Overestimated global dryland expansion with substantial increases in vegetation productivity under climate warming

Drylands are serviced as an essential component of the earth’s ecosystem. The potential changes in dryland areas are of great importance to the environment, but various debates remain as to whether and to what extent drylands are expected to expand. Here we employ a physically-based potential evapotranspiration (E P) model accounting for vegetation response to climate change to quantify potential changes in dryland areas, on the basis of a commonly used indicator, aridity index (multiyear mean E P over precipitation). Results show that by the end of this century, drylands will expand slightly by ∼5%, while vegetation productivity will increase by ∼50%. Elevated CO2 slows down the increase rate of E P that impedes the expansion of drylands, but greatly promotes vegetation growth with increases in both leaf assimilation and canopy foliage. These findings improve our understanding of the potential changes in dryland and their ecological impacts in a warmer climate.


Introduction
Drylands generally refer to the regions with water stress, covering ∼40% of the land surface, and are essential for global environments and sustainability (Lian et al 2021). With climate warming, whether dryland will expand remains a matter of debate. Some literature, using potential evapotranspiration (E P )based indicators, such as aridity index (AI, the ratio of E P to precipitation) and/or Palmer drought severity index (Palmer (1965)), reported that drylands will significantly expand with rising temperature (Dai 2013, Feng and Fu 2013, Huang et al 2016, Park et al 2018, Yao et al 2020. Nevertheless, this conflicts with the findings on the basis of other indicators, such as surface runoff and/or eco-hydrological indices (Sheffield et al 2012, Yang et al 2018, Berg and McColl 2021, which show little or no change in dryland areas. The estimated rapid expansion in dryland areas generally comes from the dramatic increases in E P , calculated by the Penman-Monteith (Penman 1948, Allen et al 1998 and/or temperature-based (Thornthwaite 1948) models. However, the responses of vegetation to changing environments, especially CO 2 fertilization, are often neglected in those traditional E P models (Roderick et al 2015, Milly andDunne 2016), possibly resulting in an overestimated arid future and causing conflicts between atmospheric and hydrologic indicators (Milly and Dunne 2016, Swann et al 2016, Yang et al 2019, Berg and McColl 2021, Lian et al 2021.
Another focus of concern is the potential changes in drylands vegetation productivity, represented by gross primary productivity (GPP). With satellite observations, the positive effects of elevated CO 2 are found to overwhelm the negative effects of rising temperature (shown as vapor pressure deficit), promoting vegetation growth in the past decades (Donohue et al 2013, Ukkola et al 2016, He et al 2019, Zhang et al 2020, Manzoni et al 2022. Nevertheless, a recent study claimed that the imbalance of GPP between expanded and historical drylands may lead to decreases in GPP per unit dryland area (Yao et al 2020), which seems to run counter to the expectation. Specifically, the increases in total ecosystem-level GPP come from two components, i.e. changes in leaf-level assimilation rate (A) and canopy structure (represented by leaf area index, LAI), and how these two components contribute to GPP changes remains unclear yet. Besides, the quantification of the positive role of elevated CO 2 and the negative impacts of rising atmospheric vapor deficit (VPD) on GPP changes also remains to be explored (Donohue et al 2017, Manzoni et al 2022. Motivated by the above issues, based on Coupled Model Inter-comparison Project Phase 5 (CMIP5) climate models (Taylor et al 2012), we aim to answer two scientific questions: (a) with a physically-based and vegetation-accounted E P model, will the drylands expand or not, and what will be the magnitude of change? (b) with the re-identified dryland area changes, how does the vegetation productivity indicated by GPP change, and what are the relative contributions of two opposite effects from elevated CO 2 and rising VPD? To answer the first question, we develop a new E P equation based on an optimal surface resistance model that quantifies the vegetation response to climate change. For the second question, we first analyze the direct GPP output from the CMIP models and then use a bulk model to decompose the respective contributions of A and LAI on GPP changes. A minimalistic model is further employed to investigate the role of CO 2 and VPD on GPP changes across the global drylands in a changing climate.

E P model
The original Penman-Monteith (PM) equation encapsulates the influencing factors for E P estimation as (Penman 1948, Monteith 1965: where λ (J kg −1 ) is the latent heat of water vaporization, ∆ (kPa K −1 ) is the slope of the saturated vapor pressure versus temperature curve, R n (W m −2 ) is the available radiation, γ is the psychrometric constant, ρ a (kg m −3 ) is the air density, C p (1010 J kg −1 K −1 ) is the specific heat of the air at constant pressure, r a (s m −1 ) is the aerodynamic resistance, VPD is the vapor pressure deficit calculated by air temperature and humidity (Murray 1967), and r s (s m −1 ) is the surface resistance.
To determine r a and r s , a kind of reference crop (RC) was defined by the Food and Agriculture Organization of the United Nations as: the vegetation with a height of 0.12 m, a surface albedo of 0.23, and r s of 70 s m −1 (Allen et al 1998). Thus, the equation (1) yields: where U 2 is the wind speed at a height of 2 m, and T is the air temperature. Equation (2) is known as the PM-RC model and has been widely used in the field of hydrology, atmospheric science, and agriculture. However, in a warming climate, the value of r s is affected by changing environmental variables such as elevated CO 2 and increased VPD, which is no longer fixed at 70 s m −1 (Norby et al 1999, Ainsworth and Rogers 2007, Medlyn et al 2011, Novick et al 2016, Liu et al 2020. Here we employ the optimal model proposed by Medlyn et al (2011) to quantify the response of leaf-level r s (denoted as r s l ) to external variables: where g 0 (mol m −2 s −1 ) is minimum stomatal conductance at nighttime, g 1 (kPa 1/2 ) is vegetation 'marginal water use efficiency' , C a (ppm) is the concentration of atmospheric CO 2 , and A (µmol m −2 s −1 ) is the net assimilation rate. The value of g 0 is very low and can be taken as zero ( is the net assimilation rate under non-water-stressed conditions, and f (ψ s ) is the soil moisture-induced photosynthesis reduction function. The parametrizations of g 1 , A ww , and f (ψ s ) are given in text S1. The performance of the equation (3) has been proved against global field observations (Sabot et al 2022).
The canopy-level r s (denoted as r s c ) can be further calculated as: Combing equations (2)-(4) and under nonwater-stressed conditions (corresponding to the definition of E P ), we obtain a new E P model (see details in the text S1): Estimations of parameters g 1 and A ww are shown in text S1. Equation (5) has a clear physical mechanism and allows us to fill the salient gap that E P cannot capture the effects of rising CO 2 on vegetation.
In the following analysis, we respectively use the PM-RC model and new model to calculate AI, and detect the trends of AI changes in the coming century according to climate model data (see description below). When the vegetation response is taken into account, the AI can be used to predict potential changes in dryland areas, inherently coordinating with other indicators, such as the ecohydrologic index which also emphasizes the impacts of vegetation (Berg and McColl 2021). Drylands are divided into four subtypes: regions with AI <0.05 are classified as hyperarid, 0.05-0.2 as arid, 0.2-0.5 as

Changes in GPP
The ecosystem/canopy-level GPP and LAI are linked through assimilation per leaf area (A): The fractional changes in GPP can be estimated by the fractional changes in A and LAI as: that is, relative changes in GPP (∆GPP/GPP) can be decomposed into A-change-induced and LAIchange-induced parts. There is no direct output of A from the CMIP5 model (see description of data use below), thus the A in equation (7) is inversed by GPP/LAI. Besides, we modify a minimalistic model to estimate relative changes in GPP as (see derivation in text S2): It should be noted that the variables on the righthand of equation (8) are not independent, specifically, LAI is impacted by CO 2 and VPD. In this case, the negative sign ahead of the LAI term does not indicate a negative relationship between GPP and LAI. Equation (8) is not suitable for contribution analysis but can help us to understand the relative role of C a and VPD on GPP changes.

Data
We use monthly outputs of 14 CMIP5 models under a high-emission scenario (RCP8.5, 2006-2100) (table S1). All models provide precipitation, surface radiations, air temperature, wind speed, air specific humidity, and LAI data, but only ten models provide GPP data. The original data are resampled to a common 1 • spatial resolution by using the first-order conservative remapping scheme (Jones 1999). We calculate all variables from the individual CMIP5 model and show the standard deviation among all 14 models. To determine the parameters in the E P model, we also select the free air CO 2 enrichment experiments data from previous studies (Ainsworth and Rogers 2007) (text S1).

Results
With the new E P model, by the end of this century, we found an increase of ∼5% (with an absolute value of 39.1% of the earth's land surface to 41.2%) of global dryland areas (figure 1), which is much smaller than the projections by PM-RC model (figure S1, with an  increase of ∼15%) because much small increases in E P (figure S2). North and South America and Europe show 15%-20% expansions, but little change is detected in Asia and Africa. This indicates that, although present dryland areas in America and Europe are not as large as Africa or Australia, they will expand much faster in relative terms in the future. Figure S3 shows the drylands expansion in four subtypes. Hyperarid drylands show the largest increase of ∼10%, the arid region increases ∼6%, and semiarid and dry subhumid have similar increases of ∼4%. Overall, the expansion of drylands is not as severe as claimed by previous reports (which are also on the basis of AI).
The vegetation productivity shows a remarkable increase of ∼55% across global drylands. Europe and South Africa show the largest increases of ∼80%, Australia has the lowest increase of ∼30%, and increases in other continents are ∼50%-60% (figure 2). GPP per unit area also indicates a significant positive trend, and the magnitudes of increases are ∼40%-50% among continents except for a relatively small increase of ∼20% in Australia. GPP changes in four subtypical drylands are shown in figure S4. GPP will begin to increase after the 2050s in hyperarid drylands, while the other three subtypes show increasing trends in the near future. This may be due to the effects of CO 2 fertilization in the severe aridity regions emerge only at a high CO 2 concentration, at which CO 2 outweighs the constraints of available water.
LAI is expected to increase by ∼25%, and A shows an increase of ∼30% by 2100 ( figure S5). The decomposition analysis shows that the changes in GPP during 2086-2100 compared to the baseline of 2006-2020 are driven by concurrent increases in LAI and A (figure 3). A has an overall larger contribution across the globe, while LAI plays a more important role in North America, Europe, and Asia. In four subtypical drylands, GPP changes in arid regions are mainly driven by increases in A, while LAI and A are comparable in other areas (figure S6).
GPP changes estimated by equation (8) is roughly consistent with direct outputs from CMIP5 models (figure S7). In 2081-2100, the relative changes in LAI, CO 2 , and VPD are ∼23%, ∼110%, and ∼40%, respectively. This suggests that despite the present and future water limits (widespread increase in atmospheric water demand), increased CO 2 will greatly enhance vegetation growth, at least until the end of this century.

Discussion and conclusion
The main conclusion of this study is: in a warmer climate, the expansion of global drylands is slight, but the increases in vegetation productivity are large (figures 1 and 2). Our findings contradict some existing studies, which claimed dramatic increases in global dryland areas (Dai 2013, Feng and Fu 2013, Huang et al 2016. The reason for the contradiction is that traditional E P models do not consider the responses of vegetation to climate change, especially the effects of CO 2 . Those models may be suitable for historical conditions, under which the CO 2 concentration is relatively steady with slight increases. However, under future scenarios, a rapidly rising CO 2 concentration will significantly impact vegetation behavior through the leaf-level stoma and canopy structure (Ainsworth andRogers 2007, Vicente-Serrano et al 2020). In the new E P equation (equation (5)), the CO 2 effects are involved in the leaf-level r s l model. The r s l model is physicallybased and also considers other influencing factors, such as VPD. Leaf-level r s l and canopy-level r s c are linked by LAI (equation (4)), allowing us to consider both impacts of stoma and canopy structure, which outperforms traditional models under a changing climate.
Both LAI and A will increase with CO 2 fertilization (figure S5), which is inconsistent with the view of Donohue et al (2013). They claimed that due to the constraints of available water, the changes in A of drylands vegetation are little, and the effects of CO 2 are expressed through promoting canopy development, i.e. increases in LAI. However, the field experiments and related theories have demonstrated that despite the water limits and closure of stoma, both of A and LAI would increase at a high-level CO 2 ( Yao et al (2020) pointed out that GPP per unit area will decrease by applying the historical spatial AI-GPP relationship to future scenarios. The decrease may be due to the issue of space-for-time substitution and well-mixed CO 2 in the atmosphere cannot explain the spatial variability of GPP (McColl et al 2022). Some underlying processes, such as the increased light interception from larger LAI and higher light use efficiency in the context of elevated CO 2 , would also in turn enhance the GPP (McCarthy et al 2006). Thus, we believe that both the total GPP and GPP per unit area will increase in the future (figure 1), and this is further supported by the simple diagnostic model (equation (8)), which explicitly shows the overwhelming role of CO 2 fertilization.
Finally, it should be noted that the current study is subjected to some limitations. First, in the new E P equation, the differences in carbon assimilation taken by C3 and C4 vegetation are not considered, but we categorize the vegetation into three specific species, namely, tree, shrub, and grass. Second, a linear relationship of vegetation carbon assimilation and CO 2 is used according to field measurements, and a fine and more accurate relationship needs a further investigation. Third, the LAI used to estimate E P is not measured under potential states (non-water-limit conditions), but the magnitude of LAI arguably has minimal impact on long-term projections of drylands expansion ( figure S8). At last, in the minimalistic model, we show that with the temperature increasing, a higher VPD will impede the vegetation growth, but temperature impacts on other mechanisms like the nutrition process and hydraulic traits are not full represented here, and remain in future study.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).