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Comparison of regional carbon flux estimates from CO2 concentration measurements and remote sensing based.. Chen, Baozhang; Chen, Jing M.; Mo, Gang; Black, T. Andrew; Worthy, Douglas E. J. 2008-05-31

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Comparison of regional carbon flux estimates from CO2concentrationmeasurements and remote sensing based footprint integrationBaozhang Chen,1Jing M. Chen,1Gang Mo,1T. Andrew Black,2and Douglas E. J. Worthy3Received 1 June 2007; revised 7 September 2007; accepted 7 December 2007; published 7 May 2008.[1] Quantification of terrestrial CO2sources and sinks at regional scales (C24102–106km2)is fundamental to improving our understanding of the terrestrial carbon cycle. Twoindependent methods to extract the gross primary productivity (GPP) from atmosphericCO2concentration measurements were explored and compared in this study. Themethods are (1) planetary boundary layer (PBL) carbon budget analysis that allows theestimation of regional GPP at daily time steps from hourly CO2concentrationmeasurements and (2) spatially explicit hourly carbon cycle modeling based on remotesensing and then integrating the daily flux field with a concentration footprintfunction depending on wind and stability. These methods have been applied to a 28-mtower at an old black spruce site near Candle Lake (C24100 km NE of Prince Albert:53.98717C176N, 105.11779C176W). The estimates of daily GPP by these two approaches agreedwell for 2003 (slope = 0.99; r2= 0.89). In order to test these methods of inferring theregional GPP from mixing ratio measurements, we also compared the estimates ofregional GPP with estimates made using eddy covariance (EC) flux measurements,although their respective source areas are different. They had similar seasonal patterns,but the regional estimates were consistently smaller than the local EC flux derived GPPthroughout the growing season in 2003. These estimates of annual regional GPP were649–664 g C mC02for 2003 while the EC-derived annual GPP was 819–847 g C mC02.The annual difference was about 20–25%. The EC flux footprint of the tower wasrelatively homogeneous old black spruce while the concentration footprint, which was afew orders of magnitude larger than the flux footprint, covered boreal evergreen anddeciduous broadleaf forests, grassland, cropland, and lakes. Nonforested land occupiedabout 10–50% of the concentration footprint depending on wind direction and speed andwas less productive than the black spruce forest. The discrepancies between regional andlocal GPP estimates reflected the differences in underlying land surfaces representedby the different footprint areas.Citation: Chen, B., J. M. Chen, G. Mo, T. A. Black, and D. E. J. Worthy (2008), Comparison of regional carbon flux estimates fromCO2concentration measurements and remote sensing based footprint integration, Global Biogeochem. Cycles, 22, GB2012,doi:10.1029/2007GB003024.1. Introduction[2] Ecosystem functioning and its role in the carbonbalance are much better understood than before as a resultof measuring and analyzing energy and CO2fluxes made atsites using the eddy covariance (EC) technique [Baldocchiet al., 2001]. Direct measurements of the terrestrial carbonflux using these techniques have nearly continuous temporalcoverage at an increasing number of sites across continents[Black et al., 1996; Baldocchi et al., 2001]. EC measure-ments are a rich source of information on temporal vari-ability and environmental controls of CO2exchangebetween the atmosphere and terrestrial ecosystems [Law etal., 2002]. However, EC measurements under Fluxnetprograms represent only a very small fraction of the landarea, typically less than 1–3 km2for each site.[3] The atmosphere integrates surface fluxes over manytemporal and spatial scales and links scalar sources andsinks with concentrations and fluxes. This principle hasbeen successfully used to develop inverse models to esti-mate annual carbon budgets [Tans et al., 1990; Enting et al.,1995; Fan et al., 1998; Bousquet et al., 1999; Gurney et al.,2002]. However, because of model limitations and paucityGLOBAL BIOGEOCHEMICAL CYCLES, VOL. 22, GB2012, doi:10.1029/2007GB003024, 20081Department of Geography and Program in Planning, University ofToronto, Toronto, Ontario, Canada.2Biometeorology and Soil Physics Group, Faculty of Land and FoodSystems, University of British Columbia, Vancouver, British Columbia,Canada.3Air Quality Research Branch, Meteorological Service of Canada,Toronto, Ontario, Canada.Copyright 2008 by the American Geophysical Union.0886-6236/08/2007GB003024$12.00GB2012 1of15of continental CO2observations these studies have yieldedcarbon fluxes only at coarse resolution, over large spatialregions (i.e., at continental scale [Rodenbeck et al., 2003]).[4] Progress in carbon balance studies has been achievedat the extreme ends of the spatial-scale spectrum, eitherlarge continents (larger than 106km2, e.g., global inversemodeling) or small vegetation stands (less than 1–3 km2,e.g., EC measurements). Methods to estimate CO2sourcesand sinks at the intermediate scale between continental andlocal scales are notably lacking. Moreover, the carbon cyclein different regions can vary markedly in response tochanging climate [Friedlingstein et al., 2003; Fung et al.,2005]. Reliable estimates of terrestrial CO2sources andsinks at intermediate spatial scales (finer than those used inglobal inversions and larger than local EC flux measure-ments and roughly defined as the range between 102and106km2) are required to quantitatively account for the largespatial variability in sources and sinks in the near-field of ameasurement location [Gerbig et al., 2003], as well asfundamental to improving our understanding of the carboncycle [Crevoisier et al., 2006].[5] It is extremely unreliable to upscale stand-level fluxes(i.e., EC measurements) to a region by simple spatialextrapolation and interpolation because of the heterogeneityof the land surface and the nonlinearity inherent in eco-physiological processes [Levy et al., 1999]. It is alsochallenging to apply atmospheric inversion technique toregional scales for quantifying annual carbon budgets be-cause at such intermediate scales the atmosphere is oftenpoorly constrained [Gloor et al., 1999; Matross et al.,2006]. Moreover, aggregation errors and errors in atmo-spheric transport, both within the boundary layer andbetween the boundary layer and free troposphere, can alsobe formidable obstacles to using these approaches to obtainquantitative estimates of regional carbon fluxes [Lin et al.,2006]. Hence, there is a strong motivation to developmethods to use atmospheric observations to quantify andvalidate estimates of the carbon balance at these intermediatescales [Lin et al., 2006; Bakwin et al., 2004; Matross et al.,2006; J. M. Chen et al., 2007]. Observations of CO2overthe continent within the atmospheric boundary layer reflectexchange processes occurring at the surface at a regionalscale (102–105km2). The flux information contained inCO2concentrationdatarepresentsfootprintsofupto105km2[Gloor et al., 2001; Lin et al., 2004], which are severalorders of magnitude larger than the direct EC flux footprint.This information is therefore much needed in our effort toupscale from site to region. Moreover, the number of CO2mixing ratio measurements above the land surface, made byeither tower or aircraft, is steadily increasing. Previousefforts to interpret the signal of regional CO2exchangemaking use of tower concentration data have focused onsimple one-dimensional planetary boundary layer (PBL)budgets that rely on gradients in CO2concentrations be-tween the boundary layer and the free troposphere [Bakwinet al., 2004; Helliker et al., 2004]. These methods arelimited to monthly resolution because of the need to smoothand average over several synoptic events [Matross et al.,2006].[6] The objective of this study is to explore pragmatic andreliable methods to extract the gross primary productivity(GPP) from atmospheric CO2concentration measurementson the basis of PBL analysis. Making use of an integratedecosystem-boundary layer model for simulating ecosystemfluxes and atmospheric diffusion [Chen et al., 2004], wehave previously developed a PBL carbon budget method-ology that allows the estimation of regional GPP on a dailybasis from hourly concentration measurements [B. Chen etal., 2006a, 2006b; J. M. Chen et al., 2007]. As part of thisstudy, we develop another novel methodology to retrieveregional GPP by superimposing the daily concentrationfootprint on the underlying daily GPP field simulated usinga spatially explicit ecosystem model driven by remotesensing inputs. The comparisons of these two independentregional GPP estimates, i.e., one is concentration derivedand the other is concentration footprint integrated, havebeen made for a 28-m tower at an old black spruce site nearWhite Swan Lake, Saskatchewan Canada. From this study,we seek to address the following questions. (1) How well dothe estimates of regional GPP from these two independentmethods match each other? (2) How well do both methodsof deriving regional GPP compare with EC-derived localGPP and what are the reasons? (3) Are these methodologiesapplicable to retrieving other components of the terrestrialcarbon cycle (i.e., net ecosystem productivity FNEPandecosystem respiration R)?2. Materials2.1. Study Site Descriptions[7] The research site (53.98717C176N, 105.11779C176W, and629 m above the sea level) is located approximately100 km NE of Prince Albert, Saskatchewan, Canada. It isreferred to as Southern Old Black Spruce (SOBS) and wasestablished in 1994 as past of the Boreal EcosystemsAtmosphere Study [Sellers et al., 1997]. The EC fluxfootprint area is dominated by black spruce (Picea mallanaMill.) but approximately 15% of the forest consists ofdeciduous tamarack (Larix laricina (DuRoi) K. Koch).The height of the dominant trees is 11 m. The stand densityis C246350 stems per hectare. Its leaf area index (LAI) isabout 3.5–3.8 m2mC02. The last disturbance occurred in1879. Some Labrador tea (Ledum groenlandicum Oeder) isin the understory with a ground cover of mostly feathermoss(Pleurozium spp.). This forest is located in a boggy areawith many small pockets of standing water. The landscapein the region is predominantly flat, with slight topographicalundulations. On the basis of a 40-year climate record madeat Waskosia Lake station, the mean annual and growingseason (May to September) air temperatures in the regionare 1.0C176C and 13.4C176C, respectively, and the mean annualprecipitation is approximately 440 mm, of which 40% fallsas snow. This site has an elevated water table and isgenerally wet. The texture of the mineral soil is sandy clay.The surface organic layer is 20–30-cm thick and carbonstorage in this layer is 39.2 kg C mC02. Further site detailsare given by Jarvis et al. [1997], Griffis et al. [2003], andKljun et al. [2006].GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES2of15GB20122.2. Land Surface Characteristics of theConcentration Footprint[8] The daily concentration footprint areas of the 28-mtower accumulated for a year could be as large as a circlearound the tower up to a 350-km radius (see section 4.2). Asshown in Figures 1 and 2, the areas within the footprint arequite heterogeneous. Land cover types (LC) in these areasinclude conifer forest, deciduous forest, mixed forest, shrub,grass, crop, and nonvegetation type (Figure 1). The domi-nant LC is conifer forest around the tower within a 100-kmradius; while the area to the southeast (>180 km from thetower) is dominated by grass or crop types. The dominantLC types of deciduous and mixed forests are located in theareas to the southeast and southwest from the tower betweenC24100 and C24180 km. Figure 2 shows a LAI map for August2003, as an example. LAI varied from 0.5 to 8 m2mC02inthe footprint. The LAI for the area surrounding the towerwithin a 100-km of radius was C243.5–4.5 m2mC02.2.3. EC and CO2Concentration Measurements[9] Half-hourly CO2and water fluxes and other meteo-rological variables at this site were measured on a 28-mwalk-up scaffold tower using the EC technique. The ECinstruments were mounted at the 25-m height. They includeda three-dimensional sonic anemometer-thermometer (modelR3; Gill Instruments Limited, United States; Lymington,UK) and a closed-path infrared gas analyzer (model 6262;LI-COR Incorporated, Lincoln, Nebraska, United States)operating in absolute mode for measuring fluctuations inCO2and water vapor density. Details about the EC systemwere given by Black et al. [1996], Arain et al. [2002], andGriffis et al. [2003].[10]CO2concentration was measured at both the 20-mand 28-m heights according to World Meteorological Ob-servation (WMO) Global Atmospheric Watch standardswith an accuracy of 0.1 ppm at 15 min intervals. Calibrationsusing a WMO standard were made at approximately 1-weekintervals. Gaps with no valid data at any level were less than10% year round. Small data gaps of 1 to 2 h were filled bylinear interpolation.3. Methods3.1. Model Framework and Assumptions[11] Meteorological processes such as the entrainment oftropospheric air during boundary layer growth, synoptic-scale subsidence of the troposphere, radiative processes,Figure 1. Land cover types around the SOBS tower for 2003.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES3of15GB2012mesoscale circulations (e.g., sea/lake breezes) and boundarylayer cloud formulation tend to counter the influence of theland surface by facilitating mixing between the PBL and thetypically drier and warmer overlying troposphere [Hellikeret al., 2004]. The PBL air mass moves over the terrestrialsurface (C24500 km dC01under typical fair weather condi-tions), dispersing trace gases horizontally and vertically dueto divergence and wind shear [Raupach et al., 1992].Hence, the air composition in the surface layer is deter-mined by the initial composition of the air mass and theexchanges with the underlying surface and the overlyingfree troposphere [Helliker et al., 2004]. It has been notedfrom three-dimensional atmospheric transport model simu-lations [e.g., Fung et al., 1983] that meridional transport canresult in substantial displacement of the actual change in theatmospheric burden of CO2in latitudinal zones from thecorresponding surface fluxes that drove them. The influenceof large-scale atmospheric transport on CO2concentrationin the atmospheric boundary layer is hence expected, andthis should interact with concentration gradients generatedby regional exchange with the surface. Suppose we want toestimate surface fluxes in a given region (e.g., the dailyconcentration footprint area), on the basis of mass conser-vation, the atmospheric concentration of a gas (e.g., CO2,expressed as C) measured in a terrestrial tower at a referenceheight (observed values, i.e., in the land surface layer)reflects the combination of some background atmosphericconcentration and variable amounts of that gas added fromsources in both the vertical and horizontal directions:Cobs¼ CbgþDCsurfþDCadv; ð1Þwhere Cobsand Cbgare, respectively, the observed atmo-spheric CO2concentration at a reference site and thebackground value; DCsurfis the change in the CO2mixingratio caused by local surface fluxes of carbon, which mightresult mostly from local biological activities, biomassburning and the fossil fuel combustion; DCadvis the changein the CO2mixing ratio due to advection resulting from ahorizontal CO2gradient. Equation (1) works in many timeframes, e.g., hourly, daily, and monthly. The CO2mixingratios in terrestrial ecosystems are also found to bedominated by biological activities during the growingseason under the condition that the upwind ecosystemsFigure 2. Leaf area index (LAI) map for the region surrounding the SOBS tower for the first 10 d ofAugust 2003.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES4of15GB2012behave in a very uniform way [Bakwin et al., 1998;Potosnak et al., 1999]. In this study, we tried to explore asimple method to infer regional GPP in daily time stepsfrom continuous CO2mixing ratio measurements in thesurface layer using a 1-D model. We therefore assume thatDCadvcan be ignored since DCsurfC29 DCadvin the dailyshort time frame.[12] The boundary layer interacts with the surface (includ-ing horizontal advection) and the background atmosphere onsimilar time frames. While changes in the atmosphericbackground CO2by many factors, such as advection, deepconvection, subsidence, etc., are normally much slower thanthat in measured surface CO2. The relaxation time ofchanges in the background atmospheric CO2(i.e., the CO2concentration in free troposphere in this study) is muchlonger than that in the PBL driven by the exchange of CO2with the surface in the daily concentration footprint area(about 1 order longer, e.g., 10 d versus 1 d). Hence, thebackground CO2changes could be ignored.[13] We also neglected the difference between the freetropospheric CO2value and value observed within themarine boundary layer (‘‘MBL reference’’). The MBLreference CO2[Masarie and Tans, 1995] is a weeklyvarying concentration field with spatial increment of0.05 sine of latitude constructed from observations withinthe MBL [Globalview-CO2, 2005]. We used the MBLreference for free troposphere because of the absence ofdirect observations, though observations from the highobservational density from intensive field sampling pro-grams showed significant deviations of free troposphericconcentrations from the MBL references in some regionsover the continent. However, during the daytime, the changein free tropospheric CO2is expected to be small. It is thedaytime change that affects the deviation of daily GPP.3.2. Method 1: PBL Carbon Budget Analysis3.2.1. An Integrated Ecosystem-Boundary LayerModel for Estimating Ecosystem Fluxes andAtmospheric Diffusion[14] In order to isolate photosynthesis signals from atmo-spheric CO2data, we employed an integrated ecosystem-boundary layer model to simulate dynamics of CO2in thePBL. This model consists of two components: (1) anecosystem model (BEPS: the Boreal Ecosystem ProductivitySimulator) [Chen et al., 1999; Liu et al., 1999, 2002]; and (2)a one-dimensional atmospheric model (VDS: Vertical Dif-fusion Scheme) [Chen et al., 2004; B. Chen et al., 2005].[15] The version of BEPS used in this study is a newversion that includes a land surface scheme: Ecosystem-Atmosphere Simulation Scheme (EASS) [B. Chen et al.,2007]. It has the following characteristics: (1) satellite dataare used to describe the spatial and temporal information onvegetation, and in particular, we use a foliage clumpingindex (W) in addition to LAI to characterize the effects ofthree-dimensional canopy structure on radiation, heat andcarbon fluxes; (2) energy and water exchange and carbonassimilation in soil-vegetation-atmosphere systems are fullycoupled and are simulated simultaneously; and (3) theenergy and carbon assimilation fluxes were calculated withstratification of sunlit and shaded leaves to avoid short-comings of the ‘‘big-leaf’’ assumption. This updated versionhas been systematically validated using eddy covarianceflux data [Ju et al., 2006; B. Chen et al., 2007] at Canadianforest sites and used for upscaling land surface fluxes [J. M.Chen et al., 2007] and isotope studies [B. Chen et al.,2006a, 2006b; Chen and Chen, 2007].[16] VDS is a one-dimensional bottom-up and top-downvertical mixing model [Chen et al., 2004; B. Chen et al.,2005] similar to those of Wyngaard and Brost [1984] andMoeng and Wyngaard [1989] simulating the transportprocesses of scalar entities (e.g., CO2, temperature) fromthe surface layer up to the top of PBL. VDS has twodifferent schemes (modules) to treat different situations ofthe PBL structures (stable boundary layer: SBL or convec-tive boundary layer: CBL) [Chen et al., 2004; B. Chen etal., 2005]. The selection of a stable or free convectionscheme is determined by atmospheric stability. In VDS, themixed layer is stratified into 50-m thick layers and constantbottom-up and top-down mixing coefficients are usedthroughout the PBL at a given time [Zhang and Anthes,1982]. This model configuration allows CO2concentrationin each layer to vary with time according to the verticalconcentration gradient and the mixing coefficients at eachtime step (30 s) in stead of using the quasi-steady stateassumption for the vertical gradient [Moeng and Wyngaard,1989]. The integrated ecosystem-boundary layer model isforced by the near-surface meteorological variables, includ-ing air temperature, air relative humidity, incoming short-wave radiation, wind speed, and precipitation. The landsurface data, including vegetation (i.e., LC, LAI) and soildata are also needed as model inputs. Most vegetationparameters were derived from satellite images. As shownin Figures 1 and 2, LC and LAI were derived from satelliteimages at a 1-km resolution (directly from VEGETATIONimages, or up-scaling from Landsat TM) [Chen et al.,2002]. The LAI map is generated with 10-d intervals withannual total of 36 maps. W was derived from multiangularPOLDER 1 data [J. M. Chen et al., 2005]. Data on soiltexture (sand, silt and clay fractions) and carbon pools areobtained from the Soil Landscapes of Canada (SLC) data-base, version 1.0 and 2.0 [Shields et al., 1991; Schut et al.,1994; Lacelle, 1997]. For the one-dimensional BEPS-VDSsimulations, the average values of LAI and W near theSOBS (a radius of 1 km) are obtained from these maps, andthe LC type is taken as the dominant type of conifer. Forestimating the entrainment of CO2at the top of the mixedlayer, the background atmospheric value (i.e., the freetropospheric CO2) is needed for the top condition of ourone-dimensional model. As mentioned above, we use thelatitudinally interpolated MBL CO2as a substitute for thefree troposphere.3.2.2. Method for Deriving Daily GPP From CO2Concentration Measurements[17] As the air CO2mixing ratio at a given height isdetermined by both the surface metabolism and atmosphericmixing processes. It would be possible to isolate the signalsfor the metabolism if atmospheric diffusion is accuratelymodeled. This requires that both the exchange of CO2between the ecosystem and the atmosphere and the atmo-spheric transport within the PBL are accurately simulated.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES5of15GB2012This integrated ecosystem-boundary layer model (BEPS-VDS) simulated well the surface fluxes (both photosynthe-sis and respiration) and the concentration of CO2in thesurface layer (see section 4). After the first ‘‘normal’’ modelrun, we implement a hypothetical model run by switchingoff GPP in the model, i.e., setting GPP = 0. In the this run,only the GPP produced by BEPS is set to zero whilekeeping all other hourly fluxes unchanged from the previ-ous run, including respiration and entrainment. A new CO2profile produced in the second model run is purely drivenby R, which is simulated by BEPS for the grid cell aroundthe tower. The reduction of observed CO2from the simu-lated values at the measurement height is entirely due toGPP, that is, the amount of the reduction is the part of CO2removed by GPP. The signals of GPP are hence isolated by‘‘turning off’’ the GPP in BEPS and quantifying theaccumulated air CO2decrease (the difference between theobserved and simulated values with GPP = 0) from dawn todusk. Near dusk, the planetary boundary layer is still wellmixed, so this increase in CO2can be converted into GPPusing boundary layer CO2mass budgeting. This methodol-ogy has been applied to a 13-year CO2record observed onthe Fraserdale tower, Ontario, Canada, to study the temper-ature effect on the boreal carbon cycle [J. M. Chen et al.,2006; B. Chen et al., 2006a, 2006b] and validated usingsimultaneous CO2flux and concentration data at the WLEFtall tower (Wisconsin, United States [J. M. Chen et al.,2007]).3.3. Method 2: Remote Sensing Based FootprintIntegration3.3.1. An Analytical Scalar Concentration FootprintModel[18] The scalar concentration footprint ‘‘source’’ area isthe ‘‘view of the concentration sensor’’ on a tower. Thescalar concentration footprint function (f) describes the fluxportion ‘‘seen’’ by the scalar concentration sensor. Ourconcentration footprint model is a modified version of thatof Schmid [1994]. All upwind sources encompassed by themeasurement point at a height (zm) above the groundpotentially contribute to the measured scalar concentration(C). The measured departures of CO2concentration fromthe background values Cbg, therefore, is the result of anintegration of the product of the surface flux (F,inmmolmC02sC01) and footprint function (f) over the entire upwindsource area:C 0;0;zmðÞ¼CbgþZ1C01Z1C01Fx;y;0ðÞfx;y;zmðÞdxdy; ð2Þwhere C is in mmol mC03; f is in s mC03; x is the stream-wisedistance in meters; and y is the crosswind distance from thecenter line in meters.[19] The scalar concentration footprint function (i.e., thedownwind concentration distribution of a unit point source(plume) occurring at the origin (x = y =0,z C21 0)) is theproduct of the crosswind-integrated concentration footprint,fyin s mC02, and the crosswind distribution function DyinmC01[Pasquill, 1974; van Ulden, 1978; Horst and Weil,1992],fx;y;zmðÞ¼Dyx;yðÞfyx;zmðÞ: ð3ÞDispersion in the lateral (y) direction is calculated as aGaussian function [Pasquill, 1974],Dyx;yðÞ¼1ffiffiffiffiffiffi2ppsyexp C0y22s2y !; ð4Þwhere syis the standard deviation of the plume in the ydimension, depending on atmospheric stability and upwinddistance (x). In accordance with the short-range limit ofstatistical turbulence theory [Pasquill, 1974; Schmid, 1994],syis approximated as svx/C22u, where svis the standarddeviation of lateral wind fluctuations.[20] The crosswind-integrated concentration footprint, fyat the upwind distance x is described asfyx;zmðÞ¼Dzx;zmðÞC22uxðÞ; ð5Þwhere Dzis the vertical concentration distribution functionin mC01and C22u is the effective velocity of the plume in m sC01;C22u is forced by mass conservation to beC22uxðÞ¼Z10uzðÞDzx; zðÞdz; ð6Þwhere u(z) is the horizontal wind velocity in m sC01.Following an analytical solution of Eulerian advection-diffusion equation by van Ulden [1978], Dzis expressed asDzx; zmðÞ¼AC22zxðÞexp C0BzC22zxðÞC18C19rC20C21; ð7Þwhere C22z is the mean plume height; the coefficients A and Bequal rG(2/r)/G(1/r)2and G(2/r)/G(1/r), respectively; G isthe Gamma function and r is a shape parameter and r =2+m C0 n, where m and n are the exponent of the wind velocitypower law and the exponent of the eddy diffusivity powerlaw, respectively; u(z)=Uzmand K(x)=kzn, where U and kare the effective speed of plume advection and an effectiveeddy diffusivity coefficient, respectively. For mathematicalsimplicity, we need to explicitly express C22z(x) and C22u(x)tosolve equations (5) and (7) by integration of equation (13)of van Ulden [1978] asC22zxðÞ¼Br2kUC18C191=rx1=r; ð8aÞC22uxðÞ¼G 1þmðÞ=rG 1=rðÞr2kUC18C19m=rUxm=r: ð8bÞGB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES6of15GB2012[21] This is a very Simple Analytical Footprint model onEulerian coordinates (SAFE). On the basis of the K-theoryand assuming horizontally homogeneous turbulence, ananalytical solution of f(x, y, zm) is obtained from thefunctional form of the concentration distribution and theshape of the wind profile (equation (3)). The dimensionsand orientation of f(x, y, zm) depend on the location andheight of the sensor, wind direction, wind velocity, surfaceroughness, and atmospheric stability.[22] Footprint estimates can be classified as stochasticLagrangian, analytical approaches, or large-eddy simula-tions. Lagrangian models can be applied in any turbulenceregime (even in inhomogeneous or nonstationary condi-tions), while most analytical models are constrained tohomogeneous turbulence. The values of the upwind tail ofconcentration footprint estimated by a three-dimensionalLagrangian stochastic dispersion model are generally higherthan those by an analytical footprint model [Kljun et al.,2003]. At these large separation distances between thesource and the receptor, the mean plume height could bewell above the surface layer, and thus beyond the validityrange of the K-theory-based analytical model. To avoid themodel biases resulting from the limitation of our analyticalmodel, we neglected the very small contribution from thelong upwind tail. In the model implementation, we simplysort f(x, y, zm) values in a descending order and thenaccumulate the values from the largest to the smallest untila given fraction P is achieved. The source area WPincludesall grids (pixels) that have f(x, y, zm) larger than the cutoffpoint, and the fraction P is the ratio of the cumulativefootprint function within WPto the whole integrated sourcefunction,P ¼8P8tot¼RRWPfx; y;zðÞdxdyR1C01R1C01fx;y;zðÞdxdy; ð9Þwhere 8Pand 8totare the integrals of the footprint functionover WPand the total area, respectively. In this study, we setP to 0.90. The footprint function f(x, y, zm) at every gridpoint within WPis then normalized by the integral of thefootprint function over WPfor each day to yield the dailyweighted footprint function (f),f x; yðÞ¼fx;y;zmðÞdxdy=ZZWPfx;y;zmðÞdxdy: ð10ÞTheintegralofdailyweightedfootprintfunction(f)equals1.[23] The SAFE model was coupled with EASS. Thesensible heat flux simulated by EASS is needed for calcu-lating the atmospheric stability in SAFE. SAFE needs thesame model inputs as BEPS (see section 3.2.1) with theadditional input of hourly wind direction and its deviation.3.3.2. Method of Calculating Regional Net CO2Fluxon the Basis of Footprint Estimation and EcosystemModeling[24] The surface flux information contained in CO2con-centration measured at the tower (Fregion) is the integration ofsurface CO2flux (F) weighted with concentration footprintfunction (f) for each pixel over the upwind footprint sourcearea (WP),Fregion¼ZZWPFx; yðÞf x;yðÞdxdy: ð11ÞThe surface CO2flux F(x,y) can be net CO2flux or anycomponent of carbon fluxes, i.e., GPP or R. In this study, wefocus on GPP. The spatially explicit BEPS model was usedto simulate GPP at 1 km resolution over the concentrationfootprint area of the SOBS tower. The daily concentrationfootprint function (f) for each pixel (same size as BEPS)was simulated using SAFE.3.4. Method for Deriving Local GPP From ECMeasurements[25] The surface flux was calculated as the sum of theeddy flux, measured at 25 m, and the rate of change ofstorage in the air column below the flux measurement level.The surface CO2flux provides a direct measurement of thenet ecosystem exchange (FNEE)—the net exchange rate ofCO2between the ecosystem and the atmosphere. FollowingBarr et al. [2004], two adjustments were applied to FNEE:the nighttime FNEEdata were excluded at low u*(here, u*<0.35 m sC01) and an energy-balance-closure adjustment wasapplied by dividing the measured FNEEby the fractionalenergy balance closure (here, 89%), calculated as the ratioof the sum of the sensible and latent heat fluxes to theavailable energy flux. FNEEprovides a direct measure of thenet ecosystem production (FNEP= C0FNEE). At local scale(i.e., EC flux footprint area), FNEPresults as the differencebetween carbon gains by GPP and carbon losses by R (i.e.,FNEP= GPP C0 R). Positive values of FNEPcorrespond toCO2uptake by the ecosystem.[26] R and GPP were partitioned from FNEPmeasure-ments. The measured R was estimated as R = C0FNEPduringperiods when GPP was known to be zero, i.e., growing-season nighttime and non-growing-season (periods whenboth air (Ta) and 2-cm soil (Ts) temperatures were lowerthan 0C176C). GPP was obtained from measured FNEPandestimated daytime Rdas GPP = FNEP+ Rd. The core of thismethodology was to first derive simple annual empiricalrelationships (for example, Rd= f(Ts)) from measured data.Rdvalues were estimated from an empirical logistic equa-tion (fitted to the measured R values from the entire year[Barr et al., 2004],Rd¼ fTs;tðÞ¼rttðÞr11þexp r2ð r3C0TsðÞ; ð12Þwhere Tsis soil temperature at the 5-cm depth; r1, r2, and r3are the empirical parameters, held constant over the year;and rt(t) is a time-varying parameter. The values of rt(t)were estimated within a 100-point moving window as theGB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES7of15GB2012slope of a linear regression (forced through zero) of themodeledRestimatesfrom(equation(12))versusmeasuredR.4. Results4.1. Atmospheric Diffusion and Ecosystem Modeling[27] A critical step in our methodology of extracting thephotosynthesis signal from the CO2record is to ensure thatatmospheric diffusion is simulated with a reasonable accu-racy. Although the integrated ecosystem-boundary layermodel has been shown to perform well in the previousstudies [Chen et al., 2004; B. Chen et al., 2005, 2006a,2006b; J. M. Chen et al., 2007], model validation ofsimulated CO2mixing ratio against measurements at thisSOBS tower was also made in this study. Figure 3 providesexamples of the simulated CO2mixing ratios in comparisonwith observed values for five consecutive days in July 2003.The simulated curves generally followed the observedvalues closely, even though the simulation was made witha simple one-dimensional model. The simulated curveswere generally smoother than the observed values becauseof the assumption of horizontal homogeneity used in the 1-Dmodel. There were synoptic events (frontal systems) caus-ing abrupt changes in CO2concentration, and simulatedvalues from the 1-D model had the largest departure frommeasurements under these circumstances (e.g., 9 July, asshown in Figure 3). Similar simulation results were obtainedfor all days in 2003, and the results were summarized inTable 1 in terms of regression statistics between modeledand observed CO2concentrations. The r2value increasesand the root mean square error (RMSE) decreases as themodeled hourly values are averaged for daily and 10-dperiods, suggesting that the 1-D model can generallycapture the underlying ecosystem variability for regionalcarbon balance estimation.[28] To ensure that atmospheric diffusion is simulatedwith an acceptable accuracy for our purpose of using aCO2record for deriving ecosystem information, we shouldalso have the first order estimate of the CO2flux to and fromthe underlying the surface. Figure 4 shows comparison ofthe EC-measured FNEEand GPP derived from EC fluxmeasurements with simulated FNEEand GPP for the sameperiod as shown in Figure 3. The model simulationsgenerally had good agreement with observations.[29] After gaining confidence in modeling the atmospher-ic diffusion and ecosystem metabolism, we applied themethodology illustrated in section 3.2.2 and J. M. Chen etal. [2007] to the entire record of CO2in 2003. Daily GPPvalues were computed from the hourly CO2concentrationfor the whole year (see section 4.4).4.2. Estimates of Daily Concentration Footprint[30] SAFE was applied to the SOBS tower for 2003. Tobe compatible with BEPS, the grid size in SAFE was set tobe 1 km C2 1 km. The calculated footprints are shown inFigure 5 for four arbitrary days in 2003. The parameters forcharacterizing the daily mean wind and atmospheric stabil-ity for these 4 d are listed in Table 2. The footprint peak wasabout 10 km upwind of the tower, and the upwind tailwithin the cutoff point extended up to 250–350 km depend-ing on weather conditions (Figure 5a). The crosswinddistribution followed the assumed Gaussian distribution,but the decline rates from the peak isopleth depended onthe atmospheric stability and the standard deviation of thelateral spread (Figure 5b). Different days had differentfootprints (Figures 6a and 6b) as the air flowed fromdifferent directions with different widths of dispersion.The northwest winds contributed the most to the annualfootprint for the SOBS tower in 2003, while northeast windscontributed the least (Figure 7).4.3. Simulated GPP Field at 1 km Resolution[31] The spatially explicit BEPS model was used forsimulating the GPP over the concentration footprint areaof the SOBS tower. Values of the daily total GPP at 1 kmresolution for 11 and 24 August were shown in Figures 6cFigure 3. Comparison of measured (symbols) and mod-eled (solid line) CO2mixing ratios for 6–10 July 2003.Table 1. Statistics for the Regression Between Modeled andObserved CO2Concentrations on the SOBS Tower for Hourly,Daily, and 10-d Mean Valuesar2RMSE (ppm) Sample Size (n)Hourly 0.67 4.8 6910Daily 0.73 2.3 29110 d 0.87 2.1 36aThe r2is the linear regression coefficient, and RMSE is the root meansquare error, =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1nPni¼1CmodiðÞC0CobsiðÞ½C1382s.Figure 4. Comparison of the EC-measured half-hourly netecosystem exchange (FNEE) and EC flux derived GPP withBEPS simulated half-hourly net ecosystem exchange (FNEE)and GPP for 6–10 July 2003.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES8of15GB2012and 6d, as examples. The differences between these 2 dwere apparent. On the basis of the simulated daily GPP anddaily weighted concentration footprint, we calculated thedaily regional GPP values that influence the concentrationmeasurements at the tower using equation (11) for thewhole year (Figure 9).4.4. Comparison of GPP Estimates[32] In order to test the performance of BEPS, modelparameters were not ‘‘tuned’’ to obtain a better match withthe tower observations, and the land surface inputs werederived from remote sensing images instead of using themeasurements. As shown in Figure 8, the simulated dailyGPP in the 1 km pixel containing the SOBS tower generallyfollowed the EC flux derived GPP (r2= 0.76) well becausethey represent the similar local source area (EC fluxfootprint area: about 1 km2surrounding the tower), butthe model tends to underestimate the measured GPP in themiddle growing season. Estimates of GPP using the PBL-budget method are likely representative of a regional scaleowing to the large source area that affects the mixing ratio(concentration footprint area: about 103–105km2). Thesource areas are the same in the PBL-budgeting(method 1) and the concentration-footprint-integrating(method 2) approaches. The estimates of daily GPP bythese two approaches were compared in Figure 9. The PBL-budgeted estimates were in good agreement with the con-centration-footprint-integrated estimates (slope = 0.99; r2=0.89). In order to test these methods to infer the regionalGPP from mixing ratio measurements, we also comparedthe estimates of regional GPP with EC flux derived GPPalthough their source areas are different. Regression analy-sis revealed that they were highly correlated but concentra-tion-derived daily GPP only reached about 80% of themagnitudes of EC flux derived daily GPP (Figure 10).The seasonal patterns of the weekly averages of GPPestimated by these four approaches (at both local andregional scales) were quite similar although the spatialscales represented by these four sets of estimates were verydifferent (Figure 11). Similar to regression analysis at dailytime steps (Figure 10), we also see from Figure 11 that theregional GPP estimates were consistently much smaller thanthe local GPP for all days in 2003. This is consistent withcharacteristics of the source areas (different land covertypes) represented by these two quantities. The EC fluxfootprint area (local GPP) is dominated by a black spruceforest while the concentration footprint areas (regional GPP)include forest, shrub, grass, agriculture crop fields and openwater bodies, all of which are likely to be less productive.Seasonal budgets of GPP estimates were summarized inTable 3 and Figure 12. The estimates of annual GPP wereabout 819–847 g C mC02for the smaller area surroundingthe tower and 649–664 g C mC02for the region around thetower, respectively. The differences in GPP estimates bydifferent methods for the similar spatial scales were within4%. The regional estimates were about 20–25% lower thanthe local estimates and most of the differences occurredduring the early to middle growing season (i.e., May to July,Figure 12).5. Discussion[33] This study makes use of measurements of the high-frequency CO2mixing ratio on a short tower to estimate thenet CO2exchange at daily or longer timescales. The PBLdynamics naturally integrate the effects of land ecosystemson the atmosphere at a regional scale. Because of theconvective boundary layer (CBL) dynamics, the influenceof the inhomogeneous surface on the atmospheric CO2issmoothed, and the evolution of atmospheric CO2with timein a day represents the integrated influence of the surfaceflux over the concentration footprint. The surface area thatinfluences the PBL for 1 d is estimated to be about 104km2[Raupach et al., 1992]. Mixing within the CBL occursrapidly (C2415 min) relative to the timescale for substantialchanges in surface fluxes (C241 h except near sunrise andsunset). This allows simple mass-balance approaches torelate average CBL concentrations to the surface flux [Styleset al., 2002]. The daily GPP extracted from hourly CO2concentration measurements (method 1) should representthe upwind area of the tower in the mean wind direction ona given day. The daily concentration footprint area was estimat-ed to be around 103–104km2, smaller than 104–105km2forTable 2. Parameters for Characterizing the Wind and AtmosphericStability for the Four Arbitrary Days as Shown in Figure 5au(m sC01)sv(m sC01)sd(degrees)u*(m sC01)1/L (C210C03)(mC01) Rb11 Jul 3.3 1.8 20.4 0.48 C09.9 0.1511 Aug 3.7 2.6 25.1 0.53 C030.8 0.0824 Aug 5.2 2.2 14.8 0.74 C01.6 0.0524 Sep 3.9 2.3 15.7 0.54 C03.2 0.05aWhere u is the wind velocity, svis the standard deviation of lateral windvelocity fluctuations, sdis the standard deviation of lateral wind directions,u*is the friction wind speed, 1/L is the reciprocal of Obukhov length, andRbis the bulk Richardson number.Figure 5. Simulated concentration footprint cross sectionsfor four arbitrary days in 2003. (a) Along the wind directionand (b) across the wind direction from center line of themean flow. The parameters for characterizing the dailymean wind and atmospheric stability are listed in Table 2.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES9of15GB2012multiple days [Gloor et al., 2001; Lin et al., 2004]. Though itis difficult to separate the near-field and the far-field effects onthe estimated daily GPP using our methodology, the far-fieldeffect on daily GPP estimation is quite small. We thereforeexpect the biases in estimated daily GPP by neglecting thechange in background atmospheric CO2in our one-dimen-sional ecosystem-boundary layer model are not significant.[34] Moreover, satellite data provide independent infor-mation on the spatial and phenological variations of GPPusing an ecosystem model such as BEPS. Given a reason-able estimate of the actual footprint under certain micro-meteorological conditions and a simulation of the surfaceflux field by BEPS based on remote sensing, we cancalculate the daily regional GPP values that influence theconcentration measurements using equation (11) (method 2).This is an effective method to retrieve the regional carbonflux information which is ‘‘seen’’ by the concentrationsensor on the tower.Figure 6. Simulated footprint and gross primary productivity (GPP) maps at 1 km resolution on twoarbitrary days. (a) The footprint and (b) GPP maps for 11 August 2003. (c, d) The corresponding maps for24 August 2003.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES10 of 15GB2012[35] The PBL carbon budget (i.e., concentration-derived)method uses a one-dimensional ecosystem-boundary layermodel. By ‘‘turning off’’ the modeled GPP and estimatingthe actual GPP through PBL budgeting from the accumu-lated increase in CO2concentration, modeled after GPP is‘‘turned off’’, from the observed CO2concentration atsunset, we greatly reduce the error due to surface heteroge-neity. However, this methodology does not tell which thesource area the concentration-derived GPP represents. Asthe air flows from different directions over different under-lying surfaces, large day-to-day variations are expectedeven though the micrometeorological conditions are similar.The combination of concentration footprint estimation withremote sensing based GPP estimation provides an opportu-nity to evaluate the reliability of the concentration-derivedGPP as it explicitly considers the source areas for theconcentration measurements. The significance of concen-tration-derived flux information is its large concentrationfootprint consisting of many cover types of different vegeta-tion densities, and so far there has been no other ways tovalidate carbon cycle information derived from atmosphericCO2mixing ratio measurements.[36] In this study, these two independent regional GPPestimates showed close agreement. However, it must berealized that it is still possible that both of them have similarbiases, i.e., simultaneously overestimated or underesti-mated. We assume the MBL reference CO2as a substitutefor background value (free tropospheric value) for the twomethods. The departures of free tropospheric concentrationsfrom MBL reference over the continent was reported to beC243 ppm in some regions, with an averaging value of C241–2 ppm according to the CO2Budget and RectificationAirborne study (COBRA) measurements [Gerbig et al.,2003; Lin et al., 2004, 2006]. Such systematic departurescan be explained in large part by advection from differentlatitudes and by time lags in vertical propagation of con-Figure 7. Annual concentration footprint for the SOBS tower for 2003.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES11 of 15GB2012centration changes at the surface, within the MBL, to thefree troposphere [Gerbig et al., 2003]. A typical verticalCO2gradient (PBL-free troposphere) was lager than 10 ppmduring summer growing season in the research area. SupposethedifferenceinCO2concentrationbetweenfreetroposphereand MBL is 1.5 ppm in summer, the potential errors inestimated regional GPP by the presented methods could beless than 5–10% from substituting the MBL reference.[37] It is therefore also paramount that the ecosystemmodel used to derive the flux field for footprint integrationis validated at some locations within and near the footprintarea. Our confidence in both the concentration-derived andfootprint-integrated regional GPP estimates is gained fromthe fact that the BEPS model used for GPP mapping agreedwell with EC-derived GPP at a given site within the fluxfootprint. This eases our concern about possible significantmodel biases. The comparisons of these regional GPPestimates with EC flux measurements showed that theyhad similar seasonal patterns but the regional estimates wereconsistently smaller than local EC-derived GPP throughoutthe growing season in 2003. The annual differences wereabout 20–25%. The spatial representations of these twoGPP estimates are very different: the EC footprint is therelatively homogeneous old black spruce while the concen-tration footprint is covered by boreal needle evergreen anddeciduous broadleaf forests, shrub land, grass land, cropland, and lakes. The discrepancies between these two GPPestimates reflect the differences in the underlying landsurface. From the GPP maps modeled by BEPS we havequantitatively evaluated that GPP values for nonforest typesare much lower than that of the SOBS site, and this isconsistent with the fact that both concentration-derived andconcentration-footprint-integrated GPP values are consider-ably lower than the EC measurements. This large differenceindicates the importance of considering the surface hetero-geneity when we attempt to extrapolate site measurementsto the region. It is encouraging to see that atmospheric CO2concentration data can be used effectively for this upscalingpurpose.[38] There are three main assumptions made in obtainingthe concentration-derived GPP during daytime [see J. M.Chen et al., 2007]. In using this methodology, cautionshould be taken against potential errors due to (1) conditionswhen the PBL is not well mixed during the day, (2) highlyheterogeneous atmospheric conditions such as those causedby water-land interfaces and complex terrain, and (3) diur-nally variable anthropogenic CO2sources. At nighttime, theatmosphere is highly stratified, and the similarity of uniformvertical mixing within the PBL is no longer valid. ThisFigure 8. Comparison of BEPS simulated daily GPP ofthe 1 C2 1 km pixel which contains the SOBS tower withthat derived from EC flux measurements. The inset showsthe linear regression between these two GPP estimates.Figure 9. Comparison of concentration-derived regionalGPP with footprint-integrated regional GPP on a daily timebasis for 2003. The inset shows the linear regressionbetween these two GPP estimates.Figure 10. Comparisons of concentration-derived andfootprint-integrated regional GPP with EC-derived localGPP on a daily time basis.Figure 11. Mean 5-d GPP estimated by four differentapproaches based on EC flux and CO2concentrationmeasurements at the SOBS site, 2003.GB2012 CHEN ET AL.: REGIONAL CARBON FLUX ESTIMATES12 of 15GB2012methodology is therefore not applicable to extracting night-time FNEEor R.[39]CO2concentration data can be possibly used to inferFNEEand R by tuning an ecosystem model when theatmospheric diffusion during daytime and nighttime isreasonably well simulated [B. Chen et al., 2006a, 2006b].It is feasible to retrieve R and FNEEat regional scale bycombining concentration footprint modeling with ecologicalmodeling based on remote sensing. Simple PBL budgetanalysis making use of the differences in the CO2mixingratio between the surface layer and the free troposphere(CFT) to compute FNEEon a monthly basis has beenexplored [Helliker et al., 2004; Bakwin et al., 2004; Lai etal., 2006]. All of them used the marine boundary layer datato estimate CFT. The CO2entrainment at the CBL top iscritical to this methodology. Helliker et al. [2004] estimatedthe vertical transfer by analyzing the budget of water vaporin the CBL with the surface flux of water vapor measuredby EC methods, while the others used National Centre forEnvironmental Prediction (NECP) reanalysis data for thesame purpose. These simple budget analyses have beenshown to be successful on monthly and seasonal bases, butbiases and uncertainties are still considerable [Bakwin et al.,2004;Laietal.,2006;Crevoisieretal.,2006].Incomparisonwith this methodology for net carbon exchange, ourmethods of deriving GPP during the daytime and R duringboth nighttime and daytime has the advantage of infer-ring carbon components necessary for model validationand ecosystem parameter optimization for regional (i.e.,C24105km2) applications.6. Conclusions[40] To quantify regional carbon fluxes using high-frequency CO2concentration measurements, we haveexplored and compared two independent methods: (1) PBLcarbon budgeting using an integrated ecosystem-boundarymodel (i.e., BEPS-VDS), and (2) remote sensing basedconcentration footprint integration using a spatially explicitecosystem model (BEPS) driven by remote sensing inputsand a new concentration footprint model (SAFE). Thefollowing three conclusions were drawn from the applicationof these methodologies to the SOBS tower in 2003 after thevalidation of BEPS using EC measurements at the site:[41] 1.Bothconcentration-derivedandfootprint-integratedGPP values agreed well and the model used for GPPestimation within thefootprint agreedwell with ECmeasure-ments, suggesting that these two methods are both useful forobtaining regional carbon flux information.[42] 2. These two methods have advantages and disad-vantages: the concentration-derived GPP does not indicatethe size of the source area, while the remote sensing basedfootprint integrating method quantifies the source area. Theformer is vulnerable to PBL height simulations and requiressome assumptions (see section 5), while the latter issensitive to model parameterization in both the ecosystemmodel (i.e., BEPS) and footprint model (SAFE). To use thetwo methods as a pair is a practical and effective means toderive regional carbon fluxes (i.e., GPP in this study) withhigh temporal resolution (i.e., at daily time steps). Combin-ing these two methods has an obvious advantage over thoseapproaches for net carbon flux [e.g., Helliker et al., 2004;Bakwin et al., 2004].[43] 3. 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