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journal homepage: www.elsevier.com/locate/ecolmodelMultiyear heterotrophic soil respiration: Evaluation of acoupled CO2 transport and carbon turnover model
M. Herbst a,∗ , H.J. Hellebrand b , J. Bauer a , J.A. Huisman a , J. Šimůnek c ,L. Weihermüller a , A. Graf a , J. Vanderborght a , H. Vereecken aa Agrosphere, ICG-4, Forschungszentrum Jülich GmbH, D-52428 Jülich, Germanyb Leibnitz-Institut für Agrartechnik Bornim e.V., Max-Eyth-Allee 100, D-14469 Potsdam, Germanyc Department of Environmental Sciences, University of California, Riverside, CA 92521, USAa r t i c l e

i n f oa b s t r a c t

Article history:

Modelling of soil respiration plays an important role in the prediction of climate change.

Received 31 July 2007

Soil respiration is usually divided in a fraction originating from root respiration and a het-

Received in revised form

erotrophic fraction originating from microbial decomposition of soil organic carbon. This

29 January 2008

paper reports on the coupling of an one-dimensional water, heat and CO2 ﬂux model

Accepted 15 February 2008

(SOILCO2) with a pool concept of carbon turnover (RothC) for the prediction of soil het-

Published on line 28 March 2008

erotrophic respiration. In order to test this coupled model, it was applied to a bare soil
experimental plot located in Bornim, Germany. Soil temperature and soil water content

Keywords:

measurements were used for comparison with the respective model predictions. An 8 years

Soil organic carbon

data set of CO2 efﬂux measurements, covering a broad range of atmospheric conditions, wasHeterotrophic soil respiration

used to evaluate the model. In a ﬁrst step we quantiﬁed the improvement of the CO2 efﬂux

Model

prediction due to the coupling of the ﬂux model with a pool concept of carbon turnover. The

Soilco2

humus pool decomposition rate constant and its soil water content dependent reduction

RothC

were derived from the ﬁrst 5 years of CO2 efﬂux measurements using inverse modelling.
The following 3 years of measurements were used to validate the model. The overall model
performance of CO2 efﬂux predictions was acceptable with the measured and simulated
mean daily respiration being 0.861 and 0.868 g C m−2 d−1 , respectively, and a mean absolutedifference between modelled and measured rates of 0.21 g C m−2 d−1 . The inverse estimationof the humus decomposition rate constant resulted in a value of 0.04 year−1 , which is higher
than the default value in RothC. This is attributed to the agricultural practice during theexperiment.
© 2008 Elsevier B.V. All rights reserved.

1.

Introduction

Soil respiration, as a part of the carbon cycle, is one key factor in the prediction of climate change (IPCC, 2007; Smith etal., 2003; Davidson and Janssens, 2006). In this context, the∗accurate modelling of soil respiration plays a major role, sincemodels, that are validated for present conditions may be used
to predict soil CO2 efﬂux under future boundary conditions,like increased temperatures or elevated CO2 levels. Changes
in the soil carbon pools contribute signiﬁcantly to soil res-

Corresponding author. Tel.: +49 2461 618674; fax: +49 2461 612518.
E-mail addresses: m.herbst@fz-juelich.de (M. Herbst), jhellebrand@atb-potsdam.de (H.J. Hellebrand), j.bauer@fz-juelich.de (J. Bauer),s.huisman@fz-juelich.de (J.A. Huisman), Jiri.Simunek@ucr.edu (J. Šimůnek), l.weihermueller@fz-juelich.de (L. Weihermüller), a.graf@fzjuelich.de (A. Graf), j.vanderborght@fz-juelich.de (J. Vanderborght), h.vereecken@fz-juelich.de (H. Vereecken).
0304-3800/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2008.02.007

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e c o l o g i c a l m o d e l l i n g 2 1 4 ( 2 0 0 8 ) 271–283

piration. These changes, in combination with shifts in plant
carbon ﬁxation, determine ecosystem carbon storage belowground and its exchange with the atmosphere (Paustian etal., 2000). Small changes in the soil carbon stocks have aconsiderable impact on the atmospheric CO2 at the global
scale (Eliasson et al., 2005), since soil organic matter contains
about twice as much carbon as the earth’s atmosphere. A goodunderstanding of the inﬂuence of soil water content and temperature on the microbially mediated release of CO2 from soil
carbon stocks is crucial for an accurate prediction of climate
effects on global carbon cycling (Fang and Moncrieff, 2001; Zaket al., 1999). A global increase in decomposition rates due toincreased temperatures could cause the release of more soil
carbon. However, if the soil temperature increase coincides
with drier soil conditions, the increase could be dampened(Zak et al., 1999). Thus, a sound estimation of soil respiration
as a function of soil temperature and water content is crucial
to the understanding of global climate change.
Existing models to predict soil respiration can be divided in
two categories that differ in temporal scale and methodology.
On the other hand, models like SOILCO2 (Šimůnek and Suarez,
1993), the model of Cook et al. (1998) or the model of Pumpanen
et al. (2003) were developed to estimate the soil CO2 efﬂux atthe scale of hours to days. These models focus on a physically
based description of CO2 transport in the soil. Typically, thesemodels treat the CO2 production in a simpliﬁed way by using
an optimum respiration rate as a source term constant in time
and/or space (Šimůnek and Suarez, 1993; Pumpanen et al.,2003). On the other hand, carbon turnover models like RothC(Coleman and Jenkinson, 2005), CENTURY (Parton et al., 1994)
or CANDY (Franko et al., 1997) usually operate at the temporal scale of months to decades using pool concepts to accountfor microbiological carbon decomposition (Smith et al., 1997).
RothC, like all other carbon turnover models, assumes that
CO2 production by microbial decomposition is immediately
rejected to the atmosphere. Further, the carbon turnover models are mostly bulk models based on a conceptual approach(Smith et al., 1997; Molina and Smith, 1998). Although thesemodels account for the inﬂuence of the abiotic factors soil
temperature and soil water content on carbon decomposition(Smith et al., 2003), they do not resolve these variables over thedepth of a soil proﬁle. Usually soil organic matter is partitioned
into at least two pools or compartments, characterised by different decomposition rate constants. Typically, the models inthis category lack a feedback mechanism between local CO2
concentration in the soil proﬁle and microbial CO2 production from carbon decomposition, although it should be notedthat some of the CO2 transport models of the ﬁrst category
also neglect this (Suwa et al., 2004; Hashimoto and Komatsu,
2006).
The availability of combined CO2 transport and carbon
turnover models is still limited. To our knowledge, there arethree models that use a pool concept of carbon turnover in
combination with a CO2 transport module. One is PATCIS(Fang and Moncrieff, 1999), which applies a two-pool carbon
concept but is focussed on forest ecosystems and requires
soil water content and temperature as input. Another one is
PASTIS (Cannavo et al., 2006), which applies a combined C
and N biotransformation module (Garnier et al., 2003). The
third one is the model of Jassal et al. (2004), which applies a

two-pool carbon turnover concept with a CO2 transport model
very similar to the model of Šimůnek and Suarez (1993). In
this paper, we coupled a model of water ﬂux, heat and CO2transport (SOILCO2, Šimůnek and Suarez, 1993) with the poolconcept of a well-known and state-of-the-art carbon turnovermodel (RothC-26.3, Coleman and Jenkinson, 2005) to allow fora closed soil carbon balancing and a holistic description ofsoil carbon cycling and respiration. We envision that the useof a carbon pool model leads to a better description of theCO2 production and the dynamics of the soil carbon stocks,
whereas the use of a ﬂow and transport model improves thedescription of the soil state variables, which in turn determine the rate constants in the pool model. In contrast to
the three ‘coupled’ models mentioned above, the coupled
SOILCO2/RothC model has the advantage of using an established concept with pools, that are measurable (Falloon et al.,
1998; Skjemstad et al., 2004; Zimmermann et al., 2007) and forwhich rate constants and environmental correction factors are
documented. To test the coupled model of CO2 transport andcarbon turnover, the predictions for heterotrophic soil respiration are compared to respiration measurements made with aclosed chamber system on a bare soil plot. The aims were to (i)test the coupled model concept and to validate the model forthe prediction of CO2 efﬂux; (ii) improve our understanding of
the inﬂuence of soil water content and temperature on microbial CO2 production under ﬁeld conditions; and (iii) estimate
the decomposition rate constants of the recalcitrant carbon
pools by model inversion with measurements of CO2 efﬂux.
It should be noted that soil respiration is usually divided ina fraction originating from root respiration (autotrophic) andanother fraction originating from microbial decomposition ofsoil organic carbon (heterotrophic). For long-term averages,
the heterotrophic fraction is almost as large as the autotrophic
fraction and contributes signiﬁcantly to the production of CO2
by soils (Akinremi et al., 1999; Smith et al., 2003; Saiz et al.,2006). Unfortunately, it is cumbersome to separate root respiration from CO2 originating from microbial activity in anexperimental way (Trumbore, 2006; Scott-Denton et al., 2006).
In this study, the focus is on heterotrophic respiration. Futurestudies should also consider root respiration and its interaction with environmental variables.

2.

Materials and methods

2.1.

Soil water, heat and CO2 ﬂux

SOILCO2 (Šimůnek and Suarez, 1993) is a physically based onedimensional model for soil water and heat ﬂux as well as forCO2 transport. Since the original approaches of SOILCO2 forwater, heat and CO2 ﬂux in the water and gas phase were not
modiﬁed in the coupled model, we describe them only brieﬂy.
The unsaturated soil water ﬂux is described by the Richards
equation:



∂ ∂h
∂
k(h)
=
∂h ∂t
∂z

 ∂h
∂z



−1

−Q

(1)

where t is the time [T], z is the vertical coordinate [L],  isthe volumetric water content [L3 L−3 ], h is the pressure head[L], k is the unsaturated hydraulic conductivity [L T−1 ] and Q

Author's personal copye c o l o g i c a l m o d e l l i n g 2 1 4 ( 2 0 0 8 ) 271–283

is a source/sink term [T−1 ]. The soil water capacity ∂/∂h andthe unsaturated hydraulic conductivity function k(h) are calculated according to Van Genuchten (1980). Soil heat transport
is described by:Cp ()



∂
∂T
∂T
∂T
=
()
− Cw qw
∂t
∂z
∂z
∂z

(2)

where T is the soil temperature [K],  is the apparent thermal
conductivity [W L−1 K−1 ], Cp is the volumetric heat capacityof the porous medium [J L−3 K−1 ], Cw is the volumetric heat
capacity of the soil water [J L−3 K−1 ] and qw is the water ﬂux[L T−1 ].
Transport of CO2 is simulated by considering diffusion Jda[L T−1 ] and convection Jca [L T−1 ] in the gas phase, as well as dispersion Jdw [L T−1 ] and convection Jcw [L T−1 ] of CO2 dissolvedin the liquid phase:∂cT∂= − (Jda + Jdw + Jca + Jcw ) + S
∂t
∂z

(3)

where cT [L3 L−3 ] is the total volumetric concentration of CO2
and S [L3 L−3 T−1 ] is the production term of CO2 . The concentration of CO2 in the liquid phase is assumed to be ininstantaneous equilibrium with the gas phase concentration.
The predominant transport process for CO2 is the diffusion in
the gas phase, calculated according to
Jda = −a Da

∂ca
∂z

(4)

where  a is the volumetric air content [L3 L−3 ], ca is the volumetric CO2 concentration in the gas phase [L3 L−3 ] and Da
is the effective soil matrix diffusion coefﬁcient of CO2 in thegas phase [L2 T−1 ]. This effective diffusion coefﬁcient accounts
for the tortuosity of the pore space and is calculated by theMillington–Quirk approach:
7/3Da = Das as(5)where Das is the diffusion coefﬁcient of CO2 in free air [L2 T−1 ]and  s is the saturated water content [L3 L−3 ]. The estimationof the CO2 transport caused by air advection in the soil isbased on a piston gas ﬂow assumption, which implies that any
water volume change in the soil proﬁle must be immediately
matched by a corresponding change in gas volume: Lrqa (z) = qw (0) − qw (z) +roots  P [L3 L−3 T−1 ]:S = S + P

(7)

The value of  S in the original SOILCO2 is calculated from an
optimal CO2 production rate  S0 [L3 L−2 T−1 ], which is constantin time and distributed with an exponential function over the
proﬁle depth:S (z) = S0 a e−a(Lr −z)(8)where Lr is the proﬁle depth [L]. The exponential functionis scaled with the constant a to ensure that the function isnormalized according to the depth of the soil proﬁle.
For the modiﬁed version of SOILCO2, the pool concept of the
carbon turnover model RothC-26.3 (Coleman and Jenkinson,2005) is used to estimate the CO2 production by soil microorganisms. It is assumed that soil organic matter (SOM) is
composed of a variety of organic compounds, which are characterised by different decomposition rates. C-pools group
substances with decomposition rates of the same order ofmagnitude. In the RothC model, SOM is partitioned into ﬁvecompartments, where the inert organic matter pool (IOM)[M L−3 ] is resistant to decomposition. The other four compartments are actively decomposed. These are the decomposable
plant material (DPM) [M L−3 ], the resistant plant material (RPM)[M L−3 ], the microbial biomass (BIO) [M L−3 ] and the humiﬁedorganic matter (HUM) [M L−3 ]. Incoming plant carbon is partitioned between DPM and RPM. Both DPM and RPM decompose
to form CO2 , BIO and HUM. The partitioning between CO2 , BIO
and HUM depends on the clay content of the soil using thefollowing equation:b=

CO2= 1.67 (1.85 + 1.6 e−0.0786 clay 100 )BIO + HUM

(9)

where the clay fraction [M M−1 ] is expressed on a gravimetricbasis. The fraction of CO2 carbon xCO2 is thus equal to b/(b + 1).
Both BIO and HUM decompose to generate more CO2 , BIO and
HUM. The ratio CO2 /(BIO + HUM) for the decomposition of BIO
and HUM is the same as for the decomposition of DPM and
RPM. The decomposition process is assumed to follow ﬁrstorder kinetics:

∂Cx= Cx (−x
fj )
∂t

(10)

j

Q(z) dz(6)zwhere qa is the soil air ﬂux [L T−1 ] and Lr is the length of the soil
proﬁle [L]. For a more detailed description of the CO2 transport
processes the reader is referred to the work of Šimůnek andSuarez (1993).

where the change of the concentration of any soil organic matter pool Cx [M L−3 ] with time is characterised by the respective
optimum decomposition rate x [T−1 ], which is scaled withthe product of the reduction factors fw for pressure head, fT
for temperature and fCO2 for CO2 concentration:


2.2.

273

fj = fT fw fCO2

Production of CO2

(11)

j

In the original version of the SOILCO2 model the total source
term of CO2 production S [L3 L−3 T−1 ] is the sum of the production by soil micro-organisms  S [L3 L−3 T−1 ] and plant

For the decomposition of DPM and RPM, Eq. (10) can beextended by the input from plant material CP inp [M L−3 ]. This

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can be written in the discrete form as:Cp,i = (Cp,i−1 + yinp,x CP inp,i−1 ) e−

f t

(12)

j j

where Cp is the concentration of the pool [M L−3 ], the index
p loops over the fast pools DPM and RPM and yinp,x = 0.59 for
x = DPM and 0.41 for x = RPM (Coleman and Jenkinson, 2005),
i is the index for the time increment and t is the length of
the time step [T]. The incoming carbon from plant material Pin[M L−2 ] is distributed evenly across the soil up to a given depth
Dp [L] to calculate the carbon input from plant material:
CP inp =

Pin
Dp

(13)

Thus, the concentration of the decomposed carbon from DPM
and RPM dp [M L−3 ] is equal to:dp,i = (Cp,i−1 + yinp CP inp,i−1 )[1 − e−

f t

j j

]

(14)

The BIO and the HUM pool are charged by all active pools:

Cs,i = Cs,i−1 e



−

4
j

fj t

+ xp

dr,i

(15)

r=1

where xp is equal to (1 − xCO2 ) × 0.45 and (1 − xCO2 ) × 0.54 for
BIO and HUM, respectively. Here, index s loops over the BIO
and HUM pool, and index r loops over the four pools DPM, RPM,
BIO and HUM. The concentration of the decomposed carbon
from BIO and HUM ds is equal to:ds,i = Cs,i−1 [1 − e−

f t

j j

]

(16)

Thus, the total mass concentration of CO2 carbon [M L−3 ]equals the sum of the CO2 carbon produced from DPM, RPM,
BIO and HUM:

The reduction of the CO2 production as a function of theCO2 concentration is based on Michaelis–Menten kinetics(Šimůnek and Suarez, 1993). The original SOILCO2 approach
was slightly modiﬁed in order to obtain a value of 1.0 for optimum conditions:fCO2 (ca ) =0.21 − ca
0.21∗ + 1 − 0.42 − K ∗0.42 − ca − KM
M

fCO2 (ca ) = 0.0

for ca < 0.21

(20)

for ca ≥ 0.21

∗ is thewhere ca is the CO2 concentration [L L−3 ] and KM
Michaelis’ constant for the CO2 concentration [L3 L−3 ], which
was set to 0.19 cm3 cm−3 .
The reduction factors for pressure head are calculated
according to Šimůnek et al. (1996):

fw (h) = 1.0

for h1 ≤ h ≤ +∞log10 |h| − log10 |h2 |fw (h) =log10 |h1 | − log10 |h2 |for h2 ≤ h < h1

fw (h) = 0.0

for − ∞ ≤ h < h2(21)where h1 is the pressure head for optimum conditions [L], andh2 is the pressure head below which CO2 production ceases[L]. According to Rodrigo et al. (1997) this functional relation
between pressure head and CO2 production, originally developed by Andrén and Paustian (1987), was frequently applied
to describe the inﬂuence of soil water availability on microbialactivity.
Compared to Šimůnek and Suarez (1993), the original
Arrhenius-type temperature reduction function was shiftedto obtain values of 1 for the RothC reference temperature Tref[K] of 282.4 K:
fr (T) = e[E(T−Tref )/RT Tref ](22)

where T is the absolute temperature [K] and E is the reaction
activation energy [M L2 T−2 n−1 ].

4

CCO2 C,i = xCO2

dr,i

(17)

2.3.

Experimental data

r=1

The CO2 mass concentration CCO2 [M L−3 ] is calculated fromthe CO2 carbon mass concentration CCO2 C [M L−3 ] by scaling
with the ratio between the molecular mass of CO2 and C,
which is 0.044 kg mol−1 /0.012 kg mol−1 . The CO2 mass concentration is converted into a volumetric concentration assuming
an ideal gas:
VCO2 =CCO2 RT
MCO2 P(18)

where VCO2 is the volumetric CO2 concentration [L3 L−3 ], R is
the universal gas constant (=6.2 × 1014 kg cm2 d−2 K−1 mol−1 )[M L2 T−2 K−1 n−1 ], T is the absolute temperature [K], MCO2 is themolar mass of CO2 (=0.044 kg mol−1 ) [M n−1 ], and P is the atmospheric pressure (=7.6 × 1012 kg cm−1 d−2 ) [M L−1 T−2 ]. The CO2
production rate, which replaces the  S of the original approachin Eq. (7), is calculated according to
S =

VCO2
t

(19)

The data was obtained at the experimental plot of the Instituteof Agricultural Engineering in Bornim, close to Berlin (Germany). The predominating soil type is an arenosol (Hellebrand
et al., 2003), which properties are summarized in Table 1. The
bare soil plot, where the CO2 efﬂux measurements were carried out, was kept free from plants by grubbing up to a depth of
10 cm whenever a small amount of weeds became visible. Dueto this weeding practice small amounts of fresh plant input,
mainly root material, were incorporated into the soil at theweeding dates. However, we further simply refer to the plot
as a ‘bare soil plot’, since this is the closest description of theexperimental conditions.
Average daily soil temperature at a depth of 20 cm wasdetermined from measurements made between 1 February
1999 and 31 October 2000 (Fig. 1). Soil water content was determined gravimetrically at 12 plots surrounding the bare soil
plot by using mixed samples taken from 0 to 30 cm depth
from 25 March 2003 to 20 December 2005. The 12 plots wereplanted with different crops. Mean average soil water content
and standard deviation are calculated by bulking the data from

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e c o l o g i c a l m o d e l l i n g 2 1 4 ( 2 0 0 8 ) 271–283

Table 1 – Properties of the soil genetic horizons: clay fraction (<2 ␮m), silt fraction (2–53 ␮m), soil organic carbon SOC, bulk
density b and soil hydraulic properties according to Van Genuchten (1980): saturated water content  s , residual watercontent  r , inverse of the bubbling pressure ˛, shape parameter n and saturated hydraulic conductivity Ks
HorizonDepth (cm)Clay (g g−1 )Silt (g g−1 )SOC (g g−1 )

Ap
Ahl
Bt
Cv

0–30
30–60
60–82
82–100

0.062
0.060
0.174
0.122

0.159
0.183
0.206
0.257

0.00840.00550.00200.0010Fig. 1 – Simulated (red line) and measured (points) soil
temperature at 20 cm depth. (For interpretation of thereferences to colour in this ﬁgure legend, the reader isreferred to the web version of the article.)

the 12 plots (Fig. 2). Typically, the plots were sampled every
week. Since the plots were cropped, only the measurements
outside the vegetation period were considered in the model
validation.
From January 1999 until December 2006, CO2 efﬂuxes were
measured with a closed chamber system and an automatedgas chromatograph (GC) approximately every second day(Hellebrand et al., 2005). The gas ﬂux chambers had a volume
to area ratio of 0.315 m (volume 0.064 m3 , diameter 0.509 m).

␳b (g cm−3 )␪s (cm3 cm−3 )␣ (cm−1 )n (−)

Ks (cm d−1 )

1.35
1.45
1.50
1.50

0.428
0.386
0.350
0.367

0.139
0.110
0.097
0.084

1.42
1.44
1.34
1.38

442.8
235.1
88.0
86.9

Fluxes were measured between 9.00 and 10.00 a.m. Two evacuated gas samplers (100 cm3 bottles with taps) were connectedto each box. The ﬁrst one was opened when the box was puton the water sealed ring inserted in the soil and the second
one after about 1 h enclosure time. The samplers were thenconnected to the GC injection control system. The GC used
an electron capture detector to determine the CO2 concentration. The increase in concentration observed for 1 h periods
was used to calculate the CO2 efﬂux (Hellebrand et al., 2003).
In order to detect erroneous ﬂux measurements, e.g. due to difﬁculties with air tightness during the sampling procedure, thewhole data set was ﬁltered. A moving average of ﬁve consecutive measurements was calculated and measurements thatwere not within the range of the moving average ± the standard deviation of the entire data set (=0.56 g C m−2 d−1 ) werediscarded (4% of the measurements). During the ﬁrst 5 years(t ≤ 1825 d), the period for which the model was inverted, 861
CO2 efﬂux measurements were available. For the following
3 years (validation period, 1825 d < t < 2920 d), 566 measurements were available. Due to the weeding practice small
amounts of fresh plant material entered the soil. In orderto match the modelled SOC in the top soil with the measured SOC values, it was found that 177 g C m−2 year−1 (thisis the net primary production) must have entered the soil
as fresh plant material. The respiration of this fresh plantmaterial contributed to 43% of the total measured CO2 respiration. The amount of fresh plant material was obviously linked
to a certain amount of autotrophic respiration, which also
contributed to the measured CO2 ﬂuxes. Assuming that the
autotrophic respiration was 50% of the net primary productionof every year (Kirschbaum et al., 2001), which was assumed to
be 177 g C m−2 year−1 , the autotrophic respiration was 21.5% of
the total measured respiration. To ensure that the model inversion for the estimation of the carbon pool decay rates was only
based on heterotrophic CO2 ﬂuxes, the measured CO2 ﬂuxes
were reduced by 21.5%.

2.4.

Fig. 2 – Simulated (green line) and measured average (dots)
soil water content (0–30 cm depth), bars indicate standard
deviation. (For interpretation of the references to colour inthis ﬁgure legend, the reader is referred to the web versionof the article.)

Model setup and initialization

The reference evapotranspiration was computed according to
the Penman–Monteith approach from daily air temperature,
air humidity, wind speed and sunshine duration (Smith etal., 1996). The latter was used to estimate daily net radiation. The meteorological data was measured at the stationof the German Weather Service located in Potsdam, approximately 10 km away from the experimental plot in Bornim. The
potential reference evapotranspiration was converted into therequired potential evaporation (Fig. 3) by scaling with a factorof 0.9 (Penman, 1948).

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depth, a Dirchlet boundary (h = −200 cm) was imposed. For
heat transport, the air temperature measured at 2 m was used
as a time dependent Dirichlet boundary condition at the soil
surface. The bottom boundary was set to a constant soil temperature using a Dirichlet boundary condition (Table 3). The
atmospheric CO2 concentration was imposed as a time independent Dirichlet boundary condition at the top of the soil
proﬁle, while a no-ﬂux boundary condition was imposed at thebottom for the CO2 transport. For the discretization in space,
we used 100 elements of 1 cm thickness each.
Fig. 3 – Measured daily precipitation (black surface),measured air temperature at 2 m (red dots), simulated
potential evaporation (blue line) and simulated actual
evaporation (green line) for the simulation period. (Forinterpretation of the references to colour in this ﬁgurelegend, the reader is referred to the web version of thearticle.)2.5.

The soil hydraulic properties (saturated water content
 s [L3 L−3 ], inverse of the bubbling pressure ˛ [L−1 ], shapeparameter n and saturated hydraulic conductivity Ks [L T−1 ])were estimated with the pedotransfer functions of Rawls andBrakensiek (1985) from clay content, silt content and bulk density (Table 1). The residual water content  r was assumed to be
zero for all soil horizons. Since no measurements were available, the bulk density was set to standard values increasing
with proﬁle depth. Except for the plough horizon, the carbon
content of the deeper soil layers was not known and therefore
estimated (Table 1).
The initial relative fraction of each carbon pool [M M−1 ] wasassumed to be constant with depth (i.e. fraction of IOM is 8%
of soil organic carbon for each soil horizon, see Table 2). Since
the plot was cleared 2 years before the start of the experiment, it was assumed that no fresh plant material was present
anymore. Thus, the RPM and DPM pool were initially set tozero. The IOM fraction was calculated from the total SOC
using the pedotransfer function developed by Falloon et al.
(1998). After consideration of DPM, RPM and IOM, the remaining soil organic carbon must equal the sum of the HUM and
the BIO pool. The relatively small BIO fraction of this sum wasdetermined by assuming a BIO to HUM pool ratio of 0.0272(Zimmermann et al., 2007). These pool fractions were thenused to initialise the model (Table 2).
The upper boundary for the water ﬂow was deﬁned byatmospheric conditions. At the bottom of the proﬁle at 1 m

Model inversion

The coupled SOILCO2/RothC model was inverted for theparameter h2 of the water content reduction function (Eq.
(21)) and the decomposition rate constant for the HUM pool
HUM . The inverse estimation of the HUM decomposition rate
constant was necessary because the original rate constantresulted in a rather strong underestimation of the CO2 efﬂux.
The h2 parameter was also inverted since it inﬂuenced the estimation of HUM and was not known a priori. The h2 parameter
slightly affects the temporal course of CO2 production within
a year, whereas HUM strongly inﬂuences the total amount of
CO2 production. The Nelder–Mead Simplex algorithm (Nelder
and Mead, 1965) was used to invert the model. The objectivefunction used in the inversion equally weighted the coefﬁcientof determination between measured and modelled daily CO2
efﬂuxes and the overall sum of measured and modelled CO2
efﬂux. To allow a consistent comparison between the original
SOILCO2 model and the coupled model, the SOILCO2 model
was inverted for the h2 parameter and the optimal CO2 production S0 in Eq. (8) with the same procedure.

2.6.

Inversion and validation criteria

For the inversion and validation we used various criteria toquantify the agreement between the measurements and themodel predictions. The ﬁrst criterion was the mean absolute
error MAE, which is simply the mean of the absolute residuals.
Also a commonly used criterion for model validation is theroot mean square error (RMSE), where the root of the meansquared residuals is calculated. MAE and RMSE have the unitof the considered variable. The squared residuals are also used
for the second criterion applied, which is the coefﬁcient ofmodel efﬁciency EF (Nash and Sutcliffe, 1970). Here they areused to determine the proportion of the deviation from theTable 2 – Initial RothC pools of the arenosol and pool fractions; biomass carbon BIO, humic fraction HUM, inert organic
matter IOM and total soil organic carbon SOC
HorizonBIO (g C m−2 )HUM (g C m−2 )IOM (g C m−2 )SOC (g C m−2 )

Ap
Ahl
Bt
Cv

84
59
16
7

3050
2138
591
242

273
191
53
22

3406
2388
660
270

Fraction (%)

2

90

8

100

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Table 3 – Selected model input parameters and initial conditions
Parameter

Value

∗
Km
E
Das
Dws
w
h1
hini
Cini
Ctop
Tbot
Dp
T

Michaelis’ constant
Activation energy
Diffusion coefﬁcient of CO2 in air
Diffusion coefﬁcient of CO2 in water
Dispersivity in water
Critical pressure head
Initial pressure head
Initial CO2 concentration
CO2 concentration at soil surface
Bottom soil temperature
Incorporation depth of plant material input
Thermal dispersivity

observed mean, which can be explained by the model:nn22(x − xo )i −(x − xs )i
i=1 o
i=1 o
n
2
(x − xo )i
i=1 o

EF =

(23)

R2 = ⎣⎤2n(x − xo )i (xs − xs )i
i=1 o
n
2
(x − xo )i
i=1 o

⎦

cm3 cm−3
kJ mol−1
cm2 d−1
cm2 d−1cm
cm
cm
cm3 cm−3
cm3 cm−3◦
Ccm
cm

IA is also dimensionless and ranges between 0 and 1:

where xo is the observed value at time t, xs is the simulation
result at time t and xo is the arithmetic mean of the observed
values. The EF is a dimensionless criterion. Values between−∞ and 1 can be calculated for this index, the latter indicatingthat observation and model are completely in agreement. The
coefﬁcient of determination R2 is given by

⎡

0.19
55.5
13737.6
1.529
1.5
−70
−200
0.001
0.00033
8
10
1.5

Unit

(24)

n
2
(x − xs )i
i=1 s

where xs is the arithmetic mean of the simulated values. The
Index of Agreement IA (Willmott, 1981) was also applied. The

IA = 1 −n
2(x − xs )i
i=1 o
n
2
(|xo − xo | + |xs − xo |)i
i=1

(25)

Because R2 , EF and IA are dimensionless, they can be used tocompare the model quality between different variables, while
the RMSE gives an idea of the model error in the units of thevariable under consideration.

3.

Results and discussion

3.1.

Soil water content and temperature

The comparison between measured and simulated soil temperature at 20 cm depth (Fig. 1) indicates very good agreement(R2 = 0.93, n = 639). Slight differences occurred mostly during
the second half of the year, at the end of summer and autumn
1999 (time steps 220–350), when the soil temperature wasslightly underestimated. The mean absolute error (MAE) was
1.43 K and the root mean square error (RMSE) of 1.76 K wasFig. 4 – Simulated and measured daily respiration ﬂuxes (a) and residuals between the simulated and measured respiration(b) for the original model and the coupled model version.

Author's personal copy
278

0.64
0.36
0.68
0.44
0.61
0.70
0.66
0.41
0.87
0.79
0.91
0.83
0.90
0.92
0.88
0.81
0.64
0.44
0.70
0.49
0.67
0.72
0.67
0.48
0.223
0.234
0.388
0.302
0.335
0.229
0.197
0.238
0.183
0.184
0.281
0.242
0.248
0.183
0.158
0.189
264.5
290.7
435.7
333.0
389.1
315.1
261.8
255.2
252.5
307.3
434.5
335.4
383.3
305.8
272.6
221.7
0.37
0.49
0.61
0.64
0.33
0.60
0.52
0.52
406.1
537.5
627.0
762.6
428.3
626.3
600.2
502.3
1999
2000
2001
2002
2003
2004
2005
2006

IA
R2
RMSE (g C m−2 d−1 )MAE (g C m−2 d−1 )Model CO2 (g C m−2 year−1 )Measurements of CO2(g C m−2 year−1 )Ea /Ep (−)

Fig. 4a presents a comparison between measured and modelled soil respiration of the original SOILCO2 model and thecoupled model developed in this study. The original SOILCO2
model underestimates the measured CO2 efﬂuxes during
spring and early summer when fresh plant material entered
the topsoil. Fig. 4b shows that the residuals between the measurements and the coupled SOILCO2/RothC are on averagecloser to zero than for the original SOILCO2. In particular thethird and the ﬁfth year of the modelling period show rather
large residuals for the original SOILCO2, which is not given tosuch an extent for the coupled model. The effect of adding
fresh plant material on soil respiration cannot be modelledby the original approach using a time-invariant optimum CO2
production rate of 0.44 cm3 cm−2 d−1 , as determined by the
inversion (Eq. (8)). The original SOILCO2 model has a R2 of
0.18, an IA of 0.64, a MAE of 0.36 g C m−2 d−1 and a RMSE of
0.49 g C m−2 d−1 . It should be noted that, both the original
approach as well as the coupled SOILCO2/RothC model areable to reproduce the total amount of CO2 efﬂux for the ﬁrst 5
years, which is simply a result of using this total amount in theobjective function for the inversion. The measured mean respiration rate over the inversion period is 0.939 g C m−2 d−1 . In
case of the coupled model, the inversion of the HUM decomposition rate signiﬁcantly improves the agreement between
simulated and measured CO2 efﬂuxes. Fig. 4a shows that themodelled soil CO2 efﬂux is in acceptable agreement with themeasurements for the coupled model (R2 = 0.66, IA = 0.90). The
MAE and the RMSE for the ﬁrst 5 years are 0.23 g C m−2 d−1 and0.30 g C m−2 d−1 , respectively. The inter-annual variations arewell captured by the model, except perhaps for the second
year (2000), for which the largest deviation between measured
and simulated annual sums of heterotrophic respiration isdetected (Table 4).
The inversion resulted in a decomposition rate constant for
the humus pool of 0.04 year−1 and a value of −9678 cm for h2 .
This decomposition rate of the HUM pool is 2.0 times higher
than the original value of 0.02 year−1 (Jenkinson, 1990). The
original value was determined from 10 years long experiments
on cropped plots. Due to root respiration, higher soil CO2 con-

P (mm year−1 )Soil respiration

Year

3.2.

Table 4 – Yearly precipitation P, ratio actual evaporation Ea to potential evaporation Ep , measured CO2 efﬂux, model CO2 efﬂux, mean absolute error MAE, root meansquare error RMSE, coefﬁcient of determination R2 , Index of Agreement IA and model efﬁciency EF, between model and measurements

only slightly higher. The measured mean temperature at 20 cm
depth during that validation period was 11.4 ◦ C, whereas themodel mean was 10.4 ◦ C. This might be the result of the bottom boundary condition, which could have been slightly too
low for that period. Even at 1 m depth, there may be some temperature variations over the years which might have caused asmall error due to the deviation of the actual 1 m temperaturefrom the long-term average we used as the lower boundary
condition.
The soil water content measurements outside the vegetation period were also used for model validation. The
modelled mean soil water content of the 0–30 cm soil layer
was in good agreement with the weekly measurements (Fig. 2),
which is supported by a MAE of 0.021 cm3 cm−3 , a RMSE
of 0.026 cm3 cm−3 and a coefﬁcient of determination of 0.55
(n = 57). The mean of the measured soil water content was
0.160 cm3 cm−3 , which was slightly overestimated by themodel with a predicted mean of 0.167 cm3 cm−3 .

EFe c o l o g i c a l m o d e l l i n g 2 1 4 ( 2 0 0 8 ) 271–283

Author's personal copye c o l o g i c a l m o d e l l i n g 2 1 4 ( 2 0 0 8 ) 271–283

279

Fig. 5 – Depth/time diagrams on model results of CO2 concentration, soil temperature and pressure head for the Ap horizon.

centrations are always found for cropped plots than for baresoil, which might lead to a reduction of CO2 production due
to high CO2 concentrations (Hashimoto and Komatsu, 2006).
Since reduction according to the soil CO2 concentration, as
an indicator for an oxygen deﬁcit, is not taken into accountin the original RothC model (Jenkinson, 1990; Coleman andJenkinson, 2005), it is conceivable that this partly explains thehigher decomposition rate found in this study. In addition,a likely explanation for the higher inverted decomposition
rate is the grubbing of the soil in order to remove the weeds.
Every mechanical disturbance and destruction of soil aggregates destroys the physical protection of the humus carbon
and enhances the availability of labile carbon and increases
the CO2 production (De Gryze et al., 2006). This higher production will lead to an increased decomposition rate in a model
inversion. It should be noted that Skjemstad et al. (2001) also
found a more labile RothC humus pool (decomposition rate of
0.03 year−1 instead of 0.02 year−1 ) than originally assumed by
Jenkinson (1990). However, the uncertainty associated to theinversely determined HUM pool decomposition rate constantof 0.04 year−1 is rather large. For example, the sensitivity of
the rate constant towards the correction of the measurements
for autotrophic respiration is rather high. If no correction for
autotrophic respiration would be carried out the inversely estimated decomposition rate constant for the HUM pool would
be even larger and amount to 0.06 year−1 , which is 2.8 times
higher than the original value of Jenkinson (1990). This points
at the sensitivity of the inversely estimated rate constants tothe estimated autotrophic respiration.
In Fig. 5 we plotted simulated proﬁles of CO2 concentrations and the inﬂuencing soil state variables against time.
Fig. 5 shows that high CO2 concentrations in the topsoil (upper
30 cm), causing high CO2 efﬂuxes, are strongly driven by soil
temperature. However, also the inﬂuence of soil water content
is visible in terms of the pressure head. For example, after adry period during the summer of 2001 (t = 850), indicated byrather high values of log10 (h), the soil respiration peaks due
to a precipitation event. Apparently, the precipitation stimulated the microbial carbon decomposition, which was low
because of the lack of soil water despite high soil temperatures.
Fig. 6a shows that the errors in the prediction of CO2
efﬂuxes are unbiased. There is no trend to over- or underestimate ﬂuxes in dependence of the ﬂux density. The deviations
between measurement and model generally vary randomly
around the 1:1 line. Fig. 6a also shows that the errors in themodelled CO2 efﬂux during the inversion period are independent from the meteorological conditions, since the errors foreach single year vary similarly around the 1:1 line.
In order to validate the parameters found by the model
inversion, the modelled and measured CO2 efﬂux (four parallels) of the following 3 years were analyzed. For this validation
period, measurements and model are also in agreement (Fig. 7
and Table 4). The coefﬁcient of determination for this period
is 0.65 and the Index of Agreement is 0.89. The MAE and the
RMSE are 0.18 and 0.22 g C m−2 d−1 , respectively. The measured
yearly sums of CO2 efﬂux slightly decreased from 2004 to 2006,
which is well reproduced by the model, although the total
amount predicted by the model for 2006 was too high (Table 4).
Fig. 6b reveals that the errors between measured and simulated CO2 efﬂuxes during the 3 years of the validation period
show no bias. Fig. 6b also shows that the errors during the validation period are on average as close to the 1:1 line as for the
inversion period, which is further conﬁrmed by the similar R2
for the inversion and validation period. The MAE and RMSE
are even smaller for the validation period.
The question arises whether the remaining discrepancies
between model and measurements result from an insufﬁcient description of the dependency of CO2 production on
soil temperature or on soil water content. In order to answer

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Fig. 6 – Correlation of simulated and observed daily CO2
ﬂux for the single years of the model inversion period (a);correlation of simulated and observed daily CO2 ﬂux for the
inversion and the validation period (b).

Fig. 7 – Simulated daily ﬂuxes, measured daily ﬂuxes,
cumulative simulated ﬂuxes and cumulative measured
ﬂuxes of CO2 for the validation period, bars indicate
standard deviation of the four measurements.

Fig. 8 – Correlation between the ratio simulated/observed
daily CO2 efﬂuxes and the estimated reduction according totemperature (top) and pressure head (bottom). The
reduction factors f(T) and f(h) are average values of theupper 30 cm.

this question, we plotted the natural logarithm of the ratio
between measured and calculated CO2 efﬂux against the
reduction factors for temperature and pressure head averaged
for the Ap horizon (upper 30 cm). Fig. 8 reveals that there isno temperature dependency of the deviations between measured and predicted CO2 efﬂuxes. The ﬁtted linear regression
shows an intercept very close to zero and a slope of 0.002,
which is also very close to zero. For the pressure head, theintercept is also very close to zero, but there seems to be aslight bias to overestimate the CO2 efﬂux for wet soil conditions, when f(h) is close to 1 (Fig. 8). Nevertheless, thisdependency is small compared to the overall noise. The slopeof the respective linear regression is 0.39, which indicates thatthe relation between soil water status and CO2 production wasprobably a bigger source of errors than the relation between
soil temperature and CO2 production. This might also partly
explain the deviations between measured and predicted CO2
efﬂuxes for 2000 (365 d < t < 730 d) and 2002 (1095 d < t < 1460 d).
These results also show that soil water content is relevantAuthor's personal copye c o l o g i c a l m o d e l l i n g 2 1 4 ( 2 0 0 8 ) 271–283

for respiration under ﬁeld conditions, which corroborates theexperimental ﬁndings of Akinremi et al. (1999) amongst others.
Besides potential deﬁcits in the model, three othermeasurement-related factors may also contribute to the disagreement between measured and modelled daily CO2 efﬂux.
First of all, the high spatial variability of CO2 efﬂux might play arole (Aiken et al., 1991; Rochette et al., 1991; Pringle and Lark,
2006). Fig. 7 shows that during the last 3 years (2004–2006),
when four locations were sampled, a high standard deviation
was detected in the measurements. Second, the temporal variability of CO2 efﬂux might also have an inﬂuence (Dugas, 1993;
Janssens et al., 2000; Nakadai et al., 2002; Tang and Baldocchi,
2005). CO2 sampling was carried out during the morning forabout 1 h every day. Typically, measurements during the morning give a good approximation of daily mean ﬂuxes (Saiz et al.,2006) with a bias smaller than 5% (Parkin and Kaspar, 2004).
However, in some situations the daily ﬂuxes estimated fromjust 1 h might deviate from the actual daily mean (Akinremi
et al., 1999). Finally, the errors in the CO2 ﬂux measurements
associated with every soil respiration measurement with achamber system probably also contributed to the disagreement between model and measurements (Janssens et al.,2000).

3.3.

Carbon balance

Soil respiration did not decrease signiﬁcantly during the eight
experimental years. It was impossible to reproduce the measured temporal evolution of the CO2 efﬂux without assumingthat most of the heterotrophically respired CO2 originatesfrom the recalcitrant pools, since the ‘fast’ pools were rather
empty and recharged only moderately from plant material
input. Usually, the recalcitrant carbon stocks contribute only
a minor portion to soil CO2 efﬂux (Ryan and Law, 2005), but
in our experiment about 57% of the heterotrophic CO2 production originates from the decomposition of the HUM pool.
The SOC content measured at the beginning of the experiment
for the upper 30 cm was 3406 g C m−2 (standard deviation of
599 g C m−2 ). The coupled model predicted a SOC content of
3081 g C m−2 at the end of the experiment, equivalent to a lossof 10%. The SOC content measured at the end of the experiment was 3025 g C m−2 (standard deviation of 375 g C m−2 ).
Fig. 9 shows that the simulation results for the topsoil areclose to the measured SOC content. The simulated SOC content for the soil horizon below (30–60 cm depth) was also ingood agreement with the measured SOC content at the end of
the experiment. Unfortunately, no measurements were available for the SOC content of the deeper soil layers at the startof the experiment. In the model, the initial SOC content of
the entire soil proﬁle was assumed to be 6724 g C m−2 . At
the end of the experiment, the simulated SOC content was
5546 g C m−2 , equivalent to a loss of 18%. This soil carbon
loss of 1178 g C m−2 is accompanied by a heterotrophic CO2 –C
emission of 2516 g C m−2 (measured: 2513 g C m−2 ). The gap
is explained by the input of fresh plant material, which wasaccounted for by assuming a rather small carbon input fromplant material of 177 g C m−2 year−1 .
In general, it should be noted that it is rather difﬁcult tovalidate the carbon turnover in the model for this experiment,

281

Fig. 9 – Simulated and measured soil organic carbon (SOC)
contents at the beginning and at the end of the model
period, bars indicate standard deviation of themeasurements.

since the loss of carbon over the 8 years is rather small compared to the accuracy of the measurements. In general themeasurements seem to support the trends predicted by themodel (Fig. 9). However, it should be remembered that the
carbon balance was also used to initialize the model withrespect to soil organic content of the deeper soil layers andthe input of fresh plant material, which means that the resultspresented in Fig. 9 cannot be considered as an independentvalidation. In addition, the inverse determination of the HUM
pool decomposition rate constant from this experiment is
uncertain because of the unknown SOC contents in the subsoil
layer, the accuracy of the SOC measurements, the unknown
parameter h2 of the soil water content reduction function andthe unknown amount of fresh plant material. For example,
the latter has a big inﬂuence on the carbon balance of the topsoil (0–30 cm). Assuming that no input of fresh plant material
occurred leads to a relative carbon loss of 23% instead of the
ﬁnally simulated loss of 10%, which is quite close to the measured value of 11%. Scaling the amount of fresh plant material
reveals the sensitivity of topsoil carbon loss to this input variable. Scaling factors of 0.5, 1.5 and 2.0 applied to the amountof fresh plant material lead to topsoil carbon losses of 17, 4.4
and −1.9%. The latter indicates even an increase of topsoil carbon content. This points to the fact, that for any experimental
setup in terms of carbon balancing the input of carbon from
fresh plant material should be determined as accurately as
possible.

4.

Summary and conclusions

The comparison between the original SOILCO2 and the coupled SOILCO2/RothC revealed a signiﬁcant improvement of
the CO2 efﬂux estimation with the coupled model presented
in this study. The coupled model shows an improved R2 of
0.66 compared to the original SOILCO2 with an R2 of 0.18. The
model inversion with the coupled model for the ﬁrst 5 years
allows the accurate prediction of CO2 efﬂux for the following 3 years. Against the background of the use of literature

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values and pedotransfer functions for the model parameterisation, the overall model performance is acceptable. The
model was able to predict the inter-annual variability of CO2
efﬂux well. Thus, the coupling concept is seen as a promising tool to describe the heterotrophic part of the carbon cycle
in soils from the input of plant residues to the release as
CO2 .
The calibration of the HUM pool decomposition rate constant revealed that it is possible to determine a ‘slow’ carbon
pool decomposition rate constant from long-term soil respiration measurements under ﬁeld conditions. The inversely
determined value of 0.04 year−1 is higher than the one suggested by the model developers, which is mainly attributed tothe agricultural practice during this experiment. The uncertainty in the inversion of the HUM pool decomposition rate
constant mainly arises from the initial organic carbon contents, the unknown amount of input from fresh plant material
and the unknown parameter h2 of the soil water content
reduction function.

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