The dependence of soil CO
2
ef¯ux on temperature
C. Fang*, J.B. Moncrieff
Institute of Ecology and Resource Management, University of Edinburgh, Darwin Building, May®eld Road, Edinburgh EH9 3JU, UK
Received 7 July 1999; received in revised form 10 April 2000; accepted 14 June 2000
Abstract
Assessing the global C budget requires a better understanding of the effect of temperature on soil CO2ef¯ux both from experiments and
developments in theory. Intact soil cores (ca. 31 cm in diameter and 45 cm in depth) were collected from a farmland and a sitka spruce site near Edinburgh, Scotland, and incubated in a growth chamber with varying temperature and soil moisture contents. There was no in¯uence of incubation time on the measured soil respiration rate found in this study and this is different from previous studies that commonly use a re-constructed soil sample. Both soils showed an exponential increase in respiration rate with temperature. No optimal temperature for soil respiration was found with soil temperature up to 328C. The in¯uence of soil moisture content, varying between 20 and 50 vol%, on soil respiration and its response to temperature was not obvious. Most equations describing the relationship between soil respiration and temperature ®tted the observed data well. However, based on model andQ10analysis, the Arrhenius model may be better than the others
in its performance and theoretical basis, despite a tendency to underestimate somewhat the response of soil respiration at low temperature. A simple empirical equation,Rsa T2Tminb;is presented, which is more responsive at low temperature than the Arrhenius and exponential
models.q2001 Elsevier Science Ltd. All rights reserved.
Keywords: Soil respiration; CO2ef¯ux; Temperature response;Q10value; Modelling
1. Introduction
Worldwide concern with global change and its effects on our future environment requires a better understanding and quanti®cation of the processes contributing to global change. Studies on the role of soil processes and a much better understanding of the rate functions, stability and resi-lience of soil processes are needed to quantify the large-scale surface ¯uxes of water, heat and greenhouse gases and also to determine the effects of land use and land cover changes (IACGEC, 1996). One of the key questions to be addressed is the future dynamics of the large amount of C that is currently stored in soil organic matter. The ef¯ux of soil carbon is highly sensitive to changes in surface temperature and relatively small changes in surface temperature may have a major in¯uence on the magnitude of soil ef¯ux. The potential increase in CO2release from the
soil caused by future elevated temperature may have a posi-tive feedback effect on the atmospheric CO2 and global
change (Kirschbaum, 1995).
Accurate prediction of climate effects on C cycles
depends on a clear understanding of the effect of tempera-ture on the microbially mediated release of CO2from soil
organic matter (MacDonald et al., 1995). The effects of temperature on soil respiration are commonly observed using laboratory incubation as the respiration rate under ®eld conditions is confounded by many factors. However, a common problem of incubations with a restructured soil sample is that respiration rate is high at ®rst due to the disturbance by sample preparation and then gradually declines to a low level (Winkler et al., 1996). Even after the initial ¯ush, CO2ef¯ux may be several times higher than
that observed at the end of the incubation under constant conditions (Liebig et al., 1995; Torbert et al., 1995). The observed response of soil respiration to temperature included the in¯uence of incubation time using this commonly used incubation method. This leads to a biased response of soil respiration at different incubation times and may also result in an underestimation of the temperature sensitivity of soil respiration at high temperature as the in¯uence of time course is likely to be more signi®cant at warmer temperature. However, such a time course of soil respiration rate was not observed in our previous incubation of an intact soil (Fang and Moncrieff, 1998, soil sample size ca. 40£40£50 cm3). A similar result was reported by Thomson et al. (1997) for a larger soil monolith,
Soil Biology & Biochemistry 33 (2001) 155±165
0038-0717/01/$ - see front matterq2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 8 - 0 7 1 7 ( 0 0 ) 0 0 1 2 5 - 5
www.elsevier.com/locate/soilbio
* Corresponding author. Tel.: 144-131-650-7731; fax: 1 44-131-662-0478.
100£100£100 cm3. Such an intact soil incubation techni-que may minimise the error in observed temperature sensi-tivity of soil respiration.
The responses of soil respiration and other mineralisation processes in the soil to temperature are commonly described using exponential and Arrhenius equations. Both equations describe an exponential increase in respiration with increas-ing temperature but with a different theoretical basis (Ellert and Bettany, 1992). However, uncertainties remain in understanding and describing the relationships. Different types of model have been used: exponential or Arrhenius equations (Lloyd and Taylor, 1994; MacDonald et al., 1995; Thierron and Laudelout, 1996); linear models (Rochette et al., 1991); quadratic models (Holthausen and Caldwell, 1980); logistic models (Schlentner and Van Cleve, 1985; Jenkinson, 1990); and the model using a temperature time equivalence (Feng and Li, 1997). Although these models have been reported to be successful in ®tting data obtained by an individual experimenter under some speci®c circum-stances, they suggest different explanations for the response of soil respiration to temperature. The Q10 value, which
de®nes the temperature dependence or sensitivity to temperature variation of soil respiration, when derived from different models is different, whether by magnitude or with respect to temperature. A ®rst-order exponential model (kaebT; where k is the rate constant and T the temperature) is most commonly used and the Q10value is
conceptually constant with temperature for this model. In other models,Q10is a variable with temperature in different
ways (Howard and Howard, 1993; Lloyd and Taylor, 1994; Winkler et al., 1996), with aQ10value from about 8 at 08C to
about 2 at 308C (Kirschbaum, 1995), and from about 12.8 at 0.38C to 2.2 at 258C (Lomander et al., 1998b). There is no doubt that simulating soil respiration without a good under-standing of the variation in temperature sensitivity of soil respiration will limit a model's utility.
An exponential increase in soil respiration with respect to temperature is commonly accepted and was observed for biological systems over a limited range of temperatures (O'Connel, 1990; Thierron and Laudelout, 1996; Winkler et al., 1996). At high temperature, the sensitivity of soil respiration to temperature may be reduced. Enzymes may be deactivated or killed by a further high temperature. Such an optimal temperature for soil respiration was observed mostly in incubation experiments with a re-constructed and small volume soil sample. It is not yet clear whether an optimal temperature is common for intact soil in the laboratory or under ®eld conditions in the normal tempera-ture regime in which the soil has developed. The response of soil processes to high temperature and how to quantify this are surely important in environments subject to global warming.
The objectives of this study were: (1) to observe the response of soil respiration to the variation in temperature under laboratory conditions with an intact soil incubation technique; (2) to examine the hypothesis that an optimal
temperature for soil respiration possibly exists in the normal range of temperature in which the soil developed, to observe and analyse the response of soil respiration to an abnormally high temperature; and (3) to test the abilities of describing the temperature dependence of soil respiration of different models and their limitations.
2. Materials and methods
2.1. Soil sampling
Undisturbed intact soil samples, of dimension about 31 cm in diameter and 45 cm in depth, were sampled in early August 1998, from Langhill Farmland of the Univer-sity of Edinburgh and a mature sitka spruce plantation in Bush, about 10 km south of Edinburgh, Scotland. The farm-land was covered by dense grasses (5±10 cm tall) and the forest ¯oor was covered with some sparse understory plants when soils were sampled. The soil is an imperfectly drained brown earth (Scottish system) in Langhill and is a sandy brown forest soil with a litter layer of about 5 cm at the sitka spruce site. Relatively uniform sampling areas in both sites were chosen to minimise the in¯uence of spatial variation in soil properties on soil CO2 ef¯ux and all soil
samples were taken as close to each other as possible. Metal frame cylinders, of the same inner dimension as the soil core, were used for soil sampling. The frame cylinder was made of 1 mm steel plate in order to get suf®cient strength for holding soil cores and to have a rapid heat transport between the soil cores and the ambient atmosphere during incubation and laboratory ef¯ux measurements. To obtain the soil cores, the cylinder was forced a few centimetres into the soil and the soil around it was removed carefully. The cylinder was then pressed further into the soil. This process was repeated until the lower end of the cylinder was at a depth of about 45 cm and the soil core was cut along the lower end of the cylinder. Soil cores were then put into metal containers, 40 cm in diameter and 6 cm deep, to be incubated in a growth chamber. During the sampling, care was taken not to disturb the plants on the surface of the sampled soil. Six and four samples were taken from the farmland and the sitka spruce site, respectively.
2.2. Soil incubation
whether the response of soil respiration to increasing temperature is different to that when temperatures decrease. Three moisture treatments were applied to the samples from the farmland: (1) wet soil, when the bottom of the samples was immersed in water about 6 cm deep and sprayed with water on the top surface daily; (2) medium wet, immersed in water 1 cm deep and sprayed with water on the top once every 2 days; and (3)relatively dry, no water underneath the soil core, only sprayed with some water to the top during the weekend. The actual volumetric moisture content varied by 40±50%, around 30 and 20% for these treatments, respectively. For forest soil, only treatments (1) and (3) applied.
2.3. CO2ef¯ux measurement
Two weeks were allowed before ef¯ux measurements were started in order for soil cores to recover from any sampling disturbance. For measuring CO2ef¯ux, a plastic
chamber collar (5 cm high and 13.3 cm in ID) was pressed into the soil to a depth of about 3 cm at the centre of the surface of each soil core. The green parts of grasses within the collar, as well as any new grasses growing out during the incubation, were cut off. After reaching a steady tempera-ture, the CO2ef¯ux was measured from all soil cores using a
fast-response open-top dynamic chamber, described in Fang and Moncrieff (1998). Four rounds of ef¯ux measurements were made at each temperature set within about 5 h. In each round, CO2ef¯uxes from each soil core were measured, in
turn, with a LI-COR 6262 under the following conditions: 4 l min21of air through the chamber, 3 min before starting logging was allowed for the chamber to achieve an equili-brium ef¯ux, logged at 1 Hz and averaged over 3 min. After ®nishing all four rounds of sampling, the incubation temperature was then changed (increased or decreased) by the pre-set step.
The soil temperature was continuously monitored using thermocouples at three different positions in each soil core C. Fang, J.B. Moncrieff / Soil Biology & Biochemistry 33 (2001) 155±165 157
Fig. 1. (a) Temperature variation in the soil core at depths of 5 and 30 cm. Arrows indicate the time when the room temperature was changed. (b) Variations in CO2ef¯ux with consequently ascending and descending temperature: Ð ascending temperature and - - - descending temperature in period 1; ´ ´ ´ ascending
temperature and - ´ ´ - descending temperature in period 3. (c) Variation in CO2ef¯ux when temperature was alternately increased and decreased:Xincreasing
(at 5 cm depth, there was one sensor at the centre and another at 5 cm from the wall of cylinder; at 30 cm depth, there was only one in the centre) in order to check whether equilibrium of soil temperature was achieved after changing the incubation temperature and to calculate the average temperature of each soil core at a speci®c incubation temperature.
Soil moisture content was monitored using the TDR method. Water content re¯ectometers (model CS615, Campbell Scienti®c Instrument Co.) were inserted into each soil core to 30 cm depth to determine the average moisture content in the soil layer.
3. Results
3.1. Factors in¯uencing incubation
There are three points which need to be addressed when considering an incubation experiment with an intact soil core: (1) Does the temperature within the soil core respond evenly and consistently to the change in incubation temperature? (2) Is there a time in¯uence on the measured CO2ef¯ux during the incubation? (3) Is the response of soil
respiration to increasing temperature different from that when temperature is decreased?
Fig. 1a shows the time course of temperature at different depths in the soil core after the incubation temperature was
changed. No obvious difference was found between these temperatures, neither in magnitude nor trend. The soil core achieved thermal equilibrium within 30 h after the incuba-tion temperature was changed. However, after 18 h of the temperature change, the variation in soil temperature at different points was within 0.28C in the next 6 h.
The in¯uence of incubation time on measured CO2ef¯ux
was not found in either farmland or forest soils during the 120-day incubation (Fig. 1b, only samples 5 and 10 are shown, others are similar). The variations in CO2 ef¯ux
were similar for different incubation times. Compared with the ef¯ux observed in period 2 when temperature was increased and decreased alternately (Fig. 1c), continu-ously increasing or decreasing the temperature seems not to affect the response of soil respiration to temperature. The variation in soil respiration rate (when temperature varied from the maximum to minimum) was almost the same as that when temperature was increasing.
The in¯uence of soil moisture content, whether on the density of CO2ef¯ux or on the temperature dependency of
soil respiration, was not signi®cant among the three moist-ure treatments in our study (Fig. 2).
3.2. CO2ef¯ux
Both soils show an exponential increase in respiration rate with respect to temperature (Fig. 3, scatter plots), with a minimum ef¯ux of 0.035 and 0.057 mg CO2m22s21 for forest soil and farmland soil at about
108C, respectively. The ef¯ux from forest soil was more responsive to temperature, although with a considerable scatter among different samples.
No optimal temperature for soil respiration was found with soil temperature up to 328C (when room temperature was about 408C). There was no suggestion, as shown by Fig. 3 and a good ®t with various models (Table 1), that the increased rate of soil respiration with temperature would slow down at such a high temperature.
3.3. The relationship between soil respiration and temperature
Table 1 lists ®tted relationships between soil respiration and temperature from different types of equations.
Linear and power equations are simply empirical expres-sions of an increase in soil respiration with increasing temperature without any theoretical basis. The linear equa-tion gave a relatively poor ®t for forest soil, based on the coef®cient of determination of regression R20:763;but had a reasonable ®t for farmland soil where respiration rate increased more slowly R20:848:Two kinds of power functions provided a better estimation.
The quadratic model produces a better ®t for farmland soil R20:886 than with the forest soil R20:803; similar to that of the linear equation, because forest soil is more responsive to temperature. Residual analysis (not shown here) suggested that both linear and quadratic models C. Fang, J.B. Moncrieff / Soil Biology & Biochemistry 33 (2001) 155±165
might underestimate the respiration rate at high temperature. There is only one parameter in the quad-ratic model, and this limits its ¯exibility. The Kucera and Kirkham (1971) model with an extra parameter of varying power provided more ¯exibility to such a model, which has a better ®t than the quadratic model for forest soil R20:862: There is not much differ-ence among the ®ts of the Kucera and Kirkham model and other more sophisticated models.
Equations based on exponential, Arrhenius and logis-tical functions provided good ®ts with the measured data. Residual analysis did not show a systematic varia-tion in differences between simulated and measured data, although the residual is more variable in forest soil than in farmland soil.
Fig. 3 shows the ®tted curves for the original Arrhenius equation and the residual between simulated and measured data (curves ®tted with other models are not shown because they are very similar). The ®t gives an activation energy of 83.6 and 61.4 kJ mol21 for forest and farmland soil, respectively.
Taking into account a possible biased simulation with the Arrhenius equation, Lloyd and Taylor (1994) suggested an
Arrhenius type equation:
Rsae2E0= T2T0 1
whereRsis the soil respiration rate;Tis the temperature and
T0is a temperature parameter, both having units of K;ais a
parameter; E0, also in K, is a parameter but no longer the
activation energy of the Arrhenius equation. The equation was thought to give a better, unbiased estimation of soil respiration with varying temperature.
Fitted with our data, by forcingT0to be2170.9 for
farm-land and 2134.5 K for forest soil to get the best ®t, the Lloyd and Taylor equation produced a very similar simula-tion to that of the Arrhenius model (®tted curves are not shown because of the overlap with that of the Arrhenius equation), and its performance at low temperature was close to that of the Arrhenius model. The extra parameter ofT0did not provide a signi®cantly better ®t than the
Arrhe-nius equation.
Schlentner and Van Cleve (1985) introduced an equation to describe the relationship of soil respiration with temperature.
C. Fang, J.B. Moncrieff / Soil Biology & Biochemistry 33 (2001) 155±165 159
Rs
1
a1b2 T210=10 1c 2
where T is the temperature in 8C; a, b, c are model parameters to be determined. This equation is a kind of logistic function giving an `S' type response in soil respiration to temperature, with a minimum Rs at c
when temperature is low and a maximum at 1=a1c when temperature is high. A similar model but without parameter c was used by Jenkinson (1990). Both models are suitable for ®tting with normalised CO2 ef¯ux data
(normalised against the ef¯ux at temperature T0). For
®tting with un-normalised data, an additional parameter d is required (Table 1). Although both equations provided a good ®t with our data, as indicated by the coef®cient of determination (R20:904 and 0.866 from Eq. (2) and R20:902 and 0.858 from Jenkinson's for farmland and forest soil, respectively), their improve-ment over exponential models is not signi®cant (Table 1). Fitted parameter a in Jenkinson's model is not statistically signi®cant for both farmland and forest soil, suggesting that regressions may be overwhelmingly dependent on the term of b2 T210=10 and the model may not be signi®cantly different from the exponential equation when ®tted with our data. The application of both models is strictly limited within the temperature
range in which the models were ®tted because of the discontinuity of models, caused by a negative parametera.
A second-order exponential equation also ®tted our data well over the whole temperature range. Such an equation was introduced by O'Connel (1990) to de®ne the relation-ship of soil respiration with temperature when there is an optimal temperature for respiration
Rsea1bT 120:5T=Topt 3
whereaandbare parameters;Toptis the optimal temperature
for soil respiration to be determined. Eq. (3) can be written as a general form of a second-order exponential equation RaebT1cT2:Fitted with the data here, a negative but not statistically signi®cantToptwas produced (Table 1). A
nega-tive optimal temperature for soil respiration is unlikely to be correct. Compared with the common ®rst-order exponential equation, there is no obvious improvement given by this second-order equation.
Taking into account that exponential, Arrhenius and logis-tic models may not be sensitive enough to the increase in soil respiration rate with an increasing temperature when the temperature is low, a simple empirical model which combines the models of Kucera and Kirkham (1971),Y a T110b, and Lomander et al. (1998b), Y b T2Tmin2;
C. Fang, J.B. Moncrieff / Soil Biology & Biochemistry 33 (2001) 155±165
Table 1
Fitted relationships between soil respiration and temperature. Equations were ®tted by nonlinear regression of SPSS. The Marquardt±Levenberg algorithm was used to determine the parameters that minimise the sum of squares of differences between the dependent variable values in the equation models and the observed values. The number of observed ef¯uxes were 240 for farmland soil and 160 for forest soil
*signi®cant at 95% con®dence byT-test; **not signi®cant; ***forced to the value to get a best ®t. AllFvalues are signi®cant at 99.9% probability. A coef®cientdis added to the original equation for Jenkinson, and Schlentner and Van Cleve equations
Equation Fitted parameters R2 Fvalue
Linear:Ya1bT Farm soil:a20:143*;b0:0164* 0.848 1331
Jenkinson (1990):Y d
a1b2 T210=10 a20:02688**;b2:147*;d0:0740* 0.902 2181 a20:05487**;b2:37*;d0:03705* 0.858 949 Schlentner and Van Cleve (1985):Y
can be introduced as:
Rsa T2Tminb 4
wherea,b,Tminare parameters;Tmincan be taken as a
tempera-ture when soil respiration totally stops. Eq. (4) is more ¯exible to ®t different data sets than the Kucera and Kirkham model because of the parameterTmin. It is more responsive than the
exponential, Arrhenius and logistic models at low tempera-ture, but less responsive than exponential and Arrhenius models at high temperature. If we think that the activation energy in the Arrhenius model has to be changed inversely with temperature to give an unbiased estimate of the respira-tion rate, Eq. (4) may be one of the alternatives.
Although the ®tted curves (R20:901 and 0.862 for farmland and forest soil, respectively) do not provide a better ®t over the whole range of temperature than the Arrhenius and other equations, they do have a faster response at low temperature (Fig. 4).
3.4. Q10value
The temperature dependence of soil respiration, commonly referred to as theQ10value, has been the focus
of many studies. The value ofQ10is the factor by which the
respiration rate differs for a temperature interval of 108C, and is de®ned as:
Q10 RT110
RT
5
where RT and RT110 are respiration rates at temperatures
of T and T110, respectively(Winkler et al., 1996). For the ®rst-order exponential equation, which assumes Q10
is a constant over the temperature, the Q10value can be
calculated as:
Q10 R2=R110= T22T1 6
where R2 and R1 are respiration rates observed at
C. Fang, J.B. Moncrieff / Soil Biology & Biochemistry 33 (2001) 155±165 161
Fig. 4. The natural logarithm of CO2ef¯ux from farmland (a) and forest soil (b) against the reciprocal of absolute temperature: Ð simulated with Arrhenius
temperatures T2 and T1, respectively. The calculation of
Q10 is different with other models and a relationship has
to be ®tted ®rstly with the model used.
In Fig. 5, the scattered points are Q10values calculated
using Eq. (6) with observed data at temperature intervals of .28C. Any unlikely large (.14) or small (#1) Q10values
have been discarded from Fig. 5. The Q10 values showed
scatter for both soils but high values ofQ10at low
tempera-ture are visible. The Q10 values for different models are
obtained with simulatedRTandRT110with the model to be
tested (Table 2).
Despite the fact that most equations ®tted the observed data well and provided similar estimates of soil respiration at different temperatures, derived Q10
values from these equations change in rather different ways. The linear equation gives a large Q10 at low
temperature and then Q10 decreases quickly with
temperature. The quadratic equation provides a univer-salQ10variation to any data set, i.e. the response of soil
respiration to temperature is the same in every ecosys-tem. The ®rst-order exponential equation produces a ®xed Q10 value at different temperature for soil
respira-tion in a speci®c ecosystem. O'Connel's and Jenkin-son's equations have Q10 values rising with increasing
temperature, which was contrary to the commonly accepted view that Q10 decreases with increasing
temperature. In the Jenkinson model, the Q10 value is
dependent on both parametersa and b. The reliability of Q10 derived from the model is in doubt because ®tted
parameter a were not signi®cant. For the Schlentner and C. Fang, J.B. Moncrieff / Soil Biology & Biochemistry 33 (2001) 155±165
Fig. 5. Comparison ofQ10values among different models: (a) farmland soil; (b) forest soil. Ð quadratic, ´ ´ ´ Eq. (4), - - - O'Connel, - ´ ´ - Arrhenius, Ð Ð Schlentner and Van Cleve.
Table 2
Q10values derived from different ®tted relationships with Eq. (5).Q10value at 108C for forest soil with linear equation is not available because of a negative ef¯ux was estimated with the ®tted relationship
Equation Q10at 108C Q10at 308C
Farmland Forest Farmland Forest
Linear 8.8 NA 1.5 1.5
Quadratic 4.0 4.0 1.8 1.8
Kucera and Kirkham 3.1 4.9 1.9 2.4
Eq. (4) 2.8 4.7 2.0 2.5
First-order exponential 2.3 3.1 2.3 3.1
O'Connel 2.2 2.6 2.4 3.7
Arrhenius 2.4 3.4 2.2 2.9
Lloyd and Taylor 2.4 3.3 2.2 2.9
Jenkinson 2.2 2.6 2.6 5.8
Van Cleve model, Q10 decreases with temperature when
temperature is low but increases with temperature at high temperature.
For the Arrhenius and Lloyd and Taylor models, theQ10
values are very close and slowly decrease with temperature. Compared with Eq. (4) and the Kucera and Kirkham equa-tion, the Arrhenius and Lloyd and Taylor models have smal-lerQ10at low temperature but larger at high temperature.
4. Discussion
4.1. The effect of incubation on soil respiration rate
The in¯uence of incubation time on soil respiration rate was not observed in this study with medium size intact soil samples. For an incubation of a small re-constructed soil sample, the consistent decrease in respiration rate after an initial ¯ush is interesting and is yet to be explored. Two things may cause the decline in respiration rate: (1) roots are removed from the soil sample in most small sample incubation studies, which may deactivate microbes during the incubation; (2) soil organic matter may be eventually exhausted by microbial decomposition which therefore causes a decrease in respiration rate, although the organic matter content was reported to be considerably stable after some incubation time by some researchers (Winkler et al., 1996; Grisi et al., 1998). Recently, Lomander et al. (1998a) reported a consistent decline in soil respiration rate in a small sample incubation even with roots added to the soil samples. The role of roots in soil respiration is complicated and remains unresolved. During most of our 120-day incu-bation, most of the initial grasses in the area outside the chamber collar were alive and died only near the end of incubation. New grass within the chamber collars kept growing during the incubation. Plant roots were always active during the experiment, although their activity was inevitably hindered by ongoing incubation. Considering the difference between a small sample incubation and intact soil incubation or under ®eld conditions, an active root respiration and interaction between roots and microbes may be crucial for the consistency of the soil respiration rate with time. Kelting et al. (1998) observed that the presence of active roots would signi®cantly change the response of soil respiration to temperature under ®eld condi-tions.
Little is known about the in¯uence of changing tempera-ture by different ways during incubation (continuously increasing/decreasing, or increasing and decreasing temperature alternately). It was shown in this study that the procedure of temperature changing did not signi®cantly affect soil respiration rate. Recently, Chapman and Thurlow (1998) obtained a similar result in their peat incubation experiment, except samples from two locations where respiration rate for increasing temperature was consistently lower than that for decreasing temperature. However, the
consistently lower respiration rate for their incubation may have resulted, or partly resulted, from a possible in¯uence of incubation time, because the temperature was ®rstly decreased from high to low and then back.
4.2. The effect of moisture content on soil respiration
The soil moisture content may affect the magnitude of soil respiration as well as its response to temperature due to the interaction between moisture and temperature. Parker et al. (1983) reported that the activation energy for soil respiration decreased from 84.9 to 39.5 kJ mol21 when a desert soil was wetted. Howard and Howard (1993) also reported systematic differences of the Q10 value among
treatments of different moisture content. Such an in¯uence, whether on the density of CO2ef¯ux or on the temperature
dependency of soil respiration, was not signi®cant among the three moisture treatments in our study. The in¯uence of moisture content on soil CO2¯ux is complicated through its
effect on respiratory activity of roots and microbes and on gas transport through the soil (Fang and Moncrieff, 1999). The inhibition of soil moisture content on CO2 ef¯ux is
signi®cant only at its lower end (dry soil) or high end (wet soil). Between dry and wet soil, moisture content has no obvious effect on respiration rate. Our result matches previously accepted theory and other studies (Tesarova and Gloser, 1976; Schlentner and Van Cleve, 1985; SÏimu-nek and Suarez, 1993; Goto et al., 1994).
4.3. The optimal temperature of soil respiration
Most reported optimal temperatures for soil respiration were under laboratory conditions with an incubation of re-constructed soil samples, with the only one exception reported by Parker et al. (1983). Parker et al. used a static chamber of alkaline absorption to measure soil CO2ef¯ux
under ®eld conditions and observed an optimal temperature near 418C for soil respiration in a desert soil in New Mexico. It is dif®cult to try to explain the occurrence of an optimal temperature in this case. One possible reason may be that it is an adaptation of microbes and plants in the desert habitat to decrease respiration rate at high temperature to protect themselves from exhaustion. Such a mechanism may not happen in less worse environments. Another possible reason for this observed optimal temperature is the method used in measuring CO2ef¯ux. The ef®ciency of liquid alkaline to
absorb CO2will signi®cantly decrease at high temperature
(Edwards and Sollins, 1973), which may lead to an under-estimation of CO2ef¯ux at high temperature.
of litter during laboratory incubation and increasing temperature further will cause a reduction in microbial respiration. A lower optimal temperature, around 208C, was reported by Thierron and Laudelout (1996). A similar optimal temperature was found for the soil nitri®cation rate between 20 and 258C in laboratory studies but not for soil respiration, although the increase in respiration rate slowed down when the temperature was high (Grundmann et al., 1995). The maximum hourly temperature during summer in the Edinburgh area is about 23±248C. According to the results of this study, an optimal temperature for soil respira-tion in this region is unlikely to happen, even under global warming, for ®eld soils if other environmental factors favour soil biological processes.
4.4. Soil respiration models
All models ®tted well with our data, except the linear model when ®tted for forest soil. It is dif®cult to say which model is the best one because of the close coef®cients of determination. A good ®t of a model against the experi-mental data does not necessarily suggest the actual mechan-ism presumed by the model.
Although the Arrhenius equation has a basis in thermo-dynamics, it may somewhat oversimplify the mechanism of soil respiration to temperature (Ellert and Bettany, 1992). This equation uses the reciprocal of absolute temperature to predict the variation in respiration rate, which suggests that the equation may not be sensitive enough to the variation in soil respiration when temperature is low. Lloyd and Taylor (1994) pointed out that a larger value of activation energy under lower temperature for the equation would give an unbiased simulation. Fitted with our data, the bias is not signi®cant (Fig. 3), but there seems to be an underestimation in the response of soil respiration at low temperature for farmland soil (Fig. 4).
Despite of a third parameter (T0), the Lloyd and Taylor
equation does not differ much from the original Arrhenius equation. If we rewrite the Arrhenius equation as Rs
ae 2E=R T20(R is the universal gas constant andEthe acti-vation energy), it is clear that the Arrhenius equation uses 0 K as a reference temperature, but the Lloyd and Taylor equation usesT0. Because of the extra parameter, the Lloyd
and Taylor equation is more ¯exible. If there does exist a bias in the original Arrhenius model, as Lloyd and Taylor (1994) reported, about the relationship between respiration rate and temperature, the Lloyd and Taylor model may give a better ®t by moving the curve to ®t experimental data. The disadvantage of the Lloyd and Taylor equation is in losing the theoretical basis of the original Arrhenius equation. Fitted with our data, the Lloyd and Taylor model produced a close result to the Arrhenius equation, although T0
(2170.9 and2134.5 K for farmland and forest soil, respec-tively) is quite different from 0 K. Because of the case dependency of parameterT0, more case studies are needed
to compare and discuss the difference, especially in model
sensitivity at low temperature, between the Arrhenius and Lloyd and Taylor equations.
Lloyd and Taylor (1994) claimed that their model could provide an unbiased ®t with data collected from the litera-ture. However, it is dif®cult to understand the methodology they used in normalising the data sets that were originally observed in various ecosystems. They assumed that soil respiration from the 15 sources have different rate constants at 108C but with the same temperature dependence (e.g. the same activation energy or Q10value). This assumption is
unlikely to be correct. For any equation to be tested, each data set obtained from a speci®c circumstance has to be treated individually using the same equation but with differ-ent temperature dependence and parameters. The relation-ship between soil respiration rate and temperature was inevitably distorted by the method they used. It is worth pointing out that the Lloyd and Taylor equation does not change activation energy inversely with temperature as sometimes reported (LeiroÂs et al., 1999).
For Eq. (4), ®tted Tmin (226.58C for farmland and
213.48C for forest soil) is a feature of soil respiration response to temperature but cannot be taken as an actual minimal temperature in the soil because its value was derived from the variation in respiration rate over the normal temperature regime. Under an abnormally low temperature, soil respiration may be controlled by other mechanisms that are not clear yet. Further studies are neces-sary to test the ®tness of Eq. (4) with data from different sources over a wide range of temperature.
4.5. Q10value
Comparing theQ10values determined by different studies
is dif®cult. SomeQ10values were calculated using observed
data with Eq. (6) (Howard and Howard, 1993; Kirschbaum, 1995). Others were derived from different ®tted relation-ships, i.e. they were simulated (MacDonald et al., 1995; Winkler et al., 1996; Lomander et al., 1998b). Different Q10 values may be obtained for different models with a
same data set.
Comparing the ®tness and the Q10 value for different
models, it is obvious that a good ®t between a model and experimental data does not ensure a suitable Q10 will be
estimated with the model. Apart from a conceptual inade-quacy for some equations, such as quadratic and second-order exponential equations, a possible reason for an inade-quate Q10 value with some models is that the regression
analysis is not always sensitive enough, especially at low temperature when the respiration rate is low, to re¯ect the actual response of soil respiration to temperature. If we assume that soil respiration has a higher Q10value at low
temperature than at high temperature and that Q10 varies
with different soil ecosystems, quadratic and ®rst-order exponential models have a disadvantage because of their ®xed Q10. The O'Connel, Jenkinson, and Schlentner and
Q10for these models are case dependent and an
unreason-ableQ10may be derived. A Q10analysis may be a useful
approach for choosing a suitable model in simulating the variation of soil respiration with temperature.
5. Conclusions
According to our experiment, the incubation of a medium size intact soil will overcome the in¯uence of incubation time on measured soil respiration rate. An optimal temperature for soil respiration under ®eld conditions is unlikely to happen in middle latitude area and a general conclusion regarding the existence of a possible optimal temperature for different ecosystems requires further study. Choosing an equation simply by a regression method will not ensure model suitabil-ity, especially when the model will be extrapolated outside the temperature range to which the model was ®tted.Q10analysis
is a useful means to help choosing a suitable model. Based on model andQ10analysis, the Arrhenius model may be the best
equation to describe the relationship between soil respiration and temperature both for its performance and theoretical basis. However, it may somewhat underestimate the response of soil respiration at low temperature.
Acknowledgements
We thank Prof Keith Smith of Edinburgh University for help in soil sampling. We are grateful to the UK NERC for support under grant GR9/03624.
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