Half-hourly data of the “Faidherbia-Flux” site from 2018 to 2023 were extracted from the database. The eddy-covariance system (Li-COR SMARTFLUX including a Gill MasterPro 3D sonic anemometer and a LI-7500 RS open path CO₂ and H₂O gas analyzer) was mounted at 20 m high on a 30 m high mast and monitored the ecosystem exchange of sensible heat (H), latent heat (LE), and CO₂ above the agroforestry system including trees, crops, and soil. Climate variables measured at 20 m high include air temperature and relative humidity (also measured at 2 m high), wind speed, atmospheric pressure, and rainfall by making use of the CS215 Campbell, the WindSonic 4 Campbell, the SMARTFLUX, and the Texas Electronics model TE525MM instruments, respectively. Net radiation was measured at 20 m by a nRlite net radiometer (Kipp & Zonen).

The eddy-covariance raw data were acquired at a frequency of 20 Hz using SMARTFLUX and post-processed using the advanced mode of the EddyPro v7.0 software by making use of the SMARTFLUX “.ghg” files. The following options were used in EddyPro: (1) raw data processing (automatic angle-of-attack correction for wind components (Gill sonic anemometers), double axis rotation for tilt correction, block average detrend method for turbulent fluctuations, covariance maximization with default for time-lag compensation); (2) compensation for density fluctuations (WPL terms, Webb et al., 1980); (3) quality checks – flagging policy (Foken et al., 2005); (4) statistical tests for raw data screening following (Vickers and Mahrt, 1997); (5) estimation of random uncertainty due to sampling error (Finkelstein and Sims, 2001); (6) spectra and cospectra calculation and corrections (low-frequency range according to Moncrieff et al. (2005) and high frequency range according to Moncrieff et al. (1997)). Footprints were computed according to Kormann and Meixner (2001), using the FREddyPro R package (Xenakis, 2016). Gap-filling and partitioning of CO₂ data were performed using the ReddyProc R package (Wutzler et al., 2018), selecting the daytime partitioning model of Lasslop et al. (2010). The partitioning of GPP between tree and crop takes advantage of the reverse phenology of Faidherbia albida: trees are completely defoliated during the rainy season, when crops are growing and are leafy during the dry season, when crops are absent. A simple temporal separation is therefore sufficient to distinguish tree and crop contributions.

Tree leaf area density was estimated by optical indirect measurements every ten days at 4 azimuths under 13 trees and above (in a nearby clearing) at the plot scale using the Li-Cor LAI2200, at dawn to have 100 % diffuse light and further analyzed following the “isolated tree” protocol (Li-Cor, 2012; Taugourdeau et al., 2014). Tree leaf area index (LAI) was computed by multiplying the crown volume by leaf area density and dividing by the projected crown area. Tree LAI was filtered for anomalous data which occur when below and above canopy measurements do not perfectly represent the same sky area and gap-filled using visual estimation of the proportion of leaves in the crowns, monitored every ten days by one single operator.

Crop LAI dynamics were derived at the semi-hourly time-step from normalized difference vegetation index measurements using a proxy detection of normalized difference vegetation index sensor placed on the tall mast and directed to the crops (Pontailler et al., 2003), with data filtering according to Soudani et al. (2012) and an annual calibration of normalized difference vegetation index with the actual crop LAI from crop harvest in subplots, according to Diongue et al. (2022) and Roupsard et al. (2020).

The dominant soil around Niakhar contains 88.1 ± 4.9 % sand, 6.1 ± 0.6 % silt, and 5.8 ± 1.6 % clay and is poor in organic matter (Diongue et al., 2022; Roupsard et al., 2020). The soil depth is about 8 m limited by the Eocene sandstone bedrock. Soil humidity at nine depths (15, 30, 50, 75, 100, 125, 150, 175, and 200 cm) were recorded with automated time domain reflectometers (CS615, Campbell Scientific, UK) (Diongue et al., 2022). Groundwater fluctuations between 5 and 6 m were recorded with piezometers and revealed a brackish water table at a depth of approximately 6 m (Diongue et al., 2023). The soil water content in the capillary fringe of the groundwater (SWCC) was measured with a time domain reflectometer probe inserted at 4.8 m deep in a well.

The rubisco activity (Vcmax) and the electron transport rate (Jmax) were measured from A_Ci and A_PAR curves every two weeks for 3 days in a row, in the same tree on sunlit leaves of the top canopy from January to April (Vandewalle, 2024).

Vegetated areas in the model are defined by up to 14 plant functional types (PFTs) in addition to bare soil. A PFT is characterized by a classification scheme that takes into account morphology (tree or grass), leaf morphology (needleleaf or broadleaf), phenology (evergreen, summer-green, or rain-green), photosynthetic pathway (C₃ and C₄), and climatic zones (boreal, temperate and tropical) (Krinner et al., 2005; Poulter et al., 2015). Each PFT is assigned a fraction of the pixel area (the sum of all PFT fractions being 1).

The soil water column is divided into three hydrological tiles with homogeneous soil hydrological properties (Boucher et al., 2020), one for bare soil, one for short vegetation, i.e. croplands and grasslands, and one for tall vegetation, i.e. trees. Within each soil tile all PFTs share the same water, inducing competition, whereas there is no interaction between the water consumption of vegetation in different soil tiles. The energy budget is calculated for each PFT independently and then averaged according to the area fraction of each PFT into a pixel-level energy budget. There is therefore no competition for light between different PFTs.

For this study, three PFTs were used: bare soil, tropical deciduous summer-green trees, and C₄ crop with areal cover fractions of 0.1, 0.15, and 0.75 respectively to simulate the observed tree density.

The soil representation in the standard configuration of ORCHIDEE is based on a multi-layer physical description of the soil. By default, the soil depth is set at 2 m (Fig. 2) and the soil is discretized into 11 layers of increasing thickness following a geometric series with a ratio of two (Campoy et al., 2013; de Rosnay et al., 2002). In the Faidherbia configuration, the soil depth was increased to 7 m (Fig. 2), and the soil was discretized into 120 layers following Ducharne et al. (2018) to ensure numerical schemes' stability. A finer resolution was used in the upper soil layers with a geometrical increase of soil layers from surface to 0.15 m (ratio: 1.8) to capture the strong gradient of soil moisture and temperature near the surface. From 0.15 to 6.5 m, a constant layer thickness of 0.065 m is applied to simplify the model where gradients are less pronounced. Between 6.5 and 7 m, the geometric progression resumes to ensure numerical stability as strong soil moisture gradients are again modelled as a result of free drainage at the soil bottom.

Soil texture in the standard configuration, defined by the fractions of sandy loam, loam, and clay loam, is homogeneous in the pixel and controls the soil parameters, i.e., field capacity and wilting point, Van Genuchten parameters (Boucher et al., 2020), which are assumed constant through time. In the Faidherbia configuration, soil texture and soil hydrological parameters were taken from Diongue et al. (2022) and Roupsard et al. (2020) as summarized in Table S1.

In the standard configuration, the bottom soil layers allow free drainage which prevents simulating groundwater dynamics. In the Faidherbia configuration, groundwater was simulated by forcing a dynamic water content of soil layers between 4 and 5 m and imposing water saturation below 5 m, following Campoy et al. (2013). Groundwater forcing was exclusively implemented for the hydrological tile dedicated to tree PFTs.

In ORCHIDEE, the structural root profile defines the root biomass distribution in the soil and hence depends on the carbon allocation. In turn, the functional root profile defines which soil layers plants can draw water from. As only the functional profile was modified in this configuration, root profile hereafter refers to this functional profile, which is defined following Eq. (1): 1Rf(i)=0,if i=10,if ∑i=2nmax0,Wi-Wp,i≤0max0,Wi-Wp,i∑i=2nmax0,Wi-Wp,i,if i>1 and ∑i=2nmax0,Wi-Wp,i>0 where i is the index for each soil layer, Rf represents the root profile at position i (unitless) and ranges between 0 and 1, n is the total of soil layers, Wi represents the soil moisture at position i (kg m⁻²) and Wp,i represents the wilting point moisture at position i (kg m⁻²).

In the standard model configuration, maximum crop root depth is 0.8 m and maximum tree root depth is 2 m (Fig. 2). In the Faidherbia configuration, crop and tree root depths were increased to 2 and 7 m respectively to match field observations and the root profile was adjusted to be partially consistent with recent observations of Siegwart et al. (2023). It was assumed that crops use water from soil layers up to 2 m in depth, whereas tree roots take up water from depths below 4 m (Fig. 2). Tree water uptake from superficial roots was ignored, an assumption supported by their observed low contribution to total tree water use (Roupsard et al., 1999) and is further explained in the discussion Sect. 4.1 and 4.2. Thus from Eq. (1), the adjusted root profile for Faidherbia albida is calculated following Eq. (2): 2Rf(i)=0, if i<i4m0, if i≥i4m and ∑i=i4mnmax0,Wi-Wp,i≤0max0,Wi-Wp,i∑i=i4mnmax0,Wi-Wp,i, if i≥i4m and ∑i=i4mnmax0,Wi-Wp,i>0 where i is the index for each soil layer, i4m represents the index of the soil layer at 4 m, Rf represents the root profile at position i (unitless) and ranges between 0 and 1, n is the total of soil layers, Wi represents the soil moisture at position i (kg m⁻²) and Wp,i represents the wilting point moisture at position i (kg m⁻²). All soil and root depths, and soil water content parameters used in this study are summarized in Table S1.

In the standard configuration, leaf onset for tropical trees is driven by soil moisture constraints on growth (Eamus et al., 2013; Murphy and Lugo, 1986) and is therefore modelled as a function of water stress as calculated over the whole soil column (Botta et al., 2000). The detailed calculation of water stress is provided in Sect. S1 in the Supplement. Leaf onset can be triggered by three conditions: (1) either when a given time has passed since the minimum soil moisture for plant growth was recorded, and (2) the weekly moisture availability is higher than monthly moisture availability, or (3) when the monthly moisture availability exceeds a prescribed critical moisture availability. In the Faidherbia configuration, a time delay was added to these previous water stress conditions based on observations by Roupsard et al. (2022), who found that the first leaves of Faidherbia albida appeared on average 30 d after groundwater rise (Fig. 2).

In the standard model configuration, the phenology for the crop PFT is based on a combination of growing degree days (Chuine, 2000) and water stress (Botta et al., 2000). In the Faidherbia configuration, the same temperature and water stress conditions apply but a rainfall amount threshold was added, specifying that leaf onset can only occur if there is a minimum of 10 mm of rainfall over three days (Berg et al., 2010; Marteau et al., 2011; Ndiaye et al., 2024). This constraint ensures that leaf emergence is not triggered by very minor precipitation events.

In the standard configuration, crops are harvested abruptly just after the senescence stage starts, unlike trees, in which leaf biomass gradually dies during the senescence period. This abrupt crop harvest does not reflect the harvesting practices of farmers in the study region, because the most common practice is to pull or cut the panicle of the millet stalk just below where the grain is formed (Hedayetullah and Zaman, 2022). The stalks can then be harvested from 80 cm above the ground (Kajuna, 2021; Lericollais, 1999), leaving some leaves which regrow at the internodes and thus allowing photosynthetic processes to continue before complete stalk mortality. In the Faidherbia configuration, in order to represent this process, a parameter was defined as a delay between senescence start and harvest adding a senescence stage in the crop life cycle. The newly defined crop senescence stage reproduces senescence and turnover processes used in the standard model for grasslands (Fig. 2) where biomass die-off depends on the growing degree days and leaf lifespan consistent with millet photoperiodism (Adole et al., 2019; Sanon et al., 2014). This adjustment results in a slow biomass decay until harvest when all parts of the crops are removed.

In the standard configuration, ORCHIDEE simulates C₃ plant leaf-level photosynthesis using the extended Farquhar et al. (1980) model from Yin and Struik, (2009). This model considers the influence of rubisco activity (Vcmax) and electron transport rate (Jmax) on CO₂ assimilation. Most model parameters follow Yin and Struik, (2009) except Vcmax and Jmax, which are constrained by nitrogen use efficiency and acclimate to growth temperature (Kattge and Knorr, 2007; Medlyn et al., 2002). In the standard configuration, Vcmax is calculated from leaf nitrogen content at the top of the canopy and nitrogen use efficiency (NUE) of Vcmax which is prescribed for each PFT. In contrast, Jmax is calculated as a linear function of Vcmax and growth temperature (Kattge and Knorr, 2007). In the Faidherbia configuration, site observations of Vcmax and Jmax were used to parameterize NUE and Jmax (Sect. 2.2.3).

For trees, the “reverse phenology” of Faidherbia albida with its growing season in the dry season was reproduced by the model with an RMSE of 0.15. Simulated and observed peaks in LAI were aligned with the dry growing season and the wet dormant season of this tree species (Fig. 3e). Over the evaluation period, a maximum measured tree LAI of 0.81 was recorded, while maximum simulated LAI values reached 0.73. However, during 2 out of 3 evaluation years, the maximum tree LAI was overestimated by the model by 11 % and 13 % in 2020–2021 and 2022–2023 respectively (Fig. 3e). The interannual variability of the simulated tree LAI was lower in the simulations than in the observations with a standard deviation of the maximum LAI of 0.002 in simulations compared to 0.09 in observations, and a standard deviation of the maximum LAI day relative to the emergence day is 1 d in simulations and 17 d in observations over the evaluation period (Fig. 3e).

Regarding crops, the model simulated a maximum daily LAI of 0.90 compared to the observed maximum daily crop LAI of 1.20 with an RMSE of 0.26 over the evaluation period (Fig. 3f). With a single parameter set being used irrespective of the crop species, the model goodness-of-fit did not appear to depend on the actual crop sown. The day of maximum LAI was simulated with a delay of +17, -7, -10 d in 2021 to 2023 respectively (Fig. 3f). For crops, similar to trees, the model underestimated the interannual variability of LAI over the evaluation period. Specifically, the maximum crop LAI was underestimated by 28 %, 24 %, and 22 % in 2021, 2022, and 2023, respectively (Fig. 3f).

The observed daily tree GPP reached a peak value of 4.74 gC m⁻² d⁻¹, closely matched by the model's maximum prediction of 4.75 gC m⁻² d⁻¹ (Fig. 3g). During the evaluation period, the r2 between simulation and observation of the daily tree GPP was 0.16 (n=666) and RMSE of 0.97 gC m⁻² d⁻¹. However, the model consistently underestimated the annual GPP of trees, with errors ranging from 2 % to 22 % throughout the evaluation period (Table 1).

For crops, the observed daily GPP peaked at 15.76 gC m⁻² d⁻¹, while the model's maximum prediction was lower, at 13.41 gC m⁻² d⁻¹ (Fig. 3h). The RMSE for daily crop GPP was 1.80 gC m⁻² d⁻¹, and the r2 between simulated and observed values was 0.76 in the evaluation (n=1095; Fig. 3d). The model underestimated the peak daily crop GPP in 2021 (Fig. 3h). On an annual scale, the crop GPP was underestimated by 9 % to 19 % between 2021 and 2023 (Table 1).

Day-to-day variability in EC-derived GPP was lower than that of simulated GPP. This variability was pronounced for trees (Fig. 3c and g) and present but weaker for crops (Fig. 3d and h). The coefficient of variation over the whole period for the simulated GPP is 0.6 for trees and 1.6 for crops compared to 0.3 and 1.7 for observed tree and crop GPP.

For the whole ecosystem, the total annual GPP was underestimated by 18 %, 6 %, and 16 % in 2021, 2022, and 2023, respectively (Table 1). Tree contributions to the total annual ecosystem GPP varied between 32 % and 37 % in observations and between 33 % and 37 % in simulations during the 2021–2023 period.

The daily simulated latent heat flux reached a maximum of 11.56 MJ m⁻² d⁻¹ compared to the daily observed maximum of 12.66 MJ m⁻² d⁻¹ in the evaluation (Fig. 4d). The model tended to overestimate low daily latent heat flux values by the end of the dry seasons between 2021 and 2023. The evaluation yielded an RMSE of 2.12 MJ m⁻² d⁻¹ and a correlation between simulated and observed daily latent heat flux of 0.49 (n=1095) (Fig. 4d and g).

The maximum simulated sensible heat flux was 11.42 MJ m⁻² d⁻¹ , exceeding the observed maximum of 9.46 MJ m⁻² d⁻¹ between 2021 and 2023 (Fig. 4e). The evaluation indicated an r2 of 0.67 and an RMSE of 2.40 MJ m⁻² d⁻¹ for daily sensible heat flux (n=1095). However, the model consistently overestimated both low and high daily sensible heat flux values (Fig. 4e and h).

For net radiation, the simulated daily maximum was 16.08 MJ m⁻² d⁻¹ , higher than the observed daily maximum of 14.42 MJ m⁻² d⁻¹ in the evaluation (Fig. 4f). Between 2021 and 2023, the model consistently overestimated daily net radiation during the dry season. Over the evaluation period, the RMSE was 2.31 MJ m⁻² d⁻¹, and the model explained 72 % of the variability in observed daily net radiation (Fig. 4f and i).

Compared to the reference scenario with no variability in the yearly cycle of groundwater availability, SWCC_var scenarios mimic: (i) an average deficit of 19 % from October 2019 to June 2020 and (ii) an average excess of 27 % from October 2020 to June 2021 (Figs. 6a and S5a). Compared to the reference scenario with no variability in rainfall, the Rvar scenarios capture distinct rainfall patterns over the study years: (i) an annual rainfall deficit of 63 mm (12 %) in 2019, primarily driven by an early-season deficit of approximately 66 mm in July, (ii) an annual rainfall excess of 53 mm (10 %) in 2020, notably due to an early-season surplus of about 84 mm in July, and (iii) an annual rainfall deficit of 146 mm (28 %) in 2021, characterized by alternating periods of excess, such as 50 mm in July, and deficits, including 134 mm in September (late-season) (Figs. 7a and S6a).

As expected, variations in groundwater dynamics only affected tree GPP as the crop roots are too shallow to rely on groundwater (Fig. 6). For trees, accounting for groundwater variability resulted in a similar pattern in both years with a decrease in tree GPP compared to the reference at the start of the Faidherbia growing season and an increase in GPP towards the end of the season corresponding to a shift in the growing period of the Faidherbia trees (Figs. 6b and S5b). Since the early-season GPP deficit is larger than the late-season excess, these two response stages combined result in an overall decrease in tree GPP of less than 10 gC m⁻² yr⁻¹, corresponding to approximately 2 % in both 2019–2020 and 2020–2021, during the dry seasons for the RavgSWCC_var and RvarSWCC_var scenarios (Figs. 6b and 8b).

As expected, rainfall variability primarily influenced crop GPP (Fig. 7a–b), given that tree phenology is shifted to the dry season and tree roots in the model exclusively access groundwater resources. For crops, the GPP response to rainfall variability differed depending on the timing of the anomalies. In 2019, where rainfall was below the reference and early-season deficits were predominant, crop GPP decreased by at least 20 gC m⁻² yr⁻¹ (less than 4 %) under both RvarSWCC_avg and RvarSWCC_var scenarios (Figs. 7b and 8d). Conversely, in 2020, the rainfall surplus, particularly in early-season, led to an increase in crop GPP, with gains of approximately 65 gC m⁻² yr⁻¹ (11 %) under the same scenarios. Despite a severe late-season rainfall deficit in 2021, crop GPP did not show a corresponding decline. Instead, early-season rainfall excess appeared to offset the deficit, resulting in a crop GPP increase of about 86 gC m⁻² yr⁻¹ (14 %) for both scenarios (Figs. 7c and 8c).

At the ecosystem level, in the RvarSWCC_var scenario, where both rainfall and soil water content in the capillary fringe of the groundwater table varied (Fig. 8a–d), simulations indicated a decrease in ecosystem GPP of approximately 78 gC m⁻² yr⁻¹ (about 8 %) in 2019. In contrast, during 2020 and 2021, ecosystem GPP increased by 10 % to 14 %, corresponding to approximately 118 gC m⁻² yr⁻¹.

During the dry seasons, energy flux (LE and H) anomalies in the RavgSWCC_var scenario were strongly correlated with tree GPP anomalies (Fig. 6b–d). LE decreased by 8 MJ m⁻² yr⁻¹ (< 1 %) during 2019–2020 and by 11 MJ m⁻² yr⁻¹ (< 1 %) during the 2020–2021 dry season. In contrast, H increased from 5 to 11 MJ m⁻² yr⁻¹ over the same periods (Figs. 6d and S5d).

In the RvarSWCC_avg scenario, where only rainfall varied annually, energy flux anomalies were driven by crop GPP anomalies (Fig. 7b–d). LE declined by approximately 2 MJ m⁻² yr⁻¹ (< 1 %) in 2019 but increased from 14 MJ m⁻² yr⁻¹ (< 3 %) in 2020 to 68 MJ m⁻² yr⁻¹ (10 %) in 2021. During the 2019 rainy season, H increased by approximately 9 MJ m⁻² yr⁻¹ (< 3 %), whereas it declined by 2 MJ m⁻² yr⁻¹ (< 1 %) in 2020 and by 48 MJ m⁻² yr⁻¹ (11 %) in 2021 (Figs. 7d and S6d).

In the RvarSWCC_var scenario, energy flux anomalies were influenced by anomalies in tree GPP, crop GPP, and rainfall (Fig. 8). Consistent with ecosystem GPP anomalies, LE decreased by approximately 54 MJ m⁻² yr⁻¹ (5 %) in 2019 but increased from 60 MJ m⁻² yr⁻¹ (4 %) in 2020 to 116 MJ m⁻² yr⁻¹ (11 %) in 2021. In 2019, H increased by 41 MJ m⁻² yr⁻¹ (6 %), while it declined by 35 MJ m⁻² yr⁻¹ (< 3 %) in 2020 and by 81 MJ m⁻² yr⁻¹ (5 %) in 2021 (Figs. 8e and S7e).