Introduction

Terrestrial vegetation absorbs around one-third of anthropogenic carbon dioxide (CO2) emissions through photosynthesis1,2. This is known as gross primary productivity (GPP), and represents the largest carbon flux between land and atmosphere3,4. It has been suggested that soil moisture critically influences plant photosynthesis5,6, yet accurately characterizing the impact of soil moisture on GPP is notoriously challenging in Earth system models7,8, leading to large uncertainties in assessing carbon-climate feedbacks9. A deep understanding of the response and acclimation of GPP to soil moisture is increasingly essential5,10.

In general, an increase in soil moisture can enhance GPP, as water is a primary limiting factor for plant photosynthetic processes5,7,11. As a result, most current models consider the stress of water deficit on GPP by implementing an empirical function (β) related to soil moisture5,9. The value of β ranges from 0 to 1, with β = 1 representing maximum photosynthesis without any soil moisture limitation9,12. Nevertheless, more and more recent studies observed a depressive effect of excessive soil water on GPP13,14,15,16, even in drylands that are typically water-deficient8. That depression is proposed to occur likely due to progressive soil anoxia and nutrient leaching, which restrict microbial and root metabolism and lower plant nutrient absorption, thereby impairing photosynthetic activity17,18,19,20,21,22. In this context, the GPP variations mediated by soil moisture should be expected as a unimodal (or hump-shaped) function with an apparent optimum soil moisture (\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), corresponding to maximum GPP; Fig. 1). \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) indicates the transition of soil moisture effects on GPP from positive to negative. Despite this GPP-soil moisture framework is conceptually established13,15, the quantification of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) remains limited. To date, there has been no observation-based assessment of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) at the global scale. Even less is known about whether ecosystem GPP can acclimate to changes in soil moisture via shifting \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\). Recognizing these is pertinent to improve model performance in simulating carbon cycle and to develop climate change mitigation policies, given that most land areas are projected to experience a significant hydrological variability5,23,24.

Fig. 1: Conceptual diagram of relationship between soil moisture and gross primary productivity (GPP).
figure 1

The green vertical line indicates optimum soil moisture for GPP (\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)). An increase in soil moisture increases GPP when the soil moisture is below \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), but decreases GPP when the soil moisture is above \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\).

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To quantify \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) directly, we use eddy covariance observations from FLUXNET datasets and derive the daily GPP-soil moisture response curves at globally distributed 143 sites. We then examine the relationship between soil moisture and \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) using eddy covariance observations, along with a field manipulation experiment. The complement of experiment is important, because it can systematically examine the causal effect of soil moisture on \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\). We address two central research questions: (i) whether \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) exists widely and (ii) how \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) changes with soil moisture.

Results

Widespread presence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)

We determined \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) by fitting a concave quadratic model of soil moisture to GPP at daily scale, only when this model showed a superior performance (i.e., lower Akaike Information Criterion) than a saturation model (Supplementary Fig. 1; see Methods), along with statistically significant model parameters (P ≤ 0.05; Supplementary Fig. 2). This detected presence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) at 108 sites covering large areas and most vegetation types from a total of 143 sites in our dataset (Fig. 2; Supplementary Fig. 3 and Table 1). Across the 108 sites, \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) ranged from 5.8 to 56.9%, with median of 20.9%. We then selected a representative response curve from each vegetation type (Fig. 2b), which indicated that GPP elevated with soil moisture but depressed when the soil moisture is above \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\). The paired t-test showed a non-significant difference between the Spearman’s correlation coefficients of soil moisture and GPP without and with controlling for air temperature, vapor pressure deficit, and incoming shortwave radiation (Supplementary Fig. 4; see Methods), suggesting that the air temperature, vapor pressure deficit, and incoming shortwave radiation had a negligible effect on the nonlinear relationship between GPP and soil moisture. Hence, the observed transition from an increase to a decrease in GPP with increasing soil moisture (i.e., the presence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)) was not caused by these confounding factors.

Fig. 2: Distribution of optimum soil moisture for gross primary productivity (\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)) derived from FLUXNET sites.
figure 2

a Location of the 108 sites used in this study with detected \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\). The original map is from spData package in R. b Response of gross primary productivity (GPP, ln-scaled) to daily soil moisture at the 10 sites from 10 different vegetation types. The solid curve indicates the fitting of concave quadratic model, and the dotted line represents the detected \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\). Site name is shown in parentheses after each vegetation type. The vegetation types are as follows: CRO, croplands; CSH, closed shrublands; DBF, deciduous broadleaf forests; EBF, evergreen broadleaf forests; ENF, evergreen needle-leaf forests; GRA, grasslands; MF, mixed forests; OSH, open shrublands; SAV, savanna; WSA, woody savanna. ***, P ≤ 0.001; **, P ≤ 0.01; *, P ≤ 0.05.

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Dependence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) on soil moisture

We tested the relationship between growth soil moisture (SMgrowth, measured by average soil moisture during the peak growing season; see Methods) and \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across sites using linear regression analysis. The results showed that \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) was positively correlated with SMgrowth across the 108 sites, with a linear regression slope of 0.92 (Fig. 3a), and this relationship still held even when sites with a very strong GPP-soil moisture relationship were selected (Supplementary Fig. 5). It reflects the spatial acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change, and the slope indicates the acclimation pace. This acclimation was also observed across different vegetation types, with a slope of 0.75 (Fig. 3b). Consistently, relative weight analysis further confirmed that \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) was majorly determined by SMgrowth (Supplementary Figs. 6 and 7), even accounting for other potential co-varying factors including air temperature, incoming shortwave radiation, vapor pressure deficit, soil temperature, total precipitation, leaf areas index, soil organic carbon, soil bulk density, soil sand fraction, soil cation exchange capacity, and soil pH.

Fig. 3: Acclimation pace of optimum soil moisture for gross primary productivity (\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)) to cope with spatial variation of growth soil moisture (SMgrowth).
figure 3

a Linear regression of SMgrowth to \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across 108 sites. b Linear regression of SMgrowth to \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across vegetation types. Point with error bar indicates mean with standard error. Point size is proportional to the number of sites in each vegetation type. CRO, croplands, n = 10; CSH, closed shrublands, n = 2; DBF, deciduous broadleaf forests, n = 18; EBF, evergreen broadleaf forests, n = 9; ENF, evergreen needle-leaf forests, n = 29; GRA, grasslands, n = 21; MF, mixed forests, n = 7; OSH, open shrublands, n = 4; SAV, savanna, n = 5; WSA, woody savanna, n = 3. Solid line and shaded area indicate the linear regression fit and its 95% confidence interval respectively. ***, P ≤ 0.001; **, P ≤ 0.01; *, P ≤ 0.05.

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We also revealed the relationship between \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) and SMgrowth at individual sites where at least 5 years of data were available to represent the temporal acclimation (Supplementary Table 2). We found that SMgrowth significantly increased \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) at temporal scale with median slope of 0.91, but its effect interacted with site, indicting geographically divergence in acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change (Fig. 4a, b). The relative weight analysis showed that precipitation was most responsible for this divergence (Supplementary Figs. 8 and 9; see Methods). Specifically, the stimulation of SMgrowth on \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) was larger in sites experiencing less precipitation (Fig. 4c), implying that dry ecosystems could acclimate more quickly to water changes than wet ecosystems.

Fig. 4: Acclimation pace of optimum soil moisture for gross primary productivity (\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)) to cope with temporal variation of growth soil moisture (SMgrowth).
figure 4

a Linear regression of SMgrowth to \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across years at each site with ≥ 5 years of data (color lines). Each point represents one site-year data, with data from the same site being in the same color. SMgrowth, site, and SMgrowth×site indicate the effects of SMgrowth, site, and their interaction on \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) respectively. b Probability density of the SMgrowth-\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) slope. The black dotted line is the median (0.91), and the gray dotted line is the zero. c Linear regression of precipitation (ln-scaled) to SMgrowth-\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) slope, with each point representing the slope at a site. Error bar represents the standard error on each slope. Solid line and shaded area indicate the linear regression fit and its 95% confidence interval respectively. ***, P ≤ 0.001; **, P ≤ 0.01; *, P ≤ 0.05.

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To further verify the causal effect of SMgrowth on \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), we derived the GPP-soil moisture relationships and \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) at different precipitation levels in a field manipulation experiment (Fig. 5a and b; see Methods). We found that \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) showed significant increasing trend over increasing SMgrowth across precipitation treatments (Fig. 5c), consistent with the eddy covariance results. At the same time, an increase in SMgrowth significantly decreased plant biomass allocation to belowground (fBNPP) (Supplementary Fig. 10). This plant parameter was significantly correlated with \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) (Supplementary Fig. 11), suggesting that SMgrowth shifted \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) mainly via changing fBNPP along the precipitation gradient in this experiment.

Fig. 5: Effect of growth soil moisture (SMgrowth) on optimum soil moisture for gross primary productivity (\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)) derived from a field experiment manipulating precipitation.
figure 5

a View of the experimental plots. b Quadratic relationships between soil moisture and gross primary productivity (GPP, ln-scaled). The colored dotted lines indicate the detected \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) in differential precipitation levels (1/12P, 1/4P, 1/2P, 3/4P, P and 5/4P, where P was the annual precipitation). c Linear regression of SMgrowth to \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across precipitation levels. Solid line and shaded area indicate the linear regression fit and its 95% confidence interval respectively. ***, P ≤ 0.001; **, P ≤ 0.01; *, P ≤ 0.05.

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Discussion

Several studies have shown examples of an apparent optimum soil moisture at which GPP reaches the maximum (\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\))13,15. However, it is still unclear whether \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) exists globally and what the underlying drivers are, impeding our understanding and predictive power of terrestrial biosphere feedback to a changing climate. We used global eddy covariance observations to detect the widespread \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) over large geographical regions spanning from 37.4° S to 71.6° N and 121.6° W to 148.2° E. We found that the distribution of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) was primarily shaped by local growth soil moisture (SMgrowth) condition, with drier ecosystems having lower \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) than wetter ecosystems.

The widespread \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) indicates that the minimum GPP usually occurs at both soil moisture extremes, while the maximum GPP at moderate soil moisture. When exposed to water-deficient conditions, plants reduce their water loss to avoid hydraulic failure by closing stomata, thereby suppressing photosynthesis25,26. Drought can further restrict photosynthesis by enhancing photorespiration and then producing reactive oxygen species (ROS), which has been reported to damage the activity of essential photosynthetic enzymes (e.g., Rubisco)27,28. Excessive soil water limits plant photosynthesis possibly via aggravating soil anoxia that decreases the metabolic activity of plant roots and aerobic microorganisms (such as bacteria involved in ammonification and nitrification), and via inducing nutrient leaching that exacerbates nutrient limitation in plant photosynthetic processes17,18,19,20,21,22,29,30. Thus, the \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) arises from the intertwined effects of physical, physiological, and biochemical processes. Moreover, we acknowledge that the eddy covariance-observed transition from an increase to a decrease in GPP with increasing soil moisture might be caused not only by soil moisture itself, but also by other potentially confounding environmental factors (e.g., light and heat)6,31,32. But we found that the nonlinear relationship between soil moisture and GPP remained consistent after controlling for air temperature, vapor pressure deficit, and incoming shortwave radiation (Supplementary Fig. 4), suggesting that the existence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) was unlikely caused by these confounding factors. This was further corroborated by a recent study showing that the correlation coefficient of soil moisture and GPP did not vary despite accounting for CO2 and climate conditions6.

The tight link between \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) and SMgrowth potentially reflects the hydrological acclimation of vegetation. For example, when SMgrowth increases, plants upregulate their \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) in order to obtain more GPP returns. In contrast, when SMgrowth decreases, the downregulated \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) can alleviate plant damage caused by drought in terms of GPP loss. The explanation is that a decrease in SMgrowth starts to inhibit GPP only when the SMgrowth falls below \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), so a lower \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) means a higher threshold response to soil water deficit. To the best of our knowledge, this study is among the first to reveal the acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change.

We further found this acclimation to be scale-dependent. In particular, \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) generally showed a lower acclimation pace over time than across space. This suggests that spatial acclimation should not be conflated with temporal acclimation. The spatial acclimation reflects the ability of vegetation to cope with a changing environment through long-term changes in genetic material, community structure, and distribution over generations33,34,35. Nevertheless, the temporal acclimation is mainly based on reversible adjustments in plant morphology and physiology, as well as transient changes in ecosystem structure and functioning, without these long-term mechanisms33,34. Thus, the space-for-time substitutions proposed in previous studies could not be a valid approach for predicting vegetation acclimation to future climate change (e.g. 31,36), and continuous monitoring and long-term manipulation experiments are necessary10.

Interestingly, the temporal acclimation showed divergent paces among different sites, with precipitation being the dominant driver. The \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) exhibited a greater response to SMgrowth in sites with lower precipitation. This implies that soil drought would limit GPP more in wet than in dry ecosystems. Specifically, when SMgrowth decreases, a higher acclimation pace in drier ecosystems can result in a larger downregulation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), meaning a stronger resistance to drought. These findings challenge a popular hypothesis that arid and semi-arid ecosystems are more sensitive to soil water deficit than more mesic ecosystems5,10,37,38. Nevertheless, questions remain on what mechanisms accelerate the acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change in dry ecosystems. Further examination in future network control experimental studies is necessary, such as International Drought Experiment (IDE)39.

It should be noted that the acclimation observed by eddy covariance measurements was based on evidence of correlation between SMgrowth and \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), without indicating causal effect of SMgrowth on \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\). To this end, we further used a field experiment, which only manipulated water and kept other factors constant40. We found that there was a lower \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) in treatments with lower SMgrowth. Among the 8 biotic and abiotic factors examined, plant biomass allocation is shown to be the primary mechanism responsible for this acclimation. Specifically, decreased SMgrowth reduced \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) mainly by increasing belowground biomass allocation. The potential explanation is that a high biomass allocation to root system not only facilitates plant communities to directly access belowground water resources but also mitigates the water loss via reducing aboveground transpiration22,41,42,43, thereby downregulating soil moisture requirement to maximize photosynthesis. Taken together, these findings provide direct experimental evidence for the acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change. That being said, whether the mechanism proposed by our experiment is also responsible for the eddy covariance-observed acclimation remains unclear. We cannot further test this issue due to the lack of corresponding datasets in eddy covariance observations.

Our study sheds light on understanding and prediction of climate-carbon feedbacks at least in a couple of ways. First, the widespread \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) suggests that extremely low and high soil moisture both can inhibit plant photosynthesis. Unfortunately, most current Earth system models only consider the stress of water deficit on plant photosynthesis by implementing an empirical function related to soil water content5,9, without representing the depressive effect of excessive soil water, which could result in an overestimation of global GPP in models. Thus, we suggest that developing alternative models that account for the existence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) has the potential to more realistically predict land carbon sequestration under climate change. Notably, this does not imply a complete rejection of the empirical function which does not consider \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), as there are still some sites where the concave quadratic model did not perform better than the saturation model (Supplementary Fig. 1). Second, the acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change has important implications for ecosystem resistance to soil drought. Previous studies that did not account for this acclimation likely exaggerated the negative effects of future drought on territorial carbon sinks (e.g. 5), especially for arid ecosystems that exhibit large acclimation pace. That being said, we only used the surface soil moisture data due to the limited measurements of deep soil moisture. Therefore, further investigation of the \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) and its acclimation is warranted in future studies that consider deeper soil moisture, especially in forest ecosystems, where plant roots are typically distributed at soil depths greater than one meter and have great potential to access groundwater resources44. Third, plant hydraulic or functional traits are critical in reflecting the acclimatation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change. As shown in our experiment, plants downregulated \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) under soil water deficit mainly by allocating more biomass to the root system.

In summary, our study provides compelling evidence for the widespread \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) and its acclimation to SMgrowth change using global eddy covariance observations and a field experiment. With decreasing SMgrowth, ecosystems tended to downregulate their \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), implying a higher threshold response to soil drought in terms of GPP loss. This acclimation would play a key role in stabilizing future land carbon sinks, as most areas are projected to have drier soils5. Our results also shed light on mechanisms by revealing the potential role of plant traits in driving the acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change. Given the importance of GPP in the global carbon cycle, our findings provide new insights for Earth system models to improve the predictive power of carbon cycling in the context of climate change.

Methods

Eddy covariance observations

To generate the GPP-soil moisture response curves, we used daily soil moisture and GPP from the eddy covariance observations provided in the FLUXNET datasets45, as the daily observations eliminate potential noise from the diurnal variation pattern of photosynthesis (such as midday depression in photosynthesis)35,46. The GPP estimates based on the nighttime partitioning method (i.e., GPP_NT_VUT_REF) were used8. Volumetric soil water content (%) was measured to determine soil moisture. The surface soil moisture data (SM_1: 0 to 10 cm, varying across sites) was used in this study, given that deeper soil moisture was only measured at a limited number of sites (<30)47. As plant responses to water variation may differ between growing and non-growing seasons, we focused only on the peak growing season, which is defined as June to August in the northern hemisphere and December to February in the southern hemisphere6,48. If >10% of 1-growing season data were missing from a site, that particular site-year was excluded from the analysis completely. We also excluded sites without soil moisture measurements and removed all wetland sites because these sites have a perched water table as well as infrequently exhibit soil moisture limitations49. These data filtering processes finally resulted in a total of 143 individual sites used in our study.

For each site-year, based on ordinary least squares, we determined \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) by fitting a concave quadratic model of soil moisture to GPP (Eq. 1), only when this model showed a superior performance (i.e., lower Akaike Information Criterion) than a saturation model (Supplementary Fig. 1), along with statistically significant model parameters (P ≤ 0.05). The concave quadratic model has been commonly used in previous studies to detect the optimal photosynthetic environment at site or global scale (e.g. 13,31,50). The saturation model indicates that GPP increases as soil moisture increases in a manner consistent with the concave quadratic model when the soil moisture is below a certain threshold, but then levels off when the soil moisture is above this threshold (Supplementary Fig. 1), which is the similar representation of soil moisture stress effects on GPP in Earth system models51. Thus, compared to the saturation model, the observed superior performance of the concave quadratic model in fitting the data can be attributed solely to its consideration of the depressive effect of excessive soil moisture on GPP (i.e., the presence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)). We did not further consider other saturation models (e.g., exponential and sigmoid functions), as these models differ greatly from the concave quadratic model in their formula structure and it is thus unclear whether the observed superior performance of the concave quadratic model is really because it takes the depression of excessive soil moisture on GPP into account or simply because it fits the data better overall. The data quality (NEE_VUT_REF_QC, ranging from 0 to 1) of each observation was used as its weight in model7. Before fitting, GPP was logarithmically transformed (i.e., ln(GPP)), which is a commonly employed technique used in ordinary least squares to improve normality and minimize heteroscedasticity of the data52,53.

$${{\rm{GPP}}}=a{({{\rm{SM}}}-{{SM}}_{{opt}}^{{GPP}})}^{2}+{{GPP}}_{\max }$$
(1)

Where SM represents the soil moisture, \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) and GPPmax are the vertex of the parabola, and a is parameter estimate of the fitted quadratic model and represents the direction and extent of curvature. Negative values of a mean that the curve is concave.

Considering that light and heat are potentially correlated or covariant with soil moisture6, we used partial Spearman’s correlation analysis and paired t-test to evaluate the impacts of air temperature, vapor pressure deficit, and incoming shortwave radiation when analyzing the GPP-soil moisture response curves. In particular, we first used the partial Spearman’s correlation analysis to estimate the strength of the nonlinear relationship between soil moisture and GPP while controlling for air temperature, vapor pressure deficit, and incoming shortwave radiation, as well as estimated it without controlling for any factors. We then used the paired t-test to test whether there is a significant difference between the Spearman’s correlation coefficients without and with controlling for air temperature, vapor pressure deficit, and incoming shortwave radiation. The results showed a non-significant difference (Supplementary Fig. 4), suggesting that the air temperature, vapor pressure deficit, and incoming shortwave radiation had a negligible effect on the nonlinear relationship between GPP and soil moisture. Thus, the observed transition from an increase to a decrease in GPP with increasing soil moisture (i.e., the presence of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\)) was not likely caused by these confounding factors. Among the 143 sites, GPP at 108 sites exhibited hump-shaped response curves with increasing soil moisture (Supplementary Fig. 3 and Table 1); we selected a site-year from each vegetation type to show a representative response curve (Fig. 2b).

To identify the acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to soil moisture at spatial scale, we first averaged \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across multiple years within each site. We then performed linear regression analysis to assess the relationship between \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) and average soil moisture during the peak growing season (SMgrowth) across sites, and the acclimation pace was defined by the regression slope31,35. If an increase in SMgrowth does not result in a proportional increase in \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) (i.e., SMgrowth-\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) slope < 1), the increased SMgrowth would be more likely to suppress GPP once \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) falls below SMgrowth. Conversely, if an increase in SMgrowth results in a proportional or higher increase in \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) (i.e., SMgrowth-\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) slope ≥ 1), the increased SMgrowth would be more likely to stimulate GPP. We also conducted a relative weight analysis with the R package rwa to explore the potential effects of other climatic, soil and vegetation factors on the variability of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across sites. The relative weight analysis considers collinearity among predictors, and partitions the explained variance across multiple predictors by transforming correlated predictors into orthogonal variables, performing a linear model on the transformed variables and then transforming the resulting coefficients back to the original metric8,54. The climatic factors included mean air temperature (Tem, °C), incoming shortwave radiation (ISR, W m−2), vapor pressure deficit (VPD, kPa), soil temperature (ST, °C), and total precipitation (Pre, mm) during the peak growing season from FLUXNET datasets. As vegetation structure variable, leaf areas index (LAI) for each site was extracted from global monthly LAI dataset according to its latitude and longitude55. All the above factors were averaged for each site over the years of observation. The soil properties included soil organic carbon (SOC, %), soil bulk density (BD, kg dm−3), soil sand fraction (Sand, %), soil cation exchange capacity (CEC, cmol kg−1) and soil pH (pH), which were directly retrieved from the Regridded Harmonized World Soil Database v.1.2 in the Oak Ridge National Laboratory Distributed Active Archive Center for Biogeochemical Dynamics.

To further get an understanding of the acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change at temporal scale, we revealed the relationship between \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) and SMgrowth at individual sites where at least 5 years of data were available (Supplementary Table 2). Before that, analysis of covariance (ANCOVA) was used to test whether this relationship was significantly different among different sites, with SMgrowth as the continuous variable and site as the categorical variable. Due to significant interaction between SMgrowth and site in the ANCOVA (Fig. 4), the relationship between SMgrowth and \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across years was established in each site, indicting geographically divergence in temporal acclimation of \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to SMgrowth change (Fig. 4). To this end, we conducted a contribution analysis for this divergence among SMgrowth-\({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) slopes using relative weight analysis, along with linear regression analysis (Supplementary Figs. 8 and 9). The potential contributors included Tem, ISR, VPD, ST, Pre, LAI, SOC, BD, Sand, CEC, and pH.

Field manipulation experiment

To verify the causal effect of SMgrowth on \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), we used a long-term precipitation manipulation experiment in an alpine meadow (32°50′ N, 102°34′ E, 3500 m a.s.l.). This experiment began in 2015, and consists of six precipitation levels: 1/12P, 1/4P, 1/2P, 3/4P, P and 5/4P, where P was the annual precipitation. There were five replications under each precipitation level, thus 30 plots (2 × 3 m) in total, following a fully factorial randomized block design. The experimental plots are presented in the Fig. 5a.

We conducted systematic measurements of ecosystem characteristics in 2022, during which precipitation treatments have significantly altered ecosystem structure and functioning as shown in He et al.40. For example, there were significant changes in soil moisture, species richness and dominance, and community stability along the precipitation gradient. These, in turn, would influence ecosystem water use capacity and potentially shift the response of GPP to soil moisture40,56, facilitating the capture of changes in the \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) under different precipitation treatments. Using a transparent static chamber (0.5 × 0.5 × 0.5 m) attached to an infrared gas analyzer (LI-6400, LI-COR, Lincoln, NE, USA), we measured GPP based on ecosystem CO2 fluxes twice per month during the peak growing season (June–July–August) to reflect the temporal dynamics of GPP. Simultaneous with each measurement of GPP, soil moisture at a 0 ~ 10 cm depth in each plot was recorded for consistency with eddy covariance observations. Based on these measurements, we derived \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) in each precipitation level using the concave quadratic model (Eq. 1) as used for the eddy covariance observations. We then averaged soil moisture within each precipitation level to represent SMgrowht, and used linear regression to test the relationship between SMgrowht and \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) across precipitation levels. We also measured a serial of plant and soil properties that potentially regulate \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) to determine the mechanisms behind the effect of SMgrowht on \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\), including plant community height (CH), plant biomass allocation to belowground (fBNPP), and soil temperature (ST), total carbon (TC), total nitrogen (TN), pH, NH4+ and NO3−. Pearson’s correlation analysis was applied to quantify the role of these properties in regulating \({{\rm{SM}}}^{{\rm{GPP}}}_{{\rm{opt}}}\) variation along SMgrowht. More detailed information on experimental site, design, and measurements can be found in the Supplementary Methods in the Supplementary Information.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.