Integrated Modeling of Photosynthesis and Transfer of Energy, Mass and Momentum in the Soil-Plant-Atmosphere Continuum System

Abstract. Root water uptake is an important component of the terrestrial water balance and a critical factor that influences energy, water vapor, and carbon exchange among soil, vegetation and atmosphere interfaces. However, most of the current vegetation photosynthesis models do not account for root water uptake, which compromises their applications under water stressed conditions. To address this limitation, this study integrates photosynthesis and transfer of energy, mass and momentum in the soil-plant-atmosphere continuum system, via a simplified 1D root growth model and a resistance scheme (from soil, through root zones and plants, to atmosphere). The coupled model was evaluated with field measurement of a maize canopy. The results indicated that the simulation of land surface fluxes was significantly improved due to considering the root water uptake, especially when vegetation is experiencing sever water stress. This finding highlights the importance of enhanced soil heat and moisture transfer, as well as dynamic root distribution, on simulating ecosystem functioning.



Model
Sink term calculation of soil water balance Root water uptake process Hydraulic redistribution (Richards and Caldwell, 1987) Compensatory uptake (Jarvis, 2011) Root fraction LSMs CLM4.5 Actual transpiration, root fraction of each soil layer and soil integral soil water availability (Fu et al., 2016) The Ryel et al. (2002) Function Not considered Empirical function CLM4.0 Actual transpiration, root fraction of each soil layer and soil integral soil water availability (Couvreur et al. 2012, Sulis et al., 2019 HRWU scheme (RWU model based on hydraulic architecture) HRWU scheme Empirical function CLM3 & IBIS2 Actual transpiration, physical root distribution and the water availability in each layer (Zheng and Wang, 2007) The Ryel et al. (2002) Function Dynamic root water uptake Empirical function CoLM Total transpiration, root fraction in each layer and water stress factor (Zhu et al., 2017) The Ryel et al. (2002) Function and the Amenu and Kumar (2007) function Empirical approach with a compensatory factor Empirical function CABLE Maximal efficiency of water uptake by roots and available soil water  The Ryel et al. (2002) Function Not considered Empirical function Crop Models APSIM Potential transpiration and water supply factor, but neglect root distribution (Keating et al., 2003) Not considered Not considered Empirical function CropSyst Difference in water potential between the soil and the leaf, and a total soil-root-shoot conductance (Stöckle et al., 2003) Not considered Considered by the leaf and soil water potential Linear decrease in soils with no limitations to root exploration DSSAT Water uptake per unit of root length is computed as an exponential function, and the actual RWU is the minimum of potential transpiration and the maximum capacity of root water uptake (Jones et al., 2003) Not considered Water uptake per unit of root length as a function of soil moisture Using an empirical function EPIC EPIC assumes that water is used preferentially from the top layers, and the potential water supply rate decreases exponentially downward. (Williams et al.,2014) Not considered Not considered Not considered SWAP Based on the potential transpiration, root fraction and an empiric stress factor relationship (van Dam, 2000) Not considered Based on soil water potential Function of relative rooting depth WOFOST The simplest one, it calculates water uptake as a function of the rooting depth and the water available in that rooting depth without regard to the soil water distribution with depth (Supit et al., 1994) Not considered Not considered Empirical function SPACSYS According to empirical root length density distribution in a soil layer, potential transpiration and soil moisture (Wu et al., 2005) Not considered Not considered 1D (empirical function) or 3D root system (process based) STICS Based on the potential transpiration, root fraction, and soil water distribution, but not process based (Beaudoin et al., 2009) Not considered Not considered 1D root length density profile https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License.

SCOPE and SCOPE_SM Models
SCOPE is a radiative transfer and energy balance model (Van der Tol et al. 2009). It simulates the transfer of optical, thermal and fluorescent radiation of the vegetation canopy and computes ET by using an energy balance routine. SCOPE includes a radiative transfer module for incident solar and sky radiation to calculate the top of canopy outgoing radiation spectrum, net radiation and absorbed photosynthetically active radiation (aPAR), a radiative transfer module for thermal 100 radiation generated internally by soil and vegetation to calculate the top of canopy outgoing thermal radiation and net radiation, an energy balance module for latent heat, sensible heat and soil heat flux, and a radiative module for chlorophyll fluorescence to calculate the top of canopy radiance spectrum of fluorescence at leaf level.
Compared to other radiative transfer models which simplify the radiative transfer processes based on Beer's Law, SCOPE has well-developed radiative transfer modules which consider the various leaf orientation and the multiple scattering. 105 SCOPE can provide detailed information about net radiation of every leaf within the canopy. Furthermore, SCOPE is based on energy balance and it can simulate soil surface temperature which is a vital boundary condition needed by STEMMUS. In addition, Bayat et al. (2019) developed SCOPE_SM, which was based on SCOPE but considering the effect of soil moisture (as model inputs). Therefore, SCOPE_SM provides the basic framework to couple SCOPE with STEMMUS, however both SCOPE and SCOPE_SM ignored the soil heat and mass transfer processes and the dynamics of root growth. Appendix A.1 110 lists the main equations of calculating water stress factor within SCOPE (Bayat et al. 2019), the detailed formulation of SCOPE is referred to Van der Tol et al. (2009).

STEMMUS Model
STEMMUS model is a two-phase mass and heat transfer model with explicit consideration of the coupled liquid, vapor, dry air and heat transfer in unsaturated soil (Zeng et al. 2011a,b;Zeng and Su, 2013;Yu et al. 2018). STEMMUS provides a 115 comprehensive description of water and heat transfer in the unsaturated soil, which can compensate what is currently neglected in SCOPE. The boundary condition needed by STEMMUS includes surface soil temperature, which is the output of SCOPE. In addition, STEMMUS already contained an empirical equation to calculate root water uptake and a simplified root growth module to calculate root fraction profile. As such, STEMMUS has an ideal model structure to be coupled with SCOPE. The main governing equations of STEMMUS are listed in Appendix A.2. 120

Dynamic Root Growth and Root Water Uptake
To obtain the root resistance of each soil layer, we incorporated a root growth module to simulate the root length density profile (see Appendix A.3). The simulation of root growth refers to the root growth module in the INRA STICS crop growth https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License. model (Beaudoin et al., 2009), which includes the calculations of root front growth and root length growth. The root front growth is a function of temperature, with the depth of the root front beginning at the sowing depth for sown crops and at an 125 initial value of transplanted crops or perennial crops (Beaudoin et al., 2009). The root length growth is calculated in each soil layer, considering the net assimilation rate and the allocation fraction of net assimilation on root, which is subsequently a function of LAI (leaf area index) and root zone water content (Krinner et al. 2005). The root length density profile is then used to calculate the root resistance to water flow radially across the roots, soil hydraulic resistance, and plant axial resistance to flow from the soil to the leaves (see Appendix A4). 130

SCOPE_STEMMUS Coupling
The coupling starts with an initial soil moisture (SM) profile simulated by STEMMUS, which enables the calculation of the water stress factor, a reduction factor of the maximum carboxylation rate (Vcmax ), SCOPE is then used calculate net photosynthesis (An) or gross primary productivity (GPP), soil respiration (Re), energy fluxes (Rn, LE, H and G), transpiration (T), which is passed to STEMMUS as the root water uptake (RWU). Then, the net ecosystem exchange (NEE) 135 can be calculated based on An and Re. Surface soil moisture is also used in calculating soil surface resistance and then calculating soil evaporation (E). Furthermore, SCOPE can calculate soil surface temperature (Ts0) based on energy balance, which was subsequently used as the top boundary condition of STEMMUS. Based on RWU, STEMMUS calculates the soil moisture in each layer at the end of the time step, and the new soil moisture profile will be the soil moisture at the beginning of next time step, which is repeated as such till the end of simulation period. The time-step of SCOPE_STEMMUS is 140 flexible and the time step used in this study was half hour. Figure 1 shows the coupling scheme of STEMMUS and SCOPE, and Table B.1 shows all the parameter values used in this study.

Evapotranspiration partitioning
Most studies in partitioning evapotranspiration (ET) use sap flow and micro lysimeter data from in-situ measurements. In this study, we used a simple and practical method to separate evaporation (E) and transpiration (T) proposed by Zhou et al. (2016). Although the behavior of plant stomata is influenced by environmental factors, the potential water use efficiency (uWUEp, g C hPa 0.5 /kg H2O) at stomatal scale in the ecosystem with a homogeneous underlying surface is assumed to be 150 nearly constant (Medlyn et al., 2011), and variations of actual uWUE (g C hPa 0.5 /kg H2O) can be attributed to the soil evaporation (Zhou et al., 2016). Thus, the method can be used to estimate T and E with the quantities of ET, uWUE and uWUEp. Another assumption of this method is that the ecosystem T equal to ET at some growth stages, so uWUEp can be estimated using the upper bound of the ratio of √ to ET (here GPP refers to Gross Primary Productivity, and VPD to Vapor Pressure Deficit) (Zhou et al., 2014;Zhou et al., 2016). 155 Zhou et al. (2016) used the 95 th quantile regression between √ and ET to estimate uWUEp, and showed that the 95 th quantile regression for uWUEp at flux tower sites was consistent with the uWUE derived at the leaf scale for different ecosystems. In addition, the variability of seasonal and interannual uWUEp was relatively small for a homogeneous canopy.
Therefore, the calculations of uWUEp, uWUE, and T at the ecosystem scale were as follows: The calculation of VPD was based on air temperature and relative humidity data, and the method of gap-filling was the Marginal Distribution Sampling (MDS) method proposed by Reichstein et al. (2005). To calculate GPP, the complete series of net ecosystem exchange (NEE) was partitioned into gross primary production (GPP) and respiration (Re) using the 165 method proposed by Reichstein et al. (2005). Finally, ET was calculated using the latent heat flux and air temperature. Based on GPP, ET and VPD data, T can be calculated using the method proposed by Zhou et al. (2016).
Meanwhile, Zhou et al. (2016) discussed the uncertainty of this method, which was mainly caused by: (1) the uncertainty in the partitioning of GPP (less than 10%) and Re based on NEE, which would result in some uncertainty in uWUE; (2) due to the seasonal variation of atmosphere CO2 concentration, the assumption of uWUEp being constant would cause some 170 uncertainty (less than 3%); (3) the assumption of T being equal to ET sometimes during the growing season would cause some uncertainty when vegetation is sparse.

Field measurements
To evaluate the performance of SCOPE_STEMMUS in modeling ecohydrological processes, simulation was conducted to compare SCOPE_STEMMUS with SCOPE, SCOPE_SM, and STEMMUS using the observation of fluxes (from 10 June 175 2017 to 10 October) at the Yangling station (34°17′ N, 108°04′ E, 521 m a.s.l.). Figure 2 illustrates the variations of environmental factors during the maize growing season. As shown in the subfigures, the incoming shortwave radiation ranged from 0 to 1100 W m -2 and decreased significantly after Days-After-Sowing (hereafter as DAS) 67. In contrast, the incoming longwave radiation was relatively stable, which was about 400 W m -2 during the maize season. The air temperature was relatively high at initial stage and gradually decreased to 5 o C at the late stage. The soil moisture was maintained at a 180 high level except during a drought episode from DAS 15 to 40, and the relative humidity (RH) at the late stage was higher than that at the early stage. Two irrigations were carried out on DAS 7 and DAS 41, and the volume of irrigation were 28mm and 64mm, respectively. The leaf area index (LAI) and canopy height (hc) were measured and the peak value was 4.39 m 2 m -2 and 1.95 m, respectively. Due to the lack of field measurement on root length and soil moisture profile of root zone, we used the simulated results of SCOPE_STEMMUS as the input data of SCOPE_SM to compare the performance of 185 SCOPE_SM with that of SCOPE_STEMMUS. The Eddy Covariance (EC) system was installed on a height-adjustable tripod, The EC system included a three-dimensional sonic anemometer, an open path infrared gas analyser, and a data logger.
The detailed descriptions of the instruments can refer to Wang et al. (2020).

Performance Metrics
The metrics used to evaluate the performance of coupled SCOPE_STEMMUS model include: (1) Root Mean Squared Error (RMSE); (2) coefficient of determination (R 2 ); and (3) the index of agreement (d). They are calculated as: where is the ith predicted value, is the ith observed value, ̅ is the average of observed values, and n is the number of samples.

Soil moisture modeling
Comparison of simulated soil moisture (SM) using STEMMUS and SCOPE_STEMMUS and observed ones is presented in Figure 3. The simulated soil moisture at 20 cm depth agreed with the observed values in terms of seasonal pattern. Although slight overestimation occurred at initial and late stages, the dynamics in soil moisture resulted from precipitation or irrigation were well captured. Per the nature of the two models, the coupling of SCOPE with STEMMUS is not expected to improve the simulation of soil moisture. However, compared to SCOPE_SM, which used soil moisture measurements as inputs, the coupled SCOPE_STEMMUS improves the simulation of soil moisture dynamics as measured. The deviation between the model simulations and the measurements can be attributed to the following two potential reasons. First, the field observation has errors to a certain extent and the soil moisture sensors may be not well calibrated. Second, in this simulation, we assumed that the soil texture was homogeneous in the vertical direction, whereas the soil properties (e.g. soil bulk density 215 and saturated hydraulic conductivity) may vary with depth in reality, and at different growth stages due to field management practices. For example, the soil bulk density at 40 cm was much higher than that at 20 cm due to the mechanical tillage, especially in the early stage.

Soil temperature modeling
Simulated soil temperatures (Ts) by STEMMUS and SCOPE_STEMMUS at 20 cm and 40 cm depth are shown in Figure 4.
In general, both two models can capture the dynamic of soil temperature well. For the simulation of 20 cm temperature, for STEMMUS and SCOPE_STEMMUS, RMSE value was 2.56 o C and 2.58 o C, respectively; d value was 0.92 and 0.92, 225 respectively. For the simulation of 40cm temperature, RMSE value was 2.06 o C and 2.07 o C, respectively; d value was 0.93 and 0.93, respectively. These results indicate that both models can simulate well soil temperature. However, there also exist some differences between simulation and observation. The largest difference occurred in DAS 40, when the field was irrigated with the flooding irrigation method. This irrigation activity may lead to the boundary condition errors (i.e., for soil surface temperature), which cannot be estimated well enough (e.g., there is no monitoring of water temperature from the 230 irrigation). Meanwhile, the measurement may also have some errors in this period. The fact for the observed soil temperature https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License.
at 20 cm and 40 cm to decrease to almost the same level at the same time indicates a potential pathway for preferential flow in the field (see precipitation/irrigation at DAS 40 in Figure 2), and the sensors captured this phenomenon. Nevertheless, the model captures the soil temperature dynamics.

Energy balance modeling
A comparison of the observed and modeled half-hourly net radiation (Rn), sensible heat flux (H), latent heat flux (LE), and soil heat flux (G) using original SCOPE, SCOPE_SM, and SCOPE_STEMMUS were presented in Figure 5. For net 240 radiation and soil heat flux, the simulations of all three models show good agreements with observations. For net radiation, the coefficients of determination (R 2 ) for SCOPE, SCOPE_SM and SCOPE_STEMMUS were 0.99, 1.00, and 0.99, respectively. For soil heat flux, the R 2 for SCOPE, SCOPE_SM and SCOPE_STEMMUS were 0.81, 0.79, and 0.80, respectively. For latent heat flux, SCOPE_STEMMUS has a better performance than SCOPE and SCOPE_SM, and the R 2 for SCOPE, SCOPE_SM and SCOPE_STEMMUS were 0.82, 0.84, and 0.85, respectively. Furthermore, 245 SCOPE_STEMMUS and SCOPE_SM have a similar performance in the simulation of sensible heat flux, which were better than the performance of SCOPE, the R 2 for SCOPE, SCOPE_SM and SCOPE_STEMMUS were 0.70, 0.75, and 0.74, respectively.

Daily ET, T and E modeling 255
Simulated daily evapotranspiration (ET) results by SCOPE, SCOPE_SM, STEMMUS and SCOPE_STEMMUS are presented in Figure 6. As shown in the subfigures, the R 2 by SCOPE, SCOPE_SM, STEMMUS and SCOPE_STEMMUS were 0.76, 0.82, 0.80 and 0.81, respectively. The RMSE of these four models were 0.84, 0.69, 0.76, and 0.74 mm day -1 respectively. For the ET simulation by SCOPE, there were large differences between simulations and observations when the vegetation suffered water stress. For SCOPE_SM, STEMMUS and SCOPE_STEMMUS, because of taking into account the 260 dynamic variation of soil moisture, the simulated ET were closer to observations when the crop experienced water stress. It indicates that SCOPE_STEMMUS, STEMMUS and SCOPE_SM can predict ET with a relatively higher accuracy, especially when the maize was under severe water stress (DAS 30 to 40), and SCOPE_STEMMUS and SCOPE_SM performed similarly well. It is noteworthy that although STEMMUS has considered the effect of soil moisture on ET, the accuracy of STEMMUS was lower than the coupled model (see DAS 40 and DAS 110 in Figure 6). The possible reason is 265 https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License.
the better representation of transpiration in SCOPE model (see Figure 7), which separates the canopy into 60 layers, while STEMMUS only treats the canopy as one layer. The performances of SCOPE_STEMMUS and SCOPE_SM were better than that of STEMMUS. The possible reason is the better simulation of the radiative transfer and energy balance at leaf level in the coupled SCOPE_STEMMUS model (as also in SCOPE_SM) and the more accurate root water uptake (compared to that in SCOPE_SM). Nevertheless, SCOPE_STEMMUS slightly underestimated transpiration when the plant is undergoing severe water stress and slightly 280 overestimated it after the crop was irrigated. This is mainly because the actual Vcmax was not only influenced by drought but also related to leaf nitrogen content (Xu and Baldocchi, 2003), which was not considered in this study.

Figure 7 Comparison of observed and modeled daily plant transpiration (T) (To: observed T; Tm: modeled T).
285 Figure 8 shows the modeled and observed half-hourly canopy transpiration. The simulations by SCOPE_STEMMUS and SCOPE_SM are consistent with observation and both are much lower than that by SCOPE. The performances of SCOPE_STEMMUS and SCOPE_SM were consistent with that of SCOPE in the early morning and late afternoon, when the photosynthesis is mainly limited by incident radiation rather than by water stress, intercellular CO2 concentration and Vcmax.
In the midday, with increasing incident radiation, the photosynthesis was mainly limited by water stress and Vcmax, exactly 290 when the simulations by SCOPE_STEMMUS and SCOPE_SM are much better than that by SCOPE. https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License. Figure 9 for soil evaporation, the simulation by SCOPE_STEMMUS is closer to observation than those by other models. When using SCOPE to simulate soil evaporation, the soil moisture is set as constant (i.e., 0.25 m 3 m -3 ). 295

As shown in
Therefore, SCOPE generally underestimates soil evaporation when soil moisture is higher than 0.25 and overestimates soil evaporation when it is lower than 0.25. Due to the lack of measurement of soil surface moisture in this study, we use the average soil moisture at root zone simulated by SCOPE_STEMMUS as the input data for SCOPE_SM to calculate soil surface resistance and soil evaporation. Although STEMUS can capture variation of soil evaporation reasonably well, it has higher RMSE value than SCOPE_STEMMUS. This is probably attributed to the comprehensive consideration of radiation 300 transfer in SCOPE, which is lacking in STEMMUS. Consequently, the simulation of soil net radiation of the coupled model was more accurate than STEMMUS alone. The RMSE value of SCOPE_STEMMUS was 0.60 mm day -1 , which was lower than those of other three models (i.e. 0.67, 0.65, and 0.64 mm day -1 respectively). For SCOPE_STEMMUS, the major differences between simulations and observations occurred in rainy days, which may be caused by errors of soil surface resistance estimation during these periods or the uncertainty of ET partitioning method. 305

Daily NEE modeling
Simulated NEE by SCOPE, SCOPE_SM and SCOPE_STEMMUS and observed NEE were presented in Figure 10. As 310 shown, similar to the simulation of transpiration, SCOPE cannot respond to water stress when simulating NEE. After introducing soil water stress factor in SCOPE_STEMMUS and SCOPE_SM, the simulations of NEE were improved in both models. The consistency between simulated and observed NEE at mid and late stages were higher than those at early and rapidly growth stages. The difference usually occurred when soil moisture increased. The reason is that the simulated NEE https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License. was calculated by GPP and Re, and Re was not only influenced by soil temperature, but also by soil moisture. However, in 315 this study, we only considered the effect of soil temperature on Re. Many studies evidenced that soil respiration increased with increasing soil moisture, especially when rain or irrigation occurred. Generally, in the summer, soil temperature decreases when raining or irrigating. However, the model only considers the effect of reduced soil temperature on Re, while ignores the positive effect of increasing soil moisture. As such, the simulated soil respiration would decrease with soil temperature dropped. For the late stage, as soil moisture was stable and maintained at a high level, the difference between 320 simulated and observed soil respiration was relatively small. This can also demonstrate that the errors of NEE simulation were mainly caused by the effect of soil moisture on soil respiration.

Leaf water potential, water stress factor, and root length density
Leaf water potential was a parameter to reflect plant water status. The simulated half-hourly leaf water potential and water stress factor are presented in Figure 11. The leaf water potential was lower when vegetation suffering water stress compared 330 to other periods. The reason is that soil water potential is low due to the low soil moisture and the leaves need to maintain an even lower water potential to suck water from the soil and transfer it to leaves. During mid and late stages, the leaf water potential was sensitive to transpiration demand due to the slowdown of root system growth. As the continuous measurements of the leaf water potential is not available, we compared the simulated leaf water potential to the measurements reported in other literatures. 335 https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License.
Many studies have measured midday leaf water potential or dawn leaf water potential. Fan et al. (2015) reported that the leaf water potential of well-watered maize was maintained high between -73 to -88 m and leaf water potential would decrease when soil water content was lower than 80% of field capacity. Martineau et al. (2017) reported the midday leaf water potential of well-watered maize was around -82 m and the midday leaf water potential decreased to -130 m when the maize was suffering water stress. Moreover, O'Toole and Cruz (1980) studied the response of leaf water potential to water stress in 340 rice and concluded that the leaf water potential of rice can be lower than -80 to -120 m when the vegetation is under water stress and the leaves start curling, which was similar to the simulated leaf water potential of maize in this study. Aston and Lawlor (1979) revealed the relationship between transpiration, root water uptake and leaf water potential of maize. These field studies found that leaf water potential is often very low and it reaches valley values at midday. Elfving (1972) developed a water flux model, which was based on SPAC system and evaluated with the orange tree. In his study, the valley 345 value of leaf water potential under non-limiting environmental conditions was about -120 m, which was slightly lower than the simulation in this study.
In this study, the calculation of water stress factor considered the effect of soil moisture and root distribution. The severe water stress was from DAS 30 to DAS 40, and the coupled model performed very well in this period. As the feedback, water stress can also influence root water uptake and root growth, and then influence soil moisture and root dynamic in the next 350 time step. It indicates that the water stress equation used in this study can characterize the reduction of Vcmax reasonably well.

Figure 11 Simulation of ψleaf (leaf water potential, m) and WSF (water stress factor). (The dashed lines represent the range of midday leaf water potential reported in other sites.)
Root length density is another vital parameter in root water uptake calculation. As shown in Figure 12, the root length 355 density was high from 10 to 20 cm depth and gradually decrease from 20 cm to 121 cm. Many previous studies have revealed that root length density was influenced by soil moisture, bulk density, tillage, and soil mineral nitrogen (Amato and Ritchie, 2002;Chassot et al., 2001;Schroder et al., 1996). In this study, as we assumed the soil was homogenous, SCOPE_STEMMUS considered the effect of soil moisture but neglected the effect of bulk density and soil mineral nitrogen. https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License. Amato and Ritchie (2002) also found a similar result as this study about the root length density in a maize field. Peng et al. 360 (2012) studied temporal and spatial dynamics in root length density of field-grown maize and found 80% root length density distributed at 0-30 cm depth with peak values from 0.86 to 1.00 cm cm -3 . Ning et al. (2015) also reported a similar observation of root length density. Chassot et al. (2001) and Qin et al. (2006) reported that root length density can reach 7 cm cm -3 at Swiss midlands. Aina and Fapohunda (1986) also found that root length density can reach 2.5 cm cm -3 if the maize was well-watered. In Stuttgart, Germany, Wiesler and Horst (1994) observed the root growth and nitrate utilization of 365 maize under field condition. The observed root length density was 2.45-2.80 cm cm -3 at 0-30 cm depth which was much higher than in other studies, and decreased to 0.01 cm cm -3 at 120-150 cm depth, which was consistent with the observation of Oikeh et al. (1999) at Samaru, Nigeria. Zhuang et al. (2001b) proposed a scaling model to estimate the distribution of root length density of field grown maize. In their study, measured root length density in Tokyo, Japan decreased from 0.4-0.95 cm cm -3 at top soil layer to about 0.1 cm cm -3 at the bottom layer. Zhuang et al. (2001a) observed that the root length density 370 of maize was mainly distributed at 0-60 cm depth and the maximum values were about 0.9 cm cm -3 . These studies indicate that the root length density values were quite variable when it was observed at different sites, nevertheless the simulated root length density was in order of magnitude similar to the observations in previous studies.

Conclusions
A fundamental understanding of coupled energy, water and carbon flux is vital for obtaining the information of ecohydrological processes and functioning under climate change. The coupled model, SCOPE_STEMMUS, integrating radiative transfer, photochemistry, energy balance, root system dynamic, and soil moisture and soil temperature dynamic, 380 has been proven to be a practical model to simulate detailed land surface processes such as evapotranspiration and NEE. In https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License. the coupled model, STEMMUS could provide root zone moisture profile to SCOPE, which was used to calculate water stress factor. On the other hand, SCOPE can provide soil surface temperature to STEMMUS, which was used subsequently as the top boundary condition. The performance of the coupled SCOPE_STEMMUS model in ET partitioning was improved due to the comprehensive radiative transfer scheme in SCOPE. The coupled model has been successfully applied in a maize field. 385 Through the inter-comparison of SCOPE, SCOPE_SM, STEMMUS, and SCOPE_STEMMUS, we concluded that the coupled STEMMUS_SCOPE can be used to investigate vegetation states under water stress conditions, and to simultaneously understand the dynamics of soil heat and mass transfer, as well as the root growth. However, there are some needs for further studies to enhance the capacity of STEMMUS_SCOPE in understanding ecosystem functioning. Frist of all, the estimation of soil boundary condition especially during the irrigation period, which has significant influence on the 390 simulation of soil temperature, needs further improvement. Second, the soil respiration model used in SCOPE, which neglected currently the effect of soil moisture, should be upgraded in the coupled model. Nevertheless, the SCOPE_STEMMUS may be used as an observation operator to assimilate remote sensing data such as solar-induced chlorophyll fluorescence, to improve the estimation of water and carbon fluxes. SCOPE_STEMMUS could also be used to investigate regional or global land surface processes, especially in arid and semi-arid regions, due to its sensitivity to water 395 stress conditions.
Code and data availability. The development and validation of SCOPE_STEMMUS in this paper were conducted in MATLAB R2016a. The exact version of the model used to produce the results used in this paper is archived on Zenodo (Wang et al., 2020). The original source of the SCOPE model and STEMMUS model was obtained from Van der Tol et al. (2009) and Zeng et al. (2011a, b), respectively. The tower-based eddy-covariance measurements used for 400 model validation were obtained from the authors in Yangling, China (Wang et al., 2019).
Author contributions. YW, YZ, LY, PY, CV, ZS and HC designed the study, Developed the code, conducted the analysis, and wrote the manuscript with YW and HC collected and shared their eddy-covariance measurements for the purpose of model validation. All authors gave comments and contributed to the final version of the manuscript.
Competing interests. The authors declare that they have no conflict of interest. The C4 Photosynthesis is calculated in the SCOPE model as the minimum of three processes (Farquhar et al., 1980); (1) carboxylation rate limited by Ribulose biphosphate-carboxylase-oxygenase activity (known as Rubisco (enzyme)-limited, Vc, where is the maximum carboxylation rate (μmol m −2 s −1 ), is the intercellular CO2 partial pressure (Pa), is a pseudo-first-order rate constant for PEP carboxylase with respect to , is the atmospheric pressure; An is the net photosynthesis (μmol m −2 s −1 ); WSF is the total water stress factor, J is the electron transport rate (μmol m -2 s -1 ), Ci is the intercellular CO2 concentration (μmol m −3 ) and Ca is CO2 concentration in the boundary layer (μmol m −3 ), m is Ball-Berry parameter and RH is relative humidity at the leaf surface (%). 425 In the study of Bayat et al. (2019), water stress factor was calculated based on the root zone soil moisture content neglecting the distribution of root length. In this study, water stress factor considered both root length distribution and water content in root zone. We use a sigmoid formulation rather than the piecewise function by Bayat et al. (2019). The calculations are as follows: is the soil water content at wilting point; is the soil water content at field capacity; is the saturated soil water content; WSF(i) is the water stress factor at each soil layer; RF(i) is the ratio of root length in soil layer i and its calculation can be found in the appendix A.4; SM(i) is the soil moisture at each soil layer.

A.2.1 Soil water conservation equation
where , (kg m −3 ) are the density of liquid water, water vapor, respectively; qL , qV (m 3 m −3 ) are the volumetric water content (liquid and water vapor, respectively); z (m) is the vertical space coordinate (positive upwards); S (cm s −1 ) is the sink 440 term for the root water extraction. K (m s −1 ) is hydraulic conductivity; h (cm) is the pressure head; Ts (°C) is the soil temperature; and Pg (Pa) is the mixed pore-air pressure.
(kg m -2 s -2 ) is the specific weight of water. DTD (kg m -1 s -1 °C -1 ) is the transport coefficient for adsorbed liquid flow due to temperature gradient; DVh (kg m -2 s -1 ) is the isothermal vapor conductivity; and DVT (kg m -1 s -1 °C -1 ) is the thermal vapor diffusion coefficient. DVa is the advective vapor transfer coefficient (Zeng et al. 2011a,b). ℎ , , and (kg m -2 s -1 ) are the liquid water fluxes driven by the gradient of matric 445 potential, temperature, and air pressure, respectively. ℎ , , and (kg m -2 s -1 ) are the water vapor fluxes driven by the gradient of matric potential, temperature, and air pressure, respectively.

A.2.2 Dry air conservation equation
where is the porosity; (kg m −3 ) is the density of dry air; Sa (=1-SL) is the degree of air saturation in the soil; SL (=θL/ ) 450 is the degree of saturation in the soil; Hc is Henry's constant; De (m 2 s -1 ) is the molecular diffusivity of water vapor in soil; Kg (m 2 ) is the intrinsic air permeability; ma ( kg m -2 s -1 ) is the air viscosity; qL (kg m -2 s -1 ) is the liquid water flux; a (= V) is the volumetric fraction of dry air in the soil; and DVg (m 2 s -1 ) is the gas phase longitudinal dispersion coefficient (Zeng et al., 2011a,b).

A.2.3 Energy balance equation 455
where Cs, CL, CV, Ca (J kg −1 °C −1 ) are the specific heat capacities of solids, liquid, water vapor, and dry air, respectively; (kg m −3 ), (kg m −3 ), (kg m −3 ), and (kg m −3 ) are the density of solids, liquid water, water vapor, and dry air, respectively; s is the volumetric fraction of solids in the soil; , , and are the volumetric fraction of liquid water, 460 water vapor, and dry air, respectively; Tr (°C) is the reference temperature; L0 (J kg −1 ) is the latent heat of vaporization of https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License. water at temperature Tr; W (J kg −1 ) is the differential heat of wetting (the amount of heat released when a small amount of free water is added to the soil matrix); and (W m −1 °C −1 ) is the effective thermal conductivity of the soil; qL, qV, and qa (kg m -2 s -1 ) are the liquid, vapor water and dry air flux.

A.3.1. Root front growth
The depth of the root front is firstly initialized either with the sowing depth for sown crops or with an initial value for transplanted crops or perennial crops. The root front growth stops when it reached certain depth of soil or a physical/chemical obstacle preventing root growth, but also stops when the phenological stopping stage has been reached.
where ∆ is root front growth at t-th time step; (cm) is root zone depth; ( 0 C) is air temperature; Tmin ( 0 C) is the minimum temperature of root growth; Tmax ( 0 C) is the maximum temperature of root growth; RGR (cm 0 C -1 day -1 ) is the root growth rate of root front.

A.3.2. Root length growth 475
In this study, the root distribution in the root zone was realized via simulating the root length growth in each soil layer.
is the allocation fraction of net assimilation to root, and is assumed as a function of leaf area index (LAI) and root zone water content. is the net assimilation rate (μmol m −2 s −1 ). is ratio of carbon to dry organic matter in root, is root length density (m), and is radius of the root (0.15*10 -3 m), and ∆ _ (m m -3 ) is total root length growth. 480 The limiting factors for allocation are preliminarily computed and they account for root zone soil moisture availability , and light availability .
where is the averaged soil moisture stress factor in the root zone.
where (= 0.15) is the minimum allocation coefficient to fine roots, and 0 is a coefficient that indicates the theoretically unstressed allocation to fine roots.
where ( ) is the allocation fraction of root growth length in layer i, ∆ ( ) is the root growth length in layer i.
where and −1 is the root length of layer i at time step t and time step t-1.
where is the total root length in root zone, ( ) is the root length in soil layer i. 495

A.4. Root water uptake
The equation to calculate root water uptake and transpiration was as follows: where ψs,i is soil water potential of layer i (m), ψl is leaf water potential (m), rs,i is the soil hydraulic resistance (s m −1 ), rr,i is the root resistance to water flow radially across the roots (s m −1 ), and rx,i is the plant axial resistance to flow from the soil to 500 the leaves (s m −1 ). el and ea are vapor pressure of leaf and the atmosphere (hPa), respectively, and ra and rc are aerodynamic resistance and canopy resistance (s m −1 ), respectively.
is the density of dry air (kg m -3 ). is the density of water vapor.
is the atmospheric pressure (Pa). 0.622 is the ratio of the molar mass of water to air.
, is described as a function of soil moisture by Van Genuchten (1980), and the relevant parameters were shown in Table  B.1. 505 The is calculated by Reid and Huck (1990) as: where B is the root length activity factor, K is hydraulic conductivity of soil (m s −1 ), is root length density (m m −3 ), and Δ is the thickness of the soil layer (m). B is calculated as: where is root radius (m).
The r r is estimated as (Reid and Huck, 1990): where is root radial resistivity (s m −1 ).
The xylem resistance is estimated by Klepper et al. (1983): 515 where is root axial resistivity (s m −3 ), is the depth of the midpoint of soil layer, and is a fraction defined for a specific depth as the number of roots which connect directly to the stem base to total roots crossing a horizontal plane at that depth. We can consider it equal to 0.22 based on Klepper et al. (1983).
The updated root water uptake term is: 520 Different from other studies which need to calculate the compensotary water uptake and hydraulic redistribution after calculating the standard water uptake of each soil layer, the sink term in this study is calculated by a physically-based model which contain the effect of root resistance and soil hydraulic resistance rather than only considering the root fraction, so the compensary uptake and hydraulic redistribution have been considered when calcualting the sink term. 525 https://doi.org/10.5194/gmd-2020-85 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License.