Estimation of Actual Evapotranspiration and Its Components at Hourly and Daily Scales Using Dual Crop Coefficient Method for Water-Saving Irrigated Rice Paddy Field

Abstract

Accurately partitioning actual evapotranspiration ET_{c act} into soil evaporation E_s and plant transpiration T_{c act} is crucial for improving water use efficiency and devising precise irrigation schedules. In water-saving irrigated rice fields, ET_{c act}, E_s and T_{c act} were estimated using a dual crop coefficient method based on three approaches: FAO56 adjusted, locally calibrated and leaf area index LAI-based coefficients. Continuous measurements of hourly and daily ET_{c act}, E_s and T_{c act} with weighing lysimeters were used to validate these coefficients. Results showed that hourly ET_{c act}, E_s and T_{c act} exhibited a distinct inverted “U” shape single-peak trend. Daily ET_{c act} and T_{c act}, along with the corresponding crop coefficients K_{c act} and basal crop coefficients K_{cb act}, initially increased and then decreased throughout the rice growth stages, while daily E_s and soil evaporation coefficient K_{e act} were high during the initial stage and gradually decreased as the development stage progressed. FAO56 adjusted coefficients consistently underestimated both hourly and daily ET_{c act}, E_s and T_{c act}. Locally calibrated basal crop coefficients K_{cb Cal} were determined as 0.28, 1.17 and 1.09 for the initial, mid-season and end-season stages, respectively, and locally calibrated turbulent transport coefficient of water vapor K_{cp Cal} (recommended as 1.2 by FAO) was determined to be 1.59. Based on these calibrated coefficients, estimates of hourly and daily evapotranspiration ET_{c Cal}, soil evaporation E_{s Cal} and plant transpiration T_{c Cal} performed poorly during the initial stage but showed improved accuracy during subsequent growth stages. Hourly and daily evapotranspiration and its components based on LAI-based coefficients exhibited similar performance in estimating measurements, albeit slightly inferior to FAO56 calibrated coefficients. Overall, both the FAO56 calibrated coefficients and LAI-based coefficients are recommended for estimating evapotranspiration and its components at daily and hourly scales. These research findings provide valuable insights for optimizing irrigation regimes and improving water use efficiency in rice cultivation.

1. Introduction

The process of evapotranspiration ET_{c act} is recognized as the primary contributor to water loss in terrestrial ecosystems [1,2]. Actual evapotranspiration ET_{c act} consists of two main components, soil evaporation E_s and plant transpiration T_{c act}. Transpiration T_{c act} is the movement of water from the soil through plant organs or tissues into the atmosphere, and is considered to be a plant physiological process [3], making T_{c act} strongly correlated with crop growth, biomass accumulation, and yield [4,5]. However, soil evaporation E_s is the physical process by which water vapor diffuses directly through the soil surface [6], and is typically considered to have no direct contribution to crop growth, and should be reduced by management practices (e.g., proper irrigation strategies and ground-mulching) [7]. The two separate processes of E_s and T_{c act} occur simultaneously; partitioning accurately ET_{c act} into E_s and T_{c act} is essential for understanding terrestrial hydrological cycles, developing precise irrigation schedules, and enhancing water use efficiency by minimizing soil evaporation and maximizing water productivity [4].

Evapotranspiration and its components can be derived from a range of measurement systems including lysimeters, eddy covariance, Bowen ratio, water balance (gravimetric, neutron meter, other soil water sensing), sap flow, scintillometry, and even satellite-based remote sensing [8,9,10,11,12]. However, all of these measurement techniques are sometimes expensive and require substantial experimental care; terse and efficient models are required to evaluate ET_{c act} and its components utilizing readily available meteorological variables. Most models estimate ET_{c act} from either a hydrological or micrometeorological perspective, with differences in their assumptions and requirements [13,14]. Among the ET_{c act} models, the Shuttleworth–Wallace and dual crop coefficient model are common approaches to predict E_{s act} and T_{c act} separately [15,16]. Shuttleworth–Wallace is a direct model for estimating ET_{c act} components and requires a set of coefficients, including soil and canopy surface resistances, and aerodynamic resistances. Obtaining these coefficients can pose challenges due to their complex nature and the specific requirements for each parameter [7,17,18]. In contrast, the FAO-56 dual crop coefficient approach has overcome these deficiencies since its crop coefficient has contained all differences between the reference surface and the physiologies, physics and morphologies of the crop in question [19]. In particular, the dual crop coefficient model has been a preferred approach due to practical simplicity for fewer input data and robustness for separately predicting E_s and T_{c act} [20,21], which has been widely adopted for estimating ET_{c act} in different crops and climatic regions [16,22].

In the dual crop coefficient approach, the crop coefficient K_c is split into soil evaporation coefficient K_e (describing E_s) and basal crop coefficient K_cb (describing T_{c act}), with a stress coefficient K_s used to adjust K_{cb act} where water and salinity stresses occur [23]. Determination of K_e and K_cb under local climatic conditions is fundamental for improving efficient irrigation management in various field crops [24]. The dual crop coefficient approach has been widely used in estimating total ET_{c act}, or partitioning total ET_c into E_s and T_c [25,26]. The need for estimating hourly ET_{c act}, E_s and T_{c act} has arisen due to more refined water management and irrigation scheduling [27]. K_c, K_e and K_cb are usually determined daily based on corresponding curves [28]; whether these daily values are appropriate for estimating hourly ET_{c act}, E_s and T_{c act} remains uncertain. These issues underscore the importance of evaluating the accuracy of the dual crop coefficient approach in estimating both hourly and daily ET_{c act}, E_s and T_{c act}. Such evaluations will contribute significantly to enhancing the understanding of the ET_{c act} process and providing guidance for potential improvements of ET_{c act} modeling. Furthermore, the leaf area index LAI is closely related to the K_cb [29], estimating K_cb based on LAI was first proposed in FAO56 [30], and subsequently has been revised and used widely [7,31]. However, whether LAI-based K_cb is appropriate for simultaneously estimating ET_{c act}, E_s and T_{c act} needs to be validated.

Rice ranks among the three major global food crops [32]. Several water-saving irrigation practices for rice cultivation have been developed to reduce water requirements for adaptation to the increasing incidence of water scarcity, agricultural droughts and multi-sectoral competition for water [33]. The alternating wet and dry conditions caused by water-saving irrigation techniques resulted in soil water stress [34], which has been documented on a dual crop coefficient method for estimating ET_{c act} [28]. Tabulated basal crop coefficients for flooded paddies were proved inappropriate for the diversity of rice water management [30]. Pereira et al. (2021) provided updated coefficients for various irrigation methods, and presented updated K_cb as 0.15, 1.15 and 0.85 for the initial, mid-season and end-season stages under standard conditions for intermittent irrigated paddies [25]. However, the estimation of E_s and T_{c act} has received limited attention in alternate drying and wetting irrigated rice paddies. It remains uncertain whether updated coefficients presented by Pereira et al. (2021) are appropriate for estimating ET_{c act}, E_s and T_{c act} [25]. Therefore, the current research aims to address this knowledge gap by pursuing the following objectives: (1) characterizing the daily and seasonal variations in ET_{c act}, E_s and T_{c act}, as well as the seasonal variations in daily K_{c act}, K_{e act}, K_{cb act} and (2) estimating daily K_{c act}, K_{e act}, K_{cb act} based on three approaches, namely FAO56 adjusted coefficients based on coefficients presented by Pereira et al. (2021), FAO56 locally calibrated coefficients, and LAI-based coefficients, and (3) estimating hourly and daily ET_{c act}, E_s and T_{c act} though a dual crop coefficient approach to verify the validity of the estimates of daily K_{c act}, K_{e act}, K_{cb act} [25]. These attempts will contribute to a better understanding to develop precise irrigation scheduling by minimizing soil evaporation and maximizing water productivity in rice cultivation.

2. Materials and Methods

2.1. Experimental Site and Measurements

2.1.1. Site and Experiment Description

This study was conducted in 2015–2016 at the Kunshan Irrigation and Drainage Experiment Station (31°15′50″ N; 120°57′43″ E) in the Taihu Lake Region of China. The region experiences a subtropical monsoon climate, characterized by an average temperature, mean relative humidity, seasonal precipitation of 24.6 °C, 79.2%, 476.1 mm in 2015, and 25.5 °C, 78.2%, 555.4 mm in 2016. The rice field in the study area extended approximately 200 m in all directions, and an automatic-weighed micro-lysimeters system, buried within the rice field, was installed in the northwest section of the experimental site to measure ET_{c act} and E_s. Rice seedlings (Japonica Rice NJ46) in both lysimeters and the rice field were transplanted at inter- and intra-row spacing of 0.23 and 0.16 m on 27 June 2015 and 2 July 2016, followed by respective growth periods of 120 days and 125 days. Throughout the growing seasons, a local water-saving irrigation technique was applied. Specifically, shallow water levels were kept during the re-greening stage or within 3–5 days after pesticide and fertilizer application. At other times, irrigation was irrigated just to saturate the soil without causing flooding. Lower soil moisture thresholds in the root zone for the irrigation method were 60–80% of saturated soil moisture content during different growth stages (

Table 1. Thresholds for local alternate drying and wetting irrigation methods during different stages of rice growth.

Stages	Re-Greening	Tillering			Jointing-Booting		Heading-Flowering	Milk Maturity	Yellow Maturity
		Early	Middle	Later	Early	Later
Upper thresholds *	25 mm	θs1	θs1	θs1	θs2	θs2	θs3	θs3	Drying
Lower thresholds	5 mm	0.7θs1	0.65θs1	0.6θs1	0.7θs2	0.75θs2	0.8θs3	0.7θs3
Monitored root zone depth (cm)	-	0–20	0–20	0–20	0–30	0–30	0–40	0–40	-

Note: * The threshold during the re-greening stage is the water depth. θ_s1, θ_s2 and θ_s3 are the average saturated soil volumetric moisture content for the 0–20, 0–30, and 0–40 cm soil layers. θ_s1, θ_s2 and θ_s3 are 52.0%, 50.1% and 47.9%.

). After heavy rain, excessive water was drained to maintain a field water depth within 5 cm. Fertilizers and pesticides were applied according to local farmer practices [35,36].

2.1.2. Meteorological Observation and Soil Water Conditions

Meteorological data, including net radiation, air temperature, relative humidity, atmospheric pressure, wind speed and precipitation, were recorded every 30 min by an automatic meteorological station (WS-STD1, DELTA-T, Cambridge, UK). The meteorological station was installed complying with the installation standards on an extensive surface of green grassland, which is frequently cut and has no water shortage. Soil moisture at 0.10 m, 0.20 m and 0.30 m depths, covering different root zone depths during the rice season (Table 1), were monitored every 30 min using CS616 soil moisture reflectometers (Campbell Scientific Inc., Logan, UT, USA). The meteorological data and soil moisture were recorded every half hour, the corresponding hourly and daily values were calculated by averaging two adjacent half-hour values and by averaging all half-hour values over a natural day, respectively. Additionally, soil moisture conditions were monitored daily at 8:00 a.m. during rice seasons for irrigation management. Specifically, water depths were measured using a vertical ruler (resolution, 0.5 mm) when paddies were flooded, and soil moisture was recorded using time domain reflectometry equipment (TDR, Soil moisture, Goleta, CA, USA) with 20 cm waveguides for non-flooded periods. The detailed observational results of meteorological observations and soil water conditions can be found in Lv et al. (2024) [37].

2.1.3. Measurement of Evapotranspiration and Its Components

Hourly evapotranspiration (ET_{c acth}) and hourly soil evaporation (E_{s h}) were measured using an automatic-weighed micro-lysimeters system, which was buried within and surrounded by the rice field. To ensure consistent environmental conditions, identical cultivation practices, including tillage, sowing date, planting density, rice varieties, irrigation frequency and amount, were applied to the micro-lysimeters and the surrounding rice field. The automatic-weighed micro-lysimeters system comprised two micro-lysimeters (50 cm diameter, each containing four rice plant hills) for evapotranspiration, two (30 cm diameter) for soil evaporation, and two (30 cm diameter) for load cell calibration. Each lysimeter was equipped with the necessary instrumentation to accurately control the same deep drainage and drainage with the surrounding rice field. Detailed descriptions of the configuration, location and measurement of the automatic-weighed micro-lysimeter system can be found in the study by Liu et al. (2018) [38]. Throughout the rice growing seasons, the irrigation, deep seepage, drainage and the weights of micro-lysimeters were recorded hourly for each micro-lysimeter, and the difference in these values between the two lysimeters for measuring ET_{c acth} and those for measuring E_{s h} were less than 3%. The ET_{c acth} and E_{s h} were calculated directly from the hourly water balance. The measured hourly rice transpiration T_{c acth} was determined by the difference between ET_{c acth} and E_{s h}.

$${ET}_{\mathrm{c} \mathrm{acth}} (E_{\mathrm{s} \mathrm{acth}})=I+P-{ W}_{\mathrm{s}}-{ W}_{\mathrm{d}}-∆M$$

(1)

T_{c acth} = ET_{c acth} − E_{s h}

(2)

where ET_{c acth} (mm h⁻¹), E_{s h} (mm h⁻¹) and T_{c acth} (mm h⁻¹) are, respectively, actual hourly evapotranspiration, soil evaporation and rice transpiration; I (mm h⁻¹) and P (mm h⁻¹) are, respectively, irrigation and precipitation; W_s (mm h⁻¹) and W_d (mm h⁻¹) are, respectively, deep seepage and drainage, which are drained though a 1 cm pipe and collected by a graduated cylinder to measure its volume, described in detail by Liu et al. (2018) [38]; ΔM (mm h⁻¹) is the hourly change in soil water storage, determined by converting kilograms into millimeters per hour based on $∆M = {\displaystyle \frac{W_{\mathrm{i}} - W_{\mathrm{i}-1}}{A_{\mathrm{ML}}}}$, where W_i (kg) and W_i−1 (kg) are, respectively, the weight of the micro-lysimeters for the current and previous hours, and A_ML (m²) is the area of the micro-lysimeter. The hourly W_s, W_d and ΔM from two micro-lysimeters, for measuring either evapotranspiration or soil evaporation, were a lower difference than 5%, and these hourly ET_{c acth}, E_{s h} and T_{c acth} were calculated by averaging two measurements.

The measured values of daily evapotranspiration ET_{c actd}, soil evaporation E_{s d} and rice transpiration T_{c actd} were determined by summing up the hourly measurements throughout a natural day.

$${ET}_{\mathrm{c} \mathrm{actd}}={\sum }_{i=1}^{24}{ET}_{\mathrm{c} \mathrm{acth}}$$

(3)

$$E_{\mathrm{s} \mathrm{actd}}={\sum }_{i=1}^{24}{E}_{\mathrm{s} \mathrm{acth}}$$

(4)

$$T_{\mathrm{c} \mathrm{actd}}={\sum }_{i=1}^{24}{T}_{\mathrm{c} \mathrm{acth}}$$

(5)

where ET_{c actd} (mm d⁻¹), E_{s d} (mm d⁻¹) and T_{c actd} (mm d⁻¹) are, respectively, actual daily evapotranspiration, soil evaporation and rice transpiration.

2.2. Dual Crop Coefficients, Soil Evaporation Coefficients and Basal Crop Coefficients Based on Field Approach

Under nonstandard field conditions where inadequate soil water restricts the crop’s ability to meet the evaporative potential of the atmosphere, the actual dual crop coefficients were split into the actual soil evaporation coefficient and actual basal crop coefficient. The actual basal crop coefficient was adjusted using a stress coefficient to account for the stress conditions compared to standard conditions [30]. It is assumed that the dual crop coefficient, soil evaporation coefficient, and basal crop coefficient remain constant throughout the day.

$$K_{\mathrm{c} \mathrm{act}}={\displaystyle \frac{{ET}_{\mathrm{c} \mathrm{actd}}}{{ET}_{0\mathrm{d}}}}$$

(6)

$$K_{\mathrm{e} \mathrm{act}}={\displaystyle \frac{E_{\mathrm{s} \mathrm{actd}}}{{ET}_{0\mathrm{d}}}}$$

(7)

$$K_{\mathrm{cb} \mathrm{act}}={\displaystyle \frac{T_{\mathrm{c} \mathrm{actd}}}{K_s{ET}_{0\mathrm{d}}}}$$

(8)

where K_{c act}, K_{e act} and K_{cb act} (dimensionless) are the actual dual crop coefficient, soil evaporation coefficient and basal crop coefficient; ET_0d (mm d⁻¹) is the reference daily crop evapotranspiration, and K_s (dimensionless) is the soil moisture deficit coefficient.

Reference crop evapotranspiration ET₀ at daily or hourly scales (ET_0d or ET_0h) can be calculated by the Penman–Monteith Equation.

$${ET}_{0 }={\displaystyle \frac{0.408∆(R_n-G)+\gamma \frac{C_n}{T+273}{U}_2(e_s-e_a)}{∆+\gamma (1+{ C}_d{U}_2)}}$$

(9)

where ∆ (kPa °C⁻¹) is the slope of the saturation vapor pressure-temperature curve, $∆ = 4098\left[0.6108\exp \left({\displaystyle \frac{17.27T_{\mathrm{a}}}{T_{\mathrm{a}} + 227.3}}\right)\right]/{\left(T_{\mathrm{a}} + 227.3\right)}^2$, with T_a (°C) being the average air temperature; R_n (MJ m⁻² d⁻¹ or MJ m⁻² h⁻¹) is the net radiation at the crop surface, with the unit conversion of W m⁻² = 0.0864 MJ m⁻² d⁻¹ = 0.0036 MJ m⁻² h⁻¹; G (MJ m⁻² d⁻¹ or MJ m⁻² h⁻¹) is the soil heat flux density at the soil surface, which is negligible at the daily scale, and calculated as G = 0.1R_n during daytime and G = 0.5R_n during nighttime at the hourly scale; γ (kPa °C⁻¹) is the psychometric constant, γ = 0.665 × 10⁻³ P, with P (kPa) being the atmospheric pressure, U₂ (m s⁻¹) is the wind speed at 2 m height, e_s (kPa) is the saturation vapor pressure, $e_{\mathrm{s}} = 0.6108\left[\exp \left({\displaystyle \frac{17.27T_{\max }}{T_{\max } + 227.3}}\right)+\exp \left({\displaystyle \frac{17.27T_{\min }}{T_{\min } + 227.3}}\right)\right]/2$ at the daily scale and $e_{\mathrm{s}} = 0.6108\exp \left({\displaystyle \frac{17.27T_{\mathrm{hr}}}{T_{\mathrm{hr}} + 227.3}}\right)$ at the hourly scale, with T_max (°C) and T_min (°C) being, respectively, the highest and lowest temperature within a day, and T_hr (°C) being the average temperature within an hour; e_a (kPa) is the saturation vapor pressure, $e_{\mathrm{a}} = 0.6108\left[\exp \left({\displaystyle \frac{17.27T_{\min }}{T_{\min } + 227.3}}\right){\displaystyle \frac{{RH}_{\max }}{100}} + 0.618\exp \left({\displaystyle \frac{17.27T_{\max }}{T_{\max } + 227.3}}\right){\displaystyle \frac{{RH}_{\min }}{100}}\right]/2$ at the daily scale and $e_{\mathrm{a}} = 0.6108\exp \left({\displaystyle \frac{17.27T_{\mathrm{hr}}}{T_{\mathrm{hr}} + 227.3}}\right){\displaystyle \frac{{RH}_{\mathrm{hr}}}{100}}$ at the hourly scale, with RH_max (%) and RH_min (%) being, respectively, the maximum and minimum relative humidity within a day, and RH_hr (%) being the average relative humidity within an hour; C_n is the numerator constant that changes with reference type and calculation time step, with values of 900 K mm s³ Mg⁻¹ d⁻¹ for daily scale and 37 K mm s³ Mg⁻¹ h⁻¹ for hourly scale; C_d is the denominator constant that changes with reference type and calculation time step, with values of 0.34 s m⁻¹ for daily scale, 0.24 s m⁻¹ during daytime and 0.96 s m⁻¹ during nighttime for hourly scale [39,40]. The soil moisture deficit coefficient K_s can be expressed as [28]

$$K_s=\left\{\begin{array}{c}1 \theta \ge {\theta }_{\mathrm{s}} \\ ln(1+\theta )/ln101 {\theta }_{\mathrm{c}}\le \theta <{\theta }_{\mathrm{s}}\\ \alpha exp\left[(\theta -{\theta }_{\mathrm{c}})/{\theta }_{\mathrm{c}}\right] \theta <{\theta }_{\mathrm{c}} \end{array}\right.$$

(10)

where θ is the relative volumetric soil moisture content; θ_s (%) is the saturated volumetric soil water content; θ_c is the critical relative soil moisture, θ_c = 0.8 θ_s for paddy rice; a is an empirical coefficient, and a = 0.95 for paddy rice.

2.3. FAO Dual Crop Coefficients Method

The FAO dual crop coefficient method is employed to simultaneously estimate evapotranspiration, soil evaporation, and crop transpiration.

$${ET}_{\mathrm{c}}=K_{\mathrm{c}}{ET}_{0 }=(K_{\mathrm{e}}+K_{\mathrm{s}}{K}_{\mathrm{cb}}){ET}_0$$

(11)

$$E_{\mathrm{s}}=K_{\mathrm{e}}{ET}_0$$

(12)

$$T_{\mathrm{c}}=K_{\mathrm{s}}{K}_{\mathrm{cb}}{ET}_0$$

(13)

where ET_c (mm d⁻¹ or mm h⁻¹) is the estimated evapotranspiration based on FAO56-adjusted, calibrated or LAI-based coefficients at the hourly (ET_{c Adjh}, ET_{c Calh}, ET_{c LAIh}) or daily (ET_{c Adjd}, ET_{c Cald}, ET_{c LAId}) scale; E_s (mm d⁻¹ or mm h⁻¹) and T_c (mm d⁻¹ or mm h⁻¹) are the corresponding soil evaporation and rice transpiration at the hourly (E_{s Adjh}, E_{s Calh}, E_{s LAIh} and T_{c Adjh}, T_{c Calh}, T_{c LAIh}) or daily (E_{s Adjd}, E_{s Cald}, E_{s LAId} and T_{c Adjd}, T_{c Cald}, T_{c LAId}) scale, and the ET₀ is the corresponding daily or hourly crop evapotranspiration estimated using Equation (9); K_c (dimensionless) is the estimated dual crop coefficient; K_cb (dimensionless) is the estimated basal crop coefficient; and K_e (dimensionless) is the estimated soil evaporation coefficient.

Following the FAO 56 procedure, the dual crop coefficient method divides crop growth into four stages, namely initial, development, midseason and late-season stages. The duration of initial, development, midseason and late-season stages are 18, 29, 56, 17 days in 2015 and 16, 26, 67, 16 days in 2016, respectively. The K_cb remains constant at K_{cb ini} during the initial stage, increases lineally from K_{cb ini} to K_{cb mid} during the development stage, remains constant at K_{cb mid} during the midseason stage, and decreases from K_{cb mid} to K_{cb end} during the late-season stage. Tabulated K_cb values in the FAO 56 manual are for flood paddies [30], which were proved inappropriate for the diversity of rice water management, and updated K_{cb ini}, K_{cb mid} and K_{cb end} are presented as 0.15, 1.15 and 0.85 for intermittent irrigated paddies [25], which are adopted in the current research, as the intermittent irrigation is similar to the local alternate drying and wetting irrigation method [41]. K_{cb mid} and K_{cb end} should be adjusted based on the local RH_min, U₂ and canopy height by the following equation.

$$K_{\mathrm{cb} \mathrm{Adj}}=K_{\mathrm{cb} \mathrm{Upd}}+\left[0.04\left(U_2-2\right)-0.004\left({RH}_{\min }-45\right)\right]{\left({\displaystyle \frac{h}{3}}\right)}^{0.3}$$

(14)

where K_{cb Adj} (dimensionless) is adjusted K_{cb mid} or K_{cb end}; K_{cb Upd} (dimensionless) is updated K_{cb mid} or K_{cb end} provided by Pereira et al. (2021) [25]; h is the average plant height during the midseason or late-season stage, which was measured every five days by a vertical ruler (resolution, 1 mm), and was interpolated linearly for days between two consecutive measurements; detailed observational data for h can be found in Lv et al. (2024) [37].

The seasonal variation in K_cb also can be dynamically calculated by introducing a function of leaf area index [30,31].

$$K_{\mathrm{cb} \mathrm{LAI}}=K_{\mathrm{cmin}}+(K_{\mathrm{cbfull}}-{ K}_{\mathrm{cmin}})\left[1-exp(-CLAI)\right]$$

(15)

$$K_{\mathrm{cbfull}}=\min \left(1.0+0.1h, 1.2\right)+\left[0.04\left(U_2-2\right)-0.004\left({RH}_{\min }-45\right)\right]{\left({\displaystyle \frac{h}{3}}\right)}^{0.3}$$

(16)

where K_{cb LAI} (dimensionless) is calculated K_cb based on the leaf area index, K_cmin (dimensionless) is the minimum crop coefficient for bare soil, typically ranging from 0.15 to 0.20 [30]; K_cbfull (dimensionless) is the maximum basal crop coefficient when the crop completely covers the ground; C (0.7) is the canopy attenuation coefficient of solar radiation; LAI (m² m⁻²) is the leaf area index, which was measured every five days using a CI-203 leaf area meter (CID, Liverpool, NY, USA) during rice seasons, and was interpolated linearly for days between two consecutive measurements; detailed measurements of LAI are provided in Lv et al. (2024) [37].

The K_e depends on soil moisture conditions

$$K_{\mathrm{e}}=\left\{\begin{array}{c}{K}_{\mathrm{cmax}}-K_{\mathrm{cb}} \mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{d} \\ \mathrm{m}\mathrm{i}\mathrm{n}\left[K_{\mathrm{r}}\left(K_{\mathrm{cmax}}-K_{\mathrm{cb}}\right),{ f}_{\mathrm{ew}}{K}_{\mathrm{cmax}}\right] \mathrm{n}\mathrm{o}\mathrm{n}\text{-}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{d} \end{array}\right.$$

(17)

where K_cmax (dimensionless) is the maximum value of K_c following irrigation or rain; K_r (dimensionless) is the evaporation reduction coefficient, dependent on the cumulative depth of water depleted from the topsoil; and f_ew (dimensionless) is the fraction of the soil that is not covered by vegetation and well wetted by irrigation or rain.

$$K_{\mathrm{cmax}}=\max \left(\left\{K_{\mathrm{cp}}+\left[0.04\left(U_{2 }-2\right)-0.004\left({RH}_{\min }-45\right)\right]{\left({\displaystyle \frac{h}{3}}\right)}^{0.3}\right\},\left\{K_{\mathrm{cb}}+0.05\right\}\right)$$

(18)

where K_cp (dimensionless) is the turbulent transport coefficient of water vapor, representing the impact of the reduced albedo of wet soil and the contribution of heat stored in dry soil prior to wetting events, which is recommended as 1.2 by FAO 56, and should be adjusted based on actual soil wetting-drying cycle conditions [28].

$$K_r=\left\{\begin{array}{c}1 D_{\mathrm{e},\mathrm{i}-1}\le REW\\ {\displaystyle \frac{TEW\text{-}{D}_{\mathrm{e},\mathrm{i}-1}}{TEW\text{-}REW}} D_{\mathrm{e},\mathrm{i}-1}>REW\end{array}\right.$$

(19)

where REW (mm) is the maximum depth of water that can be evaporated from the topsoil layer without restriction during the energy limiting stage, adopted as 9 mm for the study area [30]; TEW (mm) is the maximum cumulative depth of water that can be evaporated from the soil when the topsoil has been initially completely wetted, TEW = 1000(θ_FC − 0.5θ_WP)Z_e, with θ_FC (0.35 m³ m⁻³), θ_WP (0.20 m³ m⁻³) and Z_e (0.1 m) being the field capacity, wilting point, depth of the surface soil layer dried by evaporation; and D_e,i−1 (mm) is the cumulative depth of evaporation (depletion) from the topsoil at day i − 1 after rainfall or irrigation, 0 ≤ D_e,i−1 ≤ TEW.

$$D_{\mathrm{e},\mathrm{i}}=D_{\mathrm{e},\mathrm{i}-1}-\left(P_{\mathrm{i}}-{RO}_{\mathrm{i}}\right)-{\displaystyle \frac{I_{\mathrm{i}}}{f_{\mathrm{w}}}}+{\displaystyle \frac{E_{\mathrm{i}}}{f_{\mathrm{ew}}}}+T_{\mathrm{ew},\mathrm{i}}+{DP}_{\mathrm{e},\mathrm{i}}$$

(20)

where P_i (mm), RO_i (mm), I_i (mm), E_i (mm) and T_ew,i (mm) are, respectively, the daily precipitation, runoff, irrigation, evaporation, transpiration from the exposed and wetted soil surface layer on day i; DP_e,i (mm) is the deep percolation on day i, ${DP}_{\mathrm{e},\mathrm{i}}=\left\{\begin{array}{c}a{h}_{\mathrm{w}}+b flooded \\ 1000K_0/(1+K_0\epsilon t/∆z) non\text{-}flooded\end{array}\right.$ [42], with h_w (mm) being the depth of the water layer on the field surface; a and b being fitted parameters; K₀ (0.3 m d⁻¹) being the saturated hydraulic conductivity; ε (140) being an empirical constant; t being the number of days since the soil reached its last saturation state; and ∆z (100 mm) being the calculated depth of the surface soil layer.

f_ew = min(1 − f_c, f_w)

(21)

where f_c (dimensionless) is the fraction of ground cover which can be fitted using a quadratic function based on measured values [26], f_c = −0.0002DAT² + 0.022DAT + 0.1436 in the current study; and f_w (dimensionless) is the fraction well wetted by irrigation or rain, fixed as 1.0 according to the typical values under different irrigation conditions [30], except for the furrow irrigation and trickle irrigation.

2.4. Model Calibration and Evaluation

K_{cb act}, K_{e act} and K_{c act} were estimated following three approaches, namely FAO56 adjusted coefficients (Equation (14)), FAO56 calibrated coefficients, and LAI-based coefficients (Equation (15)). For FAO56 calibrated coefficients, K_{cb ini}, K_{cb mid} and K_{cb end} were calibrated based on K_{cb act}, and K_cp in Equation (18) was corrected after irrigation when D_e,i < REW based on K_{e act}. Finally, the ET_{c acth}, E_{s h}, T_{c acth} and ET_{c actd}, E_{s d}, T_{c actd} were estimated based on these estimated coefficients (Equations (11)–(13)). Statistics of determination coefficient R² and root mean square error RMSE (Equations (22) and (23)) were used to illustrate the performance of these coefficients in estimating ET_{c acth}, E_{s h}, T_{c acth} and ET_{c actd}, E_{s d}, T_{c actd}.

$${\mathrm{R}}^2={\displaystyle \frac{{\left({\sum }_{\mathrm{i}=1}^n(O_{\mathrm{Simi}}-\overline{O_{\mathrm{Sim}}}\left)\right(O_{\mathrm{Meai}}-\overline{{ O}_{\mathrm{Mea}}})\right)}^2}{{\sum }_{\mathrm{i}=1}^n{(O_{\mathrm{Simi}}-\overline{O_{\mathrm{Sim}}})}^2{\sum }_{\mathrm{i}=1}^n{(O_{\mathrm{Meai}}-\overline{{ O}_{\mathrm{Mea}}})}^2}}$$

(22)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{\mathrm{i}=1}^n{(O_{\mathrm{Simi}}-{ O}_{\mathrm{Meai}})}^2}$$

(23)

where O_Simi is the estimated ET_c, E_s or T_c; O_Meai is the corresponding actual ET_{c act}, E_s or T_{c act}; $\overline{O_{\mathrm{Sim}}}$ is the average estimated ET_c, E_s or T_c; $\overline{O_{\mathrm{Mea}}}$ is the average actual ET_{c act}, E_s or T_{c act}; and n is the total amount of data.

3. Results and Discussion

3.1. Averaged Diurnal Variations in Hourly Evapotranspiration, Transpiration, and Evaporation

During various growth stages, ET_{c acth}, E_{s h}, and T_{c acth} displayed a characteristic inverted “U”-shaped unimodal pattern. Specifically, ET_{c acth}, E_{s h}, and T_{c acth} remained stable around 0 mm h⁻¹ during the night and rapidly increased after sunrise, reaching their peak values around noon. Subsequently, ET_{c acth}, E_{s h}, and T_{c acth} gradually decreased until sunset, eventually approaching 0 mm h⁻¹ (Figure 1). Occasionally, negative values of ET_{c acth}, E_{s h}, and T_{c acth} occurred during the night due to high nighttime relative humidity and near-dew-point atmospheric temperature, resulting in moisture condensation on the soil surface and rice plants [38].

During initial, development, midseason and late-season stages, the average ET_{c acth} were, respectively, 0.17, 0.22, 0.17, 0.12 mm h⁻¹ in 2015 and 0.16, 0.28, 0.17, 0.06 mm h⁻¹ in 2016, the average E_{s h} were, respectively, 0.14, 0.10, 0.04, 0.02 mm h⁻¹ in 2015 and 0.15, 0.13, 0.05, 0.01 mm h⁻¹ in 2016, and the average T_{c acth} were, respectively, 0.03, 0.13, 0.13, 0.09 mm h⁻¹ in 2015 and 0.00, 0.15, 0.12, 0.04 mm h⁻¹ in 2016. Atmospheric evaporation capacity, soil moisture status, and canopy coverage were the main factors influencing ET_{c acth}, E_{s h}, and T_{c acth} [43,44]. Soil evaporation depended on meteorological conditions under sufficient available soil moisture content conditions, and decreased rapidly as available soil moisture content decreased [45]. During the initial stage, the average leaf area index LAI, standing water layer duration, and soil moisture content θ without standing water during the initial stage were approximately 0.52 m² m⁻², 13 days, and 46.5% in 2015, and 0.60 m² m⁻², 9 days, and 44.5% in 2016, respectively. The low canopy coverage exerted minimal impact on the solar radiation absorbed by the soil surface, the high soil moisture content ensured sufficient water available for soil evaporation, making the E_{s h} predominant during the initial stage. The ET₀, representing the atmospheric evaporation capacity [46], were, respectively, 0.11 mm h⁻¹ and 0.13 mm h⁻¹ during the initial stage in 2015 and 2016. The higher ET₀ was the primary reason for the higher E_{s h} in 2016 compared to 2015. During the early stage of the rice growth period, newly transplanted rice plants during tillering stage were typically characterized by weak physiological growth, resulting in relatively low T_{c acth} during this period. Despite the relatively higher atmospheric capacity in 2016, there was no discernible difference in T_{c acth} between 2015 and 2016. After entering the development stage, LAI increased rapidly due to vigorous tillering, leading to an increase in T_{c acth}. Meanwhile, the solar radiation absorbed by the soil surface decreased with the increase in canopy coverage. The T_{c acth} became the predominant process, with the average ratio of T_{c acth} to ET_{c acth} exceeding 50% during this stage. During the development stage, although LAI had not yet reached its maximum value, ET₀ was already at its peak level, resulting in peak values of T_{c acth} and ET_{c acth} among the four stages. During the midseason stage, rice LAI continued to increase until reaching its peak, and soil evaporation decreased continuously. This led to an increase in the ratio of T_{c acth} to ET_{c acth} to 77.0% and 73.2%, and a decrease in the ratio of E_{s h} to ET_{c acth} to 23.0% and 26.8% in 2015 and 2016, respectively. During the late-season stage, the lower leaves of the rice canopy began to senesce, reducing LAI and canopy coverage, while E_{s h} were lower than that during the midseason stage due to decreased atmospheric evaporation capacity and soil moisture content.

3.2. Seasonal Variations in Daily Evapotranspiration, Transpiration, and Evaporation

ET_{c actd}, E_{s d} and T_{c actd} ranged from 1.06 to 8.90 mm d⁻¹, from 0.23 to 5.32 mm d⁻¹ and from 0.30 to 7.09 mm d⁻¹ in 2015, and ranged from 0.50 to 9.04 mm d⁻¹, from 0.12 to 7.10 mm d⁻¹ and from 0.05 to 7.23 mm d⁻¹ in 2016. The trend of ET_{c actd} closely followed that of E_{s d} during the initial stage, while aligning with T_{c actd} during the development, midseason and late-season stages (Figure 2). During the initial stage, rice seedlings were characterized by low canopy coverage, and the field maintained a high soil moisture content. Consequently, T_{c actd} remained low, and ET_{c actd} were primarily dominated by E_{s d}. Notably, E_{s d} exhibited synchronous variations with solar net radiation. The higher solar net radiation in the initial stage of 2016 resulted in a significantly higher average E_{s d} (3.70 mm d⁻¹) compared to that of 2015 (3.26 mm d⁻¹). As the rice plants entered the development stage, both ET_{c actd} and T_{c actd} increased with the rise in LAI, while E_{s d} decreased due to increasing canopy coverage. By the mid-season stage, the daily variations in ET_{c actd} and T_{c actd} gradually became consistent. During the late season stage, as the lower leaves of the rice canopy began to senesce and LAI decreased, both ET_{c actd} and T_{c actd} decreased, while E_{s d} remained at a lower level. Additionally, the variations in ET_{c actd}, E_{s d}, and T_{c actd} differed between different growing years during the same growth stage, primarily due to meteorological factors and differences in field moisture conditions.

During the 2015 and 2016 rice seasons, ET_{c actd} respectively ranged from 1.06 to 8.90 mm d⁻¹ and from 0.50 to 9.04 mm d⁻¹ (with average values of 4.17 mm d⁻¹ and 4.26 mm d⁻¹, totaling 500.11 mm and 532.53 mm). Meanwhile, E_{s d} ranged from 0.23 mm d⁻¹ to 5.32 mm d⁻¹ and from 0.12 mm d⁻¹ to 7.10 mm d⁻¹ (with average values of 1.56 mm d⁻¹ and 1.73 mm d⁻¹, totaling 186.85 mm and 216.70 mm), T_{c actd} ranged from 0.30 mm d⁻¹ to 7.09 mm d⁻¹ and from 0.05 mm d⁻¹ to 7.23 mm d⁻¹ (with average values of 2.61 mm d⁻¹ and 2.53 mm d⁻¹, totaling 313.26 mm and 315.84 mm) (Figure 2). ET₀ were 3.0 mm d⁻¹ and 3.1 mm d⁻¹, standing water layer duration were 30 and 35 days, and soil moisture content during non-submerged periods were 40.0% and 41.6% during the 2015 and 2016 rice seasons. The weak atmospheric evaporative capacity, indicated by low ET₀, and low soil moisture content in rice fields resulted in lower ET_{c actd} and E_{s d} in 2015 compared to 2016. Crop transpiration reached its maximum during the mid-season stage, and frequent rainfall, associated with low atmospheric evaporative capacity, reduced rice transpiration, resulting in lower T_{c actd} in 2016 compared to 2015. The average ET_{c act} was 500.11 mm in 2015 and 532.53 mm in the 2016 rice season, which were comparable to the values for flooded rice during the dry seasons (451–531 mm) [47], to the values for paddy rice in Southwestern Japan (421–492 mm) [48], to the value for dry-seeded rice under overhead sprinkler irrigation systems in the tropics (499 mm averagely) [49], and to the values for intermittent irrigated paddies in South Sulawesi (539.1 mm) [50].

During the initial stage, daily E_{s d} and T_{c actd} ranged, respectively, from 1.40 to 4.73 mm d⁻¹ (3.26 mm d⁻¹ averagely and 58.70 mm totally) and from 0.30 to 1.74 mm d⁻¹ (0.77 mm d⁻¹ averagely and 13.86 mm totally) in 2015, and ranged, respectively, from 0.85 to 7.10 mm d⁻¹ (3.70 mm d⁻¹ averagely and 59.20 mm totally) and from 0.05 to 0.93 mm d⁻¹ (0.28 mm d⁻¹ averagely and 4.49 mm totally) in 2016 (Figure 2). With canopy coverage below 10%, soil evaporation predominated over rice transpiration, resulting in significantly higher E_{s d} than T_{c actd}, with the ratio of E_{s d} to ET_{c actd} exceeding 80%. During the development stage in both years, E_{s d} ranged from 0.91 to 5.32 mm d⁻¹ (2.28 mm d⁻¹ averagely and 66.25 mm totally) and from 0.65 to 4.75 mm d⁻¹ (3.09 mm d⁻¹ averagely and 80.28 mm totally), respectively. Meanwhile, T_{c actd} ranged from 0.85 to 5.57 mm d⁻¹ (3.06 mm d⁻¹ averagely and 88.60 mm totally) and from 2.07 to 6.21 mm d⁻¹ (3.71 mm d⁻¹ averagely and 96.50 mm totally), respectively. With the rapid increase in LAI and significant enhancement in transpiration, while receiving decreasing solar net radiation, E_{s d} decreased and T_{c actd} increased, and ET_{c actd} gradually shifted towards being dominated by T_{c actd} during the later development stage. During the mid-season stage, LAI gradually reached its peak and the canopy almost reached a closed state, soil evaporation continued to decrease, with total daily E_{s d} of 51.98 mm and 72.36 mm and total daily T_{c actd} of 173.61 mm and 198.46 mm for 2015 and 2016, respectively, and T_{c actd} dominated ET_{c actd}. During the late-season stage, rice leaves gradually withered and dropped, and LAI decreased, leading to a decline in crop coverage. However, the available soil moisture for evapotranspiration decreased due to the lower soil moisture content during this stage, resulting in a decreasing trend in soil evaporation. Influenced by both field soil moisture status and meteorological conditions, ET_{c acth}, E_{s h}, and T_{c acth} exhibited a multi-peak and multi-valley pattern during the rice growing season, similar to results reported for other crops [42].

3.3. Actual Dual Crop Coefficients, Soil Evaporation Coefficients and Basal Crop Coefficients

Throughout the entire rice growing season, the ranges of K_{c act} in 2015 and 2016 were from 0.71 to 3.19 and from 0.70 to 2.61, with average values of 1.46 and 1.39, respectively (Figure 3). During the initial stage, the average values of K_{cb act} were 0.30 and 0.10, and the average values of K_{e act} were 1.37 and 1.07 for 2015 and 2016, respectively. With low ground coverage and sufficient soil moisture during the initial stage, transpiration was minimal, and evaporation dominated, resulting in the minimum value of K_{cb act} and the maximum value of K_{e act} occurring. As rice growth progressed, the crop canopy gradually covered the soil surface, reducing the influence of soil evaporation on evapotranspiration, leading to a decrease in K_{e act} and an increase in K_{cb act}. The average values of K_{e act} during the development stage period in 2015 and 2016 were 0.56 and 0.59, and the average values of K_{cb act} were 0.74 and 0.77, respectively. During the mid-season stage, as the crop canopy approached or reached complete coverage of the ground surface, K_{cb act} gradually became dominant, and minimal differences between K_{cb act} and K_{c act} (0.31 in 2015 and 0.32 in 2016) occurred. Rice leaves withered and ground coverage decreased during the late-season stage, K_{e act} increased slightly and K_{cb act} decreased, and K_{cb act} dominated K_{c act}.

During initial, development, midseason and late-season stages, K_{c act} in 2015 and 2016 were 1.67, 1.24, 1.54, 1.34 and 1.17, 1.33, 1.45, 1.46, respectively (Figure 3). These K_{c act} values were notably higher than the range of 0.40 to 1.05 observed in the rice-growing regions of Japan [51], but were similar to the range of 1.10 to 1.60 in the monsoon regions of Asia [52]. These K_{c act} values in the current study also fell within the ranges observed in South India (0.88 to 1.99), Pakistan (0.80 to 1.95), and North India (0.62 to 2.32). The average differences in K_{c act} between 2015 and 2016 ranged from −0.13 to 0.51, indicating inter-annual differences in K_{c act}; these findings align with monitoring results from drainage lysimeters at the research site [53], and are consistent with conclusions drawn from other regions [49].

3.4. Simulation of Dual Crop Coefficients, Basal Crop Coefficients and Soil Evaporation Coefficients

Based on local average RH_min, U₂ and canopy height, the K_{cb Upd} for the mid-season and end-season stages were adjusted K_{cb Adj} as 1.07 and 0.77, respectively. Additionally, K_cb during different stages and K_cp were calibrated, the calibrated basal crop coefficient K_{cb Cal} for the initial stage, mid-season, and end-season stages were determined as 0.28, 1.17, and 1.09, respectively, and the calibrated K_cp value K_{cp Cal} was found to be 1.59. Furthermore, LAI-based basal crop coefficient K_{cb LAI} was also estimated by Equation (15). Based on the three approaches of calculating K_cb, namely K_{cb Adj}, K_{cb Cal} and K_{cb LAI}, the corresponding curves for K_cb, K_e and K_c, respectively, were plotted (Figure 4).

The performance of K_c in estimating K_{c act} depends on K_e and K_cb, as the K_c = K_e + K_sK_cb. Generally, K_{cb Adj} underestimated K_{cb act}, especially during the early midseason and late-season stages, and K_{e Adj} considerably underestimated K_{e act} throughout the rice growing period, thus K_{c Adj} significantly underestimated K_{c act} in the rice seasons. The underestimation of K_{c Adj} was mainly attributed to the low K_{e Adj}, and the low K_{e Adj} can be attributed to the underestimation of K_cmax after irrigation or rainfall (Equation (17)). Additionally, the turbulent transport coefficient of water vapor K_cp (1.2) in the FAO56-recommended K_cmax (Equation (18)) accounts for factors such as the decrease in reflectance of wet soil and the distribution of heat stored in dry soil before soil moisture, as well as the effect of soil wetting intervals greater than 3 (or 4) days [30]. Frequent soil wetting (due to rainfall or irrigation) reduces the opportunity for the soil to absorb heat between wetting events, leading to a decrease in K_cp, while infrequent soil wetting increases K_cp [28]. In this study, the rice growth periods in 2015 and 2016 were 120 days and 125 days, respectively, with soil wetting occurring 9 times, and the soil wetting intervals were much greater than 3 (or 4) days. The notably small K_cp resulted in the underestimation of K_cmax, thereby causing K_{e Adj} to underestimate K_{e act}.

Compared to the FAO56 adjusted values, K_{cb Cor} increased by 0.13, 0.10 and 0.32 for the initial, mid-season and end-season stages, and K_{cp Cal} increased by 0.39. K_{cb Cal} and K_{cp Cal} were effective in capturing the seasonal variations in K_{cb act}, K_{e act}, and K_{c act} during the rice growth period. During the initial, mid-season stages, and late-season stages, the K_cb values for dry-seeded rice were reported as 0.05–0.08, 0.37–0.44, and 0.87–0.95, respectively [49], while for flooded rice they were 0.86, 1.11, 0.84 during dry seasons and 1.04, 1.04, 0.96 during wet seasons [54]. Current K_{cb Cal} (0.28) for the initial stage fell between those for dry-seeded and flooded rice, while K_{cb Cal} (1.17 and 1.09) for mid-season and the end of end-season stages were higher than both dry-seeded and flooded rice. The calibrated K_cb for the mid-season and late-season stage were reported as 1.52, 0.63, respectively, and the calibrated K_cp was 1.29 for the drainage lysimeter in the same experimental area [28], which differed considerably from the current study. Focusing on the overall estimation of ET_{c act}, specified groundwater levels and different rice variety in drainage lysimeters may account for the differences in K_{cb Cal} and K_{cp Cal}. K_{cb LAI} clearly outperformed K_{cb Cal} in estimating K_{cb act} during the development stage, while K_{e LAI} indicated a consistently higher value compared to K_{e act} during the later mid-season and early late-season stages. Moreover, LAI-based crop coefficients showed comparable performance to calibrated coefficients. Overall, these LAI-based crop coefficients effectively estimated seasonal variations in K_{c act}, K_{e act}, and K_{cb act} throughout the rice growth period, albeit with slightly reduced accuracy compared to K_{cb Cal} and K_{cp Cal}.

3.5. Estimation of Hourly Evapotranspiration and Its Components

Based on three approaches of calculating dual-crop coefficients, namely FAO56 adjusted, calibrated, and LAI-based coefficients, hourly evapotranspiration, soil evaporation and rice transpiration were estimated (Figure 5). The estimated evapotranspiration ET_{c Adjh}, soil evaporation E_{s Adjh}, and rice transpiration T_{c Adjh} at the hourly scale, based on FAO56 adjusted coefficients, significantly underestimated actual values. And the ET_{c Adjh}, E_{s Adjh} and T_{c Adjh} respectively accounted for 62.4% to 87.1%, 17.7% to 91.1%, and 8.7% to 90.9% of the variance in ET_{c acth}, E_{s h} and T_{c acth}, with RMSE and R² ranging from 0.040 to 0.142 mm h⁻¹ and from 0.767 to 0.951 for ET_{c acth}, from 0.013 to 0.114 mm h⁻¹ and from 0.751 to 0.884 for E_{s h}, and from 0.032 to 0.097 mm h⁻¹ and from 0.040 to 0.949 for T_{c acth} during various stages in the 2015 and 2016 rice seasons. The hourly evapotranspiration ET_{c Calh}, soil evaporation E_{s Calh}, and rice transpiration T_{c Calh} based on FAO56 calibrated coefficients demonstrated the effective estimation of ET_{c acth}, E_{s h}, and T_{c acth} across various stages of rice growth. Compared to the FAO56 adjusted coefficients, the ET_{c Calh} consistently accounted for a higher percentage of ET_{c acth} during all growth stages, and E_{s Calh} also exhibited enhanced performance. The T_{c Calh} showed strong performance in estimating T_{c acth} during the development stage, mid-season stage, late-season stage, and entire growth period. The poor performance of T_{c Calh} in estimating T_{c acth} during the initial stage was possibly due to the weak rice plant, as the new transplanted rice plants did not engage in normal physiological growth activities during the early initial stage [55]. LAI-based coefficients also performed well in estimating ET_{c acth}, E_{s h}, and T_{c acth} during the rice growth period. However, there were slight differences between FAO56 calibrated and LAI-based coefficients in terms of RMSE, k, and R². On average, RMSE was slightly higher for ET_{c acth} and T_{c acth} and slightly lower for E_{s h} with LAI-based coefficients compared to FAO56 calibrated coefficients. Additionally, k and R² were closer to 1 for FAO56 calibrated coefficients, indicating slightly superior performance compared to LAI-based coefficients. Overall, both FAO56 calibrated and LAI-based coefficients provided satisfactory estimates of ET_{c acth}, E_{s h}, and T_{c acth} during the rice growing season, with FAO56 calibrated coefficients showing slightly better performance.

3.6. Estimation of Daily Evapotranspiration and Its Components

The estimated daily evapotranspiration ET_c derived from the FAO56 adjusted, calibrated, and LAI-based coefficients is presented in Figure 6. Similarly, the estimated daily soil evaporation E_s and daily rice transpiration T_c obtained using these three methods are shown in Figure 7 and Figure 8, respectively. The corresponding statistical metrics for ET_c E_s and T_c are provided in

Table 2. Performance of the dual crop coefficient method based on FAO56 adjusted, calibrated, and leaf area index based coefficients in estimating daily evapotranspiration ET_c, soil evaporation E_s, and crop transpiration T_c.

Rice Season	Crop Coefficients	ETc/Es/Tc	Statistic	Initial	Development	Midseason	Late-Season	Entire Rice Season
2015	FAO56 adjusted coefficients	ETc Adjd	RMSE	1.841	1.481	1.260	0.633	1.355
			k	0.641	0.773	0.729	0.815	0.739
			R2	0.187	0.840	0.877	0.717	0.791
		Es Adjd	RMSE	1.450	1.026	0.820	0.224	0.944
			k	0.671	0.676	0.197	0.893	0.616
			R2	0.119	0.578	0.727	0.100	0.690
		Tc Adjd	RMSE	0.492	0.943	0.655	0.502	0.698
			k	0.471	0.829	0.879	0.794	0.851
			R2	0.418	0.728	0.807	0.876	0.841
	FAO56 calibrated coefficients	ETc Cald	RMSE	1.477	0.808	0.598	0.458	0.826
			k	0.880	0.996	0.949	1.063	0.964
			R2	0.206	0.869	0.881	0.754	0.806
		Es Cald	RMSE	1.252	0.782	0.307	0.305	0.663
			k	0.865	0.979	0.851	1.342	0.915
			R2	0.128	0.583	0.564	0.363	0.708
		Tc Cald	RMSE	0.326	0.755	0.577	0.290	0.567
			k	0.866	0.964	0.961	0.977	0.962
			R2	0.418	0.774	0.807	0.794	0.853
	leaf area index-based coefficients	ETc LAId	RMSE	1.544	0.778	0.689	0.427	0.867
			k	0.943	1.051	0.910	1.038	0.976
			R2	0.244	0.906	0.864	0.764	0.799
		Es LAId	RMSE	1.251	0.645	0.423	0.473	0.671
			k	0.824	0.913	1.150	1.575	0.911
			R2	0.136	0.650	0.450	0.196	0.675
		Tc LAId	RMSE	0.612	0.727	0.765	0.375	0.691
			k	1.379	1.078	0.818	0.876	0.912
			R2	0.476	0.846	0.827	0.810	0.786
2016	FAO56 adjusted coefficients	ETc Adjd	RMSE	0.845	1.665	1.240	0.355	1.228
			k	0.885	0.776	0.753	0.782	0.776
			R2	0.835	0.749	0.911	0.941	0.918
		Es Adjd	RMSE	1.015	1.125	1.073	0.146	1.007
			k	0.805	0.794	0.184	0.765	0.692
			R2	0.807	0.642	0.792	0.772	0.788
		Tc Adjd	RMSE	0.383	1.101	0.710	0.292	0.743
			k	1.191	0.797	0.947	0.791	0.895
			R2	0.013	0.567	0.804	0.836	0.826
	FAO56 calibrated coefficients	ETc Cald	RMSE	1.221	0.790	0.633	0.204	0.735
			k	1.212	1.006	0.976	1.047	1.013
			R2	0.873	0.748	0.916	0.939	0.914
		Es Cald	RMSE	0.736	1.042	0.512	0.093	0.661
			k	1.039	1.102	0.706	1.164	1.008
			R2	0.846	0.648	0.637	0.912	0.852
		Tc Cald	RMSE	0.811	0.739	0.760	0.159	0.714
			k	2.186	0.937	1.035	1.009	1.004
			R2	0.013	0.634	0.804	0.912	0.836
	leaf area index-based coefficients	ETc LAId	RMSE	1.482	0.832	0.674	0.207	0.821
			k	1.315	1.049	0.937	1.052	1.023
			R2	0.945	0.794	0.913	0.939	0.899
		Es LAId	RMSE	0.591	0.765	0.529	0.219	0.568
			k	1.001	1.057	0.936	1.558	1.015
			R2	0.885	0.652	0.525	0.887	0.870
		Tc LAId	RMSE	1.433	0.634	0.753	0.188	0.809
			k	3.442	0.995	0.884	0.887	0.925
			R2	0.018	0.666	0.804	0.932	0.777

ET_{c Adjd}, E_{s Adjd} and T_{c Adjd} denote, respectively, estimated daily ET_c, E_s and T_c based on FAO56 adjusted coefficients; ET_{c Cald}, E_{s Cald} and T_{c Cald} denote, respectively, estimated daily ET_c, E_s and T_c based on FAO56 calibrated coefficients; ET_{c LAId}, E_{s LAId} and T_{c LAId} denote, respectively, estimated daily ET_c, E_s and T_c based on leaf area index-based coefficients. RMSE, k, R² denote the root mean square error, the slopes of the linear regression between simulated and measured values, and the coefficient of determination.

. The daily evapotranspiration ET_{c Adjd}, soil evaporation E_{s d} and rice transpiration T_{c Adjd} based on FAO56 adjusted coefficients consistently underestimated, respectively, ET_{c actd}, E_{s d} and T_{c actd} by 11.5% to 35.9%, 10.7% to 81.6% and 5.3% to 52.9% across various stages in both 2015 and 2016. Compared with FAO56 adjusted coefficients, the FAO56 calibrated coefficients performed much better in estimating ET_{c actd} during various rice growth stages, and ET_{c Cald} accounted for 96.4% and 101.3% of the variance in ET_{c actd} in the 2015 and 2016 entire rice season. Similarly, E_{s Cald} also demonstrated relatively better performance in estimating E_{s d} during rice seasons compared to the adjusted coefficients, with reduced RMSE values and higher R². Except for the initial stage, the estimated daily rice transpiration based on FAO56 calibrated coefficients T_{c Cald} performed well in estimating T_{c actd}, being from 93.7% to 103.5% of T_{c actd}, respectively. The LAI-based coefficients exhibited limitations in accurately estimating E_{s d} during the late-season stage and T_{c actd} during the initial stage. Despite these shortcomings, the LAI-based coefficients showed competitive performance in estimating T_{c actd} during other growth stages. Comparative analysis between the calibrated and LAI-based coefficients revealed slight differences in performance metrics such as RMSE, k, and R². On average, the FAO56 calibrated coefficients outperformed the LAI-based coefficients, with lower RMSE values for ET_{c actd} and T_{c actd} estimation and closer proximity to 1 for k and R² during rice seasons. Overall, the study underscores the efficacy of FAO56 calibrated and LAI-based coefficients in accurately estimating ET_c, E_s and T_c during various rice growth stages, highlighting their potential for enhancing agricultural water management practices. The related literature was lacking for rice K_cb values, especially for alternate drying and wetting irrigated rice paddies. Based on the general guidelines to derive K_cb from the single crop coefficient in FAO56 [30], the updated K_cb for the mid-season stage were defined by assuming K_cb = K_c − 0.05, and decreased K_cb for the end-season stage by 0.10–0.15 from K_c [25]. The assumption in K_cb for FAO56 adjusted coefficients, as well as variations in irrigation methods, may contribute to difference in performance among FAO56 adjusted coefficients, FAO56 locally calibrated coefficients, and leaf area index LAI-based coefficients in estimating ET_{c actd}, E_{s d} and T_{c actd}.

4. Conclusions

Actual hourly evapotranspiration ET_{c acth}, soil evaporation E_{s h}, and rice transpiration T_{c acth} exhibited a distinct inverted “U” shape single-peak trend. Daily actual evapotranspiration ET_{c actd}, soil evaporation E_{s d}, and rice transpiration T_{c actd} exhibited a variation aligned with the corresponding crop coefficient K_{c act}, soil evaporation coefficient K_{e act} and basal crop coefficient K_{cb act}. During the initial stage, ET_{c actd} was primarily influenced by E_{s d} as T_{c actd} remained relatively low, and minimum K_{cb act} and maximum K_{e act} correspondingly occurred. As the development stage progressed, both ET_{c actd} and T_{c actd}, along with K_{c act} and K_{cb act}, increased and became dominant, while E_{s d} and K_{e act} decreased. By the mid-season stage, ET_{c actd} and T_{c actd} respectively followed the variation in K_{c act} and K_{cb act}, and E_{s d} and K_{e act} were relatively low. During the late-season stage, both ET_{c actd} and T_{c actd}, along with K_{c act} and K_{cb act}, decreased, while E_{s d} and K_{e act} remained low.

The estimated crop coefficient K_{c Adj} and soil evaporation coefficient K_{e Adj} based on FAO56 adjusted coefficients, based on updated basal crop coefficients for intermittent irrigated paddies, significantly underestimated K_{c act} and K_{e act} throughout the rice growing period. The locally calibrated basal crop coefficient K_{cb Cal} for initial, midseason and end-season stages, and turbulent transport coefficient of water vapor K_{cp Cal} were determined as 0.28, 1.17, 1.09, and 1.59, respectively. The crop coefficients K_{c Cal}, soil evaporation coefficients K_{e Cal}, and crop coefficients K_{cb Cal}, based on FAO56 calibrated coefficients, effectively estimated K_{c act}, K_{e act} and K_{cb act} throughout the rice growth period. The leaf area index LAI-based coefficients also performed well in estimating K_{c act}, K_{e act} and K_{cb act} throughout the rice growth period. Corresponding with the above coefficients, the estimated evapotranspiration ET_{c Adj}, soil evaporation E_{s Adj}, and rice transpiration T_{c Adj} at hourly and daily scales, based on the FAO56 adjusted coefficients, consistently underestimated the measured values. Hourly evapotranspiration ET_{c Calh}, evaporation E_{s Calh}, and transpiration T_{c Calh} based on FAO56 calibrated coefficients effectively estimated ET_{c acth}, E_{s h}, and T_{c acth} during different rice growth stages. ET_{c Cal} performed well in estimating measured values, while E_{s Cal} and transpiration T_{c Cal} showed poor performance during the initial stage but demonstrated good accuracy during the subsequent stages. Compared with FAO56 adjusted coefficients, hourly and daily evapotranspiration ET_LAI, evaporation E_{s LAI}, and transpiration T_{c LAI} based on LAI-based coefficients also performed well in estimating measurements, albeit slightly less accurately than FAO56 calibrated coefficients.