# Dryness controls temperature-optimized gross primary productivity across vegetation types

Bingxue Wang, Weinan Chen, Junhu Dai, Zhaolei Li, Zheng Fu, Sangeeta

Sarmah, Yiqi Luo, Shuli Niu

► To cite this version:

Bingxue Wang, Weinan Chen, Junhu Dai, Zhaolei Li, Zheng Fu, et al. Dryness controls temperature-optimized gross primary productivity across vegetation types. Agricultural and Forest Meteorology, 2022, 323, pp.109073. 10.1016/j.agrformet.2022.109073. hal-03738350

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Distributed under a Creative Commons Attribution 4.0 International License
1 Dryness controls temperature-optimized gross primary

2 productivity across vegetation types

3 Bingxue Wang<sup>a#</sup>, Weinan Chen<sup>a,b#</sup>, Junhu Dai<sup>b,c,d</sup>, Zhaolei Li<sup>a</sup>, Zheng Fu<sup>e</sup>, Sangeeta

4 Sarmah<sup>a</sup>, Yiqi Luo<sup>f</sup>, Shuli Niu<sup>a,b1</sup>

5

6 <sup>a</sup>Key Laboratory of Ecosystem Network Observation and Modeling, Institute of
Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China

8 <sup>b</sup>College of Resources and Environment, University of Chinese Academy of Sciences,
Beijing 100049, P.R. China

10 c Key Laboratory of Land Surface Pattern and Simulation, Institute of Geographic

11 Sciences and Natural Resources Research, CAS, Beijing 100101, China

12 d China-Pakistan Joint Research Center on Earth Sciences, CAS-HEC, Islamabad
13 45320, Pakistan

14 <sup>e</sup>Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL,
CEA-CNRS-UVSQ, Université Paris-Saclay, Gif-sur-Yvette, 91191, France

16 <sup>f</sup>Center for Ecosystem Science and Society and the Department of Biological Sciences,
Northern Arizona University, Flagstaff, AZ 86011, USA

18

19 <sup>1</sup>To whom correspondence may be addressed:

20 S, Niu: sniu@igsnrr.ac.cn

21 <sup>#</sup>These authors contribute equally to this work.

22

23
24 Abstract

25 Temperature response of gross primary productivity (GPP) is a well-known property
26 of ecosystem, but GPP at the optimum temperature (GPP_Topt) has not been fully
discussed. Our understanding of how GPP_Topt responds to warming and water
28 availability is highly limited. In this study, we analyzed data at 326 globally distributed
29 eddy covariance sites (79°N-37°S), to identify controlling factors of GPP_Topt.

30 Although GPP_Topt was significantly influenced by soil moisture, global solar
31 radiation, mean annual temperature, and vapor pressure deficit in a non-linear pattern
32 (R² = 0.47), the direction and magnitude of these climate variables' effects on GPP_Topt
depend on the dryness index (DI), a ratio of potential evapotranspiration to
precipitation. The spatial pattern showed that soil moisture did not affect GPP_Topt
across energy-limited sites with DI < 1 while dominated GPP_Topt across water-limited
sites with DI >1. The temporal pattern showed that GPP_Topt was lowered by warming
or low precipitation in water-limited sites while energy-limited sites tended to maintain
a stable GPP_Topt regardless of changes in air temperature. Vegetation types in humid
climates tended to have higher GPP_Topt and were more likely to benefit from a warmer
climate since it was not restricted by water conditions. This study highlights that the
response of GPP_Topt to global warming depends on the dryness conditions, which
explains the nonlinear control of water and temperature over GPP_Topt. Our finding is
essential to realistic prediction of terrestrial carbon uptake under future climate and
vegetation conditions.
47

48 **1 Introduction**

49 Gross primary productivity (GPP) is the most important component of the
50 terrestrial carbon cycle and its great variability can lead to large uncertainty in
51 modeled dynamics of terrestrial carbon sequestration (Beer et al., 2010; Friedlingstein
52 et al., 2020). Global warming profoundly affects GPP. Theoretically, ecosystem GPP
53 increases with ambient temperature till the temperature reaches an optimum
54 temperature (T<sub>opt</sub>) corresponding with peaked GPP (GPP_T<sub>opt</sub>), above which GPP
55 declines sharply (Huang et al., 2019; Kumarathunge et al., 2019). T<sub>opt</sub> and GPP_T<sub>opt</sub> are
56 the two most critical parameters in the temperature response of GPP. Thus, the
57 adjustment of the two key properties to a warmer climate determines the magnitude of
58 future carbon uptake (Way and Yamori, 2014). However, most previous studies on
59 thermal acclimation and adaptation of ecosystem-scale photosynthesis focused on T<sub>opt</sub>
60 (Kumarathunge et al., 2019; Sendall et al., 2015), less on GPP_T<sub>opt</sub>. It has been well
61 documented that the inter-annual variability of GPP is determined by peak GPP more
62 than any other drivers (Musavi et al., 2017; Xia et al., 2015; Zhou et al., 2016).
63 Therefore, revealing the key climate variables of maximum photosynthetic capacities
64 contributes to more accurate prediction of GPP and the carbon cycle-climate feedbacks
65 (Gu et al., 2009; Yi et al., 2012).
A recent leaf-level study claimed that the maximum photosynthetic capacity, represented by the maximum rates of Rubisco carboxylation ($V_{cmax}$), is optimized to the climate variables including light, temperature, vapor pressure and atmosphere pressure across the globe (Smith et al., 2019). Since the mechanisms and parameters of the photosynthesis-temperature response differs between different biological hierarchical levels, knowledge of leaf-level photosynthetic capacity is not necessarily applicable for understanding the controlling factors of GPP and its peak rate (GPP$_T_{opt}$) at the ecosystem scale (Huang et al., 2019; Smith et al., 2019). Although Huang et al. investigated the determinant of the temporal variation in GPP$_T_{opt}$ globally (Huang et al., 2018), the major climate variables of the spatial variation of GPP$_T_{opt}$ is still unknown.

Warming stimulates leaf-level photosynthesis at high soil moisture but reduces it under dry spells (Humphrey et al., 2018; Reich et al., 2018; Smith and Dukes, 2018), thus it is reasonable to hypothesize that water availability also influences the response of GPP$_T_{opt}$ to temperature. Previous studies have found that the inter-annual variation of terrestrial carbon uptake and atmospheric CO₂ growth rate is strongly correlated to the terrestrial water storage, indicating a close interplay between carbon and hydrological cycles (Humphrey et al., 2018). However, it is still unknown how the responses of GPP$_T_{opt}$ to different climate variables varied with dryness conditions.

Carbon and water cycles in the terrestrial ecosystems are closely coupled. It is well-described by Budyco's curve through incorporating the concept of water and
energy limits that evapotranspiration was mainly controlled by the balance between
potential evapotranspiration and precipitation (i.e. the dryness index, DI) (Budyko et
al., 1974; Potter and Zhang, 2009; Yi and Jackson, 2021) (Fig. 1). When DI < 1,
evapotranspiration is limited by available energy; when DI > 1, evapotranspiration is
limited by available water (Fig. 1). Given the close relationship between GPP and
evapotranspiration (Beer et al., 2009; Yu et al., 2008), the concept of water and energy
limits possibly applies to the determinant climate variables of GPP_Topt as well.
Additionally, different vegetation types vary in climatic preference (Lin et al., 2015;
Wang et al., 2017; Whittaker, 1975). Cropland, grassland and forest naturally differ in
Vcmax and peak vegetation growth (Huang et al., 2018). None has ever studied the
variation of GPP_Topt among vegetation types and teases apart the effects of vegetation
types and different climate variables.

Using data from 326 FLUXNET eddy covariance sites across large geographical
gradients from 37°S to 79°N, we explore the major climate variables of GPP_Topt across
space. Extensive ecological researches have demonstrated that control of water over
carbon process is nonlinear (Huxman et al., 2004; Luo et al., 2017) across large
geographic areas while within a site carbon processes usually respond linearly to
available water (Luo et al., 2017). We hypothesize that GPP_Topt responds to water
availability and other environmental drivers non-linearly across the 326 sites (H1).
The response of GPP_Topt to different climate variables depends on dryness
conditions, i.e., water availability determines GPP_Topt in water-limited ecosystems
while temperature boosts GPP_Topt in energy-limited ecosystems (H2). We also
hypothesize that GPP_T<sub>opt</sub> respond to climate variables differently among vegetation

types (H3).

<figure><img src="image_2.png" /></figure>

111

Figure 1 A Budyko curve (revised from Yi and Jackson, 2021). When PET < P,

evapotranspiration is limited by available energy; when PET > P,

evapotranspiration is limited by available water. Here, EI = ET/P, DI = PET/P,

where ET is evapotranspiration, PET is potential evapotranspiration, P is

precipitation.

117

## 2 Material and methods

### 2.1 Site information and climate data

We obtained daily mean GPP and air temperature from standardized files of the

LaThuile and FLUXNET2015 databases. The data were quality-controlled and

gap-filled by consistent methods as described in previous reports (Chu et al., 2017; Niu
et al., 2012). Data with remained gaps less than 5% in a whole year were selected for further analysis, leaving a total of 326 sites with 1634 site-years data spanning from 37°S to 79°N (Fig. S1). Daily mean GPP and air temperature ($T_{air}$) instead of hourly data was used to generate GPP-$T_{air}$ response curve, avoiding the influence from the diurnal pattern. Specifically, for each site-year, the daily air temperatures were binned in 1 °C. The daily air temperature and the corresponding GPP in each temperature bin was averaged to construct the GPP-$T_{air}$ response curve. The peaked GPP ($GPP_{T_{opt}}$) was determined by calculating the running mean of every three temperature bins.

Mean annual temperature (MAT, °C), mean annual precipitation (MAP, mm yr⁻¹), growing season temperature (GST, °C), growing season precipitation (GSP, mm yr⁻¹), global solar radiation (GSR, MJ m⁻² d⁻¹) and growing season vapor pressure deficit (VPD, kPa) of each site were obtained from World Clim (Fick and Hijmans, 2017), which are the average for the years 1970-2000. The warmest quarter in a year is considered as the growing season. Humidity index was obtained from FAO dataset (Food and Agriculture Organization of the United Nations, 2015), which is calculated the ratio of precipitation to potential evapotranspiration (P/PET). The reciprocal of humidity index is dryness index (DI, PET/P). Soil moisture (mm) is obtained from CPC soil moisture data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at https://www.esrl.noaa.gov/psd/. These data were used to investigate the spatial variation in $GPP_{T_{opt}}$.

Vegetative patterns of the sites used in this study were divided into 13 vegetation types according to the International Geosphere-Biosphere Programme (IGBP) (Peel et
al., 2007): deciduous broadleaf forest (DBF, n=42), evergreen broadleaf forest (EBF, n=26), evergreen needle leaf forest (ENF, n=77), deciduous needle-leaf forest (DNF, n=1), mixed forest (MF), closed shrubland (CSH), opened shrubland (OSH), grassland (GRA, n=61), cropland (CRO, n=34), savannah (SAV, n=12), woody savannah (WSA, n=6), and wetland (WET, n=32). For the statistical analysis, closed shrubland (CSH, n=8), opened shrubland (OSH, n=14) are merged to shrubland (SH). Savannah (SAV) and woody savannah (WSA) were merged into savannah (SAV). The global vegetation distribution was derived from MODIS (MOD12Q1 Land Cover Science Data Product) at a spatial resolution of 1 km using the classification scheme of IGBP.

## 2.2 Statistical analysis

GPP_Topt of each site was averaged across multiple years of data. The response of GPP_Topt to climate variables was examined by ridge regression in order to control the collinearity of climate variables across space. GPP_Topt was logarithm transformed to meet the assumption of homogeneity of variance. We further estimated the relative contributions of climate variables by traditional R square partitioning of multivariate regression and gradient boost regression (machine learning) using “hier.part” and “gbm” packages, respectively.

The relationship between each climate variable and GPP_Topt was examined by polynomial regression and localized polynomial regression (LOESS). We found that GPP_Topt-water availability response function is nonlinear saturating and GPP_Topt-energy response function is concave down. We estimated the saturation point
166 of water availability and turning points of energy using breaking point analysis with R package "segmented".
167

168 We analyzed the interaction between climate variables and DI as well as vegetation types by analysis of variances (ANOVA). Rolling window analysis was applied to climate variables to investigate the effects of DI on the partial slope of GPP_Topt to climate variables with window size of 90 sites. We first sorted the 326 sites by DI. Then the mean DI was calculated for every neighboring 90 sites and a multivariate regression was performed within each group with GPP_Topt as response variable and SM, VPD, MAT and GSR as explanatory variables. By testing with different sites of moving window, the 90 sites moving - window allowed a sufficient sample size and most robust goodness of fit for the regression analysis although the results were similar among different sites of moving windows. Based on previous analysis that groups the 326 sites by DI, within each DI group, the function between climate variables and GPP_Topt is linear except for GSR. Thus we used the following function in each 90 neighboring sites.
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180

181 GPP_Topt = f(SM, VPD, MAT, GSR, GSR², GSR³)

182 The responses of GPP_Topt to each climate variable were considered as the effect
183 of each climate variable with other climate variables controlled. Then we plotted the
184 partial coefficients derived from this function against the average DI of the
185 corresponding sites. R package "zoo" was used to perform the rolling window analysis.
186 Then we tested the effects of vegetation types on GPP_Topt using the function below:

187 GPP_Topt = f((SM, SM², VPD, MAT, GSR, GSR², GSR³)*vegetation types)
This function was then used to predict the global distribution of current GPP_Topt.

The average MAT, SM, VPD, GSR and DI are calculated for each vegetation type to evaluate the climate preference (Yi and Jackson, 2021). The sensitivities of GPP_Topt to SM (SMsen) and MAT (MATsen) were estimated for each vegetation types. The normalized GPP_Topt of each vegetation type is calculated by setting climate variables at the average level (SM=345mm, VPD=0.78 kPa, MAT=9.6 °C, GSR=13.4 MJ m⁻² d⁻¹). Principle component analysis (PCA) was used to investigate the relation between climate preference and the sensitivity of GPP_Topt to climate variables as well as normalized GPP_Topt among vegetation types.

The temporal variation of GPP_Topt in response to MAT and MAP was investigated using linear mixed-effect model with R package "nlme". Site was treated as random effect, allowing both slope and intercept of regression to vary between sites. Sites that have more than five years' data were used in the analysis (Fig. S2). We divided sites into water-limited (red) and energy-limited (blue) by DI. Note that neither energy nor water availability explained GPP_Topt well when the dryness index was between 0.77-1.06 (Fig. S3) and it is difficult to define whether these sites are water-limited or energy-limited. Thus sites with dryness index between 0.77-1.06 were excluded from the analysis to avoid confusion (Fig. S3). We end up with 33 sites and 385 site-year data for energy-limited sites, 27 site and 252 site-year data for water-limited sites.

All statistical analyses were performed using R x64 3.3.1 for Windows at α level=0.05. Graphs were constructed using package "ggplot2".
210 **3 Results and Discussions**

211 **3.1 Nonlinear control of climate variables over GPP_Topt**

212 Soil moisture (SM), global solar radiation (GSR), mean annual temperature
213 (MAT) and air vapor pressure deficit (VPD) explained 47% of the spatial variation in
214 GPP_Topt (Fig.2, Table S1). Our ridge regression analysis suggested that mean annual
215 precipitation (MAP), growing season precipitation (GSP) and dryness index (DI) are
216 lurking variables for GPP_Topt (Table S1). Soil moisture was the most important
217 climate variable for controlling GPP_Topt, explaining 36% of the spatial variation by
218 itself (Fig. 2a, Fig. S4, Table S2). GPP_Topt linearly increased with soil moisture but
219 plateaued when soil moisture is larger than 353 ± 39 mm and maintained a constant
220 GPP_Topt at the rate of 8 g C m⁻² d⁻¹ (Fig. 2a). GPP_Topt-precipitation function showed
221 a similar non-linear saturation pattern and the saturation points for growing season
222 precipitation and mean annual precipitation were 306 ± 39 and 804 ± 55 mm,
223 respectively (Table S2). Similar relationship is observed between aboveground net
224 primary productivity and precipitation across large spatial scales (Luo et al., 2017).
<figure><img src="image_3.png" /><figcaption>Figure 2 Effects of soil moisture, global solar radiation (GSR), vapor pressure deficit (VPD) and mean annual temperature (MAT) on GPP\_T<sub>opt</sub>. GPP\_T<sub>opt</sub> (g C m<sup>-2</sup> d<sup>-1</sup>) is plotted against soil moisture (SM, mm), global solar radiation (GSR, MJ m<sup>-2</sup> d<sup>-1</sup>), vapor pressure deficit (VPD, kPa) and mean annual temperature (MAT, °C). The blue line is the weighted least squares fit determined by a nearest neighbor algorithm (LOESS) and light green shadow represents the 95% confidence interval. The vertical dashed line indicates the turning points of each climate variables and the grey shadow is the 95% confidence interval calculated by segmented regression. The horizontal dashed line indicates the peak GPP\_T<sub>opt</sub> at optimum climate conditions.</figcaption></figure>

Temperature and global solar radiation (GSR) represent thermal and light energy respectively. Vapor pressure deficit (VPD) is a combined effect of thermal energy and water. GPP\_T<sub>opt</sub>-energy response curves were nonlinear concave down across space. The turning points of GSR, MAT, and VPD were 13.5 MJ m<sup>-2</sup> d<sup>-1</sup>, 8.5 °C and 0.8 kPa, respectively (Fig. 2b-d, Table S2). These turning points of energy delineate a low-energy range over which GPP\_T<sub>opt</sub> increased with increasing energy and a
high-energy range over which GPP_Topt decreased with excess energy. Vcmax is modeled to linearly increase with light, which explains overestimated photosynthetic capacity in wet, tropical forest since a linear function fails to capture the suppression of photosynthetic capacity at high light level (Smith et al., 2019). During the periods of global dimming, plants photosynthesized more efficiently and sequestrated more carbon (Wild, 2009), agreeing with our results since most sites locate in a radiation range that further increase in GSR suppresses GPP_Topt (Fig. 2b).

## 3.2 The effects of climate variables depend on the dryness condition

The existence of the thresholds of soil moisture indicates a transition from water-controlled stage to energy-controlled stage for GPP_Topt. Therefore, the effects of soil moisture, light, temperature and air dryness depended on dryness conditions, as indicated by the significant interaction between these climate variables and DI (Table 1). We divided sites into energy-limited group and water-limited group (Fig. 3) based on the balance between water demand (PET, potential evapotranspiration) and water supply (P, precipitation), using the same concept of Budyko's curve (Budyko, 1961; Budyko et al., 1974) that well-describes evapotranspiration.

<table><caption>Table 1 Analysis of variance of the interaction between climate variables and dryness index. Climate variables: Soil moisture (SM, mm), Global solar radiation (GSR, MJ m⁻² d⁻¹), Growing season vapor pressure deficit (VPD, kPa), Dryness index (DI, PET/P), Mean annual temperature (MAT, °C), Growing season precipitation (GSP, mm yr⁻¹), Growing season temperature (GST, °C), Mean annual precipitation (MAP, mm yr⁻¹). GPP_Topt is log transformed.</caption><thead><tr><th></th><th>Sum Sq</th><th>Mean Sq</th><th>F value</th><th>P</th><th></th></tr></thead><tbody><tr><td>SM</td><td>41.43</td><td>41.43</td><td>167.17</td><td>&lt;0.001</td><td>**</td></tr></tbody></table>
<table><tr><td>VPD</td><td>5.75</td><td>5.75</td><td>23.2</td><td>&lt;0.001</td><td>**</td></tr><tr><td>MAT</td><td>3.37</td><td>3.37</td><td>13.58</td><td>&lt;0.001</td><td>**</td></tr><tr><td>GSR</td><td>2.29</td><td>2.29</td><td>9.23</td><td>0.003</td><td>*</td></tr><tr><td>DI</td><td>0</td><td>0</td><td>0.01</td><td>0.913</td><td>N.S</td></tr><tr><td>SM*DI</td><td>2.09</td><td>2.09</td><td>8.42</td><td>0.004</td><td>*</td></tr><tr><td>VPD*DI</td><td>0.98</td><td>0.98</td><td>3.95</td><td>0.048</td><td>*</td></tr><tr><td>MAT*DI</td><td>5.44</td><td>5.44</td><td>21.93</td><td>&lt;0.001</td><td>**</td></tr><tr><td>GSR*DI</td><td>2.31</td><td>2.31</td><td>9.31</td><td>0.002</td><td>*</td></tr></table>

265

The response function of GPP_Topt to soil moisture, air temperature and vapor pressure deficit became linear within water- and energy-limited group (Table 2). Thus, we were able to extract the partial linear slope of GPP_Topt to soil moisture, air dryness and mean annual temperature along the dryness gradients using moving window analysis. Variations caused by solar radiation were represented by a third-degree polynomial function since GPP_Topt-GSR response curve is still non-linear within water-limited and energy-limited groups (Table 2).

<table><caption>Table 2 Influences of climate variables in energy-limited (DI < 1) versus water-limited (DI > 1) regions. Soil moisture (SM, mm), Global solar radiation (GSR, MJ m⁻² d⁻¹), Growing season vapor pressure deficit (VPD, kPa), Dryness index (DI, PET/P), Mean annual temperature (MAT, °C), Growing season precipitation (GSP, mm yr⁻¹), Growing season temperature (GST, °C), Mean annual precipitation (MAP, mm yr⁻¹). GPP_Topt is log transformed. Coefficients that are significant at α=0.05 level are bolded.</caption><thead><tr><th>Group</th><th></th><th>Slope</th><th>SE</th><th>t-value</th><th>P</th><th>R<sup>2</sup></th><th>AIC</th></tr></thead><tbody><tr><td>Energy-limited</td><td>SM<sup>1</sup></td><td>0.55</td><td>0.61</td><td>0.90</td><td>0.368</td><td>N.S</td><td>0.28</td><td>194</td></tr><tr><td>DI &lt; 1</td><td>SM<sup>2</sup></td><td>-0.43</td><td>0.56</td><td>-0.77</td><td>0.442</td><td>N.S</td><td></td><td></td></tr><tr><td>n=143</td><td>GSR<sup>1</sup></td><td>-0.54</td><td>0.85</td><td>-0.64</td><td>0.521</td><td>N.S</td><td></td><td></td></tr></tbody></table>

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<table><tbody><tr><td></td><td>GSR<sup>2</sup></td><td>-1.55</td><td>0.58</td><td>-2.67</td><td>0.008</td><td>*</td><td></td><td></td></tr><tr><td></td><td>GSR<sup>3</sup></td><td>1.90</td><td>0.52</td><td>3.67</td><td>&lt;0.001</td><td>**</td><td></td><td></td></tr><tr><td></td><td>GST</td><td>0.01</td><td>0.02</td><td>0.26</td><td>0.80</td><td>N.S</td><td></td><td></td></tr><tr><td></td><td>MAT</td><td>0.01</td><td>0.01</td><td>0.66</td><td>0.51</td><td>N.S</td><td></td><td></td></tr><tr><td></td><td>VPD</td><td>0.37</td><td>0.33</td><td>1.11</td><td>0.27</td><td>N.S</td><td></td><td></td></tr><tr><td rowspan="2">Water-limited<br>DI &gt; 1<br>n=183</td><td>SM<sup>1</sup></td><td>2.10</td><td>0.68</td><td>3.11</td><td>0.002</td><td>*</td><td>0.53</td><td>268</td></tr><tr><td>SM<sup>2</sup></td><td>-0.84</td><td>0.53</td><td>-1.57</td><td>0.118</td><td>N.S</td><td></td><td></td></tr><tr><td></td><td>GSR<sup>1</sup></td><td>-4.45</td><td>0.98</td><td>-4.52</td><td>&lt;0.001</td><td>**</td><td></td><td></td></tr><tr><td></td><td>GSR<sup>2</sup></td><td>-1.91</td><td>0.59</td><td>-3.24</td><td>0.001</td><td>*</td><td></td><td></td></tr><tr><td></td><td>GSR<sup>3</sup></td><td>0.97</td><td>0.55</td><td>1.77</td><td>0.078</td><td>N.S</td><td></td><td></td></tr><tr><td></td><td>GST</td><td>0.01</td><td>0.02</td><td>0.36</td><td>0.718</td><td>N.S</td><td></td><td></td></tr><tr><td></td><td>MAT</td><td>0.04</td><td>0.01</td><td>3.35</td><td>0.001</td><td>**</td><td></td><td></td></tr><tr><td></td><td>VPD</td><td>-0.51</td><td>0.16</td><td>-3.22</td><td>0.002</td><td>*</td><td></td><td></td></tr></tbody></table>

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GPP_T<sub>opt</sub> linearly increased with soil moisture (P = 0.002, Table 2) and became increasingly more sensitive to soil moisture along the dryness gradients (Fig. 3a).

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However, the sensitivity to water peaked when dryness index was around 2.1 - 2.4 and decreased with further increase in aridity. Vegetation types that occur in extremely arid region have relatively low productivity and highly adapted mechanisms to cope with extreme drought compared with semiarid regions, causing the reduced sensitivity of GPP_T<sub>opt</sub> to soil moisture when dryness index was larger than 2.4 (Liu et al., 2018; Liu et al., 2020). GPP_T<sub>opt</sub> linearly increased with soil moisture across water-limited sites and did not affect GPP_T<sub>opt</sub> across energy-limited sites (Table 2, Fig. 3a).

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Consequently, a nonlinear saturation function was observed between GPP_T<sub>opt</sub> and soil
moisture across the 326 sites, supporting the double asymmetric model of the
controlling of water availability over carbon cycles (Knapp et al., 2017). The linear
increase in GPP_Topt with soil moisture across water-limited sites is consistent with the
linear increment of carbon process with water availability in grassland that often occurs
in water-limited habitat (Zhou et al., 2009). Vcmax model excludes the influence of soil
moisture or precipitation (Smith et al., 2019) because its parameters are derived from
greenhouse studies that did not consider the influences from drought. Thus, the current
model might overestimate GPP_Topt in water-limited regions. Since soil moisture is the
most important climate variable for controlling GPP_Topt (Fig. S4), it is imperative to
include soil moisture into the model for estimating GPP_Topt.

<figure><img src="image_4.png" /><figcaption>Figure 3 Dependence of the sensitivity of GPP_Topt to climate variables on the dryness gradients. Violin plots of the sensitivity of GPP_Topt to soil moisture (SM) (a), mean annual temperature (MAT) (b), and vapor pressure deficit (VPD) (c)</figcaption></figure>
across the dryness gradients (PET/P). White dots indicate the median values, black boxes cover the interquartile range, and thin black lines reach the 5th and 95th percentiles.

308

High air temperature enhanced GPP_Topt (P=0.012, Table S1, Fig. 3b), similar to the leaf model that Vcmax increases with air temperature (Smith et al., 2019).

Warming-induced air dryness enhanced GPP_Topt in very mesic regions but suppressed GPP_Topt in dry regions (Fig. 3c). Air dryness consistently reduced GPP_Topt across sites with a dryness index larger than 1.5 (Fig. 3c), which is also defined as dryland by UNESCO (Unesco, 1979). Ecosystem carbon process is generally depressed in water-logged environment (Taylor et al., 2017), explaining air dryness caused stimulation of GPP_Topt in mesic areas. GPP_Topt is withheld by air dryness in water-limited regions, consistent with a recent study reporting that increased air dryness reduces the global vegetation growth in the new era (Yuan et al., 2019). High temperature induced increase in vapor pressure deficit is also accused for faster mortality of tree seedlings common to the forest-grassland ecotone (Will et al., 2013).

However, the leaf-level model assumes an increase of Vcmax with VPD throughout the whole range of VPD (Smith et al., 2019). Leaf-level knowledge about photosynthetic capacity is from greenhouse studies that usually do not impose drought stress, which possibly explains the discrepancy between leaf-level and ecosystem-level knowledge.

Thus, only the most mesic sites benefit from increasing VPD (Fig. 3c). Direct upscaling of leaf-level knowledge to ecosystem level will overestimate the carbon uptake capacity in water-limited regions.
GPP_Topt is determined by and increases with water or energy, depending on which one is more limiting. The strong climate control of GPP_Topt (R²: 40%-50%, Fig. S3) supports photosynthetic coordination theory that photosynthetic capacities are controlled by climate, instead of soil nitrogen (Prentice et al., 2013; Smith et al., 2019). However, neither energy nor water availability explained GPP_Topt well when water-limit and energy-limit reached equilibrium (dryness index between 0.77-1.06, Fig. S3). The decoupling of climate variables and GPP_Topt was reflected by the oscillation of the slopes when dryness index was around 1 (Fig.2). Other factors, such as soil nutrients and microbes, possibly come into play when energy-limit and water-limit reach equilibrium.

None of the previous study has ever revealed that the major climate variable for GPP_Topt differs between water-limited and energy-limited sites. Therefore, ignoring the effects of dryness causes bias because the estimated parameters would depend on the ratio of water-limited sites to energy-limited sites. In addition, a model generated for the whole globe may work well in mesic region but not in drylands, or vice versa. Grouping sites based on the most limiting factor and applying different algorithms more realistically represents the nature process, as a result, improving the accuracy of ESMs' projection of carbon influx in the future.

### 3.3 Temporal variation in GPP_Topt as influenced by water- and energy-limitation
Dryness affects the temporal variation in GPP_Topt in response to mean annual temperature (MAT) and mean annual precipitation (MAP). Inter-annual change in MAT does not affect the temporal variation in GPP_Topt in energy-limited sites yet reduces GPP_Topt by 0.17 g C m⁻² d⁻¹ per 1 °C increase in MAT (P = 0.01, Fig. 4a, c). GPP_Topt tends to be higher in wetter years in both energy- and water-limited sites (Fig. 4b, d). However, water-limited sites are about 1.6 times more sensitive to changes in precipitation than energy-limited sites. Consequently, drought causes greater reduction in carbon uptake in water-limited regions. Given the relationship between carbon uptake and GPP_Topt, energy-limited sites are more likely to maintain a stable carbon uptake across years while water-limited sites are more susceptible to warming or drought. This rationale is in agreement with a recent report that water-limited regions are responsible for most of the inter-annual variation (IAV) in atmospheric CO₂ growth rate. The predicted wide-spreading drought by the next century (Girvetz and Zganjar, 2014) will turn many energy-limited ecosystems into water-limited ecosystems, indicating a larger IAV of atmospheric CO₂ growth rate in the future.
<figure><img src="image_5.png" /></figure>

Figure 4 Relationship of temporal variation in GPP_Topt with mean annual temperature (MAT, °C) and mean annual precipitation (MAP, mm) depends on dryness. Mean annual temperature and precipitation's effects on the temporal variation in GPP_Topt in 33 energy-limited sites (a, b). Mean annual temperature and precipitation's effects on the temporal variation in GPP_Topt in 27 water-limited sites (c, d). There are 385 site-year and 252 site-year data for energy-limited and water-limited sites, respectively. Black dashed lines are the fixed effect linear regression slope between sites from the mixed-effect model; colored lines indicate the temporal patterns within sites. Climate anomaly is calculated by deducing the mean value of each site from the value of each year of that site.

## 3.4 The response of GPP_Topt to climate variables also depends on vegetation types

Incorporating vegetation types increased R² from 47% to 67% (Table S2, Table S3), substantially improving the prediction power of the model. The sensitivity of GPP_Topt to MAT and soil moisture varied among vegetation types (Fig. 5). Warming
tended to increase GPP_Topt in vegetation types that inhabit wetter climate. Vegetation types that inhabit drier climate, such as grassland, are more responsive to changes in soil moisture. We normalized GPP_Topt by excluding the influence of climate variables.

The normalized GPP_Topt still varied among vegetation types (P < 0.001, Table S3), probably due to evolutionary adaptation to local environment (Huang et al., 2018).

Shrub and Savanna, which inhabited the most arid niche, showed the lowest GPP_Topt even with climate variables adjusted to the same value (Fig. 5c). Our finding indicates that when a natural ecosystem degraded to a less productive vegetation type, carbon sequestration is suppressed even if climate conditions go back to the previous conditions. Genetic selection or human management such as irrigation and fertilization possibly explains the higher normalized GPP_Topt in cropland (Fig. 5c), agreeing with previous studies that expanding cropland increase in maximum NDVI over time (Huang et al., 2018) and the land-use management in China and India lead the greening of earth (Chen et al., 2019).
<figure><img src="image_6.png" /><figcaption>Figure 5 Climatic preference of habitat among vegetation types in relation to the spatial sensitivity of GPP_Topt. The sensitivity of GPP_Topt to mean annual temperature (MATsen) in relation to the climatic preferences of vegetation types (a). The sensitivity of GPP_Topt to soil moisture (SMsen) among vegetation types in relation to the climatic preferences of vegetation types (b). Normalized GPP_Topt in relation to the climatic preferences of vegetation types (c). Principle component analysis (PCA) is used to investigate the relationship between climatic preference of vegetation types and MATsen, SMsen, and normalized GPP_Topt. Normalized GPP_Topt is calculated by adjusting MAT, GSR, SM and VPD to the mean level of the dataset (see material and method). The angle of two arrows indicates the relationship of the two variables.</figcaption></figure>

## 3.5 Global distribution of GPP_Topt

We predicted current global distribution of GPP_Topt based on temperature, light, soil moisture, air dryness and vegetation types (Fig. S5). The global average GPP_Topt
is 3.6 g C m⁻² d⁻¹, with spatial variations that echo the global distribution of GPP perfectly (Beer et al., 2010). Highest GPP_Topt occurs along the equator, followed by humid and temperate regions such as the great lake area in the U.S, southeast China and Europe (Fig. 6). Water deficiencies constrained GPP_Topt (Fig. 6) and GPP (Beer et al., 2010) in subtropical region, disagreeing with the leaf-level model that predicts a high Vcmax in the same region (Smith et al., 2019). The discrepancies between ecosystem and leaf knowledge contribute to different projections of carbon uptake capacity. The lack of constraining from water contributes to overestimated Vcmax in water-limited regions (Smith et al., 2019). We also found GPP_Topt to be negative related with VPD in water-limited regions while modelled Vcmax continuously increases with VPD throughout the whole range (Smith et al., 2019). Furthermore, GPP_Topt-radiation response curve is non-linear concave down while Vcmax is modeled to linearly increase with irradiance (Smith et al., 2019). A better representation of the nonlinear relationship between carbon uptake processes and light helps to reduce the uncertainty in the prediction of carbon fluxes (Nicole and Gordon, 2017).

<figure><img src="image_7.png" /></figure>
Figure 6 Globally predicted present GPP_Topt. GPP_Topt is computed using global solar radiation, mean annual temperature, growing season precipitation, soil moisture and vegetation types as predictors with resolution of 0.1°×0.1°. GPP_Topt is regressed on latitude using generalized additive model (GAM), as shown in the right panel.

## 4 Conclusions

We found a strong regulation of the maximum gross primary productivity

(GPP_Topt) across space by soil moisture, light, temperature, air dryness and

vegetation types. Responses of GPP_Topt to climate variables depend on dryness

gradients. GPP_Topt is limited by temperature under wet condition while GPP_Topt is

limited by water availability under dry condition. The concept of water and energy

limits, which originates from researches concerning evapotranspiration, applies to the

spatiotemporal variation in GPP_Topt. Global warming only reduces carbon uptake

capacity of water-limited sites due to warming-aggravated water deficiencies and air

dryness. Energy-limited ecosystems are able to maintain its carbon uptake capacity or

even benefit from warming. The responses of GPP_Topt to climate variables also

depend on vegetation types. GPP_Topt tends to be higher in vegetation types with humid

climates and is more likely to benefit from a warmer climate without water deficit

stress. These knowledge does not only improve our understanding of the

photosynthetic processes at the ecosystem level, but also aid the modelers to improve

the accuracy of coupled climate-carbon cycle process model.
454 Acknowledgments

455 This work is financially supported by the National Key Technology R & D Program
456 of China (2018YFA 0606102), National Natural Science Foundation of China
457 (31988102), and the international Collaboration Program of Chinese Academy of
458 Sciences (131A11KYSB20180010) granted to S.N. We used the eddy covariance data
459 of the FLUXNET community by the following networks: AmeriFlux, AfriFlux,
460 AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux,
461 Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux-TERN,
462 TCOS-Siberia, Swiss FluxNet and USCCC. The ERA-Interim reanalysis data were
463 provided by ECMWF and processed by Laboratoire des sciences du climat et de
464 l'environnement (LSCE). The FLUXNET eddy covariance data processing and
465 harmonization was carried out by the European Fluxes Database Cluster and the
466 AmeriFlux Management Project (with support by European Union H2020 projects
467 and U.S. Department of Energy Office of Science, respectively), with contributions
468 from the Carbon Dioxide Information Analysis Center, ICOS Ecosystem Thematic
469 Centre, and OzFlux, ChinaFlux, and AsiaFlux offices.

470 Data Accessibility Statement

471 All FLUXNET data can be downloaded at: https://fluxnet.fluxdata.org. Climate
472 variables of each site were obtained from WorldClim (https://www.worldclim.org/).
473 Humidity index was obtained from FAO dataset (https://www.fao.org/home/en/). Soil
474 moisture is obtained from CPC soil moisture data provided by the NOAA/OAR/ESRL

475 PSD, Boulder, Colorado, USA, from their Web site at https://www.esrl.noaa.gov/psd/.

476

477 **Conflict of interest**

478 The authors declare no competing financial interests.

479

480

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Graphic abstract

<figure><img src="image_8.png" /></figure>