Key Laboratory of Ecosystem Network Observation and Modeling, Synthesis Research Center of Chinese Ecosystem Research Network, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China
 Basal ecosystem respiration rate (BR), the ecosystem respiration rate at a given temperature, is a common and important parameter in empirical models for quantifying ecosystem respiration (ER) globally. Numerous studies have indicated that BR varies in space. However, many empirical ER models still use a global constant BR largely due to the lack of a functional description for BR. In this study, we redefined BR to be ecosystem respiration rate at the mean annual temperature. To test the validity of this concept, we conducted a synthesis analysis using 276 site-years of eddy covariance data, from 79 research sites located at latitudes ranging from ∼3°S to ∼70°N. Results showed that mean annual ER rate closely matches ER rate at mean annual temperature. Incorporation of site-specific BR into global ER model substantially improved simulated ER compared to an invariant BR at all sites. These results confirm that ER at the mean annual temperature can be considered as BR in empirical models. A strong correlation was found between the mean annual ER and mean annual gross primary production (GPP). Consequently, GPP, which is typically more accurately modeled, can be used to estimate BR. A light use efficiency GPP model (i.e., EC-LUE) was applied to estimate global GPP, BR and ER with input data from MERRA (Modern Era Retrospective-Analysis for Research and Applications) and MODIS (Moderate resolution Imaging Spectroradiometer). The global ER was 103 Pg C yr −1, with the highest respiration rate over tropical forests and the lowest value in dry and high-latitude areas.
 Increasing atmospheric CO2 concentration from fossil fuel combustion has emphasized our need to better understand global sources and sinks of carbon [Le Quéré et al., 2009], and their responses to environmental changes. Net ecosystem exchange (NEE) of CO2 between terrestrial ecosystems and the atmosphere is driven by ecosystem respiration (ER), the sum of soil heterotrophic respiration and plant autotrophic respiration, and gross primary production (GPP). Previous studies have found soil respiration, a major component of ER, accounts for a global annual carbon emission of 75∼80 Pg C annually [Schlesinger, 1977; Raich and Potter, 1995], which is more than 10 times the current rate of fossil fuel combustion [Marland et al., 2008]. Thus, small changes in ER can have a significant impact on the global carbon budget and therefore on the atmospheric CO2 concentration [Friedlingstein et al., 2006]. Despite the considerable scientific efforts to study ER, there is still limited knowledge on temporal and spatial variations of ER and limited understanding of the environmental controlling mechanisms and of the controlling factors involved, including climate, plant biophysics and soil properties [Reichstein et al., 2003; Rodeghiero and Cescatti, 2005; Davidson and Janssens, 2006; Palmroth et al., 2005, 2006; Mahecha et al., 2010].
 In the past decades, quite different approaches have been taken to obtain global estimations of ER. These include mechanistic models [Schimel et al., 1997; Parton et al., 1998; Schimel et al., 2000; Cramer et al., 2001] that are based on process-level understanding and analysis of ecosystem carbon fluxes and their responses to environmental change. The accuracy of the mechanistic models relies on how well these processes are represented in the models. For example, carbon allocation has been found difficult to represent well in models [Litton et al., 2007], although some rules have emerged [see Palmroth et al., 2006]. Moreover, comprehensive models attempting to incorporate many processes can suffer a drawback of having to specify a large number of parameters thus yielding a substantial uncertainty. For example, a parameter inversion study showed that only four of seven parameters in a process-based respiration model could be reasonably estimated from direct flux tower observations of NEE [Xu et al., 2006].
 Since mechanistic models are limited by our understanding of the complex processes and appropriate parameterization, ER at regional to global scales is often modeled as a simple exponential or Arhennius-type function of temperature. For example, a common form of ER is the exponential function [Luo and Zhou, 2006]:
where BR is basal respiration rate at a given reference temperature (T0; e.g., 0 or 10°C), Q10 is the relative change in ER per 10°C increase, and T is air temperature. When simulating ER or its components (i.e., soil respiration) at the global scale, BR is often considered globally invariant. One example is the study by Raich et al. , in which globally distributed soil respiration is simulated using a fixed BR value of 1.25 g C m−2 d−1. However, an increasing body of evidence suggests that the error introduced by the assumption of constant BR is not negligible [Tjoelker et al., 2001; Janssens and Pilegaard, 2003; Wang et al., 2010]. Sampson et al.  suggested that BR varies systematically with photosynthesis. Larsen et al.  found that ecosystem respiration depends strongly on photosynthesis in a temperate heath and incorporated GPP as a parameter in their respiration model. Spatial differences in global BR have also been linked to variations in leaf area index (LAI), which suggests that photosynthetic activity correlates with ER [Curiel Yuste et al., 2004; Mahecha et al., 2010; Migliavacca et al., 2011]. The large spatial variation in BR is not surprising given its underlying mechanisms which include changes in carbon substrate supply from photosynthesis and quantity of respiring biomass [Davidson and Janssens, 2006]. What is lacking is an adequate algorithm to predict variation across the globe.
 Spatial patterns of BR are rarely investigated [Reichstein et al., 2003]. Recently, Bahn et al.  found a relationship between mean annual soil respiration and soil respiration rate at mean annual temperature, which has important implications for quantifying BR. Previous studies have also shown strong correlation between mean annual ecosystem respiration and GPP [Janssens et al., 2001]. Given these findings, we argue that BR can be more reliably used in models if it is redefined in equation (1) to be ecosystem respiration at the mean annual temperature, and that this latter quantity can be easily estimated by exploiting correlations between annual GPP and ER. In this study, we evaluate the finding of Bahn et al.  using eddy covariance (EC) flux tower estimates of ER, and couple it with observed correlations between GPP and ER to develop a novel method for estimating global BR.
2. Materials and Methods
2.1. Eddy Covariance Data
 Eddy covariance (EC) data were used in this study to derive ER rate at mean annual temperature and investigate the correlation of annual mean ER with GPP. The data were obtained from the AmeriFLUX (http://public.ornl.gov/ameriflux), EuroFLUX (http://www.fluxnet.ornl.gov/fluxnet/index.cfm) [Valentini, 2003], and ChinaFLUX networks (http://www.chinaflux.org). Seventy-nine sites encompassing 276 site-years were included in this study, covering 6 major terrestrial biomes: evergreen broadleaf forest (EBF), deciduous broadleaf forest (DBF), mixed forest (MIX), evergreen needleleaf forest (ENF), grassland (GRS) and tundra (TUN) (Table 1). Supplementary information on the vegetation, climate, and soil from the sites noted above is available online. Half-hourly or hourly averaged photosynthetically active radiation (PAR), air temperature (Ta), and friction velocity (u*) were used together with NEE of CO2. When available, data sets that were gap-filled by site principal investigators were used. For other sites, data filtering and gap-filling were conducted with the following procedures.
Table 1. Name, Location, Vegetation Type, and Available Years of the Study Sitesa
Data filtering did not follow the criterion of other sites. The days were indicated as missing when missing data was >50%, and the years were indicated as missing when missing days were >50%. AP: annual precipitation (mm); AMT: annual mean temperature (°C).
 An outlier (“spike”) detection technique was applied, and the spikes were removed, following Papale et al. . Because nighttime CO2 flux can be underestimated by EC measurements under stable conditions [Falge et al., 2001], nighttime data with low-turbulence conditions were removed based on a u*-threshold criterion (site-specific 99% threshold criterion following [Reichstein et al., 2005] and [Papale et al., 2006]).
 Nonlinear regression methods were used to fill NEE data gaps [Falge et al., 2001]. Nonlinear regression relationships between measured fluxes and meteorological conditions were fitted using a 7-day moving window. Equation (1) was used to fill the missing nighttime fluxes (NEEnight), and BR and Q10 are the fitted model parameters. A Michaelis–Menten type light response function was used to fill the missing daytime fluxes (NEEday) [Falge et al., 2001]:
where FGPP,sat (gross primary productivity at saturating light), α (initial slope of the light response function), Aday and Bday are fitted parameters. The nonlinear regression procedure (PROC NLIN) in the STATISTICAL ANALYSIS SYSTEM (SAS Institute Inc., Cary, NC, USA) was used to fit the relationships between measured fluxes and environmental factors.
 To avoid uncertainties introduced by the extrapolation to daily ER (ERday), we used only observed nighttime ER to examine the equivalence relationship between mean annual ER and its rate at the mean annual temperature. Nocturnal ER and nocturnal temperature were calculated based on half-hourly or hourly values. Daily average nocturnal ER values were excluded from analysis when missing hourly data exceeded 20% of the time on a given day. Based on the daily nighttime data set, yearly mean nocturnal ER and nocturnal mean temperature were calculated. If missing daily data exceeded 20% of entire year, the value of that year was excluded. On average, 30% of the years were rejected due to insufficient nocturnal observations. The rejected years varied among sites from 60% (Blodgett) to 10% (Howland).
 In order to characterize the ER rate when nighttime air temperature equals annual mean nighttime temperature, data aggregation was conducted according to the following procedures. From temperatures of −30°C to maximum air temperature, daily temperature bins were defined through 1°C increments of air temperature. The daily nocturnal air temperature and ER were averaged through every temperature range over all years within individual sites. These binned data were used to generate temperature curves of ER at each site. An example of this curve is shown in Figure 1, and the intersection of this curve with mean annual temperature was used to determine the ER rate.
 For estimating the correlation of GPP to ER, care must be taken when relying on the empirically derived values. Vickers et al.  argued that there is a spurious correlation between GPP and ER when these component fluxes are jointly estimated from the observed NEE. Lasslop et al.  attempted to minimize spurious correlations between GPP and ER by maximizing the amount and quality of data that go into their estimation. We follow the philosophy of this approach by calculating daily ER as the sum of NEEnight and daytime ER (ERday1), extrapolated using equation (1) with daytime air temperatures and with BR and Q10 fitted by half hourly nighttime measurements. Daily GPP was synthesized based on daily NEE and daytime ER (ERday2), which was estimated by equation (2) and FGPP,sat, α, Aday and Bday were fitted only based on daytime flux measurements using a 7-day moving window. In this fashion, daily ER was estimated only based on parameters derived from nighttime measurements and GPP was estimated based on parameters using daytime measurements, which is intended to avoid issues with spurious correlation. The same data filtering criterion as given above (i.e., 20%) was used to estimate missing data.
2.2. BR Model Evaluation
 Observed ER at EC sites was used to compare simulations of ER using invariant and variable BR, where equation (1) was used to model ER using two different parameterization schemes. To estimate Q10, globally heterogeneous Q10 values of soil respiration were estimated from assimilation of observed soil carbon content into a process-based terrestrial carbon model (Carnegie-Ames-Stanford Approach model) [Zhou et al., 2009]. We assumed the temperature sensitivity (Q10 value) of ER is the same as that for soil respiration with the risk of inducing model errors. Relative Predicted Errors (RPE) and coefficient of determination (R2) were used to quantify the improvement in model predictions using the variable BR instead of the invariant. The RPE was computed as:
where and are mean simulated and observed values, respectively.
2.3. EC-LUE Model
 The spatial pattern of GPP is used as a driver for global BR. We used a simple, validated light use efficiency GPP model, the EC-LUE model, to estimate global GPP values [Yuan et al., 2007]. The EC-LUE model may have the most potential to adequately address the spatial and temporal dynamics of GPP because its parameters (i.e., the potential light use efficiency and optimal growth temperature) have been shown to be relatively invariant across the various plant functional types, and is driven by only four variables: normalized difference vegetation index (NDVI), photosynthetically active radiation (PAR), air temperature, and the ratio of sensible to latent heat flux (Bowen ratio). EC-LUE has recently been modified to include the ratio of evapotranspiration (ET) to net radiation instead of the Bowen ratio. The revised RS-PM (Remote Sensing-Penman Monteith) model was used to quantify ET [Yuan et al., 2010]. Fifty-four eddy covariance towers, including various ecosystem types, were selected to calibrate and evaluate the revised EC-LUE model. Using estimated ET by revised RS-PM model as input, the EC-LUE model showed good performance in both calibration and validation sites, explaining 75% and 58% of the observed 8-day variation of GPP, respectively.
2.4. Model Driver Data
 For global estimates of GPP, we used input data sets for net radiation (Rn), air temperature (T), relative humidity (Rh) and photosynthetically active radiation (PAR) from the MERRA (Modern Era Retrospective-Analysis for Research and Applications) [Bosilovich et al., 2008] archive for 2000∼2003 [Global Modeling and Assimilation Office, 2004]. MERRA is a NASA reanalysis for the satellite era using a new version of the Goddard Earth Observing System Version 5 (GEOS-5). MERRA uses data from all available surface weather observations globally every 3 h, and GEOS-5 was used to assimilate these point data on a short time sequence, and produces an estimate of climatic conditions over the globe, at 10 m above the land surface (approximating canopy height conditions) and at a resolution of 0.5° latitude by 0.6° longitude.
 The global 8-day MODIS (MODerate resolution Imaging Spectroradiometer) leaf area index (LAI) (MOD15A2) and 16-day MODIS NDVI (MOD13A2) were also used in this study. Quality control (QC) flags were examined to screen and reject NDVI and LAI data of insufficient quality. We temporally filled the missing or unreliable LAI and NDVI at each 1-km MODIS pixel based on their corresponding quality assessment data fields as proposed by Zhao et al. . If the first (or last) 8-day LAI (16-day NDVI) was unreliable or missing, it was replaced by the closest reliable 8-day (16-day) value. All of those satellite data sets were resampled to the geographic projection and spatial resolution of the global MERRA data set.
3. Results and Discussion
3.1. Equivalence Relation Between Mean Annual Ecosystem Respiration and Ecosystem Respiration Rate at Mean Annual Temperature
 Analysis of data from 79 EC sites with 276 site-years worldwide verified the equivalence relation between mean annual nocturnal ER and ER rate at mean annual nocturnal air temperature (Figure 2a). The slope of this correlation is not significantly different from 1, and the intercept does not significantly differ from 0 (p < 0.05). This equivalence relation is observed to be consistent in various natural ecosystem types: evergreen broadleaf forest (EBF), deciduous broadleaf forest (DBF), evergreen needleleaf forest (ENF), mixed forest (MIX), grassland (GRS) and tundra (TUN) (Figures 2b, 2c, 2d, and 2e).
 One surprising finding is that our model predicts a positive BR at several eddy flux sites where the mean annual temperatures are below 0° (e.g., US-Brw, CA-Man). Even at these sites, ER rate at mean annual nocturnal temperature can still represent mean annual nocturnal ER very well, contradictory with the assumption that biological activity is minimal when temperatures are below freezing. Slow growth of roots has been reported throughout the winter in northern ecosystems [Hansen et al., 1996]. Moreover, the ability of cold-adapted microbes to survive and grow below 0° has been documented [Gilichinsky, 1995], and respiration in frozen soils has been demonstrated repeatedly in the laboratory [Clein and Schimel, 1995; Panikov, 1999]. Microbial activity is possible in soils below 0° exploits the small amounts of unfrozen water, allowing for diffusion of microbial substrates and waste products [Ostroumov and Siegert, 1996]. Recent work has confirmed that, although rates are low, the cumulative winter CO2 flux from tundra soils may account for a significant amount of their annual carbon budget [Fahnestock et al., 1999; Grogan and Chapin, 1999; Welker et al., 2000].
 The mechanism for the equivalence across all sites is still unclear, but the studies on thermal responses of respiration may provide some insights for understanding this finding. Temperature is the most fundamental climatic factor influencing the kinetics of biochemical reactions, and impacts almost all ecosystem carbon cycle processes. At undisturbed ecosystems, thermal conditions directly determine respiring substrate supply in soil, which strongly regulates the spatial heterogeneity of ER. For example, it is widely acknowledged that soil organic content decreases along gradients of increasing temperature [Jenny, 1980; Post et al., 1982, 1985]. Plant autotrophic respiration also has been shown to adapt to the prevailing ambient temperature by adjustment of enzyme activity and substrate availability [Atkin and Tjoelker, 2003].
 Moreover, annual mean temperature works as a specific indictor for local thermal conditions because the temperature throughout the year in most regions fluctuates closely around the mean annual temperature. Correlation analyses showed that the temperature at the maximum of the frequency distribution function occurs typically around the mean annual temperature (Figure 3). Therefore respiration rate at the mean annual temperature has the highest potential to represent the most frequent value of ecosystem respiration in a given area. For this reason, a linear relation can persist with mean annual temperature and ER across sites from different regions although a nonlinear relationship exists between temperature and ER at a particular site.
3.2. Correlation Between GPP and Ecosystem Respiration
 Other lines of evidence also explain this significant correlation. Soil respiration, an important component of ER, has been found to have a strong correlation with Net Primary Production (NPP) across a variety of biomes [Raich and Schlesinger, 1992] with assimilate supply [Bahn et al., 2008], with aboveground net primary productivity in northern peatlands [Moore, 1986] and with aboveground litter production in forest ecosystems [Schlesinger, 1977; Raich and Nadelhoffer, 1989; DeForest et al., 2009]. These studies indicate a tight link between plant productivity and ecosystem respiration because primary production provides the organic substrate that drives soil metabolic activity. Plant autotrophic respiration is clearly and closely coupled with photosynthetic activity [Heilmeier et al., 1997]. However, it is also the case that the largest fraction of heterotrophic respiration originates from decomposition of young organic matter (dead leaves and fine roots). Thus, both root respiration and heterotrophic respiration will appear to be dependent on primary productivity [Janssens et al., 2001]. Consequently, the relationship between annual ER and GPP should not be surprising.
3.3. Global Estimate of Basal Ecosystem Respiration Rate
 Using our new definition of BR and by coupling the two correlations shown in Figures 2 and 4, we can easily obtain BR from estimated GPP, which has been successfully simulated by the previously described EC-LUE model [Yuan et al., 2007]. By then applying the correlation of BR to mean annual temperature through all ecosystem types, we estimated BR based on simulated GPP by EC-LUE model.
 The derived spatial pattern of the BR at global scale shows a large spatial heterogeneity (Figure 5). Since we redefined BR as ER rate at the mean annual temperature, so the spatial pattern of BR depends strongly on thermal conditions. In general, BR is high over the tropical rain forests and subtropical forest regions like the southeastern United States and the Pantanal region of South American. Basal rate decreases with latitude in the northern and southern hemispheres, which is partically caused by the decreasing mean temperature.
3.4. Global Estimation of Ecosystem Respiration
 The Q10 equation with the site-specific BR accounts for 71% of the variation of monthly ER across all study sites (Figure 6a). Individually, the coefficient of determination (R2) varies from 0.30 at Audubon site to 0.91 at the DE-Tha site (data not shown). These results were compared with those obtained with a globally invariant BR, which was set to the mean value of global BR over the vegetation regions (2.16 g C m−2 day−1). In that case, the Q10 equation only explained about 50% of variation of monthly ER across the all study sites ranging from 25% to 84% (Figure 6b), and the relative predictive error was 35% averaged over all sites, compared to 23% using the site-specific BR.
 We assessed the global spatial and seasonal patterns of ER from 2000 to 2003 by the model using our globally heterogeneous BR (Figure 7). ER of the southern hemispheric tropics remains consistently high throughout the year while that of the major deserts of northern Africa and Australia remain consistently low. The major seasonal change occurs in the high northern latitudes, where ER shows a higher variation between northern summer and winter. The variant BR model estimates that ER releases 103 Pg C yr−1 from the land ecosystems to the atmosphere (Figure 8a). Rates of ER are highest in the tropical moist forest regions and lowest in cold tundra and dry desert regions.
 Due to lack of estimate of Q10 for ER globally, we assumed that the temperature sensitivity of plant autotrophic respiration is the same as soil respiration, and used soil respiration Q10 values reported by Zhou et al.  to estimate global ER patterns. Although some studies have reported differences in the Q10 values between soil respiration and plant autotrophic respiration, a recent study showed that the root autotrophic and soil heterotrophic respiration responded equally to the temperature increase [Schindlbacher et al., 2009]. Piao et al.  reported that Q10 for plant autotrophic respiration varied from 1.9 to 2.5 across the global scales, which are close to the range of 1.2–2.6 with the mean value of 1.92 for soil respiration over the vegetation regions in the Zhou et al. . The results reported by Zhou et al.  are close to the constant Q10 value of 1.4 at various ecosystem types [Mahecha et al., 2010], Q10 value of 1.5 based on global soil respiration data set [Bond-Lamberty and Thomson, 2010] and a recent tracer-transport inverse model derived Q10 values that range from 1.96 to 2.16 [Jones and Cox, 2001]. Moreover, we compared mean Q10 values using equation (1) with those from Zhou et al.  over all sites, and found a significant correlation (Q10_Inversion = 0.69 × Q10_Zhou + 0.48, R2 = 0.36, P < 0.01).
 We can also compare global annual ER using two different methods: (1) ER estimation using only global GPP and the relation between annual GPP and ER (ERGPP); (2) ER estimation using the Q10 model and the spatially heterogeneous basal respiration in this study and Q10 values derived by Zhou et al.  (ERQ10). The results showed global mean annual ERGPP was 92 Pg C (Figure 8a), which was 89% of ERQ10 (103 Pg C; Figure 8b). The higher estimations of ERQ10 occur relatively uniformally in all parts of the globe.
 Many studies have shown that Q10 decreases with increasing temperature [Andrews et al., 2000; Janssens and Pilegaard, 2003; Chen et al., 2010], and Figure 1 also showed decreased ER at high temperature. Although Q10-type equations have been widely used to estimate ecosystem respiration at the various temporal and spatial scales, our and other previous studies showed the estimation uncertainties resulting from temporal constant of Q10. Our globally variant BR model should be beneficial in helping further constrain Q10, by reducing the number of unconstrained parameters in empirical carbon cycle models.
 BR and its spatial variability are crucial for projecting climate change impacts on terrestrial carbon cycling and future atmospheric CO2 concentration. This study has demonstrated the equivalence of the mean annual ER and the ER rate at mean annual temperature at the global scale, which offers good opportunity to retrieve the global pattern of BR by combining this finding with observed correlation of mean annual ER with GPP. Flux tower evaluation supports our redefinition of BR as the ER rate at mean annual temperature, and develops the correlation between the new BR and GPP for estimating global patterns of BR. The results showed the spatially heterogeneous BR results in a better estimation of ER at different sites. Our study provides an innovative method for generating global BR, and will be useful to estimate spatial patterns of ER.
 We acknowledge the financial support from National Key Basic Research and Development Plan of China (2010CB833504 and 2010CB950703) and the Fundamental Research Funds for the Central Universities. S. Liu was funded by the LandCarbon Project, Geographic Analysis and Monitoring (GAM) Program, and the Global Change Research and Development Program (R&D) of the U.S. Geological Survey. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. We acknowledge the work of principal investigators and collaborators in EC sites, who provided the eddy covariance flux measurements. The following networks participated with flux data: AmeriFlux, CarboEuropeIP, ChinaFlux, Fluxnet-Canada and USCCC.