Carbonyl sulfide (COS) is a useful tracer to estimate
gross primary production (GPP) because it shares part of the uptake pathway
with CO

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

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 (

Several studies found that the leaf relative uptake ratio (LRU; which is
proportional to the ratio of COS and CO

Besides uncertainties in

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

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

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

SiB4 simulates COS vegetation assimilation as a combination of three
conductances from the laminar boundary layer to the chloroplast (

The stomatal conductance

The empirical constant

GPP

The COS molecules that have diffused into the leaf mesophyll cells are
hydrolyzed in a reaction catalyzed by the CA enzyme (

Other modifying factors in Eq. (6) are the ratio of atmosphere pressure
(

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
(

Calculated

In optimizing the parameters

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.

Monthly diurnal variation of COS fluxes in 2016 at
Hyytiälä

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.

Observation-based

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

Observation-based

In the optimization steps, we minimized a quadratic cost function

To optimize the

Flow chart of the procedure to optimize COS leaf uptake's
parameters. The procedure has two steps: (1) optimize

We select GPP for the first step optimization rather than

In the optimization procedure, we specifically exploit the fact that the
nighttime COS flux carries information about nighttime

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

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.

To quantify the observational errors

Distribution of the observation error in the growth

We utilized several simulated variables from SiB4 in our optimization.
Specifically, calculated GPP

To simulate the vegetation assimilation

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

To examine the humidity stress impact in SiB4, we performed a simulation
with and without the lower threshold for

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 (

Figure 5 investigates which conductance contributes most to the total
conductance (

Monthly median value of diurnal conductances (black:

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

RMSE, MBE, and

Same as Table 1, but for COS leaf uptake, as applied in the
original

The posterior result of COS leaf uptake (“post” in Table 2) shows a slight
improvement compared to the original-state variables with

Scatter plots between observed and estimated COS leaf
uptake from original parameters with

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

Original (org) and optimized (post) state vectors for Hyytiälä and Harvard Forest in different phenological stages as defined by SiB4. Values of posterior in parentheses indicate posterior errors. The definition of the prior values is outlined in Appendix A, and the error reduction is described in Appendix B.

The

The optimized results of the BWB model parameters

Concerning the estimated errors in

The optimized parameters show significant improvement in temperature
response of the COS leaf uptake. Figure 7 presents the temperature
dependency of

Temperature dependency on

Monthly diurnal cycle of COS leaf uptake

In the upper panel of Fig. 7, we see the different roles of

The temperature responses of

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,

Same as Fig. 8 but for Harvard Forest (HVFM).

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

However, the model still overestimates

Average diurnal cycle of

However, SiB4 still tends to overestimate

The optimized model still underestimates

Figure 8c shows that the optimized

Monthly COS sink and averaged temperature in the mixed
layer (

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,

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

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

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

We have optimized the BWB model parameters for which we took advantage of
the characteristics that the nighttime COS flux informs about nighttime

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

Cost function values plotted against the value of the state
vector elements at Hyytiälä (solid line) and Harvard Forest (dotted
line). The red lines indicate a criteria cost calculated by

Contour diagram of the cost function value as a function of

Figure A2 shows contour diagrams of the cost function as a function of

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 (

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

Error reduction of state variables in two stations
(Hyytiälä (HYYT) and Harvard Forest (HVFM)). The red lines represent
median values, and the boxes represent errors. Column “pri” shows the
initial value and state error. Column “post” represents the mean of the
optimized-state variables and the corresponding standard deviation.

Covariance matrix for all state variables at Hyytiälä (HYYT) and Harvard Forest (HVFM).

The SiB4 code is available online at

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.