The following sections provide a detailed description of MeMo in the context
of existing global soil CH4 uptake. Table 1 provides a summary of all
terms, names and units used in the model description section, while Table 2
contains a short summary of the four global CH4 uptake models based on
the P96 family.
Solution of the reaction–transport equation
The R99 model solved Eq. (2) semi-numerically by (i) assuming steady state,
(ii) numerically approximating the diffusion term similar to the approach
applied in the P96 model (Table 2, Eq. 11) and (iii) assigning CH4
oxidation exclusively to a distinct soil layer of thickness ϵ at
depth zd=6 cm (Table 2, Eq. 12). However, CH4 consumption can
occur throughout a soil profile, and thus Eq. (12) (Table 2) may either
overestimate or underestimate the CH4 sink.
In the C07 model, Eq. (2) was solved analytically, providing a more accurate
and mathematically robust estimate of CH4 uptake (Table 2, Eq. 13).
Assuming steady-state conditions and constant DCH4 and kd
throughout the soil profile, integration of Eq. (2) provides a general
solution for determining CH4 concentration at depth z in soil:
CH4(z)=A×exp-kdDCH4z+BexpkdDCH4z,
where A and B are integration constants that can be determined by setting
upper and lower boundary conditions for the soil profile. The concentration
of CH4 at the soil–atmosphere interface is defined by the atmospheric
concentration of CH4 (CCH4), and thus a Dirichlet
boundary (i.e. fixed concentration) is applied at the upper boundary.
Conditions at the lower boundary are more challenging to ascribe because the
soil depth at which atmospheric CH4 is completely consumed is not
known a priori.
Negligible CH4 flux through the lower boundary (C07
solution)
The C07 model circumvents the problem by applying a homogenous Neumann
(no-flux) condition at the lower model boundary:
dCH4dzz→∞=0.
The application of this boundary condition allows derivation of the
integration constants A=CCH4 and B=0, which simplifies
Eq. (3) to
CH4z=CCH4×exp-kdDCH4×z.
The diffusive uptake of atmospheric CH4 at the soil–atmosphere
interface can then be calculated using the derivative of Eq. (4) at z=0:
JCH4=-DCH4×dCH4dzz=0=DCH4×CCH4×kdDCH4=CCH4DCH4kd.
This formulation of soil uptake of CH4 is the simplest analytical
solution to Eq. (2). It represents an improvement from the semi-numerical
representation used in the R99 model and enables complete consumption of
CH4 to be accounted for within the soil; however, the homogeneous
Neumann boundary condition applied here is only an approximation, which is
not generally valid. The simulation will not be influenced if the Neumann
boundary is infinitely far from the consumption depth of CH4, and
thus the corresponding Neumann boundary condition can be neglected. However,
if this is not the case, it will result in simulation error.
Complete consumption of CH4 at an a priori unknown
depth L (MeMo solution)
Therefore, we adopted an approach similar to the C07 model but one that is
generally valid. We assume that methanotrophy consumes atmospheric
CH4 in the soil until CH4 reaches a threshold
(CH4(L)= CH4 min) that can be imposed based on biological
limits (CH4 min = 100 ppb) or when CH4 is fully depleted
(CH4 min = 0). The integration constants in Eq. (3) thus become
A=-CCH4×expkdDCH4L-CH4minexp-kdDCH4L-expkdDCH4LB=-CH4min+CCH4×exp-kdDCH4Lexp-kdDCH4L-expkdDCH4L.
In addition to the concentration condition CH4
(L) = CH4 min, a flux condition also is imposed on the lower
boundary in order to determine depth L: -DCH4×dCH4dzz=L=FCH4, where FCH4 denotes a potential CH4 flux across the
lower boundary that can be specified (i.e. CH4
(L) = CH4 min) or set equal to zero (i.e. CH4 (L) =0). The unknown depth L is then calculated by substituting the
derivative of Eq. (3) into the expression for the lower boundary
condition:
-DCH4×dCH4dzL=-DCH4×A-kdDCH4×exp-kdDCH4L+BkdDCH4×expkdDCH4L=FCH4.
Rearranging Eq. (8) and finding its root allows for the determination of the
initially unknown depth L where CH4(L) = CH4 min:
0=-DCH4kdDCH42CCH4-CH4min×exp-kdDCH4L-CH4min×expkdDCH4Lexp-kdDCH4L-expkdDCH4L-FCH4.
Once L is known, total CH4 uptake can be calculated from
JCH4=-DCH4×dCH4dzz→z=0=-DCH4-AkdDCH4+BkdDCH4,
where A and B are defined by Eqs. (6) and (7). When L tends to
infinity,
Eq. (10) is equivalent to the C07 model solution; however, Eq. (10) also
allows for (i) complete consumption of CH4 within the soil interval,
(ii) influx of CH4 from beneath the soil profile (e.g. from thawing
permafrost or production of CH4 in oxygen-depleted microsites in
soil) and (iii) a minimum CH4 concentration at which methanotrophy
can occur in the soil column.
Figure 1 illustrates CH4 soil profiles and the penetration depth of
CH4 into soil, L, for different kd values, FCH4=0 and DCH4=D0CH4 (diffusivity in free air)
(Table 1). It is expected that L will vary spatially depending on local
kd, DCH4 and soil properties.
Computational solution of Eq. (9) for different values of kd.
Parameter L is defined as the depth where CH4 min = 0,
assuming complete removal of CH4 in soil pore spaces.
MeMo is based on the more general solution (Eq. 10) and uses local
methanotrophy rates (kd) and diffusion coefficients
(DCH4) based upon soil conditions to determine CH4
penetration depths (L). Additionally, Eq. (9) allows one to set a
minimum CH4 concentration if this parameter is known. Here, we
assume a minimum of 0 or complete consumption. We assume no in situ
production of CH4 or upward CH4 flux from below (i.e.
FCH4=0) because of a scarcity of field data for model
validation. However, a flux from below can be employed in MeMo to enable a
more comprehensive quantification of soil CH4 uptake that also
potentially accounts for consumption of upward-migrating CH4 and
autochthonous CH4 produced in oxygen-depleted microsites of finely
textured soil.
Parameters
The rate of CH4 uptake by soil is controlled by the balance between
gaseous diffusion of atmospheric CH4 into soil and the rate of CH4
oxidation by methanotrophic bacteria as described by Eqs. (14) and (20), respectively.
Thus, DCH4 and kd are key
parameters, and accurate characterization of their values is essential for
robust quantification of the soil CH4 sink.
Soil CH4 diffusivity, DCH4
Similar to the R99 and C07 models, DCH4 in MeMo is determined
from the diffusivity of CH4 in free air (D0CH4; Table 1) adjusted
for the influence of temperature (GT) and soil structure (Gsoil):
DCH4=D0CH4×GT×Gsoil.
The gaseous diffusion coefficient of CH4 in soil increases linearly
with temperature T (∘C) (Potter et al., 1996) according to the
relationship
GT=1.0+0.0055T(∘C).
The soil structure factor (Gsoil) accounts for the effects of pore size,
connectivity and tortuosity on gaseous diffusion and is determined according
to the parameterization of Moldrup et al. (1996, 2013):
Gsoil=Φ4/3ΦairΦ1.5+3/b,
where Φ is total pore volume (cm3 cm-3), Φair
is air-filled porosity (cm3 cm-3), and b is a scalar that
accounts for soil structure. Total pore volume is defined as a function of
bulk density ρ (g cm-3) and average particle density d
(Table 1) (Brady et al., 1999):
Φ=1-ρd.
The scalar b in Eq. (16) is calculated as a function of soil clay content
(fclay; %) as proposed by Saxton et al. (1986):
b=15.9fclay+2.91.
Air-filled porosity (Φair) is determined from the difference
between total pore volume and soil water content θ (%):
Φair=Φ-θ.
Rate constant for CH4 oxidation, kd
The CH4 oxidation rate (kd) is defined as the base oxidation
rate constant (k0) for an uncultivated moist soil at 0 ∘C
scaled by three factors to account for the influence of soil moisture
(rSM), soil temperature (rT) and nitrogen content
(rN):
kd=k0×rSM×rT×rN.
The R99 and C07 models used a similar equation to estimate kd but
without the rN parameter, opting instead to employ intensity of
agricultural activity as a proxy to account for the inhibitory effects of N
deposition on soil methanotrophy. Moreover, the C07 model excluded rN
from the kd formulation and used a N deposition term to modify total
CH4 uptake flux (Table 2, Eq. 13), which results in a larger N
inhibition effect. The approach employed in MeMo is to use N deposition data
directly to modify kd.
Base oxidation rate constant, k0
The base oxidation rate constant (k0) is a key parameter that exerts
significant control on kd and thus the estimated CH4 uptake flux.
For example, a 10-fold change in k0 (and thus kd) leads to a 3-fold
decrease in the depth L at which CH4 is fully depleted from soil pores
(Fig. 1) and a ∼ 3-fold increase in total uptake of CH4 (Fig. 2).
Total CH4 uptake for different values of k0 (s-1),
assuming a constant value of DCH4=D0CH4 and no
modification by soil temperature, moisture or nitrogen deposition.
Rate constants can be defined either on the basis of theoretical
considerations or through site-specific field and laboratory observations.
Rates of soil microbial processes, such as CH4 oxidation, are
controlled by microbial biomass dynamics and community structure, and thus a
complex array of environmental factors, including temperature, substrate
(CH4) concentration, land use, moisture, pH and soil type (Ho et al.,
2013). The influence of these environmental factors on microbial CH4
oxidation rates is not well characterized, and thus all factors are not
explicitly represented in models. Consequently, apparent rate constants
implicitly account for some environmental factors via fitting field
observations or laboratory experiments, resulting in parameter values that
may be more environment- and model-specific. A possible limitation of such an
approach is reduced transferability and predictive capacity in other
environments or from a regional to global scale. For example, Ridgwell et
al. (1996) derived a single global estimate of k0=8.7×10-4 s-1 by fitting Eq. (12) to 13 measured values of
JCH4, DCH4 and soil temperature from four
different studies. In contrast, Curry (2007) estimated a global k0 of
5.0×10-5 s-1 based upon fitting Eq. (13) to a 5-year
time series of JCH4 and soil temperature, moisture and
CH4 flux measurements from a single site in Colorado (Mosier et al.,
1996). The order of magnitude difference in k0 between the R99 and C07
models illustrates the potential model-specific nature of parameter values
derived from experimental and observational data, as well as the limits and
challenges for transferability. Soil methanotrophy is not unique in this
regard, and parameterization of microbially mediated processes remains a
common problem more generally in modelling approaches (e.g. Arndt et al.,
2013; Bradley et al., 2016).
CH4 uptake response factors (a, c) and uptake
fluxes (b, d) as a function of soil moisture (rSM) and
temperature (rT). Observations (shown as crosses) (rSM,
File 1 in the Supplement, Table S1; rT, File 1 in the Supplement, Table S2), MeMo
(black line), C07 (blue line) and R99 (green line).
Parameterization of k0 in MeMo has been refined using time-series data
recently published by Luo et al. (2013), which consist of daily soil
CH4 uptake rates and temperature and soil moisture data from three
contrasting environments: temperate forest (Höglwald, Germany), tropical
rainforest (Bellenden Ker, Australia) and steppe (Inner Mongolia, China). The
data sets were used to explore potential variations in apparent k0
values in different environments, including comparison with k0 values
from the R99 and C07 models; however, the uncertainty of this value could not be
characterized due to a dearth of available observational data. Data from each
site were interpolated according to Eq. (10) to derive an apparent k0
value for each biome. The k0 values for temperate forest and steppe are
similar to the k0 value employed in the C07 model; however, the apparent
k0 for tropical forest is approximately 3 times smaller than the
C07 model k0 value. The three newly derived k0 values were employed
in MeMo for their respective biomes and the k0 value from the C07 model
(k0=5.0×10-5 s-1) was used for all other regions for
which no biome-specific k0 values exist (Table 3). Similar k0
values of 5.0×10-5 s-1 for temperate forest, steppe and
short-
grass steppe indicate that this magnitude of k0 is appropriate for
many ecosystems. Yet, apart from the tropical wet forest, the data clearly
indicate additional controls and the use of k0=1.6×10-5 s-1 will thus prevent an overestimation of simulated fluxes.
Nevertheless, further research is required to better characterize this key
parameter.
k0 values from the R99 and C07 models, and new k0 values
employed in MeMo that were determined based upon temperate forest, tropical
forest and steppe data from Luo et al. (2013).
Model
Biome
k0 (s-1)
R99
Global
8.7×10-4
C07
Global
5.0×10-5
MeMo
Temperate forest
4.0×10-5
Tropical forest
1.6×10-5
Steppe
3.6×10-5
Other ecosystems
5.0×10-5
Soil moisture factor, rSM
Both low and high soil moisture levels can negatively impact soil uptake of
atmospheric CH4 (Schnell and King, 1996; von Fischer et al., 2009).
Scarcity of soil water generally inhibits soil microbial activity while
excessive moisture attenuates gas diffusion, limiting entry of atmospheric
CH4 and O2 into soil (Burke et al., 1999; McLain et al.,
2002; McLain and Ahmann, 2007; West et al., 1999).
The R99 and C07 models incorporated parameters to address the limiting effects of
low soil moisture levels on CH4 uptake fluxes. The R99 model applied
a soil moisture factor adopted from Potter et al. (1986) where rSM
was calculated as a proportional ratio of precipitation (P) plus soil
moisture (SM) divided by potential evapotranspiration (ET;
Table 4, Eq. 21). It was assumed that rSM decreases linearly when
(P + SM) / ET is less than 1. The C07 model modified the response
of soil methanotrophy to moisture using an empirical water stress
parameterization and soil water potential based on findings from Clapp and
Hornberger (1978) (Table 4, Eq. 22). A consequence of that approach is that
rSM decreases logarithmically to zero at an absolute soil water
potential of w<0.2 MPa (Fig. 3).
R99, C07 and MeMo model formulations for rSM response.
Model
Formulation
Eq.
Variable definitions
R99
rSM=1 for P+SM/ETp > 1
(21)
P= precipitation
rSM=P+SM/ETp for
SM = soil moisture stored at 30 cm depth
P+SM/ETp≤1
ETp= potential evapotranspiration
C07
rSM=1 for w<0.2 MPa
(22)
w= saturation soil water potential
rSM=1-log10w-log100.2log10100-log10(0.2)0.8 for w≥0.2≤100 MPa
MeMo
rSM=1-log101SM-log100.2log10100-log100.20.8 for SM < 0.2
(23)
SM = soil moisture
rSM=12πσe-12SM-0.20.22 for SM > 0.2
In MeMo, soil moisture (%) is used to calculate rSM and a
formulation similar to the C07 model is used for low soil moisture values. A
threshold of < 20 % soil moisture is applied because that value
corresponds to optimum conditions for CH4 oxidation in soil (Castro
et al., 1995; Whalen and Reeburgh, 1996) and because inclusion of a water
stress parameter better captures CH4 uptake flux in dry ecosystems
(Fig. 3; Curry, 2007).
Establishing parameters to quantify the impact of excess moisture on soil
methanotrophy has proven more challenging. The C07 model relied upon soil
pore space characteristics in factor Gsoil (Eq. 16) to account for
decreased gas diffusion and limitation of kd at high soil moisture
content. However, attenuation of gas diffusion is only one impact of high
soil water content and it is necessary also to account for the inhibitory
effects of excessive moisture on kd (Boeckx and Van Cleemput, 1996; van
den Pol-van Dasselaar et al., 1998; Visvanathan et al., 1999). Soil moisture
content > 20 % reduces CH4 uptake due to a restricted
diffusion of CH4 and supply of O2. The R99 and C07 models
assume that microbial CH4 oxidation remains active at a soil moisture
content of 80 %, an assumption that contradicts field investigations,
which show that CH4 uptake decreases rapidly at soil moisture levels
> 50 % (van den Pol-van Dasselaar et al., 1998). Thus, the soil
moisture factor employed in MeMo also accounts for limitation of microbial
CH4 oxidation at a soil moisture content > 20 % after which
rates of CH4 uptake begin to decrease (Adamsen and King, 1993;
Visvanathan et al., 1999). The rSM factor used in MeMo was
determined by fitting a Gaussian function to laboratory experimental data
(Table 4, Eq. 23; Fig. 3a), following the approach of Del Grosso et
al. (2000). The mean rSM and standard deviation determined using
this approach were 0.2 ± 0.2.
A soil moisture factor (rSM) was calculated for each set of
observational data from independent field sites (File 1 in the Supplement, Table S1)
based upon an optimum rate of CH4 uptake occurring at a soil moisture
content of 20 % (rSM=1). The remaining rSM values
were computed as a linear ratio of the CH4 uptake rate at 20 %
water content. Figure 3b illustrates the pattern of response in methanotrophy
rates to changes in soil moisture content in the R99, C07 models and MeMo, and
the net effect on CH4 uptake fluxes across a range of absolute soil
moisture levels used to force parameter rSM. The CH4 uptake
fluxes were calculated by varying soil moisture content while holding
constant all other environmental parameters (temperature, CCH4
and Ndep). The R99 and C07 models both predict greater CH4
uptake fluxes than MeMo at soil moisture contents > 20 % with the R99
model yielding the highest flux rates; however, the C07 model and MeMo yield
similar CH4 uptake rates for much of the soil moisture range.
Reduction of CH4 uptake flux at high soil moisture levels due to
attenuation of gas diffusion cannot be managed solely through the term
Gsoil (i.e. reduction in free pore space). MeMo also accounts for
inhibition of microbial CH4 oxidation rates at elevated soil moisture
content, predicting lower CH4 uptake flux as a result of more
realistic rSM values determined from the Gaussian response observed
in field data from three different global biomes (Luo et al., 2013).
Temperature factor, rT
Temperature exerts an important influence on rates of microbial processes, and
consequently, all models parameterize for the effects of temperature on soil
methanotrophy. The R99 model employs a Q10 function derived from
experimental data with a Q10 factor of 2 change over the temperature
interval 0 to 15 ∘C. The model assumes that bacterial methanotrophy
ceases at temperatures < 0 ∘C (Table 5, Eq. 24). The C07 model
adopts the same Q10 factor as R99 for temperatures > 0 ∘C
but employs a different response below 0 ∘C. Soil water generally
does not freeze at a surface temperature of 0 ∘C, and observations
from cold regions provide ample evidence for the presence of methanotrophic
activity at temperatures < 0 ∘C (Vecherskaya et al., 2013). The
C07 model allows for a parabolic decrease of methanotrophy rates from 0 to
-10 ∘C (Table 5, Eq. 25) based upon observations of CH4
uptake in soil at subzero temperatures (Del Grosso et al., 2000).
Parameterization of a temperature factor (rT) is revisited in MeMo
based upon availability of new experimental data for soil from different
biomes (File 1 in the Supplement, Table S2). A Q10 factor having a value of
1.95 was determined for the temperature interval 0 to 15 ∘C by curve
fitting and minimizing linear errors (r2=0.75, p=1.9×10-11;
Table 5, Eq. 26). The factor rT was determined by using the
observed CH4 uptake flux at 10 ∘C at each site as the base
of the Q10 function (Fig. 3c). An exponential decrease in CH4
uptake flux was assigned to the temperature range 0 to -5 ∘C as
recommend by Castro et al. (1995) and Del Grosso et al. (2000). Moreover, the
amount of frozen soil increases exponentially with decreasing temperatures
(Low et al., 1968), and consequently, CH4 uptake also should decline
exponentially.
R99, C07 and MeMo model formulations for rT response.
Model
T<0 ∘C
T≥0 ∘C
Eq.
R99
rT=0
rT=exp(0.0693T-8.56×10-7T4)
(24)
C07
rT=(0.1T+1.0)2 if T>-10 ∘C
rT=exp(0.0693T-8.56×10-7T4)
(25)
MeMo
rT=1/exp(-T)
rT=exp(0.1515+0.05238T-5.946×10-7T4)
(26)
The pattern of change in the rT factor and CH4 uptake flux
for the temperature range -10 to 60 ∘C is shown in Fig. 3d. The
CH4 uptake fluxes shown were calculated by varying temperature while
holding other environmental factors constant (i.e. soil moisture, N
deposition or agricultural land use, and CCH4). All models
exhibit an optimum in CH4 uptake at 25 ∘C characterized by a
maximum rT and CH4 oxidation rate. The key differences
between models are the behaviour of rT at temperatures below
0 ∘C and the amplitude of response curves. The R99 model assumes
that methanotrophic activity ceases at 0 ∘C, and consequently,
CH4 uptake rates decrease sharply at that temperature. In contrast,
the C07 and MeMo models both allow for methanotrophy at temperatures < 0 ∘C.
In general, the exponential decrease of rT employed
in MeMo more closely resembles natural patterns of soil methanotrophy at
subzero temperatures than the parabolic decline employed in the C07 model
consistent with observations reported by Castro et al. (1999) and Del Grosso
et al. (2000). Although our parameterization yields a fit similar to C07 to
the limited observations available at temperatures < 0 ∘C, the
rT used in MeMo provides a simpler solution because it does not
require multiple conditions to be met. In contrast, the C07 parameterization
increases parabolically at temperatures < -10 ∘C, which
requires an additional condition to be incorporated into the model to prevent
increased rates of CH4 uptake at very low temperatures. Soil
CH4 uptake fluxes predicted by the C07 model are greater than those
calculated using MeMo because of the different parameterization at
temperatures < 0 ∘C. Finally, the amplitude of the temperature
response curve is greater and similar in the C07 and MeMo models compared to
the R99 model, in particular, at temperatures > 25 ∘C as a result of
differences in the formulation and solution for CH4 uptake flux
(Fig. 3d).
Nitrogen deposition factor, rN
The effect of nitrogen (N) deposition on CH4 uptake is not as well
constrained as the effects of temperature and soil moisture. In general,
field observations have shown that CH4 consumption rates, and thus
uptake fluxes, decrease with N additions (Aronson and Helliker, 2010;
Butterbach-Bahl and Papen, 2002; Steinkamp et al., 2001). Different processes
have been suggested to explain this negative effect. Firstly, methanotrophs
and ammonia oxidizers are capable of switching substrates (although the
latter microorganisms typically consume N compounds preferentially if
available), and therefore the presence of N compounds reduces CH4
consumption (Bradford et al., 2001; Gulledge and Schimel, 1998; Phillips et
al., 2001; Wang and Ineson, 2003; Whalen, 2000). In addition, intermediate
and end products from methanotrophic ammonia oxidation (i.e.
hydroxylamine and nitrite) can be toxic
to methanotrophic bacteria (Bronson and Mosier, 1994; MacDonald et al., 1996;
Sitaula et al., 2000). Finally, large amounts of mineral fertilizers (i.e.
ammonium salts) can induce osmotic stress in methanotrophs inhibiting
CH4 consumption (Whalen, 2000). However, other studies suggest a
positive effect of N fertilization on CH4 oxidation rates. One of the
mechanisms invoked to explain the positive effect is a stimulation of
nitrifying bacteria to consume CH4 by increased inputs of N due to an
improvement in living conditions (Cai and Mosier, 2000; De Visscher and
Cleemput, 2003; Rigler and Zechmeister-Boltenstern, 1999). The positive
effect of N addition on CH4 oxidation rates has been observed
primarily under experimental conditions and also greatly depends on the local
microbial community structure. Therefore, we assumed that N has an inhibitory
effect on uptake of atmospheric CH4 in all scenarios.
R99, C07 and MeMo model formulations for rN response.
Model
Formulation
Eq.
Driving data
R99
rN=1.0-(0.75×I)
(27)
I= fractional intensity of cultivation
C07
rN=1.0-(0.75×I)
(28)
I= fractional intensity of cultivation
(rN outside of kd parameterization)
MeMo
rN=1-(Nsoil)×α
(29)
Nsoil=Ndep+Nfertρ×z
(30)
The C07 and R99 models both account for the negative effect of N inputs on
CH4 uptake fluxes via the factor rN. In the R99 model,
rN directly affects kd, while in the C07 model, rN
directly modifies the uptake flux. Both models parameterize the negative
effect of N inputs on CH4 oxidation rates as a function of
agricultural intensity (as a fraction of area) as a proxy for fertilizer
application (Table 6, Eq. 27). However, the mathematical description of
rN used by the R99 and C07 models does not account for the enhanced N
deposition by anthropogenic activity or direct N input via fertilizers
because its global distribution was not well known at the time of model
development. Here, we suggest a mathematical description of rN that
accounts for all anthropogenic N input sources: fossil fuel combustion,
biomass burning and fertilizer application (Lamarque, 2013; Nishina et al.,
2017).
The computation of rN in MeMo is a function of (i) the inhibitory
effect on CH4 uptake and (ii) the distribution and amount of N input
in soil (Zhuang et al., 2013). We estimated the percent reduction of
CH4 uptake per mole of N added based on field and laboratory
observations (File 1 in the Supplement, Table S3). We determined an average
inhibition α of 0.33 % mol N-1 based on the mean uptake
reduction per mole of N added. The N response function rN was
governed by Eq. (29):
rN=1-Nsoil×α.
CH4 uptake response as a function of nitrogen deposition and
fertilizer application factor rN. The linear fit (black line) is
based on observations from field (long-term) and laboratory measurements
(gray and blue dots; File 1 in the Supplement, Table S3).
In the cases where entry of N into soil is limited by bulk density ρ,
90 % of N compounds tend to remain at depths z<=5 cm before
exponentially decreasing in concentration with depth (Schnell and King,
1994). Thus, Nsoil was calculated as N input
(kg N ha-1 yr-1) divided by ρ at z=5 cm:
Nsoil=Ndep+Nfertρ×z.
Figure 4 shows the change in rN in relation to N input rate and the
form of Eq. (29).