1 Introduction

1.1 Surface–atmosphere interactions in hydrological models

Hydrological models are widely used to assess the regional impacts of climate change on the components of the hydrological cycle (Roudier et al. 2016; Hakala et al. 2019). Most of these hydrological models use conceptual offline (i.e., uncoupled) representations of the soil–vegetation–atmosphere dynamics, through the concept of potential evapotranspiration. The term “evapotranspiration” incorporates two different fluxes: water evaporation from open water surfaces (abiotic process) and plant transpiration resulting from photosynthesis activity (biotic process). Climate change affects evapotranspiration due to increases in air temperature, radiation, and the maximum amount of water vapor in the air. Hereafter, we will focus on the role of carbon dioxide (CO2) in the representation of the evapotranspiration process for hydrological simulation.

The use of potential evapotranspiration (PE) as an estimation of the atmospheric evaporative demand implicitly assumes rather stationary environmental conditions, e.g., in terms of land use and plant physiology, which is questionable in the current evolving climate and vegetation conditions (e.g., Yin et al. 2017; Bosmans et al. 2017). Such an assumption might become even more problematic when assessing the water cycle under future changing conditions, which will present drastic modifications in climate and land use. Differences between projected future AE rates and water resources obtained from conceptual hydrological models and from more integrative general circulation models were attributed by some authors to the use of a reference PE formulation with fixed parameters (e.g., albedo, constant of the stomatal and aerodynamic resistances), precluding the possibility of representing changes in vegetation processes (Kumar et al. 2016; Yang et al. 2019). This suggests that the conventional use of “reference” PE needs to be revised in order to improve the realism of hydroclimatic projections (Milly and Dunne 2016).

Adapting the PE formulations is a possible way of taking into account surface–atmosphere interactions in a simplified way. These adaptations include changes in albedo and in stomatal and aerodynamic resistances, which are sensitive to climate and to land use (Bosmans et al. 2017). Among these adaptations, integrating the role of rising atmospheric carbon dioxide (CO2), in particular, has been investigated in the past decade (e.g., Butcher et al. 2014; Islam et al. 2012; Cheng et al. 2014).

1.2 The role of carbon dioxide in plant water use and how it is parameterized in hydrological models

Plant stomata enable gaseous exchange with the atmosphere for respiration and photosynthesis and they regulate AE. It is well-known that under higher atmospheric CO2 concentrations, the gaseous exchange of plants is altered (Allen 1990, 1991). The stomatal opening regulates the carbon gain used for photosynthesis and consequently for vegetation growth. Environmental experiments have demonstrated that elevated atmospheric CO2 concentrations reduce stomatal opening for transpiration in plants (Allen 1990), resulting in a lower water loss through stomata. However, terrestrial vegetation remains an important carbon sink and the feedback from CO2 fertilization plays a role in PE. An elevated atmospheric CO2 concentration promotes plant growth and induces a larger leaf surface for AE (Le Quéré et al. 2015). It remains under discussion whether the resultant CO2‐induced lower transpiration may be canceled by higher crop transpiration through CO2‐induced increased biomass (Wada et al. 2013). Both effects have been demonstrated and quantified in controlled environments, but transposition of these results under field conditions and over longer time periods is still debated (Rosenberg et al. 1989; Bunce 2004; Cheng et al. 2014). At the global scale, Gedney et al. (2006) found that elevated atmospheric CO2 concentrations and subsequent stomatal closure were partly responsible for the general upward trend in continental-scale river runoff during the past century, which is confirmed by simulations of several climate models predicting increased runoff in some regions (Yang et al. 2019). Overall, uncertainty about how vegetation responds to future increases in CO2 and the consequences for water flow is a key question under investigation (Gerten et al. 2014). As the effect of CO2 on reduced stomatal opening and increase biomass differs across biomes, human-induced or natural vegetation changes are also likely to play a significant role in AE trends (Inauen et al. 2013; Cheng et al. 2014), and crop fields (Bosmans et al. 2017). Offline impact models such as conceptual hydrological models differ largely in the way they deal with the effects of elevated atmospheric CO2 concentrations on evapotranspiration. Most studies showed a strong increase in AE as a response to increased air temperature and vapor pressure deficit (Scheff and Frierson 2014; Naumann et al. 2018). However, some studies found that taking into account the active role of vegetation limits the increase in AE (e.g., Ma and Zhang 2022). This results in a general decrease in soil moisture and river flow, particularly in energy-limited regions (Chiew et al. 2009; Addor et al. 2014; Forzieri et al. 2014; Donnelly et al. 2017). Different results were found in studies where the authors took into account atmospheric CO2 concentrations (Kruijt et al. 2008; Guillod et al. 2018), suggesting that the inclusion of CO2 and a more explicit representation of vegetation dynamics can fundamentally change the drought response to climate change (Prudhomme et al. 2014; Pan et al. 2015; Yang et al. 2019).

The most straightforward way to take into account elevated CO2 concentrations in hydrological models is to consider the relationship between changes in CO2 concentrations and changes in stomatal resistance with the Penman–Monteith PE formulation. Based on experimental results, several equations were proposed and applied in impact studies (Allen 1990; Stockle et al. 1992; Yang et al. 2019) but few guidelines exist on the choice of the relationship and its consequences on modeling results.

1.3 Scope of the study

This study aims at quantifying the difference between several existing schemes to account for elevated atmospheric CO2 concentrations in PE estimations and subsequent runoff estimations. On the basis of previous findings, we consider in our analysis the impact of CO2 concentrations on stomatal resistance by applying three existing equations based on the modification of the stomatal resistance rs in the Penman–Monteith formulation. This study could help to improve PE representation in rainfall–runoff models for climate impact studies and to better quantify corresponding uncertainties. We perform this analysis on the French metropolitan territory, which encompasses both water-limited (in the southern part) and energy-limited (in the northern part) regions, thus potentially showing a contrasting effect of PE estimates on runoff estimation.

2 Materials and methods

2.1 Climate model projections

The past range of atmospheric CO2 concentration is not sufficient to yield to important changes in rs, and therefore, working on past observations does not make it possible to decipher the effect of CO2 on PE amounts. Consequently, we chose to work on future climate conditions using the outputs of eight CMIP5 general circulation model (GCM)/regional climate model (RCM) couples from EURO-CORDEX (Jacob et al. 2014) under two emission scenarios (Representative Concentration Pathways, RCP 4.5 and RCP 8.5; see Table 1). A 30-year reference period in the past was selected, from 1970 to 1999, to compute anomalies and the prospective period covers the entire twenty-first century. We used daily outputs of downwelling solar radiation, 2-m air temperature, 10-m wind speed, precipitation, and relative humidity. All the outputs from the eight models were projected on a common regular grid over France with an 8-km spatial resolution, corresponding to the finest resolution of the RCMs. The use of two RCP scenarios makes it possible to assess the sensitivity of the results to the range of elevated atmospheric CO2 concentration. Since RCM climate outputs are not unbiased, all results are shown as anomalies with respect to the 1970–1999 period, taken as the reference.

Table 1 The eight CMIP5 GCM/RCM couples used in this study
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The evolution of CO2 concentrations in atmospheric forcing CMIP5 projections is available online: http://www.pik-potsdam.de/~mmalte/rcps/ (Meinshausen et al. 2011). These projections report an increase of 185 ppm and 582 ppm, respectively, for RCP 4.5 and RCP 8.5, between 1991 and 2100.

2.2 Penman–Monteith PE formulation

We used the FAO56-PM equation (Allen et al. 1998):

$$\begin{array}{c}\lambda \bullet PE= \frac{\Delta {R}_{n}+\left({\rho }_{a}\bullet \frac{{C}_{P}}{{r}_{a}}\right)\left({e}_{s}-{e}_{a}\right)}{\Delta +\gamma \left(1+\frac{{r}_{s}}{{r}_{a}}\right)}\end{array}$$
(1)

where \(\Delta\) is the slope of saturation vapor pressure versus the air temperature curve (kPa °C−1), γ is the psychrometric constant (kPa °C−1), ρa is the air density (kg m–3), CP is the specific heat of air at constant pressure (J kg−1 °C−1), \({e}_{s}\) is the saturation vapor pressure (kPa) estimated from air temperature (°C) using the equation of Allen et al. (1998), \({e}_{a}\) is the actual vapor pressure (kPa) derived from \({e}_{s}\) (kPa) and relative humidity (in %), and λ is the latent heat of vaporization (J kg−1) taken as a constant. Since not all GCM/RCM projections provided net radiation Rn (MJ m−2 day−1) but instead downwelling shortwave and longwave solar radiation, net radiation was computed following the recommendations by Allen et al. (1998), using an albedo equal to 0.23 (-) and an upwelling longwave radiation as a function of emissivity and air temperature.

Assuming a grass reference surface of 0.12-m height, Allen et al. (1998) suggested an aerodynamic resistance \({r}_{a}\) (s m−1) inversely proportional to wind speed u (m s−1) and a constant stomatal resistance \({r}_{s}\) = 70 (s m−1):

$$\begin{array}{c}{r}_{a}= \frac{208}{u}\end{array}$$
(2)

2.3 Adjusting stomatal resistance with atmospheric CO 2 concentrations

From compiling mostly experimental results, several authors proposed adjusting the stomatal resistance with respect to changes in atmospheric CO2 concentrations. Allen (1990) proposed empirical adjustments of \({r}_{s}\) for soybean, sweet corn, and sweetgum based on the experiments by Rogers et al. (1983). Stockle et al. (1992) suggested adjustments of \({r}_{s}\) for different types of crops based on the experiments by Morison (1987). Kruijt et al. (2008) compiled several experimental studies to derive \({r}_{s}\) adjustments for grass, wood crops, and C4 crops. From a different perspective, Yang et al. (2019) proposed a relationship between the change in \({r}_{s}\) and the change in atmospheric CO2 concentrations, so that the estimated AE from the Choudhury model fits the estimated AE simulated by several CMIP5 models under the RCP 8.5 scenario.

These proposed adaptations of \({r}_{s}\) were all expressed as a fraction of a reference stomatal resistance \({r}_{s\_ref}\) at the atmospheric concentration of CO2 equal to 330 ppm. The resulting functional relationships between stomatal resistance and atmospheric CO2 are shown in Fig. 1.

Fig. 1
figure 1

Functional relationships between relative change in rs and atmospheric CO2 concentration. Uncertainty bounds are computed using the information from the original publications. Since Yang et al. (2019) did not explicitly take into consideration plant species, we retained the adaptations obtained from the mean climate model simulations and for the individual climate models representing the lower and upper bounds. The dashed vertical lines refer to the expected atmospheric CO2 concentrations for 2100 under RCP 2.6 (left vertical line), RCP 4.5 (middle vertical line), and RCP 8.5 (right vertical line)

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In this paper, we did not consider the effect of plant species on \({r}_{s}\), and to remain consistent with PE usage in hydrological models, we retained only the equation proposed by Kruijt et al. (2008) corresponding to grass. Consequently, three functional relationships between relative change in \({r}_{s}\) and atmospheric CO2 concentration were used. The selection was made based on actual usage of these relationships for hydrological model applications. Table 2 presents the selected relationships, their acknowledged limits, and an inexhaustive list of some applications for hydrological modeling.

Table 2 Functional relationships used in this study to assess the impact of CO2. \({r}_{s\_Stockle}\) \({r}_{s\_Kruijt}\), and \({r}_{s\_Yang}\) refer to the modified stomatal resistances taking into account elevated atmospheric CO2; \({r}_{s\_ref}\) is the reference stomatal resistance taken in this study at 70 s m.−1; and \({{\mathrm{CO}}_{2}}_{ref}\) is the reference concentration of atmospheric CO2, taken at 330 ppm in this study
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2.4 Budyko model

A change in PE does not necessarily lead to similar changes in runoff, due to the additional influence of soil moisture (Duethmann and Blöschl 2018). To account for these additional influences, we analyzed the evolution of annual runoff (Q) using the non-parametric Budyko (1974) equation:

$$\begin{array}{c}Q=P-P{\left[\frac{PE}{P}\bullet \mathit{tanh}\left(\frac{P}{\mathit{PE}}\right)\bullet \left(1-{e}^{-\frac{PE}{P}}\right)\right]}^\frac{1}{2}\end{array}$$
(3)

with P the precipitation and all variables expressed in millimeter per year. The Budyko equation is one of the most widely used approaches to determine long-term AE. This equation is derived from long-term climate observations and highlights the connection of evapotranspiration with both precipitation and PE. With climate projections of both P and PE, this approach makes it possible to investigate the potential change in runoff under several climate projections. Thus, the Budyko framework has been used in climate impact studies at the national scale (Donohue et al. 2011; Renner and Bernhofer 2012; van der Velde et al. 2014). In this study, the Budyko equation is applied at the annual time scale, for each 8 × 8-km cell of the regular grid over France. This approach allows us to assess both (a) the temporal evolution of P, PE, and runoff over the entire domain and (b) the regional differences in these evolutions. While rather crude, the Budyko formulation appeared particularly able to simulate long-term runoff over some representative French catchments (see Supplementary Materials, Fig. S1).

3 Results

3.1 Changes in climate data and Budyko runoff induced by rising atmospheric CO2

Precipitation anomalies are shown in Fig. 2 since they influence the simulated runoff in the Budyko equation. Precipitation trends are highly variable among RCMs, showing on average no trend under RCP 4.5 in the future relative to the reference period 1970–1999, and a slight decreasing trend by the end of the century under RCP 8.5 (ΔP =  − 22 mm y−1, corresponding to a relative decrease of − 2%).

Fig. 2
figure 2

Evolution of precipitation (left), PE (middle), and simulated runoff using the Budyko equation (right) relative to the 1970–1999 period for the RCP 4.5 and RCP 8.5 scenarios, averaged over France. The colored shadings represent the min–max estimation range from to climate models and the solid lines represent the mean. Data are smoothed with a 30-year running mean. Detailed values are given in Appendix

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The impact of the choice of stomatal resistance on PE is evident for both RCP 4.5 and RCP 8.5 scenarios (Fig. 2). For RCP 4.5, the ensemble of climate models projects an increasing PE in the future relative to the reference period 1970–1999. All formulations that increase \({r}_{s}\) with rising CO2 lead to a lower PE increase compared to the reference Penman–Monteith formulation. The largest increase (ΔPE =  + 78 mm y−1 by the end of the century, corresponding to a relative increase of + 11%) is obtained with the Penman–Monteith equation applied with constant \({r}_{s}\). Conversely, \({r}_{s\_\mathrm{Stockle}}\) leads to a moderate increase (ΔPE is + 33 mm y−1 by the end of the century, corresponding to a relative increase of + 5%). For RCP 8.5, the evolutions in PE anomalies diverge and the trends depend greatly on the formulation of \({r}_{s}\) chosen. The Penman–Monteith equation applied with constant \({r}_{s}\) leads again to a more pronounced increase (ΔPE =  + 149 mm y−1, corresponding to a relative increase of + 21%). Conversely, the Penman–Monteith equation with modified \({r}_{s\_\mathrm{Stockle}}\) leads to a decreasing PE at the end of the century (ΔPE =  − 20 mm y−1, corresponding to a relative change of − 3%), after a period of moderate increase until the 2070s. The two other formulations of \({r}_{s}\) tested yield intermediate positive changes. The increase in PE is more pronounced from RCP 4.5 to RCP 8.5 using \({r}_{s\_\mathrm{Yang}}\), while \({r}_{s\_\mathrm{Kruijt}}\) yields a lower increase under the RCP 8.5 scenario, showing that the increase in PE due to enhanced vapor pressure deficit is offset by the increase in stomatal resistance due to rising CO2. The PE uncertainties due to RCM projections generally increase during the period. Under the RCP 4.5 scenario, the uncertainties in PE due to climate projections are comparable to the uncertainties in PE due to the \({r}_{s}\) formulation, while PE uncertainties due to the \({r}_{s}\) formulation are larger under RCP 8.5.

The implications of these different PE evolutions for simulated runoff are evident although dependent also on precipitation evolution (Fig. 2). For the RCP 4.5 scenario, the ensemble of climate models projects a limited decrease in simulated runoff in the future relative to the reference period 1970–1999 (ΔQ ranges from − 40 mm y−1 to − 14 mm y−1 by the end of the century, corresponding to relative changes of − 6% to − 2%, respectively). For the RCP 8.5 scenario, runoff anomaly evolutions are globally negative but diverge more among PE formulations. The Penman–Monteith equation applied with constant \({r}_{s}\) leads to the most pronounced decrease (ΔQ =  − 99 mm y−1 by the end of the century, corresponding to a relative decrease of − 14%), while Penman–Monteith \({r}_{s\_\mathrm{Stockle}}\) leads to a very slight decrease (ΔQ =  − 4 mm y−1, corresponding to a relative change of − 1%). There is a large variability among climate model simulations and some climate models project positive runoff changes for both RCP 4.5 and RCP 8.5, whatever the \({r}_{s}\) formulation used.

3.2 Spatial patterns of changes

There is a meridional gradient for precipitation changes over France, with negative and positive trends in the southern and northern parts, respectively (Fig. 3). This gradient is more important for RCP 8.5 than for RCP 4.5. The magnitude of differences between the selected adaptations of stomatal resistance is in agreement with the time series presented in Fig. 2. Under RCP 8.5, \({r}_{s\_\mathrm{Stockle}}\) and \({r}_{s\_\mathrm{Kruijt}}\) formulations produce a decreasing PE (up to − 15%) in some regions, particularly over the northwestern coast. For these regions, positive trends in precipitation and negative trends in PE suggest larger spatial discrepancies in the simulated runoff. For RCP 4.5, for the reference formulation and \({r}_{s\_\mathrm{Yang}}\), an increase in PE is projected over the whole territory.

Fig. 3
figure 3

Ensemble mean of relative annual precipitation and PE changes (%) between the 1970–1999 and 2070–2099 periods under the RCP 4.5 and RCP 8.5 scenarios with different formulations of stomatal resistance

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Spatial patterns of simulated runoff changes vary dramatically across the selected formulations of stomatal resistance (Fig. 4). The decrease is general using the Penman–Monteith equation applied with constant \({r}_{s}\), with southern regions experiencing a decrease that can reach − 50%. The adaptations of the stomatal resistance provide a more nuanced picture, with a decrease in runoff in southern areas and an increase in runoff in the northern areas, up to + 30%. These uncertainties in the sign of runoff changes are also evident across climate projections, since climate model trends agree only in limited areas, whatever the PE formulation selected (Fig. 5). Only for RCP 8.5 and southern France is there agreement between the eight models on a decreased runoff.

Fig. 4
figure 4

Ensemble mean of relative annual simulated runoff changes (%) using the Budyko equation between the 1970–1999 and 2070–2099 periods under the RCP 4.5 and RCP 8.5 scenarios with different formulations of stomatal resistance

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Fig. 5
figure 5

Partition of the number of RCMs (out of 8) showing decreasing/increasing runoff using the Budyko equation between the 1970–1999 and 2070–2099 periods under the RCP 4.5 and RCP 8.5 scenarios with different formulations of stomatal resistance

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3.3 Comparison with actual evapotranspiration and runoff as estimated by RCMs

PE projections are compared to actual evapotranspiration derived from RCMs for non-water-stressed grid cells (i.e., PE/P < 0.75 during both historical and future periods), where PE and AE (actual evapotranspiration) are likely close. The results are presented in Fig. 6, in which we compare the average evolution of PE and AE over the twenty-first century for both RCP 4.5 and RCP 8.5. The RCMs show on average a small increase in AE, even in “energy-limited” regions, while the PE projections with a reference formulation (rs set at 70 m s−1) predict a very large increase. However, the formulations taking into account atmospheric CO2 (with modified rs) seem to better fit the RCMs’ AE. Nevertheless, the \({r}_{s\_\mathrm{Stockle}}\) formulation projects a decrease in PE after 2070, which is inconsistent with AE trend estimated by the RCMs. The same observation can be made for \({r}_{s\_\mathrm{Kruijt}}\) at the long lead-time.

Fig. 6
figure 6

Left: Evolution of simulated PE and RCM-AE relative to the 1970–1999 period for the RCP 4.5 and RCP 8.5 scenarios. The colored shadings represent the min–max estimation range in AE and PE estimations and the solid lines represent the mean. Data are smoothed with a 30-year running mean. Right: In blue, the non-water stressed grid cells selected over the study area, with a threshold criterion (PE/P) < 0.75, over historical and future periods; in yellow, water-limited regions over France that were not selected for the comparison

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The runoff averaged over France as simulated by RCMs (taken as precipitation minus AE) presents relatively similar trends to those obtained with the Budyko equation (Fig. 7). For the RCP 4.5 scenario, the runoff decreases slightly over time, in general agreement with the runoff estimated under the Budyko framework with the different PE formulations. For the RCP 8.5 scenario, runoff anomalies from RCMs are globally negative (except for Stockle’s formulation) but less pronounced than those estimated under the Budyko framework. The mean of the RCM ensemble leads to a very slight decrease (ΔQ =  − 31 mm y−1), a value that lies between the runoff simulated with \({r}_{s\_\mathrm{Kruijt}}\) (ΔQ =  − 40 mm y−1) and the one obtained with \({r}_{s\_\mathrm{Stockle}}\) (ΔQ =  − 4 mm y−1). The simulated runoff from the Penman–Monteith equation applied with constant \({r}_{s}\) leads to a clearly more important decrease that is close to the minimum of the runoff estimates.

Fig. 7
figure 7

Left: Evolution of simulated runoff using the RCM simulations relative to the 1970–1999 period for the RCP 4.5 and RCP 8.5 scenarios. The colored shadings represent the min–max estimation range in RCM runoff estimation and the solid lines represent the mean. Data are smoothed with a 30-year running mean. Right: Ensemble mean of relative annual RCM simulated runoff changes (%) between the 1970–1999 and 2070–2099 periods under the RCP 4.5 and RCP 8.5 scenarios

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The spatial patterns of changes in runoff (Fig. 6) corroborate these findings: for both RCP 4.5 and RCP 8.5, the spatial patterns of change given by the RCMs are close to those obtained using \({r}_{s\_\mathrm{Stockle}}\) and \({r}_{s\_\mathrm{Kruijt}}\), i.e., a distinct trend between northern and southern regions.

4 Discussion

4.1 Comparing changes with previous model experiments

The Budyko equation used in this study to simulate runoff is relatively straightforward and neglects key processes such as the seasonality of P and PE. Besides, the climate projections from RCMs used in this paper were not bias-corrected. Thus, we did not intend to produce reliable estimates of the impact of climate, but rather to investigate the spectrum of changes associated with the choice of a formulation of PE that takes into account the influence of CO2 on stomatal resistance. The regional pattern changes in annual runoff obtained in this study are, however, in agreement with previous studies (Donnelly et al. 2017; Dayon et al. 2018) that used more complex hydrological models: a pronounced decline in mean runoff in the southern part of France, no clear runoff changes in the northern part of France, with large uncertainties stemming from climate projections. We also showed that these patterns are in general agreement with RCM outputs, which means that despite the simplicity of the Budyko equation, it enables us to reproduce the simulation of more physically based coupled climate models.

Perspectives of using \({r}_{s}\) formulations accounting for CO2 in PE formulations in future studies.

As expected, taking into account the influence of CO2 on \({r}_{s}\) limits both PE and AE, and thus also limits the decline in runoff, particularly in energy-limited regions. The choice of the formulation of rs is therefore significant for studies on the impact of climate change on runoff. The three formulations tested in this paper provide quite different runoff projections compared with the classic use of the Penman–Monteith equation with constant \({r}_{s}\). The differences are obvious under the RCP 8.5 but also present under the RCP 4.5 scenario. It is noteworthy that the different trends (and sign of the trend) are highly variable compared to differences of changes in PE when considering different PE formulations (Lemaitre-Basset et al. 2021), showing that the uncertainties in projections of CO2 concentrations might be translated to large uncertainties in PE (and simulated runoff).

While the use of the Budyko framework highlights moderate-to-important impacts of taking into account CO2 in PE formulations, how this could reflect on hydrological projections made with rainfall–runoff hydrological models might not be straightforward. The impact of PE formulations on discharge projections is still under debate, some studies pointing to either a low impact (Dakhlaoui et al. 2020) or a high impact (Seiller and Anctil 2016). Specifically, the presence of a parameter calibration in most hydrological models might distort the relationship between PE anomalies and runoff anomalies (Oudin et al. 2006) and could lead to different results from those simulated with the Budyko framework.

4.2 Limitations of taking into account CO 2 in PE formulations

While there are many good reasons for adjusting \({r}_{s}\) with CO2, the choice of a single formulation is complicated. Two existing formulations, namely, the formulations by Stockle et al. (1992) and by Kruijt et al. (2008), were developed from experimental results for selected types of crops, and their range of applicability is up to 660 ppm, i.e., far below the expected CO2 content by the end of century under the RCP 8.5 scenario (935 ppm in 2100). Indeed, increasing stomatal resistance indefinitely is not realistic, as plants must continue to ensure gas exchange, even with a highly enriched CO2 atmosphere. Thus, the use of these empirical formulations for the RCP 8.5 scenario is as questionable as the use of these formulations for large-scale applications with mixed land use. The third formulation, proposed by Yang et al. (2019), was derived by fitting the AE simulated by the Choudhury model to the AE simulated by climate models, the rationale being that climate models allow us to take into account surface–atmosphere interactions more explicitly. This formulation was calibrated at the global scale and we showed that it probably needs some regional adjustments, since the runoff simulated using this formulation is not fully in line with RCM outputs over France.

The fertilization effect of atmospheric CO2 on the growth of plants may produce an opposite effect by promoting both PE and AE. Nevertheless, this theory is in fact limited in the context of long-term exposure (climate change): Ainsworth and Rogers (2007) showed a reduction in photosynthesis activity, called “down-regulation,” and a slowdown of the greening trend on many biomes was pointed out by Winkler et al. (2021). Besides, plant growth needs fertilizers (e.g., nitrogen), and their availability in the environment will limit the fertilization effect of CO2, thus reducing the CO2 sink role of terrestrial vegetation (Wang et al. 2020). This competing effect of CO2 on AE can theoretically be taken into account in rs formulations through the use of the leaf area index (LAI). However, determining LAI in the future requires a dynamic vegetation model and presents relatively high uncertainties (Yang et al. 2019). Over France, simulated LAI with different GCMs generally shows a positive trend (between 0.05% y−1 in the south and 0.1% y−1 in the north). Since the formulation proposed by Yang et al. (2019) was derived by minimizing the discrepancies between AE simulated by Budyko and GCMs, it implicitly takes into account the positive role of LAI. This may explain the lower effect of CO2 on stomatal resistance compared with Stockle et al. (1992) and Kruijt et al. (2008).

The use of simple functional relationships between \({r}_{s}\) and CO2 for correcting PE estimates may be seen as “flogging a dead horse.” Translating complex surface–atmosphere feedbacks into a simple adjustment of the PE equation neglects several other possible effects, and it is still uncertain how AE will evolve under climate change. For example, Xiao et al. (2020) showed that AE tends to decline under climate change, owing to decreased relative humidity and consequent stomatal closure due to the decreased moisture gradient at the leaf surface. Nevertheless, for most PE formulations, the opposite occurred, since reducing relative humidity increases PE. In the same time, Dong and Dai (2017) showed diverging results, with increases in AE in the past decades, associated with an important uncertainty. Finally, some studies show a plausible trend in AE without representing soil and vegetation effects, but using a parameterized relationship with observed data.

5 Conclusion

In this study, we assessed the impact of taking into account CO2 in the Penman–Monteith PE formulation. We showed that taking into account CO2 in this PE formulation leads to reduced PE amounts. On the basis of the Budyko framework, we have shown that the inclusion of CO2 in PE formulations limits the annual runoff reduction, especially in an emissive scenario, namely, the RCP 8.5 scenario, and even increases annual runoff in some regions, whereas the classic Penman–Monteith formulation leads to decreasing runoff projections over most of France, taking into account CO2 leads to more contrasting results, with runoff increase that becomes likely in the north of France, which is an energy-limited area. However, the three formulations tested involve different shades of runoff response. The results suggest that climate change impact studies that use PE formulations that do not make use of CO2 may underestimate runoff under a future climate. However, uncertainty remains in the way CO2 can be included in PE formulations, as can be seen from the three options tested here, which questions the intensity of hydrological projection changes due to the inclusion of CO2.

The common way to compute PE for hydrological models in climate impact studies ignores the negative feedback from terrestrial vegetation on AE. To correct the bias between PE evolution and AE in climate impact studies, we recommend estimating PE with an adjusted Penman–Monteith formulation, or another form (e.g., Peiris and Döll 2021). The formulation proposed by Yang et al. (2019) shows good potential for adjusting PE with respect to CO2 concentrations; nevertheless, the relationship should be recalibrated with respect to the study region. On the other hand, the models proposed by Stockle et al. (1992) and Kruijt et al. (2008) show good agreement with the moderate emission scenario RCP 4.5, which is encouraging. However, these models were developed with atmospheric CO2 concentrations limited to 660 ppm, which is much lower than the concentrations of the high emission scenario by the end of the twenty-first century. Probably due to extrapolation of the equation of rs with CO2 for these models above 660 ppm, PE estimates with these formulations lead to decreasing trends of PE by the end of century, which is not consistent with AE trends produced by RCMs. Finally, further observations are needed to include the effect of vegetation feedback on PE more precisely, including the evolution of vegetation yield through, e.g., simulated evolution of leaf area index, and limitation of the air vapor pressure deficit. The compensation between LAI and stomatal closure may depend on the type of environment (dry, wet, forest, crop field, grassland, etc.), which limits the generalization of our results to similar environments. Therefore, our conclusions show that the way PE formulations account for CO2 is a lead for a possible improvement of eco-hydrological impact studies.