BGBiogeosciencesBGBiogeosciences1726-4189Copernicus PublicationsGöttingen, Germany10.5194/bg-15-5031-2018Diffusion limitations and Michaelis–Menten kinetics as drivers of combined
temperature and moisture effects on carbon fluxes of mineral
soilsModelling temperature and moisture effects on soil C
fluxesMoyanoFernando Estebanfmoyano@uni-goettingen.dehttps://orcid.org/0000-0002-4090-5838VasilyevaNadezdahttps://orcid.org/0000-0002-1942-3738MenichettiLorenzohttps://orcid.org/0000-0001-9524-9762University of Göttingen, Bioclimatology, 37077 Göttingen,
GermanyUPMC-CNRS-INRA-AgroParisTech, UMR 7618, Bioemco, Thiverval-Grignon,
78850, FranceV.V. Dokuchaev Soil Science Institute, Moscow, RussiaSveriges Lantbruksuniversitet (SLU), Ecology Department, Ulls Väg
16, 756 51 Uppsala, SwedenFernando Esteban Moyano (fmoyano@uni-goettingen.de)24August201815165031504519February201828March201813August201814August2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://bg.copernicus.org/articles/15/5031/2018/bg-15-5031-2018.htmlThe full text article is available as a PDF file from https://bg.copernicus.org/articles/15/5031/2018/bg-15-5031-2018.pdf
CO2 production in soils responds strongly to changes in temperature
and moisture, but the magnitude of such responses at different timescales
remains difficult to predict. Knowledge of the mechanisms leading to the
often observed interactions in the effects of these drivers on soil
CO2 emissions is especially limited. Here we test the ability of
different soil carbon models to simulate responses measured in soils
incubated at a range of moisture levels and cycled through 5, 20, and
35 ∘C. We applied parameter optimization methods while modifying two
structural components of models: (1) the reaction kinetics of decomposition
and uptake and (2) the functions relating fluxes to soil moisture. We found
that the observed interactive patterns were best simulated by a model using
Michaelis–Menten decomposition kinetics combined with diffusion of dissolved
carbon (C) and enzymes. In contrast, conventional empirical functions that scale
decomposition rates directly were unable to properly simulate the main
observed interactions. Our best model was able to explain 87 % of the
variation in the data. Model simulations revealed a central role of
Michaelis–Menten kinetics as a driver of temperature sensitivity variations
as well as a decoupling of decomposition and respiration C fluxes in the
short and mid-term, with general sensitivities to temperature and moisture
being more pronounced for respiration. Sensitivity to different model
parameters was highest for those affecting diffusion limitations, followed by
activation energies, the Michaelis–Menten constant, and carbon use
efficiency. Testing against independent data strongly validated the model
(R2=0.99) and highlighted the importance of initial soil C pool
conditions. Our results demonstrate the importance of model structure and the
central role of diffusion and reaction kinetics for simulating and
understanding complex dynamics in soil C.
Introduction
Soils are a main component of the global carbon (C) cycle, storing ca.
2200 Pg of C in the top 100 cm according to recent estimates (Batjes,
2014). This soil C pool is dynamic and often exists in a non-equilibrium
state as the result of an imbalance between input and output C fluxes, in
which case it will act either as a C sink or as a C source over time. Changes in the
speed at which soil organisms decompose soil organic matter (SOM) and
mineralize soil organic carbon (SOC) into CO2 are one way in which an
imbalance can occur, producing a net sink or source of atmospheric
CO2.
It is well known that SOC mineralization and resulting CO2 fluxes are
highly sensitive to variations in soil temperature and moisture (Hamdi et
al., 2013; Moyano et al., 2013). As a result, feedback effects, either
positive or negative, are expected to occur from the interaction between
climate change and global soil C stocks (Crowther et al., 2016; Davidson and
Janssens, 2006; Kirschbaum, 2006). However, the direction and magnitude of
such feedbacks at the global scale remain uncertain. Increased soil
respiration with a resulting net loss of soil C, and thus a positive climate
feedback, is expected with the warming of permafrost soils and the drying of
wetland soils. But there is still large uncertainty and a lack of consensus
regarding the long-term response to climate variability of soils that are
non-saturated, non-frozen, and dominated by a mineral matrix (Crowther et
al., 2016), i.e. soils found under most forests, grasslands, and agricultural
lands.
Future predictions of soil C dynamics require the use of mathematical
models. Early soil C models and most still in use are based on first-order
decay of multiple C pools, with temperature and moisture having general
non-interactive effects on decay rates (Rodrigo et al., 1997). When
appropriately calibrated, these models do well at simulating soil respiration
fluxes of soils under relatively stable conditions. They are often developed
to approximate long-term steady-state conditions under specific land uses.
They are also capable of fitting long-term trends of soil C loss, such as
data from long-term bare fallow where all litter input has stopped
(Barré et al., 2010). However, they lack a theoretical basis justifying
their basic assumptions of pool partitioning and decay mechanisms. They also
generally need calibration for specific soil types or land cover types and
often fail to properly simulate observed short- and mid-term variability in
soil respiration. Some of the most relevant observations these models have
failed to reproduce include changes (typically a dampening) of temperature
sensitivities of decomposition over time (Hamdi et al., 2013), non-linear
responses to soil moisture content (Borken and Matzner, 2009), and changes
in decomposition rates in response to variations in concentrations of
organic matter (Blagodatskaya and Kuzyakov, 2008). Such model shortcomings,
which reflect missing or wrongly simulated processes, create a
difficult-to-quantify uncertainty in global long-term predictions of soil C and its
feedback to climate change. It is therefore unclear if first-order models
can predict long-term changes in C stocks under more dynamic (and therefore
realistic) environmental conditions.
Second-order models have a more realistic basic structure compared to
conventional first-order models, since they simulate organic matter
decomposition as a reaction between SOC and decomposers (i.e. a microbial or
enzyme pool). This single but fundamental change in decomposition kinetics
strongly affects predicted long-term changes in soil C, largely as a result
of the dynamics of the decomposer pool, which itself can respond to
temperature in a number of ways (Wutzler and Reichstein, 2008). Second-order
models also lead to more complex dynamics of short- to mid-term soil
respiration, with apparent temperature sensitivities that vary over time,
more in line with many observations.
The temporal variability in the response of decomposition to moisture is
most evident in the strong respiration pulses after dry soils are re-wetted,
known as the Birch effect (Birch, 1958). But studies have shown that a
successful simulation of such pulses requires the incorporation of
additional mechanisms, namely the explicit representation of a bio-available
C pool, such as dissolved organic matter (DOC), and a moisture regulation of
decomposer's access to this pool that may differ from the moisture
regulation on the decomposition reaction itself (Lawrence et al., 2009;
Zhang et al., 2014).
The response of soil respiration to temperature and moisture is highly
dynamic, both spatially and temporally (Hamdi et al., 2013; Moyano et al.,
2012). Moisture and temperature interactions have been observed in a number
of experimental studies (Craine and Gelderman, 2011; Rey et al., 2005;
Suseela et al., 2012; Wickland and Neff, 2008), but neither consistent trends
nor general explanatory theories have been identified. Improving our
understanding of these interactions is a crucial step towards increasing
confidence in models and important for interpreting modelling and experimental results
(Crowther et al., 2016; Tang and Riley, 2014). Identifying the model
structures and parameterizations that can best represent these interactive
effects has been attempted by very few studies (Sierra et al., 2015, 2017).
The objectives of this study are to compare the ability of different soil C
modelling approaches to reproduce temperature and moisture interactive
effects on soil carbon fluxes and thus to gain insight into mechanisms
underlying the observed responses. With the hypothesis that a more
mechanistic model will be better capable of simulating such interactions, we
compare different model structures, testing first-order, second-order, and
Michaelis–Menten reaction kinetics in combination with an explicit
simulation of diffusion fluxes. We then compare the best diffusion model
with versions based on common empirical moisture relationships.
Observational data
Measurements of the interaction effects of temperature and moisture on soil
respiration fluxes were obtained by incubating a crop field soil at several
fixed levels of soil moisture and variable levels of temperature over a
period of ca. 6 months, as detailed in the following.
Soils from 0 to 20 cm depth were sampled at Versailles, France, from the “Le
Closeaux” experimental field plot, cultivated with wheat until 1992 and with
maize since 1993. Mean annual temperature and rainfall are 10 ∘C and
640 mm, respectively. The soil is classified as Luvisol (FAO) silt loam (26 % sand,
59 % silt, 15 % clay) containing no carbonates. Organic carbon
contents at the start of the incubation were 1.2 % in weight. Soil
samples were prepared for elemental analysis (C, N) using a planetary ball
mill (3 min at 500 rpm). C concentrations were measured using a CHN
auto-analyser (NA 1500, Carlo Erba).
Sampled soils were thoroughly mixed, sieved at 2 mm, and stored moist at
4 ∘C in plastic bags with holes for aeration for 10 days. Soils were
then put in small plastic cylinders containing the equivalent of 90 g dry
soil. To ensure a high and equal water conductivity, all samples were
compacted to a bulk density of 1.4 g cm-3. The resulting soil porosity
was 0.45.
All samples were brought to a pF of 4.2, corresponding to about 12.5 %
volumetric moisture. Three replicate samples were then adjusted to each of
the moisture levels (2 %, 5.5 %, 12.5 %, 16 %, 20 %,
23.5 %, 27 %, 30.5 %, 34 %, 38 %, and 45 %) by adding
water or air drying. These values range from air-dry to saturated.
Immediately thereafter, the plastic cylinders were put in 500 mL jars containing
a small amount of water on the bottom (except for the 2 % and 5.5 %
moisture) to prevent soil drying and equipped with a lid and a rubber septum
for gas sampling. Because of the extremely low respiration rates, samples
with 2 % moisture were placed in 125 mL jars containing 170 g of soil.
To minimize post-disturbance effects, samples were pre-incubated at
4 ∘C for 10 days. The samples were then cycled through incubation
temperatures following the sequence 5–20–35–5–20–35 ∘C, thus
applying two temperature cycles to each sample. This was done in order to
capture possible hysteresis of temperature effects and to reduce the
covariance between a temperature response and substrate depletion (helping
constrain model parameters). Soil respiration was calculated at every
temperature step by measuring the amount of CO2 accumulated in flask
headspace. For this, samples were flushed with CO2-free air and left
to accumulate CO2 for 3 to 74 days. The variable accumulation time
was chosen so that sufficient CO2 accumulated for the micro gas
chromatographer measurements (at least 100 ppm), thus depending on the soil
temperature and moisture content. After the accumulation time, an air sample
was taken from each soil sample headspace, and respiration rates were calculated as
the accumulated amount over the accumulation time. Samples were incubated for
a total period of ca. 6 months (Fig. 1).
As shown in Fig. 1, the timing of temperature treatments was not equal for
all samples, with some temperature steps missing at low moisture levels. This
was partly due to the time required for CO2 concentrations in the
flask headspace to reach detectable limits, the time necessary for carrying
out measurements and human error. However, while important for a statistical
comparison between treatments, such differences are of little consequence
when looking at model performance and the fit between model and data, which
is the focus of this study.
Graphical representation of the incubated soil samples showing the
fixed levels of moisture content and the times at different temperatures.
Modelling approachStructure and state variables
We started with a basic soil C model with the following state variables: a
bio-unavailable polymeric C pool (CP); a bio-available dissolved
C pool (CD); a microbial C pool (CM); and two
extracellular enzyme C pools (CE), one representing the enzyme
fraction at the decomposition site (CED) and one the
fraction at the microbial site (CEM). With this model
we assume two conceptual soil spaces that are separated by a diffusion
barrier, one being the site of decomposition and the other the site of
microbial uptake and enzyme production (Fig. 2). This model thus closely
follows Manzoni et al. (2016) and otherwise builds on other published
microbial models (Allison et al., 2010; Schimel and Weintraub, 2003). We
refer to those studies for general assumptions and application of this type
of model. Aspects specific to this study are described below.
The rates of change of the model state variable were defined as
dCPdt=FLSP+FMP-FPD,dCDdt=FLMD+FPD+FEDD+FEMD-FDM-FDRG-FDEM,dCMdt=FDM-FMP-FMRM,dCEDdt=FEMED-FEDD,dCEMdt=FDEM-FEMED-FEMD,
where F represents the flux of C from one pool to another as indicated by
the subscripts, so that FPD is the flux from the polymeric pool
to the dissolved pool. The subscripts LS and LM
denote input of structural and metabolic litter (as defined by Parton et al.,
1987), which for simulating the incubated soils were set to zero, and
RM and RG are microbial growth and maintenance
respiration.
Diagram showing C pools and fluxes, as well as the points of
diffusion limitations. Second-order decay may refer also to Michaelis–Menten
reaction kinetics. Variations of this scheme were tested in this study.
Decomposition and microbial uptake
The flux of CP to CD, FPD, represents
decomposition of organic matter, a process that in soils is largely driven by
the activity of microorganisms, which produce exo-enzymes that catalyse
the decomposition reaction. UD represents the total uptake flux
by microbes of the water-soluble decomposed pool CD (microbes
being the reaction “catalysers”). Conventional soil C models simulate
decomposition as a first-order decay reaction. However, more realistic models
can be built by using either simple second-order or Michaelis–Menten reaction
kinetics. Thus, optional ways of modelling both FPD and
UD include
F=VR,F=VRC,F=VRCK+R,F=VRCK+C,
where F is the flux, V a base reaction rate, K the half-saturation
constant, R the reactant, and C the catalyst. The “reverse”
Michaelis–Menten (Eq. 9) was applied by Schimel and Weintraub (2003) as an
alternative for improving model stability and is included here for
completeness.
The value for V is not equivalent among these equations, differing by
several orders of magnitude. As a result, different parameters were used for
V in each case, namely VDm, VDmr, VD1,
and VD2. Similarly, parameters KD and KDe
were used for K in Eqs. (8) and (9), respectively. The terms [R] and
[C] are concentrations of CP and CED.
In the case of uptake, the parameters are respectively VU,
KU, CD, and CM. The four approaches for
reaction kinetics were tested in order to find the best fit between model and
data, as described in Sect. 4.
Diffusive fluxes
Diffusion fluxes depend on a concentration difference, a diffusivity term,
and the distance over which diffusion occurs (Manzoni et al., 2016). For the
purpose of modelling diffusion in soils, values of diffusivity and diffusion
distances are required that best average or represent the actual underlying
soil complexity. For practical purposes, we combined these two values into a
single calibrated parameter, a conductance (g0), representing the
compound effects of diffusivity and distance. This was done because the
values of the latter are unconstrained (from lack of information), and their
effects are inversely correlated, so simultaneous calibration would lead to a
problem of parameter identifiability. The moisture-scaled conductance (g),
which in our model is assumed equal for the CD and CE
pools, is then given by
g=g0dθ,
where dθ is a function of soil volumetric water content (VWC or
θ):
dθ=(ϕ-θth)mθ-θthϕ-θthn,
where ϕ is pore space, and n and m are calibrated parameters
(Hamamoto et al., 2010; Manzoni et al., 2016), which are variable and were
also calibrated in this study. θth is the percolation
threshold for solute diffusion, for which Manzoni and Katul (2014) reported a
value of -15 MPa. This value was not optimal in our case, so
θth was also calibrated. The diffusive flux of enzyme C
between the microbial and the decomposition spaces is then calculated as
FEMED=g(CEM-CED).
Diffusion limitations also affect the amount of the dissolved pool
(CD) available for microbial uptake. Instead of dividing
CD into a pool for each space, the conductance, g, was used as
a multiplier of the base uptake rate, VU (Eqs. 6–9). This served
to reduce the number of model pools and parameters while still retaining a
diffusivity limitation on this flux.
Microbial and enzyme dynamics
UD is split into FDM, FDRG,
and FDEM, representing the fluxes of CD
going to CM, RG, and CEM,
respectively. These fluxes are defined as
FDM=UDfug1-fge,FDRG=UD1-fug,FDEM=UDfugfge,
where fug represents the fraction of uptake going to growth,
otherwise known as microbial growth efficiency or carbon use efficiency, and
fge is the fraction of growth going to enzyme production. Enzyme
production thus depends here on uptake rather than on microbial biomass. This
approach follows the assumption that microbes produce enzymes only when new
carbon is available and save resources otherwise. CM goes to
either maintenance respiration or the CP pool according to
FMP=CMrmd1-fmr,FMRM=CMrmr,
where rmd is the rate of microbial death and rmr is
the rate of microbial maintenance respiration. The breakdown of enzymes going
to the CD pool is determined by the rate of enzyme decay,
red, as
FEDD=CEDred,FEMD=CEMred.
Temperature effects
Reaction rates (VU,VD,KU,andKD in
Eqs. 6–9), decay and respiration rates (red, rmd,
rmr) are temperature sensitive and calculated from their
reference values following an Arrhenius type temperature response:
r=rrefexp-EaR1T-1Tref,
where r is the temperature-modified rate, rref the reference
rate at temperature Tref, T temperature in kelvin,
Ea the activation energy, and R the universal gas constant.
Three parameters were used for Ea: Ea_m
and Ea_e for microbial and enzyme decay rates,
respectively, and Ea_V for other reaction rates. Temperature
thus affects the rates of decomposition and uptake, the half-saturation
constant in the Michaelis–Menten equation, and the rates of microbial
and enzyme decay. Apparent activation energies – describing the observed
temperature relationship, both in measurements and model data – were
obtained by fitting an Arrhenius equation to the temperature–flux
relationship at each level of moisture. Ea was calculated for
measured respiration, modelled respiration
(RG+RM), and modelled decomposition
(FPD).
Model calibration and comparisons
Calibrated and non-calibrated parameters for all models are given in the
Supplement (Tables S1, S2, and S3). Whenever possible, fixed parameters as
well as lower and upper bounds for calibrated parameters (Table S1) were set
according to values reported in the literature (e.g. Hagerty et al., 2014; Li et
al., 2014; Price and Sowers, 2004). Equilibrium conditions were not assumed
at the start of the experimental procedure, as such a state is unlikely for
samples that have been processed and disturbed. Therefore, initial conditions
were obtained by also optimizing the fractions of initial carbon pool sizes
(fP, fD, fM). Total organic C was set
equal to the measured value. Models were calibrated by optimizing parameters
to best fit the measured soil respiration data described in Sect. 2. Each
model was calibrated by fitting a single set of parameters simultaneously to
all the incubation data (Table S3). For this, the model was run to reproduce
each sample treatment, i.e. the applied incubation times and temperatures for
each level of moisture (Fig. 1). Accumulated soil respiration amounts were
then calculated to match those from the observed data. Measured and simulated
data from all samples were then combined, and an overall model cost was calculated
using the root mean square error (RMSE) and a weighting term, as described
below.
Parameter optimization was carried out in two steps. We first explored
parameter spaces using a Latin hypercube of parameter values. For this we
randomly selected unique parameter sets from a uniform distribution over each
parameter range (R function randomLHS, package lhs; Stein, 1987) to obtain
30 000 parameter sets. Model costs were then obtained by running models with
each set. In the second step we used the Nelder–Mead algorithm (as
implemented in the function modFit in package FME of the R programming
language; R Development Core Team, 2016; Soetaert and Petzoldt, 2010) with
initial parameter values being the set from the previous step with the lowest
model cost. For the cost calculations we used an error term (“err” argument
to FME function modCost) to weight the residuals. The error was calculated as
the normalized (0–1) standard deviation of measured values at each
combination of temperature and moisture, with 0.1 added to avoid an
unreasonable weighting of measurements with near-zero errors.
For a visual inspection of the model–data fits, we plotted both the measured
and the model relationship between soil respiration and moisture, soil
respiration and temperature, and apparent activation energy (Ea)
and moisture content.
Different model versions with their weighted and unweighted root
mean squared errors (RMSEs, in units mg C kg soil-1 h-1) and
R2 after parameter calibration. FPD: decomposition
flux; UD: dissolved C uptake flux; 1: first-order
kinetics; 2: second-order kinetics; M: Michaelis–Menten kinetics;
Mr: reverse Michaelis–Menten kinetics.
Model nameFPDUDMoisture effectRMSE (weighted)RMSE (unweighted)R211-dif11Diffusion0.280.0800.8122-dif22Diffusion0.280.0800.82M1-difM1Diffusion0.220.0650.87M2-difM2Diffusion0.220.0690.87MM-difMMDiffusion0.250.0780.84M2-satM2Eq. (21): f(θS)0.320.1090.65M2-wpM2Eq. (22): f(Ψ)0.270.0930.78Mr2-difMr2Diffusion0.240.0700.85Comparison of reaction kinetics
Models were named according to their decomposition kinetics followed by the
uptake kinetics and the moisture function, using the abbreviations:
1 for first order, 2 for second order, M for Michaelis–Menten,
Mr for reverse Michaelis–Menten, dif for diffusion,
psi for water potential function, and sat for water saturation function.
Alternative reaction kinetics leading to fluxes FPD and
UD were compared in diffusion-based models using different
combinations of Eqs. (6)–(9). Specifically, we compared first order for
decomposition and uptake (11-dif), second order for decomposition and uptake
(22-dif), and Michaelis–Menten decomposition with all combinations of uptake
(M1-dif, M2-dif, and MM-dif). In addition, we tested reverse Michaelis–Menten
decomposition with second-order uptake (Mr2-dif). We then
evaluated the model–data fit based on RMSE values as well as on a visual
inspection of the plotted relationships. A “best” model was then selected
for further analysis.
Comparison of moisture regulations: diffusion vs. empirical
A second model comparison was carried out to test the impact of different
approaches for modelling moisture effects. For this we modified the model
M2-dif (Table 1), removing diffusion fluxes and adding empirical moisture
functions. This consisted in removing all diffusion effects (so that
CEM and CED were replaced by
a single CE pool and the uptake rate, VU, was no
longer modified by g) and adding a function to scale (i.e. multiply) the
decomposition flux, FPD. This approach is equivalent to the
conventional way used to model moisture effects on soil C fluxes. Two
alternative moisture scaling functions were tested (Moyano et al., 2013), one
based on relative water saturation (M2-sat) and the other on water potential
(M2-wp):
fθS=aθS-bθS2,f(Ψ)=maxmin1-log10Ψ-log10(Ψopt)log10(Ψth)-log10(Ψopt)10,
where θS is relative water saturation; Ψ is soil water
potential; and a, b, Ψopt, and Ψth are fitted
parameters. The latter two represent the optimal water potential for
decomposition and a threshold water potential with values of -0.03 and
-15 MPa, respectively. Water potential was calculated based on
Campbell (1974) and Cosby et al. (1984). a and b are empirical parameters
and were calibrated.
Model steady state, sensitivity analysis, and validation
Equations for steady state were derived by setting the rate of change in the
state variables to zero in Eqs. (1)–(5) (where the flux terms are replaced
by their respective equations) and then solving for the state variables.
This was performed in Python using the “SymPy” package (Meurer et al.,
2017).
A sensitivity analysis was carried out on model parameters using the
“sensFun” function from the R package FME, which perturbs each parameter
individually by a small amount. We ran the model as above, i.e. simulating
the incubation and using daily output. Daily sensitivities were then averaged
to obtain an overall value. Sensitivity values were calculated for the
CP pool alone, as this pool represents the largest fraction of
soil C.
For model validation, we used soil respiration data from the study by Rey et
al. (2005), where a Mediterranean oak forest soil was incubated for 1 month
in a full factorial design at 100 %, 80 %, 60 %, 40 %, and
20 % of water holding capacity and at 30, 20, 10, and 4 ∘C. This
soil differed from the one used for model calibration in at least three aspects:
the amount of organic C (7 %), soil pore space (65 %), and texture
(classified as silty clay loam). The optimized set of parameters from the model
M2-dif was used with the exception of the initial fraction of C pools
(fP, fD, fM) and the percolation
threshold (θth), which we calibrated against the new data
(Nelder–Mead calibration). The former was required since we had no
information with which to estimate the microbial, dissolved, and enzyme C for this study
and information regarding an initial soil steady state was also lacking. In
the case of θth, we assumed that this parameter is
especially sensitive to variations in soil texture and structure. Although in
previous studies it has been determined to be equal to a water potential of
-15 MPa (Manzoni and Katul, 2014), this value did not provide a good fit
when applied to the validation data.
ResultsReaction kinetics
The calibrated values for all models are shown in Table S3. Using different
reaction kinetics resulted in variations in model performance as measured by
RMSE (Table 1). Changes in RMSE were more sensitive to the kinetics of
decomposition (FPD), with models using M and Mr
decomposition kinetics resulting in lower RMSE values compared to first-
and second-order kinetics. In terms of uptake kinetics, both first- and second-order kinetics
performed better than Michaelis–Menten kinetics.
Models M1-dif, M2-dif, and Mr2-dif all showed a good fit to the
data, with the first two having a slightly higher R2. Thus, selecting a
“best” model necessarily remains partially subjective. A visual comparison
shows some weaknesses and strengths in each case. M1-dif and
Mr2-dif better captured the variability in the data along the
respiration axis at 35 ∘C (Fig. S1 in the Supplement), while M2-dif more closely
captured the relationship at 20 ∘C and thus the temperature
sensitivities (Fig. S2). We selected the model M2-dif (R2=0.87, Fig. 3) as
the “best” model, since it better represents the actual mediation of uptake
by microbial biomass when compared to the model M1-dif. We also had no
theoretical reason to prefer Mr to M decomposition. The
decomposition and uptake equations of the model M2-dif are then
FPD=VDCEDCP/(KD+CP)UD=CDCMVUg.
Model vs. measured accumulated CO2 of incubated soil samples.
Colour depicts the range of volumetric water content (VWC). The model R2
is 0.87.
Moisture regulation
Replacing diffusion effects with empirical moisture scalars followed by
recalibration decreased model performance compared to a diffusion-based
model, both when using relative water saturation (M2-sat) and when using water potential
(M2-wp) functions (Table 1). Although empirical functions were able to
approximate the shape of the respiration–moisture relationship at
20 ∘C, they were unable to capture the variation of this response at
higher and colder temperatures, as seen in the measurements and simulated by
diffusion base models (Fig. 4). Diffusion-based models more accurately
simulated a linear relationship between respiration and moisture at lower
temperatures and a steep increase followed by a plateau at high temperatures,
with an intermediate response seen at 20 ∘C.
Relationship of soil respiration with volumetric soil moisture.
Results shown over three temperature levels (5, 20, 35 ∘C) for the
observed data (obs) and three model versions (M2-dif, M2-wp, and M2-sat).
Lines are smooth loess fits depicting the mean relationship.
Temperature sensitivities
Figures 5 and 6 show the apparent temperature sensitivities fitted to
observations and modelled fluxes at different moisture levels and for two
temperature ranges, 5–20 and 20–35 ∘C. Figure 5 compares different
reaction kinetics, and Fig. 6 different moisture functions. Michaelis–Menten
decomposition outperformed first- and second-order kinetics when simulating the
variability in Ea observed along the moisture axis as well as the
differences observed between colder (5–20 ∘C) and warmer
(20–35 ∘C) temperature ranges. The model M2-dif closely followed the
observed Ea values, which were near 100 kJ at colder
temperatures and in the 30–70 kJ range at warmer temperatures. Models
M2-sat and M2-wp captured the large differences between temperature ranges
but did not simulate the variability along the moisture axis as well as
diffusion-based models.
Temperature sensitivities of respiration and decomposition fluxes,
showing activation energy (Ea) fitted using two temperature
ranges (5–20 and 20–35 ∘C) and the equivalent Q10 derived for
a 10 ∘C range. Plotted are observed respiration data (R-obs) and
three models with different reaction kinetics (R-M2-dif, R-11-dif, and
R-22-dif). The sensitivities of the decomposition flux from the model M2-dif is
included for comparison (D-M2-dif).
Model steady state, sensitivity analysis, and validation
Model steady-state equations are provided in the Supplement. For
20 ∘C, 30 % VWC, 1.2 g d-1 C input, and 30 cm soil depth
(z), the equilibrium sizes of the model pools are 2560, 37, 120, and
4 g C for the CP, CD, CM, and
CED pools, respectively. These values are stable over
most of the moisture range and increase exponentially only at very low soil
moisture (data not shown). A similar pattern was observed for temperature,
with the CP pool increasing towards high values only at
temperatures near 0 ∘C. The same pool showed little sensitivity to
changes in C input.
Equivalent to Fig. 5 but showing observational data (R-obs) next to
models with different moisture functions (R-M2-dif, R-M2-wp, and R-M2-sat).
Table 2 shows the averaged values from the sensitivity analysis done on the
model CP pool. High sensitivities were found for g0 and n,
indicating the importance of diffusion fluxes. Large effects were also seen
for the activation energy parameters, denoting a strong general effect of
temperature. Also high were the sensitivities to KD and
fug, reflecting the importance of Michaelis–Menten kinetics for
decomposition and carbon use efficiently, respectively. Low sensitivities
were found for rates of microbial and enzyme decay.
Parameters of the model M2-diff, calibrated and non-calibrated, with
results of a sensitivity analysis (sens). Sens shows a relative measure of
the sensitivity of the model CP pool to small perturbations in the
parameter values. Values are rounded to two significant digits.
Simulation of the incubated soil from the study of Rey et al. (2005) resulted
in a very high fit to the validation data after calibration of initial SOC
fractions and θth, with an RMSE of 0.09 in fluxes that were
almost an order of magnitude higher than those used for calibration and a
model R2 of 0.99 (Fig. 7). This was reflected in a generally good
agreement between the relationships of model and observations with moisture
(Fig. 8) and temperature (Fig. 9).
Discussion
The interaction often observed in the effects of temperature and moisture on
the cycling of soil C is an indicator of the complex nature of soil systems.
Such responses are often ignored, particularly by modellers trying to
minimize model complexity and derive functions that are easy to
parameterize, but also by experimentalists focusing on finding an invariable
response to a single factor. But a careful consideration of the nature of
soils suggests that interactions should be expected, something that becomes
evident in multi-factorial experiments as well as in field measurements.
Here we found clear interactive effects in our experimental observations,
adding to the evidence that fixed empirical temperature and moisture
scalars, as used in conventional soil C models, are inappropriate for
simulating the variability often found in natural conditions.
Model vs. measured accumulated CO2 after simulating the
experiment from Rey et al. (2005). Colour depicts the range of volumetric
water content (VWC). The model R2 is 0.99.
Relationship of soil respiration with volumetric soil moisture shown
for the model M2-dif and observations from the validation data (obs). Results are
shown over four temperature levels.
Since the total amount of soil C was equal among samples and its relative
change in the 6 months of incubation was small, we expected that
second-order kinetics would do as well as Michaelis–Menten kinetics. But using
Michaelis–Menten increased the R2 by ca. 5 % compared to second- and
first-order kinetics. This combined with the fact that the model was highly
sensitive to a change in KD, more than to VD, would
indicate that Michaelis–Menten kinetics are in fact important for explaining
soil C flows. Indeed, even in this case where the CP pool is
relatively invariant, the outcome of a strong temperature effect modifying
KD (Ea of 94 kJ) cannot be reproduced by second-order
kinetics.
Apparent activation energy (Ea) and equivalent Q10
(for the temperature range 15–25 ∘C) during the validation step.
Values fitted to observed respiration (R-obs) as well as modelled respiration
(R-M2-dif) and decomposition (D-M2-dif).
The relative importance of different processes was also shown by the model
parameter sensitivity values. It is perhaps not surprising that some of the
highest values were related to diffusion and temperature, since these were
the two factors that varied in our experiment. However, these factors also
vary considerably in natural ecosystems and largely drive changes in
decomposition rates. No strong correlations between the effects of different
parameters were found, with most being below 0.6 (Fig. S4), thus giving a
degree of confidence in the estimated values. While we did not obtain
statistical confidence intervals, kernel density estimations (Figs. S5–S12)
suggest differing degrees of likelihood for different parameters. Activation
energies in particular showed narrow ranges of optimal values with a strong
dependence on model structure.
Since optimizing all parameters against our data resulted in an R2 of
0.87, it was surprising to obtain an R2 of 0.99 during model validation.
We note that few studies were found with data on moisture and temperature
interactions under controlled conditions, and this was the only validation
attempt carried out. This very high R2 is partially thanks to the
recalibration of initial pool sizes and may have to do with the reduced
amount of data coming from a simpler experimental design compared to our
study. There were only 20 data points in the validation data, one for each
temperature and moisture combination. In contrast, we had 3 replicates,
11 moisture levels, and 2 temperature cycles, and therefore more data and
associated variability. Despite these points and this being an initial
validation step, such a close agreement using independent data and a soil
that differed considerably in C content provides strong support for the model
structure we used.
Model steady state or equilibrium is attained when the rate of change of all
state variables equals zero, reflecting the state towards which the system
will tend under invariant input and forcing conditions. Even though external
drivers are in constant change in natural systems, steady-state information
can indicate the approximate model behaviour under specific average
conditions. Results here showed that the model M2-dif gives realistic values in
the range of temperature for which it was calibrated but leads to
unrealistic values under colder conditions. In addition, the CP
pool shows little sensitivity to changes in C input. While the model fitted
well the validation data, it may not be suitable when applied outside the
conditions used for development and may need further changes for field
applications. The limitations encountered are characteristic of non-linear
microbial models and mark their current limitations as predictive tools.
However, such limitations are most likely the result of missing processes
that still need to be adequately represented. For example, recent work has
shown that a density-dependent mortality rate of the microbial pool can lead
to much more realistic long-term simulations (Georgiou et al., 2017).
It is important to point out that our approach was to use a simple model with
few processes and C pools and modify only those components we tested. This
allowed us to distinguish the effects of each modification and minimize
parameter identifiability problems arising from having too many parameters
with effects that may correlate. While this allowed us to focus on specific
processes, it also meant that important mechanisms were left out. Some of
these mechanisms are oxygen limitations in saturated conditions, leaching of
CD, the coupling of the C and N cycles (introducing SOC quality
and microbial stoichiometry limitations), and organo-mineral interactions. Our
model thus needs further development to extend its application and general
predictive capacity. In its current form, it cannot be extended to litter
decomposition (Cotrufo et al., 2015) or organic soils, which will be much
more dependent on substrate quality and less affected by carbon diffusion
(Manzoni et al., 2012b). Also, peatlands and other saturated soils (Clymo,
1984; Frolking et al., 2001) will show different dynamics, reflecting the
critical role of oxygen as a limiting factor. We did not include mineral
adsorption of carbon as an active mechanism in this study. This is contrary
to recent studies that used adsorption–desorption fluxes to explain the
variability in temperature responses (Tang and Riley, 2014). However, some
values of mineral desorption rates found in the literature (Ahrens et al.,
2015) suggest that these rates, although important in the long term, are too
slow to have a noticeable impact on the timescale of this or similar
experiments, and thus on most estimates of soil respiration temperature
sensitivities. Finally, nitrogen requirements will impose limits on the
growth of microbial communities, which in models with microbial driven uptake
and/or decomposition will also regulate C fluxes (Grant et al., 1993;
Manzoni et al., 2012a). Despite such limitations, we demonstrated the effects
and relevance of combining Michaelis–Menten kinetics with diffusion in
mineral soils, with model results being well supported by the data.
Temperature effects
Unlike other calibrated parameters, the activation energy values for
microbial (Ea_m) and enzyme
(Ea_e) decay were fixed at 10 kJ, representing a
positive but low temperature sensitivity. This value was used in order to be
consistent with two main observations:
The effect of Ea_m on the amount of microbial carbon. A high Ea_m results in large
changes of microbial biomass C with temperature. However, observations often
show a negative but moderate effect of temperature on microbial biomass
(Grisi et al., 1998; Salazar-Villegas et al., 2016).
The effect of Ea_e on carbon decomposition rates. High Ea_e values result in
increasing accumulations of soil C with warming (Allison et al., 2010; Tang
and Riley, 2014) as a consequence of a decrease in the enzyme pool caused by
accelerated turnover. This is a critical aspect of enzyme-driven soil carbon
models and largely determines simulated responses to long-term warming.
Experimental evidence for Ea_e is lacking, but the
latest observations of mid-term responses to warming are compatible with low
values (Crowther et al., 2016).
The optimized Ea_V value of models with first- and
second-order decomposition kinetics were in the range 40–50 kJ, translating to a
Q10 of ca. 2. In contrast, for all but one model using M
decomposition, values were above 90 kJ, translating to a Q10 of
nearly 4. This high value was apparent in the modelled respiration fluxes
only at lower temperatures, while at temperatures higher than 20 the apparent
Q10 approximated the more commonly observed value of 2. Such results
followed closely our observations and agree well with general trends in
Q10 along the temperature axis reported by Hamdi et al. (2013). These
values were mostly stable at high levels of soil moisture but increased
sharply under drier conditions. This moisture relationship, however, is not
necessarily the norm and seems to depend on initial conditions and/or pool
dynamics, as demonstrated by the validation step (Fig. 9), where the apparent
Ea remained close to 90 kJ and thus near the parameterized
value. Also the change in Ea with moisture content followed a
different trend in the validation data, although again values increased with
lower moisture.
The difference between prescribed and observed temperature sensitivities may
be related to two factors. First, the apparent sensitivities do not represent
the instantaneous sensitivities dictated by the prescribed values but reflect
also the effects of other limiting factors that change with time. Pool sizes,
including CM and CE, may differ from the initial
conditions as time progresses, making measurements at different temperatures
not strictly comparable. The observation that Q10 values from studies
using short incubation times (hours to days) are higher compared to those
using longer incubation times (Hamdi et al., 2013) is consistent with this
idea. The second factor is related to the temperature sensitivity of the K
constant of Michaelis–Menten kinetics. Our results are well in line with the
theory discussed by Davidson and Janssens (2006), who stated that “because
the Km of most enzymes increases with temperature, the
temperature sensitivities of Km and Vmax can neutralize
each other, creating very low apparent Q10 values”. Indeed, this seems
to be the most important effect of introducing Michaelis–Menten kinetics in
our simulations – not, as first assumed, the effects of concentrations of
either the CP or CED pools, since the
choice of using M vs. Mr kinetics had only a small impact on
the results.
The model results described above are thus emergent effects leading to
apparent temperature sensitivities that vary in time but are based on
constant model parameter (Ea) values. These results demonstrate
how apparent sensitivities are the result of the offsetting effects of
different processes (e.g. sensitivities of Michaelis–Menten parameters V
vs. Km) and how different values can be measured when soil pool
dynamics change (e.g. through changes in diffusion limitations) even when the
underlying temperature sensitivities are the same. Much of the variability in
reported temperature sensitivities of soil respiration, and in particular its
relationship with soil moisture (Craine and Gelderman, 2011), may be the
result of the changing dynamics in microbial, enzyme, and dissolved C pools
during measurement times. Clearly, misleading conclusions regarding an
intrinsic temperature sensitivity of soil C decomposition are often reached
by the usual procedure of fitting a simple function to respiration vs.
temperature data.
Decomposition, which was only modelled, consistently showed a lower apparent
temperature sensitivity than respiration, with a Q10 between 1 and 2 for
our experiment and just below 3 for the validation study. These values may be
the most relevant for predicting long-term changes, since uptake and
respiration ultimately depend on C made available by decomposition. These
rather low sensitivities are consistent with some integrative studies at the
ecosystem level (Mahecha et al., 2010) and again likely respond to the
temperature sensitivities of Km and Vmax neutralizing each
other. Such results raise the question of what Ea or Q10
values – i.e. those apparent for respiration, those apparent for decomposition, or
those parameterized – are best suited for conventional first-order empirical
soil models. Since these models will tend to have similar apparent and
intrinsic behaviour, the answer is not clear and will require further
research. Ultimately, the best option may be to abandon such models and
develop better validated mechanistic alternatives for prediction purposes.
Moisture effects and diffusion limitations
Diffusion fluxes are a function of water content, diffusivity coefficients,
and pool concentrations. Different equations have been used to calculate
diffusion as a function of water content in soils (Hamamoto et al., 2010; Hu
and Wang, 2003). All these equations generally predict a strong positive
near-exponential effect of water content on diffusion. Following previous
studies (Manzoni et al., 2016), we chose the function from Hamamoto et
al. (2010). This equation allows for an adjustment of the percolation
threshold (θth) in different soils. We note that when using
the θth obtained during calibration (0.063) we also
obtained a high fit to the validation data (R2=0.97, data not shown),
so the recalibration of θth led to a noticeable but small
improvement. While the value 0.063 for our soil came close to the water
potential of -15 MPa found in previous studies (Manzoni and Katul, 2014),
this relationship did not hold for the soil used for validation, where we assumed a higher clay and silt content from its
classification. Thus, a prerequisite for applying our model to other soils is
finding a relationship between θth and soil type that holds
in all cases.
Diffusion regulations can be implemented either by simulating two separate
pools between which diffusion takes place or by determining the available
amount of a pool as a function of diffusivity (or conductance in our case) at
each time step. In our model we used a combination, simulating a diffusion
flux between enzyme pools and calculating how much CD is
available for uptake at each time step. We did not assume a diffusion
regulation of available polymeric C, an approach that is closer to empirical
functions scaling the decomposition flux directly and that has been
implemented in other microbial models (Davidson et al., 2012).
In our study especially, but also in the validation data, the moisture
response tended to become less linear and have a larger plateau at higher
temperatures. The mechanisms leading to such interactions are still unclear,
but our model comparison indicates that solute diffusion limitations play a
central role. The plateau behaviour, a decrease near saturation, and even
near-linear responses all contrast with the near-exponential relationship
between moisture and conductance given by Eq. (11) and with the fact that no
oxygen limitations at high moisture levels were modelled. They may, however, result
from a faster depletion of available carbon at high moisture levels and at high
temperatures, driving down the accumulated fluxes over time.
While a low supply of O2 usually limits respiration rates in
saturated soils under field conditions, O2 seemed to have a
negligible effect in our study. At 35 ∘C, where fluxes were highest,
no clear drop in respiration was observed near saturation, as is expected
when O2 becomes limiting. Rather, the general behaviour was well
simulated by our models using solute diffusion limitations only. Schurgers et
al. (2006) found that the anaerobic fraction in soils with air O2
concentrations over 10 % is low until very close to saturation. The
minimum flask air O2 concentrations (corresponding to 56 000 ppm of
CO2, the maximum accumulated by a sample before changing headspace
air) was over 15 % O2, which next to the small sample sizes would
not indicate an O2 limitation.
In models where decomposition and respiration are separated processes, these
fluxes can show different responses. This decoupling is especially evident
when diffusion limitations come into play. Plots of modelled fluxes against
temperature and moisture (Fig. S3) showed a different relationship when
comparing respiration and decomposition. Figure 10 shows modelled
decomposition against respiration (using M2-dif) as accumulated values, each
line being a sample at a different water content. Without any diffusion
limitation, the relationship follows a slope of ca. 0.3, determined by
1-fug, where fug is the fraction of uptake to growth
(the C use efficiency). This slope, however, changes as diffusion becomes
limiting, with temperature also playing a role as evidenced by the shifts in
the slope occurring at various intervals. With time these fluxes will tend to
equilibrate as the CD and CED pools
adjust. But the proportionality between these fluxes is not constant and will
depend on moisture, temperature, and time, even after months of incubation.
These results show that, without a proper modelling framework and when
assuming a constant proportionality, interpretations based only on
respiration activity may lead to wrong conclusions about the dynamics of
organic matter decomposition, especially at low moisture content levels and in
short- and mid-term experiments.
Modelled decomposed vs. respired C shown as accumulated values over
the entire simulated incubation, including temperature steps. Each line is a
sample at a different moisture content level.
Conclusions
As the main mechanism linking water content with the movement of substrates,
microbes, and enzymes, diffusion plays a central role in soil organic matter
decomposition. We here showed that integrating it into models can
significantly improve our understanding of soil C dynamics. Diffusion-based
models were better at simulating the effects of moisture and improved the
simulated temperature responses, thus allowing for a better interpretation
of the observed temperature sensitivities. This and similar studies indicate
that measured temperature sensitivities cannot be generalized or correctly
interpreted without having a full understanding of the relevant mechanisms,
their interactions, and the state of soil carbon and microbial pools.
We also found evidence that Michaelis–Menten kinetics plays an important
role in soil C dynamics, explaining the strong differences in temperature
sensitivities across temperature ranges. Our results are consistent with
relatively high activation energies for both the V and K Michaelis–Menten
parameters and generally lower apparent values.
Creating models that capture the variability in the response of C dynamics
across different soils and at different levels of driving factors remains
challenging. However, process-based models are of central importance for
establishing confidence in C cycle predictions and soil–climate feedbacks.
As seen here, the structure and process representation of models can be
critical for simulating the complex response of soil C fluxes to combined
changes in temperature and moisture. Diffusion as a moisture regulation of
soil C fluxes has not been used in large scale predictions, which still rely
on empirical scaling functions. Evidence of interactions seen in experiments
and presented from a mechanistic model perspective indicates that these
simpler approaches do not always hold. Further research should focus on more
extensive validation and finding the relationships necessary for extending
the application of models to diverse soil types.
All code and data used for this analysis are available
at 10.5281/zenodo.1290716 (Moyano, 2018).
The supplement related to this article is available online at: https://doi.org/10.5194/bg-15-5031-2018-supplement.
FEM developed the model, analysed the data, and wrote the paper. NV
carried out the lab experiments and revised the paper. LM contributed to
model optimization, discussions, and revisions.
The authors declare that they have no conflict of
interest.
Acknowledgements
This study was partially supported by funds from the R2DS projects “Le
carbone stable des sols: processus de stabilisation et
vulnérabilité” and “Vulnérabilité du C stable et labile du
sol aux changements climatiques: mise en évidence, facteurs explicatifs
et intégration dans un modèle de biosphère
spatialisée”.This open-access publication
was funded by the University of Göttingen. Edited by: Andreas Ibrom Reviewed by: Thomas
Wutzler and one anonymous referee
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