Evaluating the convergence between eddy-covariance and biometric methods for assessing carbon budgets of forests

Abstract

The eddy-covariance (EC) micro-meteorological technique and the ecology-based biometric methods (BM) are the primary methodologies to quantify CO₂ exchange between terrestrial ecosystems and the atmosphere (net ecosystem production, NEP) and its two components, ecosystem respiration and gross primary production. Here we show that EC and BM provide different estimates of NEP, but comparable ecosystem respiration and gross primary production for forest ecosystems globally. Discrepancies between methods are not related to environmental or stand variables, but are consistently more pronounced for boreal forests where carbon fluxes are smaller. BM estimates are prone to underestimation of net primary production and overestimation of leaf respiration. EC biases are not apparent across sites, suggesting the effectiveness of standard post-processing procedures. Our results increase confidence in EC, show in which conditions EC and BM estimates can be integrated, and which methodological aspects can improve the convergence between EC and BM.

ARTICLE

Received 19 May 2015 | Accepted 27 Oct 2016 | Published 14 Dec 2016

M. Campioli1, Y. Malhi2,*, S. Vicca1,*, S. Luyssaert3,*,w, D. Papale4,5, J. Penuelas6,7, M. Reichstein8,M. Migliavacca8, M.A. Arain9 & I.A. Janssens1

The eddy-covariance (EC) micro-meteorological technique and the ecology-based biometric methods (BM) are the primary methodologies to quantify CO2 exchange between terrestrial ecosystems and the atmosphere (net ecosystem production, NEP) and its two components, ecosystem respiration and gross primary production. Here we show that EC and BM provide different estimates of NEP, but comparable ecosystem respiration and gross primary production for forest ecosystems globally. Discrepancies between methods are not related to environmental or stand variables, but are consistently more pronounced for boreal forests where carbon uxes are smaller. BM estimates are prone to underestimation of net primary production and overestimation of leaf respiration. EC biases are not apparent across sites, suggesting the effectiveness of standard post-processing procedures. Our results increase condence in EC, show in which conditions EC and BM estimates can be integrated, and which methodological aspects can improve the convergence between EC and BM.

1 Centre of Excellence PLECO (Plant and Vegetation Ecology), Department of Biology, University of Antwerp, 2610 Wilrijk, Belgium. 2 Environmental Change Institute, School of Geography and the Environment, University of Oxford, Oxford OX1 3QY, UK. 3 LSCE CEA-CNRS-UVSQ, Orme des Merisiers, F-91191 Gif-sur-Yvette, France. 4 DIBAF, University of Tuscia, 01100 Viterbo, Italy. 5 Euro-Mediterranean Center on Climate Change, CMCC, 73100 Lecce, Italy. 6 CSIC, Global Ecology Unit, CREAF-CEAB-CSIC-UAB, Cerdanyola del Valls, 08193 Barcelona, Catalonia, Spain. 7 CREAF, Cerdanyola del Valls, 08193 Barcelona, Catalonia, Spain. 8 Max Planck Institute for Biogeochemistry, 07745 Jena, Germany. 9 School of Geography & Earth Sciences, McMaster University, Hamilton, Ontario, Canada L8S 4K1. * These authors contributed equally to this work. w Present address: Department of Ecological Science, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands. Correspondence and requests for materials should be addressed to M.C. (email: mailto:[email protected]

Web End [email protected] ).

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Evaluating the convergence between eddy-covariance and biometric methods for assessing carbon budgets of forests

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13717

The exchange of carbon dioxide (CO2) between terrestrial ecosystems and the atmosphere is one of the major interactions between the biosphere and the atmosphere

(Fig. 1), a key descriptor of ecosystem functioning and a major inuence on atmospheric CO2 concentration. Two empirical approaches are generally used to quantify ecosystem CO2 exchange at the ecosystem level: the eddy-covariance technique (EC) and biometric methods (BM).

The EC technique features sound underlying micro-meteorological principles, continuous monitoring, little perturbation or damaging of the system sampled and a sampling area (footprint) well suited for the scale of ecosystem-level estimates (Table 1). The long time series with high temporal resolution generated by EC can give detailed insights into the interactions between CO2 uxes and synoptic and seasonal variability.

Therefore, EC is very attractive for long-term monitoring of the net ecosystem-atmosphere CO2 exchange1 (or net ecosystem production2, NEP) and for the elucidation of its temporal changes and environmental controls. These properties have made EC the dominant methodology for estimating net and bulk uxes of CO2 exchange1,3,4 and the standard method in a number of long-term and large-scale research infrastructures (for example, ICOS, NEON, AmeriFlux, TERN). However, as with every experimental method, EC has some drawbacks (Table 1), three of which are of particular importance. First, advective and low-frequency ows of CO2 are difcult to capture and can potentially lead to underestimation of uxes during periods with low air turbulence,

typically ecosystem respiration at night5. This drawback is particularly important in the presence of variable topography, favouring air drainage and breezes6, or thick canopy, hindering mixing of the air within and above it7,8. Second, EC has a persistent inability to close the surface energy budget, leading to fears that if energy uxes are being underestimated, then CO2 uxes may also be underestimated1. Third, EC measures NEP directly, but its two main components, ecosystem photosynthetic CO2 uptake, or gross primary production (GPP), and ecosystem carbon (C) release, or ecosystem respiration (Reco) (Fig. 1), can only be estimated indirectly by post-processing the data of CO2 exchange9,10. In other words, EC relies on a single measurement to estimate net and bulk CO2 uxes.

The BM approach uses a well-established but un-standardized set of techniques, such as plant growth assessment, chamber-based ux measurements and repeated stock inventories that allow a direct estimation of the component processes of the ecosystem C cycle (for example, net primary production (NPP), heterotrophic respiration (Rh) and autotrophic respiration (Ra); Fig. 1; Table 1) and changes in soil and biomass stock, from which NEP, Reco and GPP can be calculated. Advantages of this approach include insights into the internal C dynamics of an ecosystem, (for example, partitioning between Ra and Rh, allocation of photosynthates between Ra and NPP and allocation of NPP between leaves, wood and ne roots), and applicability to almost any site (for example, small plots, sites with strong spatial heterogeneity, high canopy thickness or steep topography) and meteorological conditions (for example, periods with low air turbulence) without the requirements imposed by the EC technique. Typically, BM approaches are also very useful for evaluating the impact of environmental manipulative experiments on the C cycle11, whereas EC cannot be applied to experimental plots of limited size5. On the other hand, BM approaches also have drawbacks (Table 1). In particular, biometric measurements are typically performed on few replicated individuals and plant organs (for example, few leaves and branches) or small ecosystem plots that need to be up-scaled, assuming homogeneity within and among plants and in all relevant environmental variables (for example, soil moisture, nutrients, microclimate, soil type). Moreover, there is always the possibility that some potentially important components of the C budget have not been accounted for (for example, transfer of photosynthates to mycorrhizae production, ground ora productivity or loss to herbivory) and that some of the biometric techniques can disturb the portion of the ecosystem being sampled (for example, root measurements disturb the soil, stem respiration chambers can affect microclimate and pressure of the air space sampled). Finally, most biometric measurements cannot be easily monitored continuously, making the linkage between changes in uxes to specic weather events more challenging.

As the advantages of BM (for example, applicability to most sites and environmental conditions) largely match the potential disadvantages of the EC technique (and vice versa) and the two techniques are fully independent, the comparison between EC and BM has been developed as the most suited way to corroborate both approaches12. NEP estimates obtained with EC and BM have been compared in a number of studies, but no clear picture has yet emerged. Agreement of multi-year NEP estimates between methods varied widely among sites, from very good13 to very poor14. A primary cause of our limited understanding of ECBM convergence lies in the fact that existing empirical studies are based only on one or few sites (for example, ve sites12) and very few studies have attempted quantitative multi-site syntheses15. In practice, this has made it difcult to pin-point the reasons behind the observed cases with low convergence because statistical analyses have not been

NEP

Rabelowground NPPbelowground

GPP

Reco

Raaboveground NPPaboveground

Rh-soil

Rh-cwd

Figure 1 | Schematic representation of the major components of the forest carbon cycle. Raaboveground and Rabelowground: above- and below-

ground autotrophic respiration, respectively (their sum is indicated as Ra); Rh-soil and Rh-cwd: heterotrophic respiration from soil and coarse woody debris, respectively (their sum is indicated as Rh); NPPaboveground

and NPPbelowground: above- and belowground net primary production,

respectively (their sum is indicated as NPP); Reco: ecosystem respiration (Reco Ra Rh); GPP: gross primary production (GPP NPP Ra), and

NEP: net ecosystem production (NEP GPP Reco NPP Rh). Each ux

is associated with an arrow. Arrows pointing down indicate carbon (C) uptake, arrows pointing up indicate C release, whereas the up-down arrow indicates that both C release and C uptake can occur. The dark blue arrow indicates NEP, the mid-blue arrows indicate the primary components of NEP (Reco and GPP), whereas the light blue arrows indicate the components of Reco and GPP.

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Table 1 | Positive and negative characteristics of eddy-covariance and biometric methods.

Characteristics of the technique EC BM

Directness of approach1,25 *, / w

Temporal and spatial up-scaling1,18

Applicability to small-footprint studies

Interference with sampled system1

Sensitivity to low turbulence environment1,8,18

Impact of measuring set-up on microclimate1,53

Impact of complex terrain1

Compartment-level understanding and partitioning of uxes and allocation16

Unaccounted/miscounted carbon uxes at tree organ/ecosystem compartment level (e.g. understory uxes, herbivory)16,54,55

Set-up costs56

Ongoing labour requirements1

Technical capacity requirements for data collection and processing

Very positive ( ), positive ( ), negative ( ) or very negative ( ) characteristics of the eddy-covariance (EC) and biometric (BM) methods used for the determination of net ecosystem

production (NEP), ecosystem respiration (Reco) and gross primary production (GPP) of forest ecosystems. *NEP.

wReco and GPP.

Table 2 | Comparison of carbon uxes obtained from eddy-covariance or biometric methods for forests worldwide and in the main climatic zones.

BM versus EC BMDS versus EC NEP Reco GPP NEP

Global

Site replicates (n) 31 25 18 7 Absolute difference (means.e.m) 9832 12061 2567 3287

Signicance difference (P) 0.0042** 0.061 0.71 0.73 Relative difference (means.e.m in %) NA 134 54 NA

Boreal

Site replicates (n) 6 6 4 1 Absolute difference (means.e.m) 16744 18975 8959 26

Signicance difference (P) 0.013* 0.031* 0.23 NA Relative difference (means.e.m in %) NA 187 85 NA

Temperate

Site replicates (n) 22 15 11 6 Absolute difference (means.e.m) 9528 16085 59100 33102

Signicance difference (P) 0.0028** 0.079 0.57 0.76 Relative difference (means.e.m in %) NA 166 66 NA

Tropical

Site replicates (n) 3 4 3 NA Absolute difference (means.e.m) 10275 137138 182119 NA

Signicance difference (P) 1.0 0.39 0.26 NA Relative difference (means.e.m in %) NA 55 53 NA

Statistics of the comparison of net ecosystem production (NEP), ecosystem respiration (Reco) and gross primary production (GPP) at global scale and for the boreal, temperate and tropical zones, separately, assessed with eddy-covariance (EC) and two types of biometric methods: standard biometric methods based on measurements of production and respiration (BM) and biometric methods based on consecutive inventories of ecosystem carbon stocks (BM ). The difference between methods is expressed as Absolute difference (BM estimate EC estimate) and Relative difference

(BM estimate EC estimate)/((BM estimate EC estimate)/2). Difference at 0.001oPo0.01, 0.01oPo0.05 and 0.05oPo0.10 are marked with **, * and , respectively. The notation NA

indicates data not available.

undertaken yet. Comparability of BM and EC estimates for Reco and GPP has been studied even less than for NEP. We are not aware of any multi-site synthesis efforts and existing comparisons are limited to 34 sites within the same region16,17. Lack of knowledge about EC and BM comparison for Reco and GPP complicates the analysis of NEP estimates obtained by the two approaches (for example, the two approaches could give similar NEP while diverging in their estimation of the two components). As a result of the multiple limitations on the corroboration of the empirical estimates of NEP, Reco and GPP, our understanding of the uncertainty of ecosystem C uxes has stagnated for over a decade: the suspected biases of EC have not been claried18 and the uncertainties in BM estimates remain underexplored.

Here we investigate the agreement between EC- and BM-based estimates of ecosystem CO2 uxes by addressing three research questions: how do EC and BM-based uxes compare across and within the boreal, temperate and tropical forest zones? Is any discrepancy between EC and BM ux estimates related to stand, environmental and methodological variables? Can the ECBM comparison provide insights into long-standing suspected biases of the EC technique? The answers are provided by analyzing a novel EC and BM data set comprising annual estimates of NEP, Reco and GPP for 40 sites across ve continents, spanning boreal, temperate and tropical forests. The convergence between EC and BM uxes is analysed through the absolute and relative ux difference, globally and for the three climatic zones separately,

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and by testing the correlation of the ux differences with a large set of stand, environmental and methodological variables (for example, indices of topographical complexity, leaf are index, mean annual temperature, approaches to scale up the tree respiration). It is found that EC and BM provide globally comparable estimates of Reco and GPP but different NEP, which is smaller and more susceptible to biases. Moreover, biases of opposite direction are likely to cancel out when estimating Reco and GPP. Low convergence is associated with BM approaches underestimating NPP and neglecting light inhibition of leaf dark respiration, with discrepancies more pronounced for the boreal zone. Major EC biases are not apparent across sites, increasing our condence in this technique.

ResultsData set of process components of ecosystem carbon cycle. Our uniform and quality-checked data set of BM and EC-based forest C uxes comprised 31 sites with BM-based NEP (NEPBM) and

EC-based NEP (NEPEC), 25 sites with BM-based Reco (RecoBM) and EC-based Reco (RecoEC) and 18 sites with BM estimates of GPP (GPPBM) and EC estimates of GPP (GPPEC) (Supplementary Tables 14; Supplementary Fig. 1; Supplementary Data 1). About 6070% of the sites were in the temperate zone, 2025% in the boreal zone and 1015% in the tropical zone (Table 2). NEP ranged from 110 to 830 gC m 2 y 1, Reco from 460 to

3,300 gC m 2 y 1, and GPP from 600 to 3,600 gC m 2 y 1 (EC data). Furthermore, BM data allowed insights into the different components of the C cycle of the studied forests. First, NPP ranged from 170 to 1,500 gC m 2 y 1, Ra from 490 to 1,900 gC m 2 y 1 whereas soil heterotrophic respiration (Rh-soil) from 170 to 1,400 gC m 2 y 1. Second, leaves, aboveground wood and roots accounted on average for 302% (mean and s.e.m), 342% and 303% of NPP, respectively, and 394%, 223% and 384% of Ra, respectively. Third, ne roots accounted for 707% of root NPP. Fourth, Reco was composed of 553% soil respiration (Rsoil), 282% leaf respiration (Rleaf), 152% aboveground wood respiration (Rwood) and 51% heterotrophic respiration of coarse woody debris (Rh-cwd), that is, 683% by Ra and 323% by Rh.

Net ecosystem production. NEPBM agreed with NEPEC along the range of ux measurements as indicated by the slope of the regression NEPBM versus NEPEC (1.06; CI95% 0.741.53,

R2 0.54) (Fig. 2a). However, NEPEC was signicantly larger

than NEPBM (Po0.01; mean difference 9832 gC m 2 y 1; Table 2). This trend was caused by the extratropical sites, particularly in the boreal zone, where the mean difference was as large as 16744 gC m 2 y 1 (Table 2).

The difference between NEPEC and NEPBM was not correlated to the elevation variability, topographical slope and leaf area index (LAI), or to any of the other environmental and stand variables considered (Table 3). Similarly, the difference between NEPEC and NEPBM was not correlated to the type of BM approach applied (that is, different methods to measure ne root NPP, leaf NPP and Rh-soil, different quality of the allometric relationships used to estimate wood NPP and accounting or not for Rh-cwd; Table 3; Supplementary Fig. 2). Finally, the difference between NEPEC and NEPBM-DS (BM-based NEP derived from the difference in ecosystem C stocks between two points in time, thus avoiding the use of NPP and Rh data, see Methods and Supplementary Table 5) was also not statistically signicant (Table 2).

Ecosystem respiration. The regression between RecoBM and

RecoEC had a slope of 0.86 (CI95% 0.731.02; R2 0.87)

(Fig. 2b). RecoBM was on average 134% larger than RecoEC (marginally signicant at P 0.061). Although the differences

between EC- and BM-based estimates of Reco did not present any correlation with the indices of topographical complexity, LAI or any other environmental or stand variables (Table 3), RecoBM

and RecoEC were signicantly different for the boreal forests (difference 187%, P 0.031) but were not signicantly

different for the temperate (166%, P 0.079) and tropical

forests (55%, P 0.39) (Table 2).

a

1,500

1,000

NEP BM (g C m2 y1 )

500

0

500

500 0 500 1,000 1,500

NEPEC (g C m2 y1)

b

4,000

Reco BM (g C m2 y1 )

3,000

2,000

1,000

0

0 1,000 2,000 3,000 4,000

RecoEC (g C m2 y1)

c

4,000

3,000

GPP BM (g C m2 y1 )

2,000

1,000

0

0 1,000 2,000 3,000 4,000

GPPEC (g C m2 y1)

Figure 2 | Comparison of carbon uxes obtained from eddy-covariance or biometric methods for worldwide forests. (a) Net ecosystem production (NEP, n 31), (b) ecosystem respiration (Reco, n 25) and (c) gross

primary production (GPP, n 18) from eddy-covariance (EC; x axis) and

biometric (BM; y axis) methods. Bars indicate condence intervals which are derived from uncertainty ranges related to biome and latitude, constrained by a reduction factor depending on the methodology and by the number of replicate years of measurement (see Methods). The dotted line is the 1:1 line.

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Table 3 | Relationship between the difference in forest carbon uxes estimated from eddy-covariance and biometric methods and site or methodological characteristics.

Variables Category (units) NEPEC

NEPBM

RecoECRecoBM GPPECGPPBM

Difference Relative difference

Relative difference

P R2 P R2 P R2

Topography, environmental and stand variablesElevation variability m 0.89 o0.01 0.82 o0.01 0.13 0.13 Topographical slope % 0.80 o0.01 0.42 0.03 0.086w 0.17

Leaf area index m2 m 2 0.36 0.03 0.91 o0.01 0.60 0.02 Leaf type Needleleaved/broadleaved/mixed 0.27 0.04 0.24 0.07 0.44 0.04

Leaf habit Evergreen/deciduous/mixed 0.47 0.02 0.32 0.06 0.11 0.16 Fertility Low/medium/high 0.28 0.05 0.61 0.01 0.57 0.07w Climate zone Boreal/temperate/tropical 0.16 0.07w 0.12 0.15 0.34 0.08 Mean annual precipitation mm per year 0.31 0.02w 0.25 0.06 0.34 0.06 Mean annual temperature C 0.42 0.05w 0.13 0.10 0.22 0.09

Methodological variantsMethods to measure ne root NPP Sequential coring/ingrowth cores/ minirhizotron technique/other

0.22 0.11 NA NA 0.11 0.32

Allometric relationships to measure wood NPP Low/moderate/high quality 0.58 0.04 NA NA 0.69 0.02 Method of measuring leaf NPPz leaf fall collection/allometry 0.43 0.04 NA NA 0.85 o0.01

Chamber method to measure Rsoil NSNF/NSF NA NA 0.008** 0.34 NA NA Scrubbing of CO2 before Rsoil measurementy Yes/no NA NA 0.22 0.09 NA NA

Methods to measure Rh-soil Root exclusion/indirectly from estimation of root respiration/component integration/other

0.59 0.03 NA NA NA NA

Consideration of Rh-cwd Yes/no 0.16 0.07 0.84 o0.01 NA NA Variables of models for integration of Rsoil atannual scale

Soil temperature/soil temperature and water NA NA 0.16 0.10 NA NA

Variables of models for integration of Rleaf at annual scale

Temperature/temperature in combination with other

NA NA 0.13 0.11 0.32 0.07

Parameterization of models for integration of Rleaf at annual scale

Site-specic/generic NA NA 0.043* 0.17 0.40 0.04

Variability of temperature sensitivity of Rleaf in models for integration of Rleaf at annual scale

Yes/no NA NA 0.23 0.06 0.65 0.013

Consideration of light inhibition of leaf dark respiration in Rleaf

Yes/no NA NA 0.041* 0.17 0.43 0.04

Consideration of leaf growth respiration in Rleaf

Yes/no NA NA 0.94 o0.01 0.64 0.14

Consideration of wood growth respiration in Rwood

Yes/no NA NA 0.34 0.039 0.54 0.024

Variables of models for integration of Rwood at annual scale

NA NA 0.25 0.07 0.086w 0.21

Variable used to scale up Rwood at stand level Wood volume/wood area NA NA 0.37 0.04 0.44 0.04 Separation contribution of branch and stem inRwood

Yes/no NA NA 0.68 o0.01 0.42 0.04

NA, not applicable; NPP, net primary production; NSF, non-steady-state through-ow chamber (closed dynamic chamber); NSNF, non-steady-state non-through-ow chamber (closed static chamber); Rleaf, leaf respiration; Rh-cwd, heterotrophic respiration of coarse woody debris; Rh-soil, heterotrophic soil respiration; Rsoil, soil respiration; Rwood, aboveground wood respiration.

Statistics (signicance level (p) and R2) for the ordinary least squares regressions between the difference in estimates of net ecosystem production (NEP), ecosystem respiration (Reco) and gross primary production (GPP) determined with eddy-covariance (subscript EC) or biometric methods (subscript BM) and site characteristics or methodological variants of biometric methods. Difference at0.001oPo0.01, 0.01oPo0.05 and 0.05oPo0.10 are marked with **, * and , respectively.

wIn case of heteroskedasticity the square of Pearsons correlation was reported.

zOnly for sites dominated by evergreen species. yOnly for sites with NSF system to measure Rsoil.

Temperature/temperature in combination with other

The degree of the convergence between RecoBM and RecoEC differed according to the type of chamber technique used to measure Rsoil. For sites where closed static chambers or non-steady-state non-through-ow chambers (NSNF) were used, RecoBM and RecoEC did not differ signicantly (P 0.36;

Fig. 3a). On the other hand, the use of closed dynamic chambers or non-steady-state through-ow chamber (NSF) resulted in RecoBM signicantly larger than RecoEC (20%, Po0.001; Fig. 3a).

Within the NSF group, the low level of convergence between RecoBM and RecoEC did not differ (P 0.22) when standard

systems and systems prescribing scrubbing of CO2 before the ux measurements (for example, Li-Cor LI-6400-09 system; LI-COR Biosciences, Lincoln, USA) were compared (Table 3). Also the

BM approach used for measuring Rleaf had an impact on the convergence between RecoBM and RecoEC. Neglecting light inhibition of leaf dark respiration increased the difference between methods by about 20% (P 0.041; Fig. 3b; Table 3).

Likewise, models used to scale up point measurements of Rleaf to annual values also increased the difference between methods by about 20% when they had a generic formulation that is, without a site-specic parameterization (P 0.043; Fig. 3c; Table 3). The

different chamber systems for measuring Rsoil affected the convergence between RecoBM and RecoEC also when their effect was disentangled from the effect of light inhibition and parametrization type of leaf respiration (Supplementary Fig. 3). On the other hand, the effect of neglecting light inhibition was

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stronger than the parameterization type as it was the only one signicant when the two effects were disentangled. In fact, a two-way analysis of variance (ANOVA) accounting for Rleaf light inhibition (yes/no) and parametrization type (site-specic/ generic), performed only for sites with NSF measurements, showed that only light inhibition was signicant (P 0.035;

parametrization type: P 0.23; interaction term: P 0.70).

No impact was observed on the convergence between RecoBM

and RecoEC from other technical variants in measuring RecoBM. The latter included: considering (or neglecting) Rh-cwd and the growth respiration of Rleaf and Rwood; the differentiation of Rwood in stem and branch respiration; the types of model drivers (temperature or others) used for the annual estimation of Rleaf, Rwood and Rsoil; the variability of the temperature sensitivity of models of Rleaf, and the type of upscaling variable used for Rwood (wood volume or wood area) (Table 3). Similarly, the partitioning method used to derive RecoEC from NEPEC did not have a major impact on the difference between RecoEC and

RecoBM. The use of the daytime derived Reco instead of night time derived Reco decreased the divergence between RecoEC and

RecoBM (from 137% to 94%). However, this improvement was not statistically signicant (P 0.29) because daytime derived

RecoEC did not differ signicantly from night time derived RecoEC (44%, daytime RecoEC4night time RecoEC; P 0.64).

Gross primary production. The regression of GPPBM versus GPPEC had a slope of 0.84 (CI95% 0.700.99; R2 0.90). The

agreement between methods was conrmed by the small and non-signicant relative difference between GPPBM and GPPEC (54%). The mean difference between GPPBM and GPPEC was small (up to 8%) and non-signicant also when the analysis was performed for the three climatic zones separately (Table 2). As for NEP and Reco, the differences between EC- and BM-based estimates of GPP were not related to any environmental or stand variables (Table 3). The relationship between the GPPBM and

GPPEC difference and the topographical slope was marginally signicant, but this was due to one outlier (Supplementary Fig. 4; the relationship was not signicant at P 0.19 when the outlier

was removed) and was therefore considered irrelevant. The impact of different BM approaches to measure NPP, Rleaf and Rwood did not have any signicant impact on the difference between GPPEC and GPPBM, except for a minor effect of the variables used to model Rwood (P 0.086) (Table 3). As for Reco,

the use of daytime ux data, instead of night time ux data, for the calculation of GPPEC (GPPEC RecoEC NEPEC) improved

the difference between GPPEC and GPPBM (from 55% to 22%). However, this change was non-signicant (P 0.81)

mainly because daytime-data derived GPPEC did not differ than night time-data derived GPPEC (22%, daytime GPPEC 4 night time GPPEC, P 0.91).

DiscussionHere we will discuss four major points: the insight that our analysis provides on EC and on BM, the low convergence between NEPEC and NEPBM, the ECBM convergence for Reco and GPP and the different degree of the methodological convergence observed for NEP, Reco and GPP.

As no recognized reference method exists for CO2 exchange in ecosystems, in principle, it is not possible to evaluate the correctness of EC in measuring NEP, and in assessing Reco and GPP. However, our study provided several indirect indications about the general reliability of EC-based estimates of C uxes. For example, the lack of correlation of the difference between EC- and BM-based estimates of C uxes versus site topographical complexity and LAI suggests that the standard post-processing

a

0.4

Rel. diff. Reco BM Reco EC

0.2

Rel.diff. P = 0.009 P = 0.001

P = 0.36

0.0

0.2

NSF NSNF

Soil chamber system

b

Rel. diff. Reco BM Reco EC

0.4

0.2

Rel.diff. P = 0.041 P = 0.019

P = 0.56

0.0

0.2

No Yes

Accounting photoinhibition

c

0.4

P = 0.028

Rel.diff. P = 0.043

P = 0.48

Rel. diff. Reco BM Reco EC

0.2

0.0

0.2

Generic Site

Parameterization model Rleaf

Figure 3 | Impact of variants of biometric methods on the difference between ecosystem respiration from biometric methods and eddy-covariance. The relative difference between ecosystem respiration from biometric methods (RecoBM) and eddy-covariance (RecoEC)

[(RecoBM RecoEC)/((RecoEC RecoBM)/2)] when (a) using different

chamber systems to measure soil respiration (NSF: non-steady-state through-ow chamber; NSNF: non-steady-state non-through-ow chambers), (b) whether light inhibition is accounted for when estimating leaf respiration (Rleaf), and (c) employing generic or site-specic parameterization for the empirical models used to scale up the point measurements of Rleaf to the annual scale. Points indicate means and bars the standard error of the mean. The P value above each point indicates the signicance level of the difference between RecoBM and RecoEC for each case, whereas the signicance level P of each factor (that is, chamber system, accounting light inhibition, parameterization type) is indicated as rel. diff. P (relative difference between RecoBM and RecoEC) and is reported in the top right of each panel.

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procedures used to account for advective and low-frequency ows of CO2 are effective. In fact, without the appropriate amendment, increasing site topographical complexity and LAI should increase the chances of advective and low-frequency ows of CO2, causing biases in EC estimates5,6. These issues, which can be relevant for particular sites8,18, are therefore less important at multiple-site level. Another indication about the reliability of EC-based C uxes is that, estimates of RecoEC (and GPPEC) based on daytime ux data do not differ signicantly from estimates of RecoEC (and

GPPEC) based on night time ux data (as was also demonstrated elsewhere9), and their use here does not improve the convergence between EC and BM. This specically supports that problems related to low-turbulence conditions during night are in general sufciently amended by the ux data treatment5. Finally, the lack of major divergence between night time estimated RecoEC and

RecoBM further reduce the probability that estimates of NEPEC are affected by major night time overestimation, at least for temperate and tropical forests.

Contrary to EC, no standard procedures exist for BM and the BM studies included in our synthesis presented different approaches in determining the production and respiration components of the ecosystem C cycle. The methodological variation in BM was important and allowed us to detect which approach best converged with EC. Measurements of respiration were particularly affected by the methodological approach. For Rsoil (which represents the dominant component of Reco), it is known that the NSNF chamber system signicantly underestimates Rsoil, whereas the NSF system presents smaller inaccuracies19. This was indirectly reected by our results. As RecoBM was overall larger than RecoEC, the agreement of these estimates when the NSNF system was used indicates a potential case of error compensation, with the underestimation of belowground respiration compensating an overestimation of aboveground respiration (see below). On the other hand, the latter term was not compensated when the NSF was used, with RecoBM having larger values than RecoEC at sites making use of

NSF. Leaf respiration is also an important component of Reco (about 30%). Our data show that, the consideration or not in BM of light inhibition of daytime Rleaf (it was considered in only 28% of our sites) has a major inuence on the convergence between RecoEC and RecoBM. This is striking as light inhibition of daytime

Rleaf is also neglected in standard (night time derived) estimates of Reco and might not be correctly accounted for even in the daytime derived Reco20. A possible explanation is that error compensation might reduce the impact of neglecting light inhibition of Rleaf more in EC- than BM-based estimates (for example, the overestimation caused by not accounting for the light inhibition of Rleaf might be compensated by missing uxes), and should be examined further. On the other hand, our analysis did not show major issues related to scaling in BM-based estimates of respiration. For instance, Rwood, the Rwood:Reco ratio and the convergence between RecoBM and RecoEC were not related to the scaling variable used for the wood respiration rate (stand wood volume or wood surface area, P 0.30.8; Table 3;

Supplementary Table 6). On the other hand, for the leaf respiration rate that is typically scaled up using estimates of LAI, Rleaf, the Rleaf:Reco ratio and the convergence between RecoBM and RecoEC did not vary between needleleaved and broadleaved species (P 0.20.3; Table 3; Supplementary

Table 6). This is the case even though the leaf area estimates of needle-leaved species are more prone to biases than for broadleaved species21.

Methodological variants in measuring NPP did not show any signicant impact on the convergence between EC and BM. For wood, aws in allometric relationships can cause either overestimation or underestimation of NPP22 and thus errors are

compensated when multiple sites are considered. For leaves, the use of the litter trap method did not seem to provide different production estimates for deciduous or evergreen stands, as they show practically the same leaf-to-aboveground production ratio(0.450.03 and 0.450.02, respectively; P 0.99). On the other

hand, the use of litter traps or allometric relationships resulted in different leaf-to-aboveground production ratio in evergreen stands (0.320.06 and 0.450.02, respectively; P 0.022). This

indicates that these two methodologies may provide different estimates of leaf NPP for evergreen species but also that this systematic difference is too small to affect the ECBM convergence for NEP and GPP (Table 3). For ne roots, our results did not show the typical bias pattern associated with the different methods to measure NPP (for example, underestimations for ingrowth cores and overestimation for minirhizotron23), which may be due to the overall large uncertainty in ne root NPP estimates.

Our study generally nds good support for the reliability and consistency of EC and BM approaches to estimate forest C uxes at the ecosystem level. However, the low convergence recorded between NEPEC and NEPBM, with NEPEC signicantly larger than

NEPBM for extratropical forests, is an important exception. For temperate forests, the mean difference was 100 gC m 2 y 1, which is broadly comparable to the inter-annual variability for this biome13,17,24, characterized by NEP of about 300400 gC m 2 y 1 (ref. 25). For the boreal zone, the mean difference was about 170 gC m 2 y 1, which is sufciently large to confound the ecosystem sink-source status as NEP of boreal forests is typically between 40 and 180 gC m 2 y 1 (ref. 25). For instance, the mean NEPBM of the boreal sites in our data set was

6060 gC m 2 y 1 (C source) whereas the mean NEPEC was 11040 gC m 2 y 1 (C sink). The reason for this pattern is not clear, as we did not observe signicant relationships between the low convergence between NEPEC and NEPBM and climatic or environmental variables (such as mean annual temperature, mean annual precipitation and site fertility, which are all lower in the boreal zone). Probably, the relatively small C uxes in boreal forests make them more susceptible to methodological biases.

As we did not nd any indications for major overestimations of NEPEC, it is relevant to explore if the dominant BM approach used to measure NEP is affected by any systematic underestimation that could explain the difference between NEPEC and

NEPBM. As the usual approach to estimate NEPBM is by subtracting heterotrophic respiration (Rh-soil and Rh-cwd) from NPP, underestimation of NEPBM could be caused by overestimation of Rh-soil and Rh-cwd or underestimation of NPP. Rh-cwd is a relatively small ux in most sites and we have not recorded lower agreement between NEPBM and NEPEC for sites missing this component of the C cycle. Ecosystem Rh-soil is particularly difcult to measure and, in our data set, four major measurements approaches were used: root exclusion to estimate Rh-soil (60% of sites), measuring Rroot and then subtracting it from Rsoil (20% of sites), calculating Rh-soil from separate incubation of all components of the soil except roots (10% of sites) and applying a xed Rh-soil:Rsoil ratio (10% of sites) (see Methods for details). All these approaches have methodological uncertainties26. However, the fact that the difference between NEPBM and NEPEC was not affected by the four approaches to measure Rh-soil (Table 3) and that all four approaches presented an underestimation of NEPBM very similar to the global difference between NEPBM and NEPEC (Supplementary Fig. 2), point towards the conclusion that the low convergence between NEPBM and NEPEC is more likely to be related to underestimation of NPP than overestimation of Rh-soil. Underestimation of NPP is indeed considered as a key potential source of bias in the BM approach to estimate NEP (see Introduction). An analysis of the

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as Reco and GPP are derived from NEP (for EC) or rely on the measurements of the same component processes of NEP (for BM). However, the different degree of ECBM convergence among the carbon uxes is coherent with our results and likely related to the small magnitude of NEP and to the partial offset of errors of opposite direction for Reco and GPP. On the one hand, the magnitude of NEP uxes is only about 1520% of the magnitude of Reco and GPP. Therefore, NEP estimates can be more susceptible than Reco and GPP to methodological inaccuracies. On the other hand, it is important to realize that high convergence of Reco and GPP is not denitive proof of lack of systematic biases, but could be caused by error compensation.Three examples can be provided. For GPPBM, the

underestimation of NPP (discussed above) might be compensated for by overestimation of autotrophic respiratory uxes, such as Rleaf (Fig. 3b,c). For RecoBM, overestimation of

Rleaf may be compensated for by an underestimation of Rsoil (see above). For RecoEC, the overestimation caused by overlooking the light inhibition of Rleaf, might be offset by missing CO2 uxes. Overall, the compensating aspects of Reco and GPP are not important for landscape- and large-scale assessment of ecosystem CO2 uxes but should nonetheless be investigated in depth at site-level so that experimentalists can better evaluate the measurement strategy and modelers have the appropriate information on key ecosystem C cycle processes.

Table 4 | Risk of lack of convergence between estimates of forest carbon uxes obtained from eddy-covariance and biometric methods according to site and methodological characteristics.

Flux Variables

OverallNEP High Reco Moderate GPP Low

Climate zoneBoreal Temperate Tropical NEP High High Low Reco High Moderate Low GPP Low Low Low

Canopy featuresLeaf type* Leaf habitw Leaf area index NEP Low Low Low Reco Low Low LowGPP Low Low Low

Topography and soil characteristicsAltitude variability Slope Fertility NEP Low Low Low Reco Low Low Low GPP Low Moderate Low

Compartment measured with biometric methodsLeaves Wood Soil NEP Low Moderatez Moderatey

Reco High|| Low Highz GPP Moderate|| Moderatez Moderatey

The risk of lack of convergence between eddy-covariance (EC) and biometric methods (BM) estimates of net ecosystem production (NEP), ecosystem respiration (Reco) and gross primary production (GPP) for forests is reported according to climatic zone, canopy features, site (topography and soil) characteristics, and the main ecosystem compartments measured with BM, and expressed in three levels: low (non-signicant difference between BM and EC estimates and/or lack of systematic biases), moderate (difference between the BM and EC estimates at 0.05oPo0.10 and/or potential of systematic biases) and high (signicant difference at Po0.05 between the BM and EC estimates and/or systematic biases).

*Needleleaved, broadleaved or mixed. wEvergreen, deciduous or mixed.

zNot considering branch turnover in estimates of net primary production (but with an adequate assessment of the other components of the wood production, see Methods). yNot considering mycorrhizal production (but with an adequate assessment of root production, see Methods).

||Not considering light inhibition of leaf dark respiration.zUse of lower quality chamber system to measure soil respiration.

primary factors possibly causing NPP underestimation based on the literature indicated that, on average, our NPP values might be underestimated by roughly 20% because incomplete assessment of mycorrhiza NPP and NPP related to branch turnover, which were taken into account in only very few of the sites (see Methods). Furthermore, additional underestimation could have been caused by minor NPP components typically neglected (for example, root exudation, net accumulation of non-structural carbohydrates, herbivory consumption, production of volatile organic compounds22), which in general contribute between 1 and 4% of NPP16,2729. The low convergence between NEPEC and NEPBM, when NEPBM was obtained from NPP and Rh, and the difculty in quantifying NPP, suggests that stock change approaches may be a valid BM alternative to quantify NEP. For example, even if this analysis was less robust because of the small sample size, we discovered that when NEPBM was based on repeated stock inventories, the difference between EC- and BM-based estimates of NEP was not statistically signicant.

Except for Reco in the boreal zone (as mentioned above), estimates of Reco and GPP did not show signicant differences between methods. This high methodological convergence increases the condence in the knowledge gained using only EC10,11 or BM12,13 and favours the integration of EC- and BM-based estimates in synthesis studies, model-data fusion and model development. The higher ECBM convergence for Reco and GPP than NEP might appear counter-intuitive at rst,

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In conclusion, our study has shown four key ndings. First, forest NEP estimates obtained with BM and EC differ signicantly, particularly for the boreal zone, where the source/sink status is sensitive to the measurement technique. Second, BM and EC-based estimates of Reco and GPP are globally comparable for forest ecosystems but error compensation is likely to play a role in the convergence. Third, there are indirect but multiple indications that the potential biases associated with EC are, in aggregate, sufciently amended by post-processing of the data. Fourth, BM approaches underestimating NPP and neglecting light inhibition of leaf dark respiration show less convergence with EC estimates. Our results also provide manifold information with important practical implications, as they identify in which situations forest C uxes can be measured with both EC and BM methodologies (with the choice of the method depending on factors such as scientic objectives, logistics, local researcher capacity and availability of labour) and it is safe to integrate EC- and BM-based C ux estimates in synthesis studies or model-data fusion (Table 4). On the other hand, we report the mean values of difference against which the discrepancy between EC and BM can be tested in cases of low convergence (for example, for boreal forests) and which methodological aspects need to be taken most urgently into account to improve the convergence between EC and BM. Finally, we make also available the uniform forest C cycle data set that we compiled using quality-checked EC and BM data. All these evidences, elucidations and tools will substantially improve our ability to assess and simulate the CO2 exchange of terrestrial ecosystems.

Methods

Overview study data set. We constructed a data set of NEP, Reco and GPP obtained from BM and EC methodologies. The data set contains annual ux estimates, uncertainties, key information about the measurement techniques and ancillary data on environmental and stand variables. Data were retrieved from ISI-Web literature and existing databases such as the global database of forest C cycle25, FLUXNET30 and the European Flux Database Cluster31.

EC data are consistent as calculated through standard procedures, quality-check and data processing5. However, the NEP partitioning methods used to produce Reco and GPP can vary substantially and we classied them into three categories: methods based on night time data following Reichstein et al.10 or very similar algorithms3234, methods based on daytime data following Lasslop et al.9 and calculation of Reco from sundown respiration following van Gorsel et al.35. As the latter method was only applied at two sites, the analyses on the partitioning method were actually focused on the night time and daytime methods only. Contrary to EC, no standard procedures exist for BM and data in the literature are highly heterogeneous, reecting their diverse scope (for example, assessing the impact of a manipulative experiment, stand level estimates, regional assessments), local researcher capacity and practical reasons (for example, logistics, availability of labour). To obtain a uniform and quality-checked BM data set, we performed three operations. First, we retrieved details on BM for each site and classied them in multiple categories of methodological approach and up-scaling methods. Second, we considered in the analysis only sites fullling a pre-dened set of data quality criteria. Third, we related the data uncertainty to the technique adopted. Full details about the BM data set and its construction are reported below in four sections: annual estimates of production and respiration in BM data set, variables of BM data set for estimation of ux uncertainty, methodological variants of BM approach, and NEP biometric data from stock inventories.

The key environmental and stand variables used in the analysis are two indices of topographical complexity (that is, elevation variability and topographical slope) and LAI, which are thought to be related to bias in the EC-based estimates of C uxes (see Introduction). The indices of topographical complexity were measured within a 2,430 2,430 m quadrat, centered at the EC tower, obtained from NASA

ASTER DEM data36. The elevation variability was the standard deviation of the elevation of 729 pixels composing the quadrat. The topographical slope was derived from the elevation and distance of the highest and lowest pixels within the quadrat. The LAI was derived from the literature. The other variables tested for possible systematic inuences on EC and BM include leaf characteristics, climatic features and site fertility. Leaf characteristics refer to leaf habit (evergreen, deciduous or mixed) and leaf type (needleleaved, broadleaved or mixed), which might affect the measurement of LAI21 and, consequently, the upscaling of leaf measurements to the stand level. Climatic features comprise climate zone (boreal, temperate or tropical), mean annual temperature and mean annual precipitation, whichmight affect both the instrument performance and the post-processing of the data (which involve different type of modelling and extrapolations)5,37. Site fertility

was considered because it was recently found as the key driver of the CO2 exchange in forests38. It was classied in three categories (infertile, moderately fertile or fertile) based on soil type, physicochemical soil properties, and human amendments/degradation29,38,39. All the environmental and stand variables were derived from the literature or other databases and are reported in Supplementary Table 4 and Supplementary Data 1.

Annual estimates of production and respiration in BM data set. The main component processes of the ecosystem C cycle considered are: NPP, aboveground Ra, Rsoil and its components (root autotrophic respiration, Rroot and Rh-soil) and Rh-cwd:

aboveground Ra Rleaf Rwood 1

Rsoil Rroot Rh-soil 2 These variables are combined to obtain NEP, Reco and GPP:

NEP NPP Rh NPP Rh-soil Rh-cwd 3

Reco Ra Rh aboveground Ra Rsoil Rh cwd 4

GPP NPP Ra NPP aboveground Ra Rroot 5 A full list of the variables (for example, NPP, Ra) for each ecosystem component (for example, foliage, wood, ne roots, soil) is reported in Supplementary Table 7. The methods used to measure these variables are briey reported below, whereas extended methodological information for each site (for example, set-ups and measuring protocols, methods used to integrate point measurements to annual scale, methods to scale up tree level data to the stand level) is reported in Supplementary Methods. For sites with multiple-years data of NEP, Reco and GPP but with a combination of direct and indirect measurements, only years with direct measurements were considered.

Net primary production. Sites were selected when at least the three major components of the ecosystem production were measured: wood NPP, foliage NPP and ne root NPP. Wood NPP (stem, branches and coarse roots) was obtained as the increment in wood standing biomass from consecutive tree size (typically diameter) surveys and allometric relationships between tree size and wood standing biomass. Detailed information about the allometric relationships used at each site is reported in Supplementary Table 8. The quality of the relationships was classied into three categories according to their degree of species-specicity (species-specic versus generic), their geographical origin (site-specic versus regional) and their degree of exibility (full dependency on tree size versus partial use of xed productivity ratios). The categories are: high quality, for species- and site-specic relationships without xed productivity ratios; moderately quality, for species-specic relationships without xed productivity ratios but not site-specic, and low quality, for generic and/or not site-specic relationships employing also xed productivity ratios. Foliage NPP was typically obtained from leaf litter collected with litter traps (for both deciduous and evergreen species) or from tree size surveys and allometric relationships between tree size and current-year leaf biomass (for evergreen species). Fine root NPP was measured with different methods, which can be classied into three main categories: sequential coring40 (for 26% of our sites), minirhizotron-based technique41 (23% of sites) and ingrowth cores42 (19% of sites). In addition, we aggregated the other techniques (for example, process-based modelling43, empirical modelling44, mass balance approach45) in a fourth category named other methods. For a comparison across methods see Milchunas23. Only sites with site-specic estimates of wood, foliage and ne root NPP were included. Therefore, sites with ne root NPP derived from aboveground NPP, generic algorithms or global models were not considered. The majority of the sites (70%) meeting the requirement on wood, foliage and ne root NPP also presented understory NPP (generally measured with a combination of allometric relationships between plant dimension and biomass and/or harvest techniques17). NPP due to branch turnover (from branch fall surveys), reproductive organs (from litter traps) and herbivory (from leaf area or biomass consumption) was considered in 3040% of the sites. NPP due to production of volatile organic compounds and mycorrhizae production was considered in only 10% of the sites.

Aboveground respiration. To be included in our quality-checked BM data set, sites needed to comprise at least site-specic estimates of Rleaf and Rwood, fully independent to EC data. Rleaf was typically measured with chambers and infrared gas analyser, in situ, on canopy leaves37,46, or in vitro, on leaves of freshly cut branches42,47. Rwood was always measured with chambers and infrared gas analyser. Measurements were typically performed during various occasions in the growing and dormant season and integrated at annual level by using empirical models that related respiration to temperature, water status or other environmental variables37. Data were scaled up at stand level using LAI or leaf biomass, for Rleaf, and sapwood volume or area, for Rwood. About 60% of the sites presented also measurements of understory respiration (Ru; absence of Ru data was however not considered as a criterion for excluding the site). Measurement methods of Ru were similar to the ones for Rleaf and Rwood, and, often, Ru data were not presented separately but included into Rleaf and Rwood.

Belowground respiration. Rsoil was needed for a site to be included in our RecoBM data set, whereas partitioning into Rroot and Rh-soil was needed for

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inclusion in the data set of GPPBM and NEPBM, respectively (Supplementary Table 7). Rsoil was measured by using various soil chamber systems which fall into three major categories: closed static chambers or NSNF, closed dynamic chambers or NSF, and open dynamic chambers or steady-state through-ow chamber19. However, because the latter system was only used in two of our sites, we did not consider this system in our statistical analysis. On the other hand, for the NSF technique, we further classied the sites into two groups, according to whether the system prescribed scrubbing of CO2 before the ux measurements (for example,

Li-Cor LI-6400-09 system; LI-COR Biosciences, Lincoln, USA) or not19. Measurements not performed continuously were integrated at annual scale using empirical models relating soil respiration to temperature and/or soil water status. Various methods were applied to partition Rsoil into Rroot and Rh-soil. We grouped them into four categories: root exclusion methods (used in 57% of the sites), that directly measure Rh-soil in situ and indirectly derive Rroot from equation (2); estimation of Rroot (20% of sites), both in situ (using root chambers), in vitro (using excised roots) or using models (process-based or empirical models) and indirectly deriving Rh-soil from equation 2; component integration (10% of sites), that prescribes the estimation of Rh-soil from the respiration of all components of the soil (for example, litter, mineral soil layers and so on) separately, often in vitro in the laboratory, and, as for the exclusion methods, indirectly estimates Rroot (equation (2)), and other methods, which mainly assume a xed ratio between Rroot and Rh-soil26. See Hanson et al.26 for more details on all methods to partition Rsoil into Rroot and Rh-soil.

Other respiratory components. Decomposition of coarse woody debris (Rh-cwd) can be a signicant part of the total ecosystem respiration. Rh-cwd was therefore considered when reported (for 65% of the sites) but sites missing it were not excluded. Rh-cwd was typically derived from surveys of standing dead wood and estimates of decays rates, or, in a minority of cases, from chamber measurements of CO2 exchange or wood decomposition from successive surveys.

Variables of BM data set for estimation of ux uncertainty. Data uncertainty of NEP, Reco and GPP was calculated following the method described below. The data required for the estimation of the ux uncertainty are: the site latitude, the number of replicated years of measurement, and a general label of data quality. The latter has two levels: high quality data, for sites with only site-specic measurements, or fair quality data, for sites with measurements comprising also not site-specic relationships and/or models.

Methodological variants of BM approach. BM data were often obtained at different sites with different BM techniques or data processing. Therefore,we reported in the BM data set the employed approach for each site and measured variable. This was done to analyse the impact of the BM methodology on the convergence between EC and BM uxes. In particular, we considered 17 methodological variants of the BM technique (Table 3). For this analysis, we paid more attention to variables that had a large numerical impact on the stand C cycle (for example, Rsoil, ne root NPP, Rleaf, Rh-soil), whereas we paid less attention to variables that had a small numerical impact (for example, Rwood, Rh-cwd).

NEP biometric data from stock inventories. NEPBM is not only obtainable from measurements of production and respiration (equation (3)) but also derivable from the difference in ecosystem C stocks between two points in time12. NEPBM estimates obtained with the latter approach are indicated here as NEPBM-DS. Ideally,

C stocks should comprise vegetation, necromass and soil, with correction for lateral C losses (for example, harvests, leaching of dissolved organic carbon)48. In practice, complete C stock inventories are seldom done. Therefore, we included in the NEPBM-DS data set all sites in the literature (n 7) with the repeated assessment of

at least the two major ecosystem C stocks that is, wood and soil.

Data uncertainty. As ux uncertainty was available only for a minority ofsites (and its calculation method was highly inconsistent among studies), the uncertainties in uxes were approximated uniformly following Luyssaert et al.25 These authors proposed that the ux uncertainty for a site (s) can be approximated by considering three elements. First, the typical range of the ux value for the site biome (p) set as the maximal potential uncertainty range. Second, a reduction factor (RF), depending on the measuring methodology, that reduces the maximal potential uncertainty range (for example, a precise method would reduce the uncertainty interval more than an imprecise method). Third, the numberof measurement years (l), with more replicate-years reducing the uncertainty interval. Thus:

s

p RF

l

p 6

For example, to determine the NEPEC uncertainty of a temperate forest with two years of measurements, the Luyssaert et al.s approach considers that NEP of temperate forests typically ranges between 100 and 600 gC m 2 y 1 (thus

s p 350 gC m 2 y 1), that EC is precise and reduces the uncertainty to 30%

of the baseline value (RF 0.3, thus s 105 gC m 2 y 1) and that the presence

of two measurement years further reduces the uncertainty to s 74 gC m 2

y 1. In general, according to this method, p of NEP is assumed to be 350 gC m 2 y 1 for extratropical forests and 700 gC m 2 y 1 for tropical forests25, p of Reco

and GPP depends on latitude and varies from 500 to 1000 gC m 2 y 1 (ref. 25), and that RF of BM is 0.3, as for EC, for sites with high quality data and 0.6 for sites with fair quality data (see above).

The adopted approach produces uncertainty intervals comparable to the directly estimated uncertainty for EC25. Here, we observed that good agreement was achieved also for the BM uxes of extratropical forests but that relevant mismatches were detected for Reco and GPP of tropical sites where the Luyssaert et al.s approach underestimated the measured uncertainty by 6070% (Supplementary Table 9). We considered this important discrepancy not crucial for our analysis because we had only four tropical sites and repetition of the analysis with corrected uncertainty values of tropical sites (to match the directly estimated uncertainty) did not change the main results (data not shown).

Data analysis. The data were analysed in four steps, which are described below. For each case, note that the comparison of the EC and BM uxes was performed for sites with data referring to the same vegetation cover (or footprint) and to the same period or with minor temporal mismatches (for example, BM uxes available for a three-year period and EC uxes for a 2-year period) generally considered suitable for the EC and BM comparison by the original investigators (for 74%of the sites the BM and EC data were from published ECBM comparison at the site-level).

Agreement between EC and BM. We obtained a rst indication of the agreement between EC- and BM-data by calculating the regression of BMversus EC estimates along the entire range of ux measurements. Major-axis regressions were used because both variables had error terms of similar magnitude49. Agreement was inferred from the slope of the regression line and the correlation indicated by R2. In addition, for each ux and climatic zone, the agreement between the EC and BM estimates was more stringently tested by a paired t-test (in case the differences between pairs were normally distributed according to ShapiroWilks test) or Wilcoxon signed-rank test (in case the differences between pairs were not normally distributed). The same approach was used to compare NEPEC and NEPBM-DS (see above).

Impact of environmental and stand variables on the EC and BM convergence. We tested whether the difference between the EC- and BM-based estimates was systematically related to elevation variability and topographical slope (indices of topographical complexity), LAI, leaf habit and leaf type (canopy characteristics), climate zone, mean annual temperature and mean annual precipitation (climate variables) and site fertility (see above). The tests comprised univariate analyses performed regressing (with an ordinary least squares regression) the difference between the EC- and BM-based estimates and each variable, separately. To fully exploit the information available for each site, the impact of ux data uncertainty was added to the analysis by using the inverse of the ux uncertainty as weighing factor among sites (thus giving lower weight to sites with higher uncertainty on the estimates). Each analysis met the normality of residuals (tested with Shapiro-Wilks test) and the assumption of homoskedasticity (tested with Breusch-Pagan test), except in a few cases for which the White method (for heteroskedasticity correction) was used instead50.

Impact of different methodological variants on the convergence between EC and BM. The impact of different methodological approaches on the convergence between EC and BM-based estimates was tested as above with ordinary least squares regressions weighted by the inverse of the ux uncertainty. These univariate analyses served well for the purpose of the study, as preliminary analyses showed typically no relevant two-term interactions. The few signicant (Po0.05)

two-terms interactions (1 out 55 cases for GPP, 5 out of 66 for Reco and 1 out of 6 for NEP) did not have logical meaning but were related to the small sample size, that is, singularities. The only exception was represented by a signicant interaction between soil respiration chamber type and accounting for light inhibition of leaf respiration for Reco, which was considered in the data analysis (see Results). For BM, the methodological variants were 17 (Table 3). For EC, the only methodological variant was the NEP partitioning method which was of two types (see above).

Analysis of NPP data. NPP is a key component for the determination of NEPBM

and GPPBM. Five methodological aws can typically have a signicant (410%) and unidirectional (underestimation) impact on NPP estimates in forests22: not accounting tree mortality, assuming life span of ne roots to be 1 year, coarse measurements of leaf NPP in tropical forests, not measuring mycorrhizal NPP and rhizodeposition, and not correcting for NPP related to branch turnover. The rst three cases are less relevant in our data set as: site tree mortality was normally assessed, ne root production was estimated for each site and tropical sites are few in our data set and their leaf NPP was quantied accurately. On the other hand, we detected than only three and six sites (out of 31) took into account mycorrhizal NPP and NPP related to branch turnover, respectively. The impact of these missing terms was estimated by gap-lling the original NPP values using the average values of branch turnover related NPP from our data set (which was equivalent to 22% of aboveground wood NPP or 8% of total NPP, n 6; Supplementary Table 2) and of

mycorrhizal NPP from the literature (which was equivalent to 14% of total NPP,

n 6, and in agreement with culture studies51; Supplementary Table 10). The gap

lled NPP estimates were on average 20% larger than the original NPP estimates.

Overall, the analyses were performed for all uxes, that is, NEP (NEPBM versus NEPEC), Reco (RecoBM versus RecoEC) and GPP (GPPBM versus GPPEC). For Reco

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and GPP, to ensure that the impact of each given site was independent on the ux magnitude, the analyses were performed using the relative difference between the EC- and BM-based ux estimates (for example, for GPP: (GPPBM GPPEC)/

((GPPEC GPPBM)/2). For NEP, the latter approach was impeded by the presence

of both positive and negative values. We intentionally retained outliers in our analyses because they could represent cases with high discrepancy between the methodologies and thus of relevance for our scope. All analyses were performed within the R platform52.

Data availability. The data that support the ndings of this study are included in Supplementary Data 1. Data are from the literature and public databases. Details about the data and the data sources are reported in Supplementary Tables 1-5.

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Acknowledgements

M.C. and S.V. are Postdoctoral Fellows of the Research FoundationFlanders (FWO). S.L. is funded by the European Research Council (ERC) Starting Grant 242564 (DOFOCO) and YM by ERC Advanced Investigator Grant 321131 (GEM-TRAIT) and the Jackson Foundation. I.A.J. and J.P. acknowledge the European Research Council Synergy grant ERC-2013-SyG-610028 IMBALANCE-P. We thank Gianluca Tramontana for the DEM data extraction and processing. We greatly appreciate the work of the hundreds of scientists and technicians who produced the BM and EC data compared in this analysis. This work used eddy-covariance data acquired and shared by the FLUXNET community, including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux-TERN, TCOS-Siberia, and USCCC. The FLUXNET eddy-covariance data processing and harmonization was carried out by the ICOS Ecosystem Thematic Center, AmeriFlux Management Project and Fluxdata project of FLUXNET, with the support of CDIAC, and the OzFlux, ChinaFlux and AsiaFlux ofces. In particular, the FLUXNET 2015 data set was used for the following sites-years: CN-Cha (2003), CA-Qfo (2005), FI-Hyy (2003-2006), FR-Hes (1997), US-Syv (2002-2003), AU-Tum (2002-2003), CA-TP2 (2006), US-WCr (2000, 2002-2003).

Author contributions

M.C., S.V., S.L. and I.A.J. conceived the paper; M.C. performed the analyses; M.C. and Y.M. wrote the text; all authors contributed substantially to discussions and revisions.

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How to cite this article: Campioli, M. et al. Evaluating the convergence between eddy-covariance and biometric methods for assessing carbon budgets of forests. Nat. Commun. 7, 13717 doi: 10.1038/ncomms13717 (2016).

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