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Daily heterotrophic respiration model considering the diurnal temperature variability in the soil Chen, J. A.; Huang, S. E.; Ju, W.; Gaumont-Guay, David; Black, T. Andrew Mar 31, 2009

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Daily heterotrophic respiration model considering the diurnal temperature variability in the soil J. M. Chen,1 S. E. Huang,1,2 W. Ju,1 D. Gaumont-Guay,3 and T. A. Black3 Received 26 July 2008; revised 4 November 2008; accepted 3 December 2008; published 20 March 2009. [1] In daily, monthly, and annual respiration models for regional and global applications, the diurnal variation of temperature is generally ignored. As the effect of temperature on respiration is nonlinear, this ignorance may cause considerable errors in respiration estimation, but these errors have not yet been systematically investigated. This is in fact a central issue in temporal scaling of ecosystem models which are often applied in time steps equal to or larger than a day. In this study, we develop an integrated daily heterotrophic respiration model, and demonstrate first theoretically the importance of considering the diurnal amplitude of soil temperature and the vertical soil carbon distribution pattern in daily respiration estimation using the daily mean temperature. Measurements of soil respiration with roots exclusion made in a mature black spruce site in Saskatchewan, Canada, in July–September 2004 are used to validate the model. Daily heterotrophic respiration rates were underestimated by up to 15%, with a mean value of 4.5%, when only the mean daily temperature was used. This underestimation occurred under the conditions that the diurnal temperature amplitude in the forest was less than 12C and the vertical distribution of organic carbon in the top 15–30 cm was uniform. Based on the integrated daily model, this underestimation at the same site would be 38% if the amplitude increases to 20C, and in soils with steep vertical carbon distributions with a 20C diurnal amplitude, it can increase to 44%. The magnitude of this underestimation is theoretically proportional to [ln(Q10)] 2. During the experimental period, the value of Q10 for heterotrophic respiration was found to be 4.0–4.5. If Q10 = 2.0, this underestimation is reduced to about 10% at a diurnal temperature amplitude of 20C. Citation: Chen, J. M., S. E. Huang, W. Ju, D. Gaumont-Guay, and T. A. Black (2009), Daily heterotrophic respiration model considering the diurnal temperature variability in the soil, J. Geophys. Res., 114, G01022, doi:10.1029/2008JG000834. 1. Introduction [2] Soil respiration consists of two functionally different components: rhizosphere (roots and mycorrhizae) respira- tion and heterotrophic respiration from free-living microbes. It provides the main carbon efflux from ecosystems to the atmosphere and is therefore an important component of the global carbon balance [Schimel, 1995]. On average, global heterotrophic respiration emits 6876.5 Pg Cy1 to the atmosphere [Raich and Schlesinger, 1992; Raich and Potter, 1995]. Biologists have long used Q10 to describe the dependence of biological processes on temperature, a con- cept originating in the nineteenth century physical- chemistry models of Arrhenius [1889] and Van’t Hoff [1898]. The Q10 function assumes an exponential relation- ship between respiration and temperature. In recent years, some studies have sought to establish relationships of soil respiration with soil moisture and temperature [Lloyd and Taylor, 1994; Thierron and Laudelout, 1996; Davidson et al., 1998; Gulledge and Schimel, 2000; Xu and Qi, 2001a]. There is increasing evidence that Q10 of soil respiration is not seasonally constant and tends to decrease with increas- ing temperature and decreasing soil moisture [Rayment and Jarvis, 2000; Davidson et al., 2000; Xu and Qi, 2001b; Drewitt et al., 2002; Luo et al., 2001; Qi et al., 2002; Janssens and Pilegaard, 2003]. Despite these and other limitations, a simple exponential function based on a fixed Q10 value of about 2.0 has gained wide acceptance in modeling regional and global ecosystem respiration and its responses to climate change [Ryan, 1991; Aber and Federer, 1992; Melillo et al., 1993; Schimel et al., 1997; Cramer et al., 1999; Tjoelker et al., 2008]. [3] Janssens et al. [2003] suggested that if the objective of a model is to simulate the total annual soil respiration, an annual model parameterization suffices. However, if the simulation period is days or weeks, as in the case when soil respiration is affected by synoptic weather events, a short- term parameterization is required. The need for these JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, G01022, doi:10.1029/2008JG000834, 2009 1Department of Geography, University of Toronto, Toronto, Ontario, Canada. 2Meteorological Research Institute of Jiangxi Province, Nanchang, China. 3Faculty of Agricultural Science, University of British Columbia, Vancouver, British Columbia, Canada. Copyright 2009 by the American Geophysical Union. 0148-0227/09/2008JG000834 G01022 1 of 11 different parameterizations for different time steps may be due to the nonlinear response of respiration to temperature. Many models operate at monthly or seasonal or annual time steps [Parton et al., 1987; Parton and Scurlock, 1993; Peng et al., 1998; Cramer et al., 1999; Irvine and Law, 2002; Chen et al., 2003; Rodeghiero and Cescatti, 2005], and even if some models use daily time steps, they only consider variations from day to day [Russell and Voroney, 1998; Lee et al., 2002] or half-daily [Braswell et al., 2005]. So far, there have been no published works on daily models considering the effects of the diurnal temperature variation on daily respiration estimation, although there have been numerous subdaily measurements. As the response of respiration to temperature is not linear, the diurnal temper- ature amplitude would have significant influence on daily respiration estimation using dailymean temperature. Figure 1 shows that the daily heterotrophic respiration would be significantly underestimated using the mean daily tempera- ture in comparison with the correct value determined through daily integration, and this underestimation would increase with increasing diurnal temperature amplitude. Considering this nonlinear effect would, therefore, be an important tem- poral scaling step for daily, monthly and annual respiration models, which so far has been ignored. [4] In this paper, we focus on the development of a model simulating heterotrophic respiration at daily time steps with a correction for the effect of the nonlinear response of respiration to diurnal temperature variation. The objectives of this paper are: (1) to derive an analytical solution to the daily integral of heterotrophic respiration for the purpose of correcting the bias of simple Q10 models based on daily mean air temperature; (2) to validate this integrated daily model using field measurements and to demonstrate the ability of this model in capturing the effect of diurnal temperature variation erotrophic respiration in soil at daily time steps; (3) to investigate the importance of key parameters, including the diurnal temperature amplitude and the organic carbon density profile in the soil, in estimating heterotrophic respiration at daily time steps. 2. Daily Model Description 2.1. Simple Daily Model of Heterotrophic Respiration [5] In this study, we select the Q10 function [Van’t Hoff, 1898] to describe the sensitivity of heterotrophic respiration to temperature as follows: Rh ¼ R10f T   ¼ R10QT101010 ð1Þ where Rh is the heterotrophic respiration flux at the mean soil temperature T over an time interval, R10 is the rate of heterotrophic respiration at a soil temperature of 10C, and Q10 is the temperature sensitivity of heterotrophic respira- tion and is an empirical parameter, representing the relative increase of the respiratory flux as temperature increases by 10C. Equation (1) is often called ‘the Q10 model’, which is most commonly reported in the literature. As the tempera- ture sensitivity of heterotrophic respiration generally decreases with increasing temperature, the value of Q10 would change with temperature, making it seasonally dependent. Although alternatives to Q10 have been proposed by considering the increase in activation energy cost with temperature [Lloyd and Taylor, 1994], Q10 is continuously used in many recent studies [Tjoelker et al., 2008; Wythers et al., 2005] for its effectiveness in capturing the thermal acclimation effect on respiration. [6] Heterotrophic respiration is also influenced by total soil carbon, litter quality, and moisture. In order to develop a simple and effective diurnal scaling algorithm, we have chosen to consider the soil carbon vertical profile as an additional parameter to temperature, while the effects of other parameters will be evaluated through their association with existing model parameters (see section 5). Normally, the soil organic carbon content decreases with depth from the soil surface [Jobbagy and Jackson, 2000]. The total soil organic carbon in the whole soil profile is expressed as: wt ¼ Zzd 0 rb zð Þ:wg zð Þdz ¼ Zzd 0 cw zð Þdz ð2Þ where wt is the total organic carbon per unit surface area (kg m2), rb(z) is the soil bulk density (kg m 3) at depth z, wg(z) is the weighted fraction of soil organic carbon (kg kg1), cw(z) is the volumetric organic carbon content (kg m3), and zd(m) is the lower boundary of the carbon- containing soil depth. The profile of soil organic carbon with depth can be defined as: w zð Þ ¼ cw zð Þ wt ð3Þ where w(z) is in m1 and can be regarded as a weighting function for contributions of soil carbon at various depths. Daily heterotrophic respiration is often calculated using daily mean soil temperature (T ). Using equation (1) to Figure 1. A schematic showing the difference between diurnally integrated daily heterotrophic respiration (Rh,daily) and the approximate daily heterotrophic respiration (~Rh) obtained using the daily mean temperature. Rh,daily is the correct value determined by making the area under the straight line the same as that under the curve between Tmin and Tmax. Rh,daily and ~Rh are different because of the nonlinear relationship between heterotrophic respiration and temperature. G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 2 of 11 G01022 represent the hourly heterotrophic respiration and distribut- ing it with depth using w(z), we can integrate the hourly values with respect to depth and time to obtain the daily heterotrophic respiration (~Rh): ~Rh ¼ Z24 0 Zzd 0 w zð ÞRsdzdt ¼ Z24 0 Zzd 0 w zð ÞR10Q T10 10 10 dzdt ¼ 24R10Q T 10 1 10 ð4Þ where R10 represents the total hourly respiration rate at 10C after integrating w(z) with respect to z, which is time invariant if the total soil carbon does not change with time. We refer to equation (4) as a simple daily respiration model. Its simple form is derived under the assumption that the variations of soil temperature (T ) with depth and time can be ignored. It is therefore considered as an approximation. 2.2. Integrated Daily Model of Heterotrophic Respiration 2.2.1. Daily Heterotrophic Respiration [7] In order to model the diurnal variation of heterotro- phic respiration caused by the diurnal variation in soil temperature at different depths, we rewrite equation (4) as follows: Rh;daily ¼ Z24 0 Zzd 0 w zð ÞR10Q Ts z;tð Þ10 10 10 dzdt ð5Þ where Rh,daily is the daily total heterotrophic respiration calculated with diurnally variable soil temperature. Equation (5) is also referred to as an integrated daily respiration model, where Ts(z, t) is the soil temperature at time (t) and depth (z). Here, we treat R10 and Q10 to be same as those in equation (4). 2.2.2. Model for Soil Temperature [8] With the assumption that physical properties of soil are constant with depth, the equation of soil heat conduction can be expressed as [Monteith and Unsworth, 1990]: @Ts z; tð Þ @ ¼ k0 @ 2Ts z; tð Þ @z2 ð6Þ where k0 is the thermal diffusivity of soil, and Ts(z, t) is the temperature at depth z and time t. The solution of equation (6) satisfying the boundary condition which describes a harmo- nic oscillation of temperature at depth z is: Ts z; tð Þ ¼ T þ A zð Þ sin wt  z=Dð Þ ð7Þ where T is the mean soil temperature at the surface, w = 2p/24 (h1) is the angular frequency of the oscillation for daily cycles, A(z) = A(0)exp(z/D) is the amplitude of soil temperature at depth z, A(0) = Acosf is the amplitude at the surface, A is the air temperature amplitude, f = tan1(2pt/p) is a phase lag, p is the period of the temperature oscillation, and D = (2k0/w)0.5 is the damping depth. For p = 24 h, f is small and A(0)  A since the time lag (t) of temperature oscillation from the air temperature is close to zero at the soil surface. So we can present A(z) as follows: A zð Þ  A exp z=Dð Þ ð8Þ Combining equation (7) with equation (5), the total daily heterotrophic respiration with explicit consideration of the temperature variations with time and depth in the soil can be written as: Rh;daily ¼ Zzd 0 Z24 0 w zð ÞR10Q Ts z;tð Þ10 10 10 dzdt ¼ Zzd 0 Z24 0 w zð ÞR10Q TþA zð Þ sin wtz=Dð Þ10 10 10 dzdt ¼ Zzd 0 R10w zð Þ Z24 0 Q TþA exp z=Dð Þ sin wtz=Dð Þ10 10 10 dzdt ð9Þ ¼ R10Q T 10 1 10 Zzd 0 w zð Þ Z24 0 Q A exp z=Dð Þ sin wtz=Dð Þ 10 10 dzdt 2.2.3. Variation of Soil Organic Carbon With Depth [9] In this study, the contribution of soil at depth z to the total heterotrophic respiration is mainly controlled by the organic carbon amount cw(z). Based on Grant et al. [2005], who provided observed data at three boreal forest sites in Canada, the variation of soil organic carbon with depth can be generally described using an exponential function (Figure 2): cw zð Þ ¼ c0ekz ð10Þ where c0 is the volume organic carbon content at soil surface, a constant for a given site, k is a constant determining the decay rate of organic carbon content with soil depth. Substituting equation (10) into equation (3), the weight function can be rewritten as: w zð Þ ¼ cw zð Þ wt ¼ c0 wt  ekz ð11Þ Figure 2. Organic carbon content changes with soil depth at the study site (old black spruce [Grant et al., 2005]). G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 3 of 11 G01022 We can also calculate the total organic carbon through the soil depth as wt ¼ Zzd 0 cw zð Þdz ¼ Zzd 0 c0e kzdz ¼ c0 k 1 ekzd  ð12Þ This simple vertical weighting scheme is derived under the assumption that the vertical distribution of soil carbon follows a single decay rate k. 2.2.4. Integrated Daily Model of Heterotrophic Respiration With Consideration of Diurnal Temperature Variation [10] After using w = (2p/24) in equation (9) and trans- forming the variables, we obtain the following integrated result for daily heterotrophic respiration: Rh;daily ¼ R10Q T 10 1 10 Zzd 0 w zð Þ Z24 0 Q A exp z=Dð Þ sin 2p 24 tz=Dð Þ 10 10 dzdt ¼ 24R10Q T 10 1 10 Zzd 0 w zð Þ Z1 0 Q A exp z=Dð Þ sin 2pxz=Dð Þ 10 10 dzdx ð13Þ ¼ 24R10Q T 10 1 10 Zzd 0 w zð Þ Z1 0 e lnQ10 10 A sin 2pxz=Dð Þ exp z=Dð Þdzdx After making the third order Taylor series expansion of the exponential function in equation (13), it can be expressed as: Rh;daily ¼ 24R10Q T 10 1 10 Zzd 0 w zð Þdz Z1 0  1þ lnQ10 10 A sin 2px z=Dð Þ exp z=Dð Þ  þ lnQ10ð Þ 2 200 A2 sin2 2px z=Dð Þ exp2 z=Dð Þ # dx ¼ 24R10Q T 10 1 10 Zzd 0 w zð Þ þ lnQ10ð Þ 2 400 A2w zð Þ exp 2z=Dð Þ  !  dz ð14Þ Note that R1 0 sin (2px  z/D)dx = 0 and R1 0 sin2(2px  z/D)dx = 1. Based on the single decay rate assumption for soil carbon, i.e., equations (11) and (4), equation (14) can be written as: Rh;daily ¼ 24R10Q T 10 1 10 þ 24R10Q T 10 1 10 Zzd 0 lnQ10ð Þ2 400 A2w zð Þ  exp 2z=Dð Þdz ¼ ~Rh 1þ C0A 2 lnQ10ð Þ2 400wt k þ 2=Dð Þ 1 e  kþ2=Dð Þzd   ! ð15Þ It is noted that A in equation (15) in its final form is the diurnal temperature amplitude at the soil surface, not at the mean soil depth. In this way, the temperature variations in all depths are considered in this integrated result. As A is very close to the diurnal amplitude of air temperature near the surface, it can be determined using the air temperature as a close approximation. [11] Equation (15) is an integrated daily model for het- erotrophic respiration with consideration of the diurnal temperature variability at various depths and the organic matter profile in the soil. The second term in the brackets results from the nonlinear effect of temperature on hetero- trophic respiration, i.e., the relative difference between Rh,daily and ~Rh shown in Figure 1. 2.2.5. Special Cases of Integrated Daily Heterotrophic Respiration Models Uniform Soil Carbon Profile [12] Based on measurements from our experimental site (see section 3 and Table 1), the soil has roughly homoge- neous organic layer of 15–30 cm thickness above the mineral soil. As this organic layer, originating mostly from litter falls and fine-root and moss turnovers, is the main source of heterotrophic respiration, the decay rate of organic carbon with soil depth (k) from the top of this organic layer is set to zero in analyzing our experimental data, i.e., setting wt = c0 (zd  z0) (equation (13)) and k = 0 in equation (15), which is then simplified to: Rh;daily ¼ ~Rh 1þ DA 2 lnQ10ð Þ2 800zd 1 e2Zd=D   ! ð16Þ AssigningDRh = DA2 ln2 Q10 800zd (1 - e2Zd=D), equation (16) can be rewritten as: Rh;daily ¼ ~Rh 1þDRhð Þ or Rh;daily=~Rh ¼ 1þDRhð Þ ð17Þ where DRh is a term correcting for the bias of daily heterotrophic respiration estimation without considering the diurnal soil temperature variations. This correction is proportional to the square of the diurnal temperature amplitude. In our research, we regard Rh,daily as the correct daily heterotrophic respiration (calculated by the integrated daily model given in equation (15)), and ~Rh is an approximation (equation (4)) to be corrected using the correction term. Thus, ~Rh reflects the effects of mean daily temperature, and Rh,daily includes the effects of both average daily temperature and diurnal temperature amplitude. Variable Soil Carbon Profiles at Different Depths [13] For cases, where the soil organic carbon content profile cannot be well described by a single decay rate k, such as the case, where a litter/organic layer overlaying the mineral soil, or the total soil column has two or three layers with different carbon decay rates, the following equation can be used to estimate the nonlinear effect: DRh ¼ A 2 lnQ10ð Þ2 400 Xn i¼1 wiki ezi1 ki1þ2=Di1ð Þ  ezi kiþ2=Dið Þ ki þ 2=Dið Þ 1 ekiDzið Þ ð18Þ where ki is the decay rate of the i th layer of soil, wi is the weight of carbon in soil layer i to the total soil carbon, Di is the thermal damping depth for soil layer i, Dzi is the G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 4 of 11 G01022 thickness of the ith soil layer, and zi is the lower boundary (depth) of the ith layer. As there is no layer 0, the initial values of k and z are: k0 = 0 and z0 = 0. Equation (18) is derived similarly to equation (15), allowing the thermal damping depth to vary vertically to consider different materials and soil moisture contents in different soil layers. It will be used for parameter sensitivity analysis shown in section 5. 3. Experimental Data and Model Parameterization 3.1. Site Description and Physical and Biological Properties [14] This study makes use of experimental data collected in a black spruce (P. mariana) stand (125 years old in 2004) located at the southern edge of the boreal forest in central Saskatchewan, Canada (54.0N, 105.1W), which is often called the South Old Black Spruce Site for the Boreal Ecosystem-Atmosphere Study (BOREAS). The forest floor is covered by mostly (70%) feather mosses (Hylocomium splendens, Pleurozium schreberi) in wetter areas and by patches Sphagnum moss (Sphagnum spp.) and lichen (Cladina spp.) in drier area. Beneath the moss layer is an approximately 20-cm organic layer (including O and P horizons) overlying a waterlogged sandy clay (including A, B and C horizons). The drainage at the site is poor. Mean fine-root biomass (<2 mm) to a depth of 40 cm is 3.3 ± 1.0 Mg dry matter ha1 (average for 2003–2004) [Kalyn and Van Rees, 2006]. The physical and biological properties of this site [Grant et al., 2001] are shown in Table 1. The 30-year mean annual air temperature and precipitation measured at a climate station located 80 km away (1934– 1990, Waskesiu Lake, 53.6N, 106.1W) are 0.3C and 456 mm, respectively. Boreal forests globally occupy about 20 M km2 of the land surface, and black spruce is the most dominant boreal species [Hall et al., 2004]. The results from this study would therefore be significant for the global carbon cycle estimation. The thick organic layer on top of the mineral soil found at our study site is typical of black spruce forests. Because of the thermal insulation effect of this layer, the diurnal temperature amplitude in the soil under the forest cover is relatively small compared with other forest types, and the magnitude of the temporal scaling effect on heterotrophic respiration estimation found in our study would therefore represent the lower bound of this effect globally. 3.2. Experimental Data for Model Validation [15] The half-hourly measurements of heterotrophic res- piration through root-exclusion experiments were conducted in 2004 [Gaumont-Guay et al., 2008]. Two pairs of control and root-exclusion plots (2 m 	 2 m) were installed in the fall of 2001. In each square plot, trenches were dug at the edges to a depth of 75 cm to exclude all live tree roots, and the trench walls were covered with four sheets of polyeth- ylene film (100 mm thick) to prevent the penetration of new roots. The trenches were then backfilled with the excavated soil. Two additional pairs of plots were installed in Sep- tember 2003 following the same procedure, bringing the number of replicates per treatment to four. [16] Continuous half-hourly measurements of soil CO2 efflux were conducted during the growing season of 2004, although only the data acquired in July–September 2004 are used in this study to minimize the possible pulse of dead root decomposition which may last several months after trenching [Lee et al., 2003]. Gaumont-Guay et al. [2008] found that the residual dead root decomposition lingered for more than a year, and therefore the heterotrophic respiration data from the two pairs of plots installed in 2003 would contain a small fraction from dead root decomposition (not quantified), while measurements in the other two pairs installed in 2001 would be free from this effect. The contribution of the remaining slow root decomposition to the measured heterotrophic respiration could be partly offset by the removal of rhizomicrobial respiration by heterotrophs associated with the cut roots. Live root rhizomicrobial respiration was found to contribute 32% to the total root respiration of a meadow fescue [Johansson, 1992]. Meas- urements were made with a nonsteady state automated chamber system. The chambers consisted of a domed- shaped transparent lid (52.5 cm diameter 	 20.5 cm height) inserted between 3 and 4 cm below the live-moss layer. Opening and closing of the lid was done with a pneumatic cylinder assembly (Model BFT-173-DB, Bimba Manufac- turing Company, Machesney Park, IL, USA) connected to an air compressor (Model CPFAC2600P, Porter Cable, Jackson, TN, USA). About 92% of the time, the lid was open to allow rain and litter to fall into the collar area. The system measured the increase of CO2 concentration in the chamber headspace over a 2.5-min interval sequentially for the eight chambers, allowing all chambers to be measured once every half-hour. When a chamber was selected, the air was circulated between the chamber and a closed-path infrared gas analyzer (IRGA, Model LI-6262, LI-COR Inc., Lincoln, NE, USA) with an AC linear pump (Model Table 1. Physical and Biological Properties of the Soil at the Old Black Spruce Sitea Depth (m) Bulk Density (Mg m3) q0.03Mpa (m3 m3) q1.5Mpa (m3 m3) Sand (g kg1) Silt (k kg1) Organic Carbon (g kg1) PH Organic Nitrogen (mg kg1) Organic Phosphate (mg kg1) 0.01 0.10 0.40 0.20 0 0 434 3.4 8162 900 0.05 0.10 0.40 0.20 0 0 434 3.4 8162 900 0.15 0.10 0.40 0.20 0 0 434 3.4 8162 900 0.30 0.10 0.40 0.20 0 0 434 3.4 8162 900 0.47 1.52 0.213 0.049 728 214 9.8 4.3 423 53 0.72 1.66 0.183 0.05 646 287 3.6 4.9 215 27 0.96 1.66 0.022 0.012 960 19 1.0 5.8 52 7 1.20 1.66 0.034 0.013 949 30 0.5 6.6 52 7 aAbbreviations are as follows: q0.03Mpa, field capacity; q1.5Mpa, wilting point. Reference data from Grant et al. [2001]. G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 5 of 11 G01022 SPP-15EBS-101, Gast Manufacturing, Benton Harbor, MI, USA). A small fan ensured the air in the chamber was well mixed. The IRGA was located in a thermally controlled housing with a constant temperature at 38C. The IRGA was calibrated daily using CO2-free nitrogen gas (offset calibration) and a dry air gas of known CO2 concentration at  370 mmol mol1 (gain calibration). Both were from gas cylinders calibrated against a standard from the Meteoro- logical Service of Canada, Downsview, ON, Canada. Half- hourly soil CO2 efflux (Fcs, mmol CO2 m 2 s1) was calculated using the following equation: Fcs ¼ ra Ve A dsc dt ; ð19Þ where ra is the density of dry air in the chamber headspace (mol m3), Ve is the effective volume of the chamber (m 3), A is the area of ground covered by the chamber (m2), and dsc/dt is the time rate of change of the CO2 mixing ratio in the chamber headspace over a 1-min interval following lid closure (mol CO2 mol 1 dry air s1). The Ve value differs from the geometrical volume of the chambers because of moss porosity. It was measured daily using a gas injection technique described in detail by Drewitt et al. [2002] and by Gaumont-Guay et al. [2006]. [17] Compared with the control plots without root exclu- sion, heterotrophic respiration determined in plots with root exclusion was 40.6% of the total soil respiration. As root respiration was not only influenced by temperature but also by tree biological activities, they were excluded in this study. Most ecosystem models handle heterotrophic and root respiration separately, and therefore each of these components needs to be individually studied. Moss photo- synthesis and respiration were removed from the measure- ments through taking the difference between control and root-exclusion plots in each pair assuming that moss pho- tosynthesis and respiration were unaffected by the root- exclusion experiment [Gaumont-Guay et al., 2008]. In this way, the CO2 flux due to heterotrophic respiration only was obtained. Each flux value at a given time is the average of measurements of four plots. The hourly meteorological data are compiled from the data archive of Fluxnet-Canada website (http://fluxnet-canada.ccrp.ec.gc.ca/). These meteo- rological data were measured at the flux tower near cham- bers of heterotrophic respiration. 3.3. Model Parameterization [18] The parameters used the integrated daily model (equation (16)) were ed at the site or determined through data fitting (see Table 2). Based on daily soil temperature at 2 cm depth, we found different values of Q10 and R10 in different months. The values of Q10 are 4.0, 4.4 and 4.5 in July, August and September, respectively. The corresponding R10 values are 1.66, 1.77 and 1.96 gC m2 d1, respectively. Gaumont-Guay et al. [2006] showed that the Q10 value for nighttime soil CO2 efflux during the growing season was 3.1, and R10 was 1.9 at the site. There may be several reasons for the Q10 values derived from the chamber data to be considerably larger than the conven- tional value of 2.0: (1) the substrate active layer thickness increased with soil temperature, i.e., not only the microbial activity but also the total organic matter involved in respiration increased with temperature, causing a larger sensitivity to temperature than usually predicted with a constant substrate; (2) sensitivity to soil temperature is usually larger than that to air temperature [Kicklighter et al., 1994]; (3) the dynamic of soil temperature was rela- tively small in a month relative the natural variability in the measured Rh, causing errors in Q10 determination; and (4) possible measurement errors using soil chambers based on nonsteady state methods [Pumpanen et al., 2004]. Gaumont-Guay et al. [2006] found a smaller value of Q10 = 3.1 because it represents the whole growing season including May and June. It also indicates the possibility of larger errors in Q10 determination over shorter periods (reason 3 above). 4. Results 4.1. Sensitivity of Heterotrophic Respiration to Temperature at Different Soil Depths [19] To model the diurnal variation of heterotrophic respiration, we calculated the average daily air temperature and soil temperature using the half-hourly observed data. We also processed the observed half hourly heterotrophic respiration rates in each day to obtain the daily rate. Soil respiration from the root-exclusion treatment shows differ- ent temperature sensitivities at different soil depths. In this research, we use equation (1) and analyze the relationship between heterotrophic respiration and soil temperature at different soil depths using half-hourly measurements during the peak growing season. The results indicate that there are good exponential correlations between heterotrophic respi- ration and soil temperature at 2 cm and 5 cm soil depth, but at 10 cm depth the correlation is not significant (Table 3 and Figure 3). [20] Based on half-hourly measurements of heterotrophic respiration and soil temperature at different soil depths, we Table 2. Parameters at the Old Black Spruce Site for Heterotrophic Respiration Calculation Symbol Unit Description Value General w h1 Angular frequency 2p/24 k0 106 m2 s1 Thermal diffusivity 0.13 D cm Damping depth 5.98 zd cm Soil depth contributing to heterotrophic respiration 15 c0 kg m 3 Organic carbon at the soil surface 43.4 k cm1 Decay rate of organic C with depth 0 Respiration Q10 unitless Temperature sensitivity of heterotrophic respiration 4.0–4.5 R10 gC m 2 d1 Heterotrophic respiration at soil temperature of 10C 1.66–1.96 G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 6 of 11 G01022 estimated monthly Q10 values from regression analysis. As the soil temperature varied with depth while the total respi- ratory fluxwas the depth-integrated result, these values varied in a large range from 2.77 to 6.22 with depth from 2 cm to 10 cm, in confirmationwith previous studies [Gaumont-Guay et al., 2006]. At 2 cm, these monthlyQ10 values vary from 4.0 and 4.5 in the July–September period, which are used in our final analysis. Equation (15) shows that the error in daily heterotrophic respiration estimation without considering the diurnal temperature variation is proportional to (lnQ10) 2, and it is therefore important to represent the seasonal variation in Q10 in the integrated daily model. 4.2. Heterotrophic Respiration Modeling Results [21] The soil temperature at 2 cm soil depth is used to model the heterotrophic respiration obtained from the root- exclusion experiment. The average daily soil temperature, the amplitude of the air temperature at 1 m above the surface, and average heterotrophic respiration are calculated from half-hourly measurements. The total daily heterotro- phic respiration is simulated using models of equations (16) and (4), i.e., models with and without the consideration of the diurnal temperature variation. These two sets of mod- eled results are compared with measurements of daily heterotrophic respiration obtained as the summation of half hourly observations within the 24 h (Figure 4). In the comparison, the root mean square error (RMSE) was used as a criterion to evaluate the model performance (see Table 3), i.e., RMSE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPn i¼1 xi  yið Þ2 n vuuut ð20Þ where xi and yi are the modeled and measured values, respectively, and n is the number of days. The values from the simple daily model have a relatively small slope in the regression between measured and modeled values and a relatively high value of RMSE for monthly and growing season simulations (Table 4). Some of the scatter is due to irregular subdaily variations in weather conditions, espe- cially in days when it was raining and had a large variation of temperature. The R2 values are 0.78 and 0.79 for integrated and simple daily models, respectively. 4.3. Effects of Diurnal Amplitude of Temperature on Heterotrophic Respiration [22] To show the importance of the diurnal amplitude of temperature on daily heterotrophic respiration estimation, we investigate the ratio Rh,daily/~Rh between uncorrected and corrected daily values as a function of the diurnal temper- ature amplitude at the soil surface (taken as that of the air temperature near the surface, Figure 5). ~Rh is the daily total heterotrophic respiration using the simple daily respiration model after finding Q10 and R10 from the experimental data for each month, and Rh,daily is estimated using the integrated daily model (equation (15)). [23] This ratio indicates the extent of the bias error in the daily respiration model without considering the diurnal temperature variation. As mathematically described in equation (14), the effect of this amplitude on the diurnal variation of heterotrophic respiration increases with (lnQ10) 2 and the negative bias error is highly sensitive to the diurnal amplitude at the soil surface, increasing from about 10% at an amplitude of 10C to about 38% at an amplitude of 20C when k = 0 and Q10 = 4.0. The actual values of Rh,daily/ ~Rh found from the experimental data sets are also shown in Figure 5. The diurnal amplitude at the experimental site at the high latitude is generally small (2–12C with a mean of 7.0C), and the maximum bias error (underestimation) in the daily heterotrophic respiration estimation is less than 15%, with a mean of 4.5%. This error may appear to be small, but it is highly significant as 4.5% of the global heterotrophic respiration of 68–76.5 Pg Cy1 [Raich and Schlesinger, 1992] is larger than the current terrestrial carbon sink [Canadell et al., 2007]. However, compared with the temporal scaling of daily photosynthesis [Chen et al., 1999], this nonlinear effect on respiration scaling is considerably smaller. Although field measurements of het- erotrophic respiration generally have errors much larger than the scaling error found in our study, the scaling methodology can still be used to achieve a large improve- ment in regional and global terrestrial carbon cycle model- ing, which usually depends on the functional form of Table 3. Exponential Fits Between Heterotrophic Respiration Obtained Through Root-Exclusion Experiments and Soil Tem- perature at Different Soil Depths With Half-Hourly Measurements During the Peak Growing Seasona Soil Depth (cm) Fitted Equation R2 (Regression Coefficient) 2 Rs = 0.6442exp (0.1025Ts) 0.681 5 Rs = 0.5566exp (0.1231Ts) 0.623 10 Rs = 0.6730exp (0.1132Ts) 0.221 aJuly–September 2004. Rs is soil respiration for root exclusion with half- hourly measurements (mmol), and Ts is soil temperature (C). Exponential fits from equation (1). Figure 3. Relationship between heterotrophic respiration and soil temperature at 2 cm soil depth with half-hourly measurement data during the peak growing season (July– September 2004). G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 7 of 11 G01022 respiration derived from measurements while their absolute values are adjusted through spin-up procedures. 5. Discussion 5.1. Influences of Q10 and the Vertical Decay Rate (k) of Soil Carbon [24] The integrated daily model (equation (15)) demon- strates a general relationship between Rh,daily and diurnal temperature amplitude (A) at different values of k and Q10. Based on the integrated daily model, Figure 6 demonstrates that this error is also sensitive to the k value, increasing from 38% at k = 0 (cm1) to 44% at k = 0.03 (cm1) at A = 20C and Q10 = 4, or from 10% at k = 0 (cm 1) to 11% at k = 0.03 (cm1) at A = 20C and Q10 = 2. The mathematical form of this sensitivity with k is exponential as shown in equation (15). Physically, this sensitivity is caused by the fact that the diurnal temperature amplitude decreases expo- nentially with depth. With a damping depth of 6 cm, the amplitude can decrease from 10C at the surface to 4.3C at 5 cm and to 0.8C at 15 cm. The vertical distribution of soil carbon is therefore also important in the temporal scaling of the heterotrophic respiration. Based on Grant et al. [2005] who provided soil organic carbon contents at various depths at two sites, the Old Aspen and the Old Jack Pine of BOREAS, we estimated the k values to be 0.0215 and 0.0415 cm1 at these two sites, respectively. These nonzero k values suggest that the error in the simple daily respiration estimation (equation (1)) could be significantly larger at these two sites. This sensitivity of daily respiration estima- tion to the soil carbon profile suggests that considering the vertical distribution of organic carbon in soil can signifi- cantly improve of our current daily, monthly and annual respiration models of heterotrophic respiration. 5.2. Influences of Multiple Soil Layers With Different Vertical Decay Rates [25] The experimental data used in this study were obtained from a forest stand with a thick organic layer (15–30 cm) on top of the mineral soil. As most carbon in the soil is located in this organic layer which have a fairly uniform carbon density, the simple treatment of k = 0 was a good approximation. The multilayer model (equation (18)) can be used to assess the error due to ignoring the vertical carbon distribution pattern in the mineral soil. Assuming the organic layer has a thickness of 15 cm with weight w1 = 0.8 and decay rate k = 0 cm1 and the mineral soil has a thickness of 50 cm with w2 = 0.2 and k = 0.03 cm 1, it is found from equation (18) that the Rh,daily/~Rh ratio at a diurnal air temperature amplitude of 10C would be 1.077, which is about 2% less than the value of 1.095 with the simple treatment of k = 0 for the organic layer only. Under this two-layer treatment, the ratio is reduced because of the contribution of the deeper layer with smaller diurnal temperature variation to the total heterotrophic respiration. [26] In ecosystems with a moderate organic/litter layer and a carbon-rich mineral soil layer, a similar two-layer treatment can be made to equation (18). If we assume that Figure 4. The comparison of modeled and measured daily heterotrophic respiration during the growing season for the root-exclusion treatment at the Black Spruce site. Table 4. Root Mean Square Errors of the Modeling Results in Different Months in 2004 at the Old Black Spruce Sitea Month Integrated Daily Model Simple Daily Model Slope Intercept RMSE Slope Intercept RMSE Jul. 0.9235 0.1554 0.2685 0.9092 0.0683 0.2770 Aug. 0.8710 0.2533 0.2541 0.8504 0.1544 0.2606 Sep. 0.8649 0.1560 0.1669 0.8784 0.0738 0.1934 Growing season 0.9319 0.0906 0.2281 0.9124 0.0419 0.2418 aRMSE, root mean square errors. G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 8 of 11 G01022 the organic layer has a thickness of 5 cm with k = 0 and w1 = 0.2 and that the carbon-containing soil mineral layer has a thickness of 30 cm with k = 0.03 and w2 = 0.8, the Rh,daily/ ~Rh ratio at a diurnal air temperature amplitude of 10C and Q10 = 2.0 would be 1.058. If the organic layer is removed, i.e., the mineral soil has a thickness of 30 cm with k = 0.03 and w1 = 1.0, the ratio is increased to 1.067. This is because without the thermal damping effect the diurnal temperature amplitude in the mineral soil would increase. The difference in k between the two layers causes less than 1% difference Figure 5. The relationship between the ratio Rh,daily/~Rh and temperature amplitude at different Q10 values when the decay rate (k) of organic C content with depth is zero. The pluses indicate the actual values of Rh,daily/~Rh calculated using Q10 and R10 found from the experimental data for each month at k = 0. The temperature amplitude is for air 1 m above ground. Figure 6. The relationship between the ratio Rh,daily/~Rh and temperature amplitude at different decay rates (k, cm1 ganic C content with depth for Q10 = 2.0, Q10 = 3.0, and Q10 = 4.0. G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION 9 of 11 G01022 in the ratio. It is also noted from Figure 6 that the nonlinear correction, i.e., the Rh,daily/~Rh ratio, is more sensitive to Q10 and than to k within a realistic range. This implies that for general purposes, a 1-layer model with a constant k value would be useful for the first order correction of this nonlinear effect. The error caused by the k variation with depth would generally be less than 2–3% of the total heterotrophic respiration. 5.3. Influences of Litter Quality and Soil Moisture [27] In our study, we have only considered the vertical distribution of the total soil carbon without paying specific attention to the quality of the litter and organic matter. In general, soil carbon becomes more recalcitrant (longer turnover time) in deeper layers [Trumbore et al., 1996]. The influence of this carbon quality variation with depth can increase the nonlinear effect, and this increased effect can be effectively considered by either decreasing the effective carbon-containing soil depth (i.e., zd in equations (15) or (16)) or increasing the k value, to allow the more labile carbon closer to the soil surface more exposed to diurnal temperature variation. In our current study, we found the best fit with experimental data when the lower bound value of zd = 15 cm (Table 2) was used, and this may be due to the litter quality variation with depth. [28] Soil moisture not only affects the total heterotrophic respiration but also the thermal diffusivity that influences the thermal damping depth used in the model. While the influence on the total heterotrophic respiration does not change the relative Rh,daily/~Rh ratio, the influence on the damping depth can cause a considerable error in the ratio. In the example of one layer soil with a thickness of 30 cm and k = 0.03, an increase of the damping depth D from 6 cm to 8 cm would cause the ratio to increase from 1.067 to 1.087 because a larger damping depth would allow the diurnal thermal wave to penetrate deeper into the soil, causing a larger nonlinear effect on respiration. Soil moisture influ- ences the damping depth in a complex way. In dry soils, D increases with moisture, but in wet soils, it may decrease with moisture as soil water may increase the thermal capacity more than the thermal conductivity [Monteith and Unsworth, 1990]. The value of D for organic matter is quite different from that for mineral soils [Monteith and Unsworth, 1990]. We therefore suggest that different values of D be assigned to different soil layers when the multilayer model (equation (18)) is used. 6. Conclusions [29] An analytically integrated daily heterotrophic respi- ration model is developed for the purpose of its temporal scaling in daily ecological models. The scaling model is tested using field data in a mature black spruce stand in Canada. Based on the present study, the following conclu- sions are drawn: [30] 1. With detailed half-hourly measurements of hetero- trophic respiration through root exclusion experiments, we are able for the first time to test the analytical daily model. The model is simple and is shown to be capable of capturing the first order effects of diurnal temperature variability on heterotrophic respiration estimation at daily time steps (as shown in equation (4) and Figure 5). [31] 2. The effect of the diurnal temperature amplitude on heterotrophic respiration estimation at daily steps increases with the Q10 value, and the negative bias error in the daily respiration estimation without considering the diurnal tem- perature variation is highly sensitive to this amplitude, increasing from about 10% at an amplitude of 10C to about 38% at an amplitude of 20C when the vertical distribution of soil carbon is uniform. [32] 3. The diurnal temperature amplitude at the experi- mental site at the high latitude was small (2–12C, with a mean of 7.0C), and the largest negative bias error by ignoring the temperature variation in the daily heterotrophic respiration estimation was less than 15%, with a mean value of 4.5%. [33] 4. 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