The MOFLUX eddy-covariance flux tower (AmeriFlux ID: US-MOz) is located in the Central US (latitude: 38.7441, longitude: -92.2000), and characterized by a warm, humid and continental climate zone. The mean annual temperature is 13 °C and the mean annual precipitation is 1,140 mm. Important tree species in the area are white oak (Quercus alba), black oak (Q. velutina), sugar maple (Acer saccharum), shagbark hickory (Carya ovata), and eastern redcedar (Juniperus virginiana) (Gu et al., 2015). We used half-hourly measurements of evapotranspiration (ET), as well as net ecosystem carbon dioxide exchange (NEE) from which gross primary productivity (GPP) was inferred using the night-time partitioning method. The processing of carbon and water fluxes data used here follows the standardized AmeriFlux pipelines (Gu et al., 2016). Site-level leaf area index (LAI) was extracted using the GriddingMachine package (Wang et al., 2022) from MODIS (MODerate resolution Imaging Spectroradiometer) LAI products (Yuan et al., 2011). Predawn leaf water potential (Ψleaf,pd) measurements were initiated in 2004 and were carried out weekly to bi-weekly.

The 2012 drought is one of the most extensive drought events over the Central US on record, with rapid development and pronounced area encompassed by persistent dryness and warm temperatures. Specifically, the drought peaked in July, when nearly 64 % of the area experienced at least moderate drought. Wood et al. (2023) divided the 2012 growing season into four stages: peak flux (DOY 125–150), flash stress (DOY 160–180), wilted (DOY 185–240), and recovery (DOY 255–270). We slightly modified these period definitions to eliminate any gaps between them, defining the stages as follows: peak flux (DOY 125–150), flash stress (DOY 150–180), wilted (DOY 180–240), and recovery (DOY 240–280).

We conducted model simulations at several flux-tower sites that experienced the 2012 drought, including US-MMS, US-GLE, US-UMB, US-NR1, and US-UMd. The US-MMS site is located in Morgan-Monroe State Forest, Indiana, within a temperate deciduous broadleaf forest dominated by a maple–beech–oak–hickory transition community representing secondary successional stands approximately 60–80 years old (Novick and Phillips, 2022). The US-GLE site is located in northern Michigan and consists of a mixed forest composed of aspen, maple, pine, and northern hardwood species (Frank et al., 2022). The US-UMB site, also located in northern lower Michigan, is an aspen-dominated northern hardwood forest (Classen et al., 2023). The US-NR1 site is located in the Rocky Mountains of Colorado within a subalpine evergreen needleleaf forest dominated by Abies lasiocarpa, Picea engelmannii, and Pinus contorta (Blanken et al., 2026). The US-UMd site, located in northern lower Michigan, represents a temperate deciduous broadleaf forest (Gough et al., 2024).

We used the vegetation module of the land surface model developed within the Climate Modeling Alliance (CliMA) (Wang et al., 2021, 2023). The model's performance has been validated in terms of carbon and water fluxes, as well as solar-induced chlorophyll fluorescence (Braghiere et al., 2021; Wang et al., 2021, 2023). The model adopts a modular structure, allowing flexible combinations of radiative transfer schemes (broadband or hyperspectral), photosynthesis models, stomatal models, and plant hydraulic representations.

We ran CliMA Land in hyperspectral mode for radiative transfer with a vertically resolved canopy, each layer of which is further split into sunlit and shaded fractions based on uniform leaf inclination and azimuthal distributions (Wang and Frankenberg, 2022; Zhao et al., 2019). At each time step, sunlit fractions and absorbed photosynthetically active radiation (APAR) are calculated, and leaf-level photosynthesis is solved by coupling the diffusion model with the Farquhar model (Farquhar et al., 1980) (Eq. 1). LAI is prescribed from 8 d MODIS observations and linearly interpolated to daily values, thereby capturing seasonal phenology and structural changes during the 2012 drought (Fig. S1 in the Supplement). Soil respiration is modeled using the Arrhenius equation with parameterized temperature sensitivity of soil respiration. 1Anet=VcmaxCi-Γ∗Ci+Km-Rd=gs⋅(Ca-Ci) where Vcmax is the maximum rate of Rubisco activity and Km is the Michaelis-Menten coefficient for Rubisco kinetics. Γ∗ is the CO₂ compensation point in the absence of dark respiration and Rd is the dark respiration rate. Ca is ambient CO₂ concentration. Ci is the intercellular CO₂ concentration. The model details of stomatal conductance (gs) can be found in Sect. 2.4.

Canopy transpiration is computed using the diffusion model as Eq. (2). 2T=∑i=1ncanopy1.6⋅gs⋅D⋅LAIi LAI_i is the leaf area index of ith layer. D is leaf-to-air vapour pressure deficit. 1.6 is the unitless relative diffusivity of water vapor with respect to CO₂.

The hydraulic system is represented as a vertically solved soil-plant-atmosphere continuum, including two root layers and 19 canopy layers. A fixed root : stem : leaf resistance ratio of 2:1:1 is assumed (Sperry et al., 2017). Leaf water potential (Ψleaf) is updated following Darcy's law based on vertical water flow and hydraulic conductance (Eq. 3). 3ψleaf=ψsoil-F×∑i∈leaf,stem,root1Ki F is transpiration-driven vertical water flow and Ki is hydraulic conductance of each segment. Ψsoil is soil water potential.

Wood capacitance and water storage dynamics were not included. Our model does not simulate soil evaporation and re-evaporation of rainfall interception, so we used a fixed T/ET ratio (0.67, falling in range reported in Fatichi and Pappas, 2017) to link the modeled plant transpiration to ET observation. We also tested varying T/ET ratio with observation-based partitioned transpiration (Zhou et al., 2016).

The CliMA Land model incorporates several stomatal optimality models (e.g., Eller et al., 2020; Sperry et al., 2017; Wang et al., 2020) and three empirical stomatal models: Medlyn (Medlyn et al., 2011), Ball-Berry (Ball et al., 1987) and Leuning models (Leuning, 1995). In this study, we used the Medlyn stomatal model and an optimality stomatal model (Wang et al., 2021). In empirical formulations, drought responses are introduced through a water stress factor β. Two pathways of stress propagation are considered. The first one operates by adjusting parameters of the empirical stomatal models, such as the slope parameter (g1) (Eq. 4). The second pathway involves the modulation of photosynthetic capacity through down-regulation of Vcmax (Eq. 5), which also reduces stomatal conductance as photosynthesis is reduced. A schematic is shown in Fig. 1. 4gs=g0+β⋅1+g1D⋅AnetCa5gs=g0+1+g1D⋅Anet(β)Ca where D is leaf-to-air vapour pressure deficit. g0 and g1 are empirical parameters.

For the optimality-based model, stomatal conductance maximizes the difference between leaf-level carbon gain and hydraulic risk, with risk represented through leaf hydraulics and their coupling to photosynthesis (Eq. 6). 6gs=argmaxAnet-AnetEEcrit where E is the leaf-level transpiration rate, and Ecrit is the critical transpiration rate at which the leaf xylem hydraulic conductance decreases to 0.1 % of the maximum value (namely at 99.9 % loss of hydraulic conductance). Anet is the net photosynthesis rate. β does not directly scale stomatal conductance; instead, it is applied to hydraulic conductance, thereby influencing transpiration-driven water flow.

We utilized vegetation traits such as the vulnerability curve (VC), Vcmax at 25 °C, semi-empirical slope parameter (g1) that characterizes the efficiency of carbon gain relative to water cost, and maximum hydraulic conductance (Kmax), from published references wherever possible. The well-watered Vcmax value was obtained from A/Ci curves measurements made at the site in May 2012, when the plants had not been hit by the severe water stress and Ψleaf,pd was close to 0 MPa (Gu et al., 2010). We took the average of the extracted Vcmax from these measurements (65.8±18.8 µmolm-2s-1). We used the “fitaci” function in package “plantecophys” version 1.4-6 (Duursma, 2015) to derive the fitted Vcmax at 25 °C. The root mean squared error from fitting is between 0.48–2.68 µmolm-2s-1. We used g1 value for deciduous broadleaf forests from De Kauwe et al. (2015).

For the VC of white oak, we used the sigmoid format parameters from Benson et al. (2022) and transformed it to Weibull function format, which better fits the observations. VC was used to compute the stress factor β (Eq. 7). Ψ63 indicates the xylem pressure at ∼63 % loss of conductivity, and b is the shape parameter (Neufeld et al., 1992). This β formula is the same for stomatal and non-stomatal limitations. 7β=e-(ψψ63)b where Ψ63=-2.94 MPa, b=2.52.

We did not find measurements for Kmax, therefore, this parameter was fitted by minimizing the error of ET between the model simulations and eddy-covariance observations over the pre-recovery periods (Eq. 8). Different Kmax values were obtained depending on the chosen stomatal models, the location of β, and recovery assumptions (Table S1 in the Supplement). We also optimized Kmax over longer pre-drought periods, extending to earlier years, which revealed notable inter-annual variability. For instance, in years with less water stress, such as 2010, the optimized Kmax was significantly higher (2.81 mol m⁻² s⁻¹ MPa⁻¹) compared to 2012, a drought year (0.89 mol m⁻² s⁻¹ MPa⁻¹). Consequently, we optimized Kmax using 2012 data alone. 8For Kmax: error function =∑|ETmod-ETobs|SD(ETobs) Subscripts of “obs” and “mod” denote the flux observation and modeled term. The operator ∑ takes the sum of the absolute difference between flux observation and model output. The operator “SD” takes the standard deviation of flux observation.

Three scenarios are considered regarding the recovery of hydraulic conductance for each stomatal model setup, including optimality, Medlyn-Vcmax, and Medlyn-g1. In total, the “partial recovery scenario” falls between the “full recovery scenario” and the “no recovery scenario” (Fig. 1c).

Full recovery scenario (FR): Hydraulic conductance can either increase or decrease and the shape of the vulnerability curve remains constant, i.e. is not affected by the previous severe water stress condition. In other words, the water potential and hydraulic conductance can be updated without specific boundaries (Eq. 9). Only transient (or immediate) responses are considered.

KFR(t) is updated according to the water stress factor β (Eq. 9).9KFR(t)=Kmax⋅β(ψ(t))ψ(t) is leaf water potential at time t. KFR(t) is hydraulic conductance under FR at time t.

In 2012, the Central US experienced a severe drought that impacted various climatological variables, carbon and water fluxes as shown in Fig. 2 for the MOFLUX site. During the earlier growing season, the air temperature exceeded records from other years, and precipitation reached the upper limit of recorded range. These conditions resulted in an overshoot (or peak flux) detected in the fluxes of GPP and ET. However, in the summer months of June and July, the monthly mean and maximum air temperature were 3 °C higher than those of other years spanning from 2007 to 2019, while summer precipitation only reached 30 % of normal levels. Furthermore, the vapour pressure deficit (VPD) in July was almost double that of other years. Periodic measurements of community Ψleaf,pd also showed extremely negative values as low as -4 MPa near the end of August, which was a rare occurrence. This meteorological drought led to a significant reduction in LAI, GPP, NEE and ET in the middle of 2012 (Figs. 2, S1). However, in September, soil water levels began to replenish, and carbon and water fluxes gradually started to recover. While climatological stress eased at that time, fluxes only reached the lower end of the expected range from multi-year records.

All tested stomatal schemes from CliMA Land demonstrated their ability to capture seasonal variations in carbon and water fluxes during the growing season of 2012 under the assumption of full recovery (Figs. 3, S2). Prior to the recovery period, model simulations performed similarly (Fig. 3). The performance of the optimality model and empirical stomatal models did not show distinct differences when incorporating a stress factor calculated from the loss of hydraulic conductance. Using the Medlyn stomatal model, we observed no significant differences in modeled ET between simulations where the stress factor was applied to Vcmax and g1 over the entire growing season (Wilcoxon rank test: P=0.13). However, applying the stress factor to g1 produced a higher GPP simulation compared to applying the stress factor to Vcmax (Wilcoxon rank test: P<0.001). Additionally, simulations using the stress factor on Vcmax exhibited lower RMSE for GPP at the daily scale compared to those applying the stress factor to g1 (1.40 vs. 2.67 µmolm-2s-1).

Analyzing different time periods, GPP simulations showed higher RMSE during the recovery period compared to the peak, flash stress, and wilted periods, when the stress factor was applied to Vcmax (Fig. S3). During the recovery period, applying the stress factor to g1 resulted in a larger positive bias in GPP simulations relative to observations. For ET, simulations showed comparable lower biases when applying the stress factor to either Vcmax or g1 across all time periods, with no significant differences between ET simulations and flux observations over the entire growing season (Wilcoxon rank test: P>0.10).

Overall, under the full recovery assumption, model simulations tended to overestimate carbon fluxes after the drought event, especially when the stress factor was applied to g1, while accurately capturing ET dynamics (Fig. 3). In contrast, under the no-recovery assumption, modeled GPP aligned more closely with observations during the recovery period when using the optimality-based stomatal model and the Medlyn-g1 setup, though ET simulations showed an underestimation (Fig. 3). These comparisons between full and no-recovery scenarios highlight a lagged recovery process, underscoring the need to incorporate delayed recovery mechanisms in modeling carbon and water fluxes. Using the hydraulic trait parameters of Acer produced similar modeling outcomes (Fig. S4), although the underestimation of photosynthesis was relatively smaller.

The delayed recovery of carbon fluxes relative to water fluxes suggests a lagged response driven by either stomatal or biochemical limitations. To identify the presence of non-stomatal limitations in the eddy-covariance data, we computed the daily correlation between GPP and ET (Fig. 4). Our findings indicate that this correlation coefficient, representing the strength of carbon-water coupling, was relatively high during the peak flux and flash stress periods, suggesting a tightly coupled carbon and water cycle. However, during the wilted period, this correlation dropped significantly to 0.54 (compared to a multi-year average of 0.89). During the recovery period, the correlation rose to around 0.74 – higher than in the wilted period but still below the multi-year average. The weaker GPP-ET coupling derived from flux observations indicates the emergence of non-stomatal limitations during drought, which can persist into the recovery phase. In contrast, model simulations tend to overestimate this coupling, likely because GPP and transpiration are tightly linked through stomatal conductance.

Given the persistence of non-stomatal limitations after drought, we investigated whether our model could capture this lagged recovery behavior by imposing additional non-stomatal limitations. It should be noted that the water stress is derived from loss of hydraulic conductance in our modeling framework, and further applied to either Vcmax or g1, such legacy effect includes also the delayed recovery of hydraulic conductance.

We found that introducing a partial recovery setup with a fixed bound is inadequate to capture the post-drought responses of carbon and water fluxes, necessitating the data assimilation of using observations as constraint (Figs. S5, S6). After assimilating flux observations as constraints, we observed a slower alleviation of water stress compared to the full recovery assumption and a similarly delayed increase in carbon fluxes (Figs. S7, S8). When comparing improvements in RMSE for GPP and ET between the model simulation and flux observation (shown as “PR” relative to “FR”), we found that incorporating lagged recovery of Vcmax enhanced model performance for both carbon and water fluxes (Fig. 5). In contrast, applying the stress factor to g1 reduced RMSE for carbon fluxes but introduced a greater ET bias, revealing that this model setup fails to yield consistent improvements for both fluxes. These contrasting performances can be explained by the representations in the two model setups. Applying β to Vcmax represents a biochemical limitation, directly reducing photosynthetic capacity and indirectly constraining stomatal conductance via reduced assimilation. This leads to a stronger and more persistent reduction in GPP, with comparatively weaker impacts on transpiration. In contrast, applying β to g1 represents a non-biochemical (stomatal) limitation, directly reducing stomatal conductance and CO? diffusion, thereby suppressing transpiration and secondarily reducing photosynthesis. As a result, when model performance of transpiration is similar between the two setups, as in the FR scenario, where transpiration is used to constrain Kmax, photosynthesis simulated by the Medlyn-g1 tends to be slightly higher than that from the Medlyn-Vcmax configuration (Fig. 5b, c). Similarly, under the PR scenario, reducing the overestimation of carbon fluxes is accompanied by an underestimation of transpiration (Fig. 5c, f). In the optimality-based stomatal model, β acts on hydraulic conductance only, and thus affects stomatal conductance indirectly, resulting in a response similar to the Medlyn-g1 formulation and a comparable underestimation of transpiration. Overall, the flux data and our modeling experiments suggest that an impairment in Vcmax delays the recovery of carbon fluxes, with the recovery process spanning days to weeks rather than occurring immediately. This finding highlights the crucial role of biochemical limitations in shaping the post-drought recovery trajectory of terrestrial ecosystems and the asymmetric recoveries of GPP and ET. Instead of relying solely on a fixed T/ET ratio, we applied the ET partitioning approach of Zhou et al. (2016) to directly compare modeled transpiration with observation-based partitioned transpiration. This method allows the T/ET ratio to vary dynamically. We find that using either a fixed T/ET ratio or observation-based partitioned transpiration does not affect our conclusions, namely, that biochemical limitations delay the recovery of both carbon and water fluxes (Figs. S9, S10).

When analyzing the diurnal cycle, the model simulations successfully captured the overall shape of the diurnal changes in carbon and water fluxes (Fig. 6). During the peak flux period, both carbon and water fluxes reached their maximum values at noon. As conditions transitioned into the flash stress period, the peak flux shifted earlier to around 10:00 am (LT). With increasing water stress, the peak flux occurred even earlier in the morning. During the recovery periods, the diurnal shape became flatter, with the peak value returning to around noon and remaining relatively stable between 10:00 am and 03:00 pm. Under the full recovery assumption, the model predicted GPP at noon to be twice as high as observed when the stress factor was applied directly to g1, while applying the stress factor to Vcmax led to a 35 % overestimation relative to observations during the 10:00 am to 02:00 pm window. However, the partial recovery approach helped reduce the model-observation bias, particularly during daytime hours. Model simulations using both the optimality-based stomatal model and empirical stomatal models with the stress factor applied to Vcmax exhibited less bias across the four time periods.

It is important to note, however, that modeled peak ET around noon during the recovery periods was slightly dampened. From a modeling perspective, a decrease in Vcmax reduces carbon assimilation, which in turn suppresses stomatal conductance and transpiration. Thus, the stress applied to Vcmax effectively encompasses lumped effects from changes in Rubisco enzyme content (or activation) and environmental stress. The slightly weaker ET performance could also be due to potential shifts in the T/ET ratio between periods, highlighting the need for further exploration of inconsistent drought recovery in carbon and water fluxes. Since T/ET typically increases under dry conditions (Nie et al., 2021), we tested the model by increasing T/ET during the wilted and recovery periods and recalibrated it accordingly. This recalibration required slightly higher Kmax values to align with the elevated T/ET during the drought. Nevertheless, this adjustment does not alter our conclusion: the delayed recovery of carbon fluxes can be effectively addressed by incorporating biochemical limitations, thereby reducing the model-observation gap.