Exposures to temperature beyond threshold disproportionately reduce vegetation growth in the northern hemisphere

Abstract In recent decades, terrestrial vegetation in the northern hemisphere (NH) has been exposed to warming and more extremely high temperatures. However, the consequences of these changes for terrestrial vegetation growth remain poorly quantified and understood. By examining a satellite-based vegetation index, tree-ring measurements and land-surface model simulations, we discovered a consistent convex pattern in the responses of vegetation growth to temperature exposure (TE) for forest, shrub and grass in both the temperate (30°−50° N) and boreal (50°−70° N) NH during the period of 1982−2012. The response of vegetation growth to TE for the three vegetation types in both the temperate and boreal NH increased convergently with increasing temperature, until vegetation type-dependent temperature thresholds were reached. A TE beyond these temperature thresholds resulted in disproportionately weak positive or even strong negative responses. Vegetation growth in the boreal NH was more vulnerable to extremely high-temperature events than vegetation growth in the temporal NH. The non-linear responses discovered here provide new insights into the dynamics of northern terrestrial ecosystems in a warmer world.


INTRODUCTION
Climate warming in recent decades has resulted in a shift to a warmer temperature distribution in the extra-tropical northern hemisphere (NH), which has led to rapid, but spatially variable, increases in both the frequency and the magnitude of extremely high temperature (EHT) [1,2]. Such changes raise a critical, but often overlooked, question: how does NH vegetation growth respond to a warmer temperature distribution, other than just changes in the mean climatic state, and in particular what is the role of a markedly increased EHT [3]?
The impacts of mean warmer temperature on vegetation growth have been extensively investigated at a regional/global scale [4]. Recent evidence has pointed to a weakening interannual correlation between mean warmer temperature and vegetation growth in the NH over the past three decades [5]. Together with the widely documented 'northern greening' effect [6,7], this has pointed to non-linear features of the response of vegetation growth to temperature variations. The development and growth of vegetation in a stepwise manner (i.e. spanning different phenophases) depends disproportionately on the threshold-based accumulation of daily temperature and the interactions with other factors, including solar radiation, water, nutrition limitations and heat stress.
So far, the non-linear effects of temperature exposure (TE), which is defined here as the accumulated daily temperature for days on which vegetation is exposed to a specific temperature range, such as 0-1 • C, 1-2 • C, etc., during the growing season) within different temperature ranges on terrestrial vegetation growth have not been well quantified. A few studies have shown that the exposure of vegetation to even a short-term EHT event can result in considerable regional terrestrial growth failure [8]. More seriously, future climate scenarios consistently predict a continuous shift to warmer temperature distributions and a further intensification of EHT events [9][10][11][12]. Thus, a comprehensive understanding of the ecological responses of NH vegetation growth to TE within different temperature ranges is crucial for predicting terrestrial vegetation growth and the consequences for biogeochemical cycles and biophysical climate feedbacks in the future.
In this study, we aimed to quantify the responses of northern vegetation growth to TE within different temperature ranges, using multiple data streams, including the satellite-derived Normalized Difference Vegetation Index (NDVI), tree-ring index (TRI) and land-surface model simulations of net primary productivity (NPP).

Divergent effects of accumulated TE above and below the EHT threshold on vegetation growth
First, we investigated the spatial pattern in the effects of accumulated TE above (TE H ) and below (TE L ) the EHT threshold on vegetation growth over the temperate and boreal NH. The 95th percentile of the daily temperature distribution in growing seasons during 1982−2012 was identified as the EHT threshold for each grid. We then calculated the accumulated TE H and TE L during the growing season for each grid and each year during the period of 1982−2012. There shows a general reduction in the Akaike information criterion (AIC) when introducing TE H and TE L into the ridge regression model (i.e. the second model), with a mean reduction of AIC of 2.3 ± 1.5 in our study region than the first model, despite the spatial difference. The ridge regression between the NDVI GS and total growing season precipitation, TE H and TE L during 1982−2012 was statistically significant (P < 0.05) in ∼44% of the temperate and boreal NH, with a mean R 2 value of ∼0.36 (ranging from 0.24 to 0.84) ( Supplementary Fig. 3, available as Supplementary Data at NSR online). These results showed that total growing season precipitation and the accumulated TE H and TE L together could explain a large portion of the interannual variations in the NDVI GS in both the temperate and the boreal NH. We observed generally positive and negative relationships between the NDVI GS and total growing season precipitation (∼68%) and TE H (∼61%), with significant (P < 0.05) relationships in ∼35 and ∼25% of the temperate NH, respectively. Interestingly, we discovered that the accumulated TE H and TE L had divergent effects on the NDVI GS ( Fig. 1b and c). The TE H exerted a more pervasive (∼61%) negative effect on the NDVI GS in the temperate NH, especially in central USA and southern Eurasia, than the TE L (∼48%). In boreal NH, there generally shows much weaker positive response of NDVI GS to TE H than TE L , with ∼33 and ∼47% of boreal NH with significantly (P < 0.05) positive response coefficients, respectively ( Fig. 1b and c). Consistent patterns in the responses of NDVI GS to total growing season precipitation and TE H and TE L were also obtained from the ridge regression analysis with different EHT definitions (90th and 99th percentiles, Supplementary Figs 4  The divergent effects of the TE H and TE L on the NDVI GS were most striking in temperate grasslands (Fig. 2). A more strongly negative standardized interannual response of the NDVI GS to the TE H than to the TE L was found in ∼70% of temperate grasslands (Figs 1b, c and 2a). However, such divergent effects were less pronounced for temperate shrub and forests, with a greater decrease in the interannual response of the NDVI GS to the TE H than the TE L found in only ∼53 and ∼58% of shrub lands and forests, respectively (Fig. 2a). Consistently divergent effects of the TE H and TE L on landsurface model simulations of mean growing season NPP (NPP GS ) were also observed ( Supplementary  Fig. 7, available as Supplementary Data at NSR online). However, we discovered a more consistent RESEARCH ARTICLE  Difference in γ TE Figure 2. Probability density function (PDF) of the difference in the standard regression coefficients between mean growing season (April-October) Normalized Difference Vegetation Index (NDVI GS ) and accumulated temperature exposures above (TE H ) and below (TE L ) the extremely hightemperature threshold. Extremely high temperature is defined as the 95th percentile of the daily temperature distribution for growing seasons during 1982-2012. The PDF shows the differences in the standard regression coefficients between NDVI GS and growing season TE H and TE L for forest (dark green), shrubland (orange) and grassland (grass green) in the temperate (a) and the boreal (b) northern hemisphere.
In this analysis, we only considered pixels with significant (P < 0.1) ridge regressions between NDVI GS , and total growing season precipitation, TE H and TE L .
decrease in the standardized interannual response of the NPP GS to the TE H than TE L for all vegetation types in the temperate NH ( Supplementary Fig. 8, available as Supplementary Data at NSR online). Divergent effects of the TE H and TE L on the NDVI GS were also observed in some parts of the boreal NH, particularly in northern Europe, northern America and northern Russia ( Fig. 1b and c). The divergent effects of the TE H and TE L on the NDVI GS were most prominent in shrub and forest in boreal NH (Fig. 2b). There was a much weaker positive response of vegetation growth to the TE H than to the TE L in these regions, indicating that the TE H could restrict the positive response of vegetation growth to temperature, even in the boreal NH. This was verified by the consistent pattern of the divergent effects of the TE H and TE L on the NPP GS in the boreal NH ( Supplementary Fig. 8b, available as Supplementary Data at NSR online). It should be noted that these findings were not susceptible to arbitrarily different definitions of the growing season (i.e. April-October and May-September, respectively) for vegetation growth in the NH (Supplementary Figs 9 and 10, available as Supplementary Data at NSR online).

Convex pattern in the response of vegetation growth to TE within different temperature ranges
A ridge regression was performed to explore the standardized interannual responses of the NDVI GS to total growing season precipitation, mean growing season temperature and TE within different temperature ranges (at 1 • C intervals) for different vegetation types in both the temperate and boreal NH during the period of 1982−2012.
The ridge regression coefficients of TE within different temperature ranges were used to quantify the standardized interannual response of the NDVI GS to differences in TE (γ TE ) over the period of 1982−2012. We observed generally positive and negative responses of the NDVI GS to mean growing season temperature and total growing season precipitation, respectively, for forest (0.44 and -0.12, P < 0.05), shrub lands (0.34 and -0.09, P < 0.05) and grass [0.23 (P < 0.05) and -0.04 (P > 0.05)] in the boreal NH. In contrast, vegetation growth consistently displayed weak (P > 0.05) positive/negative and significantly (P < 0.05) positive responses to mean growing season temperature and total growing season precipitation, respectively, for forest (-0.04 and 0.23), shrub (0.05 and 0.23) and grass (0.09 and 0.32) in the temperate NH. Given the magnitudes of the difference in hydrothermal conditions and vegetation structures among forest, shrubland and grassland in both the temperate and boreal NH, vegetation growth would not be expected to respond uniformly to TE among the different vegetation types. However, we identified a uniformly convex pattern in the γ TE of the NDVI GS in response to TE along with an increasing temperature gradient for all vegetation types in both the temperate and boreal NH (Fig. 3). This pattern showed a gradual increase in positive γ TE until a temperature threshold, which was dependent on vegetation types, was reached. There was a weak positive γ TE or even a negative γ TE in response to a TE above the temperature thresholds. A consistent result was also found for NPP GS (Supplementary Fig. 11, available as Supplementary Data at NSR online). Tree-ring analyses showed a consistent pattern in the relationship between the responses of the TRI and TE within different temperature ranges in the temperate NH, but no such convex pattern was observed in boreal TRI chronologies (Supplementary Fig. 12, available as Supplementary Data at NSR online).
Bent−Cable regression identified the different temperature thresholds in the relationships between the γ TE of the NDVI GS and TE within different temperature ranges for temperate (boreal) forest, shrubland and grassland, with those temperature thresholds centralized within the narrow ranges of ∼17-20 (15)(16)(17)(18)(19), ∼10-14 (10-15) and ∼10-12 (10-14) • C, respectively, for the two different growing season definitions (Supplementary Table 1, available as Supplementary Data at NSR online, Fig. 3 and Supplementary Fig. 13, available as Supplementary Data at NSR online). In the temperate NH, shrubland experienced much more exposure to warmer temperatures than grassland and forest, and there was a stronger negative γ TE of the NDVI GS and NPP GS when the temperature exceeded the threshold ( Fig. 3a and Supplementary Fig. 11, available as Supplementary Data at NSR online). In contrast, grassland in the boreal NH suffered from more exposure to warmer temperatures and there was a generally negative γ TE of the NDVI GS and NPP GS

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for boreal grassland under exposure to temperatures in the right-hand tail of the daily temperature distribution curve, despite the large variations (Fig. 3b).
Finally, we compared the γ TE of the NDVI GS between years with more and fewer EHT events during 1982-2012 (see the 'Methods' section) for forest, shrubland and grassland, in both the temperate and boreal NH (Fig. 4). We observed a much larger divergence in the γ TE of the NDVI GS and NPP GS in response to TE within the same temperature ranges between years with more and fewer EHT occurrences in the boreal NH than in the temperate NH for all vegetation types (Fig. 4 and Supplementary  Fig. 14, available as Supplementary Data at NSR online). There was a much weaker positive γ TE of the NDVI GS and NPP GS in years with more than average EHT occurrences than in years with fewer than average EHT occurrences for all vegetation types in the boreal NH ( Fig. 4 and Supplementary Fig. 14, available as Supplementary Data at NSR online). However, such large divergence in the γ TE of the NDVI GS and NPP GS were not observed in any vegetation types in the temperate NH. Instead, there was a generally consistent γ TE of the NDVI GS and NPP GS in response to TE in years with more and fewer EHT occurrences (Fig. 4). However, there was a stronger negative γ TE of the NDVI GS in the temperate forest in response to TE in the right-hand tail of the temperature distribution in years with more than average EHT occurrences than in years with fewer than average EHT occurrences (Fig. 4a).

DISCUSSION
Recent warming over the NH has been positively correlated with increasing terrestrial vegetation growth (also known as 'northern greening'), which is mainly attributed to an increase in vegetation photosynthesis and an extension of the photosynthetic growing season, especially in the boreal NH [6,[13][14][15][16][17]. However, we report here that exposures to temperatures beyond a vegetation typedependent critical threshold consistently resulted in a weak positive γ TE or even a negative γ TE of vegetation growth for forest, shrubland and grassland in both the temperate and boreal NH, despite the differences in the trajectories of γ TE .
The mechanisms underlying the observed decrease in the γ TE of vegetation growth in response to increasing temperature above these critical thresholds in both the temperate and the boreal NH could not be directly determined from the statistical analyses, and they remain unclear. Nevertheless, two possible mechanisms, namely warming-induced drought stress and a non-linear response of veg- to temperature exposures (γ TE ) and TE within different temperature ranges in years with more and fewer extremely high temperature (EHT) occurrences. The top part of each frame shows the non-linear relationships between the γ TE of NDVI GS and TE within different temperature ranges in years with more (darker lines) and fewer (lighter lines) EHT occurrences for forest (a), shrubland (b) and grassland (c) in the temperate (red lines) and the boreal (blue lines) northern hemisphere (NH) during 1982-2012. The confidence intervals at the 95% level for the γ TE are marked by error bars. For each pixel within each vegetation type, we selected 7 years within the period of 1982-2012 with more EHT occurrences and 7 years with fewer EHT occurrences compared to the mean number of EHT occurrences over the same period. Lines at the bottom of each frame display the average number of days within different temperature ranges in cases with more than average (darker lines) and fewer than average (lighter lines) EHT occurrences in the temperate (red lines) and boreal (blue lines) NH for each vegetation type.
etation growth to increasing temperature, can partially explain the observed consistently convex pattern in the γ TE of the NDVI GS /NPP GS for all vegetation types in both the temperate and boreal NH. Temperature impacts on vegetation growth directly and indirectly through its effects on plant physiological processes and hydrothermal conditions. In water-limited temperate regions, warmer temperature and an increase in the number and/or duration of EHT events can intensify drought stress ( Supplementary Figs 15 and 16, available as Supplementary Data at NSR online) and thus reduce the availability of water to support vegetation growth during the warm season [18] (Supplementary Fig. 16, available as Supplementary Data at NSR online). This mechanism also makes a major contribution to the widely documented decline in vegetation growth and the observed weakening positive relationship between vegetation growth and temperature variations in such regions [5,[19][20][21]. EHT and/or EHT-induced megadroughts can even trigger widespread lagged growth recovery and even forest die-off in water-limited regions [18,22], which is mainly attributed to hydraulic failure and/or carbon starvation [20,21,23,24]. Our tree-ring analyses consistently indicated that a TE beyond a certain threshold ( Supplementary Fig. 12, available as Supplementary Data at NSR online) resulted in a weak positive or even a negative γ TE for tree growth in the temperate NH, even though most of the TRI chronologies used in this study were primarily produced for reconstructions of past temperature, and the trees sampled were generally species limited by warm-season temperatures (e.g. [25]).
Growth of all three vegetation types in the boreal NH was more susceptible to TE under high temperatures than in the temperate NH. Our findings were consistent with those of previous studies showing that the physiological processes of plants grown in water-limited regions (e.g. temperate shrublands and grasslands) have low drought sensitivity, but are more flexible in adapting to high temperatures and/or drought stress [26,27]. Although previous studies have shown that drought generally has a major influence on vegetation growth in water-limited regions, this does not necessarily mean that plant communities in these regions are more vulnerable to warming-mediated drought limitation than those in humid regions [27,28]. An increase in the occurrence of EHT events in boreal regions can also result in drier conditions or even negative water balances (e.g. in grasslands in the boreal NH) (Supplementary Figs 15b and 16, available as Supplementary Data at NSR online).
Water availability and temperature can interact to regulate the response of vegetation growth to TEs across diverse bioclimatic regions [29,30]. For example, there was a strong negative γ TE of the NDVI GS in response to TE within the right-hand tail of the temperature distribution for boreal grass in years with more EHT occurrences compared to years with fewer EHT occurrences (Fig. 4c). The vegetation growth in the boreal region was also vulnerable to drought stress [27,30] and recent longlasting global-change-type drought stress in parts of the boreal regions has triggered local forest die-off [20,31]. Vegetation in humid regions in the boreal NH is particularly sensitive to drought and responds to it over short time scales [27,28]. Furthermore, drought can significantly mediate the temperature sensitivity of vegetation growth, and increasing evidence illustrated that drought stress may reduce, or even reverse, the potential benefits of climate warming on vegetation growth in boreal regions [30], but enhance the temperature sensitivity in tropical regions [29]. Evidence from tree-ring analyses has also confirmed that drought in parts of the boreal regions has resulted in a significantly weaker positive relationship between tree growth and temperature [32]. However, we did not observe a weakening positive γ TE of the TRI in the boreal NH in response to TE over an increasing temperature gradient, when all the chronologies in the boreal NH for the period 1982-2012 were considered ( Supplementary  Fig. 12, available as Supplementary Data at NSR online). This may be attributable to the considerable variations in local climate conditions and forest histories (e.g. management) among sampling sites. In addition, trees in the northern taiga have been shown to allocate more carbon to their stems and roots, and less carbon to leaves, under the warmer and drier conditions of recent years [33], which could also partly explain the different trajectories in the γ TE between the NDVI GS and TRI in boreal forest ( Fig. 3b and Supplementary Fig. 12, available as Supplementary Data at NSR online).
Another mechanism underlying the observed decrease in the γ TE of vegetation growth in response to increasing temperatures is the non-linear response of photosynthesis to increasing temperature, with the downregulation of photosynthesis occurring once the optimal temperature threshold was crossed. This mimicked the documented convex curve of the response of photosynthesis to increasing temperature [34][35][36]. Such non-linear temperature responses of photosynthesis have been reported to be responsible for the observed weakening positive relationship between vegetation growth and mean growing season temperature variations in the NH [5]. Importantly, the non-linear temperature response of vegetation photosynthesis can be largely mediated by warmer temperature induced intensified drought stress [37].
We suggest that plant trait-mediated different ecophysiological properties among different vegetation types also contribute to the different trajectories in the γ TE of the NDVI GS /NPP GS . Our

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meta-analysis revealed that deep-rooted forests in the temperate NH generally adopt a conservative water-use strategy and have a high capacity for acquiring deep soil water (Supplementary Table 2 and Supplementary Fig. 17, available as Supplementary Data at NSR online). Shrubs in water-limited regions generally have an adaptive water-use strategy and can acquire soil water from different soil layers during the growing season ( Supplementary Fig.  17, available as Supplementary Data at NSR online). The growth of these two vegetation types is thus regarded as being more resistant to drought and/or EHT events than shallow-rooted grass, particularly in water-limited regions. However, an adaptive water-use strategy cannot fully explain the observed strongly negative γ TE of NDVI GS /NPP GS for temperate shrubland in response to the exposure to temperatures in the right-hand tail of the distribution in years with either more or fewer EHT occurrences (Figs 3a and 4b). This is most likely because the most severe water deficit was observed in temperate shrubland regions ( Supplementary Fig.  16, available as Supplementary Data at NSR online). Shallow-rooted grass ecosystems generally use water from the top soil layers (Supplementary Fig. 17 and Supplementary Table 2, available as Supplementary Data at NSR online) and tend to be more vulnerable to EHT events [38,39]. This partly explains the observed lower and higher temperature thresholds in the non-linear γ TE of NDVI GS /NPP GS for grass and forest, respectively, in both the temperate and the boreal regions.
The physiological performance of NH vegetation in warmer and more extreme climates can also be affected by non-climate factors. For example, the rising CO 2 concentration and availability of background nutrition could act together to mediate the responses of vegetation growth to drought stress and EHT events by regulating stomatal conductance and nutrient tolerance [40][41][42]. Previous studies have shown that an increasing CO 2 concentration can increase whole-plant water-use efficiency, and thus partly alleviate the harmful effects of extreme drought or heat waves on vegetation productivity, especially in water-limited regions [43]. However, such benefits are susceptible to the seasonality of water availability and its effect on vegetation functioning [40,44,45], as well as the changing community composition (e.g. species composition) [42].
An improved understanding of the mechanisms underlying the impacts of warmer temperature distributions on vegetation growth is crucial when attempting to predict future ecosystem functioning, the global carbon cycle and subsequent climate feedbacks. Further research into the role of warmer temperature distributions on different terrestrial ecosystems is urgently needed, particularly studies based on long-term ecological experiments and diagnostic simulations using improved land-surface models.

Vegetation growth, climate and stable isotope datasets
The latest (third) version of the biweekly NDVI data, with a spatial resolution of 0.083 • , produced from the Advanced Very High Resolution Radiometer (AVHRR) observations during 1982-2012 (i.e. GIMMS NDVI 3g ), was obtained from the Global Inventory Modeling and Mapping Studies (GIMMS) group (https://nex.nasa.gov/nex/projects/1349/). We resampled the NDVI data into a spatial resolution of 0.5 • to match the climate data used. The GIMMS NDVI 3g dataset has been processed to account for orbital drift, sensor degradation, intersensor differences, cloud cover, zenith angle and volcanic aerosols [46]. This dataset has been widely used to monitor interannual variations in NH terrestrial vegetation growth and productivity [5].
Gridded monthly NPP from 1982 to 2010 were obtained from the TRENDY project (http://dgvm. ceh.ac.uk/node/9). We obtained the NPP outputs for the S2 scenario (in which both the climate and CO 2 concentration are changed) from four landsurface models: LPJ, LPJ-GUESS, ORCHIDEE and VEGAS. These four land-surface models provided monthly NPP simulations at a spatial resolution of 0.5 • .
A total of 446 standard TRI chronologies were used in this study to investigate the relationships between interannual tree-growth activity and TE in the temperate (30 • -50 • N) and boreal (50 • -70 • N) NH (Supplementary Table 3, available as Supplementary Data at NSR online). Of these TRI series, 433 were selected from the International Tree-Ring Data Bank (ITRDB, http://www.ncdc.noaa.gov/ data-access/paleoclimatology-data/datasets/treering) (Supplementary Text ST1, available as Supplementary Data at NSR online). We provided another 13 standard TRI chronologies. These standard TRI chronologies were built following standard dendrochronology procedures [47].
The global gridded sub-daily climate data (including temperature, precipitation and short-wave solar radiation) between 1982 and 2012, with a spatial resolution of 0.5 • and a time resolution of 6 hours, was obtained from the Climatic Research Unit-National Centers for Environmental Prediction (CRUNCEP) dataset (version 5, http://dods. extra.cea.fr/data/p529viov/cruncep/readme.htm).
Global Standard Precipitation-Evapotranspiration Index (SPEI) data, with a time scale of 6 months over the period of 1982-2012, was compiled from SPEIbase v2.3 (http://sac.csic.es/spei/database. html) [48]. The monthly gridded precipitation and potential evapotranspiration data, with a spatial resolution of 0.5 • , were also obtained from the CRU TS3.22 dataset (http://www.cru.uea.ac.uk/ cru/data/hrg/) to calculate the mean growing season water deficits (WD) between 1982 and 2012, using Equation (1): where G S P i and P E T i were the total precipitation and potential evapotranspiration during the growing season for the i th year, respectively. Isotope-derived plant water-uptake fractions from different soil layers throughout the growing season for trees, shrubs and grasses in the temperate NH were obtained from literature surveys. Three different soil layers were roughly defined for the purposes of this study, with the shallow, middle and deep soil layers corresponding to 0−20/30, 20/30−50/70 and >50/70 cm, respectively. In some studies, seasonal water-uptake fractions were investigated. In such cases, we simply calculated the mean plant water-uptake fractions during the growing season from the three different soil layers by averaging the seasonal water-uptake fractions, although it should be noted that there is a large seasonal variation in plant water uptake. The details of the survey undertaken in the study are listed in Supplementary

Relationships between mean growing season vegetation growth and climate factors
We defined the 95th percentile of the daily temperature distribution of growing seasons during the period of 1982-2012 as the EHT threshold in each grid. We then calculated the accumulated TE above and below the EHT threshold (TE H and TE L , respectively) in each growing season for the period of 1982-2012 for each grid. Ridge regression was performed to identify the interannual relationships between NDVI GS /NPP GS and different sets of climate variables. The first model only includes the total growing season precipitation, mean growing season temperature and mean growing season solar radiation. An alternative ridge regression model (i.e. Model 2) between NDVI GS /NPP GS and total grow-ing season precipitation, mean growing season temperature, mean growing season solar radiation, and the TE H and TE L was also evaluated. The AIC was introduced to evaluate the performance of the two alternative models [49]. We found that the inclusion of mean growing season solar radiation and mean growing season temperature did not significantly improve the second model performance (Supplementary Figs 2

Non-linear responses of vegetation growth to TE
The non-linear responses of vegetation growth to climate factors during the period of 1982-2012 were investigated for different vegetation types using Equation (2): where y i t was the vegetation growth proxy represented by NDVI GS , NPP GS or TRI in region i and year t (if applicable). γ h and ∅ i t (h) were the response coefficients of the vegetation growth proxy to TE and the time distribution of TE over the growing season in region i and year t, respectively. The temperature data covered the period of 1982-2012 for region i between the lower boundary h and upper boundaryh . A quadratic function representing total growing season precipitation and linear function representing mean growing season temperature and random error are denoted as P it , T it and , respectively, whereas δ and θ are the corresponding coefficients for the total growing season precipitation and mean growing season temperature (Supplementary Text ST3, available as Supplementary Data at NSR online). We fixed the growing season to be April-October for vegetation in both the temperate and boreal NH. Another growing season definition, May-September, was also analysed to verify the robustness of our conclusions. However, the effects of temporal changes in CO 2 concentrations on the RESEARCH ARTICLE responses of vegetation growth to TE within different temperature ranges were not considered in our analyses (Supplementary Text ST4, available as Supplementary Data at NSR online).
Specifically, we approximated the time distribution of TE in Equation (2) with a 1 • C interval, as shown in Equation (3): where γ j was the regression coefficient of the vegetation growth proxy to TE within the j th temperature bin estimated by the ridge regression. The lower boundary h and upper boundaryh for TE during the growing season were calculated for forests, shrubland and grassland, respectively (Supplementary Text ST5, available as Supplementary Data at NSR online). Bent-Cable regression analyses were performed to identify possible temperature thresholds in the non-linear relationship between TE and the corresponding response coefficients of the vegetation growth proxy to TE [50]. We compared the non-linear relationships between the responses of NDVI GS to TE (γ TE ) in years with more and fewer EHT occurrences for forests, shrubland and grassland in both the temperate and boreal NH. We selected 7 years with more EHT occurrences and 7 years with fewer EHT occurrences relative to the mean number of EHT occurrences during 1982−2012 in each grid (Supplementary Text ST6, available as Supplementary Data at NSR online).