linking global terrestrial co ﬂuxes and environmental drivers: … · 2021. 5. 4. · ce orme des...

Atmos Chem Phys 21 6663ndash6680 2021httpsdoiorg105194acp-21-6663-2021copy Author(s) 2021 This work is distributed underthe Creative Commons Attribution 40 License

Linking global terrestrial CO2 fluxes and environmental driversinferences from the Orbiting Carbon Observatory 2 satellite andterrestrial biospheric modelsZichong Chen1 Junjie Liu2 Daven K Henze3 Deborah N Huntzinger4 Kelley C Wells5 Stephen Sitch6Pierre Friedlingstein7 Emilie Joetzjer8 Vladislav Bastrikov9 Daniel S Goll10 Vanessa Haverd11 Atul K Jain12Etsushi Kato13 Sebastian Lienert14 Danica L Lombardozzi15 Patrick C McGuire16 Joe R Melton17Julia E M S Nabel18 Benjamin Poulter19 Hanqin Tian20 Andrew J Wiltshire21 Soumlnke Zaehle22 andScot M Miller1

1Department of Environmental Health and Engineering Johns Hopkins University Baltimore MD USA2Jet Propulsion Laboratory California Institute of Technology Pasadena CA USA3Department of Mechanical Engineering University of Colorado Boulder Boulder CO USA4School of Earth and Sustainability Northern Arizona University Flagstaff AZ USA5Department of Soil Water and Climate University of Minnesota Twin Cities St Paul MN USA6College of Life and Environmental Sciences University of Exeter Exeter UK7College of Engineering Mathematics and Physical Sciences University of Exeter Exeter UK8Centre National de Recherche Meacuteteacuteorologique Uniteacute mixte de recherche 3589 Meteo-FranceCNRS42 Avenue Gaspard Coriolis 31100 Toulouse France9Laboratoire des Sciences du Climat et de lrsquoEnvironnement Institut Pierre-Simon Laplace CEA-CNRS-UVSQCE Orme des Merisiers 91191 Gif-sur-Yvette CEDEX France10Universiteacute Paris-Saclay CEA-CNRS-UVSQ LSCEIPSL Gif-sur-Yvette France11CSIRO Oceans and Atmosphere GPO Box 1700 Canberra ACT 2601 Australia12Department of Atmospheric Sciences University of Illinois Urbana IL USA13Institute of Applied Energy (IAE) Minato-ku Tokyo 105-0003 Japan14Climate and Environmental Physics Physics Institute and Oeschger Centre for Climate Change ResearchUniversity of Bern Bern Switzerland15Terrestrial Sciences Section Climate and Global Dynamics National Center for Atmospheric Research Boulder CO USA16Department of Meteorology Department of Geography and Environmental Science National Centre for AtmosphericScience University of Reading Reading UK17Climate Research Division Environment and Climate Change Canada Victoria BC Canada18Max Planck Institute for Meteorology Hamburg Germany19NASA Goddard Space Flight Center Biospheric Sciences Laboratory Greenbelt MD USA20International Center for Climate and Global Change Research School of Forestry and Wildlife SciencesAuburn University 602 Duncan Drive Auburn AL USA21Met Office Hadley Centre FitzRoy Road Exeter EX1 3PB UK22Max Planck Institute for Biogeochemistry PO Box 600164 Hans-Knoumlll-Str 10 07745 Jena Germany

Correspondence Zichong Chen (zchen74jhuedu)

Received 25 March 2020 ndash Discussion started 24 April 2020Revised 11 December 2020 ndash Accepted 28 March 2021 ndash Published 4 May 2021

Published by Copernicus Publications on behalf of the European Geosciences Union

6664 Z Chen et al Global CO2 fluxes from space

Abstract Observations from the Orbiting Carbon Observa-tory 2 (OCO-2) satellite have been used to estimate CO2fluxes in many regions of the globe and provide new insightinto the global carbon cycle The objective of this study isto infer the relationships between patterns in OCO-2 obser-vations and environmental drivers (eg temperature precip-itation) and therefore inform a process understanding of car-bon fluxes using OCO-2 We use a multiple regression andinverse model and the regression coefficients quantify therelationships between observations from OCO-2 and envi-ronmental driver datasets within individual years for 2015ndash2018 and within seven global biomes We subsequently com-pare these inferences to the relationships estimated from 15terrestrial biosphere models (TBMs) that participated in theTRENDY model inter-comparison Using OCO-2 we areable to quantify only a limited number of relationships be-tween patterns in atmospheric CO2 observations and patternsin environmental driver datasets (ie 10 out of the 42 re-lationships examined) We further find that the ensemble ofTBMs exhibits a large spread in the relationships with thesekey environmental driver datasets The largest uncertainty inthe models is in the relationship with precipitation particu-larly in the tropics with smaller uncertainties for temperatureand photosynthetically active radiation (PAR) Using obser-vations from OCO-2 we find that precipitation is associatedwith increased CO2 uptake in all tropical biomes a resultthat agrees with half of the TBMs By contrast the relation-ships that we infer from OCO-2 for temperature and PAR aresimilar to the ensemble mean of the TBMs though the resultsdiffer from many individual TBMs These results point to thelimitations of current space-based observations for inferringenvironmental relationships but also indicate the potential tohelp inform key relationships that are very uncertain in state-of-the-art TBMs

1 Introduction

Over the past decade the field of space-based CO2 moni-toring has undergone a rapid evolution The sheer numberof CO2-observing satellites has greatly increased includ-ing GOSATGOSAT-2 (Kuze et al 2009 Nakajima et al2012) TanSat (Yang et al 2018) and OCO-2OCO-3 (Crisp2015 Eldering et al 2019) This expanding observing sys-tem provides atmospheric CO2 observations broadly acrossthe globe making it possible to estimate the distribution andmagnitude of CO2 fluxes in many regions that have sparsein situ surface atmospheric CO2 monitoring (eg the trop-ics and the Southern Hemisphere) For example the OCO-2 satellite launched in July 2014 provides sim 65 000 obser-vations per day that pass quality screening (Eldering et al2017) this dense global set of OCO-2 observations com-bined with inverse modeling techniques has been used toconstrain regional- and continental-scale CO2 sources and

sinks (eg Eldering et al 2017 Liu et al 2017 Crowellet al 2019 Palmer et al 2019 Byrne et al 2020a)

Recent advances in OCO-2 retrievals from the NASAACOS science team have led to widespread reductions inobservation errors (eg OrsquoDell et al 2018) Reducing theerrors in satellite observations of CO2 is critical for under-standing CO2 sources and sinks using inverse modeling aseven small biases in the observations can have an impact onthe CO2 flux estimate (eg Chevallier et al 2007 2014Feng et al 2016 Miller et al 2018) For example Milleret al (2018) evaluated the extent to which OCO-2 retrievalscan detect patterns in biospheric CO2 fluxes and found thatan early version of the OCO-2 retrievals (version 7) is onlyequipped to provide accurate flux constraints across verylarge continental or hemispheric regions by contrast in afollow-up paper Miller and Michalak (2020) revisited satel-lite capabilities in light of recently improved OCO-2 re-trievals and the authors argued that new OCO-2 retrievalscan be used to constrain CO2 fluxes for more detailed regions(ie for seven global biomes)

A further challenge is to use these new global satellitedatasets to evaluate and improve process-based estimates ofthe global carbon cycle provided by terrestrial biosphericmodels (TBMs) TBMs have become an integral tool for un-derstanding regional- and global-scale carbon dynamics andfor predicting future carbon cycling under changing climateWith that said existing TBMs show large uncertainties incarbon flux estimates at multiple spatial and temporal scalesndash at regional and seasonal scales (eg Peng et al 2014King et al 2015) at global and inter-annual scales (eg Piaoet al 2020) and in historical and future projections (egFriedlingstein et al 2006 Huntzinger et al 2017)

One approach to inform TBM development is to estimateflux totals using atmospheric observations and compare thosetotals against TBMs ndash to inform the magnitude seasonal-ity or spatial distribution of fluxes (eg King et al 2015Bastos et al 2018) A more challenging approach is to esti-mate the relationships between CO2 fluxes and environmen-tal drivers using atmospheric observations and compare thoserelationships directly to the relationships in TBMs We definethe term ldquoenvironmental driversrdquo as any meteorological vari-ables or characteristics of the physical environment that canbe modeled or measured and may correlate with net ecosys-tem exchange (NEE) Several studies have shown that thesetypes of comparisons are feasible using in situ atmosphericobservations (eg Dargaville et al 2002 Forkel et al 2016Gourdji et al 2008 2012 Piao et al 2013 2017 Wanget al 2014 Fang and Michalak 2015 Shiga et al 2018Wang et al 2020) Among other studies Fang and Micha-lak (2015) used in situ atmospheric CO2 observations acrossNorth America and an inverse modeling framework to probethe relationships between NEE and environmental driversthe authors compared these relationships directly to those in-ferred from several TBMs and found that TBMs have rea-sonable skill in representing the relationship with shortwave

Atmos Chem Phys 21 6663ndash6680 2021 httpsdoiorg105194acp-21-6663-2021

Z Chen et al Global CO2 fluxes from space 6665

radiation but show weak performance in describing relation-ships with other drivers like water availability SimilarlyShiga et al (2018) used tower-based atmospheric CO2 ob-servations to explore regional interannual variability (IAV)in NEE across North America and found that TBMs disagreeon the dominant regions responsible for IAV this disagree-ment can be linked to differing sensitivities of CO2 fluxesto environmental drivers within the TBMs At an even longertemporal scale Wang et al (2014) employed the atmosphericCO2 growth rate record from Mauna Loa Hawaii USA andthe South Pole for five decades to explore the sensitivity ofthe global CO2 growth rate to tropical temperature the au-thors found that existing TBMs do not capture the observedsensitivity of the growth rate to tropical climatic variabilityimplying a limited ability of these TBMs in representing theimpact of drought and warming on tropical carbon dynamics

More recently a handful of studies have shown that it ispossible to tease out relationships between CO2 fluxes andenvironmental drivers using global satellite observations ofCO2 (eg Liu et al 2017 Byrne et al 2020b) For exampleLiu et al (2017) used observations from OCO-2 to disentan-gle the environmental processes related to flux anomalies intropical regions during the 2015ndash2016 El Nintildeo Byrne et al(2020b) assimilated in situ and GOSAT observations of at-mospheric CO2 and an inverse model framework and foundcontrasting environmental sensitivities of IAV in CO2 fluxesbetween western and eastern temperate North America

The goal of this study is to use atmospheric CO2 obser-vations from OCO-2 to quantify the relationships betweenspatiotemporal patterns in CO2 fluxes and patterns in en-vironmental driver datasets We conduct this analysis foryears 2015ndash2018 and focus on relationships that manifestacross an individual year and individual biome We specif-ically quantify the relationships using a top-down regres-sion framework and a geostatistical inverse model (GIM) Wethen compare the relationships inferred using OCO-2 obser-vations against those inferred from 15 state-of-the-art TBMsfrom the TRENDY model comparison project (v8 httpssitesexeteracuktrendy (last access 28 October 2020) seeTable S1 for a full list of TBMs Sitch et al 2015 Friedling-stein et al 2019) The primary objectives of this analysisare threefold (1) evaluate what kinds of environmental re-lationships we can infer using current satellite observationsfrom OCO-2 (2) assess where and when TBMs do and donot show consensus on the relationships between CO2 fluxesand salient environmental drivers and (3) compare the rela-tionships inferred from OCO-2 against those inferred fromTBMs with the goal of informing and improving TBM de-velopment

2 Methods

21 Overview

We quantify the relationships between CO2 observationsfrom OCO-2 and environmental driver datasets for differentregions of the globe using a top-down regression frameworkand a GIM We cannot directly observe the relationships be-tween CO2 fluxes and environmental driver datasets Withthat said an overarching idea of this study is that these rela-tionships manifest in atmospheric CO2 observations and wecan quantify at least some of these relationships using obser-vations from OCO-2 and a weighted multiple regression Thecoefficients estimated as part of the regression relate patternsin atmospheric CO2 observations to patterns in the environ-mental driver datasets

As part of this analysis we also explore differences in theestimated environmental relationships (ie regression coef-ficients) among different years and different biomes To thisend we estimate separate regression coefficients for eachof seven different global biomes and we estimate sepa-rate coefficients for each individual year of the study pe-riod (2015ndash2018) Hence each coefficient estimated hererepresents the relationship between OCO-2 observations andan environmental driver dataset across an entire year and aglobal biome Miller and Michalak (2020) explored whenand where current OCO-2 observations can be use to detectvariability in surface CO2 fluxes and the authors argue thatin most seasons the satellite can be used to constrain fluxesfrom seven large biome-based regions ndash hence the choice ofthe seven biomes used in this study (Fig 1)

We first conduct this analysis using CO2 observations fromOCO-2 We then conduct a parallel analysis using the out-puts of 15 terrestrial biosphere models (TBMs) from theTRENDY model inter-comparison project (v8) The goal ofthis step is to compare the environmental relationships (ieregression coefficients) that we infer from OCO-2 against theregression coefficients that we estimate from numerous state-of-the-art TBMs We can then identify any similarities or dif-ferences between the TBMs and inferences using OCO-2 ob-servations We specifically analyze TRENDY model outputsfor years 2015ndash2018 the same years as the OCO-2 analysisdescribed above To conduct this analysis we generate syn-thetic OCO-2 observations using each of the 15 TBMs andusing an atmospheric transport model We then run the mul-tiple regression on these synthetic observations This setupmirrors that of Fang and Michalak (2015) and creates anapples-to-apples comparison between the TBMs and OCO-2observations in each case we use atmospheric observations(either real or synthetic) and use the same set of equations toestimate the regression coefficients

The multiple regression used in this study has the follow-ing mathematical form (eg Fang and Michalak 2015)

z = h(Xβ + ζ )+ ε (1)

httpsdoiorg105194acp-21-6663-2021 Atmos Chem Phys 21 6663ndash6680 2021


Figure 1 The seven biome-based regions aggregated from a world biome map in Olson et al (2001)

where z (ntimes 1) is a vector of real or synthetic CO2 observa-tions from OCO-2 X (mtimesp) is a matrix of environmentaldriver datasets (described in Sect 22) and β (ptimes 1) rep-resents the regression coefficients that are estimated as partof the regression Each column of X represents a differentenvironmental driver dataset for a specific biome in a spe-cific year Note that we estimate all of the coefficients for thedifferent environmental drivers and different biomes simul-taneously in the regression model In addition ζ (mtimes1) rep-resents patterns in the fluxes that cannot be described by theenvironmental driver datasets and these values are unknownThis component of the fluxes is also commonly referred to asthe stochastic component and is discussed in Sect 25 h() isan atmospheric transport model (described later in this sec-tion) that relates surface CO2 fluxes (Xβ + ζ ) to the atmo-spheric CO2 observations and ε (ntimes 1) is a vector of errorsin the OCO-2 observations andor in the atmospheric modelThe statistical properties of these errors are estimated beforerunning the regression (described in Sect 24)

Note that this framework assumes linear relationships be-tween the environmental driver datasets and the OCO-2 ob-servations Numerous existing studies have used linear mod-els to approximate relationships with environmental driverdatasets For example studies have used linear models tocompare the relationships between CO2 fluxes and envi-ronmental driver datasets in TBMs (eg Huntzinger et al2011) to infer these relationships using eddy flux observa-

tions (eg Mueller et al 2010 Yadav et al 2010) and toinfer relationships between atmospheric CO2 observationsand environmental driver datasets (eg Gourdji et al 2012Fang et al 2014 Fang and Michalak 2015 Piao et al2013 2017 Roumldenbeck et al 2018)

The equations above require an atmospheric transportmodel (h()) We use the forward GEOS-Chem model (ver-sion v9-02 httpwwwgeos-chemorg last access 28 Oc-tober 2020) in this study and we further use wind fieldsfrom the Modern-Era Retrospective Analysis for Researchand Applications (MERRA-2) to drive atmospheric transportwithin GEOS-Chem (Gelaro et al 2017) The GEOS-Chemsimulations used here have a global spatial resolution of 4

latitude by 5 longitude and therefore are best able to capturebroad regional spatial patterns in atmospheric CO2

22 Environmental driver datasets

We estimate the relationships between OCO-2 observations(either real or synthetic) and environmental driver datasetsdrawn from commonly used meteorological reanalysis Wespecifically consider the following driver datasets as pre-dictor variables in the multiple regression 2 m air tempera-ture precipitation photosynthetically active radiation (PAR)downwelling shortwave radiation and specific humidity

We also include a nonlinear function of 2 m air tempera-ture as an environmental driver dataset in the regression (re-ferred to hereafter as scaled temperature plotted in Fig S1



and described in detail in Supplement Sect S3) Numerousexisting studies show that the relationship between tempera-ture and photosynthesis has a different sign depending uponthe temperature range at sufficiently warm temperatures anincrease in temperature yields a decrease in photosynthesis(eg Baldocchi et al 2017) The scaled temperature func-tion considered here can account for those differences andwe find that this function yields a better modelndashdata fit inthe regression analysis than using temperature alone Thescaled temperature function used here is from the Vegeta-tion Photosynthesis and Respiration Model (VPRM) (Ma-hadevan et al 2008) and describes the nonlinear relationshipbetween temperature and photosynthesis (Raich et al 1991)The function is shaped like an upside-down parabola (shownin Fig S1) Furthermore this type of nonlinear temperaturefunction has been commonly used in existing TBMs (egHeskel et al 2016 Luus et al 2017 Dayalu et al 2018Chen et al 2019)

The environmental driver datasets described above aredrawn from the Climatic Research Unit (CRU) and Japanesereanalysis (JRA) meteorology product (CRUJRA Harris2019) We use environmental driver data from CRUJRA be-cause it is the same product used to generate the TRENDYmodel estimates All flux outputs from TRENDY are pro-vided at a monthly temporal resolution so we input monthlymeteorological variables from CRUJRA into the regressionframework Furthermore we regrid the environmental driverdatasets to a 4 latitude by 5 longitude spatial resolution be-fore inputting these datasets into the regression This spatialresolution matches the resolution of the atmospheric trans-port simulations used in this study (described in Sect 21)The regression coefficients therefore quantify the relation-ships between OCO-2 observations and patterns in environ-mental driver datasets that manifest at this spatial and tem-poral resolution

We subsequently rerun the regression analysis using en-vironmental driver datasets drawn from a second meteoro-logical product Estimates of environmental driver data liketemperature or precipitation can vary among meteorologicalmodels and these differences among models are a source ofuncertainty in the estimated regression coefficients Hencethe use of a second meteorological product can at least par-tially account for these uncertainties We specifically rerunthe regression analysis using environmental driver datasetsdrawn from MERRA-2 We choose MERRA-2 because it isa commonly used global reanalysis product from the NASAGlobal Modeling and Assimilation Office (GMAO) Further-more we use wind fields from MERRA-2 to drive all atmo-spheric transport model simulations in this study (describedin Sect 21) so the use of MERRA-2 for the environmentaldriver datasets in the regression creates consistency with thewind fields in the atmospheric model simulations that sup-port the regression

Note that we do not include any remote sensing indices(eg solar-induced chlorophyll fluorescence or leaf area in-

dex) in the present study Rather the focus of this study is toexplore environmental drivers of CO2 fluxes and not remotesensing proxies for CO2 fluxes Also note that we standard-ize (ie normalize) each of the environmental driver datasetswithin each biome and each year before running the regres-sion as has been done in several previous GIM studies (egGourdji et al 2012 Fang and Michalak 2015) This stepmeans that all of the estimated regression coefficients (β)have the same units are independent of the original units onthe environmental driver data and can be directly comparedto one another

23 Model selection

We use model selection to decide which environmental driverdatasets to include in the analysis of the OCO-2 observa-tions and in the analysis of each TBM using synthetic ob-servations Model selection ensures that the environmentaldriver datasets in the regression (X) do not overfit the avail-able OCO-2 data (z) The inclusion of additional environ-mental driver datasets or columns in X will always improvethe modelndashdata fit in the regression but the inclusion of toomany driver datasets in X can overfit the regression to avail-able OCO-2 data and result in unrealistic coefficients (β)(eg Zucchini 2000) In addition model selection indicateswhich relationships with environmental drivers we can con-fidently constrain and which we cannot given current OCO-2observations (eg Miller et al 2018) In this study we im-plement a type of model selection known as the Bayesianinformation criterion (BIC) (Schwarz et al 1978) and var-ious forms of the BIC have been implemented in numerousrecent atmospheric inverse modeling studies (eg Gourdjiet al 2012 Miller et al 2013 2018 Fang and Michalak2015 Miller and Michalak 2020) Using the BIC we scoredifferent combinations of environmental driver datasets thatcould be included in X based on how well each combinationhelps reproduce either the real or synthetic OCO-2 observa-tions (z Eq 1) We specifically use an implementation ofthe BIC from Miller et al (2018) and Miller and Michalak(2020) that is designed to be computationally efficient forvery large satellite datasets The BIC scores in this imple-mentation are calculated using the following equation

BIC = L+p lnnlowast (2)

where L is the log likelihood of a particular combination ofenvironmental driver datasets (ie columns of X) p is thenumber of environmental driver datasets in a particular com-bination and nlowast is the effective number of independent ob-servations This last variable accounts for the fact that not allatmospheric observations are independent and the modelndashdata residuals can exhibit spatially and temporally correlatederrors (Miller et al 2018) For all simulations here we usean estimate of nlowast for the v9 OCO-2 observations from Millerand Michalak (2020) The first component of Eq 2 (L) re-wards combinations that are a better fit to the OCO-2 ob-



servations (z) whereas the second component of Eq (2)(p lnnlowast) penalizes models with a greater number of columnsto prevent overfitting The best combination of environmen-tal drivers for X is the combination that receives the lowestBIC score Miller et al (2018) describes this implementationof the BIC in greater detail including the specific setup andequations

Note that we run model selection for the OCO-2 dataand rerun model selection for each set of synthetic OCO-2datasets generated using each TBM As a result we some-times select different environmental driver datasets for theanalysis using different TBMs This setup parallels that ofHuntzinger et al (2011) and Fang and Michalak (2015)Furthermore we use the same set of environmental driverdatasets in each year of the study period (eg 2015ndash2018)a setup that parallels existing GIM studies that use multipleyears of atmospheric observations (eg Shiga et al 2018)We estimate different regression coefficients (β) for eachyear of the study period but the actual environmental driverdatasets included in the regression do not change from oneyear to the next An environmental driver dataset is either se-lected to be included for all years in a specific biome (basedon the BIC scores) or it is not used in any year of the analysis

24 Statistical model for estimating the coefficients (β)

Once we have chosen a set of environmental driver datasetsusing model selection we estimate the coefficients (β) thatrelate the real or synthetic OCO-2 observations to these en-vironmental datasets (eg Gourdji et al 2012 Fang andMichalak 2015)

β = (h(X)T9minus1h(X))minus1h(X)T9minus1z (3)

where9 (ntimesn) is a covariance matrix that describes modelndashdata residuals (discussed at the end of this section) Further-more the uncertainties in these estimated coefficients canalso be estimated using a linear equation (eg Gourdji et al2008 Fang and Michalak 2015)

Vβ= (h(X)T9minus1h(X))minus1 (4)

where Vβ

is a ptimesp covariance matrixWe test out two different formulations for the covariance

matrix 9 to evaluate the sensitivity of the results to the as-sumptions made about the covariance matrix parameters Inone set of simulations we model 9 as a diagonal matrixThe diagonal values characterize modelndashdata errors (ε) es-timated for the version 9 retrievals from the recent OCO-2model inter-comparison project (eg Crowell et al 2019)The values have an average standard deviation of 098 ppmand range from 029 to 48 ppm In a second set of simu-lations we use a more complex and more complete formu-lation of 9 9 = h(h(Q)T )+R (eg Fang and Michalak2015) where R (ntimes n) characterizes the modelndashdata errors(described above) and Q (mtimesm) is a covariance matrix

that describes ζ (the patterns in the fluxes that cannot be de-scribed by the environmental driver datasets) This formula-tion is more complete because it fully accounts for the resid-uals between z and Xβ However it is extremely computa-tionally intensive to estimate the coefficients (β) using thiscomplex formulation of 9 We cannot explicitly formulatethis more complex version of 9 due to its large size and thenumber of atmospheric model simulations (h()) that wouldbe required As a result we find the solution to Eq (3) usingthis complex version of 9 by iteratively minimizing the costfunction for a geostatistical inverse model (GIM) (Sects 25and S1) a process that takes approximately 2 weeks for eachyear of model simulations in the setup used here

We use both the simple and complex formulations of 9when analyzing the real OCO-2 observations Both the sim-ple and complex formulations of 9 yield similar estimatesfor the coefficients β as discussed in the Results and discus-sion (Sect 32) When analyzing the 15 TRENDY modelswe only use the simple diagonal formulation of9 ndash becauseof the prohibitive computational costs that would be requiredto run the more complex approach for all 15 TRENDY mod-els

Note that we estimate the values of Q the covariance ma-trix that describes ζ using an approach known as restrictedmaximum likelihood (RML) estimation (eg Mueller et al2008 Gourdji et al 2008 2010 2012) In the Supplementwe discuss the structure of Q in detail describe RML andcompare the estimated parameters for Q against existingstudies

25 Statistical model for estimating CO2 fluxes usingOCO-2 observations

To complement the analysis described above we take an ad-ditional step for the real OCO-2 observations of estimatingζ patterns in the fluxes that cannot be described by the envi-ronmental driver datasets also known as the stochastic com-ponent of the fluxes (Eq 1) This step thereby creates a com-plete estimate of CO2 fluxes using OCO-2 observations Thisadditional step accomplishes two goals First the fluxes in ζcan reveal flux anomalies or patterns that are too complex toquantify using a linear combination of environmental vari-ables andor can indicate the strengths and shortfalls of theregression Second by estimating all components of the CO2fluxes (Xβ and ζ ) we can better evaluate our inferences us-ing OCO-2 against independent ground-based observationsof CO2 This independent evaluation is important becauseOCO-2 observations and the atmospheric transport model(ie GEOS-Chem) can contain errors

We generate a complete estimate of the CO2 fluxes (Xβ+ζ ) by minimizing the cost function for a GIM (eg Kitanidis1986 Michalak et al 2004 Miller et al 2020) We describethis process in detail in Supplement Sect S1 This processrequires two covariance matrices (R and Q) and we use thesame parameters for these covariance matrices as described



above in Sect 24 Note that for the setup here we estimate ζat a spatial resolution of 4 latitude by 5 longitude to matchthat of GEOS-Chem and we estimate ζ at a daily tempo-ral resolution to better account for sub-monthly variability inCO2 fluxes Also note that minimizing the GIM cost functionyields the same estimate for the coefficients (β) as in Eq (3)provided that the covariance matrices in the GIM cost func-tion and in Eq (3) are identical The Supplement Sect S1and Miller et al (2020) describe the process of minimizingthe GIM cost function in greater detail

26 Analysis using real observations from OCO-2

For analysis using OCO-2 observations we employ 10 s av-erages of the version 9 OCO-2 observations (eg Crowellet al 2019) and include both land nadir- and land-glint-moderetrievals Recent retrieval updates have greatly reduced bi-ases that previously existed between land nadir and landglint observations (OrsquoDell et al 2018) Moreover Millerand Michalak (2020) evaluated the impact of these updatedOCO-2 retrievals on the terrestrial CO2 flux constraint in dif-ferent regions of the globe the authors found that the in-clusion of both land nadir and land glint retrievals yieldeda stronger constraint on CO2 fluxes relative to using only asingle observation type

We also include a column of X in all simulations using realOCO-2 observations to account for anthropogenic emissionsocean fluxes and biomass burning This column includesanthropogenic emissions from the Open-Data Inventory forAnthropogenic Carbon dioxide (ODIAC) (Oda et al 2018)ocean fluxes from NASA Estimating the Circulation and Cli-mate of the Ocean (ECCO) Darwin (Carroll et al 2020)and biomass burning fluxes from the Global Fire EmissionsDatabase (GFED) (Randerson et al 2018) We estimate asingle coefficient or scaling factor (β) for this column Thesefluxes are input into the regression at a 4 latitude by 5

longitude spatial resolution to match that of GEOS-ChemThe Supplement Sect S2 contains greater discussion of theseCO2 sources

27 Analysis using the TBMs

We compare the estimated coefficients (β) from real OCO-2observations against simulations using synthetic OCO-2 ob-servations generated from 15 different TBMs in TRENDY(v8) We list out all of the individual models in the TRENDYcomparison in Table S1 Model outputs from the TRENDYproject were provided at a monthly time resolution and thespatial resolution varies from one model to another (thoughmany models have a native spatial resolution of either 05

latitudendashlongitude or 1 latitudendashlongitude) We specificallyuse TRENDY model outputs from scenario 3 simulations inwhich all TBMs are forced with time-varying CO2 climateand land use

Figure 2 Correlation coefficients (r) between environmentaldrivers over temperate forests biome in year 2017 in X (a) andh(X) (b) We find that the correlation between environmentaldrivers (X) are generally low (a) eg PAR and scaled tempera-ture precipitation and specific humidity however when these en-vironmental drivers are passed through the transport model h() andinterpolated to the locations of OCO-2 observations the correlationbetween these drivers becomes much stronger (b) indicating highcollinearity

We generate synthetic OCO-2 observations using each ofthese TBM flux estimates To do so we first regrid eachof the TRENDY model estimates to a spatial resolution of4 latitude by 5 longitude the spatial resolution of theGEOS-Chem model We then run the TRENDY model fluxesthrough the GEOS-Chem model for years 2015ndash2018 and in-terpolate the model outputs to the times and locations of theOCO-2 observations



3 Results and discussion

31 Results of model selection

The model selection results highlight the strengths and limi-tations of using current OCO-2 observations to estimate rela-tionships with environmental driver datasets We use modelselection based on the BIC to determine a set of environmen-tal driver datasets to include in the analysis using OCO-2observations and using the TBMs We only select 10 envi-ronmental driver datasets when we run model selection onthe OCO-2 observations ndash both when we use environmentaldriver datasets from the CRUJRA and MERRA-2 productsWe are generally able to identify at least one or two key en-vironmental relationships in each biome using total columnCO2 observations (shown on the x axis of Fig 3) With thatsaid we are only able to quantify relationships with thesefew salient environmental variables More detailed environ-mental relationships within each biome are difficult to dis-cern

Note that we select a similar number of environmentaldriver datasets when using synthetic OCO-2 observationsthat are generated from each of the TBMs We select any-where between 8 and 13 environmental driver datasets (anaverage of 10 datasets) in the analysis using each of theTBMs This result indicates consistency between the anal-ysis using real OCO-2 observations and the analysis usingsynthetic OCO-2 observations generated using CO2 fluxesfrom each of the 15 different TBMs

Overall we have difficulty detecting the unique contribu-tions of many environmental driver datasets to variability inthe OCO-2 observations This issue is highlighted by an ex-amination of colinearity in the regression model In a re-gression we cannot estimate different coefficients (β) fortwo predictor variables (ie columns of X) that are iden-tical or nearly identical the regression cannot be used toestimate unique coefficients because the predictor variablesthemselves are not unique In regression modeling this phe-nomenon is known as colinearity The coefficients (β) es-timated for colinear variables are often unrealistic and thestandard errors or uncertainties in those coefficients (V

β) are

often unexpectedly large (eg Ramsey and Schafer 2012)Model selection is one way to reduce or remove colinearitycolinear variables by definition do not contribute unique in-formation to a regression and are therefore rarely selectedusing a model selection approach like the BIC One commonmethod for detecting colinearity is to estimate the correla-tion coefficient (r) between different columns of X a valuegreater than sim 055 can indicate the presence of colinearity(eg Ratner 2012)

We find substantial colinearity in the regression analy-sis (Fig 2) This colinearity likely plays an important rolein the model selection results in addition to errors in theOCO-2 observations and errors in the GEOS-Chem modelit represents an important but potentially overlooked chal-

lenge in relating satellite-based CO2 observations to pat-terns in environmental drivers The environmental driverdatasets are passed through the GEOS-Chem model (h())and interpolated the locations of OCO-2 observations aspart of the regression (h(X) Eqs 1 and 3) In other wordsthese driver datasets are input into GEOS-Chem in place ofa traditional CO2 flux estimate This step is necessary sothat the environmental driver datasets can be directly com-pared against patterns in the OCO-2 observations The driverdatasets (ie columns of X) that we use in the regressionare generally unique from one another (ie have unique spa-tial and temporal patterns) However the differences amongmany driver datasets disappear once those datasets have beenpassed through GEOS-Chem Figure 2 displays the corre-lation coefficients (r) among environmental driver datasetsfrom MERRA-2 for temperate forests both before (Fig 2a)and after (Fig 2b) those driver datasets have been passedthrough GEOS-Chem and interpolated to the OCO-2 obser-vations The correlation coefficients increase substantiallyfrom the former to the latter case This colinearity is inde-pendent of errors in the OCO-2 observations and indicates ahard limit on the number of relationships with environmen-tal driver datasets (ie coefficients) that we can quantify inthe regression In other words model selection results are atleast partially limited by the limited sensitivity of OCO-2 ob-servations to variations in these environmental driver datasetsndash either due to atmospheric smoothing andor due to limita-tions in the availability of OCO-2 observations in some re-gions of the globe This limitation is in addition to the un-certainties due to errors in the OCO-2 observations and theGEOS-Chem model which also have a critical impact on in-ferences about CO2 fluxes using OCO-2 observations (egChevallier et al 2007 2014 Miller et al 2018)

32 Environmental relationships inferred usingobservations from OCO-2

We are able to quantify the relationships between OCO-2observations and several key environmental driver datasetsFigures 3 and 4 display the estimated coefficients from theregression analysis using observations from OCO-2 Acrossextratropical biomes PAR is the most commonly selectedvariable This result reflects the fact that light availability isa key factor that drives CO2 flux variability in mid-to-highlatitudes (eg Fang and Michalak 2015 Baldocchi et al2017) As expected the estimated coefficients for PAR arenegative indicating that an increase (or decrease) in PAR inthe model is associated with a decrease (or increase) in NEEand an increase (or decrease) in carbon uptake Note that inthis study negative values for NEE refer to CO2 uptake whilepositive values refer to net CO2 release to the atmosphere

By contrast precipitation and scaled temperature arethe most commonly selected environmental driver datasetsacross tropical biomes The magnitude of the coefficients foreach of these two variables is similar in most biomes indi-



cating that patterns in both have similarly important associ-ations with patterns in CO2 fluxes Specifically a negativecoefficient assigned to scaled temperature indicates that anincrease in air temperature is associated with increased car-bon uptake when air temperatures are cool and reduced car-bon uptake when air temperatures are hot the scaled tem-perature function has the shape of an upside-down parabolaand temperature thus has a different association with CO2fluxes depending upon whether the air temperature is aboveor below the optimal temperature for photosynthesis (egFig S1) Indeed high temperatures in the tropics often ex-ceed the optimal temperature for photosynthesis (eg Bal-docchi et al 2017) which reduces carbon uptake (egDoughty and Goulden 2008) Furthermore negative coef-ficients for precipitation indicate that an increase in precipi-tation is associated with an increase in carbon uptake whichis in line with current knowledge that water availability fa-cilitates photosynthesis across seasonal to annual temporalscales especially in arid or semiarid regions (eg Gatti et al2014 Jung et al 2017)

In addition to this regression analysis we use a GIM toestimate the stochastic component of the fluxes (ζ Eq 1) ndashpatterns in the fluxes that are implied by the OCO-2 obser-vations but do not match any existing environmental driverdataset To this end Fig 5 shows the mean contribution ofeach environmental driver variable and the stochastic com-ponent to the GIM across years 2015ndash2018 using MERRA-2for the environmental driver datasets The magnitude of thestochastic component in this plot is small relative to the con-tribution of different environmental variables and relative tothe contribution of anthropogenic sources Furthermore thestochastic component contains very diffuse spatial patternsand these very broad patterns do not imply any clear defi-ciency in the other components of the GIM For example theregression component of the GIM (Xβ) accounts for 896 of the variance in the estimated fluxes and the stochas-tic component conversely accounts for only 104 of theflux variance Furthermore the regression component whenpassed through the GEOS-Chem model matches OCO-2 ob-servations nearly as well as the full posterior flux estimate(Figs S2 and S13) This result shows that a limited numberof environmental driver datasets can adeptly reproduce broadpatterns in CO2 fluxes across continental and global spatialscales but reinforces the conclusion that current OCO-2 ob-servations are not sufficient to disentangle more complex en-vironmental relationships

In all of the simulations using OCO-2 observations we es-timate a scaling factor (β) for anthropogenic biomass burn-ing and ocean fluxes of near one indicating that these sourcetypes have a magnitude that is broadly consistent with atmo-spheric observations Specifically the estimated scaling fac-tor estimated ranges from 097 to 105 depending upon theyear and simulation Note however that we estimate a singlescaling factor for all of these source types combined and areunable to confidently constrain separate scaling factors for

Figure 3 Estimated coefficients (β) from the TRENDY models(blue) from the ensemble mean of the TRENDY models (black)and from the analysis using OCO-2 (red) Each blue or red dot in-dicates the mean value across all 4 years of the study period Graybars indicate the full range of uncertainties in the coefficients Toconstruct these gray bars we calculate the uncertainties in the coef-ficients estimated for each individual TBM (or for the real OCO-2data) using Eq (4) They gray bars encapsulate all of the uncertaintybounds from all of these individual model calculations Further-more the analysis of OCO-2 includes simulations using MERRA-2 meteorology with a simple formulation of 9 (red square) usingCRUJRA meteorology and a simple formulation of9 (red dot) andusing MERRA-2 and a complex formulation of 9 (the same usedin the GIM red triangle) The coefficients from the analysis usingOCO-2 (red) are broadly within the range of the estimates in TBMs(blue) We further calculate the coefficient of variation (CV) of co-efficients for each environmental driver within the TBMs (b) andwe find that the largest CVs are from the coefficients for precipita-tion



Figure 4 This figure is similar to Fig 3 but shows results for individual years There are no noticeable shifts in the coefficient estimatesbetween El Nintildeo (2015ndash2016 andashb) and non-El Nintildeo years (2017ndash2018 cndashd) from the analysis using OCO-2 (red) Some individual TBMsshow differences of up to 50 in the estimated coefficient among years though many individual TBMs do not

each source a topic discussed in greater detail in the Supple-ment Sect S2

Note that the inferences described here are also broadlyconsistent with independent ground-based atmospheric ob-servations We specifically model atmospheric CO2 usingfluxes estimated from the GIM and compare against regularaircraft observations campaign data from the AtmosphericTomography Mission (ATom Wofsy et al 2018) and obser-vations from the Total Carbon Column Observing Network(TCCON Wunch et al 2011) In most instances the modelresult matches the observations to within the errors specifiedin the inverse model (ie to within the errors specified inthe R covariance matrix) and the modelndashdata comparisonsdo not exhibit any obvious seasonal biases Furthermore wealso model XCO2 using the outputs of the regression analy-sis (Xβ) and these outputs also show good agreement withOCO-2 observations (Fig S13) The Supplement Sect S4Figs S2ndashS13 and Tables S2ndashS3 describe these comparisonsin greater detail

33 Comparison between inferences from OCO-2 andTBMs

The environmental relationships (ie coefficients) estimatedfor the TBMs show a substantial range (Figs 3 and 4) thisspread highlights uncertainties in state-of-the-art TBMs andindicates that there is an opportunity to help inform these re-lationships using atmospheric CO2 observations On the onehand we are only able to infer a limited number of environ-mental relationships using current observations from OCO-2and this fact limits the extent to which we can inform TBMdevelopment using available space-based CO2 observationsOn the other hand we can infer relationships with severalkey environmental drivers (eg Fig 3) and TBMs disagreeon relationships with even these key drivers This result thusindicates the limitations of this analysis but also its strengthsSpecifically Figs 3 and 4 graphically display these resultsfrom the regression analysis ndash the coefficients estimated us-ing OCO-2 observations compared to those estimated fromthe TRENDY models The coefficients from the OCO-2 anal-ysis are almost always within the range of those estimatedusing the ensemble of TBMs With that said the coefficientsestimated for many of the TBMs are far from the value esti-



Figure 5 The contribution of different environmental driver datasets to the flux estimate from the GIM Panel (a) displays the 4-yearmean flux estimate (including both the regression and stochastic components of the flux estimate units of micromol mminus2 sminus1) and panel (b) thecontribution from anthropogenic biomass burning and ocean fluxes Contributions from different environmental drivers including scaledtemperature (c) precipitation (d) and PAR (e) describe most of spatiotemporal variability in terrestrial biospheric CO2 fluxes whereas thestochastic components (ζ ) (f) only account for a small portion of flux variability Note that the inverse modeling results shown in this figureuse environmental driver data from MERRA-2 Also note that the color bars used in panels (a)ndash(b) (c)ndash(e) and (f) are different White colorsin panels (c)ndash(e) indicate that not all environmental drivers are selected in all biomes

mated using OCO-2 implying that observations from OCO-2 can be used to inform the relationships within numerousindividual models Note that in Figs 3 and 4 the x axis isordered based upon the environmental driver variables thatare selected using OCO-2 and we show the estimated coef-ficients for TBMs in which the listed environmental drivervariable is also chosen using model selection Furthermorethe coefficients shown for the TBMs in Figs 3 and 4 are cal-culated using environmental driver datasets from CRUJRAFigure S14 displays the results for the TBMs using environ-mental driver data from MERRA-2 and the results look sim-ilar to those using CRUJRA

We specifically find large differences between the analysisusing OCO-2 and the TBMs for relationships with precipi-tation The relationships between precipitation are arguablymore uncertain within the TBMs than the relationships withother environmental variables (Fig 3a) and are more uncer-tain in tropical biomes than temperate ones This statementis particularly apparent when we examine the coefficient ofvariation for each relationship (Fig 3b) The coefficient ofvariation is a measure of the uncertainty relative to the mag-nitude of the mean and Fig 3b shows the standard deviationin the coefficients from the 15 TBMs divided by the mean co-

efficient from the ensemble of TBMs In addition the TBMsare evenly split on whether the relationship with precipitationis positive or negative across tropical biomes and our anal-ysis using OCO-2 observations agrees with models that esti-mate a negative relationship (ie precipitation is associatedwith greater CO2 uptake) There is substantial disagreementon the magnitude of this relationship even among modelsthat yield a negative relationship the estimate using OCO-2observations falls in the midrange of these TBMs for bothtropical biomes

More broadly the TBMs simulate very different water cy-cling through each ecosystem in spite of the fact that eachmodel uses the same precipitation inputs from CRUJRAThese broader differences in water cycling within the TBMsmay help explain the large uncertainties in the relationshipsbetween CO2 and precipitation and highlight an importantsource of uncertainty within these models Specifically wefind that estimated evapotranspiration (ET) across the TBMsdiffers by almost a factor of 3 among models in some seasonsand biomes and annual ET ranges from 375 to 700 mm overnorthern hemispheric tropical grasslands (Fig 6a) and from530 to 1010 mm over northern hemispheric tropical forests(Fig 6b) These large differences in ET estimates reinforce



Figure 6 Four-year-averaged evapotranspiration (ET) estimatesfrom a suite of 15 TBMs (blue) and from the ensemble mean (black)for northern hemispheric tropical grasslands (a) and for northernhemispheric tropical forests (b) Annual ETs show large differencesin magnitude across the TBMs for both tropical biomes

the very different responses of tropical ecosystems in thesemodels (both tropical forests and tropical grasslands) to pre-cipitation inputs

Indeed existing studies have indicated large uncertaintiesin the responses of tropical forests to water availability (egRestrepo-Coupe et al 2016) and have offered several possi-ble explanations Soil depths and rooting distribution are par-ticularly challenging to model in tropical ecosystems yield-ing uncertainties in the relationship between water availabil-ity and CO2 fluxes (eg Baker et al 2008 Poulter et al2009) For example Poulter et al (2009) argued that currentTBMs tend to underestimate soil depths in tropical forestswhich are critical to guarantee soil water access and to ac-curately simulate dry-season photosynthesis in TBMs Thetreatment of irrigation and other land management practicesalso differs among models and creates further uncertainty(eg Le Queacutereacute et al 2018 Pan et al 2020) To compli-cate matters the role of precipitation in carbon dynamics canvary depending on broader environmental conditions and the

timescales considered (eg Baldocchi et al 2017) For ex-ample excess precipitation is associated with limited lightavailability in regions like the humid tropics and can raisethe water table to a level that inhibits respiration With thatsaid short-term rain events have been shown to boost respi-ration (eg Baldocchi 2008)

Like precipitation relationships with PAR are also highlyuncertain in the simulations using TBMs Most models yieldrelationships with the same sign but those relationships varywidely in magnitude By contrast results using OCO-2 ob-servations are very similar to the ensemble mean of theTBMs This result is particularly interesting given that theindividual TBMs do not show consensus with one anotherThe differences among the TBMs likely stem from the factthat these TBMs exhibit widely varying seasonal cycles andpeak growing season uptake across extratropical biomes Forexample in temperate forests (eg Fig S17) the maximummonthly carbon uptake differs by a factor of 8 among theTBMs and a handful of TBMs estimate a very different sea-sonal cycle than the bulk of the TBMs with maximum uptakeduring the middle of the growing season

In contrast to the discussion of precipitation and PAR ex-isting TBMs yield much better agreement on the relation-ships between CO2 and scaled temperature (Fig 3) In tropi-cal biomes nearly all TBMs agree on the sign of the relation-ship and the estimates using OCO-2 observations are withinthe range of those estimated using TBMs Interestingly theuncertainty bounds on the coefficient estimate using OCO-2are not that much smaller than the range of coefficients fromthe ensemble of TBMs both for tropical grasslands and es-pecially for tropical forests This result points to relativelygood consensus in modeled relationships with temperaturefor tropical grasslands and forests ndash both using TBMs andOCO-2 observations However it also indicates that atmo-spheric observations from OCO-2 potentially have less op-portunity to inform these relationships than for precipitationor PAR where TBMs do not show consensus

The comparisons described above are largely from biomescentered in the tropics and midlatitudes and include few com-parisons for high-latitude biomes (eg the boreal forest ortundra biomes) For example we do not select any environ-mental driver variables for the tundra biome using OCO-2and only select PAR in boreal forests OCO-2 observationsare sparse across high latitudes both due to the lack of sun-light in winter and due to frequent cloud cover in many high-latitude regions We also only select PAR in boreal forests insimulations using 2 of the 15 TBMs This result also reflectsthe limited availability of OCO-2 observations over high-latitude regions for the analysis here we create syntheticOCO-2 observations using each TBM and apply model se-lection to each of these synthetic OCO-2 datasets Hence thesparsity of OCO-2 observations not only affects the modelselection results using real OCO-2 observations but also af-fects the analysis shown in Figs 3 and 4 using the TBMsThe fact that PAR is selected for so few TBMs is not a reflec-



tion on the important role of PAR across the boreal forest inmany TBMs

Note that the analysis described above is based upon themean relationships that we infer for years 2015ndash2018 Wealso explored how these relationships in the models varyduring El Nintildeo (2015ndash2016) and non-El Nintildeo years (2017ndash2018) (Fig 4) The relationships that we estimate do not fun-damentally change between El Nintildeo and non-El Nintildeo yearsand neither does the spread among the models This result in-dicates two conclusions (1) there is not a fundamental shiftin these relationships between El Nintildeo versus non-El Nintildeoyears suggesting that it is not the change in environmen-tal relationships but the change in environmental variablesthemselves that correlates with the change in flux estimatesand (2) the uncertainties in the relationships as estimatedby the TBMs are not higher in El Nintildeo versus non-El Nintildeoyears With that said the magnitude of the estimated coeffi-cient does change in some models between El Nintildeo and non-El Nintildeo years the changes in the coefficients are generallyless than 50 in most models and the models do not showa consistent direction of change between El Nintildeo and non-ElNintildeo years

4 Conclusions

In this study we use 4 years of observations from OCO-2and a top-down statistical framework to evaluate the rela-tionships between patterns in atmospheric CO2 observationsand patterns in environmental driver datasets that are com-monly used in modeling the global carbon cycle We are ableto quantify a limited number of these environmental relation-ships using observations from OCO-2 In spite of these limi-tations we are still able to identify relationships with a smallnumber of salient environmental driver datasets and state-of-the-art TBMs do not show consensus on some of thesekey relationships indicating an opportunity to inform theserelationships using atmospheric CO2 observations

We subsequently compare inferences using OCO-2 againstinferences from 15 state-of-the-art TBMs that have modeloutputs available for the same set of years For the broadregions and time span explored in this study we find neg-ative relationships between patterns in OCO-2 observationsand patterns in precipitation this result agrees with half ofthe TBMs which do not show consensus on relationshipswith precipitation By contrast TBMs exhibit much greaterskill in describing relationships with scaled temperature asimplied by the relatively good agreement among TBMs Infact the uncertainties in the temperature relationship acrosstropical biomes as estimated using OCO-2 observations arenearly as large as the range of estimates using TBMs

More broadly state-of-the-art TBMs disagree on the con-tribution of individual biomes to the global carbon balance aresult highlighted in several studies (eg Poulter et al 2014Sitch et al 2015 Ahlstroumlm et al 2015 Piao et al 2020) In

order to reduce these uncertainties scientists will likely needto reconcile differences in the environmental processes thatdrive these CO2 flux estimates Existing studies have usedin situ atmospheric observations to help quantify and evalu-ate these relationships across the extratropics (eg Fang andMichalak 2015 Hu et al 2019) However this task is muchmore challenging across regions of the globe with sparse insitu observations including most of the tropics In spite ofthe limitations described in this study the advent of satellite-based CO2 observations like those from OCO-2 provides anew opportunity to constrain these environmental relation-ships and thereby provide unique atmospheric constraints onthe global carbon cycle

Data availability The version 9 of 10 s average OCO-2 retrievals isavailable at ftpftpciracolostateeduftpBAKER (last access 29October 2020 Baker 2019) data information of the OCO-2 MIPis available at httpswwwesrlnoaagovgmdccggOCO2 (last ac-cess 9 November 2020 OCO-2 MIP team 2020) data informationof the ObsPack data product is available at httpwwwesrlnoaagovgmdccggobspack (last access 20 September 2020 Coopera-tive Global Atmospheric Data Integration Project 2019)

Supplement The supplement related to this article is available on-line at httpsdoiorg105194acp-21-6663-2021-supplement

Author contributions ZC and SMM designed the study analyzedthe data and wrote the manuscript SS PF VB DSG VH AJ EJEK SL DLL PCM JRM JEMSN BP HT AJW and SZ providedTRENDY model flux estimates All authors reviewed and edited thepaper

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We thank Kim Mueller and Anna Michalakfor their feedback on the research David Baker for his help withthe XCO2 data Colm Sweeny and Kathryn McKain for their helpwith aircraft datasets from the NOAAESRL Global GreenhouseGas Reference Network John Miller Luciana Gatti Wouter Pe-ters and Manuel Gloor for their help with the aircraft data fromthe INPE ObsPack data product Steven Wofsy Kathryn McKainColm Sweeny and Roacuteisiacuten Commane for their help with ATom air-craft datasets and Debra Wunch for her help with the TCCONdatasets Daven Henzersquos work is supported by NOAA grant noNA16OAR4310113 Daniel Gollrsquos work is supported by the ANRCLAND Convergence Institute The data analysis and inverse mod-eling were performed on the NASA Pleiades Supercomputer

Financial support This research has been supported by NASAROSES (grant no 80NSSC18K0976)



Review statement This paper was edited by Martin Heimann andreviewed by Julia Marshall Abhishek Chatterjee and one anony-mous referee

References

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Eldering A Taylor T E OrsquoDell C W and Pavlick RThe OCO-3 mission measurement objectives and expectedperformance based on 1 year of simulated data AtmosMeas Tech 12 2341ndash2370 httpsdoiorg105194amt-12-2341-2019 2019

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Fang Y Michalak A M Shiga Y P and Yadav V Using at-mospheric observations to evaluate the spatiotemporal variabil-ity of CO2 fluxes simulated by terrestrial biospheric modelsBiogeosciences 11 6985ndash6997 httpsdoiorg105194bg-11-6985-2014 2014

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Forkel M Carvalhais N Roumldenbeck C Keeling R HeimannM Thonicke K Zaehle S and Reichstein M En-hanced seasonal CO2 exchange caused by amplified plantproductivity in northern ecosystems Science 351 696ndash699httpsdoiorg101126scienceaac4971 2016

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Friedlingstein P Jones M W OrsquoSullivan M Andrew R MHauck J Peters G P Peters W Pongratz J Sitch S LeQueacutereacute C Bakker D C E Canadell J G Ciais P Jack-son R B Anthoni P Barbero L Bastos A Bastrikov VBecker M Bopp L Buitenhuis E Chandra N ChevallierF Chini L P Currie K I Feely R A Gehlen M GilfillanD Gkritzalis T Goll D S Gruber N Gutekunst S Har-ris I Haverd V Houghton R A Hurtt G Ilyina T JainA K Joetzjer E Kaplan J O Kato E Klein Goldewijk KKorsbakken J I Landschuumltzer P Lauvset S K Lefegravevre NLenton A Lienert S Lombardozzi D Marland G McGuireP C Melton J R Metzl N Munro D R Nabel J E M SNakaoka S-I Neill C Omar A M Ono T Peregon APierrot D Poulter B Rehder G Resplandy L Robertson ERoumldenbeck C Seacutefeacuterian R Schwinger J Smith N Tans P PTian H Tilbrook B Tubiello F N van der Werf G R Wilt-shire A J and Zaehle S Global Carbon Budget 2019 EarthSyst Sci Data 11 1783ndash1838 httpsdoiorg105194essd-11-1783-2019 2019

Gatti L V Gloor M Miller J B Doughty C E Malhi YDomingues L G Basso L S Martinewski A Correia C SBorges V F Freitas S Braz R Anderson L O Rocha HGrace J Phillips O L and Lloyd J Drought sensitivity ofAmazonian carbon balance revealed by atmospheric measure-ments Nature 506 76ndash80 httpsdoiorg101038nature129572014

Gelaro R McCarty W Suaacuterez MJ Todling R Molod ATakacs L Randles CA Darmenov A Bosilovich MGReichle R and Wargan K The modern-era retrospective

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Gourdji S M Mueller K L Schaefer K and MichalakA M Global monthly averaged CO2 fluxes recovered usinga geostatistical inverse modeling approach 2 Results includ-ing auxiliary environmental data J Geophys Res 113 1ndash15httpsdoiorg1010292007jd009733 2008

Gourdji S M Hirsch A I Mueller K L Yadav V An-drews A E and Michalak A M Regional-scale geosta-tistical inverse modeling of North American CO2 fluxes asynthetic data study Atmos Chem Phys 10 6151ndash6167httpsdoiorg105194acp-10-6151-2010 2010

Gourdji S M Mueller K L Yadav V Huntzinger DN Andrews A E Trudeau M Petron G Nehrkorn TEluszkiewicz J Henderson J Wen D Lin J Fischer MSweeney C and Michalak A M North American CO2 ex-change inter-comparison of modeled estimates with results froma fine-scale atmospheric inversion Biogeosciences 9 457ndash475httpsdoiorg105194bg-9-457-2012 2012

Harris I C CRU JRA v1 1 A forcings dataset ofgridded land surface blend of Climatic Research Unit(CRU) and Japanese reanalysis (JRA) data Jan 1901-Dec 2017 University of East Anglia Climatic Re-search Unit Centre for Environmental Data Analysishttpsdoiorg10528513f3635174794bb98cf8ac4b0ee8f4ed2019

Heskel M A OrsquoSullivan O S Reich P B Tjoelker M GWeerasinghe L K Penillard A Egerton J J Creek DBloomfield K J Xiang J Sinca F Stangl Z R Martinez-De La Torre A Griffin K L Huntingford C Hurry VMeir P Turnbull M H and Atkin O K Convergence inthe temperature response of leaf respiration across biomes andplant functional types P Natl Acad Sci USA 113 3832ndash3837httpsdoiorg101073pnas1520282113 2016

Hu L Andrews A E Thoning K W Sweeney C MillerJ B Michalak A M Dlugokencky E Tans P P ShigaY P Mountain M Nehrkorn T Montzka S A McKainK Kofler J Trudeau M Michel S E Biraud S C Fis-cher M L Worthy D E Vaughn B H White J W YadavV Basu S and Van Der Velde I R Enhanced North Ameri-can carbon uptake associated with El Nintildeo Sci Adv 5 1ndash11httpsdoiorg101126sciadvaaw0076 2019

Huntzinger D N Gourdji S M Mueller K L and Micha-lak A M The utility of continuous atmospheric measurementsfor identifying biospheric CO2 flux variability J GeophysRes-Atmos 116 1ndash14 httpsdoiorg1010292010JD0150482011

Huntzinger D N Michalak A M Schwalm C Ciais P KingA W Fang Y Schaefer K Wei Y Cook R B Fisher J BHayes D Huang M Ito A Jain A K Lei H Lu C Maig-nan F Mao J Parazoo N Peng S Poulter B Ricciuto DShi X Tian H Wang W Zeng N and Zhao F Uncertaintyin the response of terrestrial carbon sink to environmental driversundermines carbon-climate feedback predictions Sci Rep 7 1ndash8 httpsdoiorg101038s41598-017-03818-2 2017

Jung M Reichstein M Schwalm C R Huntingford CSitch S Ahlstroumlm A Arneth A Camps-Valls G CiaisP Friedlingstein P Gans F Ichii K Jain A K Kato



E Papale D Poulter B Raduly B Roumldenbeck C Tra-montana G Viovy N Wang Y P Weber U Zaehle Sand Zeng N Compensatory water effects link yearly globalland CO2 sink changes to temperature Nature 541 516ndash520httpsdoiorg101038nature20780 2017

King A W Andres R J Davis K J Hafer M Hayes D JHuntzinger D N de Jong B Kurz W A McGuire A D Var-gas R Wei Y West T O and Woodall C W North Amer-icarsquos net terrestrial CO2 exchange with the atmosphere 1990ndash2009 Biogeosciences 12 399ndash414 httpsdoiorg105194bg-12-399-2015 2015

Kitanidis P K Parameter Uncertainty in Estimation of SpatialFunctions Bayesian Analysis Water Resour Res 22 499ndash507httpsdoiorg101029WR022i004p00499 1986

Kuze A Suto H Shiomi K Nakajima M and Hamazaki TOn-orbit performance and level 1 data processing of TANSO-FTS and CAI on GOSAT Sensors Syst Next-Generation SatellXIII 7474 74740I httpsdoiorg10111712830152 2009

Le Queacutereacute C Andrew R M Friedlingstein P Sitch S HauckJ Pongratz J Pickers P A Korsbakken J I Peters G PCanadell J G Arneth A Arora V K Barbero L BastosA Bopp L Chevallier F Chini L P Ciais P Doney S CGkritzalis T Goll D S Harris I Haverd V Hoffman F MHoppema M Houghton R A Hurtt G Ilyina T Jain AK Johannessen T Jones C D Kato E Keeling R F Gold-ewijk K K Landschuumltzer P Lefegravevre N Lienert S Liu ZLombardozzi D Metzl N Munro D R Nabel J E M SNakaoka S Neill C Olsen A Ono T Patra P PeregonA Peters W Peylin P Pfeil B Pierrot D Poulter B Re-hder G Resplandy L Robertson E Rocher M RoumldenbeckC Schuster U Schwinger J Seacutefeacuterian R Skjelvan I Stein-hoff T Sutton A Tans P P Tian H Tilbrook B TubielloF N van der Laan-Luijkx I T van der Werf G R Viovy NWalker A P Wiltshire A J Wright R Zaehle S and ZhengB Global Carbon Budget 2018 Earth Syst Sci Data 10 2141ndash2194 httpsdoiorg105194essd-10-2141-2018 2018

Liu J Bowman K W Schimel D S Parazoo N C JiangZ Lee M Bloom A A Wunch D Frankenberg C SunY OrsquoDell C W Gurney K R Menemenlis D Gierach MCrisp D and Eldering A Contrasting carbon cycle responsesof the tropical continents to the 2015ndash2016 El Nintildeo Science358 httpsdoiorg101126scienceaam5690 2017

Luus K A Commane R Parazoo N C Benmergui J Eu-skirchen E S Frankenberg C Joiner J Lindaas J MillerC E Oechel W C Zona D Wofsy S and Lin J C Tun-dra photosynthesis captured by satellite-observed solar-inducedchlorophyll fluorescence Geophys Res Lett 44 1564ndash1573httpsdoiorg1010022016GL070842 2017

Mahadevan P Wofsy S C Matross D M Xiao X DunnA L Lin J C Gerbig C Munger J W Chow V Yand Gottlieb E W A satellite-based biosphere parameteriza-tion for net ecosystem CO2 exchange Vegetation Photosynthe-sis and Respiration Model (VPRM) Global Biogeochem Cy22 httpsdoiorg1010292006GB002735 2008

Michalak A M Bruhwiler L and Tans P P A geo-statistical approach to surface flux estimation of atmo-spheric trace gases J Geophys Res-Atmos 109 1ndash19httpsdoiorg1010292003JD004422 2004

Miller S M and Michalak A M The impact of improved satel-lite retrievals on estimates of biospheric carbon balance AtmosChem Phys 20 323ndash331 httpsdoiorg105194acp-20-323-2020 2020

Miller S M Wofsy S C Michalak A M Kort EA Andrews A E Biraud S C Dlugokencky E JEluszkiewicz J Fischer M L Janssens-Maenhout G andMiller B R Anthropogenic emissions of methane in theUnited States P Natl Acad Sci USA 110 20018ndash20022httpsdoiorg101073pnas1314392110 2013

Miller S M Michalak A M Yadav V and Tadic J M Char-acterizing biospheric carbon balance using CO2 observationsfrom the OCO-2 satellite Atmos Chem Phys 18 6785ndash6799httpsdoiorg105194acp-18-6785-2018 2018

Miller S M Saibaba A K Trudeau M E Mountain M Eand Andrews A E Geostatistical inverse modeling with verylarge datasets an example from the Orbiting Carbon Observa-tory 2 (OCO-2) satellite Geosci Model Dev 13 1771ndash1785httpsdoiorg105194gmd-13-1771-2020 2020

Mueller K L Gourdji S M and Michalak A M Globalmonthly averaged CO2 fluxes recovered using a geosta-tistical inverse modeling approach 1 Results using atmo-spheric measurements J Geophys Res-Atmos 113 1ndash15httpsdoiorg1010292007JD009734 2008

Mueller K L Yadav V Curtis P S Vogel C and MichalakA M Attributing the variability of eddy-covariance CO2 fluxmeasurements across temporal scales using geostatistical regres-sion for a mixed northern hardwood forest Global BiogeochemCy 24 httpsdoiorg1010292009GB003642 2010

Nakajima M Kuze A and Suto H The current sta-tus of GOSAT and the concept of GOSAT-2 Interna-tional Society for Optics and Photonics 8533 853306httpsdoiorg10111712974954 2012

OCO-2 MIP team OCO-2 v9 inverse model inter-comparisonproject [data set] available at httpswwwesrlnoaagovgmdccggOCO2_v9mip last access 9 November 2020

Oda T Maksyutov S and Andres R J The Open-source DataInventory for Anthropogenic CO2 version 2016 (ODIAC2016)a global monthly fossil fuel CO2 gridded emissions data productfor tracer transport simulations and surface flux inversions EarthSyst Sci Data 10 87ndash107 httpsdoiorg105194essd-10-87-2018 2018

OrsquoDell C W Eldering A Wennberg P O Crisp D GunsonM R Fisher B Frankenberg C Kiel M Lindqvist H Man-drake L Merrelli A Natraj V Nelson R R Osterman G BPayne V H Taylor T E Wunch D Drouin B J OyafusoF Chang A McDuffie J Smyth M Baker D F Basu SChevallier F Crowell S M R Feng L Palmer P I DubeyM Garciacutea O E Griffith D W T Hase F Iraci L T KiviR Morino I Notholt J Ohyama H Petri C Roehl C MSha M K Strong K Sussmann R Te Y Uchino O and Ve-lazco V A Improved retrievals of carbon dioxide from OrbitingCarbon Observatory-2 with the version 8 ACOS algorithm At-mos Meas Tech 11 6539ndash6576 httpsdoiorg105194amt-11-6539-2018 2018

Olson D M Dinerstein E Wikramanayake E D BurgessN D Powell G V Underwood E C Drsquoamico JA Itoua I Strand H E Morrison J C and LoucksC J Terrestrial Ecoregions of the World A New Map



of Life on EarthA new global map of terrestrial ecore-gions provides an innovative tool for conserving biodiver-sity BioScience 51 933ndash938 httpsdoiorg1016410006-3568(2001)051[0933TEOTWA]20CO2 2001

Palmer P I Feng L Baker D Chevallier F Boumlsch H andSomkuti P Net carbon emissions from African biosphere dom-inate pan-tropical atmospheric CO2 signal Nat Commun 103344 httpsdoiorg101038s41467-019-11097-w 2019

Pan S Pan N Tian H Friedlingstein P Sitch S Shi H AroraV K Haverd V Jain A K Kato E Lienert S Lombar-dozzi D Nabel J E M S Ottleacute C Poulter B Zaehle S andRunning S W Evaluation of global terrestrial evapotranspira-tion using state-of-the-art approaches in remote sensing machinelearning and land surface modeling Hydrol Earth Syst Sci 241485ndash1509 httpsdoiorg105194hess-24-1485-2020 2020

Peng S Ciais P Chevallier F Peylin P Cadule P SitchS Piao S Ahlstroumlm A Huntingford C Levy P Li XLiu Y Lomas M Poulter B Viovy N Wang T andWang X Global Biogeochemical Cycles simulated by terres-trial ecosystem models Global Biogeochem Cy 29 46ndash64httpsdoiorg1010022014GB004931 2014

Piao S Sitch S Ciais P Friedlingstein P Peylin P Wang XAhlstroumlm A Anav A Canadell J G Cong N HuntingfordC Jung M Levis S Levy P E Li J Lin X Lomas M RLu M Luo Y Ma Y Myneni R B Poulter B Sun ZWang T Viovy N Zaehle S and Zeng N Evaluation of ter-restrial carbon cycle models for their response to climate vari-ability and to CO2 trends Glob Chang Biol 19 2117ndash2132httpsdoiorg101111gcb12187 2013

Piao S Liu Z Wang T Peng S Ciais P Huang M AhlstromA Burkhart J F Chevallier F Janssens I A Jeong S J LinX Mao J Miller J Mohammat A Myneni R B PentildeuelasJ Shi X Stohl A Yao Y Zhu Z and Tans P P Weaken-ing temperature control on the interannual variations of springcarbon uptake across northern lands Nat Clim Change 7 359ndash363 httpsdoiorg101038nclimate3277 2017

Piao S Wang X Wang K Li X Bastos A Canadell J GCiais P Friedlingstein P and Sitch S Interannual variationof terrestrial carbon cycle Issues and perspectives Glob ChangBiol 26 300ndash318 httpsdoiorg101111gcb14884 2020

Poulter B Heyder U and Cramer W Modeling the sen-sitivity of the seasonal cycle of GPP to dynamic LAI andsoil depths in tropical rainforests Ecosystems 12 517ndash533httpsdoiorg101007s10021-009-9238-4 2009

Poulter B Frank D Ciais P Myneni R B Andela N BiJ Broquet G Canadell J G Chevallier F Liu Y Yet al Contribution of semi-arid ecosystems to interannualvariability of the global carbon cycle Nature 509 600ndash603httpsdoiorg101038nature13376 2014

Raich J W Rastetter E B Melillo J M Kicklighter D WSteudler P A Peterson J Grace A L Iii B M and Voumlroumls-marty C J Potential Net Primary Productivity in South America Application of a Global Model Ecol Appl 1 399ndash429 1991

Ramsey F and Schafer D The statistical sleuth a course in meth-ods of data analysis Cengage Learning 784 pp 2012

Randerson J Van der Werf G Giglio L Collatz Gand Kasibhatla P Global Fire Emissions Database Version41 (GFEDv4) ORNL DAAC Oak Ridge Tennessee USAhttpsdoiorg03334ORNLDAAC1293 2018

Ratner B Statistical and Machine-Learning Data Mining Tech-niques for Better Predictive Modeling and Analysis of Big DataCRC Press 2012

Restrepo-Coupe N Levine N M Christoffersen B O AlbertL P Wu J Costa M H Galbraith D Imbuzeiro H Mar-tins G da Araujo A C Malhi Y S Zeng X Moorcroft Pand Saleska S R Do dynamic global vegetation models cap-ture the seasonality of carbon fluxes in the Amazon basin Adata-model intercomparison Glob Chang Biol 23 191ndash208httpsdoiorg101111gcb13442 2016

Roumldenbeck C Zaehle S Keeling R and Heimann MHow does the terrestrial carbon exchange respond to inter-annual climatic variations A quantification based onatmospheric CO2 data Biogeosciences 15 2481ndash2498httpsdoiorg105194bg-15-2481-2018 2018

Schwarz G Estimating the dimension of a model The annals ofstatistics 6 461ndash464 1978

Shiga Y P Michalak A M Fang Y Schaefer K An-drews A E Huntzinger D H Schwalm C R ThoningK and Wei Y Forests dominate the interannual variabilityof the North American carbon sink Environ Res Lett 13httpsdoiorg1010881748-9326aad505 2018

Sitch S Friedlingstein P Gruber N Jones S D Murray-Tortarolo G Ahlstroumlm A Doney S C Graven H HeinzeC Huntingford C Levis S Levy P E Lomas M Poul-ter B Viovy N Zaehle S Zeng N Arneth A BonanG Bopp L Canadell J G Chevallier F Ciais P EllisR Gloor M Peylin P Piao S L Le Queacutereacute C Smith BZhu Z and Myneni R Recent trends and drivers of regionalsources and sinks of carbon dioxide Biogeosciences 12 653ndash679 httpsdoiorg105194bg-12-653-2015 2015

Wang K Wang Y Wang X He Y Li X Keeling R F CiaisP Heimann M Peng S Chevallier F Friedlingstein P SitchS Buermann W Arora V K Haverd V Jain A K Kato ELienert S Lombardozzi D Nabel J E Poulter B VuichardN Wiltshire A Zeng N Zhu D and Piao S Causes ofslowing-down seasonal CO2 amplitude at Mauna Loa GlobChang Biol 26 4462ndash4477 httpsdoiorg101111gcb151622020

Wang X Piao S Ciais P Friedlingstein P Myneni R BCox P Heimann M Miller J Peng S Wang T YangH and Chen A A two-fold increase of carbon cycle sensi-tivity to tropical temperature variations Nature 506 212ndash215httpsdoiorg101038nature12915 2014

Wofsy S C Afshar S Allen H M Apel E C Asher EC Barletta B Bent J Bian H Biggs B C Blake D Rand Blake N ATom Merged Atmospheric Chemistry TraceGases and Aerosols ORNL DAAC Oak Ridge TennesseeUSA httpsdoiorg103334ORNLDAAC1581 2018

Wunch D Toon G C Blavier J F L WashenfelderR A Notholt J Connor B J Griffith D W Sher-lock V and Wennberg P O The total carbon column ob-serving network Philos T Roy Soc A 369 2087ndash2112httpsdoiorg101098rsta20100240 2011

Yadav V Mueller K L Dragoni D and Michalak A MA geostatistical synthesis study of factors affecting gross pri-mary productivity in various ecosystems of North America Bio-geosciences 7 2655ndash2671 httpsdoiorg105194bg-7-2655-2010 2010



Yang D Liu Y Cai Z Chen X Yao L and Lu D First GlobalCarbon Dioxide Maps Produced from TanSat MeasurementsAdv Atmos Sci 35 621ndash623 httpsdoiorg101007s00376-018-7312-6 2018

Zucchini W An introduction to model selection J Math Psychol44 41ndash61 httpsdoiorg101006jmps19991276 2000


Abstract

Introduction

Methods

Overview

Environmental driver datasets

Model selection

Statistical model for estimating the coefficients ()

Statistical model for estimating CO2 fluxes using OCO-2 observations

Analysis using real observations from OCO-2

Analysis using the TBMs

Results and discussion

Results of model selection

Environmental relationships inferred using observations from OCO-2

Comparison between inferences from OCO-2 and TBMs

Conclusions

Data availability

Supplement

Author contributions

Competing interests

Acknowledgements

Financial support

Review statement

References


Abstract Observations from the Orbiting Carbon Observa-tory 2 (OCO-2) satellite have been used to estimate CO2fluxes in many regions of the globe and provide new insightinto the global carbon cycle The objective of this study isto infer the relationships between patterns in OCO-2 obser-vations and environmental drivers (eg temperature precip-itation) and therefore inform a process understanding of car-bon fluxes using OCO-2 We use a multiple regression andinverse model and the regression coefficients quantify therelationships between observations from OCO-2 and envi-ronmental driver datasets within individual years for 2015ndash2018 and within seven global biomes We subsequently com-pare these inferences to the relationships estimated from 15terrestrial biosphere models (TBMs) that participated in theTRENDY model inter-comparison Using OCO-2 we areable to quantify only a limited number of relationships be-tween patterns in atmospheric CO2 observations and patternsin environmental driver datasets (ie 10 out of the 42 re-lationships examined) We further find that the ensemble ofTBMs exhibits a large spread in the relationships with thesekey environmental driver datasets The largest uncertainty inthe models is in the relationship with precipitation particu-larly in the tropics with smaller uncertainties for temperatureand photosynthetically active radiation (PAR) Using obser-vations from OCO-2 we find that precipitation is associatedwith increased CO2 uptake in all tropical biomes a resultthat agrees with half of the TBMs By contrast the relation-ships that we infer from OCO-2 for temperature and PAR aresimilar to the ensemble mean of the TBMs though the resultsdiffer from many individual TBMs These results point to thelimitations of current space-based observations for inferringenvironmental relationships but also indicate the potential tohelp inform key relationships that are very uncertain in state-of-the-art TBMs

1 Introduction

Over the past decade the field of space-based CO2 moni-toring has undergone a rapid evolution The sheer numberof CO2-observing satellites has greatly increased includ-ing GOSATGOSAT-2 (Kuze et al 2009 Nakajima et al2012) TanSat (Yang et al 2018) and OCO-2OCO-3 (Crisp2015 Eldering et al 2019) This expanding observing sys-tem provides atmospheric CO2 observations broadly acrossthe globe making it possible to estimate the distribution andmagnitude of CO2 fluxes in many regions that have sparsein situ surface atmospheric CO2 monitoring (eg the trop-ics and the Southern Hemisphere) For example the OCO-2 satellite launched in July 2014 provides sim 65 000 obser-vations per day that pass quality screening (Eldering et al2017) this dense global set of OCO-2 observations com-bined with inverse modeling techniques has been used toconstrain regional- and continental-scale CO2 sources and

sinks (eg Eldering et al 2017 Liu et al 2017 Crowellet al 2019 Palmer et al 2019 Byrne et al 2020a)

Recent advances in OCO-2 retrievals from the NASAACOS science team have led to widespread reductions inobservation errors (eg OrsquoDell et al 2018) Reducing theerrors in satellite observations of CO2 is critical for under-standing CO2 sources and sinks using inverse modeling aseven small biases in the observations can have an impact onthe CO2 flux estimate (eg Chevallier et al 2007 2014Feng et al 2016 Miller et al 2018) For example Milleret al (2018) evaluated the extent to which OCO-2 retrievalscan detect patterns in biospheric CO2 fluxes and found thatan early version of the OCO-2 retrievals (version 7) is onlyequipped to provide accurate flux constraints across verylarge continental or hemispheric regions by contrast in afollow-up paper Miller and Michalak (2020) revisited satel-lite capabilities in light of recently improved OCO-2 re-trievals and the authors argued that new OCO-2 retrievalscan be used to constrain CO2 fluxes for more detailed regions(ie for seven global biomes)

A further challenge is to use these new global satellitedatasets to evaluate and improve process-based estimates ofthe global carbon cycle provided by terrestrial biosphericmodels (TBMs) TBMs have become an integral tool for un-derstanding regional- and global-scale carbon dynamics andfor predicting future carbon cycling under changing climateWith that said existing TBMs show large uncertainties incarbon flux estimates at multiple spatial and temporal scalesndash at regional and seasonal scales (eg Peng et al 2014King et al 2015) at global and inter-annual scales (eg Piaoet al 2020) and in historical and future projections (egFriedlingstein et al 2006 Huntzinger et al 2017)

One approach to inform TBM development is to estimateflux totals using atmospheric observations and compare thosetotals against TBMs ndash to inform the magnitude seasonal-ity or spatial distribution of fluxes (eg King et al 2015Bastos et al 2018) A more challenging approach is to esti-mate the relationships between CO2 fluxes and environmen-tal drivers using atmospheric observations and compare thoserelationships directly to the relationships in TBMs We definethe term ldquoenvironmental driversrdquo as any meteorological vari-ables or characteristics of the physical environment that canbe modeled or measured and may correlate with net ecosys-tem exchange (NEE) Several studies have shown that thesetypes of comparisons are feasible using in situ atmosphericobservations (eg Dargaville et al 2002 Forkel et al 2016Gourdji et al 2008 2012 Piao et al 2013 2017 Wanget al 2014 Fang and Michalak 2015 Shiga et al 2018Wang et al 2020) Among other studies Fang and Micha-lak (2015) used in situ atmospheric CO2 observations acrossNorth America and an inverse modeling framework to probethe relationships between NEE and environmental driversthe authors compared these relationships directly to those in-ferred from several TBMs and found that TBMs have rea-sonable skill in representing the relationship with shortwave






2 Methods

21 Overview





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Introduction

Methods

Overview


Model selection









Conclusions

Data availability

Supplement


Competing interests

Acknowledgements

Financial support

Review statement

References





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Methods

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Model selection









Conclusions

Data availability

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Competing interests

Acknowledgements

Financial support

Review statement

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Methods

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Model selection









Conclusions

Data availability

Supplement


Competing interests

Acknowledgements

Financial support

Review statement

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Conclusions

Data availability

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Competing interests

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Methods

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Model selection









Conclusions

Data availability

Supplement


Competing interests

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Financial support

Review statement

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Introduction

Methods

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Model selection









Conclusions

Data availability

Supplement


Competing interests

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Introduction

Methods

Overview


Model selection









Conclusions

Data availability

Supplement


Competing interests

Acknowledgements

Financial support

Review statement

References









































































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Introduction

Methods

Overview


Model selection









Conclusions

Data availability

Supplement


Competing interests

Acknowledgements

Financial support

Review statement

References

linking global terrestrial co ﬂuxes and environmental drivers: … · 2021. 5. 4. · ce orme des...

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