A Process-Based Model for Predicting Soil Carbon Dioxide Efflux and ConcentrationJukka Pumpanen,* Hannu Ilvesniemi, and Pertti Hari

ABSTRACTDecomposition and root respiration processes, important to C cy­

cling in terrestrial ecosystems, are affected by soil temperature, soil moisture, and other soil properties. For studying the effect of these factors on soil CO2 efflux and soil-air C 02 concentration, a dynamic model was developed. In the model, soil was described in successive layers and the processes and soil properties were described separately for each layer. The C 02 in soil layers originated from root and micro­bial respiration, which were assumed to depend on soil temperature and moisture multiplicatively. The C 02 flux between the layers was driven by diffusion, which depended on C 02 concentration, porosity, and temperature of the layers. The model predictions of C 02 effluxes and soil C 02 concentrations were close to those observed in the field. There was a clear seasonal pattern in the soil C 02 efflux and the soil- air C 02 concentration. According to the model analysis, most of the C 02 was produced in the humus layer throughout the year, but the contribution of deeper layers to total respiration was higher in winter than in summer. The C 02 concentration was strongly dependent on factors affecting the diffusion properties of the soil, that is, the soil porosity and the soil-water content. The C 02 efflux and the soil-air C 02 concentration were overestimated, if the soil-water content was not included in the soil respiration model. The model developed in this study provided a simple and an effective tool for studying the factors affecting soil C 02 efflux and C 02 concentration.

Th e s o i l as a source or sink in the global budget for C emissions is important because of possible feedback effects on global climate (Raich and Schle-

singer, 1992; Kirschbaum, 1995; Kirschbaum, 2000). Many studies have shown that soil C 02 originates pri­marily from microbial oxidation of organic matter and root respiration (Witkamp and Frank, 1969; Edwards et al., 1970; Fritz et al., 1978; Singh and Gupta, 1977; Hanson et al., 2000). The contribution of each of these sources to the total soil C 02 efflux is poorly understood and is probably extremely variable from site to site (Amundson and Davidson, 1990; Boone et al., 1998).

Soil can be described as a layered structure where processes such as respiration produce C 02 at various depths of the soil, and diffusion and convection trans­port C 02 between the soil layers and out of the soil. Soil C 02 efflux consists mainly of the respiration of the decomposing organisms (heterotophic respiration) and the respiration by living roots (autotrophic respiration) (Singh and Gupta, 1977). In addition, abiotic processes such as carbonate dissolution and chemical oxidation may contribute to the total efflux (Burton and Beau­champ, 1994). Despite the large number of studies there is still a great deal of uncertainty about the role of root respiration on the total soil respiration. Estimates of the contribution of root respiration range from 10 to

J. Pumpanen, Dep. of Forest Ecology, P.O. Box 27, FIN-00014 Univer­sity of Helsinki, Finland. Received 11 June 2001. * Corresponding author Gukka.pumpanen@helsinki.fi).

Published in Soil Sci. Soc. Am. J. 67:402-413 (2003).

90% (Nakane et al., 1983,1996; Ewel et al., 1987; Bow­den et al., 1993; Hanson et al., 2000; Maier and Kress, 2000).

The primary mechanism for transporting C 02 from the soil to the atmosphere is molecular diffusion (Freijer and Leffelaar, 1996), but significant losses of C 02 be­cause of dissolution in soil water and by chemical reac­tion with the mineral phases of the soil have also been reported (Reardon et al., 1979; Wood and Petraitis, 1984). Moreover, in deep soils atmospheric pressure fluctuations can cause mass flow of air into and out of the soil, which can affect soil C 02 concentration. Mechanisms of gas movement other than concentration- controlled diffusion are believed to account for <10% of the total C 02 lost from the upper soil and even less for the deeper unsaturated zone (Wood and Petraitis, 1984).

The need to quantify soil C fluxes and to understand the control of soil C 0 2 effluxes by environmental factors has led to the development of different types of models. Several examples exist of empirical relationships that have been established between field measurements of soil respiration, soil temperature, and water content (Bunnell et al., 1977; Linn and Doran, 1984; Skopp et al., 1990; Kiefer and Amey, 1992; Oberbauer et al., 1992; Hanson et al., 1993; Howard and Howard, 1993; Pinol et al., 1995; Raich and Potter, 1995; Davidson et al., 1998; Maier and Kress, 2000).

Buyanovsky and Wagner (1983) and Buyanovsky et al. (19.86) measured C 02 concentrations in soil over several years and then evaluated the influence of air temperature, soil temperature, and soil water content on the concentration of C 02 using regression analysis. Brook et al. (1983) and Kiefer (1990) developed a re­gression model to predict the average C 02 concentra­tions in soil using actual evapotranspiration, which was considered to reflect a variety of climate factors, such as temperature, radiation, precipitation, and soil-water storage. However, it is difficult to study the actual pro­cesses related to soil C 02 dynamics based solely on statistical analyses.

With a process based model it is possible to study the contribution of biological activity at different depths of the soil on the total soil C 02 efflux. This is particularly interesting in boreal forests where the vertical distribu­tion of soil properties near the soil surface is pro­nounced. Litter from aboveground biomass accumulates on the soil surface and a major proportion of living roots can be found in the upper 10 cm of soil (Pietikainen et al., 1999). In summer, the top of the soil is several degrees warmer than deeper soil layers whereas in win­tertime the top of the soil can be frozen for several months while bottom layers may still be active. A pro­cess-based model can take into account the biological temperature response and the size of the storage of the C 02 in the soil profile as well as the effect of air-filled

402

PUMPANEN ET AL.: PROCESS MODEL FOR PREDICTING SOIL C 02 EFFLUX 403

pore space of the soil on the gas transport from the soil to the atmosphere. With a process-based model it is possible to analyze the processes involved in C 02 flux and concentration separately in cases where models can be parameterized with independent measurements.

The number of published soil C 02 efflux models, which are based on C 02 release in decomposition in soil and on molecular diffusion of C 02 into the atmo­sphere, is rather small. Billings et al. (1998) and Johnson et al. (1994) calculated soil-surface C 02 efflux based on soil-profile C 02 concentration and the diffusion of gas through the soil profile. Cook et al. (1998) developed a one-dimensional steady-state model for C 02 diffusion from soil. The model was based on vertical decrease of the source term described by a power function and a constant diffusion coefficient. The surface-flux density of C 02 from the soil was derived from integration of the source term with depth (Cook et al, 1998).

Simunek and Suarez (1993) developed a complex sim­ulation model S0ILC02, which includes one-dimension­al water flow and multiphase transport of C 02 utilizing the Richards’ and the convection-dispersion equations as well as heat flow and a C 02-production model. Pa­rameters foi the model were obtained independently from the literature and field measurements. Solomon and Cerling (1987) developed a numerical model of C 02 transport. The three-layer model, consisting of air, snow, and soil, was based on Fick’s second law of diffusion. The C 02-production rate and the effective-diffusion co­efficients were fitted to the measured C 02 concentration and C 02 efflux.

Fang and Moncrieff (1999) developed a process-based model (PATCIS), which simulated the production and transport of C 02 in soil. In the PATCIS model, C 02 produced by respiration was transported in the soil by gaseous diffusion and liquid-base dispersion as well as gas convection and vertical water movement. The micro­bial respiration was related to the amount and quality of organic matter and the root respiration to the distri­bution of roots in the soil. Temperature and moisture responses of soil respiration were included in the model. Parameters for the model were determined from field data by minimizing the residual sum of squares.

Existing models are comprehensive and they can ef­fectively predict the C 02 efflux. However, the models often contain large number of calibrated parameters, which are difficult to determine with available data. Extensive parameterization is needed when applying these models in different ecosystems. Furthermore, the complexity of the models hampers the understanding of the interaction of the processes and variables included in the model.

The aim of this study was to develop a simple and easily parameterized dynamic model describing the re­sponse of the root and soil respiration rates and C 0 2 diffusion to soil temperature and soil moisture. We tested the model with field data spanning 2 yr with moisture conditions ranging from extreme drought to water saturation. The predicted soil-surface C 02 ef­fluxes and soil-profile C 0 2 concentrations were com­pared with the field measurements. With this model,

we assessed the significance of soil temperature and water content on soil C 02 efflux and soil C 02 concentra­tion and studied the factors affecting the seasonal pat­tern and the distribution of soil respiration within the soil profile.

MATERIALS AND METHODS Model

Basic AssumptionsThe model simulates C 02 concentration of the air in the

soil-pore space and the transport of C 02 within the soil as well as from the soil into the atmosphere. Soil C 02 efflux is the C 02 flow from the humus layer to the atmosphere. In the model, soil is described as a layered structure, which is divided into distinct horizons. Humus layer (O-horizon) is a separate organic layer above mineral soil containing organic matter of different decomposition stages, dead needles and moss on surface and humus close to the surface of the mineral soil. The mineral soil is divided into eluvial (A-), and illuvial (B-) horizons and parent material (C-horizon). All processes and soil properties are described separately for each layer. The schematic picture of the model is presented in Fig. 1. The source of C 02 in each layer is the respiration of microorgan­isms and plant roots. Oxidation of C compounds in biological organisms is controlled by temperature and soil moisture. In the model, the respiration rate of each layer depends exponen­tially on temperature and nonlinearly on soil moisture of the corresponding layer. Based on the measurements by Kahko- nen et al. (2001) at the same site, the temperature response of respiration is assumed to be similar over seasons and years.

The C 02 movement between layers is mediated by diffu­sion, which is dependent on the total porosity of soil layers, soil-water content, layer thickness, and the concentration gra­dient between the layers. The transport of C 02 within the soil by convection, caused by changes in the atmospheric pressure and by the wind turbulence is not included in the model. We assume that the contribution of convection to the transport of C 02 in shallow soils as in the reference material of this study is small (Fang and Moncrieff, 1999). The dissolution and dispersion of CCh in water are not included in the model.

Carbon Dioxide ProductionThe contribution of plant roots and microbes living in the

rhizosphere and bulk soil to total respiration has been widely studied (Anderson, 1973; Singh and Gupta, 1977; Hanson et al., 2000), but still their contribution to soil respiration is poorly understood (Boone et al., 1998.) The estimates of the compo­nents of soil respiration are highly variable the contribution of root and rhizosphere respiration ranging from 10 to 90% (Hanson et al., 2000). According to a recent studies in conifer­ous forests the contribution of root respiration varies between 33 to 62% in summer and 12 to 16% in late autumn (Widen and Majdi, 2001) and between 52 to 56% (Hogberg et al., 2001) and 50 to 73% (Maier and Kress 2000) on annual basis.

In the model, the soil respiration, r (g C 02 m-2 h-1), is presented as an outcome of microbial respiration, rm, and root respiration, rr, and the contributions of the two fractions are assumed to be equal.

■r = rm + r,. [1]

Similar temperature and moisture responses were used for both microbial respiration and root respiration within each

404 SOIL SCI. SOC. AM. J., VOL. 67, MARCH-APRIL 2003

i C-horizon! ccm c c)

Fig. 1. A schematic presentation of the simulation model. The C 0 2 production in each soil layer consists of microbial respiration (rm) and root respiration (rr), which are controlled by temperature (? ) and by soil-water content (0„). Carbon dioxide moves between the layers by diffusion and the C 02 flux (J) depends on the total porosity of soil (£*), the soil-water content and the thickness of the layers (/) as well as the concentration gradient between the layers. The C 02 fluxes are denoted by thick arrows, and thin arrows represent information between parameters and processes. The amount of C 02 in a soil horizon is denoted by C and soil layers are denoted with capital letters O, A, B, and C. In the figure, processes are presented only for O- and A-horizons.

soil horizon. This is justified by studies showing similar temper­ature responses for these components of soil respiration. Usu­ally the temperature response of soil respiration is described with a Q10 coefficient for the exponential function between soil respiration, r, and temperature, 7, (r = aexp (p r) where Q10 = exp (10p). Widen and Majdi (2001) and Buchmann (2000) measured Q10 values ranging from 2.1 to 3.22 for coniferous forest soil. Grogan and Chapin (1999) measured a Qi0 value of 3.3 for the soil respiration from a range of arctic vegetation types. These are rather similar to temperature responses deter­mined for root respiration. According to Conlin and Lieffers (1993), the Q10 for root respiration of coniferous seedlings was about 2.5 to 3.0. Burton et al. (1996) determined Q10 value of 2.7 for Acer saccharum whereas Lawrence and Oechel (1983) reported Q]0 values ranging from 1.46 to 2.65 for broadleaved seedlings in Alaska.

The effects of temperature and moisture on soil respiration are assumed to be multiplicative:

r = K W v ) [2]where r( T) is the dependence of soil respiration on tempera­ture only (g C 02 m-2 h '1) and/(6v) is the dependence of soil respiration on soil-water content. The same kind of multiplica­tive approach has previously been used in several studies (e.g., Schlentner and van Cleve, 1985; Davidson et al., 1998; Fang and Moncrieff, 1999; Moncrieff and Fang, 1999).

Numerous studies have shown the relationship between soil moisture and microbial activity (Greaves and Carter, 1920; Linn and Doran, 1984 and Davidson et al., 1998). Skopp et al. (1990) presented a function taking into account both the effects of drought and anoxic conditions in wet soils approaching the water saturation:

/(9V) = MIN{a62, b(E0 - ev)«, 1} [3]where /(0J represents the C 02 efflux evolved from soil, 0V is the volumetric water content (m3 m-3) and E0 is the total porosity (m3 m-3). Parameters a, b, d, and g are empirical constants that are fixed for a given soil (Skopp et al., 1990).

At low water contents, water availability limits respiration activity in soil. This aerobic microbial activity increases with soil-water content until a point is reached where water starts to restrict the diffusion and availability of oxygen. According to Linn and Doran (1984) many studies involving a wide range of soil types indicate that a soil-water content equivalent to 60% of soil’s water-holding capacity delineates the point to maximum aerobic microbial activity. In the study of Doran et al. (1988), the maximum aerobic microbial respiration oc­curred at volumetric water content equal to 0.55 to 0.61 times the value of total porosity for 16 soils of varying texture.

There are many possible expressions to relate the depen­dence of respiration on temperature. Here we use an exponen­tial function for the temperature response of r(T) an approach used by Boone et al. (1998), Buchmann (2000), Widen and Majdi (2001):

r(T) = a exp((3T)/p [4]where T is the temperature (°C) and a and p are fitted coeffi­cients. The temperature responses of soil respiration, which were measured per mass and collected from individual soil layers, are scaled to 1 m2 surface area using the thickness I (m) and the bulk density, p, (Mg m-3) of the corresponding soil layer.

Carbon Dioxide Transport and Carbon Dioxide Concentration of Soil Layers

The C 02 fluxes in soil are mediated primarily by diffusion, which is usually described by Fick’s law. In the existing models, soil variables are usually continuous throughout the soil profile (Simunek and Suarez, 1993; Suarez and Simunek, 1993; Bill­ings et al., 1998). However, a layered structure is very charac­teristic for podzolic soils. This is why we have treated the soil as a structure consisting of distinctive layers and formulated our flux equations in a discrete formalism. The soil layers are specified and denoted with capital letters referring to the horizons O, A, B, and C. As an example, we have presented here the equations for O- and A-horizons. Other horizons can be obtained by changing the indexes referring to respective layers. The C 02 flux between A- and O-horizon is:

AOCq — Ca

do + U)/2 [5]

PUMPANEN ET AL.: PROCESS MODEL FOR PREDICTING SOIL C 02 EFFLUX 405

where / A0 is the flux from A‘ to 0-h°nzon (g C 02 m-2 s_1), Da0 is the diffusion coefficient of C 02 between O- and A-horizons (m2 s_1), C0, CA, /0, and lA are the C 02 concentra­tion (g C 02 m-3) and thickness (m) of O- and A-horizons, respectively. The diffusion coefficient DA0, is obtained as the weighted average of the layer specific coefficients weighted by the thickness of the soil layers.

The diffusion coefficient of C 02, D, in a soil layer is a fraction of the diffusion coefficient of C 02 in air, D0, (m2 s_1) according to a model developed by Troeh et al. (1982):

where Eg is the air-filled porosity of soil (m3 m-3) and u and h are empirical parameters obtained from the literature (Glinski and Stepniewski, 1985). Eg is obtained by subtracting volumet­ric water content, 0,, from the total porosity, E0:

E% = E0 - 0V [7]The diffusion coefficient of C 02 in soil, D , was calculated

separately for each layer and is denoted with capital letters referring to the horizons.

For the temperature response of D0 we used a non-linear function by Armstrong (1979):

log(D0) = 1.99751og(7) - 9.7273 [8]where 7 is the temperature (K) of the soil layer.

Carbon dioxide was assumed to move between the layers also pushed by water replacing the air in the soil-pore space. The C 02 flux from A- to O-horizon caused by the change in the air filled porosity of A-, B-, and C-horizons, / AOp, is ex­pressed by using time discrete formalism:

{[£*& ) “ M 'm W c + [EgB(ti) - r _ Egp(tj+\)]lv + [EgA(ti) — EgA(ti+i)]lA}CA(ti)

•'AOp —ft+i “ U

[9]where EgC(t,) - EgC(ti+1) is the change in the air-filled porosity of a soil horizon and CA(f,) is the C 02 concentration of the soil horizon (g C 02 m-3) at moment f,.

The amount of C 02 in each soil layer for an area of 1 m2 is obtained using a C 02 mass-balance equation, which is expressed here for A-horizon using time discrete formalism:

V'aCa^+i) = K\Ca(4) + (rA -I- JEA + / BAp~ j AO ~ J A0p)(^/+1 — ti) [1 0 ]

where VA is the volume of the A-horizon (m3 m-2), CA is the C02 concentration in the A-horizon (g C 02 m-3), rA is the soil-respiration rate in the A-horizon (g C 02 m-2 h_1), 7BA, •/fiAp> / AO, and / AOp are C 02 fluxes from the B-horizon to the A-horizon and from the A-horizon to the O-horizon (g C 02 m~2 h~l), respectively (Fig. 1).

Values of Model ParametersValues for parameters can be determined by estimation

from measured fluxes or by measuring the processes involved. If the parameters were estimated from the measured fluxes it would be difficult to evaluate the performance of the model because the predicted values would be dependent on the mea­sured fluxes. Because of this we have avoided the estimation of the values of the parameters from the measured fluxes and

based the values of parameters on process measurements and literature sources whenever possible.

Parameters a, b, d, and g in Eq. [3] were determined by Skopp et al. (1990), for a soil of similar texture as that in this study (fine silty, mixed). With given parameters /(0V) values can be >1, when E0 > 0.50 m3 m-3. Tliis has been taken into account in the model by limiting the maximum /(0„)-value to 1 (Fig. 2). In O-, A-, and B-horizons this results in a wider range for maximum microbial respiration than in the C-horizon. According to Howard and Howard (1993) the optimal mois­ture range for respiration is wider in organic soil than in mineral soil. Vanhala (unpublished data, 1995) measured max­imum soil respiration in humus layer at volumetric water con­tent of 0.35 m3 m-3. In our study, calculated by Eq. [3], the volumetric water content not limiting respiration ranges from 0.36 to 0.50 m3 m-3 in O-horizon (Fig. 2).

Values for parameters a, p, and p for O-horizon in Eq. [4] were obtained from laboratory measured C 02 efflux and soil temperature response curves based on humus samples col­lected from the measurement site in July 1998 (Kahkonen et al., 2001). The respiration rate of the field-moist humus sam­ples was measured in the headspace of 120-mL incubation bottles at four temperature levels ranging from 2 to 17°C using the GC-TC method. An exponential curve of the form rm = a exp (07) where Q10 = exp (10 X p), was fitted on the data. For A-, B-, and C- horizons, parameters a, p, and p were obtained from the studies by Kahkonen et al. (2001), Pieti- kainen et al. (1999), and Ilvesniemi (Ilvesniemi, unpublished data, 1996) for forest soils similar to that of this study.

Values for the total porosity of the soil, £ 0, were obtained from soil water-retention curves determined separately for each soil layer (Mecke and Ilvesniemi, 1999). The soil water- retention curves for each soil horizon were measured from samples collected into steel cylinders of diameter 0.057 m and length of 0.059 m from the walls of five pits excavated at the measurement site. The thickness of the soil layers was measured at the pits and used as parameter / in Eq. [4], [5], and [9]. Values for parameters u and h in Eq. [6] were obtained from Glinski & Stepniewski (1985). Selected parameter values for u and h were determined for loam, which can be considered rather similar to the glacial till at our site concerning the particle-size distribution and the texture. The parameter val­ues are summarized in Table 1.

Model ImplementationThe model was implemented with Java programming lan­

guage using the Java Development Kit (JDK 1.17B, Sun Mi-

Relative water content (0V / E0)Fig. 2. The relation between soil respiration and soil-water content

in O-, A-, B-, and C-horizons. In the model, the maximum value of the moisture factor /(8 ,) is limited to 1.

406 SOIL SCI. SOC. AM. J., VOL. 67, MARCH-APRIL 2003

crosystems Inc., Santa Clara CA). The model simulates soil C 02 concentration and soil C 02 efflux using hourly values for soil temperatures (°C), volumetric soil water contents (m3 m-3), and ambient air C 02 concentration (g C 02 m-3) as input. The calculation proceeds in an order where first the initial values of soil parameters such as the thickness and the total porosity of soil layers and parameter values a, p, p, a, b, d, g, w, and h are given to the model (Fig. 3). Values for the soil volumetric water content, the temperature, and the ambient air C 02 concentration above the soil surface are read from the source file. The flux rates of C 02 between the soil layers (and from the humus to the air) are obtained using Eq. [5] through [9] and new values for the C 02 concentrations are obtained using Eq. [1] through [4] and [10]. Numerical integra­tion (Euler-Cauchy method) with a 6-s time step was used in the calculation (Bossel, 1994).

Field MeasurementsMeasurement Site

All field measurements were performed at SMEAR II (Sta­tion for Measuring Forest Ecosystem-Atmosphere Relations) measuring station in Southern Finland (61° 51'N lat., 24°17'E long., 181 m above sea level). For further details see Ilves- niemi & Pumpanen (1997) and Vesala et al. (1998). The station provided facilities for measuring soil moisture, temperature, soil air C 02 concentration, and soil surface C 02 efflux.

The soil of the measurement site is a basal moraine with an average depth of 0.50 m varying from 0.20 to 1.60 m. Homogeneous bedrock underlies the soil preventing the verti­cal movement of water and air. The parent material of the soil is silty glacial till and the soil is a Haplic podzol which is divided into distinct horizons (FAO-Unesco, 1990). The wa- ter-extractable acidity of the soil horizons ranged from pH 4.4 in the humus to pH 5.3 in the ground soil at 0.20- to 1.60-m depth. The exchangeable acidity was high (126-37 \imo\ g_1 of soil) in the humus and the eluvial layer, and lower (<11 \imo\ g_1) in the deeper layers. The concentration of total soil organic C decreased from 303 mg of C g_1 in the humus layer to 5 mg g_1 of C at 0.20- to 1.60-m depth, and the concentration of N from 13 mg N g-1 to 0.17 mg g_1 at the same respec­tive depths.

The tree stand on the site was sown with Scots pine (Pinus sylvestris L.) after prescribed burning in 1962. The stand has a dominant height of 13 m and 2100 stems per hectare. The dominant species in the field layer vegetation were Vaccinium myrtillus L. and Vaccinium vitis-idaea L. The ground vegetation consisted mainly of mosses Dicranum polysetum Sw., Hylo- comium splendens (Hedw.) B.S.G., and Pleurozium schreberi (Brid.) Mitt., overlying a 0.05-m layer of soil humus. Most of

Table 1. Parameters for respiration and transport functions.

SoUhorizon O A B C

a 7.613 0.430 0.237 0.0800 0.117 0.103 0.103 0.103a 3.83 3.83 3.83 3.83b 4.43 4.43 4.43 4.43g 0.854 0.854 0.854 0.854d 1.25 1.25 1.25 1.25u 0 0 0 0h 1.1 1.4 1.4 1.4P Mg m 3 0.50 1.68 1.47 1.63/ m 0.050 0.054 0.174 0.543E0 m3 m“3 0.70 0.61 0.58 0.50

the tree and herbaceous roots were found in the humus layer and 0.15-m zone in the surface horizons of the mineral soil. The annual mean temperature of the area is +2.9°C; January is the coldest month (mean -8.9°C) and July the warmest (mean +15.3°C). The yearly precipitation averages 709 mm (Climatological statistics in Finland, 1991).

DataInstrumentation for soil temperature and moisture as well

as soil-air C 02 concentration measurements were installed horizontally in each horizon in the vertical face of five pits excavated at the measurement site 2 yr before measurements were taken. All instruments were installed in the undisturbed soil at 0.20- to 0.30-m distance from the face of the pit. The pits were filled with the original soil keeping the soil layers in the original order of excavation.

Soil temperature was measured at 15-min intervals using silicon temperature sensors (Philips KTY81-110, Philips Semi­conductors, Eindhoven, the Netherlands). Soil volumetric wa­ter content was measured at 1-h intervals using the TDR- method with unbalanced steel probes (Tektronix 1502 C cable radar, Tektronix Inc., Redmond, WA) installed close to the temperature sensors. These in turn, where connected to a data logger (21X, Campbell Scientific Ltd., Leics., UK) via multiplexers (SDMX50, Campbell Scientific Ltd., Leics., UK). Temperature and moisture values used are an average of five sensors for each soil layer.

Soil C 02 efflux was measured using a newly developed open dynamic chamber system (Pumpanen et al., 2001), which had two automatic chambers. The C 02 efflux was measured once an hour. The trap-type chambers used in this study were open most of the time, thus exposing the chamber interior to ambi­ent conditions. The chambers were closed for measurements for 70 s. The chambers were transparent, and the green parts of the ground vegetation were removed from inside. An aver­age of two chambers was used to represent the measured efflux. Ambient air C 02 concentration measured in the cham­bers was used as input values in the model calculations.

Soil-air samples were collected with gas collectors, which were made out of punctured hollow nylon bars covered with a Gore-Tex PTFE 0.45-|xm membrane (W.L. Gore & Associates (UK) Ltd., Coating Division, Dundee, Scotland). Samplers were installed horizontally in the vicinity of the temperature sensors and the TDR-probes. Air samples were drawn manu­ally into polyethylene syringes (BD Plastipak 60, BOC Ohmeda, Helsingborg, Sweden) equipped with a three-way valve (BD Connecta Stopcock, Becton Dickinson, NJ). The C 02 concen­tration of the samples was determined within 6 h of the collec­tion by an infrared gas analyzer (URAS 3G, Hartmann & Braun, Frankfurt am Main, Germany). An average of five gas collectors in each soil layer was used to determine soil-air C 02 concentration of the layer.

A period of 19 mo from 1 May 1998 to 30 Nov. 1999 exclud­ing the winter months from December 1998 to April 1999 was chosen to compare the efflux and soil-profile C 02 concentra­tions, which were predicted by the model and measured at the field site. We analyzed the model performance comparing predicted and observed results with linear regression statistics of fit for the slope and intercept of the regression line. Systat 8.0 (SPSS Inc., Chicago, IL) statistical software was used in the analysis.

PUMPANEN ET AL.: PROCESS MODEL FOR PREDICTING SOIL CO, EFFLUX 407

Parameters 4 -

Environmental factors

Calculate transport between layers

Calculate respiration in each layer

Calculate new values for CO2 concentrations

_______ y_______Set new values for C02 concentrations

Time = Time + Time step

NO

Initial C02 concentrations in each soil layer, layer thickness, total porosity, parameters 0; /?, py a, by d, g, u and h

Ambient air CO2 concentration, soil temperature andsoil moisture

Fig. 3. Flow-chart of the program. The initial values of soil parameters are given to the program. Then values of measured ambient air C 02 concentration, soil temperature and soil moisture of each soil layer are imported from the data file. First, the C 02 flux between the layers is calculated. Next the respiration of each soil layer is calculated. Then new values for C 0 2 concentrations in each layer are obtained using calculated respiration and flux values. New ambient air C 02 concentration, temperature, and moisture values are imported from the data file until the end of the file has been reached.

RESULTS AND DISCUSSION SoU Carbon Dioxide Efflux

The model predicted C 02 effluxes and soil-air C 02 concentrations which both simultaneously followed the values measured in the field (Fig. 4). The predicted and the measured effluxes rose in proportion to the tempera­ture of the humus layer and the eluvial layer (Fig. 5a). According to Glinski and Stepniewski (1985) over 90% of soil respiration activity is concentrated in the humus horizon of the soil. Similar results have been presented by Pietikainen et al. (1999) who studied the vertical

distribution of microbes and roots and soil respiration in a northern boreal mixed forest in Hyytiala, Finland. They found the highest respiration rates in the upper­most 10 cm of the soil, which contributed 91 to 92% of the basal respiration of the soil, probably because most of the readily decomposable organic matter and fine roots were concentrated in the surface horizons of the soil.

We studied the importance of soil moisture on pre­dicted C 02 efflux by running the model with and without the moisture function (Eq. [3]). The study period was exceptionally variable in respect of soil water content

408 SOIL SCI. SOC. AM. J., VOL. 67, MARCH-APRIL 2003

TimeFig. 4. Measured and predicted daily average C 02 effluxes from the soil surface over 19 mo at the reference site from May 1998 to November

1999 excluding the winter months from December 1998 to April 1999. The C 02 efflux was measured continuously by two automatically operating chambers, and the efflux presented is an average of the two chambers.

(Fig. 5b) providing the opportunity to test the model response to extreme moisture conditions. When the model was run without the moisture factor, the pre­dicted C 02 effluxes were significantly overestimated (Fig. 6a, Table 2). The addition of the moisture function improved the accuracy of the model prediction (Fig. 6b). However, when applied with moisture function, the

model tended to slightly underestimate high C 02 ef­fluxes and overestimate low effluxes. The underestima­tion of high effluxes was mainly caused by Eq. [3], which was parameterized for mineral soil and is not suitable for organic soil without additional parameterization. In the model, Eq. [3] started to restrict respiration in the O-horizon already at volumetric water content of 0.35

O

25

20

15

fj 10<DE 5<D

-5

ECOE

00o>iLQ.<

00 00 00 00 CD a j 05 o>o> OJ OJ OJ 9 o> OJ o>c 6 ) 6 -O C OJD

” 5 < Oa>

O<D

Li-

Time< 3

—>3

<

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059o0)Q

Fig. 5. (a) Soil temperature (°C) was measured by temperature sensors installed permanently in the O-, A-, B-, and C-horizons. (b) Soil-water content (m3 m 3) was measured by TDR probes installed permanently in corresponding soil horizons and denoted with similar symbols. Values presented in the figure are daily averages of five temperature sensors and TDR probes installed in each soil horizon. When the soil freezes in O-horizon in late November, the TDR does not measure the volumetric water content correctly.

PUMPANEN ET AL.: PROCESS MODEL FOR PREDICTING SOIL COz EFFLUX 409

m3 m"3. The optimal moisture range for organic soil where most of the respiration occurred can be wider (Howard and Howard, 1993). It is also possible, that the root respiration was not as severely affected by the drought as the microbial respiration. According to Widen and Majdi (2001) even soil-water content as low as 0.01 m3 m-3 did not affect fine-root respiration.

Some of the differences between the measured and the predicted C 02 effluxes during the autumn and the spring could probably be explained by seasonal varia­tion in the proportion of root respiration and in the temperature response. In the model, we assumed that root respiration is equal to microbial respiration and the temperature responses are similar throughout the year. This is however, not necessarily true. Boone et al. (1998) and Widen and Majdi (2001) showed higher temperature sensitivity (Qi0) for root and rhizosphere respiration than for total soil respiration. Also the con­tribution of root respiration on total soil respiration varied seasonally. According to Boone et al. (1998) and Widen and Majdi (2001), the percentage of soil C 02 efflux emanating from roots was highest in summer and lowest in winter, which was probably resulted in part from changes in root biomass and production. The tem­perature sensitivity reflects not only the respiration of roots but also respiration by mycorrhizae and the de­composition of labile root-derived organic material (de­tritus and exudates) by microbiota in the rhizosphere (Boone et al., 1998).

According to our model, most of the C 02 was pro­duced in the humus layer throughout the year. However, the relative contribution of the deeper layers to the total respiration was at its highest in late November (Fig. 7). In 1998 the C-horizon was water saturated most of the year resulting in a very low respiration in this layer. In the late summer of 1999 when the soil was dry, the res­piration of the C-horizon exceeded that of the A-hori- zon and was equal to that of the B-horizon. The contri­bution of the deeper horizons to total respiration was higher in 1999 than in 1998 whereas the C 02 produced in the O- and A-horizons was significantly lower in the dry year of 1999.

Soil-Air Carbon Dioxide ConcentrationThere was a vertical gradient in the measured and

predicted C 02 concentrations of the soil air, the concen­trations being highest in the deepest soil horizons (Fig. 8a). The concentrations varied also seasonally. During the growing season, the C 02 concentrations were twice those of late autumn and early spring. The predicted C 02 concentrations followed the same pattern as the measured concentrations. The model slightly overesti­mated low C 02 concentrations in all soil horizons espe­cially in August and September 1999 (Fig. 8a). When the measured and predicted values were plotted on xy plot (Fig. 8b-e) in A- and B-horizons the slopes differed from the 1:1 line. The intercept was not significantly different in any of the horizons (Table 2).

Soil-water content strongly affected the C 02 concen­tration of the soil air. The measured and predicted C 02

Measured efflux (g C02 m‘2 h'1)

Measured efflux (g C02 m'2 h‘1)Fig. 6. The relation between measured and predicted C 02 efflux cal­

culated with the model (a) without moisture factor and (b) with moisture factor. Daily average values are shown in the figure. Simulation without the moisture factor shows a clear over estima­tion of the efflux.

concentrations were within the same range, when the moisture function (Eq. [3]) was applied in the model. When the moisture function was not applied, the pre­dicted C 02 concentration was overestimated in the deeper soil horizons. In 1998, C 02 concentrations up to 21.5 mmol mol-1 in the B-horizon and 164 mmol mol-1 in the C-horizon were predicted if the effect of water was not included. These were from 3 to 16 times higher than what was actually measured and predicted when the moisture factor was applied. Evidently, the micro­bial activity in deeper layers was restricted by the high water content, which limits the supply of oxygen.

Table 2. Results of the T-test of goodness of model fit as presented In Fig. 6a, 6b, 8b, 8c, 8d, and 8e.

410 SOIL SCI. SOC. AM. J., VOL. 67, MARCH-APRIL 2003

CoefficientFigure Period Parameter A M 1:1 line Regression model Std error /-value P (two-tail)

6a May 98-Nov. 99 a not included 0 037 0.01 26.21 <0.0016a May 98-Nov. 99 b not included 1 0.99 0.02 -0.55 <0.16b May 98-Nov. 99 a included 0.28 0.01 -60 <0.0016b May 98-Nov. 99 b included 1 0.72 0.02 -16.4 <0.0018b May 98-Sep. 99 a included 291.27 156.94 1.86 <0.18b May 98-Sep. 99 b included 1 0.83 0.18 -0.98 >0.18c May 98-Sep. 99 a included 43455 176.63 2.46 <0.058c May 98-Sep. 99 b included 1 0.54 0.08 -5.45 <0.0018d May 98-Sep. 99 a included 1127.22 342.41 3.29 <0.018d May 98-Sep. 99 b included 1 0.54 0.08 -5.68 <0.0018e May 98-Sep. 99 a included 2646.47 845.63 3.13 <0.018e May 98-Sep. 99 b included 1 0.86 0.11 -1 3 2 >0.1

t /-value for parameter b is b - fVst> and f-value for parameter a is a - 0/s., where a is the intercept and b is the slope of the regression line. p0 is the slope of l:l-line. In the f-test H0:b = p0 and a = 0.

TimeFig. 7. Simulated respiration in the O-, A-, B-, and C-horizons over 19 mo at the reference site from May 1998 to November 1999 excluding

the winter months from December 1998 to April 1999.

During the dry period between July and September 1999 the average measured and predicted C 02 concen­tration in the C-horizon was only about 50% of that in 1998, even though the modeled C 02 production of the C-horizon was three times higher in 1999 than in 1998. The C 02 diffusion was faster from the dry soil because of increased air-filled pore space, which occurred during the drought. The air-filled pore space is the main factor affecting the diffusion rate. When wrong porosity was used in the model, the predicted soil-air C 02 concentra­tions were unrealistic.

If the effects of soil temperature and moisture on the soil respiration are as simple as presented here, the estimation of the effects of climate change on the soil C 02 efflux would be possible with the already available data on Qi0 and meteorology. However, the soil C 02 efflux is dependent on the total C 02 assimilation, the corresponding litter production, the root exudates and the chemical composition of soil organic C, which have to be taken into account when predicting the soil C balance. Further development is needed to apply this model to various ecosystems. For example, the amount and quality of organic matter in the soil and its seasonal distribution have to be better taken into account in the model to reflect the possible seasonal variation in the

temperature response of the respiration. For long-term simulations of soil C 02 efflux, the input and output of organic matter have to be modeled in more detail. This includes seasonal patterns of photosynthesis, defolia­tion, and root growth.

Nevertheless, our model, applied with independently determined parameters, could produce results compara­ble with the measured values of soil-air C 02 concentra­tion and C 02 efflux. This suggests that, even if the model structure was very simple, the assumptions of the model were reasonable. In its present form, the model provides an effective tool for studying the factors affecting soil C 02 efflux and C 0 2 concentration. A more comprehen­sive tool for studying the C cycle of a forest ecosystem could be created by combining this model with a model describing tree growth and biomass allocation within the forest (Nissinen and Hari, 1998). This kind of model could be used for studying factors affecting the C bal­ance of a forest ecosystem.

ACKNOWLEDGMENTSThis study was supported by the Academy of Finland and

by the Graduate School in Forest Sciences established by the Ministry of Education, by the University of Helsinki and by

PUMPANEN ET AL.: PROCESS MODEL FOR PREDICTING SOIL CO, EFFLUX 411

18000

I 12000o E 3 3 6000 o vi :

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A

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0 500 1000 1500 2000Measured CO2 (//mol mol'1)

10000

o 8000

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0 1000 2000 3000 4000Measured CO2 (//mol mol*1)

2000 4000 6000 8000 10000

Measured CO2 (//mol mol'1) Measured C02 (//mol mol'1)Fig. 8. (a) Measured and predicted daily average values for soil C 02 concentration in the O-, A-, B-, and C-horizons over 19 mo at the reference

site from May 1998 to November 1999 excluding the winter months from December 1998 to April 1999. Measured values for soil C 02 concentration are an average of air samples taken from five permanently installed gas samplers in each horizon. The coefficient of variation of the samples ranged, on average, from 037 in the humus layer to 0.51 in the B-horizon. (b), (c), (d), and (e) measured and predicted daily average C 0 2 concentrations plotted on xy-plot for O-, A-, B-, and C-horizons, respectively.

the University of Joensuu. Valuable comments on a draft of the manuscript were made by Prof. Carl Johan Westman, Dr. Frank Beminger, Dr. Ari Nissinen, and Mr. Martti Peramaki. We thank the three anonymous reviewers whose comments helped us to improve the manuscript significantly. We also thank the staff of Hyytiala Forestry Field station for the facili­ties of the study and Mr. Petri Keronen, Mr. Toivo Pohja, and Mr. Erkki Siivola for their help in construction and mainte­nance of the measurement system.

APPENDIX Abbreviations

a, b empirical constants determined by Skopp et al.(1990) for fine silty soil (dimensionless)

a, p fitted constants of the tem perature response of respiration obtained from field data and Kahkonen et al. (2001) (dimensionless)

412 SOIL SCI. SOC. AM. J., VOL. 67, MARCH-APRIL 2003

Ca, Co C 02 concentration in A- and O-horizons, respec­tively (g C 02 m-3)

D diffusion coefficient of C 02 in soil matrix (m2 s-1) D0 diffusion coefficient of C 02 in air (m2 s"1) d empirical constant determined by Skopp et al. (1990)

for fine silty soil (dimensionless)E0 soil total porosity (m3 m-3)£ g soil-air filled porosity (m3 m-3)/(0V) coefficient representing the dependence of respira­

tion on soil volumetric water content (dimensionless) g empirical constant determined by Skopp et al. (1990)

for fine silty soil (dimensionless) h empirical constant obtained from Glinski and Step­

niewski (1985) (dimensionless)/ Ao C 02 flux between A- and O-horizons caused by

diffusion (g C 02 m-2 s-1)/ AOp C 02 flux between A- and O-horizons caused by

change in the air-filled porosity (g C 02 m-2 h-1)JBA C 02 flux between B- and A-horizons caused by

diffusion (g C 02 m~2 s_1)•̂ bap C 02 flux between B- and A-horizons caused by

change in the air-filled porosity (g C 02 m-2 h-1)/ thickness of soil layer (m) r soil-respiration rate (g C 02 m-2 h_1) rm microbial-respiration rate (g C 02 m-2 h-1) rt root-respiration rate (g C 02 m-2 h_1) r(T) soil-respiration rate calculated with temperature

only (g C 02 m-2 h_1)T temperature (°C) ti time (h)u empirical constant obtained from Glinski and Step­

niewski (1985) (dimensionless)V volume of a soil horizon (m3 m-2)0V soil volumetric water content (m3 m“3) p bulk density of soil layer (Mg m~3)

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