1. Introduction
Evaluating feedbacks between tropical ecosystems and long-term climate change is crucial since terrestrial ecosystems currently act as a sink for 25%–30% of annual fossil fuel emissions (Le Quéré et al. 2016), and humid and semiarid tropical ecosystems are thought to contribute substantially to both the mean strength and the interannual variability of the sink (Ahlström et al. 2015). Several studies have noted that these ecosystems are highly sensitive to variations in temperature (Cox et al. 2013; Wang et al. 2013) and drought stress (Phillips et al. 2009; Gatti et al. 2014), suggesting that the tropical sink may be modified by changing climate. Tropical ecosystems store an estimated 500 PgC as biomass that may be vulnerable to long-term climate change (Pan et al. 2011), since under a high temperature future, ecosystem carbon loss due to higher tree mortality or enhanced rates of heterotrophic respiration may exceed net uptake by plants. Moreover, gross ecosystem fluxes in the tropics are large, between 50% and 60% of global primary productivity (Beer et al. 2010), suggesting that even small changes in climate could have a large impact on global carbon uptake. Recent studies have suggested that improving observational inferences about tropical carbon–climate interactions is necessary, since these ecosystems may be near a high temperature threshold in which further increases to air temperature reduce net assimilation (Doughty and Goulden 2008).






The lack of model agreement in both the magnitude of and the mechanism driving the land carbon feedback to anthropogenic climate change underscores the need to evaluate models against observations. When evaluating coupled ESMs, simulated ecosystem properties may disagree with observational metrics due either to misparameterization of the relevant biogeochemical or biogeophysical processes or to biases in the physical climate drivers thereof. Model development and improvement, therefore, requires evaluating simulations using metrics that constrain functional responses—in other words, the relationships between driver and response variables—rather than simply comparing time series or spatial distributions of individual variables (Randerson et al. 2009).
It is further necessary to identify methods to gauge the realism of future predictions, since model agreement with present-day observations merely improves confidence that the model represents relevant processes, but cannot ensure predictive skill (Tebaldi and Knutti 2007; Bonan and Doney 2018). One method that has become increasingly prominent in climate change literature is the use of emergent constraints, which provides a methodology to evaluate long-term predictions within the context of a multimodel ensemble when a correlation exists between a short-term functional response, which can be evaluated against observations, and a long-term feedback governed by the same mechanism (Klein and Hall 2015). For example, Hoffman et al. (2014) showed that in the CMIP5 ensemble of ESMs, the atmospheric
Unfortunately, developing functional response metrics for tropical ecosystem carbon–climate interactions is difficult, in part because of a lack of large-scale observations of tropical ecosystem function. There are limited tropical sites at which fluxes are measured directly via eddy covariance (Schimel et al. 2015). Moreover, these sites may not be representative of the entire tropics, given a high degree of ecosystem heterogeneity driven both by biological diversity and abiotic factors, such as soil chemistry and local hydrology (e.g., Araujo et al. 2002; Townsend et al. 2008). Thus, we propose to exploit long-term observations of the atmospheric
Several studies have shown that the single variable to which the interannual
Metrics for carbon–climate feedbacks
While the use of emergent constraints provides a promising method to link contemporary observations to the likelihood of future model outcomes, the results must be interpreted with caution. Previous studies have acknowledged that different processes, including vegetation mortality and shifts in vegetation, operate at long time scales, which could cause decoupling between the short-term and long-term temperature responses (Randerson 2013). Here, we focus on the challenge of evaluating modeled land fluxes against observed atmospheric
The goal of this paper is to identify methods to use atmospheric
2. Methods
2.1. 
growth rate from atmospheric observations

We calculated the temperature sensitivity of the atmospheric
NOAA flask sampling sites within the MBL used in this analysis. Sites were selected with nearly continuous data coverage between 1982 and 2005, the end of the historical period for CMIP5 models.
Time series of global atmospheric
Citation: Earth Interactions 22, 7; 10.1175/EI-D-17-0017.1
We aggregated the monthly mean
The interannual growth rate anomaly was related to variations in tropical temperature via linear regression to estimate
Relationship between the observed
Citation: Earth Interactions 22, 7; 10.1175/EI-D-17-0017.1
Climate variability is not normally distributed, so the length of and gaps in the
2.2. CMIP5 carbon cycle diagnostics
We analyzed the interannual climate sensitivity of terrestrial carbon uptake for historical simulations in eight CMIP5 ESMs (Table 3) whose outputs were obtained from the Earth System Grid Federation (Williams et al. 2011). The historical simulations covered the period 1850–2005 and were forced with historical atmospheric composition changes, including greenhouse gas and aerosol concentrations resulting from anthropogenic and natural sources. CMIP5 models were also forced with historical land-use change patterns, although the implementation varied across models (Taylor et al. 2012). From these simulations, we analyzed temperature and net biospheric production (NBP) output. NBP encompasses all terrestrial processes that leave an imprint on atmospheric
CMIP5 models and the temperature sensitivities of land carbon processes. CMIP5 temperature sensitivities have been calculated directly from simulated land fluxes and indirectly using simulated atmospheric CO2. The observed temperature sensitivities are calculated only from atmospheric CO2.
To examine our hypothesis that neglecting atmospheric processes induces a bias between
We note that in comparing the simulated atmospheric
In addition to calculating
2.3. Calculating a constraint on 

We calculated an emergent constraint on the long-term temperature sensitivity of terrestrial carbon storage
3. Results
3.1. Temperature sensitivities inferred from atmospheric 
observations

The observed temperature sensitivity of land carbon uptake (
When the monthly or quarterly
Relationship between observed
Citation: Earth Interactions 22, 7; 10.1175/EI-D-17-0017.1
3.2. A functional response metric for 
for tropical ecosystem fluxes

Since our goal was to develop a functional response metric for the tropical ecosystem temperature sensitivity, we first analyzed the difference in temperature sensitivity owing to tropical versus global fluxes. In section 3.1., we showed that annual temperature variations were a more important driver of variations in the observed
Second, we analyzed the impact that atmospheric transport leaves on
Throughout the manuscript, we calculated the atmospheric
Together, these results suggest that a functional response metric to evaluate the temperature sensitivity of tropical ecosystems should be 1) minimally sensitive to the imprint of extratropical fluxes to better isolate the temperature sensitivity of tropical fluxes and 2) maximally representative of the spatially integrated fluxes despite sparse atmospheric sampling. With these criteria in mind, the relationship between the tropical land-derived
Relationship for
Citation: Earth Interactions 22, 7; 10.1175/EI-D-17-0017.1
The strong relationship between tropical land-derived
3.3. An emergent constraint on long-term tropical sensitivity
The winter
Emergent constraint on the long-term sensitivity of tropical ecosystems to climate change (
Citation: Earth Interactions 22, 7; 10.1175/EI-D-17-0017.1
Probability density functions for the long-term sensitivity of ecosystem fluxes to climate change (
Citation: Earth Interactions 22, 7; 10.1175/EI-D-17-0017.1
4. Discussion
Our results suggest that atmospheric observations can provide direct constraints on tropical land fluxes. We identified a functional response metric to diagnose the sensitivity of tropical carbon fluxes to local temperature variations using the winter seasonal atmospheric
Atmospheric
In the context of an emergent constraint, our analysis shows that different averaging time scales for the observations affect the optimized constraint, as does using atmospheric
Our results indicated that the emergent constraint on terrestrial temperature sensitivity from a multimodel ensemble shows a systematic dependence on the choice of observational constraint and the treatment of model output. There was a 20% difference in the expected value for the tropical
Given the persistent uncertainties in prediction of the land carbon sink over the twenty-first century and the fact that CMIP5 coupled models simulated as large of a spread in cumulative net carbon uptake as did an earlier generation of C4MIP models (Friedlingstein et al. 2006, 2014), analyzing model output fields that have direct relationships to observational datasets is crucial. Our results show that there is a 25% bias when
Acknowledgments
The research was supported in part by the RUBISCO Scientific Focus Area (SFA), which is sponsored by the Regional and Global Climate Modeling (RGCM) Program in the Climate and Environmental Sciences Division (CESD) of the Office of Biological and Environmental Research in the U.S. Department of Energy Office of Science. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DE-AC05-00OR22725. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups producing and making available their model output. For CMIP, the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.
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