Narrowing the spread in CMIP5 model projections of air-sea CO2 fluxes

Large spread appears in the projection of air-sea CO2 fluxes using the latest simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5). Here, two methods are applied to narrow this spread in 13 CMIP5 models. One method involves model selection based on the ability of models to reproduce the observed air-sea CO2 fluxes from 1980 to 2005. The other method involves constrained estimation based on the strong relationship between the historical and future air-sea CO2 fluxes. The estimated spread of the projected air-sea CO2 fluxes is effectively reduced by using these two approaches. These two approaches also show great agreement in the global ocean and three regional oceans of the equatorial Pacific Ocean, the North Atlantic Ocean and the Southern Ocean, including the average state and evolution characteristics. Based on the projections of the two approaches, the global ocean carbon uptake will increase in the first half of the 21st century then remain relatively stable and is projected to be 3.68–4.57 PgC/yr at the end of 21st century. The projections indicate that the increase in the CO2 uptake by the oceans will cease at the year of approximately 2070.

Intercomparison Project (C 4 MIP, which is a model intercomparison project for global climate models that include an interactive carbon cycle) was between 1.4 PgC/yr and 3 PgC/yr in 2000 and between 3.8 PgC/yr and 10 PgC/yr in 2100 30 . Additionally, 11 CMIP5 models driven by carbon emissions projected an ocean cumulative carbon uptake of 412-649 PgC in 2100 28 . The large spread in the air-sea CO 2 flux estimates could be an additional source for climate projection uncertainty 28 . Hence, the air-sea CO 2 flux simulation spread needs to be narrowed to reduce the uncertainty in future climate projections. Kessler and Tjiputra 31 have proposed that the air-sea CO 2 fluxes in the Southern Ocean could be used to constrain the future global ocean carbon uptake uncertainty. In this paper, two other methods are used to narrow the projected spread of air-sea CO 2 fluxes.
The structure of the paper is as follows. The observation-based and model data used in this research are introduced first, and the two methods and results are described in section 2. A summary and discussion is presented in the last part.

Data
In total, 13 CMIP5 models from 11 affiliations are used in this research ( Table 1). The outputs of ESM runs that were forced by CO 2 emissions and that fully coupled the carbon cycle between the atmosphere and ocean are selected to project the air-sea CO 2 fluxes. The future climate projected in the ESM runs is under the representative concentration pathways 8.5 (RCP8.5). The model resolutions vary, and most of the durations extend from 1850 to 2005 for "esmhistorical" runs and from 2006 to 2100 for "esmrcp85" runs.
Observations are also needed to evaluate and constrain the performance of the models. Direct observations of air-sea CO 2 fluxes are mainly provided by ships and buoys. Because of the difficulties in a wide and intensive observation, directly observed data are relatively sparse and lack of continuity. To make up for the lack of observations in time and space, researchers use various strategies to estimate the air-sea CO 2 fluxes. Estimated air-sea CO 2 fluxes from observations are mainly derived in six ways: the "top-down" approach 13,[32][33][34][35][36] , the "bottom-up" approach 4,37 , the isotopic ratios of CO 2 approach 38 , the combination of observed sea surface CO 2 partial pressure and gas exchange coefficient 7,39 , an approach based on the relationship between the sea surface temperature and sea surface water partial pressure of CO 2 (pCO 2 ) 40 , and an observation-based neural network approach 5,41 . Rödenbeck et al. 42 investigated various observation-based estimates from Surface Ocean pCO 2 Mapping intercomparison (SOCOM), and found both of the consistencies and discrepancies. Most of the estimates are available after 1990 and have relatively short time durations.
Since the model years are not directly comparable to the real world counterpart, due to internal variability, the air-sea CO 2 flux data with longer time durations are more suitable for evaluating and constraining the models simulations, and a continuous spatial distribution of the air-sea CO 2 fluxes is also needed to estimate the carbon sink/source in regional oceans. Here, we choose an observation-based data set by using the "bottom-up" approach 4 (http://apdrc.soest.hawaii.edu/datadoc/co2_flux.php). This approach uses a large amount of pCO 2 observations to constrain a process model and produces monthly data from 1980 with a spatial resolution of 1° × 1°. As mentioned above, this observation-based data also has uncertainties, which mainly come from the limited key processes in the model, the potential errors in the important variables and the sensitive depth for correction in the assimilation system 4 . Although uncertainties exist, this observationally constrained data remains a good choice for evaluating the model performance due to its quantitative consistency with other estimated data and improvements in the temporal length and the resolution. This data have also been chosen to validate the air-sea CO 2 fluxes in the CMIP5 models 43 .

Methods and Results
We analyzed the air-sea CO 2 fluxes simulated by the 13 CMIP5 models that provide both "esmhistorical" simulations and "esmrcp85" projection simulations.
In addition to the global ocean, three important regional oceans -the equatorial Pacific Ocean, North Atlantic Ocean and Southern Ocean -are also analyzed independently. As shown in the observed spatial distribution of the air-sea CO 2 fluxes, the largest atmospheric CO 2 source region is the equatorial Pacific Ocean, which is located between 30°S and 10°N and releases approximately 40% of the total CO 2 emissions from the global ocean. In contrast, the North Atlantic Ocean, north of 40°N, acts as a significant atmospheric carbon sink, due to the cold temperatures and formation of North Atlantic Deep Water (NADW). The net fluxes composed of the absorption and emission south of 40°S are considered as the air-sea CO 2 fluxes in Southern Ocean, which overall acts as a large atmospheric CO 2 sink. As shown in Fig. 1, a large spread in the simulated total air-sea CO 2    of 1980-2005 and projected periods are listed in Table 2, in addition to their 1σ uncertainty ranges. The relative largest uncertainties in the historical and future periods appear in the Southern Ocean and the equatorial Pacific Ocean, respectively. In comparison with the observed fluxes (Table 2), the multi-model ensemble mean overestimates the global ocean and Southern Ocean mean carbon uptake from 1980 to 2005 by approximately 0.13 PgC/yr and 0.2 PgC/yr,  respectively, while the mean state of the air-sea CO 2 fluxes in the equatorial Pacific and North Atlantic Ocean simulated by the models are generally consistent with the observation-based estimates. Note that the observation-based carbon uptake in the Southern Ocean exhibits a decreasing trend before 1996, but most of the models are unable to capture these characteristics. The overestimate of the global ocean carbon uptake may in part be because the models ignore the pre-industrial river input of carbon and start their historical simulations from a level of nearly no air-sea CO 2 fluxes, thereby they underestimating the oceanic emission of natural CO 2 .

Global Ocean Equatorial Pacific Ocean North Atlantic Ocean Southern Ocean
As projected by the multi-model ensemble mean, the global ocean carbon sink will stop increasing at approximately 2070 after a period of continuous increase. The equatorial Pacific Ocean was a stable atmospheric carbon source (emitting approximately 0.72 PgC/yr) before the atmospheric CO 2 concentration and global mean air temperature started to increase rapidly in approximately 1950. Subsequently, its release appears to decrease, and the decreasing rate is predicted to slow after approximately 2070. The carbon uptake in the North Atlantic Ocean is predicted to continuously increase until 2040, remain stable between approximately 2040 and 2070, then rapidly decrease after 2070. The changes in the air-sea CO 2 fluxes in the Southern Ocean are similar to those of the global ocean, which will stop increasing by approximately 2070.
One approach for narrowing the large spread in the projected air-sea CO 2 fluxes is through model selection based on the ability of a model to reproduce the observed air-sea CO 2 fluxes. Using the selected models based on the evaluation of their performance in the historical stage to project future changes is an effective way to reduce the spread in future projections. This process is also used in the projection of other variables [44][45][46][47] . The ability of the models to accurately simulate the mean stage, trend and variability of the air-sea CO 2 fluxes affects the future projections. Here, we use a selection method that considers the three aspects of the simulated air-sea CO 2 fluxes. We first calculate the standard deviation (σ ) of the observation-based yearly air-sea CO 2 fluxes from 1980 to 2005 and determine a selection range by adding and subtracting several σ values to the observation-based estimates. A model will be determined to be "good" at simulating the air-sea CO 2 fluxes if more than 80% of the yearly points fall within the selected range. To determine the range, the σ is increased by 0.5 times repeatedly until at least 4 models are selected. The selection ranges are shown as the grey shades in Fig. 2. The exact multiples of σ used to determine the selection range and the selected models for the global ocean and the three regional oceans (equatorial Pacific Ocean, North Atlantic Ocean and Southern Ocean) are listed in Table 3. According to the selecting process, 6 models are selected based on their ability to reproduce the air-sea CO 2 fluxes in the global ocean, and 6 models, 6 models, and 4 models are selected to simulate the air-sea CO 2 fluxes in the equatorial Pacific Ocean, North Atlantic Ocean and Southern Ocean, respectively.
As shown in Fig. 3, the air-sea CO 2 fluxes simulated by the multi-model ensemble mean of the selected models are undoubtedly in better agreement with the observation-based estimates than those simulated by the ensemble mean of all 13 models. The differences in the mean air-sea CO2 fluxes during 1980-2005 between the simulations and observation-based estimates are reduced to within 0.01 PgC/yr for the global ocean, equatorial Pacific Ocean and North Atlantic Ocean and to 0.12 PgC/yr in the Southern Ocean. Additionally, the uncertainty ranges of the estimations are narrowed in the simulation of both the historical and projected air-sea CO 2 fluxes. The characteristics of the evolution of the air-sea CO 2 fluxes projected by the selected models are basically similar to those projected by all 13 models, but they differ in the specific values. The global ocean carbon uptake at the end of the 21 st century is projected to be 3.68-4.57 PgC/yr. The air-sea CO 2 fluxes in the North Atlantic Ocean, equatorial Pacific Ocean and Southern Ocean are projected by the selected models to be 0.29-0.51 PgC/yr, − 0.20-0.10 PgC/yr and 1.65-2.55 PgC/yr, respectively, at the end of the 21 st century. Although a range of projected uncertainty still exists, especially in the late 21 st century in the North Atlantic Ocean and the equatorial Pacific Ocean, the uncertainty ranges are effectively reduced.
Considering that the observation-based product we use has an uncertainty attached to it, we also do this analysis using another product of Park et al. 40 , which extrapolates seasonal relationship between the sea surface temperature and partial pressure of CO 2 to the interannual time scale and is from the year of 1982. We find our results are almost independent of the choice of these two datasets, with the projection of 3.68-4.50 PgC/yr at the The other approach for narrowing the large spread of the projected total air-sea CO 2 fluxes is though constrained estimation based on the relationship between the historical and future air-sea CO 2 fluxes derived from the model spread (hereafter referred to as "constrained estimation"). In this approach, the relationship between the historical and future air-sea CO 2 flux conditions is first calculated for the 13 CMIP5 models, and the obtained relationship is then applied to the observation-based estimates to constrain the spread of the projected air-sea CO 2 fluxes during the 21 st century. The rationale of this method is based on the fact that the models with greater air-sea CO 2 fluxes in the historical period tend to quickly absorb atmospheric CO 2 in the 21 st century, whereas the models with lower air-sea CO 2 fluxes in the historical period tend to retain lower absorption rates for a relatively long period. The constrained estimation method has also been used to reduce the large projected spread in sea ice extent and ice-free time by Liu et al. 45 . Figure 4 shows the simulated air-sea CO 2 fluxes averaged for a historical period versus the projected air-sea CO 2 fluxes predicted by each of the 13 CMIP5 models averaged for a future period. Each dot represents a specific model. The correlation coefficients between the historical and future states are given in the upper-left corner of each graph. To represent the historical states of the different oceans, the 5-year period of 1982-1986 is chosen to represent the historical period of the global ocean and equatorial Pacific Ocean and the 23-year period of 1982-2004 and the 5-year period of 1993-1997 are chosen for the North Atlantic Ocean and Southern Ocean, respectively. These periods were chosen because the average correlation coefficients for air-sea CO 2 fluxes in these periods and in every future period of the same length are the largest for the global ocean and the three regional oceans. Note that the means of the 5-year historical periods produce the most effective forecast for the global The light blue lines and grey lines show the correlation coefficients and the constrained estimates calculated by repeating the same procedure for 12 of the 13 models (Jackknife method). This estimation is based on the relationship between the simulated air-sea CO 2 fluxes averaged for a historical period and projected period.
Scientific RepoRts | 6:37548 | DOI: 10.1038/srep37548 ocean, equatorial Pacific Ocean and Southern Ocean, while the temporal length of the most suitable period for projecting the air-sea CO 2 fluxes in the North Atlantic Ocean is more than 20 years. The importance of the 5-year period for the equatorial Pacific Ocean and global ocean may be because the variability in the air-sea CO 2 fluxes in the equatorial Pacific Ocean is dominated by the El Niño-Southern Oscillation (ENSO), which has a period of 2-7 years 40,48,49 , and because the variability in the global air-sea CO 2 fluxes is governed by the variability in the air-sea CO 2 fluxes in the equatorial Pacific Ocean 50 . The variability in the air-sea CO 2 fluxes in the Southern Ocean may be driven by the Southern Annular Mode of climate variability 51,52 . Some researchers have noted that the changes in the air-sea CO 2 fluxes in the North Atlantic Ocean may be associated with decadal variability in the North Atlantic Oscillation (NAO) and the Atlantic Multidecadal Oscillation (AMO) 53,54 , resulting in variability in the air-sea CO 2 fluxes on a decadal time scale. Figure 4 shows the scatter plot of the historical period versus the first future period of the same length of time. These plots indicate that the projected air-sea CO 2 fluxes are strongly associated with the simulated air-sea CO 2 fluxes in the historical condition. The correlation coefficients all pass the 99% significance testing based on the assumption that each model is an independent sample, confirming that the historical state is a good predictor for the future state. For the global ocean and the three regional oceans, the regression functions between the historical and future states (the solid lines in Fig. 4) are calculated, and the observation-based estimates of the historical periods are then put into the regression functions to obtain the projected air-sea CO 2 fluxes state in the corresponding period.
Repeating the same constrained estimation process for every future period of the same length of time as the historical period, all the correlation coefficients (thick blue lines in Fig. 5) and projected fluxes (thick black lines in Fig. 5) are obtained. Taking the air-sea CO 2 fluxes in the global ocean as an example, the average of the 5-year Because a specific model may unduly affect the correlation, we use the Jackknife method 55 to estimate the uncertainty in the projection. The same procedure is repeatedly performed on the remaining 12 models after removing one model every time. Thus, we obtain the ensemble of 13 additional constrained estimates. The light blue lines in Fig. 5 show the correlations in this ensemble and the grey lines represent the constrained estimates based on the 12-model relationship. Although the correlations have a relatively evident spread, most of them pass the 90% significance test, and the 13 estimates show good agreement with the constrained estimate based on the 13 models.
The projections based on the constrained estimation method are very similar to the projections based on the selected models method (Fig. 6), including the average state and evolution characteristics. This result further strengthens the projection on the air-sea CO 2 fluxes. We also repeat the constrained analysis using the observation-based estimate of Park et al. 40 , and get the similar results.

Conclusion and Discussion
Using model selection (removing the outlier models that fall outside a range of criteria based on the observation-based estimates) and constrained estimation (based on the close relationship between the simulated historical state and future state in the models), the spread projected by CMIP5 models in 21 st century is effectively reduced. Furthermore, the projections using the two different approaches exhibit strong agreement with each other. Compared to 3.70-4.69 PgC/yr projected by all the 13 models, the global ocean carbon uptake is projected to be 3.68-4.57 PgC/yr at the end of 21 st century in our study.
Based on the projections, the carbon sink capacity of the global ocean will increase with the rapid increase in atmospheric CO 2 concentrations in the first half of the 21 st century and will then remain stable with no further growth after approximately 2070. This means that the ocean carbon sink will not always adapt to the growth of anthropogenic CO 2 emissions and will stop increasing at a certain threshold of CO 2 emissions, which will make the atmospheric CO 2 concentration increase more rapidly when the ability of the ocean to absorb CO 2 reaches a plateau. By reducing the model spread in projecting the air-sea CO 2 fluxes, the changes in the future air-sea CO 2 fluxes become more evident, and the turning point is independent at approximately 2070 when we apply the narrowing methods by using the observation-based data from no matter Park et al. 40 or Valsala and Maksyutov 4 . Thus, we can use the selected models to analyze the critical cumulative emissions that affect the ocean carbon sink. The CO 2 absorption of the global ocean will stop increasing when the cumulative CO 2 emissions reach approximately 1,500 GtC (Fig. 7). The CO 2 uptake of the Southern Ocean is projected to be similar to that of the global ocean, and the critical year of stagnant growth is also predicted to be approximately 2070, in association with a cumulative CO 2 quantity of approximately 1,600 GtC. The atmospheric CO 2 source in the equatorial Pacific Ocean is projected to decrease in the early 21 st century, which appears to decrease its positive contribution to atmospheric CO 2 . The emissions will stop decreasing in approximately 2075, indicating that the equatorial Pacific Ocean will not transform from a CO 2 source into a CO 2 sink. The carbon sink capacity of the North Atlantic Ocean will also increase during the early years of 21 st century, remain stable for approximately 20 years, then weaken in the late 21 st century. The absorption of North Atlantic Ocean will stop increasing and will start to decrease at the critical cumulative CO 2 emissions of 800 GtC and 1500 GtC, respectively. The summarized findings in Fig. 7 suggest that the atmospheric CO 2 concentration may increase more rapidly after the CO 2 emissions reach 800-1600 GtC due to significant changes in the absorption abilities of the oceans.
The projections show that the CO 2 absorption of the oceans will not continue to increase with the atmospheric CO 2 concentration. Instead, they will remain stable or even decrease after the CO 2 emissions reach a certain threshold, which means that increases in the atmospheric CO 2 concentration may accelerate. The increasing CO 2 concentration will result in global warming and more frequent climate extremes 56,57 . The cumulative anthropogenic CO 2 emissions reached 515 PgC in 2011 3 ; thus, stricter CO 2 emission policies are needed to mitigate the rapid increase in atmospheric CO 2 concentration to allow the ocean to absorb more CO 2 in the future.
The limitation of our work is also needed to be addressed. The two methods used to narrow the spread in the model projections of air-sea CO 2 fluxes are partly observation-based. The observation-based estimates are used to select "good" models in the first approach and to constrain the model-based relationship in the second approach. As mentioned in the data section, direct observations of the air-sea CO 2 fluxes are very limited, and continuous data mainly come from data interpolation and assimilation approaches. So our projections contain the uncertainties from the observation-based estimates. We test our results using another observation-based product of Park et al. 40 , and get almost the same projection of the air-sea CO 2 fluxes (3.68-4.50 PgC/yr). More products of air-sea CO 2 fluxes with long time durations are needed to further estimate the projection uncertainties from the observation-based estimates in the future. Although uncertainties exist in the observation-based estimates, our approach provides two effective ways to reduce the spread of future projections of the air-sea CO 2 fluxes and is helpful for producing more reliable model-based climate projections. The more reliable observation-based estimates as well as the in-depth understanding of carbon cycle process are the basis for improving the performance of the carbon cycle models. Broader and more continuous direct observations and improved reanalysis methods are needed to reduce the uncertainty in the air-sea CO 2 flux data and further reduce the uncertainty in the future projection.