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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 2009

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Daily heterotrophic respiration model considering the diurnaltemperature variability in the soilJ. M. Chen,1S. E. Huang,1,2W. Ju,1D. Gaumont-Guay,3and T. A. Black3Received 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 onrespiration is nonlinear, this ignorance may cause considerable errors in respirationestimation, but these errors have not yet been systematically investigated. This is in fact acentral issue in temporal scaling of ecosystem models which are often applied in timesteps equal to or larger than a day. In this study, we develop an integrated dailyheterotrophic respiration model, and demonstrate first theoretically the importance ofconsidering the diurnal amplitude of soil temperature and the vertical soil carbondistribution pattern in daily respiration estimation using the daily mean temperature.Measurements of soil respiration with roots exclusion made in a mature black spruce sitein Saskatchewan, Canada, in July–September 2004 are used to validate the model. Dailyheterotrophic respiration rates were underestimated by up to 15%, with a mean value of4.5%, when only the mean daily temperature was used. This underestimation occurredunder the conditions that the diurnal temperature amplitude in the forest was less than12C176C and the vertical distribution of organic carbon in the top 15–30 cm wasuniform. Based on the integrated daily model, this underestimation at the same site wouldbe 38% if the amplitude increases to 20C176C, and in soils with steep vertical carbondistributions with a 20C176C diurnal amplitude, it can increase to 44%. The magnitude of thisunderestimation is theoretically proportional to [ln(Q10)]2. During the experimentalperiod, the value of Q10for 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 of20C176C.Citation: Chen, J. M., S. E. Huang, W. Ju, D. Gaumont-Guay, and T. A. Black (2009), Daily heterotrophic respiration modelconsidering 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 differentcomponents: rhizosphere (roots and mycorrhizae) respira-tion and heterotrophic respiration from free-living microbes.It provides the main carbon efflux from ecosystems to theatmosphere and is therefore an important component of theglobal carbon balance [Schimel, 1995]. On average, globalheterotrophic respiration emits 68C076.5 Pg CyC01to theatmosphere [Raich and Schlesinger, 1992; Raich and Potter,1995]. Biologists have long used Q10to describe thedependence 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 Q10function assumes an exponential relation-ship between respiration and temperature. In recent years,some studies have sought to establish relationships of soilrespiration with soil moisture and temperature [Lloyd andTaylor, 1994; Thierron and Laudelout, 1996; Davidson etal., 1998; Gulledge and Schimel, 2000; Xu and Qi, 2001a].There is increasing evidence that Q10of soil respiration isnot seasonally constant and tends to decrease with increas-ing temperature and decreasing soil moisture [Rayment andJarvis, 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 otherlimitations, a simple exponential function based on a fixedQ10value of about 2.0 has gained wide acceptance inmodeling regional and global ecosystem respiration andits responses to climate change [Ryan, 1991; Aber andFederer, 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 objectiveof a model is to simulate the total annual soil respiration, anannual model parameterization suffices. However, if thesimulation period is days or weeks, as in the case when soilrespiration is affected by synoptic weather events, a short-term parameterization is required. The need for theseJOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, G01022, doi:10.1029/2008JG000834, 20091Department 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.0148-0227/09/2008JG000834G01022 1of11different parameterizations for different time steps may bedue to the nonlinear response of respiration to temperature.Many models operate at monthly or seasonal or annual timesteps [Parton et al., 1987; Parton and Scurlock, 1993; Penget al., 1998; Cramer et al., 1999; Irvine and Law, 2002;Chen et al., 2003; Rodeghiero and Cescatti, 2005], andeven if some models use daily time steps, they only considervariations from day to day [Russell and Voroney, 1998; Leeet al., 2002] or half-daily [Braswell et al., 2005]. So far,there have been no published works on daily modelsconsidering the effects of the diurnal temperature variationon daily respiration estimation, although there have beennumerous subdaily measurements. As the response ofrespiration to temperature is not linear, the diurnal temper-ature amplitude would have significant influence on dailyrespirationestimationusingdailymeantemperature.Figure1shows that the daily heterotrophic respiration would besignificantly underestimated using the mean daily tempera-tureincomparison withthecorrect valuedetermined throughdaily integration, and this underestimation would increasewith increasing diurnal temperature amplitude. Consideringthis nonlinear effect would, therefore, be an important tem-poral scaling step for daily, monthly and annual respirationmodels, which so far has been ignored.[4] In this paper, we focus on the development of a modelsimulating heterotrophic respiration at daily time steps witha correction for the effect of the nonlinear response ofrespiration to diurnal temperature variation. The objectivesof this paper are: (1) to derive an analytical solution to thedaily integral of heterotrophic respiration for the purpose ofcorrecting the bias of simple Q10models based on dailymean air temperature; (2) to validate this integrated dailymodel using field measurements and to demonstrate theability of this model in capturing the effect of diurnaltemperature variation erotrophic respiration in soilat daily time steps; (3) to investigate the importance of keyparameters, including the diurnal temperature amplitude andthe organic carbon density profile in the soil, in estimatingheterotrophic respiration at daily time steps.2. Daily Model Description2.1. Simple Daily Model of Heterotrophic Respiration[5] In this study, we select the Q10function [Van’t Hoff,1898] to describe the sensitivity of heterotrophic respirationto temperature as follows:Rh¼ R10f TC0C1¼ R10QTC0101010ð1Þwhere Rhis the heterotrophic respiration flux at the meansoil temperature T over an time interval, R10is the rate ofheterotrophic respiration at a soil temperature of 10C176C, andQ10is the temperature sensitivity of heterotrophic respira-tion and is an empirical parameter, representing the relativeincrease of the respiratory flux as temperature increases by10C176C. Equation (1) is often called ‘the Q10model’, which ismost commonly reported in the literature. As the tempera-ture sensitivity of heterotrophic respiration generallydecreases with increasing temperature, the value of Q10would change with temperature, making it seasonallydependent. Although alternatives to Q10have beenproposed by considering the increase in activation energycost with temperature [Lloyd and Taylor, 1994], Q10iscontinuously used in many recent studies [Tjoelker et al.,2008; Wythers et al., 2005] for its effectiveness in capturingthe thermal acclimation effect on respiration.[6] Heterotrophic respiration is also influenced by totalsoil carbon, litter quality, and moisture. In order to developa simple and effective diurnal scaling algorithm, we havechosen to consider the soil carbon vertical profile as anadditional parameter to temperature, while the effects ofother parameters will be evaluated through their associationwith existing model parameters (see section 5). Normally,the soil organic carbon content decreases with depth fromthe soil surface [Jobbagy and Jackson, 2000]. The total soilorganic carbon in the whole soil profile is expressed as:wt¼Zzd0rbzðÞ:wgzðÞdz ¼Zzd0cwzðÞdz ð2Þwhere wtis the total organic carbon per unit surface area(kg mC02), rb(z) is the soil bulk density (kg mC03) at depth z,wg(z) is the weighted fraction of soil organic carbon(kg kgC01), cw(z) is the volumetric organic carbon content(kg mC03), and zd(m) is the lower boundary of the carbon-containing soil depth. The profile of soil organic carbonwith depth can be defined as:wzðÞ¼cwzðÞwtð3Þwhere w(z)isinmC01and can be regarded as a weightingfunction for contributions of soil carbon at various depths.Daily heterotrophic respiration is often calculated usingdaily mean soil temperature (T). Using equation (1) toFigure 1. A schematic showing the difference betweendiurnally integrated daily heterotrophic respiration (Rh,daily)and the approximate daily heterotrophic respiration (~Rh)obtained using the daily mean temperature. Rh,dailyis thecorrect value determined by making the area under thestraight line the same as that under the curve between Tminand Tmax. Rh,dailyand~Rhare different because of thenonlinear relationship between heterotrophic respiration andtemperature.G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION2of11G01022represent the hourly heterotrophic respiration and distribut-ing it with depth using w(z), we can integrate the hourlyvalues with respect to depth and time to obtain the dailyheterotrophic respiration (~Rh):~Rh¼Z240Zzd0wzðÞRsdzdt ¼Z240Zzd0wzðÞR10QTC0101010dzdt ¼ 24R10QT10C0110ð4Þwhere R10represents the total hourly respiration rate at 10C176Cafter integrating w(z) with respect to z, which is timeinvariant 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 thevariations of soil temperature (T) with depth and time canbe ignored. It is therefore considered as an approximation.2.2. Integrated Daily Model of HeterotrophicRespiration2.2.1. Daily Heterotrophic Respiration[7] In order to model the diurnal variation of heterotro-phic respiration caused by the diurnal variation in soiltemperature at different depths, we rewrite equation (4) asfollows:Rh;daily¼Z240Zzd0wzðÞR10QTs z;tðÞC0101010dzdt ð5Þwhere Rh,dailyis the daily total heterotrophic respirationcalculated with diurnally variable soil temperature.Equation (5) is also referred to as an integrated dailyrespiration model, where Ts(z, t) is the soil temperature attime (t) and depth (z). Here, we treat R10and Q10to be sameas those in equation (4).2.2.2. Model for Soil Temperature[8] With the assumption that physical properties of soilare constant with depth, the equation of soil heat conductioncan be expressed as [Monteith and Unsworth, 1990]:@Tsz;tðÞ@¼ k0@2Tsz;tðÞ@z2ð6Þwhere k0is the thermal diffusivity of soil, and Ts(z, t)isthetemperatureatdepthzandtimet.Thesolutionofequation(6)satisfying the boundary condition which describes a harmo-nic oscillation of temperature at depth z is:Tsz;tðÞ¼T þ AzðÞsin wt C0 z=DðÞ ð7ÞwhereT isthemeansoiltemperatureatthesurface,w=2p/24(hC01) is the angular frequency of the oscillation for dailycycles, A(z)=A(0)exp(C0z/D) is the amplitude of soiltemperature at depth z, A(0) = Acosf is the amplitude at thesurface, A is the air temperature amplitude, f =tanC01(2pt/p)is a phase lag, p is the period of the temperature oscillation,and D =(2k0/w)0.5is the damping depth. For p =24h,f issmall and A(0) C25 A since the time lag (t) of temperatureoscillation from the air temperature is close to zero at the soilsurface. So we can present A(z) as follows:AzðÞC25Aexp C0z=DðÞ ð8ÞCombining equation (7) with equation (5), the total dailyheterotrophic respiration with explicit consideration of thetemperature variations with time and depth in the soil can bewritten as:Rh;daily¼Zzd0Z240wzðÞR10QTs z;tðÞC0101010dzdt¼Zzd0Z240wzðÞR10QTþAzðÞsin wtC0z=DðÞC0101010dzdt¼Zzd0R10wzðÞZ240QTþAexp C0z=DðÞsin wtC0z=DðÞC0101010dzdt ð9Þ¼ R10QT10C0110Zzd0wzðÞZ240QAexp C0z=DðÞsin wtC0z=DðÞ1010dzdt2.2.3. Variation of Soil Organic Carbon With Depth[9] In this study, the contribution of soil at depth z to thetotal heterotrophic respiration is mainly controlled by theorganic carbon amount cw(z). Based on Grant et al. [2005],who provided observed data at three boreal forest sites inCanada, the variation of soil organic carbon with depth canbe generally described using an exponential function(Figure 2):cwzðÞ¼c0eC0kzð10Þwhere c0is the volume organic carbon content at soilsurface, a constant for a given site, k is a constantdetermining the decay rate of organic carbon content withsoil depth. Substituting equation (10) into equation (3), theweight function can be rewritten as:wzðÞ¼cwzðÞwt¼c0wtC1 eC0kzð11ÞFigure 2. Organic carbon content changes with soil depthat the study site (old black spruce [Grant et al., 2005]).G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION3of11G01022We can also calculate the total organic carbon through thesoil depth aswt¼Zzd0cwzðÞdz ¼Zzd0c0eC0kzdz ¼c0k1C0 eC0kzdC0C1ð12ÞThis simple vertical weighting scheme is derived under theassumption that the vertical distribution of soil carbonfollows a single decay rate k.2.2.4. Integrated Daily Model of HeterotrophicRespiration With Consideration of Diurnal TemperatureVariation[10] After using w =(2p/24) in equation (9) and trans-forming the variables, we obtain the following integratedresult for daily heterotrophic respiration:Rh;daily¼ R10QT10C0110Zzd0wzðÞZ240QAexp C0z=DðÞsin2p24tC0z=DðÞ1010dzdt¼ 24R10QT10C0110Zzd0wzðÞZ10QAexp C0z=DðÞsin 2pxC0z=DðÞ1010dzdx ð13Þ¼ 24R10QT10C0110Zzd0wzðÞZ10elnQ1010Asin 2pxC0z=DðÞexp C0z=DðÞdzdxAfter making the third order Taylor series expansion of theexponential function in equation (13), it can be expressedas:Rh;daily¼ 24R10QT10C0110Zzd0wzðÞdzZ10C1 1þlnQ1010Asin 2px C0 z=DðÞexp C0z=DðÞC20þlnQ10ðÞ2200A2sin22px C0 z=DðÞexp2C0z=DðÞ#dx¼ 24R10QT10C0110Zzd0wzðÞþlnQ10ðÞ2400A2wzðÞexp C02z=DðÞ !C1 dz ð14ÞNote thatR10sin (2px C0 z/D)dx = 0 andR10sin2(2px C0 z/D)dx =1. Based on the single decay rate assumption for soilcarbon, i.e., equations (11) and (4), equation (14) can bewritten as:Rh;daily¼ 24R10QT10C0110þ 24R10QT10C0110Zzd0lnQ10ðÞ2400A2wzðÞC1 exp C02z=DðÞdz¼~Rh1 þC0A2lnQ10ðÞ2400wtk þ2=DðÞ1C0 eC0 kþ2=DðÞzdC16C17 !ð15ÞIt is noted that A in equation (15) in its final form is thediurnal temperature amplitude at the soil surface, not at themean soil depth. In this way, the temperature variations inall depths are considered in this integrated result. As A isvery close to the diurnal amplitude of air temperature nearthe surface, it can be determined using the air temperature asa close approximation.[11] Equation (15) is an integrated daily model for het-erotrophic respiration with consideration of the diurnaltemperature variability at various depths and the organicmatter profile in the soil. The second term in the bracketsresults from the nonlinear effect of temperature on hetero-trophic respiration, i.e., the relative difference betweenRh,dailyand~Rhshown in Figure Special Cases of Integrated Daily HeterotrophicRespiration Models2.2.5.1. 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 themineral soil. As this organic layer, originating mostly fromlitter falls and fine-root and moss turnovers, is the mainsource of heterotrophic respiration, the decay rate of organiccarbon with soil depth (k) from the top of this organic layeris set to zero in analyzing our experimental data, i.e., settingwt= c0(zdC0 z0) (equation (13)) and k = 0 in equation (15),which is then simplified to:Rh;daily¼~Rh1 þDA2lnQ10ðÞ2800zd1 C0 eC02Zd=DC16C17 !ð16ÞAssigning DRh=DA2ln2Q10800zd(1 - eC02Zd=D), equation (16) can berewritten as:Rh;daily¼~Rh1þDRhðÞor Rh;daily=~Rh¼ 1 þDRhðÞð17Þwhere DRhis a term correcting for the bias of dailyheterotrophic respiration estimation without considering thediurnal soil temperature variations. This correction isproportional to the square of the diurnal temperatureamplitude. In our research, we regard Rh,dailyas the correctdaily heterotrophic respiration (calculated by the integrateddaily model given in equation (15)), and~Rhis anapproximation (equation (4)) to be corrected using thecorrection term. Thus,~Rhreflects the effects of mean dailytemperature, and Rh,dailyincludes the effects of both averagedaily temperature and diurnal temperature amplitude. Variable Soil Carbon Profiles at DifferentDepths[13] For cases, where the soil organic carbon contentprofile cannot be well described by a single decay rate k,such as the case, where a litter/organic layer overlaying themineral soil, or the total soil column has two or three layerswith different carbon decay rates, the following equationcan be used to estimate the nonlinear effect:DRh¼A2lnQ10ðÞ2400Xni¼1wikieC0ziC01kiC01þ2=DiC01ðÞC0 eC0zikiþ2=DiðÞkiþ2=DiðÞ1 C0 eC0kiDziðÞð18Þwhere kiis the decay rate of the ithlayer of soil, wiis theweight of carbon in soil layer i to the total soil carbon, Diisthe thermal damping depth for soil layer i, Dziis theG01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION4of11G01022thickness of the ithsoil layer, and ziis the lower boundary(depth) of the ithlayer. As there is no layer 0, the initialvalues of k and z are: k0= 0 and z0= 0. Equation (18) isderived similarly to equation (15), allowing the thermaldamping depth to vary vertically to consider differentmaterials and soil moisture contents in different soil layers.It will be used for parameter sensitivity analysis shown insection 5.3. Experimental Data and ModelParameterization3.1. Site Description and Physical and BiologicalProperties[14] This study makes use of experimental data collectedin a black spruce (P. mariana) stand (125 years old in 2004)located at the southern edge of the boreal forest in centralSaskatchewan, Canada (54.0C176N, 105.1C176W), which is oftencalled the South Old Black Spruce Site for the BorealEcosystem-Atmosphere Study (BOREAS). The forest flooris covered by mostly (70%) feather mosses (Hylocomiumsplendens, Pleurozium schreberi) in wetter areas and bypatches Sphagnum moss (Sphagnum spp.) and lichen(Cladina spp.) in drier area. Beneath the moss layer is anapproximately 20-cm organic layer (including O and Phorizons) overlying a waterlogged sandy clay (includingA, B and C horizons). The drainage at the site is poor. Meanfine-root biomass (<2 mm) to a depth of 40 cm is 3.3 ±1.0 Mg dry matter haC01(average for 2003–2004) [Kalynand Van Rees, 2006]. The physical and biological propertiesof this site [Grant et al., 2001] are shown in Table 1. The30-year mean annual air temperature and precipitationmeasured at a climate station located 80 km away (1934–1990, Waskesiu Lake, 53.6C176N, 106.1C176W) are 0.3C176C and456 mm, respectively. Boreal forests globally occupy about20 M km2of the land surface, and black spruce is the mostdominant boreal species [Hall et al., 2004]. The results fromthis study would therefore be significant for the globalcarbon cycle estimation. The thick organic layer on top ofthe mineral soil found at our study site is typical of blackspruce forests. Because of the thermal insulation effect ofthis layer, the diurnal temperature amplitude in the soilunder the forest cover is relatively small compared withother forest types, and the magnitude of the temporalscaling effect on heterotrophic respiration estimation foundin our study would therefore represent the lower bound ofthis effect globally.3.2. Experimental Data for Model Validation[15] The half-hourly measurements of heterotrophic res-piration through root-exclusion experiments were conductedin 2004 [Gaumont-Guay et al., 2008]. Two pairs of controland root-exclusion plots (2 m C2 2 m) were installed in thefall of 2001. In each square plot, trenches were dug at theedges to a depth of 75 cm to exclude all live tree roots, andthe trench walls were covered with four sheets of polyeth-ylene film (100 mm thick) to prevent the penetration of newroots. The trenches were then backfilled with the excavatedsoil. Two additional pairs of plots were installed in Sep-tember 2003 following the same procedure, bringing thenumber of replicates per treatment to four.[16] Continuous half-hourly measurements of soil CO2efflux were conducted during the growing season of 2004,although only the data acquired in July–September 2004are used in this study to minimize the possible pulse of deadroot decomposition which may last several months aftertrenching [Lee et al., 2003]. Gaumont-Guay et al. [2008]found that the residual dead root decomposition lingered formore than a year, and therefore the heterotrophic respirationdata from the two pairs of plots installed in 2003 wouldcontain a small fraction from dead root decomposition (notquantified), while measurements in the other two pairsinstalled in 2001 would be free from this effect. Thecontribution of the remaining slow root decomposition tothe measured heterotrophic respiration could be partly offsetby the removal of rhizomicrobial respiration by heterotrophsassociated with the cut roots. Live root rhizomicrobialrespiration was found to contribute 32% to the total rootrespiration of a meadow fescue [Johansson, 1992]. Meas-urements were made with a nonsteady state automatedchamber system. The chambers consisted of a domed-shaped transparent lid (52.5 cm diameter C2 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 pneumaticcylinder assembly (Model BFT-173-DB, Bimba Manufac-turing Company, Machesney Park, IL, USA) connected toan air compressor (Model CPFAC2600P, Porter Cable,Jackson, TN, USA). About 92% of the time, the lid wasopen to allow rain and litter to fall into the collar area. Thesystem measured the increase of CO2concentration in thechamber headspace over a 2.5-min interval sequentially forthe eight chambers, allowing all chambers to be measuredonce every half-hour. When a chamber was selected, the airwas circulated between the chamber and a closed-pathinfrared gas analyzer (IRGA, Model LI-6262, LI-CORInc., Lincoln, NE, USA) with an AC linear pump (ModelTable 1. Physical and Biological Properties of the Soil at the Old Black Spruce SiteaDepth(m)Bulk Density(Mg mC03)qC00.03Mpa(m3mC03)qC01.5Mpa(m3mC03)Sand(g kgC01)Silt(k kgC01)Organic Carbon(g kgC01)PHOrganic Nitrogen(mg kgC01)Organic Phosphate(mg kgC01)0.01 0.10 0.40 0.20 0 0 434 3.4 8162 9000.05 0.10 0.40 0.20 0 0 434 3.4 8162 9000.15 0.10 0.40 0.20 0 0 434 3.4 8162 9000.30 0.10 0.40 0.20 0 0 434 3.4 8162 9000.47 1.52 0.213 0.049 728 214 9.8 4.3 423 530.72 1.66 0.183 0.05 646 287 3.6 4.9 215 270.96 1.66 0.022 0.012 960 19 1.0 5.8 52 71.20 1.66 0.034 0.013 949 30 0.5 6.6 52 7aAbbreviations are as follows: qC00.03Mpa, field capacity; qC01.5Mpa, wilting point. Reference data from Grant et al. [2001].G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION5of11G01022SPP-15EBS-101, Gast Manufacturing, Benton Harbor, MI,USA). A small fan ensured the air in the chamber was wellmixed. The IRGA was located in a thermally controlledhousing with a constant temperature at 38C176C. The IRGAwas calibrated daily using CO2-free nitrogen gas (offsetcalibration) and a dry air gas of known CO2concentration atC24370 mmol molC01(gain calibration). Both were from gascylinders calibrated against a standard from the Meteoro-logical Service of Canada, Downsview, ON, Canada. Half-hourly soil CO2efflux (Fcs, mmol CO2mC02sC01)wascalculated using the following equation:Fcs¼ raVeAdscdt; ð19Þwhere rais the density of dry air in the chamber headspace(mol mC03), Veis the effective volume of the chamber (m3),A is the area of ground covered by the chamber (m2), anddsc/dt is the time rate of change of the CO2mixing ratio inthe chamber headspace over a 1-min interval following lidclosure (mol CO2molC01dry air sC01). The Vevalue differsfrom the geometrical volume of the chambers because ofmoss porosity. It was measured daily using a gas injectiontechnique described in detail by Drewitt et al. [2002] and byGaumont-Guay et al. [2006].[17] Compared with the control plots without root exclu-sion, heterotrophic respiration determined in plots with rootexclusion was 40.6% of the total soil respiration. As rootrespiration was not only influenced by temperature but alsoby tree biological activities, they were excluded in thisstudy. Most ecosystem models handle heterotrophic androot respiration separately, and therefore each of thesecomponents needs to be individually studied. Moss photo-synthesis and respiration were removed from the measure-ments through taking the difference between control androot-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 thisway, the CO2flux due to heterotrophic respiration only wasobtained. Each flux value at a given time is the average ofmeasurements of four plots. The hourly meteorological dataare compiled from the data archive of Fluxnet-Canadawebsite (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 determinedthrough data fitting (see Table 2). Based on daily soiltemperature at 2 cm depth, we found different values ofQ10and R10in different months. The values of Q10are 4.0,4.4 and 4.5 in July, August and September, respectively.The corresponding R10values are 1.66, 1.77 and 1.96 gCmC02dC01, respectively. Gaumont-Guay et al. [2006] showedthat the Q10value for nighttime soil CO2efflux during thegrowing season was 3.1, and R10was 1.9 at the site. Theremay be several reasons for the Q10values derived from thechamber data to be considerably larger than the conven-tional value of 2.0: (1) the substrate active layer thicknessincreased with soil temperature, i.e., not only the microbialactivity but also the total organic matter involved inrespiration increased with temperature, causing a largersensitivity to temperature than usually predicted with aconstant substrate; (2) sensitivity to soil temperature isusually larger than that to air temperature [Kicklighter etal., 1994]; (3) the dynamic of soil temperature was rela-tively small in a month relative the natural variability in themeasured Rh, causing errors in Q10determination; and (4)possible measurement errors using soil chambers based onnonsteady state methods [Pumpanen et al., 2004].Gaumont-Guay et al. [2006] found a smaller value ofQ10= 3.1 because it represents the whole growing seasonincluding May and June. It also indicates the possibility oflarger errors in Q10determination over shorter periods(reason 3 above).4. Results4.1. Sensitivity of Heterotrophic Respiration toTemperature at Different Soil Depths[19] To model the diurnal variation of heterotrophicrespiration, we calculated the average daily air temperatureand soil temperature using the half-hourly observed data.We also processed the observed half hourly heterotrophicrespiration rates in each day to obtain the daily rate. Soilrespiration from the root-exclusion treatment shows differ-ent temperature sensitivities at different soil depths. In thisresearch, we use equation (1) and analyze the relationshipbetween heterotrophic respiration and soil temperature atdifferent soil depths using half-hourly measurements duringthe peak growing season. The results indicate that there aregood exponential correlations between heterotrophic respi-ration and soil temperature at 2 cm and 5 cm soil depth, butat 10 cm depth the correlation is not significant (Table 3 andFigure 3).[20] Based on half-hourly measurements of heterotrophicrespiration and soil temperature at different soil depths, weTable 2. Parameters at the Old Black Spruce Site for Heterotrophic Respiration CalculationSymbol Unit Description ValueGeneralw hC01Angular frequency 2p/24k010C06m2sC01Thermal diffusivity 0.13D cm Damping depth 5.98zdcm Soil depth contributing to heterotrophic respiration 15c0kg mC03Organic carbon at the soil surface 43.4k cmC01Decay rate of organic C with depth 0RespirationQ10unitless Temperature sensitivity of heterotrophic respiration 4.0–4.5R10gC mC02dC01Heterotrophic respiration at soil temperature of 10C176C 1.66–1.96G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION6of11G01022estimated monthly Q10values from regression analysis. Asthe soil temperature varied with depth while the total respi-ratoryfluxwasthedepth-integratedresult,thesevaluesvariedin a large range from 2.77 to 6.22 with depth from 2 cm to10cm,inconfirmationwithpreviousstudies[Gaumont-Guayetal.,2006].At2cm,thesemonthlyQ10valuesvaryfrom4.0and 4.5 in the July–September period, which are used in ourfinal analysis. Equation (15) shows that the error in dailyheterotrophic respiration estimation without considering thediurnal temperature variation is proportional to (lnQ10)2, andit is therefore important to represent the seasonal variation inQ10in the integrated daily model.4.2. Heterotrophic Respiration Modeling Results[21] The soil temperature at 2 cm soil depth is used tomodel the heterotrophic respiration obtained from the root-exclusion experiment. The average daily soil temperature,the amplitude of the air temperature at 1 m above thesurface, and average heterotrophic respiration are calculatedfrom 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 ofthe diurnal temperature variation. These two sets of mod-eled results are compared with measurements of dailyheterotrophic respiration obtained as the summation of halfhourly observations within the 24 h (Figure 4). In thecomparison, the root mean square error (RMSE) was usedas a criterion to evaluate the model performance (seeTable 3), i.e.,RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1xiC0 yiðÞ2nvuuutð20Þwhere xiand yiare the modeled and measured values,respectively, and n is the number of days. The values fromthe simple daily model have a relatively small slope in theregression between measured and modeled values and arelatively high value of RMSE for monthly and growingseason simulations (Table 4). Some of the scatter is due toirregular subdaily variations in weather conditions, espe-cially in days when it was raining and had a large variationof temperature. The R2values are 0.78 and 0.79 forintegrated and simple daily models, respectively.4.3. Effects of Diurnal Amplitude of Temperature onHeterotrophic Respiration[22] To show the importance of the diurnal amplitude oftemperature on daily heterotrophic respiration estimation,we investigate the ratio Rh,daily/~Rhbetween uncorrected andcorrected daily values as a function of the diurnal temper-ature amplitude at the soil surface (taken as that of the airtemperature near the surface, Figure 5).~Rhis the daily totalheterotrophic respiration using the simple daily respirationmodel after finding Q10and R10from the experimental datafor each month, and Rh,dailyis estimated using the integrateddaily model (equation (15)).[23] This ratio indicates the extent of the bias error in thedaily respiration model without considering the diurnaltemperature variation. As mathematically described inequation (14), the effect of this amplitude on the diurnalvariation of heterotrophic respiration increases with (lnQ10)2and the negative bias error is highly sensitive to the diurnalamplitude at the soil surface, increasing from about 10% atan amplitude of 10C176C to about 38% at an amplitude of 20C176Cwhen k = 0 and Q10= 4.0. The actual values of Rh,daily/~Rhfound from the experimental data sets are also shown inFigure 5. The diurnal amplitude at the experimental site atthe high latitude is generally small (2–12C176C with a mean of7.0C176C), and the maximum bias error (underestimation) inthe daily heterotrophic respiration estimation is less than15%, with a mean of 4.5%. This error may appear to besmall, but it is highly significant as 4.5% of the globalheterotrophic respiration of 68–76.5 Pg CyC01[Raichand Schlesinger, 1992] is larger than the current terrestrialcarbon sink [Canadell et al., 2007]. However, comparedwith the temporal scaling of daily photosynthesis [Chen etal., 1999], this nonlinear effect on respiration scaling isconsiderably smaller. Although field measurements of het-erotrophic respiration generally have errors much largerthan the scaling error found in our study, the scalingmethodology 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 ofTable 3. Exponential Fits Between Heterotrophic RespirationObtained Through Root-Exclusion Experiments and Soil Tem-perature at Different Soil Depths With Half-Hourly MeasurementsDuring the Peak Growing SeasonaSoil Depth(cm) Fitted Equation R2(Regression Coefficient)2 Rs= 0.6442exp (0.1025Ts) 0.6815 Rs= 0.5566exp (0.1231Ts) 0.62310 Rs= 0.6730exp (0.1132Ts) 0.221aJuly–September 2004. Rsis soil respiration for root exclusion with half-hourly measurements (mmol), and Tsis soil temperature (C176C). Exponentialfits from equation (1).Figure 3. Relationship between heterotrophic respirationand soil temperature at 2 cm soil depth with half-hourlymeasurement data during the peak growing season (July–September 2004).G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION7of11G01022respiration derived from measurements while their absolutevalues are adjusted through spin-up procedures.5. Discussion5.1. Influences of Q10and the Vertical Decay Rate (k)of Soil Carbon[24] The integrated daily model (equation (15)) demon-strates a general relationship between Rh,dailyand diurnaltemperature amplitude (A) at different values of k and Q10.Based on the integrated daily model, Figure 6 demonstratesthat this error is also sensitive to the k value, increasing from38% at k = 0 (cmC01) to 44% at k =0.03(cmC01)atA =20C176Cand Q10= 4, or from 10% at k =0(cmC01) to 11% at k = 0.03(cmC01)atA =20C176C and Q10= 2. The mathematical form ofthis sensitivity with k is exponential as shown inequation (15). Physically, this sensitivity is caused by thefact that the diurnal temperature amplitude decreases expo-nentially with depth. With a damping depth of 6 cm, theamplitude can decrease from 10C176C at the surface to 4.3C176Cat5 cm and to 0.8C176C at 15 cm. The vertical distribution of soilcarbon is therefore also important in the temporal scaling ofthe heterotrophic respiration. Based on Grant et al. [2005]who provided soil organic carbon contents at various depthsat two sites, the Old Aspen and the Old Jack Pine ofBOREAS, we estimated the k values to be 0.0215 and0.0415 cmC01at these two sites, respectively. These nonzerok values suggest that the error in the simple daily respirationestimation (equation (1)) could be significantly larger atthese two sites. This sensitivity of daily respiration estima-tion to the soil carbon profile suggests that considering thevertical distribution of organic carbon in soil can signifi-cantly improve of our current daily, monthly and annualrespiration models of heterotrophic respiration.5.2. Influences of Multiple Soil Layers With DifferentVertical Decay Rates[25] The experimental data used in this study wereobtained from a forest stand with a thick organic layer(15–30 cm) on top of the mineral soil. As most carbon inthe soil is located in this organic layer which have a fairlyuniform carbon density, the simple treatment of k = 0 was agood approximation. The multilayer model (equation (18))can be used to assess the error due to ignoring the verticalcarbon distribution pattern in the mineral soil. Assuming theorganic layer has a thickness of 15 cm with weight w1=0.8and decay rate k =0cmC01and the mineral soil has athickness of 50 cm with w2= 0.2 and k = 0.03 cmC01,itisfound from equation (18) that the Rh,daily/~Rhratio at adiurnal air temperature amplitude of 10C176C would be1.077, which is about 2% less than the value of 1.095 withthe simple treatment of k = 0 for the organic layer only.Under this two-layer treatment, the ratio is reduced becauseof the contribution of the deeper layer with smaller diurnaltemperature variation to the total heterotrophic respiration.[26] In ecosystems with a moderate organic/litter layerand a carbon-rich mineral soil layer, a similar two-layertreatment can be made to equation (18). If we assume thatFigure 4. The comparison of modeled and measured daily heterotrophic respiration during the growingseason for the root-exclusion treatment at the Black Spruce site.Table 4. Root Mean Square Errors of the Modeling Results inDifferent Months in 2004 at the Old Black Spruce SiteaMonthIntegrated Daily Model Simple Daily ModelSlope Intercept RMSE Slope Intercept RMSEJul. 0.9235 0.1554 0.2685 0.9092 0.0683 0.2770Aug. 0.8710 0.2533 0.2541 0.8504 0.1544 0.2606Sep. 0.8649 0.1560 0.1669 0.8784 0.0738 0.1934Growing season 0.9319 0.0906 0.2281 0.9124 0.0419 0.2418aRMSE, root mean square errors.G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION8of11G01022the organic layer has a thickness of 5 cm with k = 0 and w1=0.2 and that the carbon-containing soil mineral layer has athickness of 30 cm with k = 0.03 and w2=0.8,theRh,daily/~Rhratio at a diurnal air temperature amplitude of 10C176C andQ10= 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 = 0.03and w1= 1.0, the ratio is increased to 1.067. This is becausewithout the thermal damping effect the diurnal temperatureamplitude in the mineral soil would increase. The differencein k between the two layers causes less than 1% differenceFigure 5. The relationship between the ratio Rh,daily/~Rhand temperature amplitude at different Q10values when the decay rate (k) of organic C content with depth is zero. The pluses indicate the actualvalues of Rh,daily/~Rhcalculated using Q10and R10found 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/~Rhand temperature amplitude at different decayrates (k,cmC01ganic C content with depth for Q10= 2.0, Q10= 3.0, and Q10= 4.0.G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION9of11G01022in the ratio. It is also noted from Figure 6 that the nonlinearcorrection, i.e., the Rh,daily/~Rhratio, is more sensitive to Q10and than to k within a realistic range. This implies thatfor general purposes, a 1-layer model with a constant kvalue would be useful for the first order correction of thisnonlinear effect. The error caused by the k variation withdepth would generally be less than 2–3% of the totalheterotrophic respiration.5.3. Influences of Litter Quality and Soil Moisture[27] In our study, we have only considered the verticaldistribution of the total soil carbon without paying specificattention to the quality of the litter and organic matter. Ingeneral, soil carbon becomes more recalcitrant (longerturnover time) in deeper layers [Trumbore et al., 1996].The influence of this carbon quality variation with depth canincrease the nonlinear effect, and this increased effect can beeffectively considered by either decreasing the effectivecarbon-containing soil depth (i.e., zdin equations (15) or(16)) or increasing the k value, to allow the more labilecarbon closer to the soil surface more exposed to diurnaltemperature variation. In our current study, we found thebest fit with experimental data when the lower bound valueof zd= 15 cm (Table 2) was used, and this may be due to thelitter quality variation with depth.[28] Soil moisture not only affects the total heterotrophicrespiration but also the thermal diffusivity that influencesthe thermal damping depth used in the model. While theinfluence on the total heterotrophic respiration does notchange the relative Rh,daily/~Rhratio, the influence on thedamping depth can cause a considerable error in the ratio. Inthe example of one layer soil with a thickness of 30 cm andk = 0.03, an increase of the damping depth D from 6 cm to8 cm would cause the ratio to increase from 1.067 to 1.087because a larger damping depth would allow the diurnalthermal wave to penetrate deeper into the soil, causing alarger nonlinear effect on respiration. Soil moisture influ-ences the damping depth in a complex way. In dry soils, Dincreases with moisture, but in wet soils, it may decreasewith moisture as soil water may increase the thermalcapacity more than the thermal conductivity [Monteithand Unsworth, 1990]. The value of D for organic matteris quite different from that for mineral soils [Monteith andUnsworth, 1990]. We therefore suggest that different valuesof D be assigned to different soil layers when the multilayermodel (equation (18)) is used.6. Conclusions[29] An analytically integrated daily heterotrophic respi-ration model is developed for the purpose of its temporalscaling in daily ecological models. The scaling model istested using field data in a mature black spruce stand inCanada. 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, weare able for the first time to test the analytical daily model.The model is simple and is shown to be capable of capturingthe first order effects of diurnal temperature variability onheterotrophic respiration estimation at daily time steps (asshown in equation (4) and Figure 5).[31] 2. The effect of the diurnal temperature amplitude onheterotrophic respiration estimation at daily steps increaseswith the Q10value, and the negative bias error in the dailyrespiration estimation without considering the diurnal tem-perature variation is highly sensitive to this amplitude,increasing from about 10% at an amplitude of 10C176Ctoabout 38% at an amplitude of 20C176C when the verticaldistribution of soil carbon is uniform.[32] 3. The diurnal temperature amplitude at the experi-mental site at the high latitude was small (2–12C176C, with amean of 7.0C176C), and the largest negative bias error byignoring the temperature variation in the daily heterotrophicrespiration estimation was less than 15%, with a mean valueof 4.5%.[33] 4. Based on the temporal scaling model, the negativebias error in daily respiration estimation using the dailymean temperature is also somewhat sensitive to the verticaldistribution of the soil carbon, the thermal diffusivityaffecting the thermal damping depth, and the effective soilcarbon-containing depth. A complete multilayer model isalso developed to evaluate the effects on these parameterson daily heterotrophic respiration estimation.[34] Acknowledgments. This research was part of the Fluxnet Can-ada Research Network supported by the Canadian Foundation for Climateand Atmospheric Sciences, the Natural Science and Engineering Council ofCanada, and BIOCAP Canada. S. E. 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(huangshue99@hotmail.com)G01022 CHEN ET AL.: TEMPORAL SCALING OF DAILY RESPIRATION11 of 11G01022


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