the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Optimizing the carbonic anhydrase temperature response and stomatal conductance of carbonyl sulfide leaf uptake in the Simple Biosphere model (SiB4)

### Ara Cho

### Linda M. J. Kooijmans

### Kukka-Maaria Kohonen

### Richard Wehr

### Maarten C. Krol

Carbonyl sulfide (COS) is a useful tracer to estimate
gross primary production (GPP) because it shares part of the uptake pathway
with CO_{2}. COS is taken up in plants through hydrolysis, catalyzed by
the enzyme carbonic anhydrase (CA), but is not released. The Simple
Biosphere model version 4 (SiB4) simulates COS leaf uptake using a
conductance approach. SiB4 applies the temperature response of the RuBisCo
enzyme (used for photosynthesis) to simulate the COS leaf uptake, but the CA enzyme might respond differently to temperature. We introduce a new
temperature response function for CA in SiB4, based on enzyme kinetics with
an optimum temperature. Moreover, we determine Ball–Woodrow–Berry (BWB)
model parameters for stomatal conductance (*g*_{s}) using observation-based estimates of COS flux, GPP, and *g*_{s} along with meteorological measurements in an evergreen needleleaf forest (ENF) and deciduous broadleaf forest (DBF). We find that CA has optimum temperatures of 20 ^{∘}C (ENF) and 36 ^{∘}C (DBF), which is lower than that of RuBisCo (45 ^{∘}C), suggesting that canopy temperature changes can critically affect CA's catalyzation activity. Optimized values for the BWB offset parameter are similar to the original value (0.010 ± 0.003 mol m^{−2} s^{−1}), and optimized values for the BWB slope parameter (ENF: 16.4, DBF: 11.4) are higher than the original value (9.0) at both sites. The optimization reduces prior errors on all parameters by more than 50 % at both stations. We apply the optimized *g*_{i} and *g*_{s} parameters in
SiB4 site simulations, thereby improving the timing and peak of COS
assimilation. In addition, we show that SiB4 underestimates the leaf
humidity stress under conditions where high vapor pressure deficit (VPD) should limit *g*_{s} in the afternoon, thereby overestimating *g*_{s}. Furthermore, global COS biosphere sinks with optimized parameters show smaller COS uptake in regions where the air temperature is over 25 ^{∘}C, mostly in the tropics, and larger uptake in regions where the temperature is below 25 ^{∘}C. This change
corresponds with reported deficiencies in the global COS fluxes, such as
missing sinks at high latitudes and required sources in the tropics. Using
our optimization and additional observations of COS uptake over various
climate and plant types, we expect further improvements in global COS
biosphere flux estimates.

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The leaf assimilation of the atmospheric trace gas carbonyl sulfide (COS)
has been suggested as a proxy to overcome the limitations of estimating
photosynthetic carbon dioxide (CO_{2}) assimilation (Whelan et al., 2018).
Observations of the net ecosystem exchange (NEE) of CO_{2} include both
gross primary production (GPP) and ecosystem respiration, and those two
individual components cannot be directly observed during daytime. COS
follows the same diffusional pathway into leaves through plant stomata as
CO_{2}. COS is then destroyed through hydrolysis catalyzed by the enzyme
carbonic anhydrase (CA) and is assumed not to be produced by any process
within leaves (Protoschill-Krebs et al., 1996; Stimler et al., 2010). The CA
chemistry is not light dependent (Protoschill-Krebs et al., 1996), in
contrast to photosynthetic CO_{2} fixation, which requires light.
Therefore, when the CA activity is accurately quantified, measurements of
COS uptake can provide information on stomatal conductance (Kooijmans et
al., 2017).

Atmospheric COS mole fractions vary around 500 parts per trillion (ppt) and are primarily influenced by biosphere uptake, ocean emissions, and anthropogenic emissions (Kettle et al., 2002). Depending on the environmental conditions, soils can act as a COS source or sink (Maseyk et al., 2014; Whelan et al., 2016). Recent studies have found that a source is missing in the tropical region (Berry et al., 2013; Glatthor et al., 2015; Kuai et al., 2015; Ma et al., 2021). Moreover, Berry et al. (2013) and Hu et al. (2021) showed that a sink is missing, or a source is overestimated at higher latitudes. These findings ask for careful evaluation of all sources and sinks, including the biosphere.

Biosphere models, such as the Simple Biosphere model, version 4 (SiB4) (Berry et al., 2013; Kooijmans et al., 2021) and the Organizing Carbon and Hydrology In Dynamic Ecosystems model (ORCHIDEE; Launois et al., 2015; Maignan et al., 2021; Remaud et al., 2022; Abadie et al., 2022) have been used to estimate ecosystem exchange of COS quantitatively. The SiB4 COS biosphere exchange was recently assessed against observations by Kooijmans et al. (2021). They stressed the need to account for spatial and temporal variations in atmospheric COS mole fractions, which largely reduce SiB4 COS biosphere uptake in the tropics (although observations to confirm this influence are lacking). The calculated reduction in the tropics was not large enough to explain the gap in the COS budget. Kooijmans et al. (2021) and Vesala et al. (2022) also found that SiB4 COS biosphere flux simulations were low compared to observations in the boreal region, consistent with the underestimations found by Ma et al. (2021). Our study follows one of the recommendations in Kooijmans et al. (2021) by focusing on the parameterization of the temperature dependence of the CA enzyme activity to improve simulations of the vegetation COS uptake in SiB4.

In SiB4, the COS assimilation is described as a series of resistances (i.e.,
inverse conductances) at the leaf boundary layer (*g*_{b}), the stomatal pores (*g*_{s}), and the leaves' interior (*g*_{i}). The *g*_{b} and *g*_{s} of COS are scaled relative to conductances for water vapor or CO_{2} with diffusivity ratios and a calibration factor. For *g*_{i}, previous studies
found that both the CA enzyme activity (Badger and Price, 1994) and mesophyll
conductance (Evans et al., 1994) scale with the maximum velocity of
carboxylation by the enzyme RuBisCo (*V*_{max, rub}). Therefore, the COS internal conductance in SiB4 is scaled to *V*_{max, rub} through a single calibration factor *α* based on laboratory leaf gas exchange
measurements (Stimler et al., 2010, 2011; Berry et al., 2013). However, the
enzymatic control of COS and CO_{2} assimilation differs. COS molecules are
hydrolyzed by the enzyme CA in the mesophyll cells (Protoschill-Kreb et al.,
1996). In contrast, photosynthesis is further controlled by the enzyme
RuBisCo. Thus, CO_{2} has a different point of uptake compared to COS. The
enzyme activity depends on the enzyme abundance and is related to
environmental parameters such as temperature and pH (Michaelis and Menten,
1913). In particular, the CA enzyme does not require light to catalyze COS
hydrolysis, whereas the RuBisCo enzyme does require light (Stimler et al.,
2010). Different temperature responses of RuBisCo and CA were reported by
Boyd et al. (2015) with the C_{4} plant *Setaria viridis*. They measured that *V*_{max, rub}
increased with temperature in the range 10 to 40 ^{∘}C, whereas the CA
activity decreased above 30 ^{∘}C. Currently, however, there is limited
information about the temperature response function of CA.

Several studies found that the leaf relative uptake ratio (LRU; which is
proportional to the ratio of COS and CO_{2} deposition velocities) varies
with temperature under conditions where light was not limiting
photosynthesis (Cochavi et al., 2021; Stimler et al., 2010; Sun et al.,
2018; Kooijmans et al., 2019). More specifically, the LRU decreased with
increasing temperatures above 15 ^{∘}C, indicating that COS uptake has
a lower optimum temperature than CO_{2} uptake, possibly driven by
different temperature responses of the CA and RuBisCo enzymes. Therefore, to
accurately simulate the relation between COS and CO_{2} exchange in
leaves, it is necessary to use separate temperature response equations for
the internal conductance to CO_{2} and COS.

Besides uncertainties in *g*_{i}, uncertainties in *g*_{s} can also affect the accuracy of simulated COS assimilation. A common approach for simulating *g*_{s} is the semi-empirical Ball–Woodrow–Berry (BWB) model (e.g., Ball et
al., 1987; Ball, 1988; Collatz et al., 1992). This model is also applied in
SiB4 and utilizes a set of related variables (e.g., photosynthesis, relative
humidity, and CO_{2} concentration at the leaf surface) and two empirical
constants. One of the constants (*b*_{1}) describes the slope of the relation
between *g*_{s} and GPP. The other constant (*b*_{0}) represents the residual *g*_{s} in the dark. The current implementation of the BWB model in SiB4 has only one pair of *b*_{1} and *b*_{0} values for C_{3} plants and only one pair for C_{4} plants, whereas the BWB constants should ideally be prescribed for each plant functional type (PFT) separately to obtain accurate *g*_{s} (Miner et al., 2017). To constrain *b*_{0} requires information on nighttime *g*_{s}. However, obtaining *g*_{s} estimates from nighttime water vapor flux
measurements in the field is highly uncertain due to observational
constraints (Papale et al., 2006; Wehr et al., 2017; Wehr and Saleska,
2021). As an alternative, nighttime COS uptake was previously reported
(White et al., 2010; Belviso et al., 2013; Commane et al., 2013, 2015;
Berkelhammer et al., 2014; Billesbach et al., 2014; Wehr et al., 2017;
Kooijmans et al., 2017), and when the soil uptake is properly accounted for,
this flux could provide information on stomatal opening. Several multi-year
measurement datasets of CO_{2} and COS biosphere and soil fluxes are now
available (Commane et al., 2015; Wehr et al., 2017; Vesala et al., 2022).
Multi-year datasets make it possible to distinguish valid signals from noise
and to use COS to provide information on *g*_{s} and constrain the BWB model parameters.

This research aims to optimize the temperature response of CA and BWB model
parameters to better estimate COS assimilation in the SiB4 model. To do so,
we will use eddy covariance (EC) measurements of the COS leaf flux, GPP
derived from NEE, and *g*_{s} derived from the EC COS flux. The optimization
will be based on observations from two PFTs: a boreal evergreen needleleaf
forest (ENF) at Hyytiälä, Finland, and a temperate deciduous
broadleaf forest (DBF) at Harvard Forest, USA. The optimized parameters will
be applied in a global simulation of the SiB4 biosphere model to evaluate
the effects on the global COS biosphere sink.

## 2.1 Modeling COS leaf uptake

### 2.1.1 SiB4 biosphere model

The SiB4 model is a prognostic land surface model that calculates the COS
flux as described in Berry et al. (2013). The main application of the model
is to estimate land–atmosphere exchange of carbon, energy, and water budgets
(Sellers et al., 1986; Sato et al., 1989). SiB4 has a time step of 10 min
and operates on a spatial resolution of 0.5^{∘} × 0.5^{∘}.
Unlike the previous SiB3 model, which relies on satellite information to
specify the time-varying phenological leaf state, version 4 fully simulates
the terrestrial carbon cycle using a process-based model (Haynes et al.,
2019).

As each vegetation type has different physiological and phenological
characteristics, SiB4 simulates photosynthesis in a heterogeneous land cover
with different plant functional types (PFTs) per site or grid cell, each
with separate fractions. These PFTs consist of nine natural vegetation
classes and three specific crop types (maize, soybeans, and winter wheat),
plus the separation of C_{3} and C_{4} plants in generic cropland and grassland.
Besides responses of plant growth to temperature, humidity, radiation, and
precipitation, the model accounts for environmental stress factors as a
limitation to plant growth: the leaf humidity stress (*F*_{LH}), the
root-zone water stress (*F*_{RZ}), and the canopy temperature stress
(*F*_{T}). Several variables (e.g., *V*_{max, rub}) are prescribed according
to phenological stages: leaf out, growth, maturity, senescence, and dormant
stages. The leaf-out stage begins when the environmental conditions are
suitable for photosynthesis to take place, and the growth stage is
determined when the canopy is large enough to support photosynthesis. The
maturity starts when the leaf amount is maintained. When plants experience
stress and photosynthetic capacity is reduced, it is prescribed as
senescence. In the dormant stage, plants do not have leaves in the canopy,
or conditions are unsuitable for photosynthesis (Haynes et al., 2020).

### 2.1.2 Module for COS vegetation uptake in SiB4

SiB4 simulates COS vegetation assimilation as a combination of three
conductances from the laminar boundary layer to the chloroplast (*g*_{b}, *g*_{s}, and *g*_{i}) multiplied by the atmospheric COS mole fraction (Berry et al., 2013):

where *F*_{COS} is the COS vegetation assimilation in the canopy (pmol m^{−2} s^{−1}), and *C*_{COS} is the COS mole fraction in the canopy air
space (pmol mol^{−1}). The factors 1.94 and 1.56 account for the smaller
diffusivity of COS with respect to H_{2}O through the boundary layer and
stomatal pores, respectively (Seibt et al., 2010; Stimler et al., 2010).
Note that *g*_{i} includes all conductances downstream of the stomata, such as the mesophyll conductance. Within SiB4, the aerodynamic conductance is used to connect the mole fraction in the canopy air space to the atmosphere.

The stomatal conductance *g*_{s} (mol m^{−2} s^{−1}) in SiB4 is
calculated by using the BWB model. This model relates *g*_{s} and GPP as a function of environmental factors with two empirical constants *b*_{0} and *b*_{1}:

where GPP_{SiB4} (mol C m^{−2} s^{−1}) is the canopy CO_{2} assimilation, CO_{2s} (mol C mol air^{−1}) is the CO_{2} mole fraction at the leaf surface, *F*_{LH} (–) is the leaf humidity stress factor, LAI is the leaf area index (–), and *F*_{RZ} is a non-dimensional term that accounts for root-zone water stress. *F*_{LH} is related to relative humidity at the leaf surface and is calculated as a ratio of the water vapor mixing ratio at the leaf surface to the water vapor mixing ratio in the leaf internal space (Sellers et al., 1992). The value of *F*_{LH} for ENF has a lower bound of
0.7, making ENF more resilient to humidity stress. However, Smith et al. (2020) found that with the 0.7 threshold in place, SiB4 did not accurately
simulate the drought response for European ENF ecosystems. Therefore, we
removed this lower bound in the optimization but will show the impact in a
sensitivity study in Sect. 3.5.1.

The empirical constant *b*_{1} is the slope of the linear relationship
between *g*_{s} and GPP_{SiB4}; and *F*_{LH}, CO${}_{\mathrm{2}\mathrm{s}}^{-\mathrm{1}}$, and *b*_{0} (mol m^{−2} s^{−1}) is the intercept indicating minimum *g*_{s} (Ball et al., 1987;
Ball, 1988). The choice for *b*_{1} significantly impacts simulated
transpiration (Leuning et al., 1998; Lai et al., 2000; Bauerle et al., 2014)
and is prescribed in SiB4 as 9.0 for C_{3} plants and 4.0 for C_{4} plants. The coefficient *b*_{0} is 0.01 mol m^{−2} s^{−1} for most PFTs but 0.04 mol m^{−2} s^{−1} for crops and C_{4} plants. The prescribed *b*_{0} term is
converted from the leaf to the canopy scale by multiplying by LAI.

GPP_{SiB4} is explicitly calculated in SiB4 as the minimum of three
assimilation rates limited by enzyme activity (*w*_{c}), light (*w*_{e}), and carbon compound export (*w*_{s}) (Haynes et al., 2020). The three rates are calculated by functions ${f}_{\mathrm{c},\mathrm{e},\mathrm{s}}$ described in detail in Sellers et al. (1996a) depending on a canopy temperature (*T*_{can}, K):

Here, *p*CO_{2i} (Pa) is the internal partial pressure of CO_{2},
*p*O_{2}(*T*) (Pa) is the temperature response of partial pressure of O_{2}, APAR (mol m^{−2} s^{−1}) is the absorbed photosynthetically active radiation, and *γ*^{∗} (Pa) is the CO_{2} photo-compensation point. Note that GPP_{SiB4} is used in SiB4 to calculate the COS leaf flux via *g*_{s}, as described in Eq. (2) and evaluated independently from GPP calculated by the
BWB model (GPP_{BWB}), which will be introduced in Sect. 2.3.1.

The COS molecules that have diffused into the leaf mesophyll cells are
hydrolyzed in a reaction catalyzed by the CA enzyme (*g*_{i}). Since the enzyme activity and mesophyll conductance are analogous and the terminal COS concentration is assumed to be zero, SiB4 presumes that the two conductances can be combined and that the *g*_{i} (mol m^{−2} s^{−1}) scales with *V*_{max, rub} at 298 K (mol m^{−2} s^{−1}) as follows (Berry et al., 2013):

*V*_{max, rub} varies with phenological stage (PS) (see Table 3) and is scaled with a *T*_{can} response function *f*(*T*_{can})_{SiB4} that prescribes
the relative increase per 10 K increase (*Q*_{10}) as 2.1 as follows:

In SiB4, the canopy temperature *T*_{can} is calculated from the temperature above the canopy using the leaf surface energy balance (Sellers et al., 1996b), and *T*_{can} is normally obtained from a meteorological analysis
dataset. In this study, however, we use the air temperature measured above
the canopy to obtain *T*_{can} needed by SiB4. Likewise, we use the
specific humidity measured above the canopy, which is used by SiB4 to
calculate the leaf humidity stress factor *F*_{LH} at leaf surface level, needed in Eq. (2).

Other modifying factors in Eq. (6) are the ratio of atmosphere pressure
(*P*; hPa) to the surface pressure (*P*_{sfc} = 1000 hPa) and the
ratio of the temperature to the reference temperature (*T*_{0} = 273.15 K). *F*_{LC} (–) is the scaling factor from leaf to canopy, accounting for a fraction of absorbed photosynthetically active radiation (FPAR) and other factors such as light scattering and leaf projection. The calibration parameter *α* (–) was obtained from simultaneous measurements of COS and CO_{2} uptake (Stimler et al., 2010, 2012; Berry et al., 2013) and was estimated as 1400 for C_{3} and 8862 for C_{4}
plants. These numbers were derived from a limited number of observations, so
the values of *α* do not capture variability between plant species and
seasons. Kooijmans et al. (2021) derived *α* from ecosystem observations of six sites throughout the growing season and found an average *α* of 1616 ± 562 (C_{3} plants). Here, the standard deviation indicates large variability over time and between sites. The impact of *α* on *g*_{i} will be described in Sect. 2.1.3.

### 2.1.3 A new approach to describe *g*_{i}

Each enzyme has its own kinetic characteristics, with activity generally
increasing with temperature up to an optimum temperature and decreasing
above this temperature. To derive a more realistic enzyme activity that also
accounts for an optimum temperature, we propose a temperature response
(*f*(*T*_{can})_{new}) based on an Arrhenius-type equation that applies Michaelis–Menten kinetics. The Arrhenius equation has been used for
*V*_{max, rub} and maximum rate of photosynthetic electron transport to estimate GPP (e.g., Dreyer et al., 2001; Galmés et al., 2016). A similar
model was previously used in COS soil models (Sun et al., 2015; Ogée et
al., 2016). The equation is described as (Peterson et al., 2004; Daniel et
al., 2010)

Here, three variables for enzyme kinetics are included: Δ*H*_{a} (J mol^{−1}) is the activation free energy of the CA enzyme, Δ*H*_{eq} (J mol^{−1}) is the enthalpy change when the enzyme converts from an activated to inactivated state, and *T*_{eq} (K) is the temperature at which activated and inactive enzymes' concentrations are equal (Daniel et al., 2010; Sun et al., 2015). The factor *A*_{T} normalizes Eq. (8) such that, equivalent to Eq. (7), *f*(*T*_{can})_{new} = 1 at *T*_{can} = 298 K. We adopt *A*_{T} as the value of $f({T}_{\mathrm{can}}{)}_{\mathrm{new}}^{-\mathrm{1}}$ when *T* is equal to *T*_{eq}. *R* is the universal gas constant (8.3145 J K^{−1} mol^{−1}). Figure 1 shows that *α* and the three kinetic parameters have different effects on the temperature response of *g*_{i} (Eq. 6). The calibration parameter *α* affects
the strength of *g*_{i} (Fig. 1a), and its accuracy is therefore
crucial for accurate COS flux simulations. With Δ*H*_{a} increasing (Fig. 1b), *g*_{i} decreases (increases) for temperatures above (below) the optimal temperature. Δ*H*_{eq} has the opposite effect, albeit with a different response to Δ*H*_{a} (Fig. 1c). Both Δ*H*_{a} and Δ*H*_{eq} affect *g*_{i} depending on the temperature range. Finally,
Fig. 1d shows that *T*_{eq} determines the optimum of the temperature
response curve without having impact on the magnitude of *g*_{i}.

## 2.2 Observations

In optimizing the parameters *g*_{s} and *g*_{i}, we used the following variables obtained from observation to calculate COS leaf uptake (Eq. 1):
the COS ecosystem flux, the COS soil flux, *C*_{COS}, temperature, and
specific humidity, as well as GPP partitioned from NEE measurements. These data
were collected and derived at Hyytiälä in Finland during 2013–2017
(Kooijmans et al., 2017; Sun et al., 2018; Vesala et al., 2022) and at
Harvard Forest in the United States during 2012 and 2013 (Commane et al.,
2015, 2016; Wehr et al., 2017). To validate the optimization
results, we used the observation-based *g*_{s} and *g*_{i} (Sect. 2.2.2).

### 2.2.1 COS flux, GPP, and mixing ratio

We used canopy COS uptake derived from COS EC measurements for Hyytiälä (Kohonen et al., 2020; Vesala et al., 2022) and Harvard Forest (Wehr et al., 2017). The effect of storage in the canopy airspace was included by collocated COS profiles (Kooijmans et al., 2017; Kohonen et al., 2020).

GPP at Hyytiälä has been obtained from NEE using multi-year parameter fits (Kolari et al., 2014; Kohonen et al., 2022). For Harvard Forest, we chose to use the GPP derived from the isotope spectrometer measurements because it is more accurate and reliable with frequent and rigorous calibrations (Wehr et al., 2016).

COS soil flux measurements were available for the 2016 growing season at Hyytiälä and for the 2012 and 2013 growing seasons at Harvard Forest. For the soil flux in other years at Hyytiälä, we applied the monthly average diurnal cycle of the soil flux from 2016 to the other years (2013–2015 and 2017). The seasonal and diurnal variation of the soil flux is small compared to the total ecosystem uptake of COS (Sun et al., 2018). Hence, the averaged value of 2016 can be safely used for other years.

To convert the data frequency of observations to SiB4's 3 h time resolution, we calculated the median value of each variable in each 3 h interval and for each month. We only used data points when more than three data points were present and when all variables required for the optimization were available. Figure 2 shows the resulting average diurnal cycle per month for COS ecosystem, soil, and vegetation fluxes (ecosystem flux minus soil flux). Note that positive fluxes indicate uptake. Again, we note that we use the averaged soil flux at Hyytiälä because its variability is much smaller than the leaf flux.

### 2.2.2 Conductances *g*_{s} and *g*_{i}

Observation-based *g*_{s} was derived from sensible heat flux and
evapotranspiration measurements using the flux gradient (FG) equations
(Baldocchi et al., 1991; Wehr and Saleska, 2015, 2021). A
key step in the derivation of *g*_{s} is the estimation of transpiration from
evapotranspiration. At Harvard Forest, transpiration was estimated by an
empirical equation established during times of minimal non-stomatal
evaporation (i.e., a few days after rain, removing mornings with dew
evaporation), as described in Wehr et al. (2017). At Hyytiälä, we
simply restricted our analysis to periods of minimal non-stomatal
evaporation by eliminating data when the dew point was equal to or greater
than the air temperature or when the accumulated precipitation for the past
2 d was more than 0.01 mm.

The FG approach leads to significant uncertainties for nighttime data because the leaf-to-air water vapor gradient is too small under stable conditions (Wehr et al., 2017). We thus excluded nighttime *g*_{s} when the values were smaller than 0.05 mol m^{−2} s^{−1}. To reduce the effect of random noise on *g*_{s}, we used an average diurnal cycle (based on 3 h medians) for each month.

Observation-based *g*_{i} was extracted by rewriting Eq. (1) as follows:

Here, we used the observation-based *g*_{s} from the FG equation as discussed above and filtered observations of *C*_{COS} and *F*_{COS}. Additionally, we used simulated *g*_{b} from SiB4, as we do not have observed *g*_{b} available
and as the value of *g*_{b} only has a minor effect on *F*_{COS}, which will be further discussed in Sect. 3.1. Although outliers of observed *g*_{s}, *C*_{COS}, and *F*_{COS} were removed already, a significant number of outliers in *g*_{i} appeared because of error propagation. To avoid excessive
noise, we only retained *g*_{i} values in the interquartile range (25–75 percentile) of 3 h for each month.

## 2.3 Optimization

### 2.3.1 Procedure

In the optimization steps, we minimized a quadratic cost function *J*(*x*) based on Bayes' theorem (Tarantola and Vallette, 1982; Enting et al., 1993):

Here, *x* represents the state, *x*_{a} the prior settings of the state, and *σ*_{a} the error assigned to the parameters. In the second term, *y* represents the observations and *H*(*x*) the model evaluation using the state *x*. The error *σ*_{y} represents the observational error. The details of *σ*_{a} and *σ*_{y} will be described in Sect. 2.3.2 and 2.3.3, respectively.

To optimize the *g*_{s} and *g*_{i} parameters, we intend to use the information from GPP and COS leaf uptake measurements sequentially. Thus, we propose a two-step approach in combination with an iterative minimization of the cost functions, as outlined in Fig. 3. In the first step, we optimally estimate *g*_{s} parameter *b*_{1} by minimizing *J*(*x*) which sums GPP differences between estimation (*H*(*b*_{1}) in Eq. 10) and observation.

We select GPP for the first step optimization rather than *g*_{s}, because derived GPP from NEE has been evaluated more frequently than
observation-based *g*_{s}. We use only positive GPP_{obs} values (uptake) because our target parameter *b*_{1} in the first step cannot be optimized when GPP is zero. Here, we do not use GPP_{SiB4} because SiB4 does not apply the BWB model for GPP calculation as described in Eqs. (3)–(5). For this reason, we cannot optimize BWB parameters with GPP_{SiB4}. Instead, we estimated GPP by rewriting the BWB model using an observation-based *g*_{s} (Sect. 2.2.2),
modeled RH at the leaf surface (*F*_{LH}), and simulated CO_{2s} from SiB4. Hereinafter, the estimated GPP by the BWB model is called GPP_{BWB}:

In the second optimization step, we optimize the *b*_{0} and *g*_{i}
parameters (*α* in Eq. 6 and *T*_{eq} in Eq. 8). These parameters are optimized by minimizing the differences between calculated and observed *F*_{COS}. *F*_{COS} is calculated with three conductances using Eq. (1). Specifically, *g*_{s} is estimated with Eq. (2) using the optimized *b*_{1} from step 1. Here, we used GPP_{SiB4} to satisfy our aim of optimizing the SiB4 model parameters. Note that GPP_{BWB} from Eq. (11) cannot be used
here because it would make the estimated *g*_{s} equal to observation-based *g*_{s}. Based on sensitivity studies in Appendix A, we decided to select *α*, *b*_{0}, and *T*_{eq} as target parameters and to fix Δ*H*_{eq} and Δ*H*_{a} at 100 and 40 kJ mol^{−1}, respectively.

In the optimization procedure, we specifically exploit the fact that the
nighttime COS flux carries information about nighttime *g*_{s} through the parameter *b*_{0}. The alternative, i.e., optimizing *b*_{0} already in step 1,
would ignore the information of nighttime *g*_{s} brought by COS flux
observations. Consequently however, we have to iterate the procedure
several times to reach convergence. Figure 3 specifies which observations
and observation-based quantities are used in each step (*g*_{s},
GPP_{obs}, *F*_{COS, obs}, *C*_{COS} highlighted as grey) and which variables are simulated by SiB4 (e.g., *T*_{can},*F*_{LH}, GPP_{SiB4}, CO_{2s}, *g*_{b}).

We applied the simplicial homology global optimization (SHGO) from the SciPy python library to minimize the cost functions. SHGO is appropriate for solving non-continuous, non-convex, and non-smooth functions (Endres et al., 2018). SHGO also allows the definition of a valid parameter range, as will be discussed in Sect. 2.3.2 and in Appendix A.

The *V*_{max, rub} was found to vary over the phenological stage and per PFT (Woodward et al., 1995; Wolf et al., 2006; Kattge et al., 2009; Walker et al., 2014), which also affects the calibration factor *α*. Therefore, we
optimized *α* for each PFT and each phenological stage. In contrast,
*b*_{0}, *b*_{1}, and *T*_{eq} were only separately determined for the
different PFTs, assuming local characteristics for each PFT. We did not
include *V*_{max, rub} in the state variables because this would require
SiB4 CO_{2} simulations. These simulations need several parameters, like
carbon cycle pools, which are difficult to estimate. Therefore, we focus
this research on estimating *V*_{max, CA} by optimizing *g*_{i}-related parameters.

### 2.3.2 Initial parameters and prior errors

The first term in the cost function (Eq. 10) ties the values of the parameters to realistic values. We additionally confined the parameter values within realistic physical ranges using the SHGO algorithm. Initial parameters and prior errors were chosen based on thresholds outlined in Appendix A, and they will be compared with optimized results in Sect. 3.3. The variation in the resulting cost function shows distinct differences between Hyytiälä and Harvard Forest, which reinforces our strategy to optimize parameters for each station separately.

### 2.3.3 Observation errors

To quantify the observational errors *σ*_{y}, we first calculated
the 3 h average coefficient of variation (CV) relative to the mean
of the observed COS vegetation flux in each phenological stage and observed
GPP for the entire growing season. Figure 4 shows the results of
observational errors. The GPP error is applied in step 1, and the COS leaf
uptake error is used in step 2 in the optimization. We multiplied the CV
with the mean in each phenological stage. Here, we classify the error of the
COS leaf uptake in each phenological stage because we optimized *α* in
each stage. In Fig. 4, we found that the errors differ slightly per
phenological stage. At Hyytiälä, the errors are larger in the growth
stage compared to the maturity stage, possibly due to the unstable weather
conditions in growth stage. The COS leaf uptake error is larger at both
stations during nighttime than during daytime. A potential reason can be the
relatively higher uncertainty in the EC method during stable nighttime
conditions.

## 2.4 SiB4 simulations

We utilized several simulated variables from SiB4 in our optimization.
Specifically, calculated GPP_{SiB4}, *g*_{b}, *T*_{can}, and *V*_{max, rub} and functions *F*_{LH}, *F*_{RZ}, and *F*_{LC} were used to calculate COS leaf
uptake. In addition, LAI and CO_{2s} were used to estimate GPP_{BWB}. Furthermore, we introduced the new temperature function
(*f*(*T*_{can})_{new}) in the *g*_{i} calculation (Sect. 2.2.3) to calculate COS
leaf uptake and excluded $P{P}_{\mathrm{sfc}}^{-\mathrm{1}}$ and ${T}_{\mathrm{can}}{T}_{\mathrm{0}}^{-\mathrm{1}}$ from Eq. (3) due to minor impacts of these factors for these ecosystems.

To simulate the vegetation assimilation *F*_{COS} at the two stations, we used the Modern-Era Retrospective Analysis for Research and Application,
version 2 (MERRA-2) (Gelaro et al., 2017) as meteorological driver data.
Only air temperature and leaf-specific humidity were taken from
observations. To initialize the carbon pools, we spun up the model to
equilibrate the pools. The spin-up was performed from 2000 to 2010 with 10
iterations. We used observed *C*_{COS}, and ambient CO_{2} mole fractions were prescribed at 370 ppm.

To estimate the global impact of our findings, we performed a global SiB4
simulation from 2016 to 2018 to evaluate the influence of the new parameters
on the monthly COS biosphere fluxes which are averaged for 3 years. The
atmospheric COS mixing ratio *C*_{COS} were taken from optimizations
using the TM5 chemical transport model (Ma et al., 2021; Kooijmans et al.,
2021). We used 3 h *C*_{COS} averaged over 2016 to 2018 by Kooijmans et al. (2021). As we found that all target parameters differ between ENF and DBF (Appendix A), the application of the optimized parameters to other PFTs
will likely be incorrect. Hence, we applied the optimized parameters only to
ENF and DBF and used the standard values of SiB4 for the other PFTs.
However, to confirm the *f*(*T*_{can})_{new} effect on COS leaf uptake, we applied *f*(*T*_{can})_{new} to all PFTs with averaged optimum *T*_{eq} from the two stations (303 K) and fixed Δ*H*_{eq} (100 kJ mol^{−1}) and Δ*H*_{a} (40 kJ mol^{−1}) as described in Appendix A. The soil flux
is estimated following Ogée et al. (2016) as implemented by Kooijmans et
al. (2021).

To examine the humidity stress impact in SiB4, we performed a simulation
with and without the lower threshold for *F*_{LH} of 0.7 for ENF (see Sect. 2.1.2). Additionally, we replaced the RH at leaf level calculated by SiB4 by
RH measured above the canopy. Results will be shown in Sect. 3.5.1. To
account for the optimized humidity impact on the global COS leaf uptake, we
simulated the global COS leaf uptake without the 0.7 threshold of *F*_{LH} for ENF.

## 2.5 Error reduction and statistics

To determine the uncertainty in the optimized model parameters, we employed a Monte Carlo optimization procedure as described in detail in Appendix B. In short, 100 optimizations were performed. In each optimization, we perturbed the state with random Gaussian noise on the state and the observations (Chevallier et al., 2007; Bosman and Krol, 2023), according to the errors in the state and observations (Fig. 4). Posterior error statistics will be reported in Table 3.

Additionally, we quantified the performance of the optimization by
calculating the root mean square errors (RMSEs), mean bias errors (MBEs),
and the chi-square metric (*χ*^{2}). The *χ*^{2} metric quantifies the
average deviation from the observations, expressed in *σ*_{y} units.
Thus, *χ*^{2} = 1 signals that, on average, the model fits the observation within 1*σ* indicating a realistic error setting.

## 3.1 Impact of each conductance

Figure 5 investigates which conductance contributes most to the total
conductance (*g*_{t}). In these plots, all conductances are prior values before optimization. *g*_{s} and *g*_{i} were derived from observations (Sect. 2.2.2). We find that *g*_{t} is determined mainly by *g*_{i} and *g*_{s}. During daytime, *g*_{i} is the lowest conductance in almost all months at Hyytiälä but is comparable to *g*_{s} in Harvard Forest. The value of *g*_{b} is the highest and hence has the smallest impact on *g*_{t}.
Therefore, to improve the accuracy of COS leaf uptake simulation effectively, parameters of *g*_{s} and *g*_{i} are evaluated and optimized,
and *g*_{b} is kept to its standard value.

## 3.2 Optimization performance

We obtained optimized parameters after five iterations. By design, the
optimized results reduced the deviations between model and observation of
GPP and COS leaf uptake. This improvement is quantified by statistical
indexes in Tables 1 and 2, respectively. GPP_{BWB} is improved slightly compared to the prior (Table 1), with RMSEs reduction from 4.08 to 3.84 µmol m^{−2} s^{−1} at Hyytiälä and 8.35 to 7.89 µmol m^{−2} s^{−1} at Harvard Forest. MBEs are decreased from −1.48 to −0.61 µmol m^{−2} s^{−1} at Hyytiälä and from −4.97 to −3.46 µmol m^{−2} s^{−1} at Harvard Forest (Table 1). The *χ*^{2} was reduced by about 0.09 at Hyytiälä and by 0.08 at Harvard Forest. The improvement in GPP_{BWB} reflects the effect of optimizing *b*_{1} and *b*_{0} in the BWB model.

The posterior result of COS leaf uptake (“post” in Table 2) shows a slight
improvement compared to the original-state variables with
*f*(*T*_{can})_{new} in RMSE (from 7.67 to 5.73 pmol m^{−2} s^{−1} at Hyytiälä and from 10.45 to 9.54 pmol m^{−2} s^{−1} at Harvard Forest) but significantly improved MBE (from −5.10 to −0.01 pmol m^{−2} s^{−1} at Hyytiälä and from −2.53 to −1.99 pmol m^{−2} s^{−1}
at Harvard Forest, see “Post” in Table 2). The large RMSE reflects the
typically large random noise of COS flux observations (Kooijmans et al.,
2016; Kohonen et al., 2020). However, *χ*^{2} drops by 0.41 at
Hyytiälä and by 0.38 at Harvard Forest, confirming that the
optimization properly reduced the mismatch between observations and the
model within the error statistics. Figure 6 compares the optimized COS leaf
uptake to the original SiB4 simulation in scatter plots. Where the original
simulation with *f*(*T*_{can})_{SiB4} and previous-state variables was often underestimating the observations, the optimized results resemble the observations over a larger range of the data.

## 3.3 Optimized parameters

The optimized parameter values with posterior errors are listed in Table 3.
The optimized SiB4 parameters differ between the stations, likely because
the dominant PFT and the climate conditions differ between Hyytiälä
and Harvard Forest. For instance, the optimum temperature is smaller at
Hyytiälä (19.85 K) than in Harvard Forest (35.85 K), which are
slightly smaller than *T*_{eq}. Thus, the optimum temperature reflects the temperature dependence of the enzyme and its adaptation to temperature (Lee et al., 2007). This indicates that regional temperature information is
important for correctly estimating *g*_{i} globally. The optimum temperature can be compared with other observations. For instance, Burnell and Hatch (1988) observed increasing CA activity with maize grown in a temperate temperature range from 20 to 30 ^{∘}C, relative to a temperature of 17 ^{∘}C. Thus, we can assume the optimal temperature lies above 17 ^{∘}C. Another study by Boyd et al. (2015) observed the C_{4} plant *Setaria viridis* with a temperature of 28 ^{∘}C/18 ^{∘}C day/night, and a
reduced CA activity is suggested at temperatures above 25 ^{∘}C. This
optimum temperature falls between our values derived for Hyytiälä
and Harvard Forest.

The *α*, which is the enzyme activity of CA relative to the
*V*_{max, rub}, is reduced from the default value of 1400 to 1316 (in growth) and 1331 (in maturity) at Hyytiälä. At Harvard Forest, *α* values are larger than the original values in SiB4 for leaf-out (1780), growth (1740), and maturity (2224) phenological stages. Here it should be noted that the change of *α* should be interpreted in combination with the new temperature function *f*(*T*_{can})_{new} of *g*_{i}. Since we only optimize
*T*_{eq} for two PFTs (with identical and fixed values for Δ*H*_{a} and Δ*H*_{eq}) and *T*_{eq} only shifts *f*(*T*_{can})_{new} (Fig. 1), the magnitude of *g*_{i} is primarily determined by parameter *α*. The different
values of *α* derived for different phenological stages will be discussed in Sect. 3.4.

The optimized results of the BWB model parameters *b*_{0} are similar to the
original values used in SiB4, but *b*_{1} values are mostly higher. The
parameter values *b*_{0} for Hyytiälä (0.013 mol m^{−2} s^{−1})
and Harvard Forest (0.007 mol m^{−2} s^{−1}) are slightly changed
compared to the initial value (0.010 mol m^{−2} s^{−1}). For the
optimized BWB model parameter *b*_{1}, the empirical slope between *g*_{s} and
GPP, we find a considerable increase at Hyytiälä (16.38) and a
slight increase in Harvard Forest (11.43), compared to the prescribed SIB4
value of 9.0. Our optimized values are larger than the values presented in a
review paper for the evergreen gymnosperm tree which showed *b*_{1} = 6.8 and are similar to *b*_{1} = 8.7 for the deciduous angiosperm tree (Miner et al., 2017). As will be discussed in Sect. 3.5, the higher slope at
Hyytiälä is possibly related to an incomplete separation of observed
transpiration rates from the latent heat flux.

Concerning the estimated errors in *b*_{0}, *b*_{1}, and *T*_{eq}, we find that errors have been reduced significantly compared to the prior error range. This indicates that the available data constrain these parameters well. Only the *α* parameters of Harvard Forest are less well constrained. Also, the
skill of the optimization to independently optimize the parameters is high,
as quantified by the posterior covariances that are presented in Appendix B.

## 3.4 Optimized temperature response

The optimized parameters show significant improvement in temperature
response of the COS leaf uptake. Figure 7 presents the temperature
dependency of *g*_{i} and COS leaf uptake from the original and optimized simulations output and observations. As stated before, the original
*f*(*T*_{can})_{SiB4} describes the CA enzyme activity as an exponentially increasing response to temperature, which does not resemble the
observations. The optimized *g*_{i} and COS leaf uptake follow the
temperature dependence of the observation more closely than the original
*f*(*T*_{can})_{SiB4}. In Harvard Forest, an underestimated bias is shown at a
lower temperature under 10 ^{∘}C, mostly corresponding to nighttime.
This underestimate is related to the uncertainty in nighttime *g*_{S} and the
small data volume at low temperatures (details in Sect. 2.2.2).

In the upper panel of Fig. 7, we see the different roles of *α* and
*f*(*T*_{can})_{new} in the improvement of *g*_{i} response to temperature as the red and orange lines. Without the *α* correction applied (posterior with *α* = 1400;
orange line), the optimized *g*_{i} resembles the fluctuations in the
observations, but there remains a bias in the amplitude. In contrast, when
the optimized value of *α* is included (red line), the amplitude of *g*_{i} is improved. Compared to the optimization that excluded *α*, the MBE is reduced
from 0.006 to 0.003 mol m^{−2} s^{−1}. Due to the different optimized
*α* values in each phenological stage, the improvement of the red line shows the appropriate temperature responses. For instance, in Harvard Forest, *α* in leaf out and growth (1798 and 1740) mostly corresponds to lower
temperatures. At these stages, the impact on *g*_{i} is smaller because *g*_{i} is smaller than that at high temperature. At high temperatures, there are more significant corrections of *g*_{i}, which correspond to the maturity stage value of *α* (2224).

The temperature responses of *g*_{i} and COS leaf uptake now show an optimum
temperature. As can be observed in Fig. 7a, the optimum temperature of the
observation-based *g*_{i} is seen as 293 K (19.85 ^{∘}C) at
Hyytiälä. At Harvard Forest, the optimum temperature is 309 K (35.85 ^{∘}C) but falls outside the observation range. The optimum curve affects the COS leaf uptake at both stations with changing peak
temperatures (Fig. 7b). The accuracies of *g*_{i} and *F*_{COS} are improved significantly at temperatures both below and above around the optimum temperature at both sites.

## 3.5 Application in SiB4

### 3.5.1 Monthly diurnal variation

Figures 8 and 9 display the SiB4 simulation results obtained with the
original and optimized parameterizations compared to observations for
Hyytiälä and Harvard Forest, respectively. As a result of the
optimization, the monthly diurnal variation of the optimized COS vegetation
flux, *g*_{s}, and *g*_{i} are closer to observations than the original SiB4 simulations. The observed COS leaf uptake and *g*_{s} show diurnal and seasonal fluctuations at both measurement sites, with the highest values around midday and in summer. For *g*_{i}, we observe a weak diurnal cycle throughout the year and higher daytime maximum values in summer, driven by the temperature dependence of CA.

At Hyytiälä, COS leaf uptake in the original SiB4 model was
underestimated during daytime in all months. The fluxes increased too slowly
in the morning for all months (Fig. 8a). These issues are solved by
optimizing the BWB model parameters and temperature response function. In
the case of *g*_{s} (Fig. 8b), the original SiB4 simulation showed the
correct timing of the increase and decrease of *g*_{s} in the morning and afternoon but underestimated the peak daytime values. The optimized model
now better resembles the daytime *g*_{s} values.

However, the model still overestimates *g*_{s} in the late afternoon of summer months at Hyytiälä. We speculate that one of the reasons lies in an inaccurate humidity, or humidity stress in SiB4. Figure 10 shows a
diurnal cycle of *g*_{s} simulations averaged from April to August with different choices on how the humidity stress factor is treated (Sect. 2.5). When the default 0.7 threshold of humidity stress (*F*_{LH}) in ENF is applied in SiB4, *g*_{s} is overestimated in the afternoon at Hyytiälä (dotted blue line). When we removed the minimum threshold of *F*_{LH} for ENF, *g*_{s} simulations during midday are improved (note that the threshold
was only implemented for ENF, not for DBF, and thus the blue dotted line is
not visible for Harvard Forest in Fig. 10).

However, SiB4 still tends to overestimate *g*_{s} in the morning and late afternoon. The overestimated *F*_{LH} in SiB4 can result from three factors: (1) an overestimated water vapor flux in the boundary layer to the leaf surface, (2) an underestimated boundary conductance, or (3) an
underestimated leaf surface temperature. Since we do not have observations
of the leaf surface temperature, we have confirmed that the estimated canopy
temperature has a tight 1 : 1 relationship with the observed air temperature.
We speculate that the main reason for the overestimated *F*_{LH} is the uncertain water vapor flux. When we base the *g*_{s} calculation on the
observed RH above the canopy, the diurnal cycle is better simulated (dashed orange line in Fig. 10). The overestimated water vapor pressure implies that
SiB4 tends to underestimate the humidity stress in the late afternoon when
converting observed specific humidity above the canopy to humidity at leaf
surface level. We suggest evaluating the boundary conductance (point 2
above) with observations.

The optimized model still underestimates *g*_{s} at Hyytiälä in April, September, and October (Fig. 8b). This might indicate that we did not properly separate stomatal transpiration rates from the observed latent heat flux. The simulated mean ratios of evaporation to evapotranspiration in
these 3 months are 66 %, 60 %, and 95 %, respectively, and
these values are higher compared to the other months (43 % to 53 %). Thus, we speculate that the observed evapotranspiration does not solely represent stomatal transpiration in these months due to larger evaporation rates, leading to overestimated *g*_{s} in the observations.

Figure 8c shows that the optimized *g*_{i} often resembles the observed daytime *g*_{i} better than the original SiB4 simulation. Only in April is the optimized *g*_{i} overestimated at Hyytiälä. Again, this can likely be explained by the underestimated *g*_{s}, which is used to derive
observation-based *g*_{i} (see Sect. 2.2.2).

At Harvard Forest, the optimized SiB4 model generally simulates the
magnitude of the COS leaf uptake well (Fig. 9a). The model overestimates
the COS leaf flux only in the afternoon during the summer months. However,
*g*_{s} values are generally overestimated, and SiB4 simulates two peaks during daytime. This indicates that humidity stress is only briefly
occurring at midday in SiB4. However, in reality, the humidity stress
likely remains a limiting factor in the afternoon under conditions with high
vapor pressure deficit (VPD) (Kooijmans et al., 2019). Observations show
that *g*_{s} typically peaks in the early morning and decreases in the
afternoon due to higher afternoon VPD. Figure 10 shows that, similar to the
Hyytiälä simulation, the afternoon decrease in *g*_{s} at Harvard Forest is better simulated when we use the RH observed above the canopy. In Fig. 9c, the optimized *g*_{i} during the daytime agrees well with the observation-based *g*_{i}, except for several drops or peaks in July and October, likely caused by observational errors or uncertainty of the observed *g*_{s}.

### 3.5.2 Global application

Figure 11 shows the SIB4 calculated changes in the monthly COS biosphere
flux after applying the optimized temperature function and stomatal
parameters. The global COS sink remains almost preserved (original: 701 Gg S yr^{−1}, optimized: 704 Gg S yr^{−1}), but the regional budgets change
significantly. For example, the optimized model estimates larger COS uptake
for all seasons in boreal and temperate regions and smaller uptake in the
tropics. These changes are explained by the new temperature function of
*g*_{i} in Fig. 7. However, since the new temperature function is based on only two observation sites in the boreal and temperate regions, the
calculated uptakes need more verifications with observations obtained in
other areas and in different climate conditions, such as the tropics.

The higher uptake at high latitudes and lower uptake at the tropics are nevertheless consistent with inverse modeling results presented in previous studies (Ma et al., 2021; Hu et al., 2021) and would help towards closing the COS budget. Still however, the temperature response function and BWB parameters are now based on measurements of only two sites in only two biomes. With more measurements over different vegetation types, these parameters could also be optimized for a wider range of ecosystems.

To simulate more accurate COS leaf uptake in the SiB4 model, we have
proposed a new temperature function *f*(*T*_{can})_{new} for the CA enzyme and have optimized *g*_{s} and *g*_{i} parameters using observations in ENF
(Hyytiälä) and DBF (Harvard Forest) systems. The optimized model
reduced the MBE from −5.10 to 0.01 pmol m^{−2} s^{−1} at
Hyytiälä and from −2.53 to −1.99 pmol m^{−2} s^{−1} at Harvard Forest. Furthermore, *χ*^{2} decreases by about 0.41 and 0.38,
respectively.

The new function now considers an optimum temperature for enzyme activity,
contrary to the initial temperature function used in SiB4 where an
exponential increase of the temperature function was adopted from the
RuBisCo enzyme activity. The new temperature function is characterized by an
optimum temperature of 293 K (19.85 ^{∘}C) (Hyytiälä) and 309 K (35.85 ^{∘}C) (Harvard Forest). The new temperature response
increases *g*_{i}, and thereby the COS flux when the temperature is below the
optimum temperature (mostly at high latitudes), and decreases the COS uptake
at higher temperatures. (e.g., close to the Equator). Globally, these
modifications help to close gaps in COS budget that were identified in
earlier studies. In this study, we have interpreted the decreasing *g*_{i} at
higher temperatures as an optimum enzyme activity with the widely applied
assumption that there are no COS emissions in leaves. However, COS emissions
have recently been reported at high temperatures (Maseyk et al., 2014;
Commane et al., 2016; Gimeno et al., 2017). To determine reasons for
reducing COS leaf flux and internal conductance at high temperatures, it
will be necessary to analyze the possibility that leaf emissions exist in
observations in the future.

We have optimized the BWB model parameters for which we took advantage of
the characteristics that the nighttime COS flux informs about nighttime
*g*_{s} and thus the parameter *b*_{0}. The improved correspondence between model and observations shows that COS observations can help to constrain the relation between *g*_{s} and GPP better. In addition, we showed that SiB4
underestimates the leaf humidity stress under conditions where high VPD
should limit *g*_{s} in the afternoon. This can be improved with more
accurate relative humidity values and removing the threshold of humidity
stress that was implemented in SiB4 specifically for ENF.

The optimized parameters show different values depending on the PFT. Therefore, extending our approach with more observations in different climate zones and over different PFTs will help obtain accurate COS fluxes on a global scale. This approach would reduce the uncertainty in the global COS budget and provide additional constraints on GPP.

To evaluate the impact of the various parameters in *f*(*T*_{can})_{new} in the optimization as state variables, we implemented a sensitivity test of a total cost function combined with cost_{1} and cost_{2}, excluding the
background term in the cost function equation (Eq. 10). Figure A1 shows the
shape of the cost function when one parameter is varied within an acceptable
range while the other parameters are fixed (Daniel et al., 2010; Sun et
al., 2015) (details in Sect. 2.3.2). Based on the shape of the cost
function, we used a pragmatic approach to select realistic parameter ranges.
Variable values that push the cost function beyond 3.45 (Hyytiälä)
and 5.14 (Harvard Forest) were considered outside the allowed physical range
(red lines in Fig. A2). These thresholds are determined by the cost function
value assuming that the modeled *H*(*x*) is the 75-percentile value of observation in 3 h observation in each month. Variables *α*, *b*_{0}, *b*_{1}, and *T*_{eq} (Fig. A1a, b, c, and f) have more significant impacts on the cost function than Δ*H*_{a} (Fig. A1d) and Δ*H*_{eq} (Fig. A1e). Overall, costs in Harvard Forest are higher than at
Hyytiälä, likely because DBF has larger diurnal and seasonal
variations in the observed fluxes than ENF. We set the optimization range as
an initial value ±1.5 state error to apply SHGO algorithm.

Figure A2 shows contour diagrams of the cost function as a function of
*T*_{eq} and other parameters of *f*(*T*_{can})_{new}. The gradient is the cost function indicates the relative importance of each parameter. Δ*H*_{eq} does not interact with *T*_{eq}, but Δ*H*_{a} is inversely proportional to *T*_{eq} to minimize the cost. The cost function is most sensitive to variations in *T*_{eq}, and therefore we decided to fix Δ*H*_{eq} and Δ*H*_{a} at 100 and 40 kJ mol^{−1},
respectively, and to base our optimization on the state variables *α*,
*b*_{0}, *b*_{1}, and *T*_{eq}.

To evaluate the ability of constrain the parameters, we performed an
ensemble optimization with 100 different members. In each optimization,
noise was added to the parameters (*ε*_{a}) and to the observation (*ε*_{y}). Random perturbations were drawn from a normal distribution with zero mean and standard deviations *σ*_{a} for the state parameters (*x*) and *σ*_{y} for the observations (*y*). The new cost function of an individual
optimization thus becomes

We optimized each ensemble with the same *y* (observationally derived GPP and
COS leaf uptake) and *x* but added noise to each ensemble member (Chevallier
et al., 2007). Subsequently, we calculated the posterior uncertainty as the
1 standard deviation of the posterior distribution of the optimized
parameters.

Figure B1 shows the prior and posterior distribution of the parameters at the two stations. All posterior parameters show considerable reductions of variations (error), with optimized values that are listed in the main text in Table 3.

Additionally, we calculated a correlation matrix between the posterior-state parameters at the two stations, which is shown in Fig. B2. Overall, each parameter does not interact significantly (covariances < 0.7).

The SiB4 code is available online at https://gitlab.com/kdhaynes/sib4v2_corral (SiB4 project members, 2020). TM5-4DVar model codes are available on the TM5-4DVAR website (https://sourceforge.net/projects/tm5/; Krol et al., 2013).

Observation data are downloaded from the original publications as mentioned in Sect. 2.2.

AC, LMJK, and MCK devised the study. AC optimized ecosystem parameters and analyzed the results with the consultation of LMJK and MCK. KMK and RW provided observation data and site-specific insights. AC wrote the paper, and all the authors provided comments.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank everyone that contributed to the collection of data for the Hyytiälä and Harvard Forest sites. The ecosystem dataset by eddy covariance at Hyytiälä was supported by ICOS Finland (319871) and the Atmosphere and Climate Competence Center (ACCC) Flagship (Vesala et al., 2022). The soil dataset at Hyytiälä was collected from Sun et al. (2018). Data from Harvard Forest are supported by the AmeriFlux Management Project (Wehr et al., 2017; Commane et al., 2015).

This work was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. We acknowledge computing resources from the Netherlands Organization for Scientific Research (NWO; grant no. NWO-2021.010).

This research has been supported by the European Research Council, H2020 European Research Council (grant no. 742798).

This paper was edited by Christopher Still and reviewed by Georg Wohlfahrt and one anonymous referee.

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