Soil exchange of carbonyl sulfide (COS) is the second largest COS flux in terrestrial ecosystems. A novel application of COS is the separation of gross primary productivity (GPP) from concomitant respiration. This method requires that soil COS exchange is relatively small and can be well quantified. Existing models for soil COS flux have incorporated empirical temperature and moisture functions derived from laboratory experiments but not explicitly resolved diffusion in the soil column. We developed a mechanistic diffusion–reaction model for soil COS exchange that accounts for COS uptake and production, relates source–sink terms to environmental variables, and has an option to enable surface litter layers. We evaluated the model with field data from a wheat field (Southern Great Plains (SGP), OK, USA) and an oak woodland (Stunt Ranch Reserve, CA, USA). The model was able to reproduce all observed features of soil COS exchange such as diurnal variations and sink–source transitions. We found that soil COS uptake is strongly diffusion controlled and limited by low COS concentrations in the soil if there is COS uptake in the litter layer. The model provides novel insights into the balance between soil COS uptake and production: a higher COS production capacity was required despite lower COS emissions during the growing season compared to the post-senescence period at SGP, and unchanged COS uptake capacity despite the dominant role of COS emissions after senescence. Once there is a database of soil COS parameters for key biomes, we expect the model will also be useful to simulate soil COS exchange at regional to global scales.

Carbonyl sulfide (COS) is an atmospheric trace gas, with average
concentration of around 480 pmol mol

Laboratory studies have shown that soil COS uptake is a function of soil
temperature and moisture, microbial CA enzyme activity, and ambient COS
concentration

Existing models have also not considered the possibility of COS production in
oxic, upland soils, based on the assumption that they usually behave as a COS
sink

Here we develop a diffusion–reaction model for soil COS flux, with four major
advantages compared to previous empirical approaches:

Diffusion is explicitly resolved, providing a more realistic concentration-dependent uptake in the soil column.

The model accounts for flux activity in surface litter layers.

The model includes COS production terms.

Litter and soil COS uptake and production terms can be constrained or optimized using field data.

We construct a two-phase 1-D diffusion model with microbial COS source–sink
terms in soil and litter layers to calculate surface COS fluxes. Diffusion of
COS in the soil and litter is described by Fick's law in porous media,

For computational efficiency, diffusion in the aqueous phase is not
prognostically evaluated but forced by the solubility equilibrium. By
invoking Henry's law, the above equation assumes that the aqueous
concentration is always in equilibrium with the gaseous concentration,
ensuring mass balance. Approximating aqueous diffusive flux with this
assumption does not significantly bias the surface flux (see Supplement), since
aqueous diffusivity of COS is several orders of magnitude smaller than the
gas-phase diffusivity

Advective transport is not considered since the evaluation data sets were not
affected by advection. However, advection effects on surface COS flux may not
be negligible when there is strong wind pumping causing pressure fluctuations

We use a face-centered finite-volume grid for discretizing the soil column,
with 26 computational nodes down to 1 m depth. The vertical grid is
constructed using an equation similar to that in the Community Land Model 4.5

The depths of the layer interfaces are defined as

The use of face-centered rather than node-centered control volumes generally gives better evaluation of diffusive fluxes across interfaces.

We use the Crank–Nicolson method to discretize the diffusion–reaction
equation, which ensures numerical stability when using large time steps

We first discretize spatially Eq. (

The diffusivity at the interface,

The flux at the topmost layer is thus

Again,

By rewriting Eq. (

The above linear ODE system is then discretized at time step

Therefore, the evolution in time is,

At each time step, the concentration profile is evolved to the next time step with the diffusion–reaction operator. Thus, the model can simulate transient conditions in real time.

The diffusivity of COS in soil media (

For COS,

In solubility equilibrium, the chemical potentials of COS in gas phase
(

For a dilute solution, as

Temperature dependence of

The dimensionless Henry law constant,

Thus, we can build a nonlinear regression model for temperature dependence of
the dimensionless Henry law constant:

Using

Because both COS uptake and production activities exist in soils and the net
COS flux exhibits a linear response to COS concentration

Soil COS uptake (

We assume that the temperature limitation function for soil COS uptake
reflects the temperature dependence of enzyme activity, which is described as

Other enzymes in soil microbes may also contribute to COS uptake, for
example, COSase, nitrogenase and CS

COS solubility function used in this study (pink), obtained from
regression with

Typical fit values of

The temperature dependence (Eq.

COS solubility functions in the literature and in this study.

Site-specific parameters (SR: Stunt Ranch, CA; SGP: Southern Great Plains, OK).

For the parameterization of moisture dependence, we use a simple bell-shaped
function, described by the form of the Rayleigh distribution function:

Soil COS production is represented as an
exponential function of temperature,

Litter was present at one of the model evaluation sites (Stunt Ranch). We
obtained an equation for litter COS fluxes based on an incubation experiment
with litter at the Stunt Ranch site

Litter porosity is usually much larger than that of soils. In the model, the
porosity at the grid point near the litter–soil interface is interpolated so
as to prevent numerical instability caused by discontinuity
(Fig.

Soil porosity and moisture profiles at the SGP site

Temperatures of the litter layers were interpolated between soil and chamber
air temperature by assuming a logarithmic temperature profile in the surface
layer, according to mixing length theory

Southern Great Plains, OK (SGP): soil COS fluxes were measured from 1 April
to 31 May 2012 in a wheat field at the ARM (Atmospheric Radiation Measurement) Southern Great Plains Central
Facility (36.61

Stunt Ranch, CA (SR): surface COS fluxes were measured from 1 April to
15 April 2013 in a Mediterranean oak woodland at the University of California
Stunt Ranch Santa Monica Mountains Reserve (34

Site-specific parameters are summarized in Table

Soil temperature profiles are modeled with the observations at 5 cm depth.
The temperature signals are considered as a superposition of fast varying
diurnal signals (

For the SR data, we observed that the temperature optimum for COS uptake is

Soil moisture was measured at 5 cm depth at both sites, and additionally at
30 cm at SGP. We generate soil moisture profiles for the SGP site by
interpolating between the 5 and 30 cm data and assuming constant soil
moisture below 30 cm (cf. 1-D simulations with gravity drainage boundary
condition in

Since litter was present at the SR site, litter layers are included in model
simulations when validating the model with the SR data set. The 2 cm thick
litter layer is represented in the top six grid points. Litter porosity was
measured to be 0.94 m

In the evaluation, soil COS uptake and production capacities
(

Summary of model evaluation results.

The simulated COS fluxes at the SGP site are generally in good agreement with
the observations (Fig.

From the incubation experiments,

The observed COS emissions were higher in the senescence and post-harvest
stages (after DOY 134) than during the growing season. However, when the
temperature dependence is considered, the COS production capacity in the
growing season (before DOY 130) must be higher than after harvest to account
for the high fluxes under relatively low soil temperatures (

Typical simulated profiles of COS concentration.

Surprisingly, to simulate the strong diurnal variability of COS emissions in
the senescence and post-harvesting stages, the high emissions need to be
counteracted by continuing COS uptake, with the same uptake capacity as
during the growing season. Without uptake activity, COS would accumulate in
the soil column from high production in the daytime and still exhibit high
emissions at night. An additional contribution to daytime emissions could
have come from photochemical production of COS, as observed for SGP soil in
lab incubations

The observation period at SR started with a rain event and thus at high LWC.
We set the starting LWC to 0.32 g g

The simulated COS profiles show that the presence of litter layers on top of
the soil reduces the COS supply available to the soil, especially when there
is strong uptake in the litter layers, thus limiting the contribution of soil
uptake to the overall surface uptake (Fig.

Laboratory studies have found that soil COS uptake has an optimum at
19–30 % water-filled pore space fraction (WFPS) and approaches zero as
WFPS becomes higher

Modeled sensitivity of surface soil COS uptake to water-filled pore
space fraction (purple) at soil temperatures of 13, 15, 20 and
22

We also show that for diffusion-controlled, concentration-dependent uptake,
the surface flux does not increase linearly with soil COS uptake capacity
(

One of the main advantages of using a depth-resolved model is that it enables
the analysis of changes in uptake and production capacities over time, or
between sites. For example, an unexpected finding was that the production
capacity parameter at SGP needed to be decreased after the senescence stage
(from

The uptake and production parameters that best fit at each site and during
distinct phenological periods can be obtained by optimization procedures used
with a particular soil data set, another significant advantage of a
depth-resolved model. Given reasonable initial guesses of the uptake and
production parameters, the optimization runs iteratively over the data with
the gradient descent or Newton's method until the minimal sum of square
errors is attained. An example of data optimization applied to the SR data set
is in

An idealized numerical experiment to test the sensitivity of COS
flux to soil COS uptake capacity, with

Increase of surface COS uptake (in percentage) from 10-fold changes
of

We found that soil COS uptake is largely determined by activity in the top
10 cm of the soil. For each layer, we calculated how much the surface uptake
would increase as a result of increasing the COS uptake capacity
(

The COS flux model can be integrated into more comprehensive land surface
models (e.g., CLM4.5 and SiB3) to simulate global fluxes. Soil temperature and
moisture are usually generated from prognostic equations in these models.
Litter layers would need to be added as they are often not represented
separately but embedded in soil layers as soil organic carbon (e.g., in
CLM4.5). Several parameters may be biome-specific: (1) the uptake and
production capacities of COS (

The

This study presents a mechanistic diffusion–reaction model coupling physics and biogeochemistry to simulate soil COS flux, as well as its evaluation with field data. The model explicitly accounts for diffusion in the soil column, COS production, and COS exchange in the litter layer. The model reproduced well-observed fluxes at two sites and has enabled us to gain novel (and unexpected) insights such as the higher COS production capacity at SGP during the growing season despite lower soil COS emissions, and the continuing COS uptake capacity required to partly counteract the large COS emissions at SGP after harvest. We also demonstrate that diffusion must be considered to accurately simulate surface COS fluxes. Diffusion control on surface uptake is evident in its sensitivity to soil water content and the sub-linear response of uptake flux to soil COS uptake capacity. For large-scale simulations of soil COS fluxes, further lab and field studies are needed to establish a database of soil and litter COS uptake and production capacities and parameters for typical soil types across key biomes.

List of variables and parameters.

The numerical solver described by Eq. (

We thank Mary Whelan, Joe Berry and Ian Baker for valuable discussions. This study was supported by a China Scholarship Council (CSC) fellowship to W. Sun, and the European Research Council (ERC) Starting Grant no. 202835 to U. Seibt.Edited by: C. Sierra