also find a relatively high importance of g~i,COS~ emphasizes the need to take into account g~i,COS~ on the total conductance of COS uptake ([@r17]). The day--night difference of g~s,COS~ is larger than that of g~i,COS,~ and therefore g~s,COS~ has a relatively larger effect on day--night differences of F~COS~ than g~i,COS~ has. This means that the diurnal change of F~COS~ is largely controlled by g~s,COS~. Furthermore, g~i,COS~ has a relatively larger limiting role on F~COS~ during daytime than during nighttime ([*SI Appendix*, Fig. S4](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)). This variable role of g~i,COS~ over a day explains why the relation between F~COS~ and g~s,COS~ is different between different moments of the day, as depicted by different light levels in [Fig. 2 *E* and *F*](#fig02){ref-type="fig"}. If F~COS~ is used to determine g~s,COS~, and the limiting role of g~i,COS~ on F~COS~ is ignored, this would lead to underestimation of daytime g~s,COS~. When the F~COS~--g~s,COS~ relationship is assumed to be the same for daytime and nighttime (following the blue curve in [Fig. 2 *E* and *F*](#fig02){ref-type="fig"}), g~s,COS~ would be equal to 0.012 and 0.020 mol m^−2^⋅s^−1^ for chambers 1 and 2, respectively, at F~COS~ of −3 pmol m^−2^⋅s^−1^ (the average F~COS~ at high light levels). These values are, respectively, 46% and 48% smaller than what is actually observed (following the orange curve in [Fig. 2 *E* and *F*](#fig02){ref-type="fig"}). Therefore, ignoring the role of g~i,COS~ would lead to a substantial underestimation of g~s,COS~.

Seasonal Variation of LRU Influenced by Environmental Variables. {#s4}
----------------------------------------------------------------

[Fig. 3](#fig03){ref-type="fig"} shows the light-saturated LRU per month binned by VPD. The monthly median LRU decreases by 0.2 from April to July. No significant correlation between LRU and VPD can be detected before June, whereas a significant decrease of LRU with VPD is observed in June and July (indicated by the significance levels in [Fig. 3](#fig03){ref-type="fig"}). The fact that the LRU--VPD correlation follows the progression of the growing season is associated with the increase of daytime VPD. Early in the season F~COS~ and F~CO2~ are not solely limited by stomatal conductance but rather by low temperatures, as is shown in [*SI Appendix*, Fig. S5](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental). The low temperatures suppress enzyme activities or mesophyll diffusion and therefore g~i,COS~ has a relatively larger limiting effect on F~COS~ than g~s,COS~ early in the season. In the course of the season the limitation of VPD on stomatal conductance becomes stronger, which manifests in the LRU--VPD relationship. This emphasizes that the LRU--g~s,COS~ correlation ([*SI Appendix*, Fig. S3](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)) only applies when both F~COS~ and F~CO2~ are controlled by stomatal conductance; i.e., at high temperatures and high light conditions.

![Seasonal variation of light-saturated LRU. (*Top*) LRU per month plotted as the median of three equal-sized bins of VPD (kPa) for chamber 1 (*Left*) and chamber 2 (*Right*). Only data above the light saturation point of F~CO2~, i.e., 700 µmol m^−2^⋅s^−1^, are included to minimize the effect of PAR on LRU. The month of February is not included because in that month PAR does not reach values above 700 µmol m^−2^⋅s^−1^. The error bars represent the 25th and 75th percentiles of data in each bin. The median LRU of all VPD classes is plotted per month in gray. Significance levels (P) of linear regressions of LRU against VPD are given per month. (*Bottom*) The number of data in each bin.](pnas.1807600116fig03){#fig03}

Light and Humidity-Dependent LRU Required for Accurate COS-Based GPP Estimates. {#s5}
-------------------------------------------------------------------------------

In [Fig. 4](#fig04){ref-type="fig"} we compare COS-based GPP estimates (GPP~COS~) from COS ecosystem fluxes (determined from eddy-covariance measurements and subtracted estimates of the soil flux) with GPP from a traditional flux-partitioning method based on extrapolating nighttime respiration to the daytime ([@r28]) (GPP~NEE~). GPP~COS~ is determined using different parameterizations of LRU: (*i*) a fit of the measured LRU (averaged over chambers 1 and 2) against PAR, which captures the decrease of LRU toward simultaneously increasing VPD and PAR (GPP~COS-fit~; see [*SI Appendix*, Fig. S6](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental) for the LRU--PAR relationship) and (*ii*) LRU fixed at 1.1 (the average LRU that we find at high light levels) and 1.6 \[similar to what has been frequently used in other literature ([@r7], [@r15], [@r29])\], where the latter is shown in [Fig. 4](#fig04){ref-type="fig"} as GPP~COS-const~. The shading of the GPP estimates represents the uncertainty based on Monte Carlo sampling of all parameters contributing to the GPP calculations ([*Methods*](#s8){ref-type="sec"}). The GPP~COS~ uncertainty is larger than that of GPP~NEE~, partly because the relative uncertainty of COS mole fraction measurements (∼1.7% of a typical ambient level of 450 ppt) is greater than that of CO~2~ mole fraction measurements (∼0.06% of a typical value of 400 ppm) ([@r30]). Still, [Fig. 4](#fig04){ref-type="fig"} shows that the accuracy of GPP~COS~ is sufficient to detect differences between GPP~COS~ and GPP~NEE~. We also calculated GPP~COS~ with the measured hourly LRU to determine to what extent uncertainty in the LRU--PAR function adds uncertainty to GPP~COS-fit~. The uncertainties did not decrease with measured LRU values compared with the LRU---PAR function, implying that the empirical function captures the variability of LRU over the measurement period well.

![GPP estimates based on COS and standard methods. Diurnal cycles of GPP between 18 May and 13 July 2017 based on NEE partitioning (GPP~NEE~; red) and observed COS ecosystem fluxes \[using EC measurements with soil flux estimates subtracted ([@r45])\] following [Eq. **1**](#eq1){ref-type="disp-formula"} (GPP~COS~). For GPP~COS~, LRU is determined with two different representations: from a PAR-dependent fit ([*SI Appendix*, Fig. S6](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)) of LRU based on the continuous branch measurements, where the average of chambers 1 and 2 is taken (GPP~COS-fit~; blue); LRU fixed at 1.6 (GPP~COS-const~; green), which is similar to what has been frequently used in other literature ([@r7], [@r15], [@r29]). The averages (thick lines) and uncertainties (shaded areas) are based on 1,000 subsamples of Monte Carlo simulations that include uncertainties of all contributing components in the GPP calculation in each bin ([*Methods*](#s8){ref-type="sec"}). We calculated the summed GPP from the average diurnal cycle for each representation (for daytime data only), which is shown in the top right corner.](pnas.1807600116fig04){#fig04}

With the constant LRU, the earlier peak of F~COS~ leads to an earlier peak in GPP~COS-const~ compared with GPP~NEE~. The peak of ecosystem F~COS~, and thus that of GPP~COS-const~, is 2 h later than the peak of F~COS~ measured at the branch level at the top of the canopy. The reason for the delay between the F~COS~ peak from branches and ecosystem is that the diurnal pattern of the bulk canopy conductance is more symmetric, because light rather than g~s~ is limiting CO~2~ assimilation in the lower canopy, in contrast to the top of the canopy ([@r31]). When GPP~COS~ is calculated with the average LRU that we find at high light levels (1.1), we find GPP~COS~ (13.4 ± 1.3 g C m^−2^⋅d^−1^; daytime data only) to be overestimated by 72% compared with GPP~COS-fit~. A fixed LRU value of 1.1 is not even sufficient for peak daytime values of GPP~COS~, because cloudy days would have lower PAR, leading to higher LRU and lower GPP~COS~. When GPP~COS-const~ is based on the LRU value that is frequently used in other studies (1.6), GPP~COS~ is underestimated at high light levels, but overestimated in the early morning and late afternoon ([Fig. 4](#fig04){ref-type="fig"}) with the daytime sum being 7% overestimated compared with GPP~COS-fit~ (daytime data only). These comparisons demonstrate that a constant LRU does not capture the variability of GPP. To the contrary, the diurnal cycles of GPP~NEE~ and GPP~COS-fit~ track closely in the early morning and late afternoon. The sum of daily GPP estimates differ by 13% (6.8 ± 0.3 and 7.8 ± 0.9 g C m^−2^⋅d^−1^ for GPP~NEE~ and GPP~COS-fit~, respectively). If LRU is held constant at a too-high value toward high PAR---when the different response of F~COS~ and F~CO2~ to stomatal closure is ignored---this would lead to an underestimation of GPP during daytime.

Ideally, COS would be used to validate other flux-partitioning methods and to assess assumed relations, such as the relation between respiration and temperature that is used to determine GPP~NEE~ ([@r28]). Recent studies in a temperate deciduous forest and an Arctic tundra have found that the standard flux-partitioning technique typically overestimates daytime ecosystem respiration and thereby overestimates GPP ([@r32], [@r33]). Here we find that GPP~COS-fit~ is 13% higher than GPP~NEE~. The separation between GPP~COS-fit~ and GPP~NEE~ around noon that is larger than the uncertainty ([Fig. 4](#fig04){ref-type="fig"}) shows that GPP~COS-fit~ can be used to detect biases in other methods. However, the LRU that we used to calculate GPP~COS-fit~ is based on PAR levels at the top of the canopy and does not account for lower PAR levels within the canopy. Accounting for a lower PAR within the canopy is expected to result in a higher canopy-integrated LRU and lower GPP~COS-fit~ than those currently shown in [Fig. 4](#fig04){ref-type="fig"}. The extent to which GPP~COS~ would decrease, and how it then compares with GPP~NEE~, would have to be investigated by taking into account the canopy profiles of leaf area density and light attenuation and the empirical LRU--PAR relation that is found in this study. It also has to be tested from field measurements how LRU behaves under different light regimes within the canopy, where light-use efficiency can be higher for diffuse radiation than for direct radiation ([@r34]). The current GPP~COS~ estimate does not allow for drawing conclusions about the bias of GPP in other methods, but the current state of knowledge is not far from application of COS as a tool to cross-validate other flux-partitioning methods.

The Implications in Large-Scale GPP Estimates. {#s6}
----------------------------------------------

The application of COS as a GPP tracer in terrestrial biosphere models can make use of LRU to scale the COS vegetation fluxes to those of CO~2~. The relationships of LRU with PAR and VPD that are presented in this study are needed to make sure that the diurnal and seasonal variability of LRU is accounted for in terrestrial biosphere models ([@r36][@r37]--[@r38]). With accurate representation of LRU, the use of COS could potentially help improve the representation of diurnal variations of GPP in such models ([@r29], [@r38]). Furthermore, a time-integrated LRU is a useful measure to make the link between plant COS uptake and gross CO~2~ uptake when large-scale biosphere models do not resolve diurnal cycles. For the months May--July we find that the time-integrated ratio of COS and CO~2~ deposition velocities (based on branch measurements) is 1.6 (daytime only); including the months February--April the value is equal to 2.0 due to lower light conditions early in the season ([*SI Appendix*, Fig. S7](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)). Taking into account the nighttime data, the time-integrated F~COS~ to F~CO2~ ratio is 1.9 and 5.3 for May--July and February--July, respectively. These values apply to the branch level, in this case particularly to branches at the top of the canopy. For an accurate conversion of F~COS~ to GPP on the ecosystem and regional scales one needs to account for vertically varying PAR levels within the canopy. Furthermore, for upscaling to regional and global scales, the LRU--PAR relationship would have to be determined for other plant species in different ecosystems, given that large variability in LRU has previously been found between plant species ([@r8], [@r12], [@r14][@r15]--[@r16], [@r39]). For example, nighttime COS uptake by vegetation was shown to be small in a Mediterranean climate ([@r39]), leading to lower variation of LRU with PAR than what we found in this study for a boreal forest. These differences in LRU response in different climatic regions show that results from LRU dependencies in a single biome cannot be generalized across different climatic regions.

Moreover, the strong relationship between F~COS~ and g~s~ that was shown in this study can be used in process-based modeling studies to constrain the CO~2~ diffusion pathway. Large improvements can be made particularly on the extent of nighttime stomatal opening, which is otherwise poorly quantified.

Conclusion {#s7}
==========

The different responses of F~COS~ and F~CO2~ to environmental variables, especially light, should not be ignored when COS flux measurements (either at leaf, ecosystem, regional, or global scales) are used to interpret changes in photosynthetic CO~2~ uptake. Our findings show that the strong variability of LRU with environmental variables and phenological stages must be incorporated to obtain accurate estimates of GPP from COS measurements. The LRU--PAR relationship found in this study can help to scale up LRU to ecosystem, regional, and global scales. Furthermore, the close relationship between F~COS~ and g~s~ that we observed can provide additional constraints to both the carbon and water cycles. With recent efforts to characterize sources and sinks of COS in ecosystems, accurate COS-based GPP estimates are now within reach and will allow testing and validation of other flux-partitioning methods.

Methods {#s8}
=======

Branch Measurements. {#s9}
--------------------

Measurements were performed at the Station for Measuring Ecosystem--Atmosphere Relations II (SMEAR II) in Hyytiälä, Finland (61°51′ N, 24°17′ E, 181 m above sea level), which is dominated by Scots pine (*Pinus sylvestris L.*) ([@r40]). Four automated gas-exchange chambers were installed at the top of the canopy in two Scots pine trees between February 16 and July 17, 2017; details of those chamber meausurements are provided in [*SI Appendix*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental). PAR was measured by quantum sensors (Li-Cor LI-190) inside and outside the chambers. Temperature sensors (thermocouples and PT100) were placed inside the chambers. During measurements, the chambers were closed for 4 min and each chamber was measured once every hour. Air was pumped through a 4-mm (inner) diameter Synflex (Decabon) tube of 65-m length from the branch chambers to a quantum cascade laser spectrometer (QCLS) (Aerodyne Research Inc.) with a flow of 1--1.5 L min^−1^ which was constantly recorded with Honeywell flowmeters (AWM5101VN). No active supply flow was provided, but ambient air could enter the chamber through small holes in the chamber housing ([@r41]). The sample tubing outside the instrumentation cabin was heated to prevent condensation on the tubing walls. The QCLS measured COS, CO~2~, CO, and H~2~O mole fractions (1 Hz) from the branch chambers along with half-hourly cylinder measurements for calibration. We corrected for the spectral water vapor interference of COS ([@r30]). The overall uncertainty including scale transfer, water vapor corrections, and measurement precision was determined to be 7.5 parts per trillion for COS and 0.23 parts per million for CO~2~ ([@r30]). More information about the instrumentation and the calibration method can be found in Kooijmans et al. ([@r30]) and the deployment of the instrument at the SMEAR II station in Kooijmans et al. ([@r42]).

Fluxes were calculated from the change of molar concentrations within the chamber during chamber closure through the following mass balance equation:$$\text{V}\frac{\text{dC}}{\text{dt}} = \text{FA} + \text{q}\left( C_{\text{a}} - \text{C} \right),$$

where C is the molar concentration of each species inside the chamber (mol m^−3^), C~a~ the ambient molar concentration (mol m^−3^), V the chamber volume (m^3^), F the uptake or emission rate (mol m^−2^·s^−1^), A the leaf area (m^2^), and q the flow rate (m^3^ s^−1^). The measured mole fractions of the gas species (mol mol^−1^) are converted to molar concentrations using the ideal gas law with average temperature during chamber closure and pressure measurements at the site. The fluxes were calculated from least-square fit of the time series of molar concentrations inside the chamber and by solving [Eq. **2**](#eq2){ref-type="disp-formula"}. C~a~ was determined from open chamber measurements during a few minutes before chamber closure.

We measured fluxes in empty chambers (called "blank" measurements) to test and correct for gas exchange by the chamber and possibly by tubing materials. We measured blanks for all chambers in July and during a few days in March, May, and June. The fluxes were corrected for the blank emissions as is further described in [*SI Appendix*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental).

In [*SI Appendix*](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental) we also discuss the effect of leaf mitochondrial respiration on F~CO2~ and LRU. Since we do not have the means to quantify diurnal changes of leaf mitochondrial respiration we approximate leaf-level LRU with the observed F~CO2~.

Stomatal Conductance. {#s10}
---------------------

With transpiration measurements (F~H2O~) available, we would ideally calculate stomatal conductance to water vapor (g~s,H2O~) from F~H2O~ normalized by VPD, where F~H2O~ is simultaneously determined along with F~COS~ and F~CO2~ from the branch chamber measurements. However, in chamber measurements, transpiration is underestimated at high relative humidity (RH) levels because the transpired water vapor can get adsorbed on the chamber walls. Measurements of F~H2O~ therefore may not provide reliable g~s,H2O~ estimates at high humidity levels. Therefore, we determined g~s,H2O~ from the Ball--Berry model where the empirical slope (m) and intercept (g~0~) parameters are determined from g~s-H2O~, which is determined with F~H2O~ and VPD under low-humidity conditions. We use a threshold for RH (70%) to avoid the effect of condensation on the chamber walls. The Ball--Berry model describes g~s,H2O~ as function of F~CO2~, RH and the atmospheric CO~2~ mole fraction ([@r43]):$$\text{g}_{\text{s},\text{H}2\text{O}} = \text{m} \cdot \text{F}_{\text{CO}2} \cdot \frac{\text{RH}}{\text{C}_{\text{a},\text{CO}2}} + \text{g}_{0}.$$

The model parameters m and g~0~ are determined through linear regression with an R^2^ of 0.98 and 0.99 for chambers 1 and 2, respectively. With the regression being linear, we do not expect that using the Ball--Berry model rather than the measured g~s,H2O~ leads to a bias in the results. As the Ball--Berry model does not allow for g~s,H2O~ estimates in the dark when there is no photosynthesis, we determined the nighttime g~s,H2O~ based on F~H2O~ normalized by VPD (for RH \< 70%). The leaf temperature used for VPD was calculated from a leaf energy balance model that incorporated heating by incoming shortwave radiation and cooling by transpiration and sensible heat transfer ([@r44]). The RH used for VPD calculations was determined from water vapor mole fractions in the open chamber a few minutes before chamber closure.

GPP Estimates. {#s11}
--------------

We determined GPP from NEE and extrapolated nighttime respiration following the traditional flux-partitioning method in Reichstein et al. ([@r28]). In addition to these NEE-based GPP estimates, we calculated GPP through [Eq. **1**](#eq1){ref-type="disp-formula"} using different representations of LRU: with a PAR-dependent fit to the measured LRU ([*SI Appendix*, Fig. S6](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental)) and with LRU fixed at 1.1 and 1.6. Vegetative COS fluxes were determined from eddy-covariance (EC) measurements in 2017 and soil COS fluxes that were characterized at the site in 2015 ([@r45]). The EC measurements of COS fluxes were made with a second QCLS of the same make at 10-Hz frequency together with a sonic anemometer (Solent Research HS1199; Gill Ltd.) at 23-m height. EC fluxes of COS were calculated from COS mixing ratios (corrected for water vapor in air) using the EddyUH software package developed at the University of Helsinki ([@r46]). Storage fluxes were estimated from mole fractions at 18 m assuming a constant height profile. More details about the flux and storage calculation procedure can be found in Kooijmans et al. ([@r42]). Data with low friction velocity (\<0.3 m⋅s^−1^) were filtered out. Soil COS fluxes were measured in 2015 at the Hyytiälä site and showed no seasonal or diurnal cycle ([@r45]). An average soil flux of −2.7 pmol m^−2^⋅s^−1^ was subtracted from the ecosystem fluxes such that the remaining flux represents the vegetative COS exchange. The averages and uncertainties shown in [Fig. 4](#fig04){ref-type="fig"} are based on 1,000 subsamples of Monte Carlo simulations that include uncertainties of all contributing components in the GPP calculation. That is, the SE of F~COS-EC~ and NEE; the COS soil flux uncertainty of 1.1 pmol m^−2^⋅s^−1^ ([@r45]); the SE of the fitting parameters of the LRU-PAR relation (using the median PAR in the calculation), or no uncertainty in LRU in the case of a constant LRU; the uncertainties of COS and CO~2~ mole fractions of 6.0 ppt and 0.13 ppm respectively ([@r30]), and the range of respiration calculations from figure 11 in ref. [@r47].

Meteorological Data. {#s12}
--------------------

In addition to the temperature and PAR sensors installed at the branch chambers we use the data that are made available through the SmartSMEAR database that contains continuous data records from all SMEAR sites (available at <https://avaa.tdata.fi/>).

Statistical Tests. {#s13}
------------------

The significance of correlations is tested with two-sided *t* tests of which the significance levels (P) are reported. To reduce the effect of outliers we test the linear correlation of data based on bin-averaged medians, where the bins are of equal size. The number of samples of the original data are reported for each *t* test. The number of bins are mentioned in figure legends.

Code and Data Availability. {#s14}
---------------------------

Data and code related to this paper are available in refs. [@r48][@r49]--[@r50].

Supplementary Material
======================

We thank the technical staff at the SMEAR II station in Hyytiälä and M. de Vries, B. A. M. Kers, H. A. Been, and H. G. Jansen from the University of Groningen for their help during preparation and maintenance of the field campaign. This research was supported by the Startup Grant (awarded to H.C.) at the University of Groningen, the National Oceanic and Atmospheric Administration Climate Program Office Grant (NA13OAR4310082), the European Union's Horizon 2020 research and innovation program (Grant 654182), the Vilho, Yrjö, and Kalle Väisälä Foundation, Integrated Carbon Observation System-Finland (Grant 281255), Academy of Finland Center of Excellence program (307331), and the NSF CAREER Award 1455381 (to U.S.).

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Data deposition: The data used in this work are available from <https://zenodo.org/record/1211481#.XB4Lb9IzbIU>. The dataset includes branch fluxes and mole fractions of COS and CO~2~, LRU, stomatal conductance, internal conductance, eddy-covariance fluxes of COS and CO~2~, GPP, and meteorological information. The code used to calculate the chamber fluxes from measured mole fractions is available from <https://zenodo.org/record/1197330#.XB4OLNIzbIU>. The code used to generate the main results in this work is available from <https://zenodo.org/record/1211499#.XB4PStIzbIU>.

This article contains supporting information online at [www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental](https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807600116/-/DCSupplemental).

[^1]: Edited by Steven C. Wofsy, Harvard University, Cambridge, MA, and approved December 18, 2018 (received for review May 2, 2018)

[^2]: Author contributions: L.M.J.K., W.S., J.A., K.-M.E., K.M., U.S., T.V., I.M., and H.C. designed research; L.M.J.K., W.S., J.A., K.-M.E., K.M., and H.C. performed research; L.M.J.K., W.S., J.A., K.-M.E., and H.C. analyzed data; and L.M.J.K., W.S., J.A., K.-M.E., K.M., U.S., T.V., I.M., and H.C. wrote the paper.

[^3]: ^1^Present address: Meteorology and Air Quality Group, Wageningen University and Research Centre 6700 AA, Wageningen, The Netherlands.
