Interactive comment on “ Investigating effects of different evapotranspiration ( ET ) schemes on soil water dynamics and ET partitioning : a large lysimeter case of summer maize in a semi-arid environment northwest of China ”

The paper investigates the effects of two different methods to estimate ET (direct and indirect) on the output of the STEMMUS model. This model couples the transfer of heat, water, and vapor in the soil. Furthermore the authors look at the sensitivity of the STEMMUS model on the ET partitioning. The paper describes the STEMMUS model and compares the output with lysimeter results for a single growth cycle in a semi-arid region (China). The paper is well written and structured, except for the abstract which


Introduction
The soil water movement is the central physical process of the land surface models (LSMs), which interacts with surface infiltration, evaporation, root extraction and underground water recharge.Accurate description of this process is necessary for the appli-Introduction

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Full cation of LSMs to achieve efficient and optimum water resources management.While it has been widely accepted that water vapor and heat transport should be coupled into the soil water model, especially in arid or semi-arid environment (Bittelli et al., 2008;Saito et al., 2006;Zeng et al., 2009aZeng et al., , b, 2011a, b), b), it is still not clear how such coupling can affect the soil water dynamics in crop fields, via different evapotranspiration (ET) schemes.
The ET plays a critical role in the process of soil water movement, as it controls the water distribution of surface and root zone soil layers through soil evaporation and transpiration.A common procedure to estimate ET is the so-called indirect ET scheme (ET ind ), which transfers the reference crop evapotranspiration (ET 0 ) into actual crop evapotranspiration (ET c ) using a simple multiplicative crop factor.Recent theoretical developments allow the adoption of a more robust Penman-Monteith (PM) equation description of ET.The direct ET scheme (ET dir ) is a one-step calculation procedure, which expresses the stomatal and aerodynamic controls in terms of various resistances in the PM equation.Independent from land surface models (LSMs), much effort has been made to compare the performances of different approaches to estimate ET (Federer et al., 1996;Stannard, 1993).The performance of different ET equations varied with the characteristics of land cover and climate (Shuttleworth and Wallace, 2009;Zhou et al., 2007).Ershadi et al. (2015) highlighted the need to provide guidance on selecting the appropriate ET method for use in a specific region.
Further evaluation confirmed that different ET schemes can significantly affect the performance of LSMs (Anothai et al., 2013;Chen et al., 2013;Federer et al., 1996;Kemp et al., 1997;Mastrocicco et al., 2010).Vörösmarty et al. (1998) made a comparison between reference surface (PETr) and surface cover-dependent (PETs) potential ET schemes in a global-scale water balance model (WBM) and concluded that WBM simulations were highly sensitive to the PET schemes and using the PETs methods would produce quite reasonable estimates of actual ET over a broad geographic domain.Recent assessment of HYDRUS-1-D model with different ET schemes indicated that using PM equation gave a better model performance in simulating soil water con-Introduction

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Full tent (Mastrocicco et al., 2010).However, most of these results evaluated the model performances only for individual variable (e.g.soil water content or ET) or neglecting the heat or vapor transport effect (Anothai et al., 2013;Kemp et al., 1997;Vörösmarty et al., 1998).
The other fact is that the uncertainties of crop growth parameters were not fully tested although with a significant influence on the model performance (Federer et al., 2003).
Previous studies generally concluded based on the combined analysis of the entire growing season (Padilla et al., 2011).However, these results could be inappropriate to some extent.Unlike the soil properties, the crop growth parameters had a significantly interactive effect with changing environment during the growing season (Teuling et al., 2006).The roughly seasonal assessment would conceal the crop modulating mechanism with changing environment.The objectives in this paper are two fold: (i) investigating how different ET schemes will affect the soil water dynamics in a crop field located in Northwest China, semi-arid environment, with a coupled model considering transfer of water, vapor and heat in the soil, (ii) with the calibrated coupled model, the sensitivity analysis will be implemented to explore the influence of crop growth parameters on the ET portioning.In the following section, the field experiment, data collection and the numerical models will be introduced.The results were discussed in Sect.3. The summary and conclusion were drawn in Sect. 4.

Field experiment
The lysimeter experiment was conducted in the Yangling Irrigation Experiment Station located in northwest of China ( 34• 17 N, 108 • 04 E, and elevation 521 m a.m.s.l.-above mean sea level).The experimental site is located at a semi-arid to sub-humid climatic region with a mean annual precipitation of 630 mm and a mean annual air temperature Introduction

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Full of 12.9 • C. The soil at the location is silt clay loam with the field capacity of 23.5 % and the bulk density of 1.35 g cm −3 .The groundwater level is at least 50 m lower than the soil surface (Kang et al., 2001), thus the capillary rise from the groundwater can be neglected for the current study.
The lysimeter is made of steel with the size of 3 m length, 2.2 m width and 3 m depth.
There are a filter layer, a weighing facility and a drainage system for measuring the amount of deep percolation at the bottom of the lysimeter.In order to apply the irrigation water, the steel wall is 5 cm higher than ground surface.The detailed description of the lysimeter is given in Fig. 1.A mobile rainproof shelter above the lysimeter was installed to control the precipitation.Summer maize was sown on 23 June and harvested on 2 October with the plant population of 40 plants within the area of 6.6 m 2 .Irrigation was applied when soil water content dropped to a pre-set lower limit (i.e. 60 % of the field capacity).The amount of irrigation was crop ET measured by the lysimeter during the intervals of two irrigation events.Two supplemental irrigations were applied at the starting days (DOY 178 and 184) to ensure summer maize uniformly grow.

Data collection
Soil moisture and temperature was measured using the pre-calibrated sensors, which were installed at the depth of 20,40,60,80,100,200,225,250 cm.Hourly measurements were made throughout the growing season.Considering the possible damage caused by tillage and other agricultural management, soil moisture and temperature sensors were not equipped at top soil layers.Top soil water content was measured using gravity oven method weekly.Crop ET was determined using the lysimeter weighting system (e.g. with the precision of 0.021 mm).The ET measurements were made hourly and summed to daily values during the growing season.Soil evaporation (E ) was measured by weighing the micro-lysimeter at 08:00 LT daily.The micro-lysimeter was placed between two crop rows with the diameter of 12 cm and the depth of 20 cm.After significant precipitation and irrigation, we replaced the soil in the micro-lysimeter to keep the soil moisture in the micro-lysimeter similar to that of field conditions.Other Figures

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Full details are referred to previous studies over this lysimeter (Kang et al., 2003;Wang et al., 2007).Meteorological data were obtained from a standard weather station located inside the experimental site.The data included daily maximum and minimum air temperature, air humidity, daily precipitation, sunny hours and wind speed at 10 m height.
Hourly values of air temperature, air humidity and wind speed were generated from daily measurements using a trigonometric function, detail description can be found in Saito et al. (2006).
Leaf stomatal conductance was measured using the portable photosynthesis equipment (LI-6400, Li-Cor, USA) a few days after irrigation.Measurements were made on three functional leaves within the time intervals between 10:00-14:00 LT, when the stomatal conductance of summer maize reached its peak and kept steady (Zhang et al., 2011).Leaf area and plant height were measured from the average of at least 3 plant samples at intervals of 7-10 days starting at 14 days after planting.The crop stages or phenology were assessed following the recommendation by Allen et al. (1998).Dates for each crop development phase were shown in Table 1.

Numerical model
The STEMMUS (Simultaneous Transfer of Energy, Mass and Momentum in Unsaturated Soil) model was used to simulate coupled liquid water, water vapor and heat flow in unsaturated soil.In order to use STEMMUS for the lysimeter experiment, a macroscopic root water uptake module was incorporated into the STEMMUS.

STEMMUS
In STEMMUS, the extended version of Richards' equation with modification made by Milly (1982) was numerically solved to consider the vertical interactive process between atmosphere and soil.The governing equation of the liquid and vapor flow can be expressed as: Introduction

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Full where ρ L and ρ V (kg m −3 ) are the density of liquid water and water vapor; θ L and θ V (m 3 m −3 ) are the volumetric water content (liquid and vapor); z (m) is the vertical space coordinate; q L and q V (kg m −2 s −1 ) are the soil water fluxes of liquid and water vapor (positive upwards), respectively; and S (s −1 ) is the sink term for the root water extraction.
The liquid water flux, separated into isothermal q Lh (pressure head driven) and thermal q LT (temperature driven), is described as: where K Lh (m s −1 ) and K LT (m 2 s −1 • C −1 ) are the isothermal and thermal hydraulic conductivities, respectively; h (m) is the pressure head; and T ( • C) is the soil temperature.The water vapor flux, separated into isothermal q Vh (pressure head driven) and thermal q VT (temperature driven), is described as: where D Vh (kg m −2 s −1 ) is the isothermal vapor conductivity; and is the thermal vapor diffusion coefficient, given in Zeng et al. (2011a).
The root water uptake term described by Feddes et al. (1978) is where α(h) (dimensionless) is the reduction coefficient related to soil water potential; S p (s −1 ) is the potential water uptake rate.where b(x) is the normalized water uptake distribution, which describes the vertical variation of the potential extraction term, S p , over the root zone, described in Šimůnek et al. (2008).T p is the potential transpiration.Following De Vries (1958)'s work, the heat transport function in unsaturated soil can be expressed as where C s , C L and C V (J kg −1 • C −1 ) are the specific heat capacities of solids, liquid and water vapor, respectively; ρ s (kg m −3 ) is the density of solids; θ s is the volumetric fraction of solids in the soil; T r ( • C) is the arbitrary reference temperature; L 0 (J kg −1 ) is the latent heat of vaporization of water at temperature T r ; 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 λ eff (W m −1 • C −1 ) is the effective thermal conductivity of the soil.Dry air transport in unsaturated soil is originally taken into account in STEMMUS, the balance equation can be written as Thomas and Sansom (1995 where ε is the porosity; ρ da (kg m −3 ) is the density of dry air; S a (= 1 − S L ) is the degree of air saturation in the soil; S L (= θ L /ε) is the degree of saturation in the soil; H c is the Henry's constant; D e (m 2 s −1 ) is the molecular diffusivity of water vapor in soil; K g (m 2 ) is the intrinsic air permeability; µ a (kg m −2 s −1 ) is the air viscosity; D Vg (m 2 s −1 ) is the gas phase longitudinal dispersion coefficient.Note that the effects of dry air movement were not considered in the current study.Introduction

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Initial and boundary conditions
In general, the soil surface water flow boundary can be characterized as a flux-type boundary controlling by the atmospheric forcing, including soil evaporation, precipitation and irrigation.
where E s (kg m −2 s −1 ) is the actual soil evaporation rate; P and I (m s −1 ) are precipitation and irrigation rate, respectively.After an intense irrigation or precipitation, ponding would occur at the soil surface, the surface boundary thus changed to a pressure-type boundary.It is assumed that surface runoff at the study site was negligible and the maximum height of the surface ponding layer was assigned 5 cm according to the lysimeter structure (Fig. 1).Since there is a filter layer at the bottom of the soil profile (Fig. 1), saturated water can be easily drained out of the lysimeter.The bottom boundary was considered as a seepage face condition (Šimůnek et al., 2008).The soil surface temperature deduced from the in-situ measurements was set as the upper boundary condition for the heat transfer, and the bottom temperature was fixed as the lower boundary condition.The initial soil moisture and temperature profile could be determined by interpolating the measured values at the starting day.

Transpiration and soil evaporation
Two different parameterizations of ET components were adopted in land surface models.A common procedure is based on reference crop evapotranspiration (ET 0 ) and then partition into soil evaporation and transpiration using crop factors (Feddes et al., 1974;Šimůnek et al., 2008;Wu et al., 1999), which was noted as the ET ind scheme.where ET 0 (mm day −1 ) is the reference ET; R n (MJ m −2 day −1 ) is the net radiation at the crop surface; G (MJ m −2 day −1 ) is the soil heat flux density; T a ( • C) is the air temperature at 2 m height; u 2 (m s −1 ) is the wind speed at 2 m height, can be obtained from wind speed data at 10 m height using a logarithmic wind profile function; e a and e s (kPa) are the actual and saturation vapour pressure; ∆ (kPa • C −1 ) is the slope of vapor pressure curve; γ (kPa • C −1 ) is the psychrometric constant.The actual potential transpiration (T p ) can be estimated by multiplying ET 0 with the crop basal coefficient K cb , describing the difference between actual and reference crop surface.
Several researches have related K cb to the dynamics of vegetation (Er-Raki et al., 2007;González-Dugo and Mateos, 2008;Sánchez et al., 2012), the general expression defined by Duchemin et al. (2006) is where τ is the extinction coefficient, chosen as 0.6 (Kemp et al., 1997).Although τ may slightly change in responses to the structural differences in crop development (Allen et al., 1998;Tahiri et al., 2006), it is convenient here to consider τ as a constant (Allen et al., 1998;Shuttleworth and Wallace, 1985;Zhou et al., 2006).K cb, max is the basal crop coefficient at effective full ground cover.Instead of the evaporation coefficient used in FAO dual K c − ET 0 , we adopted a simple evaporation parameterization similar to (Feddes et al., 1974;Kemp et al., 1997;Wu et al., 1999), in which the potential soil evaporation is given by Ritchie ( 1972) where λ (MJ kg −1 ) is the latent heat of vaporization.Actual soil evaporation can be achieved using a simple relationship proposed by Linacre (1973) and verified by Kemp Introduction

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Full where θ 1 and θ 1,Fc are the actual volumetric water content and water content at field capacity of the top soil layer; h 1 (cm) is the water matric potential of top soil layer; k and m are the parameters primarily dependent on soil depth and soil texture, varying from 0.8 to 1 and 2 to 2.3, respectively, for a soil depth of 10 to 20 cm; θ 1+2 and θ 1+2,Fc are the actual volumetric water content and water content at field capacity of the top 1st and 2nd soil layers.
The other scheme is one-step calculation of actual soil evaporation and potential transpiration by incorporating canopy minimum surface resistance and actual soil resistance into Penman-Monteith model.LAI is implicitly used to partition available energy into canopy and soil.We call it the ET dir scheme.Compared to an alternative approach proposed by Shuttleworth and Wallace (1985), the interactive effect between canopy and soil was assumed negligible in the ET dir scheme.This simplicity sounded reasonable, as indicated by Kemp et al. (1997) that no significant difference in simulating transpiration and soil evaporation was found for both schemes.
where R c n and R s n (MJ m −2 day −1 ) are the net radiation at the canopy surface and soil surface, respectively; ρ a (kg m −3 ) is the air density; c p (J kg Full The net radiation reaching to the soil surface can be calculated using the Beer's law relationship of the form and the net radiation intercepted by the canopy surface is the residual part of total net radiation The minimum canopy surface resistance r cmin is given by where r lmin is the minimum leaf stomatal resistance; LAI eff is the effective leaf area index, which considers that generally the upper and sunlit leaves in the canopy actively contribute to the heat and vapor transfer.The soil surface resistance can be estimated using an exponential form proposed by Van De Griend and Owe (1994), where r sl (10 s m −1 ) is the resistance to molecular diffusion of water surface; a (0.3565) is the fitted parameter; θ 1 is the topsoil water content; θ min is minimum water content above which soil is able to deliver vapor at a potential rate.Introduction

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Soil properties parameters
The Van Genuchten's analytical model (Van Genuchten, 1980) was used to simulate the soil moisture retention curve, which described the relationship between soil water potential and water content.Soil samples of top 20 cm were taken to obtain the parameters of the moisture retention curve.Soil saturated hydraulic conductivity could be determined by laboratory method, which was 10.50 cm day −1 .This value is lower than the recommended value for silt clay loam (13.60 cm day −1 ) by Saxton et al. (1986), but within the range of 10.30 to 14.30 cm day −1 , given by Wang et al. (2008) for the local soil.The soil hydraulic and thermal properties are given in Table 2.

Crop growth parameters
Leaf area index (LAI) was determined using measured leaf area.To simulate the seasonal dynamics of LAI, a linear interpretation was used between dates from the emergence to the first measurement and a simple quadratic function gave a good fitting for the measurements of LAI (R 2 = 0.96) (Fig. 2a).Effective leaf area index (LAI eff ), used in the ET dir scheme, was equal to actual LAI when LAI was lower than 2 m 2 m −2 , and was assigned to half of the actual LAI for values higher than A piecewise linear function, defined in Feddes et al. (1978) and Feddes and Roats (2004), was used to describe the response of root to soil water potential α(h).The input water potential parameters were: (i) −15 cm for the water potential below which roots start to extract water, (ii) −30 cm for the water potential below which roots extract water at the maximum possible rate, (iii) higher limit −325 cm and lower limit −600 cm for the limiting water potential values below which roots can no longer extract water at the maximum rate (assuming a potential transpiration rate of 0.5 and 0.1 cm day −1 , respectively), (iv) −15 000 cm for the water potential below which root water uptake ceases.

Numerical simulations and experiments
The extended STEMMUS model was run using either the ET ind scheme or the ET dir scheme.Coupled water flow and heat transport equations were numerically solved using the Galerkin's finite element method for the spatial discretization and a fully implicit, backward difference approach for the temporal discretization.Plant root water uptake and soil water flow are fully coupled and equations are solved simultaneously at the same time step.The soil profile considered in this study was set to 3 m, as deep as the lysimeter, which was divided into 38 nodes with a finer discretization at upper soil layers (1 cm) than the lower soil layers (20 cm).Large lysimeter measurements, including

Water balance closure
The water balance closure was implemented by comparing soil water storage using two different methods.The direct method was based on the summation of soil water content over the root-zone where V t is the soil water storage in the root zone at the specific time t; ∆x i is the thickness of i th soil layer; θ i and θ i +1 are model simulations of water content at the upper and lower surface of the i th soil layer, at the specific time t; rz represents the summation over the root zone.
Soil water storage could be also derived by the inversion of water balance equation within the root-zone where V 0 is the soil water storage in the root zone at initial time, calculated by the integration of initial soil moisture over the root zone; T a is the actual crop transpiration, derived from the integration of root water uptake over the root zone; q 0 and q N are simulated water flux at the surface and bottom of the root zone.

Crop growth scenarios
To (Z r /Z r_ref ) to show the impact of changed biological factors.These three growth parameters were set to a 20 % increase or decrease based on their reference values.The influence of a 20 % increase and decrease of LAI, Z rmax and R gr was shown in Fig. 2. The influence of 20 % increase of LAI on relative LAI eff could be divided into three stages: (i) constantly 1.2 times larger stage, (ii) constantly equal stage, (iii) transition stage (Fig. 2b).The influence of 20 % decrease of LAI showed a similar three-stage trend.However, the 20 % decreased LAI (Fig. 2b, dash grey line) made the relative values of LAI eff entered stage ii, i.e. constantly equal stage, later at the leaf growing stage while earlier at the leaf senescent stage than the 20 % increased LAI (Fig. 2b, solid grey line).Compared to the reference root depth dynamics, for the 20 % increased Z rmax scenario, the relative values of root depth (Z r /Z r_ref ) increased gradually until reached its maximum value at the late growing season.While for the 20 % increased R gr scenario, the Z r /Z r_ref had a rapid increase up to the maximum value and then dropped down during the late growing season.On the contrary, the influence of a 20 % decrease of Z rmax and R gr showed opposite trends to the 20 % increase on the relative root depth dynamics.The influence of 20 % decreased R gr showed a lag effect on the Z r /Z r_ref compared to the 20 % increase of R gr (Fig. 2d).Thus, the values of Z r /Z r_ref for the 20 % decreased R gr scenario were smaller at earlier growing season (before around DOY 196) while larger at late growing season (after around DOY 196) than the 20 % increased R gr scenario.

Performance matrixes
To assess the model performance, several performance matrixes were used as in previous studies (Wei et al., 2015;Zhao et al., 2013).The determination coefficient R 2 , achieved by performing a linear regression between observed and model simulated values; the root mean square error (RMSE), characterizing the variance of the model errors; as well as the index of agreement (d index) (Willmott, 1981;Willmott et al., 1985) could be computed as follows: Introduction

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Full where n is the number of observations, P i and O i are pairs of observed and model predicted values for a specific variable (soil water content, ET, etc.), P and O are the overall mean of observed and model predicted values.A good agreement between observed and model predicted values is characterized as a high value for the determination coefficient, d index and a low value for RMSE.

Soil water content
Simulated soil water content, with two ET schemes, were compared with observations at the depth of 20, 40, 60, 80 and 100 cm (Fig. 3).The soil water content at the 20 cm with the ET ind scheme was in good agreement with the observation.Though a slight underestimation at the initial stage, the effects of incoming water flux (precipitation and Introduction

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Full irrigation) on soil water dynamics were well represented, as evidenced with d index of 0.81 and RMSE of 0.017 cm 3 cm −3 .For the deeper soil layers, however, sensorobserved fluctuations of soil water content were much smaller when compared to simulated values, thus induced large discrepancies.The values for d index ranged from 0.26 to 0.66 and RMSE ranged from 0.019 to 0.025 cm 3 cm −3 for the soil depth from 40 to 100 cm.Soil water content simulated with the ET dir scheme had similar results as with the ET ind scheme (Fig. 3).However, owning to more underestimation, the model with ET dir scheme performed a little worse than with the ET ind scheme.The d index values ranged from 0.20 to 0.73 and RMSE ranged from 0.020 to 0.036 cm 3 cm −3 for the soil depth from 20 to 100 cm.
Using both ET schemes, the extended STEMMUS model underestimated soil water content at early the growing season.From the point of water balance, this underestimation may be explained by more soil water consumption mainly due to topsoil evaporation, indicating that both ET schemes overestimated soil evaporation at early the growing season.The other possible reason was that the irrigation applied during this period was too small to be uniformly distributed and thus single-point soil moisture observation lost its ability to represent the heterogeneous soil moisture variations.Such underestimation disappeared when large amount of water was applied at later the growing season (Fig. 3, 20 cm).
The discrepancies increased with soil depth for both ET schemes.The reason lay here may be two-fold.On one hand, the soil moisture observations were doubtable, as no significant fluctuation with irrigation occurred at deeper soil layers, which was also inconsistent with the results for the same experiment site (Kang et al., 2001).The doubtable observations may be linked to the installing position of the soil moisture sensors (either equipped at positions dominated by preferential flow or adjacent to the macropores).On the other hand, the assumption of homogeneous soil texture was inappropriate as discussed by previous studies (Zeng et al., 2011a).Soil hydraulic Introduction

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Full parameters controlled the liquid water flux partition through soil layers, larger infiltration rate could result in greater fluctuation of soil water content at deeper soil layers.

Root zone water balance
According to Eqs. ( 20) and ( 21), simulated soil water storage based on the integration of soil water content and the inversion of water balance equation over the root-zone with two ET scheme were compared in Fig. 4. Soil water storage calculated with both schemes agreed well for the ET ind scheme.The value of RMSE was 5.88 mm and the d index value was 0.98.Similarly, a good agreement was found when using the ET dir scheme with values of RMSE and d index equaled to 5.13 mm and 0.99.Overall, the results based on the performance matrixes and the visual comparison of soil water storage dynamics revealed that the numerical solution using both the ET ind and ET dir scheme effectively reproduced the closure of water balance even under dramatically changed surface boundary flux conditions.Simulated results using two ET schemes showed similar trends of soil water storage throughout the growing season (Fig. 4).As expected, the largest increases occurred after large irrigations.Using the ET dir scheme tended to result in lower soil water storage than the ET ind scheme.The differences between two ET schemes were generally increasing while soil drying.

Soil temperature
Figure 5 presented the dynamics of sensor-observed and the simulated soil temperature with two ET schemes at various soil depths.Compared to the observation, the simulation with both ET schemes started with a good agreement and followed with a slight overestimation after the first main irrigation.Irrigation events had a significant impact on the soil temperature simulation due to the uncertainties of soil surface temperature.Nevertheless, the seasonal variations of soil temperature could be satisfacto- 20 to 100 cm, ranged from 0.76 to 0.95 with the ET ind scheme and 0.78 to 0.95 with the ET dir scheme.The values of RMSE ranged from 1.19 to 1.71 • C with the ET ind scheme and 1.14 to 1.61 • C with the ET dir scheme for the soil depth from 20 to 100 cm.

Estimation of ET
Combined with simulation results of soil water content, accurate ET estimates could help with the visualization of soil water balance, reduce deep percolation, improve irrigation efficiency and ultimately optimize water resources management.Therefore, the capability of the extended STEMMUS model with different ET schemes in reproducing the dynamics of ET is of great importance and requires fully evaluation with observed ET data.

ET at hourly time scale
The performance of both ET schemes to estimate the diurnal pattern of ET throughout the growing season was shown in Fig. 6a-c and Table 3.The hourly ET rates simulated using the ET ind scheme generally agreed well with lysimeter-observed ones (Fig. 6a).The comparison at hourly time scale in Fig. 6a indicated that the ET ind scheme tended to underestimate ET after main irrigation events.The largest underestimation was found after the third main irrigation, occurring at the mid-season of the maize growth stage.The results summarized in Table 3 suggested that the greatest disagreement among the growth stages was found at the initial stage with the values of d index and RMSE being 0.84 and 0.10 mm h −1 , compared to 0.94 and 0.11 mm h −1 , 0.93 and 0.11 mm h −1 , 0.90 and 0.07 mm h −1 during other development stages.
Compared to the ET ind scheme, the ET dir scheme performed better in simulating hourly revolution of ET over the entire maize growing season (Fig. 6b and Table 3).There was no significant underestimation after main irrigation events.The main disagreement for the ET dir scheme occurred at early the growing stage.The values for d index and RMSE were 0.90 and 0.10 mm h −1 , 0.96 and 0.09 mm h −1 , 0.98 and Introduction

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Full 0.08 mm h −1 , 0.93 and 0.06 mm h −1 for the initial, crop development, mid-season and late season growing stages, respectively.Furthermore, Fig. 6c presented a detail diurnal pattern of observed and simulated ET at mid-season stage, in which two ET schemes showed different behaviors after irrigation.Better performance was achieved using the ET dir scheme when compared to the ET ind scheme.For the ET ind scheme, significant underestimation was found at midday hours when the ET rates greater than 0.5 mm h −1 .This underestimation could be explained by the underestimated soil evaporation during this period (see Fig. 8), indicating that the parameterization of soil evaporation in the ET ind scheme was inappropriate during high water demand conditions.Considering the aerodynamic component, the ET dir scheme showed a reasonable representation of hourly ET rates.Nevertheless, the main diurnal patterns simulated using the ET ind scheme agreed with observed ET variations as well as the ET dir scheme except for the high water consumption periods.

ET at daily time scale
Compared to lysimeter observed daily ET rates, both ET schemes showed similar trends over the entire growing season (Fig. 7).Lacking of considering the blocking effects of stochastic clouds on the net radiation, large overestimation of ET rates for both schemes would occur on some cloudy days (Fig. 6,DOY 196,197,221 and 241).Daily ET rates simulated with the ET dir scheme had a more fluctuation than the ET ind scheme.Moreover, two ET schemes differed in the crop stage-specific behavior.There was an average underestimation for the ET ind scheme while a slight overestimation for the ET dir scheme at initial growing season.Daily ET rates at mid-season growth season tended to be underestimated by the ET ind scheme while successfully described by the ET dir scheme.Overall, daily ET rates simulated by the ET dir scheme performed better than the ET ind scheme as indicated by the d index and RMSE values being 0.96 and 0.74 mm day −1 for the ET dir scheme, while 0.89 and 1.06 mm day −1 for the ET ind scheme.

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Full Observed soil evaporation with micro-lysimeter was used to assess the performance of both ET schemes to simulate soil evaporation (Fig. 8).Statistical results indicated the ET dir scheme had a closer agreement than the ET ind scheme with values of RMSE and d index being 0.51 mm day −1 and 0.84, 0.73 mm day −1 and 0.64.Unfortunately, during periods between two supplemental irrigations at early the growing season (DOY 177-183), the soil evaporation measured by the micro-lysimeter was not available.Thus, it was difficult to make a conclusion on the model performance during this period.At late the growing season, using both ET schemes tended to underestimate daily evaporation rates after main irrigation events.Such underestimation may be caused by the use of micro-lysimeter.The observed soil evaporation may be higher than the actual soil evaporation, since the micro-lysimeter cut off the soil water loss due to the root water extraction in the evaporative soil layer.The similar behavior was reported for maize by Zhao et al. (2013) and Wei et al. (2015) at the same latitude sites.Compared to the ET dir scheme, using the ET ind scheme resulted in a much lower values of evaporation rates, especially after irrigations at the initial and mid-late growing season (see also Table 4).During these periods, the local irrigations intensified the vertial vapor gradient and the relative sparse vegetation cover highlighted the importance of aerodynamics component.Thus, larger underestimation and less fluctuation of soil evaporation with the ET ind scheme could be partially explained by the simplification of aerodynamic and surface resistance components in the calculation.

Cumulative ET
A comparison between cumulative ET of observed and simulated using the ET ind and ET dir scheme was shown in Fig. 9.The cumulative ET for lysimeter observed, ET ind and ET dir simulated are 334.18,369.37 and 354.89 mm, respectively.Both ET schemes overestimated seasonal ET when compared to lysimeter observations.Two periods, crop development and late season stage, were contributed to the overestimation when using the ET ind scheme.While for the ET dir scheme the primary overestimation appeared at initial and crop development stage, accounting for 70 % of the overestima-9998 Introduction

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Full  4).The deviation of total ET to the observed value for the ET dir scheme was greater than the ET ind scheme, 35.18 and 20.71 mm, respectively.This nearly 15 mm difference was mainly attributed to a larger amount of evaporation for the ET dir scheme during the initial growth stage (Table 4), which consequently resulted in more severe soil water depletion (Fig. 3, 20 cm).

Characteristics of ET partitioning
Crop stage-specific soil evaporation (E ), plant transpiration (T ), evapotranspiration (ET) and evaporation fraction (E/ET, EF) were presented in Table 4. Similar to previous studies (Kang et al., 2003;Zhao et al., 2013), the proportion of evaporation (e.g. the evaporation fraction) was largest at the initial stage, then decreased over crop development and reached its smallest value at mid-season stage, whereas a significant rebound was found during the late season.The dynamic role of evaporation was mainly attributed to the crop vegetation development (Hu et al., 2009;Liu et al., 2002).The evaporation fraction of four development stages ranged from 24.38 to 86.58 % for the ET dir scheme and 10.31 to 81.01 % for the ET ind scheme, similar to previously published results (Paredes et al., 2015;Wei et al., 2015;Zhao et al., 2013).Some differences were found in simulating individual components of crop ET when using two different ET schemes.The ET dir scheme showed a larger evaporation and smaller transpiration than the ET ind scheme throughout the growing season, resulting in an overall greater evaporation fraction.
The overall evaporation fraction for both ET schemes was 24.05 and 36.44 %, lower than the range from 43.57 to 52.52 %, a 4 year field observations in the same region but with significantly higher frequency of wetting events (Wang et al., 2007), close to observations of 30.3 % (Liu et al., 2002) and 33 % (Kang et al., 2003) and within the range of 20 to 40 %, reviewed by Kool et al. (2014) for most of row crops.Introduction

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Crop growth scenarios
To investigate the uncertainty of crop growth parameters, different crop growth scenarios introduced in Sect.2.5.2 were adopted to run the STEMMUS with both ET schemes (Fig. 10).The reference scenario (REF) was compared to changed LAI, Z rmax and R gr scenarios.The relative values (e.g.T/T ref and EF/EF ref ) were used here to facilitate comparisons between parameters and scenarios.
Under the changed LAI scenario, the dynamics of seasonal relative values of transpiration (T/T ref ) was a tradeoff between increasing LAI and decreasing soil water availability while other factors maintained unchanged throughout the growing season.It was showed in Fig. 10a that, for the ET ind scheme, the sensitivity of transpiration to LAI decreased until its value approached to 2 m 2 m −2 , leveled off as both factors were equally important and finally elevated as soil water availability was decreasing.For the ET ind scheme, more sensitive to LAI was presented at early the growing season, which was consistent with previous studies.In Fig. 10 g, the dynamics of the relative values of evaporation fraction (EF/EF ref ) showed a similar trend with the seasonal variation of LAI (Fig. 2a), indicating that small differences in soil water availability appeared to have a negligible effect on the relative evaporation fraction (EF/EF ref ) over the entire growing season.The LAI dynamics could explain much of the seasonal variation of the relative EF.It was worth to be noted that there was an asymmetry variation of relative EF for the same LAI disturbance, indicating that EF was nonlinearly dependent on LAI disturbance (Fig. 10g).
For the ET dir scheme, more complicated behavior of the relative transpiration than the ET ind scheme was showed (Fig. 10d).Compared to the ET ind scheme, similar trend of the sensitivity of relative transpiration to LAI was found when LAI dominated at the early growing season.More fluctuation was showed at the middle season.A suppression effect appeared at the end of growing season (i.e.Increasing LAI resulted in lower transpiration than the reference scenario).This behavior could be explained by the different selection of LAI in estimating transpiration between two ET schemes (LAI

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Full for ET ind scheme, LAI eff for ET dir scheme) (Fig. 2a).Compared to the ET ind scheme, the response of relative EF to LAI showed similar trends at early the growing season with a less sensitivity for the ET dir scheme.Differences were found at late the growing season with a negligible effect of LAI on relative EF when the maize got senescent (Fig. 10j).
Under the changed maximum rooting depth and root growth rate scenarios, the interactive effects of root depth dynamics and soil water availability on transpiration and evaporation fraction were explored.Seasonal transpiration ratio was an increasing function of soil water depletion until reaching its threshold in both scenarios.The effects of changed maximum rooting depth on relative transpiration and evaporation fraction were elevated as the soil was drying.Larger sensitivity was found at late the growing stage.On the contrary, the influence of soil drying on the sensitivity of transpiration and evaporation fraction to root growth rate was decreasing until no significant effects was found when the root reached its maximum depth.The most influenced period occurred at the early growing season.This behavior can be explained by the difference of root depth dynamics in both scenarios.As shown in Fig. 2b and c, the effects of changing maximum rooting depth is increasing until reach its maximum value at late the growing season while the effects of changing root growth rate primarily dominates at the early growing season.Furthermore, there was an asymmetric variation of relative transpiration and evaporation fraction for the same disturbance of root growth rate, larger variation for conditions of decreasing root growth rate by 20 % while less variation for the increasing conditions (especially at DOY 225, in Fig. 10c, f, i, and l).Such asymmetric variation can be explained by the lag effect described in Sect.2.5.2.Two ET schemes differed in their variations of sensitivity to root growth parameters, with a higher sensitivity for the ET dir scheme with the same parameter disturbance.This is probably due to the ET dir scheme is more sensitive to soil water depletion than the ET ind scheme (Fig. 3), with the consideration of aerodynamic and surface resistances.
Based on the crop growth scenarios results, some suggestions could be presented to reduce the proportion of soil evaporation in total evapotranspiration.Under the same irrigation and atmospheric forcing conditions, we can increase the leaf area index by properly increasing the planting density (Fig. 10g and j).Unlike the LAI, the sensitivity of transpiration to root growth parameters depended more on the soil water depletion, which indicated that the effects of dynamic root growth parameters should not be dismissed in arid environment.In fact, a variety of maximum rooting depth values were reported for maize previously (Canadell et al., 1996;Hsiao et al., 2009;Liu et al., 1998), due to different genotypes and rhizosphere environment.Under conditions of soil drying, plants tend to increase root depth to maintain a certain of water extraction (Hund et al., 2009;Verma et al., 2014), which was also evidenced with Fig. 10b, c, e and f.

Summary and conclusion
With the in situ data collected in a large lysimeter experiment, we used the extended STEMMUS model in a semi-arid environment to investigate how the coupling transfer of water, vapor and heat in the soil can affect the soil water dynamics in a crop field, with different evapotranspiration schemes (ET ind and ET dir ).The simulated soil water content using the ET ind scheme had a closer agreement than those simulated with the ET dir scheme when compared with measured values at the 20 cm soil depth.However, disagreements increased for deeper soil layers, either the inaccuracy of soil moisture observations or the heterogeneity of soil hydraulic parameters was responsible for the discrepancies and required further investigation.Simulation of soil temperature was relatively good for both ET schemes.
Evaluating the performance of the two ET schemes in estimating hourly, daily and cumulative evapotranspiration showed that the ET dir scheme performed better except for the cumulative evapotranspiration, 15 mm more overestimation, than the ET ind scheme when compared to lysimeter observations.Caution should be taken in partitioning ET, because individual ET components (soil evaporation, transpiration) were not fully or accurately measured.This study suggests that the ET dir scheme gave better simulation of soil evaporation than the ET ind scheme, especially at the late growing season.Introduction

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Full It confirmed that the aerodynamic and surface resistance terms were necessary for evaporation estimation.The crop growth scenarios results revealed the interactive effects of LAI, maximum rooting depth and root growth rate with soil water availability on relative transpiration and evaporation fraction.When LAI is smaller than 2 m 2 m −2 , LAI played an important role in controlling transpiration.The effects of maximum rooting depth and root growth rate only functioned at drying period, the former was more important at late the growing season while the latter dominated at the early growing season.As the disturbance of crop growth parameters has a significant effect on the simulation results, further consideration of the dynamics of crop growth parameters with changing environment is needed.Introduction

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Full   Van Genuchten, 1980) and thermal (De Vries, 1963) properties including saturated (θ s ) and residual (θ r ) water content; curve-fitting parameters (α and n); saturated hydraulic conductivity (K s ); specific heat capacities of the water (C w ), air (C a ), quartz (C q ), clay (C c ) and organic matter (C o ).
Soil sample Hydraulic properties Thermal properties Full  Full  Full The gray dotted and solid lines are water storage calculated as the integration of soil water content and the inversion of water balance equation within the root-zone, using the ET ind scheme, i.e.V 1,ind , V 2,ind , respectively.The black dotted and solid lines are with the ET dir scheme.Introduction

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Full .Relative daily variations, under changed leaf area index (LAI), maximum rooting depth (Z rmax ) and root growth rate (R gr ), of crop transpiration (a-c, using ET ind scheme; d-f, using ET dir scheme) and evaporation fraction (E/ET, g-i, using ET ind scheme; j-l, using ET dir scheme) with measured precipitation and irrigation.• increase LAI, Z rmax and R gr by 20 %, • decrease LAI, Z rmax and R gr by 20 %.Note that scale for (g) differs from others.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ET 0 = 0.408(R n − G) + γ 900 T a +273 u 2 (e s − e a ) ∆ + γ(1 + 0.34u 2 Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | et al. (1997) for bare soil.Three successive stages are arbitrarily divided as: are the aerodynamic resistance for canopy surface and bared soil, respectively; r cmin (s m −1 ) is the minimum canopy surface resistance; r s (s m −1 ) is the soil surface resistance.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 2.4 Model parameters 4 and was assumed equal to 2 m 2 m −2 for the transition from 2 to 4 m 2 m −2 (Tahiri et al., 2006).Maximum rooting depth was set to 1.2 m according to Allen et al. (1998).A classical logistic growth function was used to estimate root growth dynamics throughout the growing season, in which the root growth rate was determined from the assumption that 50 % of the rooting depth would be reached after 50 % of the growing season had elapsed, as described in Šimůnek et al. (2008) (see Fig. 2b for the root growth dynamics).The normalized water uptake distribution b(x), which described the verti-Discussion Paper | Discussion Paper | Discussion Paper | cal variation of the potential extraction term, S p , over the root zone was determined following Šimůnek et al. (2008).
soil moisture, soil temperature, ET and soil evaporation were used to assess the model performance.The validation of the soil water balance closure within the root zone gave an additional test of the effectiveness of the extended STEMMUS.In addition, since uncertainty may exist in the estimation of crop growth parameters, sensitivity test was implemented to explore how the simulation results vary with fluctuate precipitation and irrigation under different crop growth scenarios.Figures Back Close Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | investigate how biological factors control shallow soil water dynamics, three additional crop growth scenarios were used: (i) changed leaf area index (LAI), (ii) changed maximum rooting depth (Z rmax ) and (iii) changed root growth rate (R gr ) scenarios.The reference scenario (REF) was compared with changed LAI (LAI/LAI _ref ), Z rmax and R gr Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | rily achieved with both ET schemes.The overall d index values, for the soil depth from Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | tion (Table Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 5 .Figure 6 .Figure 8 .Figure 9 .
Figure 5.Comparison of observed and simulated soil temperature, at selected depths: 20, 40, 60, 80 and 100 cm, with measured precipitation and irrigation.The black dots represent the observation, the solid black line is the simulation with the ET ind scheme, and the solid gray line is the simulations with the ET dir scheme.
is the specific L. Yu et al.

Table 3 .
Summary statistics of correlation between observed and simulated hourly ET for each crop development stage, when using the ET dir scheme and ET ind scheme separately.

Table 4 .
Evaporation (E ), transpiration (T ), evapotranspiration (ET) and evaporation fraction (E/ET, EF) for each development stage of maize, when using the ET dir scheme and ET ind scheme separately.The actual evapotranspiration (ETc) was shown as well.