Common methods for measuring soil denitrification in situ
include monitoring the accumulation of

Field experiments with arable silt loam soil for measuring denitrification
with the

From our model and experimental results we conclude that field surface
fluxes of

Corrected denitrification rates can be obtained by estimating subsurface flux and storage with our model. The observed deviation between experimental and modelled subsurface flux revealed the need for refined model evaluation, which must include assessment of the spatial variability in diffusivity and production and the spatial dimension of the chamber.

Denitrification in ecosystems is complexly controlled by interaction of labile C, abundance and community structure of denitrifiers, pore structure, soil and root respiration, and mineral N dynamics (Müller and Clough, 2014). It is difficult to keep conditions in the lab identical to the field, where some conditions dynamically change due to climatic factors but especially due to the activity of plants. Hence, field measurements are indispensable for reliable determination of denitrification in ecosystems.

When chamber methods are used to determine soil gas fluxes to the
atmosphere, a certain fraction of the produced gas is not emitted at the
surface but remains in the soil (Parkin et al., 2012). This is because the
accumulation of gases in the closed chamber decreases concentration
gradients between soil and chamber atmosphere, causing lowering of surface
fluxes with increasing chamber deployment time (Healy et al., 1996). This
effect has been addressed in numerous studies (Venterea et al., 2009; Healy
et al., 1996; Sahoo et al., 2010). To correct bias from this effect, several
approaches have been developed and compared (Parkin et al., 2012).
Denitrification estimates based on measurements of

Estimating bias from the diffusive loss of

Our objectives were thus to determine the significance of the fraction of

The

In order to measure denitrification in arable soil, depth of confinement, and
also of
labelling, typically includes the

To keep our modelling as simple as possible we assume a simplified process
dynamics where in terms of N transformation, only nitrate reduction by
microbial denitrification occurs, with

The bias in determining denitrification rates from the accumulation of

Conceptual model describing the dynamics of diffusive fluxes
(black dotted arrows) of

We define the fluxes of

The

Relative

Accumulation of

Following

Before closing the chamber, the upper soil boundary is the free atmosphere,
where gas exchange is fast enough to preclude

Production leads to accumulation of

After a certain time, the steady state is reached, where all fluxes reach constancy.

Closing the chamber changes the upper boundary, since chamber concentration increases due to surface flux (Fig. 2a). Consequently, subsoil and storage flux are rising again, whereas surface flux is decreasing.

Numerical finite element modelling (FEM) was used for simulating gas
transport during the chamber measurements (COMSOL Multiphysics, Version 5.2,
COMSOL Inc., Burlington, Massachusetts, US) to estimate surface and
subsurface fluxes of

Two different experimental set-ups were modelled and used in the field. The
first experimental set-up (A_bottom_open) is described by the conceptual model above and includes an open bottom cylinder containing the labelled

Modelled set-ups.

Molecular gas diffusion was assumed to be the only transport mechanism in the soil. The left and right side and the bottom of the modelled domain were defined as impermeable (Neumann boundary condition). The upper boundary of the atmospheric layer was set to atmospheric gas concentrations as the Dirichlet boundary condition and acts therefore as a sink for the gases produced. To increase computational efficiency, a 2-D axisymmetric modelling approach was chosen, since the cylinder and the chamber were round objects. The modelled volume was set to sufficiently large volume with a soil depth of 1.0 m and a diameter of 1.0 m to ensure that the dimension of the modelled area does not affect the modelling outcome within the cylinder and chamber area.

Gas transport was modelled for all isotopologues of

Different experimental set-ups and scenarios were modelled with the lower end of the cylinder being sealed or open (A_bottom_closed; A_bottom_open), describing the field set-up that was actually used (Table 1). Also further theoretical set-ups have been modelled to evaluate the effect of the dimension of the cylinder and labelled zone (B scenarios).

Time-dependent modelling of the open chamber set-up was performed to assess
the time that is needed after the initiation of the system, i.e. after
adding labelled

To model chamber measurement, two modelling steps were run. In a first modelling step, steady-state concentration distributions assuming steady denitrification were modelled for the open chamber. The resulting concentration distributions were then used in a second modelling step as input for time step 0 for the time-dependent modelling of the closed chamber (Fig. 2a and b). This approach was used for all modelling scenarios.

Parameter sweeps were conducted for the set-ups used in the field (A_bottom_open and A_ bottom_ closed; Table 1) to assess the theoretical effect of soil moisture, pore volumes and production rates. This was done to account for these transport-related effects in the calculation of the flux measurements. For all parameter combinations a new model was calculated.

Total pore volume was set to 0.51 m

Range of parameter values used to assess effect of soil gas transport and production rates.

The output of the parameter sweeps of scenario A_ bottom_open and scenario A_bottom closed included
combinations of soil water content, production rates of the soil core,
chamber concentrations, and fluxes into the chamber and into the subsoil of
the respective gas species. This dataset allowed for linking the gas
concentration in the chamber after 2 h at a given soil moisture with the
respective production rate. Non-linear functions were fitted to the dataset
(PROC NLIN, SAS 9.2, SAS Institute Inc., Cary, North Carolina, USA) so that the original
production of a gas species could be directly calculated from the
concentration after 2 h of the respective gas, the total pore volume and the
soil moisture. Instead of soil water content, the soil gas diffusion
coefficient

Four additional theoretical experimental set-ups were modelled to assess the
effect of the soil cylinder length and the length of the labelled zone
within the cylinder (B-scenarios, Table 1). For these set-ups the same soil
parameters were used as for the field scenarios. To assess the effect of soil
moisture, the model was run at soil water contents of 0.24, 0.34 and 0.44 m

Underestimation of gas production was quantified as the difference between the
production (

Experiments were part of a field campaign to measure

Four aluminium cylinders of 35 cm length and tapered at the lower end were
driven into the soil to 30 cm depth, thus leaving the upper end 5 cm above
the soil surface.

Soil water content was determined by weight loss after 24 h drying at
110

Samples were analysed using an Agilent 7890A gas chromatograph (Agilent
Technologies, Santa Clara, CA, USA) equipped with a pulsed discharge
detector (VICI, V-D-3-I-7890-220). Precision, as given by the standard
deviation (

Gas samples were analysed for

Results of flux measurements with the bottom open or bottom closed were compared
by a paired

Modelling results of Scenario A_bottom_open (imitating the field set-up) demonstrated 3-D
spatial distribution of gas concentrations and the resulting diffusive
fluxes with the highest concentrations in the centre of the

Chamber closing leads to an increase in maximum concentrations (Fig. S1) and also to lowering of surface fluxes (Figs. 3 and 4).

Relative fluxes of

Relative fluxes following chamber closing with different water contents in scenario A_bottom_open (surface flux, storage flux and subsoil flux starting at positive values, at zero and at negative values, respectively).

After chamber closing, surface flux decreases continuously while subsurface
flux increases, and the storage flux initially increases before gradually
decreasing. This shows that the lowering of surface flux with the increasing
time of chamber closing results from increasing subsoil flux but also from
further accumulation of denitrification products in pore space. While
surface flux is largest among all fluxes at chamber closing, it is exceeded
by subsoil flux after about 1 h. With increasing SWC, and thus
decreasing diffusivity, the change in fluxes with time is lowering (Fig. 4).
The highest relative subsoil fluxes are thus obtained at the lowest SWC. For

To understand the effect of the labelling design, modelled fluxes of
scenario B_30_30, B_45_30, B_ 45_45 and B_60_45 were compared. With decreasing depth of

Impact of the depth of the active core (representing depth of

Modelled underestimation of

Underestimation of

If diffusion to the subsoil was omitted, e.g. by closing the bottom of cylinders in the field or during laboratory incubations, soil air concentrations and surface fluxes increase (Fig. 6). When comparing values with and without omitted subsoil diffusion, relative surface flux 2 h after closure was 0.75 and 0.4, respectively. But with the bottom closed, surface flux was still significantly lower than production due to continuing pore space accumulation (relative storage flux of 0.25 after 2 h).

Simulated time course of surface and subsurface fluxes with
the open bottom or closed bottom (scenario A_bottom_open and A_bottom_closed at SWC

We conducted several runs using the field scenarios A_bottom_open and A_bottom_closed to generate a dataset that allowed the parameterization of functions that describe the relation of the concentration reached after 2 h of chamber closure and the production within the labelled soil volume. This was done to allow a comparison of modelled data with the field measurements (Table 5). Moreover, we hereby give an example how denitrification rates can be calculated using empirical equations and thus without the need to run the 3-D model for each data evaluation.

We obtained the following equation to calculate the production of each gas
species of interest (

Average

The comparison between surface flux with or without closing the cylinder
bottom was conducted on 4 June 2016, with the chamber closing at 10:40
(bottom open) and 14:40 (bottom closed; CET – Central European Time; all times listed in CET). Mean surface flux of

Coefficients for the calculation of denitrification rates
using Eq. (1) based on chamber concentrations for 2 h chamber closing
time, 30 cm depth of

Comparing

The

The ability of the model to predict the time pattern of gas accumulation was
evaluated by comparing measured and simulated values. Model runs using the

Our comparison between

While the increase in

Modelling diffusive fluxes of

For laboratory studies with the

Our results show that extending chamber deployment time is not a good
strategy for improving the detection limit for denitrification. This is because
the fraction of gaseous denitrification products that is not emitted at the
soil surface is increasing with time. Although we can now estimate this
fraction with our model, uncertainties of the modelled data lead to
increasing uncertainty in denitrification estimates with chamber deployment
time. Another way to improve detection is to lower the

Because the flux dynamics of gaseous denitrification products in the soil were not taken into account in past field flux and certain laboratory studies, we assume that numerous studies underestimated denitrification significantly. It can thus be concluded that soil denitrification is probably even more relevant than assumed today.

Our model approach is suitable for estimating pore space accumulation and subsoil diffusion of denitrification products. It thus allows us to determine production based on surface fluxes in field flux studies but also in closed laboratory incubations. Principally, it could also be used to correct previously published data if necessary information on diffusivity and pore space were available. For experiments with the same dimensions and bulk density as those assumed in our regression model, it is also possible to calculate production from surface flux using the parameters of Table 4. Principally, the regression approach offers an easy way to derive production without the need to run the 3-D model. But to obtain a general solution that would fit any experimental conditions in terms of bulk density, depth of labelling, chamber design and deployment time, it will be necessary to conduct multiple model runs, which was beyond the scope of this paper.

Our approach includes several factors of uncertainty. A prerequisite for
precise quantification is the knowledge of the vertical distribution in
activity and diffusivity. Moreover, we have to assume the steady state, which is
never perfectly realized due to temporal change of diffusivity and
denitrification rates, e.g. following precipitation and thus decreasing
diffusivity, increasing moisture, changing the labelled volume. Finally,
we did not yet take into account water-phase transport. But this has some
relevance due to low diffusivity in the water phase. The impact of water-phase transport should be largest for

The general agreement between measured and modelled increase in surface flux
after closing the cylinder bottom can be seen as a first proof of our
concept to quantify denitrification rates using surface fluxes and
modelling. Reasons for the observed deviations between experimental and
model results can be manifold. In view of the aforementioned factors of
uncertainty, these could include imperfect estimation of

Which progress in flux estimation is obtained in view of incomplete
knowledge on parameters, and could incorrect parameter estimation lead to
augmented bias? Even uncertain estimates of subsoil fluxes would improve the
outcome of the

While it was beyond the scope of this study to evaluate uncertainty in detail, future work should follow up on this in order to explore the achievable accuracy in estimating subsoil flux and storage under given conditions. This should include modelling water-phase transport, depth of labelling, and the impact of spatial and temporal variability in diffusivity and denitrification rates. Moreover, controlled experiments would be needed to validate model results as far as possible.

Measurements and production–diffusion modelling showed that field surface
fluxes of

Data from measurements and modelling are available upon request from the corresponding author.

The supplement related to this article is available online at:

RW designed the overall concept. RW and DLS designed the field experiments, and DLS and NR carried them out. MM developed the model code and performed the simulations. RW prepared the paper, with contributions from JRK, DLS and MM.

The authors declare that they have no conflict of interest.

We thank Frank Hegewald for technical support in experiments, Martina Heuer and Jennifer Ehe for stable isotope analysis, Kerstin Gilke and Andrea Oehns-Rittgerod for analysis by GC, and Roland Fuß for support in statistical analyses. We further thank the supplying of an experimental field site by the Faculty of Agriculture, South Westphalia University of Applied Sciences. We are grateful to two anonymous referees for their constructive feedback.

This research has been supported by the Deutsche Forschungsgemeinschaft (grants LE 3367/1-1 and research unit 2337: “Denitrification in Agricultural Soils: Integrated Control and Modeling at Various Scales (DASIM)”).

This paper was edited by Ivonne Trebs and reviewed by two anonymous referees.