We analyzed historical and future emission-driven simulation results from 10 CMIP5 Earth System Models (ESMs). The historical simulations, referred to as experiment 5.2 or ESM historical 1850–2005 run (Taylor et al., 2012), were forced with gridded CO2 emissions reconstructed from fossil fuel consumption estimates (Andres et al., 2011). The future simulations, referred to as experiment 5.3 or ESM RCP8.5 2006–2100 run, were forced with projected CO2 emissions, following only one scenario–RCP8.5 (Moss et al., 2010). We chose the emission-driven runs because the fully coupled ESMs in these runs have interactive carbon cycle component. Global atmospheric CO2 concentrations are simulated prognostically, therefore they reflect the total effect of all the physical, chemical, and biological processes on Earth, and their interactions and feedbacks with the climate system. We obtained model output primarily from the Earth System Grid Federation (ESGF), an international network of distributed climate data servers (Williams et al., 2011). For the GFDL model, we retrieved results from its data portal (http://nomads.gfdl.noaa.gov:8080/DataPortal/cmip5.jsp). The main characteristics of the 10 models are listed in Table 1.

We first analyzed the monthly output of prognostic atmospheric CO2 concentrations to evaluate the change of CO2 seasonal amplitude (defined as maximum minus minimum of detrended seasonal cycle) from 1961 to 2099. Atmospheric CO2 was obtained primarily as the area- and pressure-weighted mean of CO2 across all vertical levels – a better representation of atmospheric carbon content than surface CO2. The INM-CM4 model does not provide CO2 concentration, so we converted its total atmospheric mass of CO2 to mole fraction. We excluded the IPSL model from analyses in Sects. 3.1 and 3.2 because its CO2 output is not available. Only CanESM2 provides three different realizations for both historical and future runs, and we simply use its first realization in our comparison. We believe this choice would lead to a more representative result than including all realizations of CanESM2 in multi-model averaging.

To extract the CO2 seasonal cycle from the monthly records, we applied the curve-fitting procedures using the CCGCRV software developed at the National Oceanic and Atmospheric Administration Climate Monitoring and Diagnostics Laboratory (Thoning et al., 1989; http://www.esrl.noaa.gov/gmd/ccgg/mbl/crvfit/crvfit.html). This algorithm first fits the long-term variations and the seasonal component in the monthly CO2 record with a combination of a trend function and a series of annual harmonics. Then the residuals are filtered with fast Fourier transform and transformed back to the real domain. Specifically, we followed the default setup of a quadratic polynomial for the trend function, 4-yearly harmonics for the seasonal component, and long/short-term cutoff values of 667 days/80 days for the filtering in our analyses. We examined the phase change of CO2 detrended seasonal cycle by counting how frequent the maxima and minima occur in different months. We used two definitions of seasonal amplitude in our analyses that yield similar results: one directly comes from the CCGCRV package, and another definition is simply maximum minus minimum of detrended seasonal cycle in each year. For each model's monthly global mean CO2, we first computed the detrended CO2 seasonal cycle as the annual harmonic part plus the filtered residue using the short-term cutoff value. Then we started to investigate the global carbon budget in each model: dCO2dt=FFE-NBP+FOA.

The left term is the change of CO2 concentration (or CO2 growth rate), which we simply computed as the difference between the current month and previous month's concentration – this leads to a half-month shift earlier than the results indicate. The right hand side (RHS) comprises of fossil fuel emission (FFE), net biosphere production (NBP, or net terrestrial–atmosphere carbon exchange, positive if land is a carbon sink), and net ocean–atmosphere flux (FOA, positive if ocean releases carbon). For each model, we checked and ensured that the sum of individual flux terms on the RHS of Eq. (1) equals to the CO2 growth rate.

Previous studies have limited the impact of FFE and FOA on trends in CO2 amplitude to less than a few percent change (Graven et al., 2013). Therefore we focused on examining the seasonal cycle of NBP in this study. To investigate whether the NBP amplitude change is mostly due to enhanced production or respiration, we inspected the seasonal cycle of NPP and respiration separately. The INM model does not provide NPP output, so it is excluded in this part of analyses. For respiration, one complication is that even though NBP represents the net terrestrial–atmosphere carbon exchange in all models (thus allowing model comparison), its further breakdown varies. For example, the GFDL-ESM2M model's NBP has component fluxes including NPP, heterotrophic respiration (Rh), land use change (fLuc), fire (fFire), harvest (fHarvest) and grazing (fGrazing). In contrast, NBP approximately equals to NPP minus Rh in CanESM2. Instead of directly adding all flux components such as Rh and fLuc for each model (which would be unnecessary and difficult since not all fluxes are provided), we defined Rh∗ (dominated by Rh) such that Rh∗=NPP-NBP. Additionally, we analyzed the spatial patterns of NBP change between future (2081–2090) and historical (1961–1970) period. We approximated NBP amplitude change as the difference between the peak seasons of carbon uptake and release by the biosphere, namely May–July and October–December averages, respectively. We chose 3-month averages for multi-model ensemble, because not all models simulate peak uptake in June and peak release in October. Monthly output of NBP, NPP and Rh∗ (derived from NBP and NPP) from all models were first resampled to 2×2∘ grids. Then the spatial and zonal means for both May–July and October–December were computed.

The CMIP5 models project that the increase of CO2 seasonal amplitude continues in the future. Figure 1a shows detrended and globally averaged monthly column atmospheric CO2 from 1961 to 2099, averaged over nine models (no IPSL). The models project an increase of CO2 seasonal amplitude (defined as maximum minus minimum in each year) by about 70 % over 120 years, from 1.6 ppm during 1961–1970 to 2.7 ppm in 2081–2090. The increase is faster in the future than in the historical period. Another feature is that the trend of minima (-0.63 ppm century-1) has a larger magnitude than the trend of maxima (0.41 ppm century-1), suggesting that enhanced vegetation growth contributes more to the amplitude increase than respiration increase. Gurney and Eckels (2011) found the trend of net flux in dormant season is larger than that of growing season. However, they applied a very different definition for amplitude, considering all months instead of maxima and minima, to analyze the atmospheric CO2 inversion results from 1980–2008. Specifically, they defined growing season net flux (dormant season net flux) as the total of any month for which the net carbon flux is negative (positive), and amplitude as the difference of the two net fluxes. It is no surprise they reached a conclusion that seems to contradict ours, since growing season is much shorter than dormant season at global scale. Figure 1b and c present detrended global mean CO2 growth rate (1 ppm =2.12 PgC month-1 for unit conversion) and global total -NBP, two quantities showing very similar characteristics as expected. All models simulate an increase in amplitude, although considerable model spread is found (Table 2). In addition, we notice a phase advance of maxima and minima by counting their time of occurrence (data not shown). Excluding models above one standard deviation from the ensemble mean yields similar results.

To illustrate how well the models reproduce the seasonal variations of CO2, we compared the multi-model ensemble global CO2 at the lowest model level – not equivalent to the height of surface CO2 measurement, but relatively close – with ESRL's global mean CO2 over 1981–2005 (Fig. 1d). The surface CO2 seasonal amplitude estimated by the model ensemble is lower than that of ESRL's global CO2 estimate (Ed Dlugokencky and Pieter Tans, NOAA/ESRL, www.esrl.noaa.gov/gmd/ccgg/trends/), however the amplitude increases are similar (Table 3). This surface station-based global CO2 estimate also indicates that the amplitude increase is dominated by the trend of minima.

We further calculated the change of relative amplitude (relative to 1961–1970) for each model. The amplitude here is computed by the CCGCRV package. As illustrated in Fig. 2, all nine models show an increase in both global mean CO2 and total NBP seasonal amplitude. CO2 seasonal amplitude has increased by 62±19 % in 2081–2090, compared to 1961–1970; whereas NBP seasonal amplitude has increased by 68±25 % over the same period (see Table 4 for details of individual models). The trend of increase is much higher in the future (CO2/NBP: 0.70 %/0.73 % yr-1 during 2006–2099) than in the historical period (0.25 % and 0.28 % yr-1 during 1961–2005 for CO2 and NBP), albeit the model spread also becomes larger in the future. When we applied the same procedure to the Northern Hemisphere (25–90∘ N) mean CO2 and total NBP for the eight models (excluding INM-CM4 which only has global CO2 mass), we saw a higher amplitude increase and larger model spread: 81±46 and 77±43 % for CO2 and NBP, respectively.

Our next major question is whether the amplitude increase of NBP is largely driven by NPP or respiration. We computed the mean seasonal cycle of detrended CO2 growth rate, -NBP, -NPP (reverse signs so that negative values always indicate carbon uptake) and Rh∗ in two periods: 1961–1970 (black) and 2081–2090 (red), for the nine models (for this and following analyses, we excluded INM which does not provide NPP, and included the IPSL model except for CO2 growth rate). The seasonal cycle of -NBP resembles that of detrended CO2 growth rate (Fig. 3a–d), confirming that the activities of land ecosystem dominate the CO2 seasonal cycle and its amplitude increase in the model simulations. Except for CanESM2 (also noted in Anav et al., 2013), and BNU-ESM (which simulates a second peak carbon uptake around November) to some extent, most models can reproduce the net uptake of carbon during spring and summer (when increasing NPP overcomes respiration) and the net carbon release during fall and winter at global scale: net carbon uptake peaks in June (five models) or July (three models) for the historical period, and exclusively in June for the future period. However, the model spread on amplitude is large: CESM1-BGC and NorESM1-ME, which has the same land model (CLM4) that features an interactive nitrogen cycle, are characterized by a small seasonal amplitude of -NBP – merely 30 % of those on the high end of the models (IPSL-CM5A-LR and MPI-ESM-LR). The seasonal amplitude of multi-model ensemble NBP, computed as maximum minus minimum (June–October), has increased from 2.7 to 4.7 PgC month-1 (Fig. 3d).

This 2 PgC month-1 amplitude increase is the sum of enhanced net carbon uptake in June and higher net release in October, and the enhancement in uptake (1.4 PgC month-1) is nearly 3 times as large as the release increase (0.5 PgC month-1).

We then investigate the June and October changes of -NPP and Rh∗, respectively. By definition, their sum should equal to the amplitude change of -NBP. NPP has increased in all months (Fig. 3e and f), with much larger changes during the NH growing season. The amplitude of multi-model ensemble NPP has increased from 4.8 to 7.1 PgC month-1, and an increase from 2.7 to 4.3 PgC month-1 is found for Rh∗. In June, NPP increase (4.5 PgC month-1) is larger than that of Rh∗ (3.1 PgC month-1), resulting in enhanced net uptake. In October, NPP increase (1.9 PgC month-1) is smaller than that of Rh∗ (2.4 PgC month-1), leading to enhanced net release. These results are consistent with trends of maxima and minima in Fig. 1. The models also indicate a shift in peak NPP from July to June, consistent with the shift of CO2 minima.

To further investigate the regional contribution to NBP amplitude increase, we plotted the 10-model mean -NBP changes (Fig. 4) over peak NH growing season (May–July, Fig. 4a) and dormant season (October–December, Fig. 4b). Because the models disagree on the time of maximum and minimum NBP (Fig. 3), our choice of doing seasonal averages would be more representative of the models than averaging over 1 month. Note that the difference between the two seasonal averages is smaller than the peak-to-trough amplitude, but here we are only concerned with the spatial pattern. We saw a stronger net carbon uptake in May–July almost everywhere north of 45∘ N, and also over the Tibetan Plateau and some places near the equator. Net carbon uptake weakens over western United States and Central America, South and Southeast Asia and central South America. The change of net carbon release in October–December generally shows an opposite spatial pattern, with a noticeably smaller magnitude north of 45∘ N.

In addition, we calculated the corresponding zonal averages (Fig. 3c). The area-weighted totals of the zonal mean curves correspond to the future minus historical averages of global total -NBP (Fig. 3d), averaged over May–July and October–December, respectively. These two curves do not account for phase difference; instead, they approximate latitudinal contribution to the amplitude increase of global total -NBP. It is apparent that this increase is dominated by regions north of 45∘ N with a weak contribution from the Southern Hemisphere tropics (0–25∘ S). The northern subtropical region and Southern Hemisphere (10–30∘ N, 35–55∘ S) partly offset the amplitude increase. It is also clear that the amplitude increase is dominated by changes in peak growing season (the green shade is larger on the left of the zero line than on its right), consistent with our findings in the previous section.

Analogous to the cold–warm seasonality in the temperate/boreal region, the tropics has distinctive dry and wet seasons, and recently Wang et al. (2014) suggested the tropical ecosystem is becoming more sensitive to climate change. In our analyses on the multi-model ensemble patterns, the tropical region exhibits a small negative contribution to the seasonal amplitude increase of global total -NBP. This does not mean the net carbon flux in the tropics, which has a different seasonal cycle phase, would experience an amplitude decrease in the future. To illustrate the seasonal amplitude change at different latitudes, we show the zonal amplitude of NBP in the historical (black) and future (red) periods for all models (Fig. 5). At every 2∘ band, we first calculated a 10-year mean seasonal cycle, then compute its amplitude (maximum minus minimum). Most models predict an increase in NBP seasonal amplitude at almost every latitude under the RCP85 emission scenario. Only two of the models, CanESM2 and MIROC-ESM, predict decreased seasonality for parts of the tropics and subtropics. Unlike in Fig. 4c, an area-weighted integral cannot be performed due to different phases zonally. The Southern Hemisphere has an opposite phase from its northern counterpart, but its magnitude is small due to its small land area. The two subtropical maxima around 10∘ N and 10–15∘ S reflect the wet–dry seasonal shift in the Intertropical Convergence Zone (ITCZ) and monsoon movement. They are comparable to the NH maxima in terms of both amplitude and amplitude increase for about a third of the models, however they are out of phase and largely cancel each other out.

To further illustrate this cancelation effect, we aggregated monthly -NBP over six large regions: the globe (90∘ S–90∘ N), northern boreal (50–90∘ N), northern temperate (25–50∘ N), northern tropics (0–25∘ N), southern tropics (25∘ S–0∘) and Southern Hemisphere (90–25∘ S; Fig. S1). It is clear that the changes of global -NBP seasonal cycle mostly come from the northern boreal region; it partly comes from the northern temperature region in a few models. The seasonal cycle of the northern tropics is characterized by spring maxima and fall minima, and prominent increases of its seasonal amplitude are found for BNU-ESM, GFDL-ESM2M and IPSL-CM5A-LR. However, they are largely counterbalanced by the southern tropics. For GFDL-ESM2M, changes in the southern tropics are larger than its northern counterpart, but even so, the net contribution of tropical regions to its global -NBP seasonal amplitude (September maxima minus June minima) increase is limited to about 25 %, the largest of all models.

As discussed in Sect. 1, two major mechanisms for amplitude increase identified in previous literature are CO2 fertilization effect and high latitudes “greening” in a warmer climate. Both mechanisms lead to enhanced ecosystem productivity during peak growing season, and consequently more biomass to decompose in dormant season, therefore increasing the amplitude of NBP seasonal cycle. Because models have different climate and CO2 sensitivity (Arora et al., 2013), their relative importance may vary. In the case of CMIP5 ESMs, two additional sensitivity experiments are recommended: fixed feedback 2 (esmFdbk2) and fixed climate 2 (esmFixClim2). The former keeps CO2 concentration fixed but allows physical climate change responding to increasing historical and future (RCP4.5) concentrations; the latter keeps climate fixed under preindustrial CO2 condition but allows the carbon cycle to respond to historical and future (RCP4.5) CO2 increase. This setup does not permit quantifying the contribution of CO2 increase and climate change to NBP amplitude increase: one major difference is the use of RCP4.5 concentrations instead of RCP8.5 emissions. However, we can still make qualitative assessments by examining the spatial patterns. We will focus on the high latitude regions, which contribute most to amplitude increase of global total NBP.

Of the 10 models we studied, only CanESM2, GFDL-ESM2M and IPSL-CM5A-LR have submitted NBP output for these two experiments (MIROC submitted output for esmFixClim2 only). Here we display the spatial patterns of -NBP changes for GFDL-ESM2M (Fig. 6) and IPSL-CM5A-LR (Fig. 7). CanESM2 results are not shown because it does not correctly reproduce the phase of global total NBP seasonal cycle. The changes of -NBP for both models during peak growing season are clearly dominated by CO2 fertilization effect (right panels). In contrast, climate change under fixed CO2 fertilization conditions has mixed effects on high latitude regions. Northern high latitude net carbon release in October–December is increased both under climate change (Fig. 6c) and elevated CO2 conditions (Fig. 6d) for GFDL-ESM2M, but over different regions. For IPSL-CM5A-LR however, net carbon release increase in regions north of 45∘ N is only obvious under elevated CO2 condition.

Our results only indicate CO2 fertilization effect is the dominant factor for NBP seasonal amplitude increase in some models. For models with strong carbon-climate feedbacks and weak/moderate water constraints in northern high latitude regions, climate change may be more important. However, we cannot find a clear example due to data availability. MIROC-ESM is known to have strong carbon-climate feedback (Arora et al., 2013). From its simulation under fixed climate (figure not shown), we found no obvious patterns of widespread net carbon release increase in dormant season, suggesting climate change may play a bigger role for this model. The HadGEM model is another possible candidate; it is also a particularly interesting model to analyze since one of its historical simulations represented the largest increase in CO2 amplitude in Graven et al. (2013). Unfortunately, for the ESM simulations, both CO2 and NBP from HadGEM are not available on the ESGF servers.

Our analyses above suggest CO2 fertilization effect is a major mechanism causing the amplitude increase in some models. If it is important in most models, we expect to see models with a larger change in mean carbon sink simulate a higher increase in seasonal amplitude. By plotting the -NBP change against NBP seasonal amplitude increase for all 10 models (Fig. 8), we found there is indeed a negative cross-model correlation (R=-0.73, p<0.05), indicating models with a stronger net carbon uptake are likely to simulate a larger increase in NBP seasonal amplitude. Note that this result is based on the 10 models we analyzed; it is subject to large uncertainty and may change substantially with inclusion or exclusion of certain model(s). Again all models show an increase in NBP seasonal amplitude, even though they disagree on the direction of future NBP change. While our study hint at a possible relationship between mean carbon sink and NBP seasonal amplitude, it is beyond our scope to discuss further, or comment on why models show such different mean sink estimate. Interested readers may refer to the insightful discussion on this issue in Friedlingstein et al. (2013).