Long term trend and interannual variability of land carbon uptake—the attribution and processes

Ecosystem carbon (C) uptake in terrestrial ecosystems has increased over the past five decades, but with large interannual variability (IAV). However, we are not clear on the attribution and the processes that control the long-term trend and IAV of land C uptake. Using atmospheric inversion net ecosystem exchange (NEE) data, we quantified the trend and IAV of NEE across the globe, the Northern Hemisphere (NH), and the Southern Hemisphere (SH), and decomposed NEE into carbon uptake amplitude and duration during each year from 1979–2013. We found the NH rather than the SH determined the IAV, while both hemispheres contributed equivalently to the global NEE trend. Different ecosystems in the NH and SH had differential relative contributions to their trend and IAV. The long-term trends of increased C uptake across the globe and the SH were attributed to both extended duration and increasing amplitude of C uptake. The shortened duration of uptake in the NH partly offsets the effects of increased NEE amplitude, making the net C uptake trend the same as that of the SH. The change in NEE IAV was also linked to changes in the amplitude and duration of uptake, but they worked in different ways in the NH, SH and globe. The fundamental attributions of amplitude and duration of C uptake revealed in this study are helpful to better understand the mechanisms underlying the trend and IAV of land C uptake. Our findings also suggest the critical roles of grassland and croplands in the NH in contributing to the trend and IAV of land C uptake.


Introduction
Since the 1960s, the land has acted as a substantial sink for atmospheric carbon dioxide (CO 2 ), sequestering about one-quarter of fossil-fuel emissions during an average year (Ballantyne et al 2012). The magnitude of land carbon (C) sink has increased over the past decades (Keenan et al 2016) but varies largely from year to year (Quéré et al 2013). The patterns have been well recognized, but the attribution and processes for causing the long-term trend and interannual variability (IAV) of land C uptake (net ecosystem exchange in a given year) remain far from clear.
The northern hemisphere (NH) and southern hemisphere (SH) differ in the dynamics of ecosystem C uptake (Field et al 1998, Schimel et al 2001, which may contribute differentially to the trend and IAV of land C sinks. In the NH, observational evidence has shown the increasing land C uptake and enhancement of terrestrial vegetation growth over the past decades (Forkel et al 2016, Nemani et al 2003, Tucker et al 2001, Zhou et al 2001. This long-term increase of land C uptake in the NH was attributed to different factors, including the increased CO 2 concentrations (Ahlbeck 2002, Kohlmaier et al 1989, Myneni et al 1997, climate warming (DeRosier et al 1996, Piao et al 2006), precipitation (Piao et al 2006), nitrogen deposition (Pan et al 2009), afforestation (Fang et al 2001), longer growing seasons (DeRosier et al 1996), expanded distribution of trees and shrubs (Forkel et al 2016, Pan et al 2011, and agriculture following the 'green revolution' (Gray et al 2014, Zeng et al 2014. However, in the SH, the land C uptake exhibits large year-to-year variability with uncertain long term trends. Tropical forest deforestation has increased widely (Pan et al 2011) and tropical lands have experienced increasing drought and heat in the SH over the past decades (Allen et al 2010, Phillips et al 2009, Zhao and Running 2010, which might reduce the land C sink in the SH. But the large areas of semiarid ecosystems with dryness-controlled in the SH (Yi et al 2010, Yi et al 2014, responded quickly to precipitation events and led to a large amount of C uptake (Ma et al 2016), which was assumed to contribute largely to the IAV of land C uptake (Ahlström et al 2015, Frank et al 2015, Ma et al 2016, Poulter et al 2014. Meanwhile, widespread observations and satellite remote sensing showed that vegetation expanded with woody encroachment over semi-arid areas and increased vegetation greenness over recent decades (Andela et al 2013, Donohue et al 2009, Fensholt et al 2012, which increased the SH land C sink. Thus, the NH and SH may play different roles in the trend and IAV of land C uptake. A comprehensive analysis of the relative contributions of the NH and SH to the trend and IAV of land C uptake has so far been lacking. Different ecosystem types may also play various roles in regulating the changes in land C uptake. At the global scale, Ahlström et al (2015) found recently that semi-arid ecosystems contributed approximately 39% of the IAV in net biome production, while tropical ecosystems, extra-tropical forests, grasslands and croplands contributed 19%, 11% and 27%, respectively. Since ecosystems are distributed quite differently in the NH (largely comprising grasslands and croplands, tundra and arctic shrub lands, extratropical forests) and the SH (largely comprising semiarid and tropical forests), we need to quantify the specific contributions of different ecosystems to the trend and IAV in the NH and SH in order to better understand the attribution regions.
For a process-based understanding, changes in annual C uptake can be decomposed into carbon uptake duration (CUD) and carbon uptake amplitude (CUA) (Gu et al 2009, Xia et al 2015. As the concept figure (figure 1) shows, numerous hypotheses can be proposed for the regulation of CUA and CUD on the changes in annual land C uptake. Increasing CUA without changes in CUD (figure 1(a)) will enhance land C uptake. Increasing CUA and simultaneously changing CUD by advancing the starting date of C uptake (figure 1(b)) could also increase the C uptake. Decreasing CUA but lengthening CUD by postponing the ending date of C uptake (figure 1(c)) may change the amount of annual ecosystem C uptake as well. However, we have limited understanding on how CUA and CUD regulate observed trends and IAV of land C uptake.
The purpose of this study was to quantify the relative contributions of different ecosystems in the NH and SH and to understand the key processes of CUA and CUD in controlling the trend and IAV of global land C uptake. Specifically, this study was conducted to address (1) how the NH and SH contribute to the trend and IAV in the land C sink over recent decades; (2) how different ecosystems in the NH and SH contribute to their trend and IAV, (3) how CUA and CUD differentially determine the trend and IAV of land C uptake in NH, SH and globe.

Atmospheric inversion data
Atmospheric inversion data used in this study were based on the Monitoring Atmospheric Composition and Climate (MACC-III) inversion system version 13.1 (http://apps.ecmwf.int/datasets/data/macc-ghginversions/). The dataset describes the CO 2 surface fluxes during the period 1979-2013 with a resolution of 3.75°Â 1.875°(longitude-latitude) and a 3-hourly Environ. Res. Lett. 12 (2017) 014018 time step using atmospheric CO 2 data sets from a global network (NOAA/ESRL,WDCGG, Carbon-Europe and RAMCES) of continuous and discrete flask samples (Chevallier et al 2007, Chevallier et al 2010. Fluxes and mole fractions are linked in the system by a global atmospheric transport model. The flux inversion builds on a variational Bayesian inversion system, like the 4D-Var data assimilation system used in MACC-II, which allows the fluxes to be estimated at relatively high resolution over the globe (Chevallier et al 2007, Chevallier et al 2010, Chevallier et al 2005. A robust Monte Carlo method from the Bayesian theory was used to quantify the uncertainty of the inverted fluxes (Chevallier et al 2007, Chevallier et al 2010, Chevallier et al 2005.

Definitions and calculations for CUD and CUA
We calculated the daily net ecosystem exchange (NEE) across the globe, NH and SH, which showed clearly seasonal dynamics during the 1979-2013 study period (figure 2). The sign convention of NEE is from the perspective of the atmosphere such that NEE is negative for ecosystem C uptake, and positive for release to the atmosphere. The starting date of C uptake was quantified as the date when the ecosystem switched from a CO 2 source to a sink, while ending date of C uptake was the date when the ecosystem switched from a CO 2 sink to a source. We defined the carbon uptake duration (CUD) as the number of days between the CO 2 sink starting date and ending date ( figure 1(a)). The CUA is defined as the maximum value of daily land C sink that was derived from the peak of NEE seasonal dynamics ( figure 1(a)).
Considering that magnitude of C source changes also change the annual net C uptake, we defined the maximum value of daily C source as carbon release amplitude (CRA). We calculated the CUA, CRA, CUD, and starting and ending dates of land C uptake during each year from 1979 to 2013.

Calculation of trend and IAV and statistical analysis
We calculated the annual NEE across the globe, NH, and SH during each year from 1979 to 2013. The normality of the dataset was assessed using the Shapiro-Wilk method, which showed that all datasets followed a normal distribution (table S1). Simple linear regression was used to detect trends in NEE, CUA, CRA, CUD, starting date and ending date of ecosystem C uptake in the NH, SH, and globe with time. The statistical significance of the trend was also analyzed using the Mann-Kendall trend test (table S2). A P value of 0.05 was used to indicate a statistically significant trend. The anomalies of NEE, CUA, CUD, starting and ending data of C uptake in each year were detrended by subtracting the linear regression value from the original value (Ahlström et al 2015, Wang et al 2014. We calculated the relative contributions of the NH and SH to the trend and IAV of global NEE, and further partitioned the trend and IAV of NEE in the NH and SH to different land cover classes according to their relative contributions. We divided the global land area into six land cover classes as in Ahlström et al (2015) using the MODIS MCD12C1 land cover classification (Friedl et al 2010), which includes extra-tropical forest, tropical forests, grasslands and croplands, semi-arid ecosystems, tundra and arctic Environ. Res. Lett. 12 (2017) 014018 shrub lands, and sparsely vegetated lands (figure S1).
Using the same methods of quantifying relative contributions as in Ahlström et al (2015), we adopted an index that scores individual geographic locations according to the consistency, over time, with which the local NEE flux resembles the sign and magnitude of the NH/SH NEE: where x it is the NEE anomaly for region i at time t (in years), and X t is the NH/SH NEE anomaly, such that By this definition, f i is the average relative NEE anomaly x it =X t for region i, weighted with the absolute NH/SH NEE anomaly jX t j. The resulting scores for a region (f i ) represent its contribution to the NH/SH variations.
The relationships of CUA and CUD with the longterm trend of NEE, and the relationships of yearly CUA and CUD anomalies with IAVof NEE in the globe, NH, and SH, were tested using regression analysis and were considered significant with P < 0.05. Statistical analyses were conducted with SigmaPlot 12.5 for Windows.

Results
Trend and IAV of land C uptake across the globe, NH, and SH In general, the land C sink (NEE for a given year) in the NH and SH both increased by 0.04 Pg C yr À1 (P < 0.01) over the past 35 years, resulting in an increase in the global land C sink of 0.08 Pg C yr À1 (P < 0.0001) (figure 3(a)). Although the land C sink across the globe, NH, and SH increased over the past Environ. Res. Lett. 12 (2017) 014018 35 years, they released CO 2 in 1983 (figure 3(a)).
The mean land C uptake across the 35 year study period across the globe (1.52 Pg C yr À1 ) and NH (1.19 Pg C yr À1 ) were far more than that of SH (0.33 Pg C yr À1 ). IAV of global land C uptake showed strong agreement with those of NH and SH ( figure 3(b)). The IAV of NH and SH C uptake was significantly correlated with the IAV of global NEE (all P < 0.0001), with a stronger correlation observed in the NH (figures 3(c) and (d)).

Relative contributions of different ecosystems in the NH and SH
The NH and SH both accounted for 50% of the trend of the global land C sink (figure 4(a)), but the relative contribution of the NH and the SH to the IAV of global land C sink were 58% and 42%, respectively (figure 4(b)). Different land cover classes had various contributions to the trend and IAVof C uptake in the NH and SH. In the NH, tundra and arctic shrub lands (55%), extratropical forests (38%), and grasslands and croplands (21%) accounted for the largest fraction of the trend of C sink over this period, while semi-arid ecosystems (À18%) had negative contributions ( figure 4(c)). In the SH, the trend of C sink was mostly contributed by semi-arid ecosystems (54%) and tropical forests (33%) ( figure 4(e)). For the IAV of land C sink in the NH, we found that grasslands and croplands (39%) and semiarid ecosystems (39%) were the dominant contributing regions ( figure 4(d)). The dominant contribution regions to SH NEE IAV were semi-arid ecosystems (59%) and tropical forests (27%), as well as grasslands and croplands (13%, figure 4(f)).
The attribution process of CUA and CUD to the trend of C uptake Across the 35 years, land C uptake significantly correlated with the carbon uptake amplitude (CUA) (r 2 = 0.56, 0.41, 0.43, all P < 0.0001) and carbon uptake duration (CUD) (r 2 = 0.27, 0.31, 0.48, for the globe, NH and SH, respectively, all P < 0.01) (figure S2). Although mean CUA across the globe and NH was significantly larger than that of the SH over the 35 years, CUA across the globe, NH and SH all increased by 0.0004, 0.0003 and 0.0002 Pg C d À1 yr À1 , respectively ( figure 5(a)). CUD in the NH significantly decreased by 0.31 d yr À1 ( figure 5(b)), while CUD in the SH and the globe did not significantly change over the past 35 years. However, if we removed the extreme high values observed in 1981, CUD across the globe also significantly increased by 0.41 d yr À1 ( figure 5(b)). Note that each hemisphere's CUD is not linearly related to global changes in CUD as the two hemispheres are out of phase.
The change of CUD was determined by the start and end date of land C uptake. At the global scale, both the starting and ending date of C uptake significantly advanced by 0.64 and 0.36 d yr À1 , respectively (figure 5(c)), extending the CUD by 0.28 d yr À1 across the 35 years ( figure 5(c)). The starting and ending dates of C uptake in the NH were significantly advanced by 0.21 and 0.52 d yr À1 , respectively, (figure 5(d)), reducing the CUD by 0.31 d yr À1 (figures 5(b) and (d)). Decreased CUD in the NH weakened the impacts of CUA increase on annual C uptake. In the SH, however, the starting date of C uptake advanced by 0.09 d yr À1 while the end date postponed 0.17 d yr À1 (figure 5(e)), extending the CUD by 0.26 d yr À1 across the 35 years (figure 5(e)). Extended CUD and increased CUA led to significant increase in NEE in the SH over the past 35 years ( figure 3(a)). Overall, the trend of land C uptake was determined by the long-term trend in CUA and CUD as summarized in the figure 7 for the globe, NH and SH.  Environ. Res. Lett. 12 (2017) 014018 The attribution process of CUA and CUD to the IAV of land C uptake The IAV of global land C uptake significantly correlated with the IAV of CUA (r 2 = 0.42, P < 0.0001) and CUD (r 2 = 0.22, P < 0.01) (figures 6 (a) and (b)). Every 1 Pg C d À1 change in CUA resulted in a 76 Pg C changes in global land C uptake (figure 6(a)). A one-day change in global CUD leads to a global land C uptake change by 0.04 Pg C yr À1 , on average ( figure 6(b)).
The IAVof land C uptake in the NH and SH were attributed to the IAV in CUA and CUD (figures 6 (c)-(f)). On average, C uptake changed 54 (figure 6 (c)) and 77 (figure 6(e)) Pg C yr À1 in the NH and SH respectively, with 1 Pg C change in CUA. A one-day change in CUD caused 0.05 (figure 6(d)) and 0.01 Pg C yr À1 (figure 6(f)) changes in annual C uptake in the NH and SH, respectively. The contributions of CUA and CUD to the IAV of land C uptake in the globe, NH, and SH are summarized in figure 7.

Discussion
Different roles of the NH, SH and ecosystems in contributing to the trend and IAV of land C uptake The trends drivers of global land C uptake changes and IAV have different attributions in the NH and SH. NEE in the NH and SH both had large variability and a strong increasing trend of C uptake over the past 35 years. But the NH rather than the SH dominated the IAVof global NEE over recent decades, while both hemispheres contributed equivalently to the trend in C uptake.
Various ecosystems contributed differentially to the trend of C fluxes in the NH and SH. Tundra and arctic shrub lands and extra-tropical forests positively contributed most in the NH, which may be due to that climate change affects processes such as plant physiology, phenology, water availability, and vegetation dynamics, ultimately leading to increased plant productivity and vegetation cover at high northern latitudes in recent decades (Forkel et al 2016). The gradual replacement of herbaceous vegetation with shrubs and trees has been observed to increase C uptake at high northern latitudes (Forkel et al 2016, Liu et al 2015, Tucker et al 2001. Extra-tropical forest area increased and thus forest biomass has increased over the past decades (Food andNations 2010, Pan et al 2011). Other ground-based studies showed that fire, logging, and other disturbances in boreal forest shifted the forest toward younger and early-successional forests, which contribute also to the increasing C sink (D'Arrigo et al 1987, Kasischke et al 2010. Results also demonstrate that grasslands and croplands positively contributed the trend of the NH land C sink. Cropland area didn't increase largely in the NH, but hybridization, irrigation and fertilization have increased crop production by threefold during the past five decades (Zeng et al 2014).
In the SH, semi-arid ecosystems were found to account for the largest fraction of the SH land sink trend. Semi-arid ecosystems in the SH have high sensitivity to precipitation and climate extremes (Yi et al 2015), which may absorb large amounts of C quickly at the suitable precipitation condition, positively contributing to the trend of C uptake (Ma et al 2016, Poulter et al 2014. For example, NEE in a forested savanna in Australia reached up to 2.5 tons C ha À1 when La Nina drove precipitation to 585 mm yr À1 (above a ∽300 mm yr À1 average) (Cleverly et al 2013). The predominance of semiarid ecosystems in explaining the SH land sink trend is consistent with widespread observations of woody  1980 1983 1986 1989 1992 1995 Year CUD (days) CUA (Pg C/day) Date of global C uptake (julian day) Date of NH C uptake (julian day) Date of SH C uptake (julian day) 1998 2001 2004 2007 2010 2013 1980 1983 1986 1989 1992 1995 Year 1998  For the IAV of C uptake, we found that semi-arid ecosystems played critical roles in both the NH and SH. It suggests that C uptake in the semi-arid ecosystems is highly dynamic from year to year. Our results are consistent with global analysis that showed that semi-arid ecosystems determine the IAV of global C uptake (Ahlström et al 2015). Besides the semi-arid ecosystems, grasslands and croplands also played an important role in the IAV of land C uptake in the NH. This may be due to that crop production is highly dependent on human activities, which vary largely across years. Changing growing times yearly such as single or double cropping, crop varieties such as highyield but low-quality, low-yield but high-quality (Jain 2010, Zeng et al 2014, and cropland use patterns, like China's Grain for Green Project (Liu and Wu 2010), all will impact the production and change the year to year C uptake in the croplands and grasslands, whose contribution to the global IAV of C uptake deserve more study.
Attribution process understanding: regulations of CUA and CUD This study decomposed annual NEE into CUA and CUD to better understand the attribution processes. We found that changes in ecosystem C uptake could be fundamentally explained by the changes in CUA and CUD ( figure S2, figure 6), and the changes in CUD were determined by the starting and ending date of C uptake (figures 5(c)-(e)). In the NH, SH, and globe, CUA increased and enhanced land C uptake ( figure 5  (a)). The other process, CUD, also lengthened across the globe and the SH, improving land C uptake even further. Advancing of starting date of C uptake was more than the advancing of ending date of C uptake, resulting in the extension of CUD in the globe (figure 5 (c)), but the SH CUD was attributable to the advancing of starting date of C uptake and postponing of ending date of C uptake (figure 5(e)). However, CUD decreased in the NH, with the advancing of starting date of C uptake contributing less than the advancing of ending date of C uptake. This partly offset the increased C sink by the increased CUA, making net C uptake trend same as that of the SH. For the C source process, our results also showed that C release amplitude (CRA) decreased Environ. Res. Lett. 12 (2017) 014018 in the NH (P < 0.05), but had no significant changes in the globe and SH (P > 0.05) during 1979-2013, which partly contributed to the increasing net C uptake in the NH during the 35 year study period. CUA, the peak of annual C uptake, means the maximal capacity of land C uptake. Long-term change in CUA largely impacts the long-term trend of C uptake. In the NH, increasing photosynthetic C uptake caused by climate change and mediated by changing vegetation cover (Forkel et al 2016), vegetation recovery (Kasischke et al 2010), afforestation (Food andNations 2010, Pan et al 2011), and the agricultural green revolution (Gray et al 2014, Zeng et al 2014, may all contribute to improve the C uptake capacity during the peak growing seasons. For the SH, the semi-arid ecosystem in the SH have high sensitivity to the precipitation and climate extremes, which may absorb large amount of C quickly with the summer rainfall events, increasing the SH CUA (Cleverly et al 2013). Meanwhile, widespread observations of woody encroachment over semi-arid areas (Andela et al 2013) and increased vegetation greenness inferred from satellite remote sensing over recent decades (Andela et al 2013, Donohue et al 2009, Fensholt et al 2012 also increase photosynthetic C uptake and CUA in the SH as noted, but it is noteworthy that the SH CUA might be weakened by the increasing tropic forest deforestation (Pan et al 2011) and the increasing risks of drought and heat (Allen et al 2010, Phillips et al 2009, Zhao and Running 2010. The increased CUD across the globe was mainly attributed to that the starting date of C uptake advanced more than the ending date. Richardson et al 2010 reported that climate warming stimulates photosynthesis more than respiration in the spring (Richardson et al 2010), leading to an earlier onset of carbon sink activity. Advanced beginning of spring and/or postponed ending of autumn seasons has been widely reported in the past studies on vegetation phenology (Linderholm 2006, Piao et al 2007, Smith et al 2004. However, in this study, we found that the ending date of ecosystem C uptake was advanced in the globe and NH over the past 35 years. The finding is supported by long-term observations at Barrow and   Environ. Res. Lett. 12 (2017) 014018 Mauna Loa, which shows the ending date of C uptake has advanced by 0.17 and 0.14 d yr À1 , respectively (Graven et al 2013). This is thought to be due to the autumn warming-induced increase in respiration being greater than that in photosynthesis, leading to an earlier end of the net C sink (Piao et al 2008).

Start-CUD
Implications for seasonal changes in atmospheric CO 2 Our findings of the increased CUA and decreased CUD of C uptake in the NH provide explanations and insight into the seasonal amplitude and phase changes in atmospheric CO 2 . The seasonal phase of atmospheric CO 2 concentration is quantified by the day of year with CO 2 concentration downward zero crossing, which corresponds to changes in the CUD in terrestrial ecosystem (Graven et al 2013, Piao et al 2008. The decreased CUD in the NH shortened the duration of atmospheric CO 2 decrease. The advanced starting and ending dates of land C uptake also led to the advance of starting and ending date of the atmospheric CO 2 decline, shifting its duration. This could explain the phenomenon that seasonal amplitude of atmospheric CO 2 in Hawaii was increased and accompanied by phase advances of about 7 days from mid-1970s to 1995 during the declining phase of the cycle (DeRosier et al 1996).
The observed increasing seasonal amplitude of atmospheric CO 2 in the NH since 1960 could be also due to the increasing CUA (Graven et al 2013, Myneni et al 1997. So, the observed changes in CUA and CUD of land C uptake are crucial for better understand the dynamic changes of atmospheric CO 2 concentration.
In conclusion, we quantified the relative contributions of the NH, SH and different ecosystems to the trend and IAV of global land C uptake. We found that the IAV of the global land C sink during 1979-2013 was mostly attributed to the changes in the IAV of the land sink in the NH rather than the SH, but the trend of global land C uptake was attributed equally to both the NH and SH. For different ecosystem types, we found grasslands and croplands played an important role in the NH, while semi-arid ecosystems contributed substantially in the SH, for both the trend and IAV of C uptake. The trend and IAV of land C uptake can be fundamentally explained by the changes in CUA and CUD, but they worked in different ways in the NH and SH. The determinant role of C uptake capacity in the peak growing season and the starting and ending date of C uptake durations revealed in this study are crucial to better understand the mechanisms underlying the long-term trend and IAV of land C uptake and the consequent changes in atmospheric CO 2 dynamics.