Soil water content and soil water potential were measured hourly by homemade time domain reflectometer (TDR) probes (Cai et al., 2016), tensiometers (T4e, UMS GmbH), and dielectric water potential sensors (MPS-2 matric potential and temperature sensor, Decagon Devices), respectively. Sensors were installed at 10, 20, 40, 60, 80, and 120 cm depth. Root measurements were taken with a digital camera (Bartz Technology Corporation) repeatedly from both left and right sides at 20 locations along horizontally installed minirhizotubes 7 m long (clear acrylic glass tubes with outer and inner diameters of 64 and 56 mm, respectively). The calibration of the sensors, root growth observation, and post-processing of the data were described in detail in Cai et al. (2016, 2017).

Five, three, and five sap flow sensors (SAG3; Dynamax Inc., Houston, USA) were installed in the irrigated, rainfed, and sheltered treatments, respectively, at the beginning of wheat anthesis when stem diameters ranged between 3 and 5 mm. Vertical and horizontal temperature gradients (dT) of each sensor were recorded at 10 min intervals with a CR1000 data logger and two AM 16/32 multiplexers (Campbell Scientific, Logan, Utah). Sensor heat inputs were controlled by voltage regulators controlled by the CR1000 data logger. The raw signal data were aggregated to 30 min intervals, and sap flow was calculated following Langensiepen et al. (2014). The number of tillers per square meter was counted every 2 weeks during the operation period of sap flow sensors (26 May–23 July 2016). Tiller numbers were used to upscale the sap flow of single tiller (g h-1) to canopy transpiration rate (mm h-1 or mm d-1).

Leaf stomatal conductance and the leaf water hydraulic head were measured every 2 weeks from 07:00 to 20:00 LT (local time) under clear and sunny conditions from tillering (20 April) to the beginning of maturation (29 June 2016). The stomatal conductance to water vapor of three to four upmost fully developed leaves was measured using a LICOR 6400 XT device (Licor Biosciences, Lincoln, Nebraska, USA) with a reference CO2 concentration of 400 ppm and a flow rate of 500 (µmol s-1) and using real-time records of photosynthetic active radiation, vapor pressure deficit, and leaf temperature provided by the instrument. Then the leaves were quickly detached by a sharp knife to measure leaf water pressure head with a digital pressure chamber (SKPM 140/(40-50-80), Skye Instrument Ltd, UK).

Plant hydraulic conductance in crop species can be estimated by measuring the transpiration and the root zone and leaf water hydraulic heads (Tsuda and Tyree, 1997). In our study, we calculated the conductance according to Ohm's law by dividing the hourly sap flow by the difference between effective root zone hydraulic head and leaf hydraulic head. The effective root zone hydraulic head was calculated based on hourly measured soil water hydraulic head and measured root length density (cm cm-2) at six depths (10, 20, 40, 60, 80, and 120 cm) in the soil profile following Eqs. (8) and (10) (see Sect. 2.3.4). During one measurement day, six hourly values of the conductance were obtained from measurements between 11:00 and 16:00 LT. The average and standard deviation of these hourly measurements were calculated for each measurement day. However, the hydraulic conductance can vary within short time periods due to the role of aquaporins (Maurel et al., 2008; Javot and Maurel, 2002; Henzler et al., 1999) or abscisic acid (ABA) regulation (Parent et al., 2009) and xylem cavitation (Sperry et al., 2003). We assumed however a constant plant hydraulic conductance during the day.

Canopy gas exchange was measured hourly on the same days when leaf water pressure heads were measured with a closed chamber system (Langensiepen et al., 2012). CO2 concentration was derived with a regression approach by Langensiepen et al. (2012). Because we were interested in comparing measured with calculated hourly instantaneous gross assimilation by the newly coupled root–shoot model (LINTULCC2 with other subroutines), the total soil respiration (i.e., heterotrophic organisms and root respiration) was subtracted from the instantaneous canopy CO2 exchange rate measured by the closed chamber. The total soil respiration was calculated based on measured soil temperature, soil water content at 10 cm soil depth, and leaf area index from crops using the fitted parameters derived from the same field and soil types (Prolingheuer et al., 2010). The calculated total soil respiration was compared and validated with the measured values in the same field in the previous years from Stadler et al. (2015).

Crop growth information was collected biweekly from 20 April until harvest on 26 July 2016. Leaf area index and crop biomass were measured by harvests of two rows (1 m each) for each treatment. Leaves were separated into green leaves and brown leaves, and the brown and green leaf area was measured using a leaf area meter (LI-3100C, Licor Biosciences, and Lincoln, Nebraska, USA). The aboveground biomass was measured using the oven drying method. Samples were first weighed in total, then separated into different plant organs (green leaf, brown leaf, stem, ear, and grain) and weighed. Subsamples were extracted afterward from these samples, weighed, dried in an oven at 105 ∘C for 48 h, and weighed again for determining dry matter. At the end of the growing season, four replicates of 1 m2 of plants were harvested from the plots to determine grain yield and harvest index.

We used the crop model LINTULCC2 (Rodriguez et al., 2001). LINTULCC2 couples photosynthesis to stomatal conductance and can perform a detailed calculation of leaf energy balances (Rodriguez et al., 2001; see Appendix A). This model was validated and compared with different crop models for spring wheat and used to simulate the effects of elevated CO2 and drought conditions (Ewert et al., 2002; Rodriguez et al., 2001). LINTULCC2 calculates phenology, leaf growth, assimilate partitioning, and root growth following the procedure outlined in Rodriguez et al. (2001).

In LINTULCC2, the assimilation rate of the sunlit and shaded leaf is calculated using the biochemical model of Farquhar and von Caemmerer (1982). Stomatal conductance (gs) was calculated according to the model Leuning (1995) for sunlit and shaded leaves separately. In LINTULCC2 CO2 uptake is calculated as a function of CO2 demand by photosynthesis and the ambient concentration of CO2, using the iterative methodology proposed by Leuning (1995) (Appendix A). For the sake of simplification, in LINTULCC2, the internal leaf CO2 concentration, Ci, is initially assumed to be 0.7 times the atmospheric CO2 concentration Ca (Vico and Porporato, 2008; Rodriguez et al., 2001; Jones, 1992). Then, the light-saturated photosynthetic rate of sunlit and shaded leaves (AMAXsun and AMAXshade; µM CO2 m-2 s-1) and the quantum yield for sunlit and shaded leaves (EFFsun and EFFshade; µM CO2 MJ-1) are calculated iteratively (Farquhar et al., 1980; Farquhar and von Caemmerer, 1982). This iterative loop ends when the difference in calculated internal CO2 mole fraction between two consecutive loops is <0.1 µmol mol-1 (Appendix A). Based on a fraction of sunlit (and shaded) leaf area and leaf area index (LAI), the leaf stomatal resistance of sunlit and shaded leaves was integrated over the canopy leaf area to the canopy resistance (rs) (Appendix B).

The canopy resistance, crop height, and calculated crop albedo (depending on both crop and soil water content of the surface layer) and the surface energy balance were used to calculate potential crop evapotranspiration (ETP in mm h-1) using the Penman–Monteith equation (Allen et al., 1998; see Appendix B). The obtained potential surface evapotranspiration is then split into evaporation and potential transpiration using 1Tpot=ETP1-e-kLAI, where k is the light extinction coefficient (0.6 in this study; De Faria et al., 1994; Mo and Liu, 2001; Rodriguez et al., 2001).

Tpot (mm h-1) represents by definition the transpiration of the crop that is not limited by the root zone water hydraulic head. In Sect. 2.3.4 it is explained how the actual transpiration, Tplant (mm h-1), is calculated as a function of the potential transpiration and the root zone soil water pressure head. The ratio Tplant/Tpot defines the water stress factor fwat, which is used in the photosynthesis model: 2fwat=TplantTpot. Originally, LINTULCC2 runs at daily time steps (which allows for the within-day variations in temperature, radiation, and vapor pressure deficit). LINTULCC2 requires daily maximum and minimum temperature, actual vapor pressure, rainfall, wind speed, and global radiation. In order to capture the diurnal response of stomata, we modified the time step of the photosynthesis and stomatal conductance subroutine from daily to hourly, while daily time steps were kept in the remaining subroutines (phenology, leaf growth, and biomass partition).

Root growth was simulated using SLIMROOT (Addiscott and Whitmore, 1991). The vertical extension of the seminal roots and the distribution of the lateral roots within the soil profile depend on the root biomass, the soil bulk density, the soil water content calculated by HILLFLOW 1D (Bronstert and Plate, 1997), and the soil temperature computed by STMPsim (Williams and Izaurralde, 2005). The supply of assimilates from the shoot (RWRT; g m-2 d-1) is given by a partitioning table based on the thermal time (van Laar et al., 1997) that is used to calculate the vertical penetration of seminal and lateral roots. The assimilate allocation for seminal root growth (ASROOT) is constrained by daily supply of assimilates from the shoot RWRT (g m-2 d-1) and the demand of assimilates from seminal roots (ASROOTdemand). 3ASROOT=minASROOTdemand,RWRT ASROOTdemand is a function of the number of seminal roots per square meter (NSROOT), which depends on the number of emerged plants per square meter and the number of seminal roots per plant, the specific weight of seminal roots WSROOT (g m-1), and the daily elongation rate of seminal roots RSROOT (m d-1): 4ASROOTdemand=RSROOT⋅WSROOT⋅NSROOT. RSROOT depends on the soil temperature and is constrained by a maximal elongation rate, RSROOTmax, and the soil-temperature-dependent rate, which is an empirical function of the soil temperature of the deepest layer where roots are growing, TBOTLAYER (K) (Jamieson and Ewert, 1999): 5RSROOT=minRSROOTmax,TBOTLAYER⋅RTFAC, where RTFAC is the temperature factor driving the penetration of seminal roots (m K-1 d-1) and TBOTLAYER (K) the soil temperature of the deepest layer where roots are growing. When soil temperature is below or equal to 0 ∘C, no seminal growth occurs. The maximum daily elongation rate of seminal roots, RSROOTmax, was set at 0.03 m d-1 for wheat according to Watt et al. (2006).

The daily increment in seminal root length (SRLIR; m m-2 d-1) is defined as 6SRLIR=ASROOT/WSROOT. Lateral roots are simulated when the root biomass supplied by the shoot is greater than the assimilate demand of seminal roots (RWRT > ASROOTdemand). Lateral root biomass is distributed stepwise from the top layer to the deepest soil layer with seminal roots.

Roots start to die after anthesis. Since the specific weight of the roots of cereal crops varies with soil strength (Colombi et al., 2017; Lipiec et al., 2016; Hernandez-Ramirez et al., 2014; Merotto and Mundstock, 1999), we chose different specific weights for the stony (F1) and silty soil (F2) from the range that was observed by Noordwijk and Brouwer (1991) and Jamieson and Ewert (1999) in soils with different soil strength (Appendix C).

HILLFLOW 1D was chosen for calculating the water pressure heads in the soil and how they change with depth and time as a function of the precipitation, soil evaporation, RWU, and water percolation at the bottom of the simulated soil profile (Bronstert and Plate, 1997). HILLFLOW 1D calculates soil water content and water fluxes by numerically solving the Darcy equation for unsaturated water flow in porous media (Bronstert and Plate, 1997). The relations between soil water hydraulic head, water content, and hydraulic conductivity are described by the Mualem–van Genuchten functions (van Genuchten, 1980). The parameters of these functions, i.e., the soil hydraulic parameters, for the different soil layers and the two sites were taken from Cai et al. (2018) (Appendix D). In this study, a soil depth of 1.5 m vertically discretized into 50 layers was considered. A free drainage bottom boundary and a mixed flux-matric potential boundary at the soil surface were implemented. The mixed upper boundary condition prescribes the flux at the soil surface by the precipitation and evaporation rates as long as the soil water pressure heads are not above or below critical heads. When these heads are reached, the boundary conditions are switched to constant pressure head boundary conditions.

The Feddes RWU model (Feddes et al., 1978; see Appendix E) was already built in the HILLFLOW 1D model (Bronstert and Plate, 1997). We implemented the Couvreur RWU model (Couvreur et al., 2012, 2014) into HILLFLOW. In both models, Tplant is calculated from the sum of the simulated RWU in the different soil layers and used to calculate the water stress factor (fwat) following Eq. (2), which was used in the photosynthesis model. In the Feddes model, root water uptake from a soil layer is proportional to the normalized root density, NRLD (m-1), in that layer and is multiplied by a stress function α that depends on the soil water pressure head, ψm (m), in that soil layer and the potential transpiration rate (see Appendix E for the definition of α): 7RWUi=αψm,i,TpotTpotNRLDiΔzi, where NRLDi is calculated from the root length density, RLD (m m-3), and discretized soil dept, Δzi (m), as 8NRLDi=RLDi/∑i=1NRLDiΔzi. The parameters of the α stress functions model were taken from Cai et al. (2018; see Appendix C). According to Eq. (7), the reduction of water uptake in a given layer depends on the soil water pressure head in that layer only and does not influence the water uptake in other layers. This means that a reduced water uptake in dried out soil layers directly leads to a reduction of the total root water uptake and plant transpiration and is not compensated by increased uptake in other layers where there is still water available.

In the Couvreur model, the root water uptake in a given soil layer is related to the water potentials in the root system and root water uptake in other soil layers so that compensatory uptake is considered in this model. Root water uptake in a certain layer is obtained from 9RWUi=TplantNRLDiΔzi+Kcompψi-ψsrNRLDiΔzi, where ψi (m) is the total hydraulic head (or hydraulic head which is the sum of the pressure head and gravitation potential heads) in layer i, ψsr (m) is the average hydraulic head in the root zone, and Kcomp (d-1) is the root system conductance for compensatory uptake. The first term of Eq. (9) represents the uptake from that soil layer when the hydraulic head is uniform in the root zone, and the second term represents the increase or decrease of uptake from the soil layer due to a respectively higher and lower hydraulic head in layer i than the average hydraulic head. The average root zone hydraulic head is calculated as the weighted average of the hydraulic heads in the different soil layers as 10ψsr=∑i=1NψiNRLDiΔzi. The plant transpiration rate is the minimum of the potential transpiration rate and the transpiration rate, Tthreshold (mm h-1), when the hydraulic head in the leaves reaches a threshold value, ψthreshold (m), that triggers stomatal closure: 11Tplant=max0,minTpot,Tthreshold. Tthreshold is calculated from the difference between the root zone hydraulic head and the threshold hydraulic head in the leaves ψthreshold that is multiplied by the plant hydraulic conductance, Kplant as 12Tthreshold=Kplantψsr-ψthreshold. In our study, we used the critical leaf hydraulic head, ψthreshold, of -200 m (equivalent to -2 MPa) (Cochard, 2002; Tardieu and Simonneau, 1998). The original Couvreur model only considers the hydraulic conductance from the roots to the plant collar, Krs, by assuming that the hydraulic resistance from plant collar to leaves is minor as compared to root system resistance. The shoot hydraulic resistance could be large in some crop plants (Gallardo et al., 1996) or in trees (Domec and Pruyn, 2008; Tsuda and Tyree, 1997). In order to simulate the leaf water hydraulic head, the whole plant hydraulic conductance (Kplant) needs to be used. The whole plant hydraulic conductance could be estimated from different components (i.e., soil to roots, stem to leaf) following an approach from Saliendra et al. (1995) or a more complex attempt by Janott et al. (2011). Because hydraulic data from plant collar to leaf are rare and difficult to obtain and account for differing species characteristics and environmental conditions, for the sake of simplification, we derived Kplant (d-1) from the root hydraulic conductance (Krs,doy), assuming that Kplant is a constant fraction β of Krs,doy (d-1): 13Kplant=βKrs,doy. We used the measured plant hydraulic conductance from sap flow, leaf water hydraulic head, soil water pressure head, and root observation (Sect. 2.2.1 above) in the lower rainfed plot to calibrate β, which was then applied for all plots (Appendix C). Kplant and Krs in anisohydric wheat are influenced by soil water availability and crop development. We followed the approach of Cai et al. (2017) to estimate the root hydraulic conductance (Krs,doy) and compensatory root water uptake (Kcomp) based on the total length of the root system below a unit surface area, TRLDdoy (m m-2), at a given day of year (DOY) (Eq. 14), which is the output from SLIMROOT: 14TRLDdoy=∑iNRLDi,doyΔzi. Assuming the same conductance for all root segments, the root system conductance scales with the TRLD: 15Krs,doy=Krs,normalizedTRLDdoy, where Krs,normalized (d-1 cm-1 cm2) is the root system conductance per unit root length per surface area. For Krs,normalized, we took the average value that was obtained by Cai et al. (2018) for the stony soil (F1) and silty soil (F2) sites: 0.2544×10-5 (cm d-1) (Appendix C).

Many studies included hydraulic conductance along the soil–plant–atmosphere pathway to simulate water transport (Verhoef and Egea, 2014; Wang et al., 2007; Tuzet et al., 2003; Olioso et al., 1996). However, both root and plant hydraulic conductance in these studies were assumed constant. In our work, the plant hydraulic conductance varied following the shoot and root development in the growing season.

We carried out a comprehensive comparison of the following modeling approaches for simulating CO2 and H2O fluxes and crop growth (Fig. 2):

HILLFLOW 1D–Couvreur's RWU–SLIMROOT–LINTULCC2 (Co)

Figure 3 shows the dry matter and LAI simulated by the Co and Fe model versus the measured data. The difference between the two samples of the two different rows for each sampling day indicated the heterogeneity in crop growth, even within a small treatment plot. Biomass and LAI simulated by the Co and Fe models were in fair agreement with observations. The r2 values of the Co and Fe models were 0.91 and 0.86, respectively, for biomass, while they were 0.76 and 0.75, respectively, for LAI (Table 1). However, both models overestimated dry matter and LAI production in the irrigated and rainfed stony plots, whereas biomass and LAI were underestimated in the sheltered silty plot. This suggests that water stress in the sheltered silty plot was overestimated. For the irrigated stony soil plot, in which the water content stayed high due to the frequent rainfall events and the additional irrigation, it is unlikely that the lower growth is due to water stress. The later start of the growth after the winter could be due to the effects of soil strength and lower soil temperature on crop development in the stony field that were not captured by the model. Soil hardness could constrain root growth while the higher stone content possibly resulted in slower warming up of the soil in spring than the silty soil which in turn slowed down root and crop development.

For the stony plots, the Fe and Co models gave similar results, whereas for the silty soil, the Co model reproduced the biomass and LAI better than the Fe model. Although the statistical parameters (r2 and RMSE) for the silty soil plots show only a slightly better fit of the Co than of the Fe model, there is a remarkable qualitative difference between the models. The Fe model simulated lower biomass and leaf area in the silty soil than in the stony soil, which is opposite to the observations. The Co model simulated similar biomass and LAI in the irrigated and rainfed plots of the silty and stony soils and higher biomass and LAI in the sheltered plot in silty soil than in the stony soil, which is in closer agreement with the observed differences in biomass and LAI between the two soils. The simulated effect of the soil type on the crop growth was qualitatively correct for the Co model but incorrect for the Fe model.

Figure 4 displays the observed root length densities from minirhizotube observations and the simulated ones. Higher root length densities were observed and simulated in the silty soil than in the stony soil. The model simulated smaller root densities in the stony soil because a larger specific weight of the roots was considered for the stony soil than for the silty soil. The simulated root density profiles showed the highest root densities near the surface, whereas the observed profiles, especially in the silty soil, showed higher densities in the deeper soil layers. The model simulated smaller root length densities in the sheltered plots than in the other plots of both the stony and silty soils. This is a consequence of the lower biomass growth that was simulated in the sheltered plots. For the stony soil, this corresponds with the observations that also showed lower root length densities in the sheltered plots than in the other plots. However, for the silty plot, the opposite was observed. For both the simulations and the observations, we compared the ratio of total root lengths in a certain plot and treatment to the total root length in the rainfed stony plot F1P2 (Appendix F). In the stony plots the ratios of the observed total root length to the reference were close to 1, but the simulated total root length in the sheltered plot was smaller than 1. The ratios of the total root lengths in the silty plot to the reference were for all plots larger than 1. Nevertheless, the ratios of observed root lengths were larger (2.27–4.03) than those of the simulated ones (1.04–1.67). The observed ratios were larger for the sheltered plot than for the other plots in the silty soil, whereas the opposite was simulated by the models. Predefined ratios of root and shoot biomass allocation for a given growth period and a source-driven root growth (van Laar et al., 1997) in our models do not allow a shift in carbon allocation to roots (for more root growth) in response to water stress. However, this should not be emphasized too much because the observed imaged root data from minirhizotubes for driving the root length might have potential errors and uncertainties (Cai et al., 2018).

Figure 5a and b show the reduction of the transpiration compared to the potential transpiration, fwat, simulated by the Fe and Co models (mid-March until harvest), and Fig. 5c and d show the simulated potential and the simulated and measured actual transpiration rates from the end of April until harvest. The Fe model simulated more water stress than the Co model and a more pronounced and earlier stress in the silty than in the stony soil. As a consequence, the simulated transpiration rates by the Fe model were generally lower than the simulated ones by the Co model. According to the fwat factors, the Couvreur model also simulated more water stress in the silty soil than in the stony soil. The effect of fwat on the cumulative transpiration and growth also depends on the timing of the lower fwat values. At the beginning of the growing season when the LAI and potential transpiration are low, the impact of a lower fwat on the cumulative transpiration and growth is lower than later in the growing season. These results are in contrast with findings by Cai et al. (2017, 2018), who found that there was no water stress simulated in the silty soil in 2014 by the Co and Fe models. However, the studies from Cai et al. (2018) used the measured root distributions instead of the simulated ones from the root–shoot model. Therefore, in their simulations, the crop had more access to water in the deeper soil layers. Second, they used the Feddes–Jarvis model, which accounts for root water uptake compensation. This could explain why they did not simulate water stress in the silty plot with the Feddes model. Thirdly, weather conditions and irrigation applications were different in their study in 2014 (less dry) from our experimental season in 2016.

According to Fig. 5c and d, during the time when sap flow could be measured (from end of May until harvest), the stress factors did not differ a lot between the Fe and Co models. For the rainfed and irrigated plots in the silty soil, the Fe model predicted a stronger reduction in transpiration near the end of the growing season than the Co model. This resulted in a smaller cumulative transpiration predicted by the Fe model than by the Co model over the measurement period in these treatments (Fig. 6). Although this gives the impression that the Co model is better in agreement with the measurements in these treatments, Fig. 5d indicates that this is due to compensating errors. Both models underestimate the measured sap flow in the beginning of the measurement period and overestimate it towards the end, and the Co model overestimates more than the Fe model. This overestimation is due to an overestimation of the LAI by both models near the end of the growing season (Fig. 3b). The reduction of the transpiration in the sheltered plots of the two soils compared to the other treatments is predicted relatively well, but the Fe model predicted more stress and a stronger reduction in transpiration than the Co model, especially in the silty soil. For this treatment, the Co model, which simulated less stress (larger fwat factors), predicted the cumulative transpiration and how it differed between the two soil types better than the Fe model.

Simulated transpiration in all treatments and both soils are plotted versus the sap flow measurements in Fig. 7. On average, the two models slightly underestimated measured Tact (Fig. 5c and d). This was also found in the study by Cai et al. (2018), in which sap flow was measured in winter wheat in 2014. However, in their study, there was a rather constant offset between the simulations and the sap flow data. One reason could be that in our study we used the simulated LAI values, whereas Cai et al. (2018) used the measured LAI values. In the stony plots, the measured LAIs are overestimated by the simulations so that one would expect an overestimation of the transpiration by the model. The opposite holds true for the silty plot. The overestimation of the LAI at the end of growing season resulted in an overestimation of the transpiration in nonsheltered plots in both soil types. Because of the small size and hollow stem of wheat plants (Langensiepen et al., 2014), it is difficult to install the microsensors and measure the temperature variation for the thin wheat stem with high time frequency under ambient field conditions. In addition, the sap flow in a single tiller is also influenced by spatial variation in environmental conditions. The variability of stem development also results in a significant stem-to-stem variability in sap flow (Cai et al., 2018). The r2 values of simulated RWU from the Co and Fe models versus sap flow are 0.62 and 0.66, respectively (Table 1 and Fig. 7a), indicating that our coupled models show a fair performance in the RWU simulation. Measuring gas exchange with closed chamber concentration measurements can significantly alter the microclimatic conditions within the chamber, especially at times of high exchange rate. However using regression functions at the starting point of measurement intervals reduces absolute errors (Langensiepen et al., 2012). The simulated gross assimilation rate (Pg) from two models matched relatively well with the gross assimilation rate measured by a manually closed-canopy chamber, with an r2 value of 0.63 and 0.61 for Co and Fe, respectively (Table 1 and Fig. 7b).

The method that we used for modeling the canopy resistance used in the Penman–Monteith equation has been reported for both short and tall crops (Dickinson et al., 1991; Kelliher et al., 1995; Irmak and Mutiibwa, 2010; Perez et al., 2006; Katerji et al., 2011; Srivastava et al., 2018). The fair agreement of RWU to sap flow in our study indicates the proper estimate of ETP based on the crop canopy resistance (with fwat=1) in winter wheat. The direct calculation of crop canopy resistance in our work allows physiological responses of the crop (stomatal conductance) to solar radiation, temperature, and vapor pressure deficit (Eq. A5) to be captured. In addition, this approach also avoids calculating grass reference evapotranspiration based on a constant canopy resistance.

The differences in simulated stress between the different models were more pronounced in May (Fig. 5) when no sap flow data were available. The Co model predicted less stress and more RWU than the Fe model in May, especially in the rainfed and irrigated plots of the silty soil. The larger stress simulated by the Fe model in the rainfed and irrigated silty plots resulted in a smaller increase in biomass that was simulated in May by the Fe model than by the Co model (Fig. 3a). The measurements of growth in the silty soil do not suggest that there was water stress in these plots in the silty soil, indicating that the Co model better simulated transpiration and growth for these cases than the Fe model. Another way to test the RWU simulated by the different models is to compare the simulated soil water contents (Fig. 8). The Co and Fe models were able to simulate both dynamics and magnitude of soil water content (SWC) in different soil depths and for different water treatments (average of RMSEs over all soil depths was 0.06 for both models; Appendix G). The Co and Fe models displayed lower water contents than the measured ones in the deeper layers at the late growing season (i.e., depth 80 and 120 cm) (Fig. 8). This could be due to the free drainage bottom boundary condition in the HILLFLOW water balance model, which implies that the water can only leave the soil profile, but no water can flow into it from below. Capillary rise in the soil can keep the lower layers relatively wet (Vanderborght et al., 2010). In our simulation, the use of a soil depth of 1.5 m may not be deep enough to capture this effect. The simulated SWC values were however very similar for both models. The larger RWU simulated by the Co than by the Fe model in the silty soil in May resulted in slightly lower simulated water contents by the Co model. But, the differences in simulated water contents by the two models were much smaller than the deviations from the observed water contents.

For a few selected days, the diurnal course of Tact (or RWU), gross assimilation rate (Pg), stomatal conductance (gs), and leaf pressure head was measured. The measured and simulated data are shown in Fig. 9. Both Co and Fe models could mimic the daytime fluctuation of RWU and Pg in the sheltered plot of the stony soil, which is consistent with the adequate simulation of root growth (Fig. 4, F1P1) and SWC dynamics (Fig. 8c, F1P1). When the simulated ψleaf reached ψthreshold=-200 m, the simulated RWU and Pg by the Co model showed a plateau (26 May in Fig. 9c, e, and i). The Co model simulated the diurnal courses of stomatal conductance better as compared to the Fe model, especially on a day with water stress (26 May; Fig. 9g and h). Using the leaf water pressure head threshold as an indication of water stress effects on stomata, Tuzet et al. (2003) and Olioso et al. (1996) also reported a considerable drop of Pg and transpiration. The sharp drop of simulated RWU and Pg, which is in contrast with measurement on the same day in the sheltered plot in silty soil, illustrated that both models overestimated the water stress. This is related to the underestimation of both root growth (Fig. 4, F2P1) and SWC (Fig. 8d, F2P1) in the deeper soil layers by two models.

The Couvreur RWU model considers the root hydraulic conductance, which relies on absolute root length. The root hydraulic conductance is used to upscale to whole plant hydraulic conductance. The simulated Kplants reproduced the measured ones in the different treatments quite well (Fig. 10). Our measured Kplant ranged from 1.5×10-5 to 10.2×10-5 d-1 (Fig. 10). These values are on the same order of magnitude as values reported by Feddes and Raats (2004) for ryegrass ranging from 6×10-5 to 20×10-5 d-1. The simulated Kplant from our coupled root and shoot Co model followed the root growth and reached a maximum at around anthesis. Kplant reduces toward the end of the growing season due to root death. For the sheltered plot of the silty field, we would expect, based on the root density measurements (Fig. 4), the highest Kplant of all treatments. However, this was not observed in the field. Based on the measured total root lengths, we would also expect that Kplant of the sheltered plot in the stony soil should be similar to Kplant in the other plots of the stony soil. But, Kplant was clearly lower in the sheltered plot of the stony soil than in the other treatments in the stony soil. In the model simulations, the lower Kplant in the sheltered plots compared to the other plots in the same soil was due to a lower simulated total root length. Since the differences in observed total root lengths were smaller (stony soil) or opposite (silty soil) to the differences in simulated total root lengths, the smaller observed Kplant in the sheltered plots must have causes that are not considered in the model. A potential candidate is the resistance to water flow from the soil to the root in the soil, which increases considerably when the soil dries out, as was the case in the sheltered field plots.

The observed field data have been shown and compared with the simulated results from the two models in the abovementioned sections, Sect. 3.1.1–3.1.3. The data were collected for both crop growth (root, LAI, and biomass) and gas fluxes at different scales (soil water flux and gas exchange from leaf to canopy) in two contrast soil types and under different water treatments. To the best of our knowledge, this is a unique experimental setup and dataset for understanding soil–plant processes as well as parameterizing and evaluating soil–plant–atmospheric models. However, due to complex and costly construction of the underground minirhizotron facilities, there were no replicates for plots in our study. LAI and aboveground biomass showed the largest variability, not only between water treatments but even in the same plot because of microclimate and soil heterogeneities. The variability of tiller development also considerably influences the stem-to-stem variability of sap flow. In addition, the small size of plot did not allow for having replicates for manual canopy chamber measurement because it might strongly have disturbed and altered crop growth, leaf gas exchange, and sap flow measurements of the surrounding areas. Nevertheless, despite these shortcomings, the data illustrated the difference and variability among water regimes in two soil types and over measured dates that are still valid for modeling comparison and validation in this study.