GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-14-6605-2021Comparing an exponential respiration model to alternative models for soil respiration components in a Canadian wildfire chronosequence (FireResp v1.0)Parameterization of soil respiration modelsZobitzJohnhttps://orcid.org/0000-0002-1830-143XAaltonenHeidiZhouXuanBerningerFrankPumpanenJukkahttps://orcid.org/0000-0003-4879-3663KösterKajarkajar.koster@helsinki.fihttps://orcid.org/0000-0003-1988-5788Department of Mathematics, Statistics, and Computer Science, Augsburg University, Minneapolis, Minnesota, USADepartment of Environmental and Biological Sciences,
University of Eastern Finland, Kuopio, FinlandDepartment of Environmental and Biological Sciences,
University of Eastern Finland, Joensuu, FinlandDepartment of Forest Sciences, University of Helsinki,
Helsinki, Finland
Forest fires modify soil organic carbon and suppress soil respiration
for many decades after the initial disturbance. The associated changes
in soil autotrophic and heterotrophic respiration from the time of the
forest fire, however, are less well characterized. The FireResp model
predicts soil autotrophic and heterotrophic respiration parameterized
with a novel dataset across a fire chronosequence in the Yukon and
Northwest Territories of Canada. The dataset consisted of soil
incubation experiments and field measurements of soil respiration and
soil carbon stocks. The FireResp model contains submodels that consider
a Q10 (exponential) model of respiration compared to models of
heterotrophic respiration using Michaelis–Menten kinetics parameterized
with soil microbial carbon. For model evaluation we applied the Akaike
information criterion and compared predicted patterns in components of
soil respiration across the chronosequence. Parameters estimated with
data from the 5 cm soil depth had better model–data comparisons than
parameters estimated with data from the 10 cm soil depth. The model–data
fit was improved by including parameters estimated from soil incubation
experiments. Models that incorporated microbial carbon with
Michaelis–Menten kinetics reproduced patterns in autotrophic and
heterotrophic soil respiration components across the chronosequence.
Autotrophic respiration was associated with aboveground tree biomass at
more recently burned sites, but this association was less robust at
older sites in the chronosequence. Our results provide support for more
structured soil respiration models than standard Q10 exponential
models.
Introduction
While containing 15 % of the total global soil area, high-latitude
permafrost soils contain a significant proportion of global organic
matter and global soil carbon content
. These
high-latitude regions are warming faster than the rest of the world,
consequentially leading to (1) drier soils during the spring and summer
, (2) increases in the intensity and
frequency of forest fires , and (3) destabilization of the permafrost extent
. For these
regions, the combination of the above factors may lead to increased
release of soil CO2 into the atmosphere from soil organic matter
. Soil respiration (denoted here as
RS) represents the product of several semi-independent processes:
autotrophic (root) respiration (denoted here as RA),
heterotrophic respiration (denoted here as RH), and to some
extent fungal respiration .
Heterotrophic respiration consists of microbial respiration of labile
carbon and microbial respiration associated with the breakdown of dead
organic matter and other by-products
. Autotrophic and
heterotrophic respiration will also be affected by permafrost warming:
while RA is strongly associated with primary productivity
, RH may
increase due to priming by newly accessible soil substrate
.
In high-latitude forests, soil respiration fluxes and soil carbon stocks
exhibit variation depending on the time since the last wildfire
. Fire
modifies soil organic carbon quality, making it harder for microbes to
access carbon
. A recent
meta-analysis by of 32 studies measuring
soil respiration following wildfires indicates two emergent patterns.
First, overall soil respiration stabilizes 10–30 years following a fire.
Second, for components of soil respiration, RA will increase and
ultimately approach a steady-state value associated with forest
succession and vegetation regrowth. On the other hand, RH may
decrease by association with post-fire changes in soil organic matter
quality, temperature, or moisture
.
For a sense of the magnitude of these changes,
found the proportion of annual
soil respiration: that is, RA changes from 5 % (following
disturbance) to 40 % (21 years post-disturbance), returning to 15 %
(150 years post-disturbance). The robustness of any patterns in
RA and RH is highly uncertain given known soil
heterogeneity in these high-latitude soils (e.g., permafrost versus
non-permafrost soils, microbial versus fungal species composition).
Observations of overall soil respiration can be linked with
process-based soil models to estimate (and perhaps benchmark) RA
and RH. Models can span a range from empirical models
to highly structured models of interacting
soil microbes .
There is agreement that a more detailed structural representation of
microbial processes is needed in ecosystem models
.
Improving the structural representation of microbial respiration in
Earth system models (e.g., accounting for microbial acclimation to
non-equilibrium temperature changes; ;
; ), when
appropriately benchmarked with data, may reduce uncertainties in the
turnover and stabilization of soil carbon
. However, there are two
main challenges to developing and evaluating more complicated soil
process models. First, soil incubation studies may lead to
underestimation of soil respiration components at larger scales
.
Second, more complex models may lead to model equifinality – or when
different models yield similar results
. The
combination of these multiple factors poses challenges for both
systematically developing and evaluating different soil respiration models.
The objective of many modeling activities (especially for the remote
sites studied here) is to strike a balance between modeling complex
processes while
also parameterizing a model with available site measurements.
We have previously measured soil biogeochemical properties (stocks and
associated respiration rates) across an established fire chronosequence
in the Yukon and Northwest Territories in Canada
.
Our previous work focused on empirical associations between respiration
and biogeochemical and environmental measurements (e.g., soil organic
matter, microbial content, and temperature) across the fire
chronosequence. These results included both field measurements and soil
incubation studies. For this study we synthesize both types of
measurements across the chronosequence to parameterize a process model
of RA and RH,
which we call the FireResp model. The FireResp model contains submodels
that represent a continuum of complexity in modeling soil carbon. We
investigate two specific hypotheses in this study.
Autotrophic respiration is positively associated with the time since
disturbance. This positive association is caused by an underlying
positive association of RA with foliage biomass.
When tested against observational data, soil models that incorporate
microbial carbon will better replicate the observed dynamics and
associated fluxes (RA, RH, and the ratio
RA/RS) across the fire chronosequence.
To evaluate our hypotheses we combine data from soil incubation
experiments with field data
at chronosequence sites. For both incubation
and field data, measurements were collected at the same time from
similar plots to minimize any spatial and temporal biases in the data.
Submodels are evaluated based on their ability to replicate measured
soil respiration (both from incubation and field measurements). To
reduce any biases with model fitting or model equifinality
we
evaluate a range of parameter estimation approaches and data types.
MethodsStudy sites
In 2015 we established a transect of sites in the northern boreal
forests of Canada (Fig. ). All of these sites are
located near Eagle Plains, Yukon (66∘220′ N, 136∘430′ W), and Tsiigehtchic, Northwest Territories (67∘260′ N,
133∘450′ W). The mean annual air temperature at these sites
is -8.8 ∘C. The sites are evergreen needle forests dominated
by Picea mariana (Mill.) BSP and Picea glauca (Moench)
Voss species. Site selection and physical characteristics of the sites
are also described in and
.
Chronosequence sites were selected from the time since the last fire (in
1968, 1990, and 2012) that burned all aboveground vegetation. We also
included a control site, where the last fire was more than 100 years
ago. The date and boundaries of the fires were determined from
geographic data from the Canadian Wildfire Information System
. We visually corroborated the geographic
location of our sites with reported fire boundaries. Previous studies
with these data
classified the 1968 site as 1969, which we attribute to this site
being classified by fire season rather than the year of burn. For this
paper we will refer to a site as a categorical variable by the year
it was burned (2012, 1990, 1968) or the control site, as “control”.
sites will be ordered by the fire year (2012, 1990, 1968, or control).
At each site we measured soil temperature, fluxes of CO2,
microbial biomass assays, soil carbon, tree biomass (foliage, branches,
and stems), and other auxiliary measurements by establishing three
different lines at each site and, within each line, three replicate
plots . Additionally, at each plot, soil
samples were collected for further analysis in soil temperature
incubation experiments. Roots were excluded from incubation soils; we
assume the measured respiration from these samples is RH. The
soil samples were incubated at 1, 7, 13, and 19 ∘C for 24 h,
and the respiration was measured from syringe samples taken at the end
of each 24 h period. The method is described in more detail in
.
The field data measured total soil carbon in the top 30 cm, whereas the
incubation data included measurements of soil carbon to a given depth
(which extended to 50 cm). To determine the total soil carbon to a given
depth in the field data we applied a multistep process. This process
assumes that the soil carbon profiles in the incubation and field data
are similar. First, for the soil carbon in each of the incubation
samples (for each replicate line and plot described above) we computed
the cumulative proportion of soil carbon (g C m-2) to 50 cm
(dots in Fig. ). We acknowledge that soil
carbon is present in deeper layers (estimated to be 59 100 g C m-2 in the top 100 cm at our sites; see
, and
https://bolin.su.se/data/ncscd/, last access: 26 September 2021). However, the objective of this
process is a representative empirical estimate of soil carbon for the
field data. Second, at each incubation sample we fit a saturating
function to the cumulative proportion of soil carbon. The function we
fit had the form yi=1-e-kDi, where yi is the
cumulative proportion of soil carbon at depth Di in incubation
sample i. Third, we computed the median ensemble average and 95 %
confidence interval from the saturating functions grouped by
chronosequence site (2012, 1990, 1968, and the control sites, Fig. ). The median ensemble average allowed
estimation of the proportion of soil carbon up to a given depth (5 or 10 cm) at each field site (Table ). These
proportions were then used for determining the amount of soil carbon at
5 or 10 cm for the field data.
Summary plot of the cumulative proportion of soil carbon collected by depth determined from the incubation data. Each facet represents when a different site in the chronosequence experienced a stand-replacing fire (2012, 1990, 1968, control). The control site was where the last fire was more than 100 years ago. The points in each plot represent a measurement from an incubation sample determined from three different lines (represented by different shapes) at each chronosequence site and, within each line, three replicate plots (represented by different colors; ). At each incubation sample we then fit a saturating function for each plot (not shown) and computed the ensemble average for each chronosequence site (median with 95 % confidence interval, red shading) from the fitted results.
The incubation data included measurements of the available soil organic
carbon extracted from incubation soils, denoted here as CA, as
described in . Briefly, soil dissolved organic C
content was measured using a total organic C analyzer (Shimadzu TOC-V CPH,
Shimadzu Corp., Kyoto, Japan) from soil extracts extracted with 0.5 M
K2SO4. Microbial carbon used in the FireResp model was
extracted using the chloroform fumigation extraction method
. Briefly, 3 g dry weight
equivalent of soil was fumigated at 25 ∘C with ethanol-free
chloroform for 24 h and extracted with 0.5 M K2SO4. The
conversion factor, also known as the extraction efficiency, for
estimating the microbial carbon is 0.45
. For the field data, we approximated
CA as linearly associated with total soil carbon CS at a
given depth, extrapolated from linear regression in the incubation data
(results not shown).
For the field samples an estimate of root carbon CR was assumed
to be proportional to total tree biomass collected at each plot
. A summary of
all input variables is reported in Table .
Summary of soil measurements for this study organized by site in the chronosequence (2012, 1990, 1968, control) and depth of measurement. The row “All depths” refers to the combination of 5 and 10 cm measurements together. Reported values are averages ± standard deviation of plots from three sample lines. Tsoil: soil temperature ∘C); fW: volumetric soil moisture (%); CS: soil carbon (g C m-2); CM: microbial carbon (g C m-2); CA: available soil organic carbon (g C m-2); CR: root carbon (g C m-2); RH: soil heterotrophic respiration from incubation studies (g C m-2 d-1); RS: total soil respiration (g C m-2 d-1).
The FireResp model predicts plot-level soil respiration (RS) and
its components: autotrophic respiration (RA), microbial
maintenance respiration (RM), and microbial growth respiration
(RG). All respiration units are reported as
g C m-2 d-1. The FireResp model expresses respiration
components with two primary functions; the different combinations of
these functions yield different submodels (described in detail below).
First, we assume that RA and RM both follow an exponential
Q10 relationship (Eq. ) parameterized by
soil temperature (Tsoil; ∘C):
RX=kXCX⋅r(fW)⋅Q10,X(Tsoil-10)/10.
Equation () is a commonly
applied (empirical) paradigm for respiration, motivated by temperature
dependencies of enzymatic reactions . This
exponential temperature model is applied for RA and RM,
similar to process models for these components at the ecosystem scale
. The function
r(fW) is an empirical function developed by
to represent the response of respiration
across a range of soil moisture conditions, where fW represents
volumetric soil moisture (%) and
r(fW)=3.11fW–2.42fW2. The variable CX represents
a soil carbon pool (g C m-2). For RA this CX
equals root carbon (CR); for RM this CX equals soil
carbon (CS) or microbial carbon (CM) depending on the type
of submodel considered (e.g., Null, Microbe, Quality, Microbe-mult, or
Quality-mult; all described below). Equation () has two
parameters: kX, the base rate of respiration (d-1) for
pool CX, and Q10,X, the temperature response of respiration
(Q10 value) (no units) for pool X. To aid the representation
of model equations, we will write Eq. () as
RX=gXCX, where
gX=kXCXr(fW)Q10,X(Tsoil-10)/10. As an
example, autotrophic respiration RA would be written as
RA=gRCR.
Second, we model microbial growth respiration (RG) via
Michaelis–Menten kinetics
:
RG=ϵμCXCMkA+CX.
Equation () arises from
first-order microbial enzyme kinetics
under quasi-steady-state assumptions .
In Eq. (), ϵ is the efficiency
converting substrate to microbial biomass (no units), μ is the
maximum microbial uptake rate (h-1), kA
(g C m-2) represents the half-saturation rate, and CX
represents the substrate for respiration. Depending on the model variant,
CX may be total soil carbon (CS) or available soil organic
carbon (CA), which represents more labile carbon for ingestion by
microbes.
The FireResp model has five different submodels which arise through
different combinations of these functional representations of
respiration. These submodels are slightly modified from a similar
approach in .
Null submodel. The Null submodel assumes soil carbon consists
of a single pool .
Here, soil maintenance respiration depends on soil carbon (so
RM=gSCS). Microbial carbon is not considered in the Null
submodel, so total soil respiration (RS) is the sum of
autotrophic and maintenance respiration (Eq. ).RS=RA+RM=gRCR+gSCS
Microbe submodel. Here, maintenance respiration is
proportional to microbial carbon, so RM=gMCM. For growth
respiration (RG) total soil carbon (CS) is the input for
pool CX in Eq. (). With these
considerations total soil respiration is expressed in Eq. ().RS=RA+RM+RG=gRCR+gMCM+ϵμCSCMkA+CS
The Microbe submodel is based on a two-pool
soil-microbe model described in .
Microbe-mult submodel. This submodel is structured similarly to
the Microbe model but with two modifications. First, growth
respiration is not considered. Second, maintenance respiration is
multiplied by a Michaelis–Menten factor.RS=RA+RM=gRCR+gMCM⋅CSkA+CS
The Microbe-mult model is designed to be an
intermediate model between the Null model and the Microbe model. The
additional multiplicative factor is a heuristic designed to represent
maintenance respiration as substrate limited by CS.
Quality submodel.. This submodel is structured similarly to the
Microbe model, but for growth respiration (RG) available soil
organic carbon (CA) is the input for pool CX in Eq. (). Total soil respiration is expressed in
Eq. ().RS=RA+RM+RG=gRCR+gMCM+ϵμCACMkA+CA
The Quality submodel is based on a multi-pool soil
model that structures the soil into different pools based on the
recalcitrance and turnover time of the soil parent material, similar
to models by . Inputs from litterfall,
enzymatic degradation, root turnover, or root exudation create a pool
of available soil organic carbon (CA) that can be incorporated
into microbial biomass. While in this case RG is represented
with Eq. (), a dynamic model of soil would
additionally include expressions for the transformation of each soil
pool through enzymatic degradation and mineralization to a more
recalcitrant pool (both under first-order kinetics).
Quality-mult submodel. This submodel is structured similarly to
the Quality model with two modifications (similar to the modifications
made in the Microbe-mult model). First, growth respiration is not
considered. Second, maintenance respiration is multiplied by a
Michaelis–Menten factor.RS=RA+RM=gRCR+gMCM⋅CAkA+CALike the Microbe-mult model, Quality-mult is a
heuristic model designed to represent maintenance respiration as
substrate limited by CA.
Table summarizes the different
parameters for each model and their allowed ranges when estimating
parameters.
Description of parameters used for the FireResp model along with the allowed range.
NameDescription (units)Allowed rangesQ10,MMicrobe Q10 (no units)[1,5]Q10,RRoot Q10 (no units)[1,5]kRBasal root respiration rate (d-1)[0,1]kMBasal microbe respiration rate (d-1)[0,0.1]kAMicrobe half-saturation rate (g C m-2)[0, 100 000]μMicrobial maximum uptake rate (h-1)[0,100]ϵMicrobial efficiency (no units)[0,1]kSHeterotrophic respiration rate (d-1)[0,0.1]fScaling parameter for heterotrophic respirationa (no units)[0.5,1.5]gRBasal root respiration ratea,b (g C m-2 d-1)[0,0.1]
a Denotes a parameter for the incubation field linear parameter estimation approach.
b Denotes a parameter for the field linear parameter estimation approach.
Parameter estimation routine
The different submodels (Null, Microbe, Quality, Microbe-mult, and
Quality-mult) may be nonlinear with respect to the parameters. For
parameter estimation we applied the Levenberg–Marquardt algorithm
. The Levenberg–Marquardt algorithm
optimizes an objective function, which in this case is the residual sum
of squares between measured and modeled soil respiration RS. The
algorithm also requires (1) the Jacobian of the model to accelerate
convergence to the optimum value, (2) an initial guess for parameters,
(3) and bounds for all parameters.
The Levenberg–Marquardt algorithm may converge to a local (rather than
global) optimum, or the estimated parameter values may be at the
boundaries of the allowed range. To ensure that parameter estimates
converged to a global (rather than local) optimum, initial parameter
guesses for the method were drawn from a uniform distribution with
reasonable bounds on parameters (Table ).
The Levenberg–Marquardt algorithm is implemented in R with the package
nlsr .
For parameter estimation, we applied a quasi-factorial design with the
field and incubation data. This design allowed us to investigate how
predictions for autotrophic (RA) and heterotrophic (RH)
respiration varied when different data are incorporated into the
parameter estimation routine. Four different data combinations were used
for parameter estimation.
Field. All model parameters (e.g., Q10,M, kM,
kA, μ, ϵ, kS, Q10,R, and
kR, depending on the type of model) were estimated with the
field data only.
Field linear. Model parameters for RH
(e.g., Q10,M, kM, kA, μ, ϵ, and
kS, depending on the type of model) are estimated with the
field data. Rather than a Q10 function for RA (Eq. ), for this approach RA equals
gRCR, where CR is provided by the field data.
We then estimated gR from the field data.
Incubation field. Two separate parameter estimations were
applied. First, model parameters for RH (e.g., Q10,M,
kM, kA, μ, ϵ, and kS, depending on
the type of model) were estimated with the incubation data. Next,
autotrophic respiration parameters (Q10,R and kR) were
estimated from field data.
Incubation field linear. Similar to the incubation field
approach, parameters relating to RH were first estimated with
incubation data. Next, using these parameter estimates, heterotrophic
respiration was computed from the corresponding field measurements
(denoted here as RH,field). Total soil respiration then equals
RS=gRCR+f⋅RH,field, with
RA=gRCR and RH=f⋅RH,field. We
then estimated f and gR from the field data.
Table shows the relationship
between the different parameter estimation approaches studied.
Relationship between the different parameter estimation approaches utilized for this study.
Data for assimilation Parameter estimation approach name ↘Incubation (for RH) and field (for RA)Field (for RA and RH)RA depends on TsoilIncubation fieldFieldRA independent of TsoilIncubation field linearField linear
Table lists the parameters estimated
for each submodel and parameter estimation approach. Data used for
parameter estimation consisted of combinations from five different
categories of sites (2012, 1990, 1968, control, or all sites together)
and three different depths (5 cm, 10 cm, or both depths together).
Additionally, with the four different parameter estimation approaches
(field, field linear, incubation field, and incubation field linear) and
five different submodels (Null, Microbe, Microbe-mult, Quality, and
Quality-mult), 300 separate parameter estimations were computed.
When parameters were estimated using (1) the incubation data, (2) field parameter estimation approach, and (3) field linear parameter
estimation approach, we applied 1000 iterations of the
Levenberg–Marquardt algorithm. Following these iterations we reduced
post-processing computational time in two ways. First, duplicated
parameter sets were reduced to a single instance. Second, we excluded
parameter sets for which the residual sum of squares was outside the 50 %
centered confidence interval. For the incubation field and incubation
field linear approaches, we used these filtered parameter sets for
subsequent estimation of the remaining parameters with field data.
Listing of parameters estimated with each submodel and parameter estimation approach. Parameters in bold-face font (incubation and incubation field linear approaches) were estimated from the incubation data first, followed by all remaining parameters with the field data.
Parameter estimation approach →FieldField linearIncubation fieldIncubation field linearNull submodel (RS=RA+RM) RAQ10,R, kRgRQ10,R, kRgRRMQ10,M, kMQ10,M, kMQ10,M, kMQ10,M, kMfNumber of parameters4344Microbe and Quality submodels (RS=RA+RM+RG) RAQ10,R, kRgRQ10,R, kRgRRMQ10,M, kMQ10,M, kMQ10,M, kMQ10,M, kMRGkA, μ, ϵkA, μ, ϵkA, μ, ϵkA, μ, ϵfNumber of parameters7677Microbe-mult and Quality-mult submodels (RS=RA+RM) RAQ10,R, kRgRQ10,R, kRgRRMQ10,M, kM, kARGQ10,M, kM, kAQ10,M, kM, kAQ10,M, kM, kAfNumber of parameters5455Model evaluation
We applied two different approaches to evaluate the reasonableness of a
model–data fit. The first approach relied on Taylor diagrams
, which facilitates intercomparison
between models when compared to measured values (in this case
RS). The Taylor diagram is structured as a polar coordinate plot;
here, the radius ν is the normalized ratio between modeled and
measured standard deviation σmodel/σmeasured and
the angle θ corresponding to the correlation coefficient r
for measured and modeled RS. Two comparisons can be visually
inferred from the Taylor diagram. First, the point located at
(ν,θ)=(1,0) represents a set of modeled values of RS
that perfectly match measured RS. Values of ν less than
unity indicate that modeled RS has less variability. Second, the
distance from a point on the diagram to (ν,θ)=(1,0) is the
centered-pattern root mean square distance. Concentric circles from the
point (ν,θ)=(1,0) help assess the centered-pattern root mean square distance for modeled results.
A second approach relies on Akaike's information criterion (AIC)
. The AIC is defined as
-2⋅LL+2⋅p, where LL is the log-likelihood and
p the number of parameters in the model. The submodel with the
lowest AIC is defined as the best approximating model for the data. We
apply the AIC to compare across submodels for a parameter estimation
approach to control for sample size effects in the AIC.
Results
With the different combinations of measurements (incubation or field
measurements), FireResp submodels (Sect. ), and
parameter estimation approaches (Sect. ) we have
over 300 different estimates of the parameters. Parameter estimates were
evaluated based on the summary distributions of modeled RA,
RH, and RS. Results were evaluated for their
reasonableness to produce estimates of RA and RH as well
as the comparisons between measured and modeled RS for incubation
and field data (Taylor diagrams).
Figure shows the Taylor diagram comparing
measured and modeled RS for the incubation data for each FireResp
submodel, faceted by the depth of soil data used for parameter
estimation (5 cm, 10 cm, or both). We combined data from all sites in
the chronosequence to make these comparisons. In general, most models had
high correlation coefficients (≈0.7–0.9); combining all the
sites together did not improve the model–data comparisons. Figure is structured similarly to Fig. and compares measured and modeled RS
for each FireResp submodel and parameter estimation approach.
Taylor diagram for comparing measured and modeled RS for the incubation data for each of the FireResp submodels. Columns in the facetted plot represent the depth of the data used for parameterization (5 cm, 10 cm, or all depths). Radii represent the normalized standard deviation between a FireResp submodel value of RS and measured RS; angles represent the correlation coefficient r (labeled). The dashed concentric circles represent contours (increments 0.25) for the normalized centered-pattern root mean square distance.
Taylor diagram for comparing measured and modeled RS for field data for each of the FireResp submodels (colors) and parameter estimation approaches (symbols). Columns in the facetted plot represent the depth of the data used for parameterization (5 cm, 10 cm, or all depths). Radii represent the normalized standard deviation between a FireResp submodel value of RS and measured RS; angles represent the correlation coefficient r (labeled). The dashed concentric circles represent contours (increments 0.25) for the normalized centered-pattern root mean square distance.
We used sparkline tables to summarize and compare the panoply of
parameter statistics (Fig. ) and model
statistics (adjusted R2 and AIC, Fig. ). In a particular column (parameter) in
Fig. , the vertical axis is scaled to the
ranges of the parameters in Table ; the
horizontal axis is ordered by the time since disturbance (2012, 1990,
1968, or control sites). For ease of presentation, Fig. displays results from the incubation field
linear approach at 5 cm; all the model results are presented in the
Supplement. Figure also
denotes edge-hitting parameters (defined here as within 1 / 10 of a
percent of the allowed parameter range) as separate colors. In contrast,
Fig. structures each sparkline plot by
the submodel studied (Null, Microbe, Quality, Microbe-mult, and
Quality-mult), facilitating comparisons between models for a given
parameter estimation and depth of data used in the parameter estimation.
In Fig. , sparkline plots for adjusted
R2 or AIC values are all respectively scaled the same for each
statistic. The models with the largest adjusted R2 or lowest AIC
value are denoted as separate colors.
Median values of parameter estimates for different FireResp submodels using the incubation field linear approach at 5 cm of depth. The horizontal axis on each sparkline plot is arranged by the year since the burn in the chronosequence (2012, 1990, 1968, or control). In each column the vertical axis scale is the same. Edge-hitting parameters (defined here as within 1 / 10 of a percent of the allowed parameter range) are denoted with the blue coloring.
Median values of the adjusted R2 and AIC from different parameter estimation approaches (field, field linear, incubation field, and incubation field linear) using measurements made at a given depth. The horizontal axis on each sparkline plot is arranged by FireResp submodels (Null, Microbe, Quality, Microbe-mult, and Quality-mult). For the adjusted R2 sparkline plot, the vertical axis ranges between 0 and 1, with gridlines every 0.25 units. The submodel with the highest adjusted R2 value is denoted with red coloring. For the AIC plots, the vertical axis ranges from 50 to 250, with gridlines every 50 units. The submodel with the lowest AIC is denoted with red coloring.
We computed RA, RH, and the proportion of soil respiration
due to autotrophic respiration (pA=RA/(RA+RH)) for each
parameter set generated through the parameter estimation routine
(Sect. ). We then computed summary statistics from
the distribution of RA, RH, and pA for each parameter
estimation approach. Summary results for the median of these
distributions for RA and RH are shown in Fig. , organized by the parameter estimation
approach. Additionally, the red shading in Fig. shows the minimum and maximum ranges of
measured RS (lines), first or third quarters (boxes), and median
RS for comparison. Figure visually
displays no significant difference in patterns of RA and
RH by the depth of the soil data used for parameter estimation (5 cm, 10 cm, or both depths together).
Median modeled fluxes of RA and RH from different parameter estimation approaches (field, field linear, incubation field, incubation field linear), soil depth data used for parameter optimization (5 cm, 10 cm, or both depths together), and submodels (Null, Microbe, Quality, Microbe-mult, and Quality-mult). The grey lines are used as a guide to show the chronosequence trend for a particular parameter estimation approach and soil depth. The box plot shows measured ranges of RS at each site in the chronosequence.
Figure is structured similarly to Fig. but shows pA=RA/(RA+RH),
which facilitates better comparison across the different types of
approaches to estimate parameters. For comparison, the green boxes show
the predicted values of pA based on RA and RH data
reported in Fig. 1 of (available
through Mendeley; ). We
computed the predicted values of pA from a loess fit using years
since disturbance and pA as variables.
Median contribution of the proportion of autotrophic respiration (pA=RA/RS) from different parameter estimation approaches (field, field linear, incubation field, and incubation field linear), soil depth data used for parameter optimization (5 cm, 10 cm, or both depths together), and models (Null, Microbe, Quality, Microbe-mult, and Quality-mult). The crossbar plot shows predicted values of pA with twice the standard error from data reported in Fig. 1 in .
Discussion
Soil models that directly incorporated microbial carbon produced
patterns of RA and RH that increased from the time since
the fire (Fig. ). As these patterns also
conform to changes in root carbon (which was proportional to tree
biomass, Table ), we have initial support
for our two primary hypotheses: (1) autotrophic respiration should be
positively associated with the time since disturbance because of changes
in aboveground foliar vegetation from forest succession, and (2) when
tested against observational data, soil models that include soil
microbial carbon will better replicate expected patterns for soil
respiration components across the chronosequence. We will further
evaluate the two hypotheses through subsequent analysis of the data used
for parameter estimation, parameter estimation approaches, and the soil
respiration models.
Evaluation of datasets for parameter
estimation
We had two categories of datasets for this study: the type of data
(incubation or field data) or the depth at which measurements were made
(5 cm, 10 cm, or both depths together). This controlled experimental
design is also represented in the Taylor diagrams (Fig. ), which comparatively shows a centered-pattern root mean square distance (distance between a point on the
Taylor diagram and (ν,θ)=(1,0)) ranging from 0.25–1 and
r ranging 0.7–0.9. For the field data (Fig. ), the centered-pattern root mean square distance
ranged from 0.5–1 and r 0.3–0.9. We attributed the differences
between Figs. and to the soil temperatures from the incubation
experiments spanning 1–19 ∘C, allowing for a wider
temperature range to characterize any exponential temperature profile.
In contrast, field measurements ranged from 4–9 ∘C (Table ). For both Figs. and , the 5 cm
depth had higher values for r and a smaller centered-pattern root
mean square distance compared to the 10 cm depth.
We did not find any noticeable site differences in submodel outputs
depending on the depth of the soil used for data assimilation (5 cm, 10 cm, or both depths together; Figs. ,
, ). While
soil model parameters (such as Q10) are expected to vary with
soil depth
we did not observe any significant depth-dependent differences in
parameter estimates (see the figures in the Supplement).
The primary reason for this result is that the inter-site variability is
larger than the variability by depth at a given site (Table and Fig. ). We
also did not find any improvements in our results when all data from
sites were pooled together (Figs. and
). From these conclusions, we will
limit the discussion to evaluating model results generated from data at
the 5 cm depth.
Evaluation of parameter estimation approaches
We cannot eliminate a parameter estimation approach (field, field
linear, incubation field, or incubation field linear) simply by the
magnitude of the estimated fluxes RA (Fig. ). Measured autotrophic respiration in
actively growing high-latitude boreal forests
or inferred from synthesis studies
can range from 0.5–4 g C m-2 d-1. Most of the modeled values of RA
for all the parameter estimation approaches are within that range. The
incubation field and field parameter estimation approaches predicted
higher RS values outside this range at the 1968 site.
While there is no universal pattern to RH following forest fire
disturbances , we have reason to believe that
the near-zero modeled values for RH for the 1968 site in Fig. may be an underestimate. For our sites we
expect modest, and perhaps decreasing (but not zero), changes in
RH from the time of disturbance for three reasons. First,
factors influencing recovery of RH are burn severity or intensity
and decomposition of pyrogenic
litter . The fires at
our sites combusted a significant amount of soil organic matter
resistant to decomposition
, thereby minimizing any
increases in RH from the decomposition of labile litter.
Additionally, from this chronosequence,
reported increased temperature
sensitivity (Q10,M) in recently burned sites, but this was
tempered by decreases in soil organic matter quality
. Second, as succession occurs, the increase
in aboveground vegetation insulates the soil, decreasing the active
layer and thereby decreasing RH.
Third, at the same chronosequence sites found
constant C:N:P and fungal-to-bacterial ratios for microbes, indicating
homeostatic regulation of the microbial community. The cumulative effect
of these confounding factors may translate into RH remaining
constant across the chronosequence.
Our models implicitly assumed an increasing exponential relationship
between temperature and respiration. The temperature sensitivity of
respiration (Q10) across ecosystems can vary (usually around 2-5)
and is generally expected to be greater than 1, but the Q10 value
may decrease as soils warm . Some degree of
additional variability is expected when considering the biochemical or
thermodynamic foundations of respiration
, the
methodological approach used to measure soil respiration
, or variation in the soil organic matter
supply .
However, an increasing exponential relationship between temperature and
respiration may not be robustly supported by observed data at the
chronosequence sites. The forest fires at each site burned a large
portion of soil organic matter and killed the roots. Immediately
following a fire, RS will be lower even if there are higher soil
temperatures. In late-successional forests, the soil is colder and the
active layer depth is shallower, even though there may be more soil
respiration due to higher quantities of roots and soil organic matter; we
observed such patterns across the chronosequence. The 2012 and 1990
sites had the highest values of Tsoil (Table ) but the lowest overall respiration
(Fig. ). Across the chronosequence,
scatterplots of respiration with temperature had a null or negative
relationship (results not shown). Empirically the
negative association of respiration with temperature would imply a
Q10 value less than unity. As a result, to compensate for these
opposing tendencies the RH parameters tend to be edge-hitting
(Fig. and the Supplement).
We recommend either the incubation field or incubation field linear
parameter estimation approach for two reasons. First, values of the
proportion of the respiration that is autotrophic
(pA=RA/(RA+RH), Fig. ) for
the field or field linear approaches are unexpectedly and
unrealistically large, attributed to the variation in RH (Fig. ). As a baseline,
reported values of
RA/(RA+RH) to be approximately 0.50, which has also been
supported in meta-analyses (Soil Respiration Database,
). Second, the incubation field and
incubation field linear approaches in Fig. show a temporal pattern in pA
similar to patterns reported in
and the predicted pA
inferred from . The modeled values of
pA are larger at late-successional sites (0.75–1), which may be
an effect of the timing of field collection (August) when RA is
at a seasonal peak
.
Evaluation of hypotheses
Our first hypothesis concerned the dependence of RA on tree
biomass. We developed this hypothesis from our previous studies, which
concluded that tree biomass was a key factor explaining patterns of soil
respiration across the chronosequence
.
For all submodels and the field linear or incubation field linear
parameter estimation approaches, RA is proportional to CR,
which is proportional to tree biomass. Values of CR increase
across the chronosequence (Table ).
However, even with this proportional association, the results in Fig. indicate less support for our first
hypothesis for two reasons. First, some modeled values RA at the
1990 site are higher than expected, especially given the association
with RA to CR. Since CR is still comparatively low
at this site, we might expect RA (and by association pA)
to be near zero as well. Additionally, the near-zero values of RA
are not a consequence of parameters relating to RA (kR,
Q10,R, or gR) being estimated as zero. (Otherwise, the
values for these aforementioned parameters in Fig. or the Supplement for all the different models and approaches would be
edge-hitting and indicated with blue-colored dots.) Second, and
perhaps more importantly, all parameter estimation approaches in Fig. predict RA to decrease between the
1968 and control sites. The modeled decreases in RA are a result
of observed decreases in RS (Fig. )
as CS increases. To compensate, estimated parameters kR or
gR decrease across the chronosequence sites (Fig. or the Supplement). The
patterns of kR or gR may be due to the parameter
estimation routine compensating for the confounding effects of
increasing CR with decreasing RS. In summary, even though
there is evidence for association between RA and tree biomass in
earlier chronosequence sites (2012 and 1990 sites), additional work is
needed to explain the reasons for the decline in RA for later
chronosequence sites (1968 and control sites). Future work could
quantify field estimates of root mass, production, and turnover
to corroborate the
values of CR used here and with the estimated decreases in
kR across the chronosequence.
Our second hypothesis concerns the structural representation of soil
respiration for soil models. Our submodels are arranged on a continuum
of complexity (Null, Microbe, Quality, Microbe-mult, or Quality-mult).
When parameterizing more complex models, parameters may be
non-informative and/or edge-hitting . Reducing
parameter dimensionality is a key consideration for model–data
assimilation in the carbon cycle
.
Considering the incubation field linear approach only, across the range
of submodels the Microbe submodel had the smallest percentage of
edge-hitting parameters (10 %), ranging from 30 %–50 % for the other
models.
While the AIC suggests a preference towards the Null submodel, we do not
believe it is a sufficient criterion to choose it over the Microbe and
Quality submodels. There was no noticeable improvement with the Null
submodel in the Taylor diagrams for the field data (in both the values
of r and the centered-pattern root mean square difference; Fig. ) or with the adjusted R2 or AIC values
(Fig. ). While all models could not
account for a majority of the variance in observed soil respiration (the
adjusted R2 values in Fig.
ranged from 0.25–0.61), no submodel significantly improved the
adjusted R2 or AIC. In other words, the model statistics
indicated that the parameter estimation approaches all performed similarly.
This model result similarity conforms to a study by
, which synthesized a range of experimental
data with different types of process-based models to predict long-term
soil organic carbon storage.
A design constraint was to construct models with the greatest potential
to be fully parameterized from the collected data. For the Quality-mult
and Microbe-mult submodels, kA was estimated at the lower end of
its range (Fig. ), essentially reducing
these models to the Quality and Microbe submodels, respectively. Even
though we cannot definitively conclude which of the two submodels
(Quality or Microbe) is the better approximating model, we recommend
that some consideration of microbial growth and maintenance respiration
be considered using Michaelis–Menten kinetics as a starting point
. Several frameworks already exist for
incorporating Michaelis–Menten kinetics
or substrate quality degradation
. Continuous (daily
or sub-daily) soil respiration measurements could better support more
complex soil models
.
Each of the models could be incorporated into a dynamic model of
ecosystem carbon cycling that also
includes temporal changes in permafrost active layer depth
.
Conclusions
We examined the ability to parameterize a range of soil respiration
models using data collected from a fire chronosequence. Importantly, we
found support for parameterizing a more complex submodel to replicate
patterns in soil respiration and its components across a fire
chronosequence. Separate analysis of soils with incubation experiments
reduces the number of parameters to be estimated; however, care must be
taken in scaling incubation studies to field measurements.
For these high-latitude sites, future work could couple the models here
to more continuous measurements of soil temperature along with a dynamic
active layer depth model . These modeling
approaches could examine the effects of gross primary productivity on
soil respiration components
.
For sites that cannot be instrumented continuously (such as the ones
studied here), this model–data integration could be supported with
periodic surveys of aboveground biomass and other remote sensing data
.
Code and data availability
Code and data necessary to reproduce all results
are available through GitHub at https://github.com/jmzobitz/FireResp
and archived on Zenodo
.
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-14-6605-2021-supplement.
Author contributions
Co-authors JZ and JP conceived the ideas
for the research project; co-authors JP, KK, and FB
collected the field data. Co-authors HA and XZ analyzed the
incubation data. All authors contributed to evaluating the results and
the writing of the paper.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special issue statement
This article is part of the special issue “The role of fire in the Earth system: understanding interactions with the land, atmosphere, and society (ESD/ACP/BG/GMD/NHESS inter-journal SI)”. It is a result of the EGU General Assembly 2020, 3–8 May 2020.
Acknowledgements
Co-author Zobitz was funded by the Fulbright Finland Foundation and
Saastamoinen Foundation Grant in Health and Environmental Sciences. This
work was funded by the Academy of Finland. Co-author John Zobitz
acknowledges Ben S. Chelton for helpful discussions on this paper.
Financial support
This research has been supported by the Academy of Finland (grant nos. 286685, 294600, 307222, 327198, and 337550) and the European Commission, Horizon 2020 Framework Programme (grant no. INTERACT (730938)).Open-access funding was provided by the Helsinki University Library.
Review statement
This paper was edited by Christoph Müller and reviewed by two anonymous referees.
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