Data-based perfect-deficit approach to understanding climate extremes and forest carbon assimilation capacity

Several lines of evidence suggest that the warming climate plays a vital role in driving certain types of extreme weather. The impact of warming and of extreme weather on forest carbon assimilation capacity is poorly known. Filling this knowledge gap is critical towards understanding the amount of carbon that forests can hold. Here, we used a perfect-deficit approach to identify forest canopy photosynthetic capacity (CPC) deficits and analyze how they correlate to climate extremes, based on observational data measured by the eddy covariance method at 27 forest sites over 146 site-years. We found that droughts severely affect the carbon assimilation capacities of evergreen broadleaf forest (EBF) and deciduous broadleaf forest. The carbon assimilation capacities of Mediterranean forests were highly sensitive to climate extremes, while marine forest climates tended to be insensitive to climate extremes. Our estimates suggest an average global reduction of forest CPC due to unfavorable climate extremes of 6.3 Pg C (∼5.2% of global gross primary production) per growing season over 2001–2010, with EBFs contributing 52% of the total reduction.

understanding the amount of carbon that forests can hold. Here, we used a perfect-deficit approach to identify forest canopy photosynthetic capacity (CPC) deficits and analyze how they correlate to climate extremes, based on observational data measured by the eddy covariance method at 27 forest sites over 146 site-years. We found that droughts severely affect the carbon assimilation capacities of evergreen broadleaf forest (EBF) and deciduous broadleaf forest. The carbon assimilation capacities of Mediterranean forests were highly sensitive to climate extremes, while marine forest climates tended to be insensitive to climate extremes. Our estimates suggest an average global reduction of forest CPC due to unfavorable climate extremes of 6.3 Pg C (∼5.2% of global gross primary production) per growing season over 2001-2010, with EBFs contributing 52% of the total reduction.

Introduction
Forests store ∼45% of terrestrial carbon (∼1600 Pg C), contributing ∼50% of terrestrial net primary production (Bonan 2008) and making them significant carbon sinks that can mitigate global warming (Nemani et al 2003, Gielen et al 2013, an effect which may be dampened by changing climate (Cox et al 2000, Friedlingstein et al 2006, Zhao and Running 2010, Yi et al 2010. The 2003 heat wave and drought reduced Europe's gross primary production (GPP) by 30%, which reversed the effect of four years of net carbon sequestration (Ciais et al 2005). It is expected that such extreme events will increase in frequency and intensity (Meehl, Tebaldi 2004, Mu et al 2011, Trenberth 2012. Studying the impacts of climate extremes on the carbon cycle of forests is important to understand carbon-climate feedback mechanisms because even a small shift in the frequency or severity of climate extremes may result in positive feedback to climate warming (Allen et al 2010, Serrano et al 2013. However, investigations into the impacts of climate extremes on the carbon cycle are still at the rudimentary level. In this study, we applied the perfect-deficit approach of Yi et al (2012) to identify extreme values of canopy photosynthetic capacity (CPC) and climate variables from flux tower data. The daily CPC is calculated as the maximum rate of GPP of the day from FLUXNET tower data at 30 min resolution. CPC forms an upper boundary for the instantaneous canopy photosynthetic rates for a specific site-year. It is hypothesized that ecosystem carbon assimilation capacity is only constrained by climate conditions, and thus a perfect CPC (PCPC) is defined as a measure of the maximum carbon assimilation potential for a site given site-specific 'perfect' climate conditions for a particular day of the year over the years for which data were sampled. Deficits of CPC can be readily identified by subtracting CPC curve from the PCPC curve.
We introduced three indices (duration, intensity and severity) to quantitatively evaluate extreme climate impacts on forests carbon assimilation capacity, indicated by CPC deficits. Principal component analysis (PCA) was applied to identify the driving forces of climate-related carbon assimilation reduction.
We used 27 forest sites from Europe, North America and South America, each with at least four years of continuous carbon and water flux records. The represented ecosystem types include evergreen broadleaf forests (EBF), deciduous broadleaf forests (DBF), evergreen needleleaf forests (ENF) and mixed forests (MF). We also utilize the MODIS GPP and land cover datasets covering 2001-2010 to determine the spatial context of changes in forest carbon assimilation at the global scale. Key objectives of this study were: (1) identify the site-inherent 'perfect' conditions for maximal productivity over the observational records; (2) discover patterns in disruption of forest carbon assimilation associated with climatic extremes; and (3) expand the application of the method (Yi et al 2012) geographically to large scale estimation of the reduced carbon assimilation caused by climate extremes.

Sites and data
2.1.1. Flux tower data. We used data from the FLUXNET 'La-Thuile' database. Data have been processed in a standard methodology described in Papale et al 2006. The data are storage corrected and u* filtered. We used growing season data (May-October) from 27 forest sites, including four EBF, seven DBF, 13 ENF, and three MF (figure 1). These sites have a minimum of four years of continuous (gap-filled) records of GPP and meteorological variables, including temperature (T a ), precipitation (P), net radiation (R n ), vapor pressure deficit (VPD). GPP was partitioned from net ecosystem exchange (NEE) based on nonlinear regression algorithms (Reichstein et al (2005)). Evaporative fraction is calculated from measured latent heat (LE) and sensible heat (H). EF is represented by the ratio between LE and the sum of sensible and LE fluxes: EF = LE/(LE + H), This can be also written as EF = LE/(R n − G), where Rn is net radiation, G is ground heat flux, and R n − G is available energy. If the near soil surface moisture declines, less energy will be used for vaporization, resulting in low EF. In contrast, if adequate water is available for plants due to sufficient precipitation or root access to groundwater, the amount of energy used for vaporization will increase, leading to high EF (Schwalm et al 2010). Because of the synthetic nature of EF in characterizing land surface conditions for soil moisture and available energy for plant to use and evaporation, it has been widely used as a drought index (Heim 2002, Nishida (2003). Here EF is the drought indicator in our analysis.

CPC
2.2.1. Forest CPC and PCPC. The concept of CPC represents the daily maximum carbon assimilation (Yi et al 2012). The daily CPC of ecosystems was defined as the maximum value of half-hourly GPP in a day, which was derived from FLUXNET NEE data by nonlinear regression (Reichstein et al 2005). A yearly CPC curve is constructed from daily GPP data (figure 2(a)). This CPC curve forms an upper boundary for the instantaneous canopy photosynthetic rates, and the area under the CPC curve represents ecosystem carbon assimilation potential-how much carbon dioxide potentially can be assimilated by an ecosystem at a site in an individual year. This data-based CPC is in good agreement with modelled photosynthetic capacity (A max ) (figure 2(a), modelling in details given in the online supplementary materials available at (stacks.iop.org/ERL/9/065002/ mmedia). PCPC is defined as a measure of the maximum carbon assimilation potential for a site given site-specific 'perfect' climate conditions for a particular day of the year over the years for which data are available. The PCPC values are calculated for each day of the year as the maximum CPC recorded on that day across all available years of site data. Thus, a PCPC curve of maximized carbon assimilation potential can be constructed (figure 2(a)). The difference between PCPC and CPC is defined as CPC deficit (figure 2(a)). We investigate the relationship between magnitudes of the CPC deficit of forests and their driving forces.
2.2.2. MODIS GPP deficit. The perfect-deficit approach was also applied to MODIS GPP datasets. The PCPC was calculated as the maximum value of monthly GPP over the years 2001-2010. The CPC deficits were calculated as the difference between monthly PCPC and monthly CPC of specific years.

Climate potential index.
We used a similar approach as above to define climate drivers or drought proxies (T a , R n , P, VPD, and EF). We extracted the yearly climatic potential curve from the daily maximum observed value of each climate variable for each site-year. Climatic envelopes were defined as the maximum values for each day-of-year observed from at least four continuous yearly records. Climatic drivers are defined as differences between climatic potential and climatic envelopes representing 'perfect' climate.

Extreme indices
2.3.1. Threshold value. The threshold levels of extremes were defined by the relative monthly CPC deficit R i = (PCPC i − CPC i )/PCPC i , here the PCPC i is the ith month PCPC (calculated by integrating daily PCPC), and CPC i is ith month CPC (from integrating the daily CPC).
Based on sensitivity analysis (Supplementary figure 1), R i = 0.3 is used as a threshold value to identify extreme CPC events. We did piecewise linear regression between R i and the fraction of months with relative CPC deficit greater than R i . The R i = 0.3 is close to the break point between a line with steep slope (more sensitive) to one with gentle slope (less sensitive). In order to emphasize severe extreme events and keep results less sensitive to the choice of R i , we therefore used R i = 0.3 as the threshold value. The legitimateness of using R i = 0.3 as the threshold value in present paper is also evidenced by previously published drought and heat wave events that occurred in 2003 in Europe and caused significant GPP reduction (Ciais et al 2005). These documented extreme events can be identified by the choice of R i = 0.3 as the threshold value in our analysis.
2.3.2. CPC deficit duration, intensity and severity. The concept of CPC deficit indices is borrowed from drought terminology (Sheffield and Wood 2007) in which a drought index is calculated as the deficit of soil moisture relative to its seasonal climatology. Similarly, an extreme index from the point of view of the carbon cycle could be calculated as the deficit of CPC relative to its PCPC. An extreme event is defined as a period of duration of n months with relative deficit ratios larger than an arbitrary level. The departure of CPC from PCPC is the extreme event magnitude M i (g CO 2 m −2 ), where i is the ith month of n months with R i exceeding 0.3 within a May-October period. The mean magnitude over the CPC deficit duration is the intensity I (g CO 2 m −2 month −1 ), The product of duration and intensity gives the CPC deficit severity S (g C m −2 ), We also define classes of extreme events based on their duration as follows: D 1-2 (1 ⩽ n ⩽ 2), short or medium term, D 3-6 (3 ⩽ n ⩽ 6), long term, where the subscript to D indicates the range of drought duration in months. (principal components). Here, PCA is used to find the correlations between CPC deficits and climate drivers during the northern growing season (May-October). Datasets were standardized before we compute the PCA. We use the first three principal components, which account for at least 70% of the whole dataset variance, to construct plots with axes formed by these three components. The correlations among CPC deficit and climatic drivers were approximately equal to the cosines of the angles between the corresponding lines in the plot (Wilks 2006) (Supplementary figure 2) (This is an approximation because the variance described is 70% and above, rather than 100%).

Smoothing algorithm.
All of the climatic drivers and model variables were smoothed using a 10 d moving average.

Results and discussion
As an example, the yearly photosynthetic capacity (A max ) curve for site IT-Ro2 (DBF) is constructed from daily data extracted using equation (S1). The physiological meaning of A max is the carbon assimilation rate at saturating values of photosynthetic photon flux density. The yearly dynamics of CPC from the perfect-deficit approach and A max from the light response model were shown in figure 2(a). Overall, the databased CPC is consistent with the model-based A max . Both CPC and A max show the severe carbon assimilation reductions during the 2003 growing season in European DBF sites. However, the modeled A max largely overestimates the carbon assimilation around the beginning and end of the growing season, and slightly underestimates it during the growing season. The index EF deficits show the similar pattern as CPC deficit ( figure 2(b)). The clear relationship between GPP deficits and EF deficits occurring at the IT-Ro2 site (figures 2(a), (b)) may indicate that drought was the major constraint to growing-season carbon assimilation in this site. As shown for the example site, we applied the perfectdeficit approach to 27 forest sites covering EBF, DBF, MF and ENF ecosystems to calculate the duration, intensity and severity of CPC deficits. Duration means the number of months with relative deficit above 0.3, intensity was calculated as the mean magnitude of CPC deficit over the duration and severity is the product of intensity and duration (see methods). CPC deficit duration, intensity, and severity for each site are listed in table 1. Severe CPC deficit events, characterized by long duration, were mostly discernible at EBF and DBF sites (D 3-6 > 3). For ENF and MF, only 4.9% and 7.7% of sites exhibit severe CPC deficit events. As shown in figure 3, at the biome scale, the EBF sites were dominated by significant reduction in carbon assimilation indicated by large CPC deficits. Over the studied sites, the EBF CPC deficits were at the highest average severity, with assimilation reduction of 824.2 g CO 2 m −2 per growing season, 1.8 months of duration, and 415.4 g CO 2 m −2 month −1 of intensity. The average severity, duration and intensity were similar for DBF sites: 673.2 g CO 2 m −2 , 1.5 months, and 412.3 g CO 2 m −2 month −1 respectively. The frequency of severe CPC deficit events in the broadleaf forests (i.e. EBF and DBF) indicates high inter-annual variability of carbon assimilation capacity in these ecosystems. In contrast, the ENF sites rarely exhibit significant CPC deficits, with aggregated average values of severity, duration, and intensity of 149.2 g CO 2 m −2 , 0.5 months, and 186.6 g CO 2 m −2 month −1 , respectively. The three MF sites behaved similarly to the ENF sites. We found that the CPC deficits of forests vary significantly by climate region. The frequency of severe CPC deficits of Mediterranean forests was high (table 1). Because Mediterranean forests usually suffer from long dry summers, drought is the most important cause of forest carbon assimilation declines in this climate zone. There, 75% of the severe CPC deficit events coincide with significant EF deficits.
We applied PCA to illuminate the correlation between CPC deficits and climatic drivers. Conventionally, deconvoluting the climatic effects of carbon assimilation is difficult, because the climatic variables and drought index usually covary strongly. PCA methods can effectively separate those effects (Jung et al 2007, Wilks 2006. As illustrated in figure 4, CPC deficit of EBF strongly correlates with EF deficit, with a mean correlation coefficient (denoted by cosine of two lines that represent EF deficit and CPC deficit) of 0.42. The cosine values between CPC deficit and other climatic variables (T a , R n , VPD and P) range from −0.04 to 0.04, indicating very weak correlations. For DBF biomes, the CPC deficit also displayed strong correlation with EF (cosine of 0.43), but slight correlation with R n (cosine of 0.18). These results suggest a drought control on CPC in these two broadleaf biomes. However, the correlations of broadleaf forest CPC deficits and precipitation were weak. This may be attributed to several reasons. First, the typical probability density of precipitation is a gamma distribution, while the PCA approach assumes that data is normally distributed. This mismatch may introduce bias to assess the role of precipitation in its correlation to CPC deficits. Second, precipitation is a sporadic input to the soil moisture budget (Noy-Meir 1973), and does not influence ecosystem activities immediately. In addition, compared to herbaceous vegetation, trees are generally more resistant to instantaneous local environmental changes (Teuling et al 2010) because they can access deep soil moisture and groundwater, which smooth out variability in response to precipitation.
A number of previous studies have suggested that, in temperate boreal forest ecosystems, the growing season photosynthetic capacity is mostly constrained by temperature (Falge et al 2002, Griffis, Black 2003. Indeed, the correlation of the CPC deficits in both ENF and MF with climatic drivers was weak (figure 4). The correlation between ENF CPC deficit and Rn was highest (cosine 0.26) out of the climatic drivers, while the MF CPC deficit had no significant correlation with any of the climate drivers or with EF.
Within the same type of forest, the climatic control of carbon assimilation capacity could vary among climatic zones (Supplementary table 1). The CPC deficits of Mediterranean EBF (Csa) was apparently controlled by drought while that of tropical (Af) EBF depended less on climatic factors. In contrast to Mediterranean (Csa) DBF, whose carbon assimilation capacity exhibited a strong dependence on drought, continental and moist tropical DBF (Cfb and Dfb) carbon assimilation capacities were less impacted by drought. Instead, Ta and radiation were stronger constraints. Figure 5 illustrates the monthly global spatial extent of CPC deficits during the growing season. Non-forested areas are masked from the analysis. We estimate a climate-attributable global reduction of forest CPC of 6.3 Pg C (∼5.2% of total terrestrial GPP) per growing season, and EBF forests contributed 51.7% of the total reduction. Although DBF displayed significant CPC deficits at the site level, the total carbon lost was small due to the small area this biome covered globally. The high CPC deficits of EBF occur in August and September, especially at the tropical forests of Brazil. The large CPC deficits in temperate and boreal forests (ENF and MF) occurred in May, most pronounced at boreal forests of Canada, northern United States, and western Russia. The ENF and MF biomes together contribute almost half of total forest carbon assimilation reduction.

Conclusions
We analyzed the effects of climate extremes on forest carbon assimilation and discussed how that might impact the carbon cycle. An observation-based estimate of those impacts was presented by introducing three indices of assimilation deficit periods: duration, intensity and severity. Our study suggests that carbon assimilation capacities of broadleaf forests (EBF and DBF) could be significantly impacted by drought, indicated by low values of EF. On the global scale, EBF contributes more than 50% of the carbon reduction of forests. Climate extreme events, specifically drought, are expected to increase in intensity and severity in the future. The present analysis can help identify and quantify the impacts of climate extremes on terrestrial carbon cycles and improve our understanding of carbon-climate feedback mechanisms.   Correlations between CPC deficits and climatic variable deficits (May-October). Shown are the median (red horizontal lines), the quartiles (colored boxes), 25th and 75th percentiles (the edges of the box). The correlations are calculated using principal component analysis. Three components are retained to form three dimensional plots, which explain at least 70% of total variations of the dataset (Supplementary table 2). Correlations are calculated as the cosines of the angles between GPP deficits and Temperature (T a ), Radiation (R n ), vapor pressure deficit (VPD), Precipitation (P), Evaporative Fraction (EF) deficits. CPC deficits of DBF and EBF are highly correlated with EF deficits, suggesting drought control of carbon sequestration among these two types of forests. In this study, we used global MODIS GPP datasets published in Zhao and Running (2010) to calculate GPP deficits by perfect-deficit approach (Yi et al 2012). Forest GPP was calculated based on MOD12C1 land cover product. Non-forested areas were masked from our analysis.