Gross primary production of Mediterranean watersheds: Using isotope mass balance approach to improve estimations

Global‐scale estimates of carbon fluxes from satellite data‐driven models are constrained by considerable uncertainties regarding Gross Primary Production (GPP) and the lack of the watershed‐scale measurements required for model calibration. Recently conducted global modelling efforts indicate that semiarid ecosystems dominate the increasing trends and inter‐annual variation of net CO2 exchange with the atmosphere, but semi‐arid regions have received little attention with regard to GPP estimation. In this study, we used the distinct isotope effect of transpiration and evaporation to calculate transpiration losses and subsequently CO2 uptake by terrestrial vegetation through the water and carbon cycle using the water use efficiency of plants. By studying two Mediterranean watersheds with contrasted environmental conditions over several hydrological years, we found a strong dependence of GPP on annual and seasonal water availability. The results demonstrated that when compared to GPP values obtained in worldwide biomes using biological methods, our isotope approach was validated, highlighting the limitations of satellite‐data‐driven models like MODIS in capturing the impact of water stress on photosynthesis and GPP estimates. These results encourage investigation of GPP by the isotope mass balance approach where direct carbon flux measurements are rare or absent in order to help to substantiate, modify or shed doubt on interpolated GPP for those regions and achieve consensus on global GPP estimates. Given the relevant role of semi‐arid ecosystems in the global carbon balance as well as the limitation of existing data sets, our improved method based on the isotope mass balance approach helps to obtain rapid and affordable estimates of GPP for semi‐arid ecosystems.


| INTRODUCTION
Vegetation plays a significant role in the Earth's climate system, as it contributes to modulating its mean state and variability by controlling natural carbon fluxes (Bloom et al., 2016;IPCC, 2019;le Quéré et al., 2018).Terrestrial plants fix atmospheric CO 2 by net photosynthesis in their leaves and the total amount of CO 2 captured through net photosynthesis is known as gross primary production (GPP) (Beer et al., 2010;Chapin et al., 2011).Both photosynthesis and GPP vary diurnally and seasonally in response to climatic conditions (light, precipitation, temperature and humidity) and nutrient availability (Anav et al., 2015).Consequently, terrestrial GPP is a critical component of the global carbon cycle by linking together water fluxes, terrestrial biota and the atmosphere and plays a pivotal role in the global carbon balance by providing the capacity to offset anthropogenic CO 2 emissions (le Quéré et al., 2018;Prentice et al., 2001).An accurate quantification of the spatiotemporal variability of terrestrial GPP is a major challenge in global climate change research (Xie et al., 2020).
Over the last decades, great progress has been achieved in the understanding and quantification of the spatiotemporal variability of terrestrial GPP, notably by the expansion of measurement networks of CO 2 exchange between ecosystems and the atmosphere through the eddy covariance technique (http://fluxnet.ornl.gov/),and the development of numerous data-driven models for GPP prediction at site, regional and global scales, including index (VI)-based models (Chen et al., 2012;Farquhar et al., 1993;Ryu et al., 2011), light use efficiency (LUE) models (Goetz & Prince, 1999;Hilker et al., 2008;Monteith, 1972;Monteith et al., 1977;Turner et al., 2005;Wei et al., 2017) and process-based models (Moorcroft, 2006;Prentice et al., 2015).
Although global terrestrial GPP estimates exist, there is no consensus across spatial and temporal scales regarding these estimations because observation techniques are not able to quantify GPP at the appropriate spatial scale.Networks of eddy covariance flux tower can provide relatively accurate information on GPP, but they are restricted in the spatial context due to the lack of direct measurements at regional or global scales and the poor capacity for extrapolation to different environmental conditions (Beer et al., 2010;Boisvenue & White, 2019;Ryu et al., 2019).The available models usually adopt different input data and model structures, which leads to diverse model performances including inconsistencies and major uncertainties in the spatio-temporal simulations (Anav et al., 2015;Xie et al., 2020).Using existing measurement networks, Xie et al. (2020) demonstrated that the predictive ability of GPP at site scale is dependent on climate and vegetation type.Moreover, the GPP model's prediction capacity suffers in regions with less reliable climate data and/or sparse coverage measurements.This lack of data regions where GPP has not been precisely quantified was not considered to have a decisive effect on the continent-scale result (Walther et al., 2002;Yao et al., 2012).
Semi-arid and in particular Mediterranean regions have received little attention with regard to GPP despite their sensitivity to climate change (IPPCC, 2019).The diversity in landscapes, disturbances and human management that impacts the balance between carbon uptake and release complicates the quantification of GPP in the Mediterranean region.Recent global modelling efforts indicate that semi-arid ecosystems have predominantly an increasing trend and inter-annual variation of net CO 2 exchange with the atmosphere, mainly driven by water availability (Ahlström et al., 2015;Poulter et al., 2014).As water exerts a primary control on CO 2 exchange in semi-arid ecosystems, there is growing concern that future changes in water availability may alter their capacity to mitigate anthropogenic emissions (Sala et al., 2012).However, due to limited data availability, the linkage between water fluxes, terrestrial biota and net CO 2 exchanges is poorly understood, and thus, a high degree of uncertainty regarding GPP estimates persists for those regions (Biederman et al., 2016).
Given the significant role of semi-arid ecosystems in the global carbon balance as well as the data limitation, there is a need to test different observation approaches in order to obtain rapid and cost-effective estimations of GPP for these ecosystems.
Considering that the hydrological cycle plays an important role in the carbon cycle, the aim of our study was to obtain first-order estimates of GPP by the isotope mass balance approach for terrestrial semi-arid ecosystems in Mediterranean regions where direct measurements are rare or absent and thus improve the global terrestrial carbon budget estimation.The proposed method is based on the fact that the water and carbon cycles are coupled during the photosynthesis process.The measure of this coupling, water use efficiency (WUE), mandates that a plant has to transpire a certain number of water molecules in order to fix one mole of carbon.Thus, knowing the hydrologic budget of a system, it is possible to calculate the associated carbon flux.This approach relies mainly on land-based hydrological (river discharge) and meteorological (precipitation) data that have been monitored for decades and is readily available for most river basins.The same technique can be applied to a variety of scales, from a small watershed to a subcontinental river, without additional complexity (Barth et al., 2007;Freitag et al., 2008;Jasechko et al., 2013;Karim et al., 2008).The proposed method requires only stable water isotope measurements and is cost effective in comparison to existing approaches such as the direct measurements required for biological approaches.
The study was conducted in semi-arid Corsica Island in France, a region never before subjected to any investigation of carbon fluxes, but located at the heart of a dense network of carbon flux measurements programmes covering most of Europe.Hydrological and meteorological conditions of the study area are well described, and the relevant data can be easily obtained from many sources.Furthermore, Corsica Island encompasses distinct hydrological, climatic and vegetation sub-regions that offers the means to study relationships between carbon cycling and various environmental parameters.The study has the following specific goals: (1) to obtain first-order estimates of GPP for watersheds with contrasted environmental conditions in semi-arid regions, adapting the isotopic approach for those regions; (2) based on these results, to evaluate the link between water fluxes, terrestrial biota and net CO 2 exchanges; and (3) to help to substantiate, modify or disprove available interpolated GPP for semi-arid regions.

| Study sites
Corsica island (western Mediterranean, France, Figure 1) has a typical Mediterranean climate, with warm, dry summers and mild, wet winters with heavy rains.Due to the high elevation, mean temperatures and precipitation vary considerably depending on the altitude.Average annual precipitation increases from about 600 mm a À1 near the coast to more than 1,600 mm a À1 at 1,500 m a.s.l., while the mean annual temperature decreases from 16 C near the coast to 10 C at 1,500 m a.s.l (Bruno et al., 2001).The inland part of the island has alpine climate conditions with high snowfall during the winter and rain occurring even during the driest months (Rome & Giorgetti, 2007).
The Tavignanu River watershed and the Fium'Altu River watershed, located in the eastern part of the island (Figure 1), were selected for this study due to their contrasted morphological and hydroclimatic conditions.
The Tavignanu River watershed extends over an area of 798 km 2 .
The main river descends from 1,875 m a.s.l. to sea level with a total length of 89.1 km (Figure 1a), resulting in a remarkably steep mean downhill gradient and showing strong contrasts in term of land cover type (Figure 1b).The drained area of the Tavignanu River watershed is composed of three main geological units: the highly fractured Hercynian granitic basement, the fractured Mesozoic calc-schist basement of Alpine Corsica and the marine sedimentary rocks from the Tertiary covered by post-glacial alluvial deposits (Figure 1c).These three geological units have an aquifer potential (Mattei et al., 2021).
The Fium'Altu River watershed is a smaller watershed covering an area of 127 km 2 .The main river flows 30.8 km through a forested low mountain range on fractured Mesozoic calc-schist basement from Alpine Corsica (Egal, 1992) to sea level (Figure 1).The presence of many springs in the metamorphic unit highlights the aquifer potential of the fractured calc-schists basement (Caritg et al., 2009).
Both river flows have an increased discharge rate from late October to May that matches seasonal precipitation patterns.During the driest months, from July to September, the flows decrease considerably but remain perennial.On a decadal scale, high discharge fluctuation is observed (Figure 2) in response to wet-dry periods.The mean annual discharge of the Tavignanu River and Fium'Altu River for the 2010-2020 period is estimated to be 11.70 and 1.36 m 3 s À1 , respectively (available at the French database Banque Hydro http://www.hydro.eaufrance.fr/)(Figure 2).

| Concept
Long-term meteorological, hydrological and land cover data together with stable water isotopes measurements are used to estimate water balance and transpiration fluxes.These results are used to calculate basin-wide annual GPP for the hydrological year 2017-2018 and 2018-2019 (Figure 3).

| Estimation of the transpiration flux
The water balance equation is the following: where ET is evapotranspiration, P is precipitation, Q is discharge and ΔS is the change in groundwater storage.Over sufficiently long time periods, ΔS becomes negligible and the equation simplifies to  Durand et al., 1993Durand et al., , 1999)).The black vertical lines show the standard deviation in the precipitation amount.The grey area shows the minimum and maximum monthly values of discharge recorded during the period considered.
F I G U R E 3 Simplified workflow to calculate GPP using isotope mass balance approach, meteorological data and vegetation information from satellite data The water input and output parameters, P and Q, are directly measurable.The evapotranspiration term (ET) includes evaporation (E), transpiration (T) and interception (I): In order to separate ET into its sub-components, we have calculated E using an isotope balance equation (Gonfiantini, 1986) with the modifications for the Mediterranean regions (Mattei et al., 2021).
The modified isotope balance approach includes monthly quantification of different water sources contributing to the river discharge by End Member Mixing Analysis (EMMA) based on the major element composition of the river water (Data S1 and Table S1, supporting information).This approach is suitable for complex flow systems involving the mixing of different water sources in various proportions over time and allows the discrimination of isotopic variation due to evaporation from that originating by mixing processes as described in Mattei et al. (2021).
The rainfall interception by the vegetation cover, I, is calculated from the maximum daily storage capacity, Smax (in mm) (de Roo & Wesseling, 1996): where LAI is the leaf area index and P is the daily rainfall.
The calculation of the interception is performed in a discretized way over the study area (250 m Â 250 m grid cells) in order to best reflect the differences in the vegetation cover.For each grid cell, the corresponding biweekly LAI data are downloaded from MODIS (Moderate-Resolution Imaging Spectroradiometer; https://modis.gsfc.nasa.gov/)and are linearly interpolated to obtain daily data.In addition, for each grid cell, the daily meteorological data from the corresponding Météo-France SAFRAN (Système d'Analyse Fournissant des Renseignements Atmosphériques à la Neige) grid cell (Durand et al., 1993(Durand et al., , 1999) ) are used to make the daily intercept calculations.The daily values obtained per grid cell are summed to obtain annual totals and perform the transpiration calculation.

| Estimation of the GPP
Subsequently, GPP can be estimated for a given basin, as follows: where T is transpiration and WUE is the water use efficiency of vegetation, which represents the number of moles of H 2 O transpired to allow the sequestration of one mole of carbon.The WUE depends on the photosynthetic strategy of the vegetation (C 3 and C 4 type) that in turn depends on the conditions in which the vegetation is located (altitude and climate).
As a description of the photosynthesis strategy of the different plant species according to their location is lacking for the study area, we used a normalized difference vegetation index (NDVI) approach to determine it (Sage & Kubien, 2007).The approach considers that the maximum activity of C 3 plants differs from that of C 4 plants.follows, using SAFRAN weather data (Jasechko et al., 2013): where VPD is the saturation vapour pressure.Durand et al., 1993Durand et al., , 1999)).

| Sampling and analytical procedures
Annual values for the Fium'Altu River watershed were 1,186 and 1,045 mm (SAFRAN grid cell; Durand et al., 1993Durand et al., , 1999)).Long-term average values (2009-2019) are 1,088 and 1,022 mm, respectively, for the Tavignanu River watershed and for the Fium'Altu River watershed (SAFRAN grid cell; Durand et al., 1993Durand et al., , 1999)).Therefore, for both watersheds, the hydrological year 2017-2018 can be considered as wet from a hydrological point of view, whereas the hydrological year 2018-2019 is close to the long-term average.The distribution of precipitation is different for the two hydrological years studied (Figure 4).In 2017-2018, precipitation is distributed throughout the year with maximum values obtained in the spring, while for 2018-2019, precipitation has high values in the fall and late spring in both watersheds.
δ 2 H values of river water and rainfall samples collected in the Tavignanu River watershed and Fium'Altu River watershed are presented in Figure 4.For both study sites, the δ 2 H composition of precipitation showed marked seasonal variations, with winter precipitation more isotopically depleted than summer rainfall.Similarly, river water also exhibited seasonal differences (Figure 4).However, in comparison to precipitation, the seasonal pattern of stream water is lagged and damped.The influence of δ 2 H-depleted winter precipitation was more pronounced in river water compared to the influence of δ 2 H-enriched summer precipitation (Figure 4).The δ 2 H values measured in both the Tavignanu River and Fium'Altu River during spring and summer months were lower compared to precipitation, with relatively stable values observed during the driest months (Figure 4).These observations reflect the important contribution of water reservoirs with longer residence times and more stable δ 2 H, integrating seasonally variable precipitation inputs to the river flow (Mattei et al., 2021).
Quantification of the different water sources contributing to the river flow by EMMA, based on the major element composition of the river water, allowed the discrimination of isotopic variation that occurred by evaporation from that originated by mixing processes and to quantify surface runoff and evaporation (Table 1).1).However, the amount of precipitation alone cannot explain the observed difference in transpiration fluxes.
While, for the Fium'Altu watershed, the amounts of precipitation of 2017-2018 and 2018-2019 are very close (1,186 and 1,045 mm, respectively), the amount of transpiration is more than twice as high in 2017-2018 than in 2018-2019 (501 and 196 mm, respectively).
The obtained results showed the dependency of transpiration on water availability throughout the year, as previously observed in other studies in different environment types (e.g., Cienciala et al., 1994;Liebhard et al., 2022;Xu & Yu, 2020).Furthermore, the amount of transpired water seems to be gradually increasing in response to the increased amount of precipitation.For the hydrological year 2017-2018, the precipitation amount over the Tavignanu River watershed was 305 mm higher than over the Fium'Altu River watershed, and the transpiration amount was 170 mm higher.For the hydrological year 2018-2019, the precipitation amount over the Tavignanu River watershed was only 46 mm higher than over the Fium'Altu River watershed, while the transpiration amount was 238 mm higher (Table 1).Temperature and light conditions were similar for both years.These results highlight that transpiration cannot increase proportionally with water availability indefinitely.In our case study, it River watershed, plants with the C 3 pathway constitute $77% of land plant species and include mostly grassland of medium to low altitude and agricultural crops (Figure 5).The beech forests within the watershed function differently depending on hydrological conditions and altitude.For the Fium'Altu River watershed, grasslands at medium to low altitude have mainly C 3 pathway (Figure 5).Plants with C 4 pathway constitute $77% of land plant species for the Fium'Altu River watershed and include mostly chestnut forests (Figure 5).This high proportion of C 4 photosynthetic pathway plants is normally expected for the vast tropical and subtropical grasslands and savanna regions (Still et al., 2003).These results show the non-uniform character of the vegetation in the Mediterranean area and the capacity of plants to adapt their photosynthetic pathway to the climatic conditions (Sage, 2004).
C 4 plants are known to have higher rates of CO 2 assimilated during photosynthesis to transpired H 2 O compared to C 3 (Ghannoum et al., 2011).Long-term measurements of WUE show averages of 1 mol CO 2 per 500 to 1,500 mol H 2 O for C 3 plants and 350 to 550 mol for C 4 plants (Jones, 1992;Molles, 2002).In the two watersheds, calculated WUE data from atmospheric conditions by type of photosynthetic pathway used by plants are very close and consistent with the previous long-term measurements (Table 2).However, considering C 3 -C 4 vegetation abundances, weighted mean of WUE varies highly from one watershed to another and for the same watershed from one year to another (Table 2).CO 2 assimilation rates of both driver of the inter-annual global carbon budget variability and the important role, recently identified, played by semi-arid ecosystems in this inter-annual variability (Ahlström et al., 2015;Biederman et al., 2016;Jung et al., 2017;Poulter et al., 2014).
The above derived transpiration flux and WUE were used to estimate the GPP in the Tavignanu River and in the Fium'Altu River watersheds (Table 2).For the Tavignanu River watershed, this calculation yields an annual GPP of 566 gCÁm À2 Áyear À1 for the hydrological year 2017-2018 and 314 gCÁm À2 Áyear À1 for the hydrological year 2018-2019.For the Fium'Altu River watershed, this calculation yields an annual GPP of 741 gCÁm À2 Áyear À1 for the hydrological year 2017-2018 and 240 gCÁm À2 Áyear À1 for the hydrological year 2018-2019.
These estimations show that unit GPP across both biomes appears to be strongly dependent on water availability.However, the relationship seems to be equivocal.Our results indicate unit GPP is not systematically higher when transpiration flux is higher.Transpiration of the Tavignanu River watershed is one third higher than transpiration of the Fium'Altu River watershed for the hydrological year 2017-2018 but the unit GPP is one third lower (Tables 1 and 2).The GPP unit is not systematically higher in areas where the C 4 vegetation proportion, with more efficient water utilization, dominates.For the hydrological year 2018-2019, the GPP unit is lower on the Fium'Altu River watershed than on the Tavignanu River watershed while the C 4 vegetation proportion is higher (Table 2).The studied ecosystems show a capacity to adapt and overcome water availability limits.The GPP variability relates to site-specific functioning that underlines the need to understand fluxes and their intra-and inter-annual drivers in semi-arid areas and to prioritize research on slow-changing controls (Anav et al., 2015;Biederman et al., 2016).

| GPP comparison
Since the current study is based on the transpiration flux estimated by isotope mass balance, we assume that possible sources of error in proposed GPP estimates could be related to the water balance and isotope mass balance, or the WUE values used for calculation.The uncertainty of the determined evaporation is controlled by the repeatability of the isotope measurements but also by estimated humidity and the estimated isotopic composition of the atmospheric water vapour (Gibson et al., 1993).The uncertainty of the transpiration estimation depends on the variability of the calculated values for interception and evaporation but is also controlled by the input data for precipitation and runoff.It remains challenging to estimate an overall uncertainty on the GPP calculation by propagation of error analyses.
To validate our results, we considered it necessary to compare our results with those obtained by other methods.
We first compared GPP calculated by isotopic approach with MODIS GPP product that has served as an effective tool to assess the terrestrial carbon budget for the entire globe since 2000 (Xie et al., 2021).The comparisons between modelled GPP and calculated GPP by isotopic approach are shown on Table 2.For both watersheds, GPP values from MODIS are higher for the hydrological year 2018-2019 than for the hydrological year 2017-2018.However, lower MODIS GPP variations under different water availability conditions are observed for both watersheds compared to those obtained by isotopic approach.The Tavignanu River watershed, consistently, has the highest GPP estimates with MODIS approach.MODIS's difficulties in accounting for water stress effect on GPP have already been well documented over different biome types and climates (Gilabert et al., 2015;Hwang et al., 2008;Mu et al., 2007;Xie et al., 2020).
However, MODIS GPP values are up to more than seven times higher than GPP values estimated by the isotopic approach.Even if MODIS's tendency to overestimate GPP at low productivity sites has previously been pointed out, the discrepancy observed was not as great (Turner et al., 2006;Xie et al., 2020).
Thus, second, we used the Global Primary Production Data Initiative (GPPDI) database that includes GPP measurements that were collected over a long time by many investigators using different methods (Olson et al., 2013).The GPPDI database was used to compare GPP calculated by isotopic approach and MODIS with those obtained by biological methods.The data set covers 2,523 individual sites and allows a direct comparison (Figure 6).When plotting GPP of worldwide biomes versus temperature and precipitation, GPP calculated with the MODIS for the Tavignanu River and the Fium'Altu River watersheds was far above GPP values recorded for all biomes and climate zones.These overestimated values might be due to the previously demonstrated inability of MODIS to capture the impact of water stress on photosynthesis (Gilabert et al., 2015, Xie et al., 2020).
This limitation is here exacerbated due to the low amount of available  When plotting GPP of worldwide biomes versus temperature and precipitation, GPP values calculated with the isotopic approach for the Tavignanu River and the Fium'Altu River watersheds fall into the zone of evergreen and deciduous temperate forests, which accurately reflects the predominant vegetation cover in the two watersheds (Figure 6).Although there is a broad picture consistency, GPP values calculated by isotopic approach for the hydrological year 2018-2019 are close to the minimum values recorded for this type of biome, and GPP values calculated by isotopic approach for the hydrological year 2017-2018 are among the maximum values recorded (Figure 6).
Therefore, the isotopic mass balance approach appears to be a suitable approach for obtaining first-order estimates of GPP for terrestrial ecosystems in those regions where direct measurements are rare or absent.
Location of the studied watersheds: topographic map (a), land use (b) and simplified geology (c) F I G U R E 2 Averaged monthly precipitation (blue bar plot) and discharge (black line) of the Fium'Altu River watershed (a) and Tavignanu River watershed (b) for the 2010-2020 period (SAFRAN grid cell; C 3 plants are more active in spring and autumn and C 4 plants in summer.Satellite data that are used to calculate the monthly NDVI are sensitive to vegetation vigour.Thus, the season with the maximum NDVI provides indirect information on the type of vegetation.If the maximum is during the summer (June, July and August), the plant is of type C 4 ; otherwise, it is of type C 3 .The listing of the plant type is done in a discretized way on the study area.Once the plant type is known, the daily calculation of WUE (H 2 O: mmol C) is performed per grid cell as seems that reached 1,200 mm of precipitation, transpiration increases less in function of water availability than under 1,200 mm.These results highlight the existence of a threshold value for the transpiration amount even when water availability, light and temperature are non-limiting factors.F I G U R E 4 Monthly variations in precipitation (black solid squares) and stream water δ 2 H (empty black circles), discharge (grey area) and rainfall (blue bar plot) for the Fium'Altu River watershed (a) and the Tavignanu River watershed (b) 3.2 | Gross primary production In this study, vegetation distribution is principally used to estimate WUE by plants in the watershed and GPP.The cross-referring data of NDVI from MODIS and land use allowed estimation of the spatial distribution of C 3 and C 4 photosynthetic pathway of plants on the Tavignanu River and Fium'Altu River watersheds.For the Tavignanu watersheds are greater for the 2017-2018 hydrological year than for the 2018-2019 hydrological year.The difference is greater for C 3 vegetation photosynthetic pathway plants than for C 4 .The two hydrological years differ mainly in the distribution of precipitation over the year and thus water availability.Obtained WUE values are above the global mean of 1 mol CO 2 per 245 to 435 mol H 2 O estimated by Jasechko et al. (2013).That is not surprising since Ahlström et al. (2015) showed that the mean proposed by Jasechko et al. (2013) is dominated by highly productive lands (mainly tropical forests).Our results confirm both the role of water availability as predominant F I G U R E 5 Plant photosynthetic pathway distribution (C 3 in purple and C 4 in pink) for the Fium'Altu River watershed (a) and the Tavignanu River watershed (b) carbon flux observation data needed to calibrate the model.These results cast doubt on MODIS GPP estimates for these two Mediterranean watersheds and underline the need to develop a flux tower observation network in different climate and vegetation types in order to improve the basic description of the carbon cycle process in modelling algorithms.Our results challenge the possibility of estimating global carbon fluxes without prior investigation of the water budget.
4 | CONCLUSIONIn this study, considering the important role that the hydrological cycle plays in carbon cycling, we provide a rapid and affordable estimation of basin-wide GPP of two watersheds with contrasted environmental conditions in the Mediterranean region.An isotope mass-balance equation adapted to the specific climate conditions was implemented to determine annual evaporation flux, which, in turn, was used to determine the amount of water transferred to the atmosphere by plant transpiration.We used a GIS-based approach to determine vegetation photosynthetic pathway distribution in order to estimate WUE and then GPP.By studying two hydrological years, our results highlighted a strong dependence of GPP on water availability throughout the year.We have found a potential threshold value in transpiration fluxes even when water availability, light and temperature are non-limiting factors.The comparison made with GPP values obtained in worldwide biomes by biological methods enabled us to validate these results and to demonstrate the limitations of MODIS to estimate GPP in these semi-arid territories.These findings can be explained by MODIS's limitations for capturing the impact of water stress on photosynthesis, which is exacerbated by the specific F I G U R E 6 GPP data of various terrestrial ecosystems plotted against annual temperature (a) and precipitation (b) (fromOlson et al., 2013).The squares and diamonds indicate corresponding data and variability for the Fium'Altu River watershed and the Tavignanu River watershed, respectively, obtained by MODIS approach (in red) and by isotopic approach (in purple) for the hydrological years2017-2018 and  2018-2019.climatic conditions and the low density of existing records for model calibration in the studied biome type.Our results underline the need to continue the effort to increase the density of networks to measure CO 2 exchange between ecosystems and the atmosphere in order to improve basic assumptions to describe the carbon cycle process used in modelling algorithms.Obtained outcomes showed the importance of the water budget estimation in global carbon flux modelling and evaluation.We recommend investigations of GPP by the isotope mass balance approach where direct carbon fluxes measurements are rare or absent in order to help to substantiate, modify or disclaim interpolated GPP in semi-arid regions and obtain a consensus on global GPP estimates.
for 2 H than for18O, with respect to the seasonal differences, the precision of 2 H analysis is advantageous over 18 O to identify changes.Water samples for major element analyses (K + , Na + , Mg 2+ , Ca 2+ , (Huneau et al., 2015)7 and September 2019, physical and chemical parameters (temperature, pH, electrical conductivity and dissolved oxygen) of the Tavignanu River and Fium'Altu River waters were measured monthly in situ at the Faiu bridge, 18 km from the mouth (Figure1), using a WTW 3310 conductivity metre, a WTW 3310 pH metre and a WTW 3310 IDS Oximeter (WTW GmbH, Weilheim, Germany).Alkalinity was determined, using a HACH digital titrator (Hach Company, Loveland, CO, United States), in the field by volumetric titration.Water samples were collected for analyses on stable water isotopes and major elements.In addition, from January 2015 to November 2019, monthly precipitation was sampled for stable water isotope analyses at four different stations of the Corsican network for isotopes in precipitation(Huneau et al., 2015): Corte 350 m a.s.l. and Bastia 5 m a.s.l.(Figure1).(CNRS UMR 6134 SPE), University of Corsica, France.Ratios of 18 O/ 16 O and 2 H/ 1 H are expressed in delta values (δ 18 O and δ 2 H) (‰) relative to the VSMOW reference material (Vienna Standard Mean Ocean Water) with an analytical precision better than 0.5‰ for δ 2 H and 0.2‰ for δ 18 O.As δ 18 O and δ 2 H co-vary in a predictable manner, only 2 H will be used for the purposes of this study.Even if absolute differences are larger Water fluxes associated with precipitation, river discharge and calculated evapotranspiration are shown in Table 1 for each studied watershed.The annual precipitation in the Tavignanu River watershed, for the hydrological years 2017-2018 and 2018-2019, was 1,491 and 1,092 mm, respectively (SAFRAN grid cell; T A B L E 2 Average annual WUE for C 3 and C 4 photosynthetic pathway plants and GPP estimated by isotope mass balance approach and by satellite data driven model (MODIS) of the Tavignanu River and Fium'Altu River watersheds for the hydrological years2017-2018 and 2018- 2019