The study site is a 12 ha cropland located in Lonzée, Belgium, with a temperate maritime climate (T‾=11.1 °C and annual precipitation of 716 mm). Cultivated for more than 85 years on a silt loam soil, this site has been equipped with an eddy covariance monitoring system and a micrometeorological station since 2004, as a part of the Fluxnet network. Since 2017, this monitoring site has integrated the ICOS network as a Level 2 station named BE-Lon (https://www.icos-cp.eu/, last access: 5 June 2025).

This study focuses on five growing seasons of winter wheat (Triticum aestivum L.) which are summarised in Table 1. Sown in late October, varieties from S17 and S22 are known to reach heading and maturity stages faster than Sahara and Smart cultivars (Meza et al., 2018, 2023). As the same cultivar was sown during S11 and S15, S11 was selected for the validation. During these five seasons, regular measurements of biomass were performed along with continuous measurements of NEE and LE. These flux data were corrected for frequency losses and filtered for low turbulence and nonstationary conditions, contributing to high-quality coverage detailed in Table 1. Flux data treatment is described in De Ligne et al. (2010) and Pastorello et al. (2020). Data collection (fluxes, biomass and soil) as well as additional information on the site, measurements, or management activities can be found in Delhez et al. (2025).

As mentioned in Sect. 2.1, S11 was not used for this multi-objective calibration but kept for validation. Parameter sets were selected from the Pareto front established with the SMPSO algorithm, and cultivar-specific parameters were taken from S15 as the same cultivar was sown during both seasons. In order to evaluate the performance of Daisy model, four criteria were estimated: (i) the RMSE expressed in the same units as the variable of interest, (ii) the rRMSE for comparison within calibration results, (iii) the Normalised Mean Error (NME) revealing bias and (iv) the model efficiency (EF) which is a normalised metric. This last criterion is also known as Nash–Sutcliffe Efficiency coefficient (NSE) and is computed as follows: 7EF=1-∑k=1nyk-dk2∑k=1ndk-dk‾2, In Eq. (7), yk and dk denote the modelled and observed values at time step k, and dk‾ is the mean observed value. The model is perfect when EF = 1, while model predictions are as accurate as the mean of observations when EF = 0, which is easily interpreted. The validation results are considered acceptable if EF is greater than 0.5 (Dumont et al., 2014).

Non-dominated solutions based on the three objective functions are depicted in Fig. 1a. The red point indicates the most balanced compromise, defined as the non-dominated solution nearest to the point representing the lowest values across all objectives. The trade-off between DM and NEE is the most clearly defined, as shown in the 2D projection (Fig. 1b), where the curved Pareto front extends over a large part of the objective space. This 2D front portrays 29 % of the solutions from Fig. 1a, and the other solutions (grey crosses) mainly lie along it. Conversely, the LE–NEE front appears angular and narrower, particularly along the LE axis (Fig. 1c). Combined with the relatively high rRMSE, it highlights the difficulty in accurately simulating observed LE as well as the limited model responsiveness for this objective.

Values of the most balanced parameter set (i.e., red point) can be found in Appendix B (Table B1) along with algorithm convergence indicator (Fig. B1). In Fig. 1a, the specific coordinates of this point are (0.27, 0.40, 0.52) which correspond to RMSE values of 0.948 t ha⁻¹, 3.44 µmol m⁻² s⁻¹ and 62.7 W m⁻² for DM, NEE and LE respectively, computed across all four growing seasons. In the following sections, the simulated outputs using this parameter set are compared to observed values in terms of dry matter as well as carbon and water fluxes.

In addition to the biomass of individual simulated organs (leaf, stem, storage organs (SOrg) and root), the aboveground vegetative biomass (leaf + stem) was also included in Fig. 2 as distinct measurements of these two organs were not systematic (Table 1). Overall, the simulated dry matter aligns relatively well with observations. Nevertheless, SOrg biomass is consistently underestimated at the end of all growing seasons, resulting in a lower simulated crop yield. Although not shown, predictions of Crop Area Index (CAI) follow a similar pattern, with greater underestimations near the end of the season.

For S15, this underestimation may be attributed to insufficient remobilisation of stem reserves, as indicated by the high simulated stem biomass in July, even greater than the combined leaf and stem observations. However, this explanation does not hold for the other seasons, where stem biomass appears realistic. Beyond the capacity of remobilised reserves, parameters such as the efficiency of this remobilisation (considered fixed in Daisy) as well as contributions from stem and ear to photosynthesis (SOrgPhotEff and StemPhotEff) may also affect SOrg biomass during the reproductive stage (after anthesis).

As depicted in Fig. 3, simulated temporal variations follow observed trends, although predictions tend to be more negative (i.e., more CO₂ uptake) during the vegetative stage. This underestimation is particularly evident for S17, also highlighted by the scatter plot, where the regression slope is significantly higher than 1 (β=1.14). This bias suggests an overestimation of photosynthesis and/or an underestimation of respiration. Despite this discrepancy, the model accurately simulates the biomass of vegetative organs during this stage. On the other hand, during the reproductive stage (when SOrg is underestimated; Fig. 2), NEE predictions no longer show a clear bias. This partly explains the observed trade-off between DM and NEE (Fig. 1b). For instance, increasing the remobilisation of stem reserves during S15 would likely result in a more accurate crop yield, but also in an undesirable increase in NEE as CO₂ is released through this process.

It is also worth noting that Daisy simulates a sudden decrease in NEE at the end of each season, which is not observed. When reaching maturity (DS = 2), plant processes are completely stopped, so is the autotrophic respiration. Actually, matured plants continue to respire and contribute to carbon fluxes until harvest.

As expected from the rRMSE values observed in Fig. 1, LE fluxes are not well captured by the model. Observed daily fluxes exhibit greater variations, frequently reaching high values or dropping below 50 W m⁻² while simulated values remain relatively stable (Fig. 4). This is also illustrated in the scatter plots, where hourly observed data easily reach 600 W m⁻², but simulated fluxes never exceed 500 W m⁻², resulting in a poor linear agreement between observed and simulated fluxes as indicated by the low value of Pearson correlation coefficients ρ (Fig. 4). This disagreement is particularly visible in mid-April 2019, with an observed daily average around 150 W m⁻² in comparison to a prediction of only ∼100 W m⁻². During this period, simulated evapotranspiration equals potential evapotranspiration, suggesting that the plant was not water-limited and that the underestimation stems from deficiencies in energy partitioning rather than water availability.

Even though there was no apparent soil water deficit, this period (18–22 April) was still characterised by elevated temperatures and a higher vapour pressure deficit (VPD) compared to preceding days. Weather data during this period are depicted in the Appendix C (Fig. C1). It does not meet the formal Belgian definition of a heatwave, but the daily mean temperatures were more than 5° C above the 1981–2010 averages. During this 5 d period, the observed stomatal conductance gs reached extremely high values (Fig. 5a), associated with an important increase in LE fluxes (Fig. 5c), while the magnitude of the carbon uptake (GPP) was not affected (Fig. 5b). These observations reveal a decrease in water use efficiency during this period, indicating that transpiration was intensified with no corresponding increase in carbon assimilation. This trend was not captured by the model, as simulated gs remained lower than 0.03 m s⁻¹ (Fig. 5a). The slight increase in predicted gs during these five days can be explained by the minor increase in carbon uptake (Fig. 5b).

In addition to the insufficient simulated transpiration, soil evaporation may also be underestimated. During these five days, soil water content at the surface (5 cm depth) decreased by 6.2 % whereas the model predicted a decrease of 4.2 % (Fig. 5d). We assume that this difference (2 %) is mainly due to an underestimation of soil evaporation rather than drainage as it is limited to the surface layer and because of the particular meteorological conditions. Considering a surface layer from 0 to 10 cm, this is equivalent to a daily contribution of 10.4 W m⁻². Hence, the underestimation of soil evaporation can partly explain the difference in LE fluxes observed in Fig. 4.

When using the most-balanced parameter set for S11, NEE is well reproduced by the model with EF greater than 0.8, rRMSE around 40 % and NME close to 0 for both time scales (Table 3a). Although rRMSE and EF also present acceptable results for DM, it is worth noting that there is an overall underestimation of this variable (NME =-0.222).

On the other hand, there is no good agreement between observed and predicted LE, especially when considering a daily time scale, as shown by the four indicators. Even when using the parameter set that minimises FLE (Fig. 1a), LE remains poorly captured by the model (Table 3b). As expected from the Pareto front, this slight improvement in LE predictions is accompanied by a degradation of NEE and DM predictions.

Considering all objectives, the chosen parameter set (red point in Fig. 1) shows satisfactory calibration results, with a total RMSE of 0.948 t ha⁻¹, 3.44 µmol m⁻² s⁻¹ and 62.7 W m⁻² for DM, NEE and LE, respectively. Compared with other models, calibrated RMSE values for total biomass are typically between 0.5 and 1.5 t ha⁻¹ (Zhang et al., 2020; Dumont et al., 2014; Casanova and Judge, 2008). Regarding NEE, reported RMSE values for daily fluxes range from 1.3 to 1.9 gC m⁻² d⁻¹ (Revill et al., 2019; Senapati et al., 2018; Lehuger et al., 2010). In the present study, the RMSE computed from hourly NEE (3.44 µmol m⁻² s⁻¹) corresponds to a RMSE of 1.49 gC m⁻² d⁻¹ when using daily fluxes, which falls in the mentioned range. Casanova and Judge (2008) reported a RMSE of 62.45 W m⁻² for hourly LE fluxes, and other studies presented values ranging from 24.65 to 48.5 W m⁻² for daily fluxes (Wang et al., 2024; Liu et al., 2020a; Dutta et al., 2016), while we found 30.74 W m⁻² using daily averages.

The calibrated parameters are all within the explored range, without relying on extreme values (Table B1), indicating a physically plausible solution. It is, however, worth noting that some cultivar-specific parameters have very different values between seasons, such as δ describing the hydraulic signalling for stomatal conductance or the photosynthetic efficiency of non-leaf organs (SOrgPhotEff and StemPhotEff). Such differences may reflect genotypic variability, but they may also be due to environmental factors not represented in the model. This is, for example, the case for the remobilisation reserve ShldResC which can be impacted by genotype and water stress (Ehdaie et al., 2006). The absence or misrepresentation of environmental factors in the model can be compensated by wider variations between cultivars. Depending on the modeller's objective, these parameters might be kept as cultivar-specific while investigating the environmental influences, or constrained across cultivars to improve model parsimony and robustness.

In addition to providing reliable solutions, Pareto-based multi-objective calibration also offers insights into internal model limitations (Kollat et al., 2012). As related by Schoups et al. (2005), the shape of the Pareto front is an indicator of model structural error. Angular fronts (e.g., NEE–LE front) suggest that different objectives can be simultaneously optimised whereas significant trade-offs (curved or linear fronts) may indicate a wrong parameterisation of the model (Wöhling et al., 2013; Efstratiadis and Koutsoyiannis, 2010). The following sections focus on the NEE–DM and NEE–LE trade-offs and discuss whether the disagreements between observations and model predictions come from uncertainty due to measurement errors or deeper structural issues.

As shown by the major trade-off in Fig. 1b, adjusting model parameters to fit NEE fluxes inevitably compromises the simulation of organ DM. The analysis in Sect. 3.2 and 3.3 reveals that this would specifically result in an underestimation of biomass. DM during the vegetative stage is well reproduced when simulated NEE is overly negative, and SOrg DM is underestimated when NEE predictions show less bias (Figs. 2 and 3). This was also observed in the validation results, with a consistent underestimation of DM while NEE showed neither over- nor underestimation. Several factors may contribute to this mismatch:

Underestimation of heterotrophic respiration. If so, as respiration is regarded as positive and photosynthesis as negative with the micro-meteorological sign convention, NEE predictions would be too negative (as observed). Improving heterotrophic respiration would affect NEE predictions but its influence on DM would be limited, which could weaken the trade-off between these variables. At this study site, Suleau et al. (2011) partitioned soil respiration into its heterotrophic and autotrophic components using soil chambers, from which they derived temperature functions. When comparing their fitted regression to simulated heterotrophic respiration, Daisy appears to underestimate both temperature sensitivity and baseline respiration rate for three growing seasons (Fig. D1), supporting this first assumption. It should be noted, however, that this regression depends solely on temperature, ignoring the seasonal variation in residue and fertilisation inputs that also affect soil respiration dynamics. Furthermore, heterotrophic respiration is most likely to be underestimated as, during the bare soil period before sowing, NEE (which only consists of soil respiration at that time) is mostly underestimated (Table D2). Adjusting soil parameters might reduce this trade-off, but it would require long-term simulations and respiration data from this study site.

When there is no evaporation from free water surfaces, the surface water balance in Daisy can be summarised as:

computation of potential evapotranspiration (PET) using the FAO56 equation

Second, soil evaporation (Esoil) is computed outside the iteration loop that couples the SVAT module with the Farquhar–Leuning models. It is constrained either by soil water availability or by the potential evaporative demand, depending on which is limiting. By contrast, fully coupled models such as the CLM model calculate resistance-based Esoil simultaneously with transpiration and sensible heat fluxes (Swenson and Lawrence, 2014). This ensures that Esoil is driven by microclimate conditions (e.g., canopy air vapour pressure) and reinforces the mechanistic coupling between the surface energy and water balances. However, the appropriate formulation of resistance-based Esoil remains an active research area, as recent studies continue to refine its parameterisation and physical basis (Schulz and Vogel, 2020; Lehmann et al., 2018).

Beside these workflow aspects, the relatively narrow Pareto shape (Fig. 1c) suggests the presence of equifinality, i.e., multiple parameter sets produce equally good results (Her and Seong, 2018). This likely reflects compensatory interactions between soil evaporation and plant transpiration. Since PET is partitioned by canopy cover, parameter changes that alter canopy development can redistribute PET between the two components while leaving total PET unaffected. Under non-stressed water conditions, the ecosystem would meet this evaporative demand, and total ET (i.e., LE outputs) would remain unchanged as well. This masking effect underscores the well-known challenge of ET partitioning in ecosystem modelling, further complicated as eddy covariance systems do not distinguish between soil evaporation and transpiration (Berg and Sheffield, 2019; Stoy et al., 2019; Scott and Biederman, 2017). Recent methods, such as flux mapping, have been developed to better understand model internal fluxes leading to equifinality (Khatami et al., 2019).

As depicted by Fig. 5, discrepancies in LE predictions were especially evident under elevated temperatures and high VPD. While these may partly stem from limitations mentioned above, they also point to deeper issues in the coupling between Farquhar and Leuning models and particularly in how it responds to atmospheric drivers.

Stomatal behaviour plays a central role in plant regulation of water loss and carbon uptake, and has therefore been extensively studied (Damour et al., 2010). While it is well established that mild edaphic drought induces a decrease in carbon assimilation by reducing the stomatal aperture (Beauclaire et al., 2024), plant responses to heatwaves and high atmospheric demand are less evident. Most studies report reduced gs under high VPD (Grossiord et al., 2020; Bourbia and Brodribb, 2024), aligning with the theoretical predictions of stomatal models (Sabot et al., 2022). On the other hand, high temperatures seem to trigger stomatal opening to promote transpiration cooling (Urban et al., 2017), but reported results vary greatly among species (Wang et al., 2026; Moore et al., 2021). Under the combined effect of high temperature and VPD, Marchin et al. (2022) observed a significant increase in gs for two well-watered species, interpreting this as a strategy to prevent leaf overheating via enhanced LE loss without any increase in carbon assimilation. They later confirmed that this behaviour, referred to as stomatal decoupling, is not restricted to well-watered species (Marchin et al., 2023).

This stomatal decoupling aligns with ecophysiological studies, highlighting the role of non-stomatal factors during photosynthesis. Inside the leaf, CO₂ diffuses through air spaces and membranes to reach the sites of carboxylation inside chloroplasts, whereas H₂O moves from the xylem network to the stomata (Flexas et al., 2012; Sack and Holbrook, 2006). These different pathways can be affected independently, where carbon assimilation can be restricted by non-stomatal factors, often dominated by mesophyll conductance (Flexas et al., 2012). Over the last decade, these non-stomatal limitations have received increased attention, especially under water-stressed conditions (Nadal and Flexas, 2018; Gago et al., 2020). Based on leaf gas exchange measurements, experimental studies proved that these limitations should be considered in leaf models linking photosynthesis and transpiration (Yang et al., 2019; Beauclaire et al., 2024; Chen et al., 2025). Despite that, these complex processes are still not fully understood, and hence barely integrated into crop or terrestrial models (Vidale et al., 2021). As an example, an empirical equation for the mesophyll conductance was implemented in the land surface model JSBACH (Knauer et al., 2019). The authors extensively discussed the environmental drivers, the modelling implications, as well as the effects on the predicted fluxes in a subsequent paper (Knauer et al., 2020).

These non-stomatal limitations, or stomatal decoupling, are not modelled in Daisy. Based on stomatal coupling (Eq. 2), the increase in VPD reduced the predicted slope between carbon assimilation and gs. Consequently, the model tended to underestimate gs and LE fluxes and overestimated sensible heat, leading to a misrepresentation of energy partitioning under such conditions. On the other hand, observations show that plants likely opened their stomata, promoting water loss, while carbon assimilation did not increase accordingly. This stomatal decoupling was particularly visible in April 2019, as the heatwave lasted several days, but also appeared during shorter warm periods, suggesting a recurrent plant strategy. Future work should (i) continue the effort in better understanding the mechanisms of non-stomatal limitations affecting carbon assimilation and (ii) incorporate these mechanisms in process-based models, particularly under such conditions.