Effects of canopy resistance parameterization on evapotranspiration partitioning and soil water contents in a maize field under a semiarid climate

Abstract

Different canopy resistance (r_c) parameterization has been used in land surface models to simulate actual evapotranspiration (ET_c) and soil hydraulic variable for crop fields. However, the influence of r_c parameterization on evapotranspiration (ET) partitioning and soil water dynamics has not been fully investigated with consideration of the coupled soil water and vapor physics. This study investigated the influential mechanisms of five r_c methods (viz., Jarvis, Katerji-Perrier, Massman, Kelliher-Leuning, and Farias) on ET partitioning and soil water contents in an irrigated maize field under a semiarid climate through a soil water and vapor transfer model. The Jarvis method presented the best ET results (R² = 0.86 and RMSE = 0.71 mm·d^–1). Different r_c parameterization mainly altered the simulated amount of soil water contents, while not changed the response of soil water dynamics to irrigation events. By the integrated analysis of the ET partitioning and root-zone water budget, different r_c methods varied in the choice of the optimum irrigation water use strategies. This study identified the direct and indirect impacts of r_c on the ET partitioning and emphasizes the necessity of both the ET partitioning and water supply sources in the decision-making for irrigation water management in semiarid regions.

Graphical abstract

Keywords

Field experiment / STEMMUS-ET model / root-zone water budget / Northwest China

1 Introduction

Soil water contents and crop evapotranspiration (ET), especially its partition into soil evaporation (E) and plant transpiration (T_r), are the key variables for the appropriate and efficient irrigation water management. Increasingly, the canopy resistance (r_c) has been reported as a crucial biophysical factor in explaining the variation of ET and ET partitioning^[1–^5]. Understanding the role of r_c in mediating the ET dynamics and soil water contents will be helpful for the agricultural irrigation water practice in semiarid regions.

ET estimation methods have been extensively studied for different ecosystems and climate^[6–^10]. Of which the Penman-Monteith (PM) model is widely used and has been verified applicable in various regions with different climate and vegetation cover^[11–^13]. Implementing the r_c and soil surface resistance, PM is extended to the two-component ET model and thus practical to partition ET into the physical component E and biophysical component T_r. ET partition was reported to be affected by soil factors (e.g., soil moisture^[14,^15]), plant factors (e.g., leaf area index (LAI), plant height^[3,^16]), and meteorological conditions (e.g., radiation, vapor pressure deficit^[17,^18]). The extent to which these factors control ET partitioning was found site-specific^[3,^19].

To better mimic the dynamics of r_c, researchers have contributed much efforts in portraying the r_c. Such work includes: (1) elaborating the influencing factors and their relative importance^[20–^25], (2) building up the empirical or mechanistic models^[26–^28], (3) making modifications or optimizations to improve the model performance, and (4) conducting model assessment and error analysis^[29–^32]. Various models have been developed, including the empirical models^[26,³⁰,^33], semi-empirical models^[31,³⁴,^35], optimum theory models^[27,^36], and mechanistic models^[37,^38]. Benefit from its simplicity and easy use, the empirical and semi-empirical models are still commonly used by land surface models or soil water models^[39–^41]. The model performance was found to vary with the temporal scale, growth stages, regions, and soil moisture conditions, which renders its necessity to conduct site-specific calibration and validation^[30,⁴²,^43]. In addition, most of the validation work only covers the bulk simulation of ET^[29,³⁰,^43], and lacks the further assessment of ET partitioning and soil water contents. This may hinder understanding of the role of r_c in affecting the efficient irrigation water management.

Soil water contents can be influenced by the water infiltration, surface soil E, root water extraction, soil water movement, and subsurface water percolation/recharge processes, of which soil water movement process is the central linkage among these processes. Soil water vapor transfer process, as it connects soil water and heat flow, has been recognized important in mimicking the dynamics of soil water movement, especially in arid or semiarid environments^[44,^45]. However, such process is seldom used in soil water models for the agricultural water resources management.

In this study, five different r_c parameterization (Jarvis, JA; Katerji-Perrier, KP; Farias, FA; Kelliher-Leuning, KL; Massman, MA) were used in the soil water model STEMMUS-ET^[45–^47], which can simulate the coupled liquid water, water vapor and heat flow in unsaturated soil, together with the root water uptake processes, to reproduce the dynamics of ET, soil E, T_r, and soil water content. Validated by the measurements collected in an irrigated summer maize field, the effect of various r_c parameterization on the ET partitioning and soil water contents were investigated. By integrating the analysis of root-zone water budget with ET partitioning, we also considered the role of r_c parameterization in decision-making for irrigation water management. The objectives of this study were: (1) to find the practical r_c parameterization for portraying ET, ET partitioning, and soil water dynamics over the maize field in semiarid regions; and (2) to investigate the influencing mechanisms of r_c parameterizations on ET partitioning, soil water dynamics, and the irrigation water management. Such results can help enrich understanding of the biophysical role of r_c in regulating ET partitioning and soil water dynamics and ultimately contribute to the improved irrigation water use for summer maize in the semiarid environment.

2 Materials and methods

2.1 Field experiment design

The field experiment was conducted at the Yangling Irrigation Experiment Station (34°17′ N, 108°04′ E, at an elevation of 521 m a.s.l.), at Northwest A&F University, Shaanxi Province of Northwest China. The experimental location is characterized as the semiarid to subhumid climate and drought-prone region. The mean annual air temperature is 12.9 °C, the mean annual precipitation is 630 mm, and the mean annual E is 1500 mm. The general soil type is silt clay loam with an average field capacity of 31.7 m³·m^–3 and bulk density of 1.35 g·cm^–3.

The field experiment was conducted in two large lysimeters under the mobile rainproof shelter (Fig.1). The dimensions of the lysimeter system are 3 m × 2.2 m × 3 m (length, width, and depth). The weight readings were automatically recorded at the hourly interval with a precision of 139 g (i.e., 0.021 mm of water) for the weighing system and 1 g for the drainage system. To control the precipitation, the mobile rainproof shelter was installed above the lysimeters. Summer maize (cv. Wuke 2, a local cultivar) was sown on 23 June 2013 at a plant population of 40 plants within an area of 6.6 m² and harvested on 2 October 2013. During the experimental periods, the irrigation was applied when the soil water content dropped below a preset threshold (i.e., 60% of the field capacity). The level of irrigation was set to replace crop water consumed since the previous irrigation, as measured by the lysimeter. Two supplementary irrigations were applied in the early growing season (27 June and 3 July) to ensure uniform growth of the summer maize (the specific irrigation time and amount was shown in Tab.1). Other agronomic practices were as use by local farmers.

2.2 Measurements and data collection

Meteorological data, including daily maximum and minimum air temperature, relative humidity, daily precipitation, sunshine duration and wind speed at 10 m above surface, were obtained from a standard weather station located inside the experimental site. Hourly values of air temperature, air humidity, and wind speed were generated from daily measurements using a trigonometric function^[48], which has been demonstrated feasible in this region^[45].

Soil moisture were measured and recorded at the hourly interval using the pre-calibrated sensors (ThetaProbe ML2x, Delta-T Devices Ltd., Cambridge, UK), which were installed at depths of 20, 40, 60, 80, 100, 200, 225, and 250 cm. Soil water content at the topsoil layers was measured using the gravimetric method weekly. Hourly crop ET was calculated from the lysimeter weighted readings, which were further summed to obtain the daily ET values during the growing season. E was measured daily using the microlysimeters, which were placed between two crop rows. The use of the microlysimeter in this study area follows the recommendations by Kang et al.^[49] and Wang et al.^[50].

Leaf area and plant height were measured every 7–10 days after sowing, based on the average of at least three plant samples. LAI was calculated by the sum of the leaf area dividing the area of the plot. Leaf stomatal conductance measurements were conducted a few days (on sunny days) after irrigation using portable photosynthesis equipment (LI-6400, Li-Cor, Lincoln, NE, USA). Values were recorded from three functional leaves during 10:00–14:00 local time, when the stomatal conductance of summer maize reached its peak and remained steady^[51]. The maximum rooting depth was about 1.2 m^[45,^52]. According the recommendations by Allen et al.^[53], the crop stages or phenology were determined as in Tab.1.

2.3 Soil water model

The STEMMUS-ET model^[45–^47] was used. The general structure of the used STEMMUS-ET model and the implementation of the different r_c parameterization in STEMMUS-ET are illustrated in Fig.2. In this study, irrigation (I) and actual E were the top boundary fluxes, and the deep drainage (q_bot) was the bottom boundary flux of the STEMMUS-ET. The two-component PM method (Eqs. (5) and (6)), incorporating the r_c (Eqs. (11)–(16)) and actual soil surface resistance (Eq. (10)), was used to calculate the crop potential transpiration (T_p) and actual soil E, respectively. The actual T_r was then estimated from the root-density-weighed T_p, considering the reduction coefficient α(h) related to root-zone water conditions.

2.3.1 STEMMUS-ET

The governing equation of the liquid and vapor flow in STEMMUS-ET can be expressed as:

(1)\frac{\mathrm{\partial }}{\mathrm{\partial }t} \left({\rho }_L{\theta }_L+{\rho }_V{\theta }_V\right)=- \frac{\mathrm{\partial }{q}_L}{\mathrm{\partial }z}-\frac{\mathrm{\partial }{q}_V}{\mathrm{\partial }z}-S

where, ρ_L and ρ_V (kg·m⁻³) are the density of liquid water and water vapor, respectively, θ_L and θ_V (m³·m⁻³) are the volumetric water content (liquid and vapor, respectively), z (m) is the vertical space coordinate; q_L and q_V (kg·m⁻²·s⁻¹) are the soil liquid water and water vapor fluxes (positive upwards), respectively, and S (s⁻¹) is the sink term for the root water extraction.

The root water uptake term can be described as^[54]:

(2)S\left(h\right)=\alpha \left(h\right)S_p

where, α(h) (dimensionless) is the reduction coefficient related to soil water potential.

(3)

where, h (m) is the soil matric potential (negative values), h₁, h₂, h₃, and h₄ are the critical thresholds of soil matric potential. When soil matric potential h is higher than h₁, soil water content is high and root experiences oxygen deficiency, and when h is lower than h₄ (wilting point), root water uptake is set equal to zero. Between h₂ and h₃, root water uptake is maximal. Between h₁ and h₂ and between h₃ and h₄, a linear function is assumed. The parameter, h_3, is dependent on the water demand of the atmosphere and expressed as a function of the potential transpiration (T_p).

S_p (s⁻¹) is the potential root water uptake rate:

(4)S_p= b\left(x\right)T_p

where, b(x) is the normalized root water uptake distribution, as described in Šimůnek et al.^[55], and T_p is the potential transpiration.

By incorporating actual soil resistance and r_c into the PM model, the actual soil E and T_p can be estimated simultaneously as:

(5)T_p= \frac{\mathrm{\Delta }{R}_n^c+{\rho }_a{c}_p{\displaystyle \frac{(e_s-e_a)}{r_a}}}{\lambda \left(\mathrm{\Delta }+\gamma \left(1+{\displaystyle \frac{r_c}{r_a}}\right)\right)}

(6)E=\frac{\mathrm{\Delta }(R_n^s-G)+{\rho }_a{c}_p{\displaystyle \frac{\left(e_s-e_a\right)}{r_a}}}{\lambda \left(\mathrm{\Delta }+\gamma \left(1+{\displaystyle \frac{r_s}{r_a}}\right)\right)}

where, Δ (kPa·°C^–1) is the slope of the vapor pressure curve, γ (kPa·°C^–1) is the psychrometric constant. R_n^c and R_n^s (MJ·m^–2·d^–1) are the net radiation reaching the canopy surface and soil surface, respectively, G (MJ·m^–2·d^–1) is the soil heat flux density (set as 0.1 and 0.5 R_n during the daytime and night time, respectively), R_n (MJ·m^–2·d^–1) is the net radiation, ρ_a (kg·m⁻³) is the air density, c_p (J·kg⁻¹·K⁻¹) is the specific heat capacity of air, \lambda (MJ·kg⁻¹) is the latent heat of vaporization, and e_a and e_s (kPa) are the actual and saturation vapor pressure, respectively. The difference between e_a and e_s is called VPD (vapor pressure deficit), r_a (s·m^–1) is the aerodynamic resistance, r_c (s·m^–1) is the canopy resistance, and r_s (s·m^–1) is the soil surface resistance.

Following Beer’s law, the net radiation reaching the soil surface R_n^s and intercepted by the canopy surface R_n^c is calculated as:

(7)R_n^s= R_n\mathrm{e} \mathrm{x}\mathrm{p}(- k_{Q}L AI)

(8)R_n^c= R_n(1-\mathrm{e} \mathrm{x}\mathrm{p}(- k_{Q}L AI\left)\right)

where, k_Q is the extinction coefficient, and LAI (m²·m^–2) is the leaf area index.

The aerodynamic resistance can be determined as:

(9)r_a= \frac{\mathrm{l}\mathrm{n}\left({\displaystyle \frac{z_m-d}{z_{om}}}\right)\mathrm{l}\mathrm{n}\left({\displaystyle \frac{z_h-d}{z_{oh}}}\right)}{{\mathrm{k}}^2{u}_z}

where, z_m and z_h (m) are the reference heights of the wind and humidity measurements, d (being 2/3 h_c) is the zero plane displacement, z_{om} (being 0.123 h_c) is the roughness length for the momentum transfer, z_{oh} (being 0.1 z_{om}) is the roughness length for the heat and vapor transfer, k is the Karman constant, u_z is the wind speed at the reference height, and h_c is the crop height.

The soil surface resistance was calculated following van de Griend and Owe^[56]:

r_s={\mathrm{r}}_{\mathrm{s}\mathrm{l}}{\theta }_{\mathrm{t}\mathrm{o}\mathrm{p}}>\theta {}_{\mathrm{m}\mathrm{i}\mathrm{n}},h_{\mathrm{t}\mathrm{o}\mathrm{p}}>-{10}^3\mathrm{m}

(10)r_s={\mathrm{r}}_{\mathrm{s}\mathrm{l}}{\mathrm{e}}^{a(\theta {}_{\mathrm{m}\mathrm{i}\mathrm{n}}-\theta {}_{\mathrm{t}\mathrm{o}\mathrm{p}})}{\theta }_{\mathrm{t}\mathrm{o}\mathrm{p}}\le {\theta }_{\mathrm{m}\mathrm{i}\mathrm{n}}, h_{\mathrm{t}\mathrm{o}\mathrm{p}}>-{10}^3\mathrm{m}

r_s=\mathrm{\infty }h{}_{\mathrm{t}\mathrm{o}\mathrm{p}}\le -{10}^3\mathrm{m}

where, {\mathrm{r}}_{\mathrm{s}\mathrm{l}} (10 s·m^–1) is the resistance to molecular diffusion of the water surface, a (0.357) is the fitted parameter, {\theta }_{\mathrm{t}\mathrm{o}\mathrm{p}} is the topsoil water content, \theta {}_{\mathrm{m}\mathrm{i}\mathrm{n}} is the minimum water content above which soil is able to deliver vapor at a potential rate, and h{}_{\mathrm{t}\mathrm{o}\mathrm{p}} is the soil water potential at the top soil layer.

2.3.2 Canopy resistance parameterization

2.3.2.1 Jarvis type canopy resistance method

Considering the minimum leaf stomatal resistance, solar radiation and LAI, the Jarvis type canopy resistance r_c,JA can be expressed as^[26,^57]:

(11)r_{c,\mathrm{J}\mathrm{A}} =\frac{r_{l,\mathrm{m}\mathrm{i}\mathrm{n}}\left(a_1\left(a_2{R}_s+1\right)\right)}{LAI{}_{\mathrm{e}\mathrm{f}\mathrm{f}}\left(a_2{R}_s+a_3\right)}

where, r_l,min (s·m^–1) is the minimum leaf stomatal resistance, can be measured under the optimal growth conditions, R_s is the downward shortwave radiation, and LAI_eff is the effective leaf area index, which represents the leaves in the canopy that actively contribute to the heat and vapor transfer. a₁, a₂, and a₃ are the model parameters, referred from ECMWF^[57].

2.3.2.2 Katerji-Perrier canopy resistance method

The Katerji-Perrier r_c method is described as^[58]:

(12)\frac{r_{c,\mathrm{K}\mathrm{P}}}{r_a}=b_1 \frac{r^{\ast }}{r_a}+ b_2

where, r_a (s·m^–1) is the aerodynamic resistance, which can be calculated as Eq. (9). b₁ and b₂ are the fitting parameters (as detailed in Table S1 (Supplementary materials)). r^* (s·m⁻¹) is the climatic resistance, can be expressed as:

(13)r^{\ast }=\frac{\mathrm{\Delta }+\gamma }{\mathrm{\Delta }\gamma }\times \frac{{\rho }_a{c}_{p}VPD}{\left(R_n-G\right)}

2.3.2.3 Massman canopy resistance method

Massman^[59] developed the r_c model as a function of photon flux density, vapor pressure deficit, and the maximum canopy conductance, i.e., the reciprocal of the minimum r_c, as:

(14)\frac{1}{r_{c,\mathrm{M}\mathrm{A}}}=g_{sm}\left(\frac{Q_p}{Q_p+c_1}\right) \left(\sqrt{\frac{c_2}{VPD}+c_3}\right)

where, g_sm (m·s^–1) is the maximum stomatal conductance, Q_p is the photosynthetically active radiation photon flux density, VPD is the vapor pressure deficit, and c₁, c₂, and c₃ are the model parameters (as detailed in Table S1).

2.3.2.4 Kelliher-Leuning canopy resistance method

The Kelliher-Leuning r_c method, considering the combined effect of plant leaf area, maximum stomatal conductance, and atmospheric radiation, vapor pressure deficit, was developed by Kelliher et al.^[60] and further modified by Leuning et al.^[28] as

(15)\frac{1}{r_{c,\mathrm{K}\mathrm{L}}}=\frac{g_{sm}}{k_Q}\mathrm{l}\mathrm{n}\left(\frac{Q_h+Q_{50}}{Q_h\mathrm{e}\mathrm{x}\mathrm{p}\left(-k_{Q}LAI\right)+Q_{50}}\right)\left(\frac{1}{1+VP{D}_a/VP{D}_{50}}\right)

where Q_h (taken as the half of incident solar radiation) is the visible radiation flux density at the top of the canopy, Q₅₀ and VPD₅₀ are the visible radiation flux density and vapor pressure deficit when the stomatal conductance is the half of the maximum value, VPD_a is the actual vapor pressure deficit. The parameters used were as detailed in Table S1.

2.3.2.5 Farias canopy resistance method

Ortega-Farias et al.^[61] proposed the r_c as the resistance to water transfer from the soil, via the plant, to the atmosphere, which is expressed as the function of climatic factors and available soil moisture.

(16)r_{c,\mathrm{F}\mathrm{A}} =r_{i}F {\left(\theta \right)}^{-1}=\frac{{\rho }_a{c}_{p}VPD}{\mathrm{\Delta }\left(R_n-G\right)}F{\left(\theta \right)}^{-1}

where r_i (s·m^–1) is the modified meteorological resistance, F(θ) is the normalized soil moisture, can be determined as

(17)F\left(\theta \right)=({\theta }_{rt} -{\theta }_w)/({\theta }_f-{\theta }_w)

where θ_rt (m³·m^–3) is the averaged volumetric soil water content in the root zone; θ_w and θ_f (m³·m^–3) are the volumetric water content at the wilting point and field capacity, respectively. Here F(θ) was set to 1, to avoid the duplicated consideration of soil water factors as with Eq. (3).

2.4 Model setup, calibration and validation

The STEMMUS-ET model was run with the fully coupled soil water, vapor, and heat flow. To accommodate the large lysimeter case, the soil profile was set as 3 m. It was further divided into 38 nodes with the relatively finer vertical discretization in the upper soil layers (0.25–5 cm at soil depth of 0–50 cm) than that in the lower soil layers (10–25 cm at soil depths of 60–300 cm).

The upper boundary was controlled by the soil E and irrigation water fluxes. The lower boundary was considered as the seepage face condition. The initial conditions for soil water and heat transport was determined by interpolating the measured soil moisture and temperature at the starting date.

Measurements in 2012 and 2013 were used to calibrate and validate the STEMMUS-ET model, respectively. The measurements and values from the relevant references were used as the initial values for the soil and plant parameters to run STEMMUS-ET^[45]. Soil hydraulic parameters, crop growth parameters, and root water uptake related parameters were further calibrated by the trial and error using the measured soil water contents at different soil depths (i.e., 20, 40, 60, 80, and 100 cm), soil E, and ET. The empirical parameters in the r_c models were optimized using the genetic algorithm with the measured ET values in 2012 as the objective value. The detailed procedure can be found in Chen et al.^[29]. The simulation results for 2012 were presented in the supplementary materials (Figs. S1–S2, Table S2). The calibrated soil and plant parameters used were as detailed in Table S1.

To assess the model performance, four commonly used performance metrics, i.e., the determination coefficient (R²), index of agreement (d), root mean square error (RMSE), and model bias (BIAS) were used:

(18)R^2= \frac{{\left[{\sum }_{i=1}^n\left(P_i-\overline{P}\right)\left(O_i-\overline{O}\right)\right]}^2}{{\sum }_{i=1}^n{\left(P_i-\overline{P}\right)}^2{\sum }_{i=1}^n{\left(O_i-\overline{O}\right)}^2}

(19)d=1-\frac{{\sum }_{i=1}^n{\left(P_i-O_i\right)}^2}{{\sum }_{i=1}^n{\left(\left|P_i-\overline{O}\right|+\left|O_i-\overline{O}\right|\right)}^2}

(20)RMSE= \sqrt{\frac{\sum _{i=1}^n{\left(P_i-O_i\right)}^2}{n}}

(21)BIAS= \frac{\sum _{i=1}^n\left(P_i-O_i\right)}{n}

where, O_i, P_i, are the measured and model simulated values, \overline{O} and \overline{P} are the mean values of the measurements and model simulations, and n is the number of data points.

3 Results

3.1 Soil water dynamics

Fig.3 shows the comparison of dynamics of soil water contents simulated using the STEMMUS-ET model with the tested five r_c methods versus corresponding observations at different soil depths. In response to large irrigation events, soil water content at 20 cm increased sharply, while such response was moderated and greatly reduced in magnitude at deeper soil layers. The soil water content at 20 cm was generally well simulated by models with different r_c methods. The statistical analysis indicated that the model using the JA, KP, and FA r_c methods performed better relative to the other methods with a d-index higher than 0.78 and RMSE lower than 0.0155 m³·m^–3 (Tab.2). KL method presented the worst simulations with the largest RMSE, and lowest d-index. In deeper soil layers (40–100 cm), however, the dynamics of soil water content with irrigation simulated by different models were more variable than the observed values. The possible reason is that the soil moisture sensors might be not in close contact with the soils at deep soil layers (e.g., adjacent to macropores), making it difficult for STEMMUS-ET model to accurately reproduce the measured soil moisture, since it did not take into account the effect of macropores on soil water and vapor transfer. The model performance was degraded with the increased soil depth, with the d-index values ranged from 0.0667 to 0.666, RMSE ranged from 0.0069 to 0.0288 m³·m^–3, and BIAS ranged from –0.0186 to 0.0099 m³·m^–3.

The difference in soil water content simulations among various r_c methods started from the second large irrigation event (2 August, in Fig.3) and gradually enlarged with time. Model using the KL method overestimated the soil water content significantly compared with models using other r_c methods. The range of difference is 0.0075–0.0306 m³·m^–3, which is comparable to the simulation errors (RMSE range from 0.0069 to 0.0288 m³·m^–3).

3.2 Evapotranspiration and evapotranspiration partitioning

3.2.1 Daily evapotranspiration

Daily ET measured from the lysimetric system was used to assess the performance of models with different r_c methods (Fig.4). In response to the irrigation, ET increased rapidly at the initial growth stage (peak value of 4.73 mm·d^–1, Fig.4), mainly due to the increased soil E. Such response was more significant in magnitude during the crop development and middle growth stages as the more efficient transpired water loss than the evaporated water loss following the irrigation events (peak value of 9.51 mm·d^–1). As the fraction of transpiration decreased at the late growing stage, the response of ET to irrigation events decreased gradually and was comparable to that of the initial stage (peak value of 5.09 mm·d^–1). Models with five r_c methods produced the different ET values (p < 0.05, Fig. S3), especially differed in the response of crop water consumption to the applied irrigation events. Except the underestimation of ET at the initial growth stage, JA and FA methods yielded an acceptable estimation against daily ET observations. KP method underestimated such response at the initial and crop development growth stages, while MA and KL methods yielded the underestimation at the initial, crop development, middle season and late season growth stages.

The PM model with five r_c methods presented an underestimation of crop ET during the initial stage, probably due to that the soil E was underestimated under low LAI (Fig.4). Other than that, JA method well simulated the dynamics of daily ET in response to the applied irrigation events, with the highest R² (Fig.4). FA method presented the slightly worse simulations with the R² of 0.83 and RMSE of 0.71 mm·d^–1. Statistical analysis indicated that the KP method had the weakest correlation against the daily ET observations with the R² lower than 0.75.

Previous studies have reported the applicability of JA methods in various regions with different ecosystems^[29,³⁰,⁴²,^62]. Li et al.^[30] reviewed various r_c parameterization and assessed their relative merits. The weak performance in ET simulations was reported for the JA method under low LAI, under which the role of soil resistance cannot be omitted. Li et al.^[30] developed the coupled surface resistance scheme, which takes into account the soil and plant components, and obtained an acceptable ET result. Similarly, Chen et al.^[29] found that the original single source PM model with the JA method cannot reproduce the observed ET while an acceptable performance was achieved with the SW model. By independently taking into account the effect of soil resistance, the two-component PM model with the JA method successfully simulated the daily ET dynamics in our study. This confirms the highlights by Chen et al.^[29] and Li et al.^[30] that the soil factors should be considered in r_c methods when the canopy is sparse.

For the KP method, an underestimation was found at the initial and crop development growth stages, and an overestimation was found at the middle season growth stages resulting in the large discrepancies, i.e., highest RMSE and lowest R² at the daily time scale. This could be due to that KP method only considers the meteorological factors and lack of the plant physiological constraints. In contrast, the MA method mostly underestimated the ET values, although with an acceptable correlation (R² = 0.78). The similar underestimation of ET was found with KL method. Nevertheless, KL method presents acceptable correlation and lowest RMSE (R² = 0.75 and RMSE = 0.35 mm·d^–1) indicating the potential advantages of taking into account the crop factors. For the FA method, the results were pleasing, particularly as this method requires no parameter calibration. This agrees with the results from Chen et al.^[29] that the FA method provided acceptable ET simulations, indicating its potential application for the estimation of maize ET in this region.

3.2.2 Soil evaporation

Fig.5 shows the performance of the models using the JA, KP, MA, KL, and FA r_c methods in mimicking the dynamics of soil E measured by the microlysimeters. Models with different r_c methods produced the similar soil E dynamics and captured the increase of E in response to the applied irrigation events. The cumulative errors rose rapidly mainly at the middle and late crop growth stages (Fig.5). These discrepancies can be explained by the representativeness bias of soil E measured by microlysimeters under conditions of the crop growth^[63,^64]. Since the microlysimeter does not take into account the soil water loss due to crop root water extraction, the observed soil E may have been higher than the actual soil E. The difference between models with different r_c methods (JA and KP, versus MA, versus KL and FA) started from 16 August (in Fig.5) and increased rapidly after the main irrigation events. The overall maximum cumulative difference was about 12.8 mm, i.e., 0.12 mm·d⁻¹, which is lower than the model estimation errors, with RMSE values ranged from 0.46 to 0.48 mm·d^–1.

3.2.3 Evapotranspiration partitioning

To further elaborate how the water is consumed during the growing season, Tab.3 presents the crop stage-specific ET, E, T_r, and evaporation fraction (EF being E/ET). Crop development and middle season stages are the two growth stages with higher water consumption rate than the initial and late season stages, with the daily average ET of 3.61 and 4.03 mm·d^–1 versus 2.68 and 1.74 mm·d^–1. All models presented the similar seasonal variation patterns, the water consumption started to increase from the initial growth stage, developed rapidly at the crop development stage, reached the maximum at the middle season stage and decreased at the late season stage.

At the initial growth stage, soil E was dominant. With the different crop transpiration estimates, EF ranged from 77.4% to 92.8% using models with five r_c methods. As the crop development, the fraction of soil E decreased and reached its minimum at the middle season stage with the range of 17.3% to 34.4%, which indicated that crop transpiration was the primary contribution to the crop water consumption. At the late season growth stage, the proportion of soil E increased a little bit, which was most likely due to the decrease of crop transpiration as the crop senesced.

The variation ranges of EF due to different r_c methods were maximum at the initial and late season growth stages as the change of crop transpiration is large, which indicated that the effect of r_c parameterization on EF was more significant at these two crop growth stages.

3.3 Root-zone water budget components

The effect of different r_c methods on the root-zone water budget components, including q_bot, ΔV, I, E, and T_r, is illustrated in Fig.6. Constraint by the structure of the lysimetric system, the surface runoff and lateral water flux can be neglected. Thus, the lysimetric system can be used to understand how the incoming water supply contributes to the crop water consumption. The applied irrigation water is the solely incoming water flux, which experiences the infiltration, soil E, soil water transport and redistribution, and root water uptake processes, then affects the bottom water flux. E and T_r are the two kind of water consumption. As the applied irrigation water amount was less than the crop water consumption, other water supply sources (ΔV and q_bot) also contributed.

All models indicated that ET was mostly consumed by crop transpiration, with the minimum fraction of 57.0% estimated by the KL method and the maximum fraction of 72.5% by the JA method. Compared to crop transpiration, soil E exhibited a compensatory contribution to ET. As for the three water supply sources (I, q_bot, and ΔV), the contribution of bottom water flux q_bot to ET is similarly simulated by five different models (small variation from 29.8% to 31.9%), which means that the steady contribution from the other two water supply sources (ΔV and I) to ET. The relative magnitude of the change of ΔV among five r_c methods is similar to that of crop transpiration, while contrary to that of incoming I. This implicitly indicated that the change of root-zone soil water storage is closely related to crop transpiration.

Given that the contribution of bottom water flux to ET was consistent among different r_c methods, their effect mainly functions in the root-zone soil layers and had minimum influence on the bottom soil layers in the experimental location. The effect of different r_c methods on root-zone water budget components is mainly twofold. First, it affects the way how the water is consumed. Models using different r_c methods presented various crop transpiration simulations, thus altered the ET partitioning strategies. Second, it alters the relative contribution of water supply sources. The greater the crop transpiration, the greater the depletion of root-zone ΔV and less utilization of I. This could be due to the fact that the recharge of the applied irrigation water cannot quickly replenish the root-zone soil water. Irrigation affects the water conditions primarily at topsoil layers while the root water uptake process is dominant at subsurface root-zone soil layers.

4 Discussion

4.1 Role of canopy resistance parameterization in modeling soil water dynamics

Soil water conditions are usually regarded as an important factor controlling r_c/conductance. It is reported that soil moisture can directly affect the r_c, but also can interact with other environmental factors and co-regulate the plant physiologic response, thus shaping the environmental controlling mechanisms of r_c^[23,^65]. Our results, conversely, investigated the effect of r_c parameterization on the model interpreting of soil water content dynamics. Results indicated that it exhibited the direct effects on the crop transpiration, then affected the root water uptake processes and altered root-zone soil water content. This is evidenced in Fig.3, with greater transpiration simulated by the JA and FA methods, and greater depletion of soil moisture from the root-zone soil layers. However, it can affect the surface soil water content, via the vertical soil water movement and water redistribution processes. Such influence is not that significant, as indicated by the small difference in the simulated soil E (Fig.5). Different r_c parameterization mainly altered the magnitude of soil water content, while not changing the response of soil water dynamics to irrigation events. This is consistent with the results from Yu et al.^[45] that the similar trend but different in the magnitude of soil water content were given by models using different ET methods.

4.2 Role of canopy resistance parameterization in modeling evapotranspiration partitioning

ET partitioning describes how the water is used via the abiotic and biotic pathways, which is important for the understanding of land surface-atmosphere interactions and efficient irrigation management. Previous studies have mostly focused on the controlling factors on ET and ET partitioning, and found that r_c, which is a function of LAI, solar radiation and soil water availability, give a better explanation^[1–^3]. In this study, we investigated the effect of r_c parameterization on the model-portrayed ET partitioning. Primarily, r_c parameterization affects the transpiration and thus the ET partitioning, especially at the initial and late season growth stages. However, it can affect soil water redistribution and surface soil water condition, which then slightly alters the soil E (as evident in Fig.5), resulting in the different EF values (Tab.3).

4.3 Implications for the irrigation water management

We coupled the analysis of root-zone water budget with ET partitioning to examine how r_c parameterization affects the decision-making about irrigation water management. Crop transpiration, which links to the photosynthesis processes and biomass/yield formation, is generally considered to be the effective use of water, while soil E is regarded as a wasteful loss of water^[66]. It is thus crucial to reduce the soil E and increase the crop transpiration, for water-saving actions in semiarid and arid environments. From the water supply perspective, improving irrigation water use efficiency and reducing ΔV are regarded as the best practices for the sustainable agriculture water conservation. Coupling the these, we proposed an integrated irrigation water use efficiency index, IUE, defined as (I/ΔV)/(E/ET) to synthetically assess the efficiency of water use in semiarid and arid regions. The higher values mean the more efficient the use of irrigation water and the smaller proportion of water loss as soil E, indicating the better irrigation water conservation management.

As shown in Fig.7, models with different r_c methods presented various values of IUE, with the KL method being the highest score and the KP method having the lowest value. If we accept the simulations provided by the KL method, all other methods would provide relatively conservative guidance on agriculture water management. This is different from the suggestions based only on ET partitioning results, where the JA method tended to give the best water use practice due to its highest crop transpiration consumption (Fig.6).

4.4 Limitations and outlook

The current work investigated the role of r_c parameterization in modeling the ET partitioning and soil water dynamics, and further elaborated the implications on the irrigation water management. Five r_c methods were incorporated into a detailed soil water and vapor coupled model. Several assumptions were adopted in our work. First, the used parameters in the r_c methods were assumed the same throughout the crop growth period. Such limitations in parameters, i.e., a single set of parameters for the whole growing season, resulted in the variation in performance in the ET estimates at different crop growth stages (Fig.4). Second, the model structure and parameters of soil surface resistance parameterization were assumed to inevitably introduce great and inscrutable uncertainties if soil and canopy surface resistance were estimated separately. Thus, in this study, we adopted the commonly used big-leaf hypothesis with the PM model to estimate the r_c. The measured ET was used in PM model to inversely derive the surface resistance, which was assumed to be the r_c (neglect the effect of soil E). Such an assumption appears questionable under the partial canopy stage (Fig.4). Nevertheless, it reliably reproduced the role of r_c under the full canopy stage (when ET is large and its temporal coverage was about 75% in this study). In the future work, the segmented r_c parameter calibration and detailed investigation of the relationship between the r_c and the mean surface resistance needs to be undertaken to improve the ET model performance and reduce the simulation uncertainties^[30,⁶⁷,^68].

5 Conclusions

The performance of five r_c parameterization was validated and its influence on the ET partitioning and soil water content were further elaborated over an irrigated maize field in a semiarid environment. Models with five r_c methods can reproduce the temporal dynamics of ET, soil E and soil water content, and their response to applied irrigation events, but differed in the magnitude. The JA method provided the most acceptable ET estimates on the basis of PM equation with the explicit consideration of the soil component. The FA method was found to have the potential to provide the reasonable ET estimates in this region. Two possible influencing mechanisms on ET partitioning were identified: (1) the direct effect of r_c parameterization on the transpiration estimations, root water uptake process and root-zone water content, and (2) the indirect effect through its influence on the water redistribution process, as it can alter surface soil water content then the soil E. The simulated ET partitioning and root-zone water budget analysis demonstrated that different r_c methods varied in the estimation of both the contribution of water supply sources and water consumption strategies. Various r_c methods differ in their choice of the optimum irrigation water use strategy, based on such simulations, that different from the outcome based solely on ET partitioning analysis. It is suggested that both the ET partitioning and water supply sources analysis should be considered when making decisions for water management in the irrigated agricultural regions in semiarid environments.

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