1. Introduction
Atmospheric CO2 seasonal cycle is controlled by the seasonal responses of terrestrial carbon cycle to climate (Forkel et al. 2016; Graven et al. 2013; Keeling et al. 1996; Randerson et al. 1997). Interannual anomalies of climate superimposed on the seasonal cycle modulate the response of terrestrial CO2 fluxes to climate season specifically. For instance, a large body of evidence shows that warmer springs are associated with an enhanced CO2 uptake (Keenan et al. 2014; Wolf et al. 2016), implying that the interannual sensitivity of the net CO2 flux [net biome production (NBP)] is positively related to spring temperature variations. In summer, since warmer years are often dryer across the temperate zone, the interannual sensitivity of NBP to temperature variations generally is negative (Angert et al. 2005). In autumn, years with warmer climate were analyzed by Piao et al. (2008) to be associated with an abnormal release of CO2 (i.e., suggesting a negative interannual sensitivity of NBP to autumn temperature), but other studies found the opposite, namely that warmer autumns extend the growing season, which results in increased CO2 uptake (Dragoni et al. 2011).
Accurate understanding of the seasonal impact of climate change on terrestrial carbon fluxes is essential for evaluating and projecting atmospheric CO2 seasonality (Forkel et al. 2016; Zhao and Zeng 2014). Earth system models (ESMs) are widely used to assess terrestrial carbon cycle responses to climate change across multiple temporal scales, but the large spread in the simulation results across ESMs has limited our ability to make inferences (Todd-Brown et al. 2014; Todd-Brown et al. 2013; Ahlström et al. 2012). In recent years, some observation-based products of carbon flux have been reported and are valuable data to test terrestrial carbon cycle process in ESMs, including satellite-derived net primary production (NPP) Smith et al. (2016) and inversion-based NBP (Chevallier et al. 2014; Chevallier et al. 2005; Chevallier et al. 2010). Using these products enables the evaluation of the performance of ESMs in modeling the seasonal responses of the terrestrial carbon cycle to climate variations.
Over the twenty-first century, global mean surface temperatures are projected to continue to rise under all representative concentration pathways (RCPs) from ESMs participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5) (Collins et al. 2013). Future warming has seasonal asymmetry, with a larger warming in winter than in summer, resulting in the reduction of the seasonal cycle of temperature (Dwyer et al. 2012). Furthermore, projected changes in precipitation are also not uniform across seasons. For instance, increases in precipitation are larger in late winter–early spring (February–April) in the northeastern United States over the twenty-first century under RCP8.5 from CMIP5 ESMs (Lynch et al. 2016). These complex seasonal patterns of climate change are a main reason that season-specific responses of the terrestrial carbon cycle to climate change over the twenty-first century remain largely unknown.
In this study, we investigate the seasonal sensitivities of terrestrial carbon fluxes to interannual climate variations in CMIP5 ESMs, and how these sensitivities change during the twenty-first century. Specifically, we aim to 1) evaluate CMIP5 ESMs for their seasonal dynamics of NPP and NBP sensitivities to interannual climate variations, 2) examine changes in seasonal sensitivities of terrestrial NBP to interannual climate variations during the twenty-first century, and 3) identify which carbon flux component, NPP or heterotrophic respiration (Rh), leads to the twenty-first century changes in seasonal sensitivities of the net CO2 balance (NBP) to interannual climate variations in ESMs.
2. Material and methods
a. Terrestrial carbon fluxes and climate variables in Earth system models
We used historical (“historical” experiment; 1850–2005) and future representative concentration pathway 2.6, 4.5, 6.0, and 8.5 simulations (RCP2.6, RCP4.5, RCP6.0, and RCP8.5, respectively; 2006–2100) of the CMIP5 ESMs (Taylor et al. 2012). Both historical carbon fluxes (NPP, Rh, and NBP) and climate variables (air temperature, precipitation, and surface downwelling shortwave radiation variables) from 17 ESMs were used, including BNU-ESM, CanESM2, CCSM4, CESM1(BGC), HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, MRI-ESM1, NorESM1-M, and NorESM1-ME. (Expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.) The number of ESMs having so-called historical and RCP2.6, RCP4.5, RCP6.0, and RCP8.5 runs is 17, 12, 16, 9, and 16, respectively (see Table S1 in the supplemental material).
We downloaded monthly output of ESMs from the Program for Climate Model Diagnosis and Intercomparison (PCMDI) server: Earth System Grid Federation (Cinquini et al. 2014) (http://cmip-pcmdi.llnl.gov/cmip5). For each individual model, only output from the first realization (r1i1p1) was used in this study. The output was regridded to 1° × 1° using the first-order conservative remapping scheme (Jones 1999) in Climate Data Operators (https://code.zmaw.de/projects/cdo) following several previous studies (e.g., Y. Liu et al. 2016; Wang et al. 2016; Zappa et al. 2015; Curry et al. 2014; Donat et al. 2014; Torres and Marengo 2014; Sillmann et al. 2013). The study region was limited to the land area with active vegetation, defined as grid cells where the annual mean normalized difference vegetation index (NDVI) during 1982–2009 was larger than 0.1. The NDVI data were the third-generation GIMMS NDVI data from AVHRR sensors (NDVI3g), obtained from the Global Inventory Monitoring and Modeling Studies (GIMMS) group (Pinzon and Tucker 2014). Please note that the active vegetation defined by historical NDVI may not be exactly the same as that in ESMs, and modeling vegetated land area may change with time.
b. Satellite-derived NPP, inversion-based NBP, and climate datasets
Global monthly satellite-derived NPP data from 1982–2011 with 1° × 1° spatial resolution were obtained from Smith et al. (2016). This NPP dataset was estimated using the Moderate Resolution Imaging Spectroradiometer (MODIS) NPP algorithm driven by the third-generation GIMMS fraction of photosynthetically active radiation (FPAR) absorbed by the vegetation (FPAR3g) and leaf area index (LAI3g) (Zhu et al. 2013), following Eq. (1) in Smith et al. (2016).
Global monthly NBP from 1979 to 2015 with 1.875° latitude × 3.75° longitude spatial resolution was obtained from version 15.2 of the Monitoring Atmospheric Composition and Climate—Interim Implementation (MACC-II) CO2 inversion product from the Laboratoire des Sciences du Climat et de l’Environnement (LSCE) (Chevallier et al. 2014, 2005, 2010). The surface–atmosphere net land carbon fluxes were estimated by atmospheric CO2 inversions using atmospheric CO2 concentration measurements across the globe and an atmospheric transport model. NBP is retrieved from the inversion after subtracting the influence of fossil fuel CO2 emissions (assumed to be perfectly known) from atmospheric CO2 gradients.
Monthly air temperature, precipitation, and cloud cover from 1901 to 2013 with spatial resolution of 0.5° × 0.5° were downloaded from the University of East Anglia Climatic Research Unit [CRU Time Series, version 3.22 (CRU TS3.22); http://catalogue.ceda.ac.uk/uuid/3f8944800cc48e1cbc29a5ee12d8542d] (Jones and Harris 2008). Both inversion-based NBP and CRU climate data were regridded to 1° × 1° before the other analysis.
c. Biome classifications
Biome classifications in this study were defined according to the standard MODIS land cover type data product (MCD12Q1; http://glcf.umd.edu/data/lc/) in the IGBP land cover type classification (Friedl et al. 2010) and the Köppen–Geiger climate classification (http://koeppen-geiger.vu-wien.ac.at/present.htm) (Kottek et al. 2006). Six biomes were considered: tropical forests, temperate forests, boreal forests, semiarid ecosystems, grasslands, and shrublands and subarctic ecosystems (Fig. S1 in the supplemental material). Forests in the MCD12Q1 were split into tropical forests, temperate forests, and boreal forests using the Köppen–Geiger classification. Semiarid ecosystems include arid areas in the Köppen–Geiger climate classification, and all savanna and shrublands at latitudes south of 50°N. Grasslands correspond to MCD12Q1 land cover definition at latitudes south of 60°N. Shrublands and subarctic ecosystems include MCD12Q1 land cover classes of savanna and shrublands at latitudes north of 50°N, and grasslands at latitudes north of 60°N.
d. Analysis
The spatial patterns of monthly sensitivities of carbon fluxes to interannual climate variations (T, P, and R) were calculated by Eq. (1) using carbon fluxes and climate variables in each 1° × 1° grid. The sensitivities in each 1° latitude band were averaged to obtain the zonal distribution of sensitivities in each month except for inversion-based NBP responses to T and P. When analysis spatial patterns of NBP sensitivity based on inversion-based NBP, we aggregated each variable over the following latitudinal bands: 50°–90°N, 23°–50°N, 23°S–0°, 0°–23°N, and 23°–50°S. To perform analysis of the seasonal sensitivities of carbon fluxes at biome scale, each variable (NPP, Rh, NBP, temperature, precipitation, and shortwave downwelling radiation) was aggregated in each biome. Then, the variables were summed over the following periods in each year: March–May (MAM), June–August (JJA), September–November (SON), and December–February (DJF). The aggregated variables in each season were detrended separately and then used to calculate the biome-averaged interannual climate sensitivities of seasonal carbon fluxes based on Eq. (1). Future changes (indicated with Δ) in γT, γP, and γR were calculated as the differences between 2069–98 and 1975–2004 assuming no change in biome area. We examined the significance of these changes using a Wilcoxon signed-rank test following Collins et al. (2013) and Y. Liu et al. (2016).
In the following text, the value of γ is represented as X ± SE, where X is the value of the interannual sensitivity of carbon fluxes γ, and SE is the standard error of γ (regression fit uncertainty). The multimodel distribution of γ is represented as 
3. Results and discussion
a. Interannual temperature sensitivities of seasonal carbon fluxes
1) Tropical forests
In tropical forests, γTNBP is negative in MAM, JJA, SON, and DJF during 1982–2005 in most ESMs (Fig. S2 in the supplemental material), resulting in negative multimodel median γTNBP ranging from 
Multimodel median seasonal γTNPP, γTRh, and γTNBP across vegetation types in the period 1982–2005 and their changes from 1982 to 2099 under RCP4.5. The dots represent observation derived γT in the period 1982–2005. The black, gray, and white dots indicate that γT is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant, respectively. The gray vertical lines across the dots indicate the standard error of observation derived γT. The bars mean the γT in the period 1982–2005. The bars with black solid, gray solid, and gray dashed borders mean that the multimodel median γT is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant using a Wilcoxon signed-rank test, respectively. The arrows mean the changes in multimodel median seasonal γT from 1982 to 2099 (ΔγT) under RCP4.5. The black and gray stars mean that multimodel median ΔγT is significant (at the 5% level) and marginally significant (at the 10% level) using a Wilcoxon signed-rank test, respectively.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Multimodel median seasonal γTNPP, γTRh, and γTNBP across vegetation types in the period 1982–2005 and their changes from 1982 to 2099 under RCP4.5. The dots represent observation derived γT in the period 1982–2005. The black, gray, and white dots indicate that γT is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant, respectively. The gray vertical lines across the dots indicate the standard error of observation derived γT. The bars mean the γT in the period 1982–2005. The bars with black solid, gray solid, and gray dashed borders mean that the multimodel median γT is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant using a Wilcoxon signed-rank test, respectively. The arrows mean the changes in multimodel median seasonal γT from 1982 to 2099 (ΔγT) under RCP4.5. The black and gray stars mean that multimodel median ΔγT is significant (at the 5% level) and marginally significant (at the 10% level) using a Wilcoxon signed-rank test, respectively.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Multimodel median seasonal γTNPP, γTRh, and γTNBP across vegetation types in the period 1982–2005 and their changes from 1982 to 2099 under RCP4.5. The dots represent observation derived γT in the period 1982–2005. The black, gray, and white dots indicate that γT is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant, respectively. The gray vertical lines across the dots indicate the standard error of observation derived γT. The bars mean the γT in the period 1982–2005. The bars with black solid, gray solid, and gray dashed borders mean that the multimodel median γT is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant using a Wilcoxon signed-rank test, respectively. The arrows mean the changes in multimodel median seasonal γT from 1982 to 2099 (ΔγT) under RCP4.5. The black and gray stars mean that multimodel median ΔγT is significant (at the 5% level) and marginally significant (at the 10% level) using a Wilcoxon signed-rank test, respectively.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γTNPP in the period 1982–2005; γTNPP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γTNPP in the period 1982–2005; γTNPP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γTNPP in the period 1982–2005; γTNPP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of simulated monthly γTRh in the period 1982–2005; γTRh is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of simulated monthly γTRh in the period 1982–2005; γTRh is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of simulated monthly γTRh in the period 1982–2005; γTRh is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γTNBP in the period 1982–2005; γTNBP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γTNBP in the period 1982–2005; γTNBP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γTNBP in the period 1982–2005; γTNBP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of multimodel median (a) γTNPP, (c) γTRh, and (e) γTNBP, and (b),(d),(f) their respective changes from 1982 to 2099 under RCP4.5. Values of γTNPP, γTRh, and γTNBP are estimated using Eq. (1); ΔγTNPP, ΔγTRh, and ΔγTNBP are calculated as the difference of γTNPP, γTRh, and γTNBP, respectively, between the periods 2076–99 (RCP4.5 runs) and 1982–2005 (historical simulations). Black dots indicate significance at the 5% level using a Wilcoxon signed-rank test. Models used are BNU-ESM, CanESM2, CCSM4, CESM1(BGC), GFDL-ESM2M, GFDL-ESM2G, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, NorESM1-M, and NorESM1-ME.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of multimodel median (a) γTNPP, (c) γTRh, and (e) γTNBP, and (b),(d),(f) their respective changes from 1982 to 2099 under RCP4.5. Values of γTNPP, γTRh, and γTNBP are estimated using Eq. (1); ΔγTNPP, ΔγTRh, and ΔγTNBP are calculated as the difference of γTNPP, γTRh, and γTNBP, respectively, between the periods 2076–99 (RCP4.5 runs) and 1982–2005 (historical simulations). Black dots indicate significance at the 5% level using a Wilcoxon signed-rank test. Models used are BNU-ESM, CanESM2, CCSM4, CESM1(BGC), GFDL-ESM2M, GFDL-ESM2G, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, NorESM1-M, and NorESM1-ME.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of multimodel median (a) γTNPP, (c) γTRh, and (e) γTNBP, and (b),(d),(f) their respective changes from 1982 to 2099 under RCP4.5. Values of γTNPP, γTRh, and γTNBP are estimated using Eq. (1); ΔγTNPP, ΔγTRh, and ΔγTNBP are calculated as the difference of γTNPP, γTRh, and γTNBP, respectively, between the periods 2076–99 (RCP4.5 runs) and 1982–2005 (historical simulations). Black dots indicate significance at the 5% level using a Wilcoxon signed-rank test. Models used are BNU-ESM, CanESM2, CCSM4, CESM1(BGC), GFDL-ESM2M, GFDL-ESM2G, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, NorESM1-M, and NorESM1-ME.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
The satellite-derived γTNPP is marginally significantly negative in SON (−109.3 ± 61.4 TgC month−1 K−1, p = 0.09) during 1982–2005, which is comparable with the multimodel median γTNPP. But in MAM, JJA, and DJF, satellite-derived γTNPP is nonsignificant, unlike negative γTNPP in the ESMs (Fig. 1a). Tropical vegetation is thought to be close to the high temperature threshold for NPP (Corlett 2011; Doughty and Goulden 2008). Most areas (88%) of current tropical forests experience mean annual temperatures greater than 20°C (Wood et al. 2012), while leaf temperatures in tropical forests are often higher than 35°C (Doughty and Goulden 2008), which is near the thermal optimum for plants under current atmospheric CO2 concentrations less than 380 ppm (Wood et al. 2012). NPP should thus become decoupled from T when temperature is optimum, and negatively related to T under above-optimal temperature. It seems that CMIP5 ESMs overestimated the negative effect of T on the NPP in MAM, JJA, and DJF with more negative γTNPP compared to satellite-derived γTNPP. Here, modeled γTNPP is calculated by the multiple regression approach in Eq. (1) using the variables outputted by individual ESMs, and therefore may not be exactly consistent with model-specific physiological processes (Rogers et al. 2017). We note that there are also uncertainties in satellite-derived NPP in tropical forests. The calculation of satellite-derived NPP is influenced by FPAR and LAI, both of which, however, can saturate in the tropical forests Smith et al. (2016). Moreover, usable optical satellite images are limited in tropical forests because of persistent cloud cover, particular in the rainy season (e.g., JJA), posing a challenge to the interannual analysis (Reiche et al. 2016). Finally, satellite-derived γTNPP could be impacted by other constraints in the light use efficiency model, including a partially temperature-driven vapor pressure deficit (VPD) constraint and a partially temperature-driven autotrophic respiration (Ra) equation.
Over tropical forests, the inversion-based γTNBP during 1982–2005 in MAM, SON, and DJF is −65.6 ± 35.4 (p = 0.078), −117.1 ± 54.6 (p = 0.044), and −67.2 ± 34.4 TgC month−1 K−1 (p = 0.065), respectively, which are comparable with ESM simulations (Fig. 1a). However, in JJA, inversion-based γTNBP is nonsignificant. It is noteworthy that the surface CO2 mixing ratio measurement sites used in the estimation of inversion-based NBP, are mainly distributed in the middle and high latitudes, and over tropical oceans, but scarce on tropical lands (Chevallier et al. 2010). This causes uncertainties of inversion-based γTNBP in tropical forests, although the inversion-based NBP in tropical forest is partly constrained by the CO2 mixing ratios measured in other regions (Chevallier et al. 2010). To better evaluate the tropical γTNBP from ESMs more accurate estimation of responses of seasonal NBP to T in tropical forests are needed. For example, manipulative warming experiments could be utilized to improve our understanding of tropical forests carbon balance responses to climate change (Cavaleri et al. 2015; Norby et al. 2016).
By the end of the twenty-first century, γTNBP of tropical forests becomes more negative in most ESMs under RCP4.5, with a multimodel ΔγTNBP ranging from 
2) Temperate forests
Temperate forests are mainly distributed across northeastern North America, central Europe, and southeastern Asia (Fig. S2). In temperate forests, multimodel median γTNBP is significant negative during 1982–2005, ranging from 
The responses of temperate forests carbon cycle to climate variations have large spatial heterogeneity. In central Europe, the relation between tree-ring width and JJA temperature is nonsignificant in Mediterranean lowland regions, but is negative around the eastern part of the Mediterranean Sea (Babst et al. 2013). Across the eastern United States, photosynthesis increased because of warming-induced increases in growing season length (earlier spring and later autumn) that were larger than warming-induced increases in carbon release, resulting in positive responses of net carbon uptake to temperature (Keenan et al. 2014). In southern China, both the diameter at breast height of trees and the forest biomass decreased over the past three decades, partly due to warming (Zhou et al. 2013). Thus, temperate forest γTNBP values may have spatially variable patterns, consistent with nonsignificant γTNBP diagnosed at regional scale from the inversion. In contrast CMIP5 ESMs appear to generally overestimate the negative effect of T on NBP in all seasons.
Over the twenty-first century, projected γTNPP does not significantly change in all seasons except in SON with a multimodel median ΔγTNPP of 
3) Boreal forests
In boreal forests, there is clear seasonal difference in γTNPP and γTNBP during the past 30 years in ESMs (Figs, 1c, 2, 4, and 5a,e). The multimodel median γTNBP in MAM is 
In JJA, NPP is decoupled from T in ESMs, and satellite-derived γTNPP is marginally significant (25.0 ± 12.4 TgC month−1 K−1, p = 0.058) (Fig. 1c). Multimodel median γTNBP in JJA is 
In SON, satellite-derived γTNPP is significantly positive with value of 10.3 ± 2.2 TgC month−1 K−1 (p < 0.001), which is captured by ESMs giving a multimodel median 
Future changes in γTNBP in boreal forests mainly depend on the balance between changes in γTNPP and γTRh. By the end of the twenty-first century, the changes in responses of NBP to T in boreal forests are season-specific in ESMs under RCP4.5 (Fig. 1c). In MAM, ΔγTNPP and ΔγTRh are comparable with multimodel median of 
4) Semiarid ecosystems
In semiarid ecosystems, multimodel median γTNBP range from 
Semi-arid ecosystems in this analysis are mainly dominated by shrublands and savannas, mainly distributed across the subtropics in the Southern Hemisphere (SH), for example, southern South America, southern Africa, and Australia (Fig. S1). In most of these regions, weather could be generally divided into two main seasons: the rainy season (approximately November–April), and the dry season (approximately May–October). Vegetation phenology is mainly controlled by terrestrial hydrological variability, rather than temperature variations in the semiarid ecosystems [e.g., savannas in northern Australia (Ma et al. 2013) and Africa (Guan et al. 2014)]. Inversion-based γTNBP are season-specific, probably partly due to the season-specific vegetation growth under various hydrological conditions. In the SH subtropics, SON and MAM are transitional periods of dry season to rainy season and rainy season to dry season, respectively, corresponding to the beginning and end of phenology of deciduous species. Compared with MAM and SON, canopy cover is much lower in that in JJA, particularly for fully deciduous species (Williams et al. 1997). Thus, the relative larger response of satellite-derived NPP to T in MAM may be partly due to the greater leaf photosynthetic substrate (canopy biomass) than that in JJA, SON, and DJF, leading to greatest γTNBP in MAM.
Over the twenty-first century, in semiarid ecosystems, projected γTNPP marginally significantly decreases in MAM under RCP4.5 with multimodel median ΔγTNPP of 
5) Grasslands
There are large differences in γTNBP between ESMs and inversion-based estimations during 1982–2005 (Fig. 1e). In MAM, the multimodel median γTNPP is 
Grasslands in this analysis are mainly distributed in the NH midlatitudes, for example, the western United States, central Asia, Mongolia, and northern and western China (Fig. S1). In these regions, temperature in MAM and SON is much lower than the optimum temperature for photosynthesis. Warming, therefore, probably increases plant growth in MAM and SON during warmer years over the past three decades. Such positive responses of grasslands NPP to T may also be partly due to elevated atmosphere CO2 concentration. It seems that the positive γTNPP is not likely due to changes in phenology during the past three decades since no generally changes in the phenology in grasslands have been observed (Zhao et al. 2015) and phenology probably is mainly influenced by precipitation rather than temperature in water-limited grasslands (Q. Liu et al. 2016; Shen et al. 2015). It is worth noting that the inversion-based γTNBP is much higher than the satellite-derived γTNPP in both MAM and SON, and therefore, maybe overestimated.
In JJA, grasslands carbon uptake is limited by water rather than temperature, for example, in western United States (Gang et al. 2015; Gremer et al. 2015) and northern China (Gang et al. 2015; Shen et al. 2016). Thus, satellite-derived NPP is decoupled from T, leading to nonsignificant γTNBP (Fig. 1e). While grasslands NPP is negatively related to T in ESMs in JJA. γTNPP in JJA are projected to decease over the twenty-first century under RCP4.5, with multimodel median ΔγTNPP of 
6) Shrublands and subarctic ecosystems
The shrublands and subarctic ecosystems in this study mainly include natural vegetation (except forests) at latitudes north of 50°N. Satellite-derived NPP is positively related with T across all seasons except DJF, with the γTNPP being 5.7 ± 1.4 TgC month−1 K−1 (p = 0.001) in MAM, 50.6 ± 8.9 TgC month−1 K−1 (p < 0.001) in JJA, and 4.7 ± 1.1 TgC month−1 K−1 (p = 0.001) in SON (Fig. 1f). ESMs capture the positive γTNPP with multimodel median γTNPP of 
Arctic regions have been subject to strong near-surface warming during past recent decades, which is almost twice the global average (Graversen et al. 2008; Hartmann et al. 2013). This warming signal extended the growing season of ecosystems at northern high latitudes via advancing spring (Hoye et al. 2007; Parmesan 2006). Meanwhile, the photosynthetic rate in subarctic ecosystems is limited by relatively low temperature, and could be enhanced by warming, thus enhancing NPP. Furthermore, multiple lines of evidence demonstrate that both the abundance and extent of shrubs increased in subarctic regions caused by warming during past recent decades (Elmendorf et al. 2012; Myers-Smith et al. 2011; Sturm et al. 2001; Tape et al. 2006). Such changes in subarctic vegetation structure may also contribute to the positive satellite-derived γTNPP, but remain to be evaluated in ESMs.
By the end of the twenty-first century, projected γTNBP becomes more positive in MAM with multimodel median ΔγTNBP of 
Changes in both γTNPP and γTRh are likely due to the dramatic warming in the twenty-first century projected by ESMs. Future dramatic warming could extend growing seasons (Ruosteenoja et al. 2016) and raise photosynthetic rates, and therefore increase γTNPP in ESMs. The projected increasingly positive γTRh across models is likely due to warming-induced increases in Rh rates (Todd-Brown et al. 2013) and organic carbon storage (Todd-Brown et al. 2014) in NH high latitudes. It is noteworthy that the permafrost carbon dynamics are not explicitly represented in CMIP5 ESMs (Schuur et al. 2015; Todd-Brown et al. 2014), resulting in large uncertainty in projection of ΔγTRh. Microbial processes are key biogeochemical mechanisms that have been shown to control the sign of the effect of future warming on soil carbon storage (Wieder et al. 2013). In addition, future climate change may increase the vulnerability of subarctic ecosystems to fire, because of drier soils and increases in lightning ignitions caused by warming (Turetsky et al. 2015). To better project the responses of carbon cycles to future climate change, we recommend that the mechanism underlying the effects of northern latitude fire on the carbon cycle and their feedbacks to the climate system should be fully considered in the next generation of ESMs.
b. Interannual precipitation sensitivities of seasonal carbon fluxes
In most ESMs, NPP is positively related with P across all biomes (except in shrublands and subarctic ecosystems), particularly in tropical forests and semiarid ecosystems, where γPNPP is significantly positive in all seasons during 1982–2005 (Figs. 6 and S13 in the supplemental material). This is probably because plant growth in tropical and subtropical regions is limited by water because of drought or above-optimal temperature in ESMs. The value of γPNPP in models is generally positive in both NH tropics and SH tropics, but with different strength in different month. Specifically, in NH tropics, γPNPP in November–April is much more positive than that γPNPP in the other months. But in SH tropics, γPNPP is much more positive in May–October compared to the other months. This is probably because the dry season occurs at different times in the NH tropics (approximately November–April) and SH tropics (approximately May–October) resulting from the intertropical convergence zone (ITCZ) movement. Drought is also likely to occur in temperate and boreal forests, and grasslands in NH summer with positive γPNPP in MAM in ESMs. The value of γPNBP in ESMs depends on both responses of NPP and Rh to P, but varies with ESMs (Figs. 6–9).
Multimodel median seasonal γPNPP, γPRh, and γPNBP across vegetation types in the period 1982–2005 and their changes from 1982 to 2099 under RCP4.5. The dots represent observation derived γP in the period 1982–2005. The black, gray, and white dots indicate that γP is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant, respectively. The gray vertical lines across the dots indicate the standard error of observation derived γP. The bars mean the γP in the period 1982–2005. The bars with black solid, gray solid, and gray dashed borders mean that the multimodel median γP is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant using a Wilcoxon signed-rank test, respectively. The arrows mean the changes in multimodel median seasonal γP from 1982 to 2099 (ΔγP) under RCP4.5. The black and gray stars mean that multimodel median ΔγP is significant (at the 5% level) and marginally significant (at the 10% level) using a Wilcoxon signed-rank test, respectively.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Multimodel median seasonal γPNPP, γPRh, and γPNBP across vegetation types in the period 1982–2005 and their changes from 1982 to 2099 under RCP4.5. The dots represent observation derived γP in the period 1982–2005. The black, gray, and white dots indicate that γP is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant, respectively. The gray vertical lines across the dots indicate the standard error of observation derived γP. The bars mean the γP in the period 1982–2005. The bars with black solid, gray solid, and gray dashed borders mean that the multimodel median γP is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant using a Wilcoxon signed-rank test, respectively. The arrows mean the changes in multimodel median seasonal γP from 1982 to 2099 (ΔγP) under RCP4.5. The black and gray stars mean that multimodel median ΔγP is significant (at the 5% level) and marginally significant (at the 10% level) using a Wilcoxon signed-rank test, respectively.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Multimodel median seasonal γPNPP, γPRh, and γPNBP across vegetation types in the period 1982–2005 and their changes from 1982 to 2099 under RCP4.5. The dots represent observation derived γP in the period 1982–2005. The black, gray, and white dots indicate that γP is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant, respectively. The gray vertical lines across the dots indicate the standard error of observation derived γP. The bars mean the γP in the period 1982–2005. The bars with black solid, gray solid, and gray dashed borders mean that the multimodel median γP is significant (at the 5% level), marginally significant (at the 10% level), and nonsignificant using a Wilcoxon signed-rank test, respectively. The arrows mean the changes in multimodel median seasonal γP from 1982 to 2099 (ΔγP) under RCP4.5. The black and gray stars mean that multimodel median ΔγP is significant (at the 5% level) and marginally significant (at the 10% level) using a Wilcoxon signed-rank test, respectively.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γPNPP in the period 1982–2005; γPNPP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γPNPP in the period 1982–2005; γPNPP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γPNPP in the period 1982–2005; γPNPP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of simulated monthly γPRh in the period 1982–2005; γPRh is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of simulated monthly γPRh in the period 1982–2005; γPRh is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of simulated monthly γPRh in the period 1982–2005; γPRh is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γPNBP in the period 1982–2005; γPNBP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γPNBP in the period 1982–2005; γPNBP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of observed and simulated monthly γPNBP in the period 1982–2005; γPNBP is estimated using Eq. (1).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Satellite-derived NPP is generally decoupled from P in most seasons, partly leading to nonsignificant inversion-based γPNBP (Figs. 6, 7a, and 9a). The decoupling between interannual variations in aboveground NPP and precipitation is also found across 11 Long Term Ecological Research network sites across North America covering forests and grasslands (Knapp and Smith 2001). This is probably because the interannual variations of precipitation are negatively related to precipitation amount (e.g., large in drier relative to more mesic regions) (Fatichi et al. 2012). The responses of NPP to P depend on both biotic (e.g., plant species and leaf areas) and abiotic factors (e.g., the strength of interannual variations in precipitation). Although humid and semihumid ecosystems (e.g., forests) have greater leaf areas and faster growing species, NPP responses are constrained by weak precipitation variations (Knapp and Smith 2001). In contrast, arid and semiarid ecosystems experience relatively large precipitation variations, but NPP responses are constrained by low plant density and leaf area (Knapp and Smith 2001). Therefore, satellite-derived γPNPP is nonsignificant in most seasons across all biomes (Fig. 6). However, a global meta-analysis shows that interannual variations in aboveground NPP are positively related to precipitation variations in grasslands at global scale (Yang et al. 2008), indicating that NPP responses to P vary with biomes or across spatial scales. In this study, satellite-derived γPNPP across global grasslands is also marginally significant in JJA with value of 123.1 ± 62.2 TgC month−1 (100 mm)−1 (p = 0.062), but is nonsignificant in MAM and SON. Different from general nonsignificant satellite-derived γPNPP, γPNPP in ESMs, however, are generally positive (Figs. 6 and 7b–r). This indicates that in current ESMs, vegetation growth is too sensitive to precipitation variations compared to satellite-derived estimations.
By the end of the twenty-first century, projected γPNPP generally does not change under RCP4.5 compared to present day across all biomes, except for temperate forests in JJA and grasslands in MAM with multimodel median ΔγPNPP of 
Spatial distributions of multimodel median (a) γPNPP, (c) γPRh, and (e) γPNBP, and (b),(d),(f) their respective changes from 1982 to 2099 under RCP4.5. Values of γPNPP, γPRh, and γPNBP are estimated using Eq. (1); ΔγPNPP, ΔγPRh, and ΔγPNBP are calculated as the difference of γPNPP, γPRh, and γPNBP, respectively, between the periods 2076–99 (RCP4.5 runs) and 1982–2005 (historical simulations). Black dots indicate significance at the 5% level using a Wilcoxon signed-rank test. Models used are BNU-ESM, CanESM2, CCSM4, CESM1(BGC), GFDL-ESM2M, GFDL-ESM2G, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, NorESM1-M, and NorESM1-ME.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of multimodel median (a) γPNPP, (c) γPRh, and (e) γPNBP, and (b),(d),(f) their respective changes from 1982 to 2099 under RCP4.5. Values of γPNPP, γPRh, and γPNBP are estimated using Eq. (1); ΔγPNPP, ΔγPRh, and ΔγPNBP are calculated as the difference of γPNPP, γPRh, and γPNBP, respectively, between the periods 2076–99 (RCP4.5 runs) and 1982–2005 (historical simulations). Black dots indicate significance at the 5% level using a Wilcoxon signed-rank test. Models used are BNU-ESM, CanESM2, CCSM4, CESM1(BGC), GFDL-ESM2M, GFDL-ESM2G, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, NorESM1-M, and NorESM1-ME.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
Spatial distributions of multimodel median (a) γPNPP, (c) γPRh, and (e) γPNBP, and (b),(d),(f) their respective changes from 1982 to 2099 under RCP4.5. Values of γPNPP, γPRh, and γPNBP are estimated using Eq. (1); ΔγPNPP, ΔγPRh, and ΔγPNBP are calculated as the difference of γPNPP, γPRh, and γPNBP, respectively, between the periods 2076–99 (RCP4.5 runs) and 1982–2005 (historical simulations). Black dots indicate significance at the 5% level using a Wilcoxon signed-rank test. Models used are BNU-ESM, CanESM2, CCSM4, CESM1(BGC), GFDL-ESM2M, GFDL-ESM2G, HadGEM2-CC, HadGEM2-ES, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MPI-ESM-LR, MPI-ESM-MR, NorESM1-M, and NorESM1-ME.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0555.1
c. Interannual radiation sensitivities of seasonal carbon fluxes
Figures S24–S39 in the supplemental material show the seasonal sensitivities of carbon fluxes (NPP, Rh, and NBP) to R in ESMs during 1982–2005 and their changes over the twenty-first century under RCP2.6, RCP4.5, RCP6.0, and RCP8.5. In most ESMs, NPP is positively related with R in tropics, and NH middle and high latitudes in NH summer (Fig. S29). However, there is no apparent correlation between Rh and R globally (Fig. S30). The γRNBP over the past three decades is generally dominated by γRNPP, rather than γRRh across global terrestrial ecosystem in ESMs (Fig. S31). By the end of twenty-first century, the changes in γRNPP has large spatial heterogeneity in ESMs under all RCPs (Figs. S36–S39). Overall, γRNBP increases in boreal forests and subarctic ecosystems under RCP8.5, but does not show apparent change in the other biomes under all RCPs (Fig. S28).
Finally, we separated the direct effect of T and P on NPP (γT_MNPP and γP_MNPP) by controlling the soil moisture in the multiple regression approach in Eq. (2). Results show that γTNPP and γT_MNPP are significant correlated across models in all biomes at all season (Fig. S40 in the supplemental material). The ratio between the multimodel median of γT_MNPP and the multimodel median of γTNPP is larger than 50% in all biomes at all season. This indicates that the temperature variation mainly directly influence NPP, rather than indirectly affect NPP via changing soil moisture. Nonetheless, the indirect effect of temperature on NPP cannot be ignored in tropical forests, semiarid ecosystems, and grasslands, particular in MAM and JJA. Probably because of these indirect effects, there are time-lag effects in vegetation growth responses to climate change in reality (Wu et al. 2015), which are recommended to be considered in the understanding terrestrial carbon cycle dynamics under climate change in future work. Different from significant γT_MNPP, NPP is decoupled from P in most models when soil moisture is controlled with insignificant γP_MNPP, particular in tropical forests (Fig. S41 in the supplemental material). This indicates that the effect of P on NPP is mainly through changing soil moisture.
4. Summary
The responses of terrestrial carbon fluxes to interannual climate variations are season-specific and change with time. However, season-specific climate sensitivities of the terrestrial carbon cycle and their changes over time due to future climate change remain largely unknown. In this paper, we evaluated CMIP5 ESMs for their seasonal interannual sensitivities of net primary production (NPP) and net biome production (NBP) sensitivities to variations of temperature T and precipitation P during 1982–2005 (γT and γP, respectively) for different biomes (tropical forests, temperate forests, boreal forests, semiarid ecosystems, grasslands, and shrublands and subarctic ecosystems). ESM interannual sensitivities were compared with satellite-derived NPP and inversion-based NBP datasets. We further investigated the changes in seasonal sensitivities of NPP, heterotrophic respiration (Rh), and NBP to T and P over the twenty-first century (ΔγT and ΔγP, respectively) under RCP2.6, RCP4.5, RCP6.0, and RCP8.5 in CMIP5 ESMs. We summarize here the main findings.
Compared with satellite-derived γTNPP in most seasons, ESMs generally capture the positive γTNPP in NH high latitudes (e.g., boreal forests, and shrublands and subarctic ecosystems), but ESMs give stronger than observed negative γTNPP across the tropics and subtropics (e.g., tropical forests and semiarid ecosystems). Satellite-derived NPP is suitable for assessing the γTNPP in boreal forests and subarctic ecosystems, while in the tropics, the uncertainties of satellite-derived NPP, especially interannual variability, are large. The calculation of satellite-derived NPP is influenced by FPAR though a light-use efficiency model and LAI, both of which, however, can saturate in the tropical forests Smith et al. (2016). Moreover, usable optical satellite images in tropical regions are limited, because of persistent cloud cover especially during the rainy season, posing a significant challenge to interannual analysis (Reiche et al. 2016). Compared with the regional-scale evaluation, the γTNPP in tropical ecosystems from ESMs may be more accurately accessed using long term NPP observations at site scale.
The responses of inversion-based NBP to T is significant in boreal forests, tropical forests, and semiarid ecosystems, but not in other biomes. In boreal forests, ESMs generally capture the positive γTNBP in MAM and SON, but underestimate the strength of negative responses of NBP to T in summer (JJA). In tropical forests and semiarid ecosystems, γTNBP across ESMs is negative in all seasons, while inversion-based γTNBP is negative only in MAM and SON and is nonsignificant in JJA. This is probably because the CO2 measurement stations are mainly distributed in the NH middle and high latitudes, and tropical oceans but rare on tropical lands (Chevallier et al. 2010). For the biomes with relative lower productivity (e.g., grasslands), the inversion-based γTNBP might be overestimated. Thus, to better understand and evaluate γTNBP in tropical ecosystems and grasslands, more accurate estimation of responses of seasonal NBP to T in these regions remains to be detected via in situ observations, such as, flux tower measurements, and manipulative warming experiments (Cavaleri et al. 2015) at whole-ecosystem scales (Fayle et al. 2015).
Over the twenty-first century, changes in γTNPP, γTRh, and γTNBP are consistent across RCP2.6, RCP4.5, RCP6.0, and RCP8.5 but are larger in magnitude under more intensive scenarios. Generally, projected γTNBP in MAM become more negative in tropical forests and semiarid ecosystems, but become more positive in boreal forests, and shurblands and subarctic ecosystems. While projected γTNBP in JJA and SON declines across all biomes. Particularly in NH high latitudes (e.g., boreal forests), the stronger negative γTNBP is due to both a decrease in negative γTNPP and an increase in positive γTRh. However, it is noteworthy that terrestrial ecosystems in the northern high latitudes contain huge organic carbon stock, which is sensitive to climate change (Koven et al. 2015; Schuur et al. 2015). Permafrost carbon dynamics is not explicitly represented in current ESMs for deep permafrost carbon (Luo et al. 2016), leading to large uncertainty in the projected changes in soil organic carbon over the twenty-first century (Todd-Brown et al. 2014). Thus, to more accurately understand the seasonal dynamic processes of terrestrial carbon cycle, it is essential to project soil carbon dynamics more realistically in ESMs in the future work.
In short, accurate understanding and representing the relationship between carbon fluxes and climate in ESMs is essential for fundamentally improving predictive responses and feedbacks of terrestrial ecosystems cycle to future climate change. In addition to considering mean annual variations in climate (Y. Liu et al. 2016), the carbon–climate correlation is recommended to be concerned separately for each season since climate variations (e.g., T and P) are known to exert different controls on seasonal CO2 fluxes. To better evaluate the performance of ESMs at regional or global scales, the quality of observation-based CO2 fluxes datasets remains to be improved, particular in tropical and subtropical zones. To better represent the carbon–climate interaction in ESMs, realistic responses of carbon fluxes to climate change are recommended to be investigated particular in tropics and northern permafrost regions using in situ perturbation experiments, such as manipulative warming experiments.
Acknowledgments
This study was supported by the National Natural Science Foundation of China (41530528 and 41561134016), the 111 Project, and the National Youth Top-notch Talent Support Program in China. P.C. acknowledges support from the European Research Council Synergy Grant ERC-2013-SyG-610028 IMBALANCE-P. We acknowledge Chris Jones and the other two anonymous reviewers for their constructive and helpful comments that greatly improved the quality of this paper.
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