Paddy Field Scale Evapotranspiration Estimation Based on Two-Source Energy Balance Model with Energy Flux Constraints and UAV Multimodal Data

Abstract

Accurate evapotranspiration (ET) monitoring is important for making scientific irrigation decisions. Unmanned aerial vehicle (UAV) remote sensing platforms allow for the flexible and efficient acquisition of field data, providing a valuable approach for large-scale ET monitoring. This study aims to enhance the accuracy and reliability of ET estimation in rice paddies through two synergistic approaches: (1) integrating the energy flux diurnal variations into the Two-Source Energy Balance (TSEB) model, which considers the canopy and soil temperature components separately, for physical estimation and (2) optimizing the flight altitudes and observation times for thermal infrared (TIR) data acquisition to enhance the data quality. The results indicated that the energy flux in rice paddies followed a single-peak diurnal pattern dominated by net radiation (Rn). The diurnal variation in the ratio of soil heat flux (G) to Rn could be well fitted by the cosine function with a max value and peak time (R² > 0.90). The optimal flight altitude and time (50 m and 11:00 am) for improved identification of temperature differentiation between treatments were further obtained through cross-comparison. These adaptations enabled the TSEB model to achieve a satisfactory accuracy in estimating energy flux compared to the single-source SEBAL model, with R² values of 0.8501 for Rn − G and 0.7503 for latent heat (LE), as well as reduced rRMSE values. In conclusion, this study presents a reliable method for paddy field scale ET estimation based on a calibrated TSEB model. Moreover, the integration of ground and UAV multimodal data highlights its potential for precise irrigation practices and sustainable water resource management.

1. Introduction

Water is an essential source for life and agriculture [1]. Globally, agriculture accounts for more than 70% of the total freshwater consumption. As the global population is projected to reach 9 billion by 2050, the demand for food will increase significantly, necessitating improvements in water use efficiency [2,3]. Evapotranspiration (ET) is a key component of water consumption in relation to field water balance [4,5,6]. Accurate estimations of ET are of great significance for guiding scientific irrigation and drainage schedules and saving water [7,8], especially in paddy fields, where the amount of available water fluctuates frequently.

The water balance method is the most representative approach for field scale ET observation [9,10] and is used to calculate ET based on the difference between “income water” (irrigation and precipitation) and “consumed water” (leakage and surface runoff) over a certain period. ET values measured using the water balance method are often used as reference values for validating other methods. However, irrigation, drainage, and infiltration processes take time. The temporal resolution of the water balance method is generally limited and usually requires a longer time period (typically on a daily scale) to achieve ideal accuracy [11]. Benefiting from a good time resolution and a theoretical foundation with fewer hypotheses, the eddy covariance (EC) method has been widely used for ET monitoring in different ecosystems [12,13]. Ultrasonic anemometers and fast-response hygrometers are commonly involved in EC systems to directly measure the turbulent flux (sensible heat flux (H) + latent heat flux (LE)) of the underlying surface and to further estimate ET values with different time resolutions. However, EC systems also encounter a problem whereby the error is quite large during day and night alternations, and the energy flux cannot be appropriately closed at the same observation time [14]. This leads to their application in scenarios with frequent water and heat exchanges, such as rice paddies, incurring higher calculation and post-processing costs. More importantly, the ET values measured through the above practical methods are usually insufficiently representative in fields with large spatiotemporal variations, thus making it difficult to guide the actual water regulation.

Given the fact that practical ET measurements have high costs and are not flexible with regard to spatiotemporal resolution, large-scale ET monitoring utilizing satellite remote sensing and low-altitude UAV remote sensing technologies has garnered increasing attention from both researchers and agricultural administrators [15,16,17,18]. Brown and Rosenberg [19] adopted airborne thermal infrared sensors for remote sensing ET monitoring by directly exploring and analyzing the relationship between thermal infrared (TIR) temperature and ET values. With the advancement of satellite remote sensing technology, the increasing diversity of earth observation data (optical, thermal infrared, and microwave sources) has driven ET monitoring towards greater precision and enhanced spatiotemporal continuity [20,21]. Methods for retrieving ET values from remote sensing platforms can be categorized into statistical models, vegetation index–surface temperature (VI-Ts) models, semi-empirical and semi-theoretical models, and surface energy balance models (SEBMs) [22,23]. Among them, the physical mechanism of the SEBM is more complete. By directly estimating components in the energy transfer process based on surface temperature, LE and ET can be better estimated using the residual method.

According to the types of resistances and processes considered, commonly used SEBMs can be categorized as single-source or dual-source energy balance models. Specifically, the Surface Energy Balance Algorithm for Land (SEBAL), which was developed by Bastiaanssen [24,25], is the most representative single-source model and has extended the applicability of SEBMs across temporal and spatial scales. Building upon the SEBAL model, Allen [26,27] developed the Mapping ET at high resolution with Internalized Calibration (METRIC) model, further enhancing the retrieval accuracy. Additionally, the Simple-Surface Energy Balance Index (S-SEBI) [28] and the Surface Energy Balance System (SEBS) [29] have also gained widespread recognition in remote sensing ET monitoring.

Compared to single-source models, dual-source energy balance models offer a more rigorous theoretical foundation by decomposing surface temperature to separately compute the energy balance processes between the canopy and soil. The Two-Source Energy Balance (TSEB) model [30] is a simplification of the Shuttleworth-Wallace (S-W) model [31] and features the Priestley–Taylor (P–T) model to partition canopy and soil temperatures, which enables the separate estimation of crop transpiration and soil evaporation [32]. The TSEB-PT model has already been used for ET estimation across river basins on a global scale. Based on TSEB-PT, the DTD [33] and TSEB-SM [34,35] models, which were constructed through enriching input, have further improved accuracy, especially under the condition of sparse coverage. However, there have been no reports on estimating ET in paddy fields using the TESB-PT model yet. This might be due to the following special conditions that are observed in paddy fields. (1) The lag effect of soil heat flux (G) and the specific heat capacity of water coverage in paddy fields are significantly stronger than those of dry land; thus, the default fixed G/Rn ratio assumption of TSEB-PT is difficult to capture their dynamic changes. (2) The canopy coverage of paddy fields is almost saturated, and the ability of remote sensing data resolution to reflect field heterogeneity needs further study. Additionally, commonly used satellite remote sensing ET products still face limitations in spatial and temporal resolution. It is difficult to accurately support irrigation and drainage in rice paddies, where the water status changes frequently. UAVs equipped with thermal infrared and multispectral sensors could offer flexible capability for field information acquisition to meet different spatial and temporal needs. Therefore, this study focuses on adapting and evaluating the TSEB model for field scale ET estimation based on UAV-based multimodal data. The specific objectives are as follows: (1) to characterize the diurnal variation of energy flux under clear-sky conditions across different growth stages; (2) to evaluate the capability of UAV-based thermal infrared data under different flight altitudes and observation times to distinguish canopy temperature differences between water and nitrogen treatments; and (3) to assess the accuracy of the adapted TSEB model for ET estimation in paddy fields.

2. Methods

The subsections are organized as follows: Section 2.1 introduces the study area and experiment arrangements to provide a brief background of the results and conclusions in this study. Section 2.2 introduces the methods of observation and measurement of energy flux and ET analysis and validation. Section 2.3 introduces the UAV platforms and flight strategy for multimodal data employed in the energy balance model. Section 2.4 introduces the ET estimation methods for accuracy comparison with measured ET values. Section 2.5 introduces the post-processing method of thermal infrared data for practicality and consistency. Section 2.6 introduces the metrics for accuracy evaluation.

2.1. Study Area

The coupling of the regulation experiment of rice water-saving irrigation schedules and nitrogen application levels was conducted at Changshu Water Conservancy Technology Promotion Station, Suzhou City, Jiangsu Province, China (31°32′47.07″N, 120°42′4.27″E). The study area has an average altitude of 1.3 m and features a humid subtropical monsoon climate. The annual average temperature is 16.6 °C, with a maximum of 38 °C and a minimum of −6.1 °C. The annual rainfall is 1321.2 mm, while the annual ET is 1364.6 mm.

The texture of the plow layer in the station is classified as silty loam. The average organic matter content is 22.00 g/kg, with a total nitrogen content of 0.77 g/kg, a total phosphorus content of 0.90 g/kg, and a total potassium content of 13.50 g/kg. The alkali-hydrolyzed nitrogen content is 355.8 mg/kg, the available phosphorus content is 30.2 mg/kg, and the available potassium content is 90.9 mg/kg. The specific properties of different soil layers are detailed in

Table 1. Basic physical properties of the soil.

Layer Depth (cm)	Clay (<2 μm) (%)	Powder (2–20 μm) (%)	Sand (2–2000 μm) (%)	Saturated Moisture Content (%)	Bulk Density (g/cm3)
5–20	1.32	62.44	36.24	42.02	1.26
20–35	1.80	65.83	32.37	40.84	1.44
35–50	2.37	66.03	31.60	39.91	1.52

.

The location of the experimental station and the treatment layout are shown in Figure 1. Two irrigation treatments were introduced—shallow frequent irrigation and controlled irrigation. Three levels of pure nitrogen application were set at 75 kg/ha, 255 kg/ha, and 375 kg/ha, resulting in a total of six treatments, as follows: (1) shallow frequent irrigation + low nitrogen (W1N1); (2) shallow frequent irrigation + standard nitrogen (W1N2); (3) shallow frequent irrigation + high nitrogen (W1N3); (4) controlled irrigation + low nitrogen (W2N1); (5) controlled irrigation + standard nitrogen (W2N2); and (6) controlled irrigation + high nitrogen (W2N3). Both the low (N1) and high (N3) nitrogen treatments were replicated twice; however, the standard nitrogen (N2) treatment was not replicated. Therefore, a total of 10 experimental plots were set up (with a size of 9 m × 9 m and a two-factor randomized arrangement) for this study.

The surrounding bounds were lined with a double-layer impermeable membrane buried at a depth of 60 cm in order to prevent the lateral seepage of water and nutrients between different treatments. During irrigation, water was pumped from an external river through pipes to the edge of each plot, with the inflow being controlled by valves and measured by water meters. Drainage was managed through independent outlet valves, allowing water to be discharged to a central ditch and either drained by gravity or pumped to the external river.

The tested rice cultivar (Changxiangjing 1813) was soaked in early June and artificially transplanted on 21 June, with a spacing of 25 cm × 15 cm. The final harvest was conducted on 25 October. For each plot, phosphorus and potassium fertilizers were applied once as basal fertilizers before transplanting, specifically at 75 kg/ha for P₂O₅ and 105 kg/ha for K₂O. Pure nitrogen was applied in a split application at rates of 35%, 35%, and 30% before transplanting, during the tillering stage, and at the panicle initiation stage, respectively. The management practices of pests, diseases, and weeds were consistent with those of local farmers. The irrigation schedule and control indicators at different growth stages are shown in

Table 2. Shallow frequent irrigation and controlled irrigation schedules.

Controlled Factors	Replanting	Tillering	Jointing–Booting	Heading–Flowering	Milking	Maturing
Shallow, frequent irrigation
Upper limit	30	30	30	30	30	0
Lower limit	10	10	10	10	10	60%–70% *
Rain storage	80	80~120	150–200	150–200	100	0
Controlled irrigation
Upper limit	100% *	100% *	100% *	100% *	100% *	80% *
Lower limit	10	80% *	80% *	80% *	80% *	Drying
Rain storage	70	80	100–150	100–150	80	0

Note: The default unit of data in the table is mm. * represents the percentage of soil-saturated water content (volume). Irrigation-controlled factors at the tillering, jointing–booting, heading–flowering, and milking stages corresponded to saturated water contents at 0–20 cm, 0–35 cm, 0–50 cm, and 0–50 cm, respectively.

.

2.2. Ground Data Measurements

2.2.1. Meteorological and Energy Flux Observations

An automatic meteorological station (Vantage Pro 2, DAVIS Instruments Corp, San Francisco, CA, USA) was installed within the experimental area for routine meteorological factor monitoring. The station was set up at a height of 2 m above the ground of short grass, with paddy fields surrounding the area. The data collection frequency was set to 30 min intervals. The monitored meteorological parameters included maximum temperature (T_max, °C), minimum temperature (T_min, °C), relative humidity (RH, %), wind speed (U, m/s), wind direction, atmospheric pressure (Pa, bar), precipitation (Prec, mm), and sunshine duration (Nsun, h). T_max, T_min, Prec, and reference evapotranspiration (ETo; calculated using the FAO-56 Penman–Monteith formula) during the growing season are illustrated in Figure 2.

Energy flux monitoring was conducted using an EC system at the State Experimental Station of Agro-Ecosystem in Changshu, which was within 200 m of the experiment area. The system mainly included a CAST3A three-dimensional sonic anemometer (Campbell Scientific Measurement Technology Co., Ltd., Logan, UT, USA), a Li-7500A open-path CO₂/H₂O analyzer and a Li-7550 data logger (LI-COR Environmental Co., Ltd., Lincoln, NE, USA). To accurately analyze energy exchange processes between the canopy and near-surface air, the system was installed at a height of 1.8 m. The underlying surface was managed by a rice paddy with the same shallow, frequent irrigation and conventional fertilization schedules as the experimental area (with synchronous transplanting and growth progression corresponding to the W1N2 treatment). During the rice-growing season, four types of flux data were obtained with a temporal resolution of 30 min—net radiation (Rn, W/m²), sensible heat flux (H, W/m²), latent heat flux (LE, W/m²), and soil heat flux (G, W/m²).

For a more accurate estimation of ET based on the LE, the enforcing closure correction method based on evaporative fraction (EF) was applied to force energy flux closure during the daytime (from 7:30 to 16:00). The enforcing closure correction method calculates the difference between available energy and turbulent fluxes and then redistributes the difference according to the proportion of LE within the turbulent fluxes. According to the results of ET observation experiments conducted in cotton fields [36], the phenomenon of LE and ET underestimation using the vorticity correlation method can be effectively reduced by enforcing closure after removing outliers and redistributing turbulent flux [37,38].

$$D^{3\mathrm{h}}=\left(R{n}^{3\mathrm{h}}-G^{3\mathrm{h}}\right)-\left(L{E}^{3\mathrm{h}}+H^{3\mathrm{h}}\right)$$

(1)

where D^3h represents the energy difference in the 3 h sliding window; W/m². Rn^3h, G^3h, LE^3h, and H^3h represent the average value of the energy flux in the 3 h sliding window, W/m².

To ensure the rationality of the EF calculation, a 3-day sliding window was employed.

$$E{F}^{3\mathrm{d}}={\displaystyle \frac{L{E}^{3\mathrm{d}}}{L{E}^{3\mathrm{d}}+H^{3\mathrm{d}}}}$$

(2)

$$L{E}^{\ast }=LE+D^{3\mathrm{h}}\cdot E{F}^{3\mathrm{d}}$$

(3)

$$H^{\ast }=H+D^{3\mathrm{h}}\cdot \left(1-E{F}^{3\mathrm{d}}\right)$$

(4)

where EF^3d represents the average evaporative fraction in the 3-day sliding window. LE^3d and H^3d represent the average value of LE and H in the 3-day sliding window, W/m². LE^* and H^* represent the calculated LE and H based on the evaporative fraction closure method, W/m².

2.2.2. Field Scale ET Observations

The actual field ET value under the shallow frequent irrigation treatment (W1) was determined using the water balance method. Specifically, the irrigation volume was measured using water meters installed in each plot, precipitation was recorded using an automatic rain gauge at the meteorological station, and leakage was determined by calculating the water level difference between the bottomless lysimeter and the lysimeter with a bottom in the study area.

$$E{T}_{\mathrm{m}}=h_{\mathrm{t}}-h_{\mathrm{t}+1}+m+p-D-L$$

(5)

where ET_m represents the measured daily evapotranspiration, mm/day. h_t and h_t+1 represent water depths on the field surface on the current observation day and the next following day, respectively, in mm. m, p, D, and L represent the irrigation amount, precipitation, drainage, and leakage, respectively, all in mm.

In detail, the water depth on the paddy surface was measured using a customized vernier caliper (with a resolution of 0.1 mm), and the measurements were conducted at 6:30 and 17:30 every day through the positioning of water gauge piles embedded during rice transplanting. The practical measurement method is shown in Figure 3.

Based on the instantaneous energy flux values obtained from the EC system, the constant EF method, which was assumed to be constant throughout the daytime, was used to upscale the instantaneous LE flux to a daily scale and further calculate the daily ET at the field scale [39,40,41].

$$E{F}_{\mathrm{i}}={\displaystyle \frac{L{E}_{\mathrm{i}}}{L{E}_{\mathrm{i}}+H_{\mathrm{i}}}}={\displaystyle \frac{\lambda E{T}_{\mathrm{i}}}{R{n}_{\mathrm{i}}-G_{\mathrm{i}}}}$$

(6)

$$E{T}_{EC}=\mathrm{86,400}\times {\displaystyle \frac{E{F}_{\mathrm{i}}}{{\lambda }_{\mathrm{d}}}}\left(R{n}_{\mathrm{d}}-G_{\mathrm{d}}\right)$$

(7)

where EF_i represents the evaporation ratio at the instantaneous observation time i. LE_i and H_i represent the latent heat flux and sensible heat flux at the instantaneous scale, respectively, W/m². λ_i and λ_d represent the latent heat of vaporization at the instantaneous scale and daily scale, respectively, in J/kg. ET_i and ET_EC represent the ET at the instantaneous scale and daily scale, respectively, mm/h and mm/d. Rn_i and G_i represent the net radiation and soil heat flux at the instantaneous scale, respectively, W/m². Rn_d and G_d represent the net radiation and soil heat flux at the daily scale, respectively, in W/m².

2.3. UAV-Based Data Acquisition and Processing

Under clear or cloudless weather conditions, the multispectral and TIR data of the rice canopy were acquired concurrently with ground measurements at the late tillering stage, jointing–booting stage, heading–flowering stage, and milking stage. The multispectral and TIR imagery were captured using a MAVIC 3M and MAVIC 3T (Shenzhen Dajiang Innovation Technology Co., Ltd., Shenzhen, China), respectively, as shown in Figure 4. In order to obtain the optimal flight regime, three different flight altitudes of 20 m, 50 m, and 100 m were set to obtain data of different resolutions, and data were recorded at five different observation times to account for different radiation conditions. Each flight was set with a heading overlap of 85% and a side overlap of 85% for high-quality image synthesis. The details for each sortie are presented in

Table 3. Detailed parameters of each flight sortie.

DOY	Time (hh:mm)	Solar Elevation Angle (°)	Flight Altitude (m)	Number of Images Obtained	Resolution (mm/pixel)
212	09:30	52.98	20 50 100	576 (249) 204 (35) 56 (18)	10 (30) 20 (70) 50 (140)
	11:00	70.45
	12:30	75.39
	14:00	60.53
	15:30	41.76
236	09:30	50.00
	11:00	65.38
	12:30	68.28
	14:00	55.36
	15:30	37.33
244	09:30	48.92
	11:00	63.33
	12:30	65.33
	14:00	52.83
	15:30	35.11
260	09:30	45.80
	11:00	58.34
	12:30	59.19
	14:00	47.64
	15:30	30.63

Note: The number of images and the ground resolution values outside the brackets correspond to multispectral data, while the values inside the brackets correspond to TIR data.

.

In detail, the MAVIC 3M is equipped with four-band multispectral imaging abilities, featuring 1/2.8 CMOS sensors and a visible light imaging sensor with a 4/3 CMOS sensor. Each multispectral sensor has an effective pixel count of 5 megapixels, a field of view (FOV) of 73.91°, and an equivalent focal length of 25 mm. The MAVIC 3T is equipped with an uncooled vanadium oxide (VOx) thermal imaging sensor and a 1/2 CMOS visible light imaging sensor. The thermal imaging sensor monitors an infrared wavelength range of 8 to 14 μm, with a pixel pitch of 12 μm. The field of view (FOV) is 61°, and the equivalent focal length is 40 mm. Both MAVIC 3M and MAVIC 3T UAVs were equipped with an RTK module to guarantee image quality and stitching accuracy.

The acquired raw multispectral and TIR images were calibrated and mosaicked using PIE-Smart v7.0 software (developed by Beijing Piesat Information Technology Co., Ltd., Beijing, China); the final output was exported in TIFF format. Multispectral data processing followed the conventional process [42], and vegetation indices such as NDVI were calculated for the inversion of LAI and vegetation coverage (f_vc) based on the threshold segmentation method. The canopy height was obtained based on the differences in the values between the DTM (digital terrain model) before transplanting and the DSM (digital surface model) at each growth stage, as obtained by visible light images (with RTK).

In particular, it should be noted that the temperature data obtained by the MAVIC 3T included TIR temperatures, which were calculated according to brightness, temperature, and surface emissivity but packaged in R_JPEG format. Thus, DJI’s open-source thermal SDK (TSDK) tool was introduced to extract the TIR data from the R_JPEG format and convert them into TIFF format. The converted TIR images were further imported into PIE-UAV software for post-processing. Additionally, a handheld infrared thermometer (Fluke MT4 MAX, Fortive Corporation, Everett, WA, USA) was used to measure the canopy temperature for TIR data calibration. For each plot, five 1 m × 1 m quadrats were selected, and the average temperature from three measurements was taken as the temperature for the quadrat; the GPS coordinates of the central point were recorded.

2.4. ET Estimation Methods

2.4.1. TSEB-PT

The TSEB model was proposed by Norman in 1995 and has been proven to be capable of evaluating ET at various scales. Based on the classic dual-source Shuttleworth-Wallace (S-W) model for sparse vegetation conditions, the Priestley–aylor (P–T) approach was employed to separate the canopy and soil temperature components. It simplifies the five complex resistance parameters of the S-W model into two components, i.e., total canopy boundary layer resistance and soil surface resistance. In this study, the TSEB model refers specifically to TSEB-PT. The core temperature decomposition process is detailed in Equations (8)–(11). For further detailed calculation processes, refer to [33,43,44].

$$T_{\mathrm{c}}=T_{\mathrm{a}}+{\displaystyle \frac{R_{\mathrm{nc}}{r}_{\mathrm{ah}}}{\rho C_{\mathrm{p}}}}\left[1-a_{\mathrm{c}}{f}_{\mathrm{g}}{\displaystyle \frac{\Delta }{\Delta +\gamma }}\right]$$

(8)

$$T_{\mathrm{s}}={\left({\displaystyle \frac{T_{\mathrm{rad}}^4\left(\theta \right)\epsilon -f_{\mathrm{c}}\left(\theta \right){\epsilon }_{\mathrm{c}}{T}_{\mathrm{c}}^4}{\left[1-f_{\mathrm{c}}\left(\theta \right)\right]{\epsilon }_{\mathrm{s}}}}\right)}^{1/4}$$

(9)

$$L{E}_{\mathrm{c}}=a_{\mathrm{c}}{f}_{\mathrm{g}}{\displaystyle \frac{\Delta }{\Delta +\gamma }}{R}_{\mathrm{nc}}$$

(10)

where T_rad(θ) represents the radiated temperature within the sensor’s field of view, K. f_c(θ) represents the crop coverage in the sensor’s field of view. r_ah represents the turbulent aerodynamic impedance of the canopy. a_c is the index of vegetation in the P–T model, where the initial value is generally considered to be 1.26 when there is no water shortage. f_g represents the coverage of green vegetation. Δ represents the slope of the curve of saturated vapor pressure versus temperature. γ represents the hygrometer constant and is generally taken to be 0.06.

In the original TSEB-PT model, soil heat flux (G) is calculated as a fixed proportion of the current net radiation (Rn), which, specifically, is 35% (c_g = 0.35). However, the diurnal variation of G was not synchronous with Rn, displaying a significant lag effect. Thus, the fixed value of ratio G/Rn could not truly reflect the flux exchange process. In order to calculate the energy fluxes of each component more accurately, a cosine diurnal variation model of G/Rn was constructed in the following form based on the correction model commonly used in the previous studies [34,45].

$${\displaystyle \frac{G}{Rn}}={\left({\displaystyle \frac{G}{Rn}}\right)}_{\mathrm{d}}\cdot \cos \left(\omega \left(t-t_{\mathrm{d}}\right)\right)$$

(11)

where G and Rn represent the instantaneous soil heat flux and net radiation, respectively, in W/m². (G/Rn)_d represents the amplitude of the constructed cosine function, which is taken as the maximum value of G/Rn during the day. ω represents a period empirical parameter, set as π/12. t and t_d represent the current time and the time corresponding to the maximum G/Rn value, respectively.

2.4.2. SEBAL

The Surface Energy Balance Algorithm for Land (SEBAL) is a widely used single-source model for field scale ET estimation using remote sensing data. The SEBAL model is established on the principle of surface energy balance and assumes the canopy and surface background as a whole. Visible, multispectral, and TIR data from satellites or UAVs are integrated to retrieve parameters such as surface albedo and temperature. These parameters are further combined with meteorological monitoring data to estimate the components of the energy balance equation. For further details on the calculation process, refer to [46,47,48,49].

The iterative solution of H using the Monin–Obukhov similarity theory is the core step in SEBAL, as shown in Figure 5. The SEBAL model assumes that at the “hot (dry) point”, the energy is entirely used to heat the surface (H ≈ Rn − G), and the LE is approximately 0. At the “cold (wet) point”, all available energy is fully utilized for evaporation (LE ≈ Rn − G), and H is approximately 0.

2.4.3. Single-Crop Coefficient Method

Since water supply in rice paddies is generally sufficient, the single-crop coefficient method [50], which considers only atmospheric stress and crop status, was applied for ET estimation. ET could be calculated by multiplying the crop coefficients (Kc) of different growth stages with the Eto, which was calculated from meteorological monitoring data [51]. Due to the lack of long-term observation data at the experimental station, the Kc values of rice used in this study were based on calibration values from the nearby Kunshan Rice Irrigation Experimental Station (31°15′15″N, 120°57′43″E) in Jiangsu Province, China. The calibrated Kc values for the sequential growth stages of rice were 1.05, 1.60, and 1.15, respectively [52,53].

2.5. Calibration and Downscaling of Thermal Infrared Data

Since the canopy TIR temperature extracted from the original images was generally higher than the temperature measured on the ground, in this study, linear regression correction was performed on the original TIR data using the ground-measured data. Additionally, to ensure that the resolution of the calibrated TIR images matched the vegetation indices calculated from multispectral images (TIR data resolutions of 30, 70, and 140 mm/pixel at 20 m, 50 m, and 100 m altitudes, respectively, while the corresponding multispectral resolutions were 10, 20, and 50 mm/pixel, respectively), a statistical downscaling method based on the correlation between the NDVI and TIR was further performed [54,55,56].

As shown in Figure 6, it was assumed that there is a linear relationship between NDVI and TIR temperature within a certain range, where pixels with higher NDVI values (pure vegetation) correspond to lower temperatures. Threshold segmentation combined with visual interpretation based on NDVI was applied for pure rice and background distinguishing. The downscaling process was as follows. (1) The high resolution NDVI map was aggregated to the coarser resolution of the TIR image. (2) The linear relationship was established by obtaining the corresponding temperature and NDVI values for different backgrounds. (3) The established relationship was applied to the original TIR image for downscaling.

2.6. Evaluation Metrics

The coefficient of determination (R²), root mean square error (RMSE), and relative root mean square error (rRMSE) were employed in this study to evaluate the accuracy of the model simulation and estimation results.

$$R^2={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left(E_i-M_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(\overline{M}-M_i\right)}^2}}}$$

(12)

$$RMSE=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{(E_i-M_i)}^2}}{n}}}$$

(13)

$$rRMSE={\displaystyle \frac{RMSE}{\overline{M}}}\times 100\%$$

(14)

where E_i and M_i represent the model estimation results and practical measured results, respectively. $\overline{E}$ and $\overline{M}$ represent the average values of the model estimation results and the practical measured results, respectively. n represents the number of samples.

3. Results

3.1. Characteristics of Energy Distribution and ET in Rice Paddies

3.1.1. Energy Flux Diurnal Variation Under Typical Clear-Sky Conditions Across Growth Stages

Figure 7 illustrates the diurnal variations in net radiation (Rn), sensible heat flux (H), latent heat flux (LE), and soil heat flux (G) on a typical clear day at different growth stages.

Table 4. Statistical values of daily energy flux at different growth stages (W/m²).

Date		31 July	24 August	1 September	17 September
DOY		212	236	244	260
Rn	Peak Value	762.90	682.50	666.70	638.50
	Peak Time	12:00	12:00	11:30	11:30
	Average	194.64	157.18	149.66	129.53
H	Peak Value	80.10	86.00	52.01	88.58
	Peak Time	12:30	12:30	12:00	12:30
	Average	0.63	13.11	2.32	14.03
LE	Peak Value	484.31	495.70	445.56	345.54
	Peak Time	12:30	12:00	12:00	12:00
	Average	133.38	120.05	107.88	99.06
G	Peak Value	151.76	124.27	136.52	112.20
	Peak Time	13:00	13:00	13:00	13:00
	Average	31.03	22.02	17.69	16.95

presents the daily peak values, peak times, and daily averages of each flux component at different growth stages. Combined with Figure 6 and Table 4, it was found that the diurnal trends in H, LE, and G were generally consistent with Rn, exhibiting a single-peak pattern with various degrees of lag effects. Among these energy flux components, Rn dominated the energy input and diurnal variation. It was generally negative before sunrise, while it rapidly increased after sunrise and reached its maximum value at noon (12:00 in July and August and 11:30 in September). After midday, it gradually dropped to a stable negative value after sunset. As the growth stage proceeded, both the daily peak value and the daily average value of Rn decreased, ranging, respectively, from 762.90 W/m² and 194.64 W/m² at the end of the tillering stage to 638.50 W/m² and 129.53 W/m² at the milking stage.

LE represents the energy consumed during the phase change of liquid water to vapor via evaporation and transpiration, which is directly related to the ET in paddy fields. Unlike the other fluxes, LE remained positive throughout the day (ranging from approximately 20 W/m² to 500 W/m²) and accounted for more than 60% of Rn during the energy peak hours, emphasizing LE or ET as the primary energy consumption in flooded paddy fields. This was attributed to the ample water content in the paddy, which resulted in a large portion of radiative energy being used for the upward transport of water vapor from both the canopy and the underlying surface.

For H, since the paddy field simultaneously experiences the processes of absorbing and releasing energy, its diurnal variation also changed from negative to positive and then back to negative. The peak value of H (about 80 W/m²) was significantly less than that of LE in the paddy field, which was opposite that in the field of dryland crops due to the difference in water supply. The lag effect of H was more noticeable than that of LE, generally achieving the peak value 0.5 h later than Rn.

G reflects the energy stored in and released from the soil–water surface system. Due to the increase in specific heat capacity caused by water surface coverage, both the transformation from negative to positive and from positive to negative in the diurnal variation process of G occurred later (1–1.5 h later), leading to difficulty in energy closure. Meanwhile, since the difference between Rn and G is usually regarded as the available energy, an accurate estimation of G is also important for further LE and ET calculation.

3.1.2. Energy Balance Characteristics and Enforcing Closure Correction

The energy balance ratio (EBR) was used to evaluate the energy flux closure in rice paddies at different growth stages and is defined as the ratio of turbulent fluxes (LE + H) to available energy (Rn − G). Figure 8 shows the diurnal variation trend in the calculated EBR values. It could be observed that the EBR of the late tillering stage showed the smallest variation, while the EBR during the other three growth stages exhibited larger fluctuations.

The EBR remained relatively stable during the daytime (between 7:30 and 16:00), with values of 0.73, 0.79, 0.74, and 0.87 for the four growth stages, respectively, indicating a relatively high degree of energy closure. However, the EBR fluctuated significantly around sunrise (6:00) and sunset (18:00). These fluctuations were mainly attributed to the differences in the observation heights of various fluxes in the EC system, as well as the evident lag effect between the diurnal variation of LE, H, G, and Rn.

Due to sufficient water supply in the paddy, LE constituted the major portion of turbulent flux. The calculated evaporative fraction (EF) values for the four observation periods were 0.90, 0.91, 0.91, and 0.86, respectively. Figure 9 illustrates the comparison of energy fluxes before and after the EF enforcing closure. Both the corrected latent heat flux (LE*) and sensible heat flux (H*) increased compared with those before correction. The R² between LE* and LE was 0.8308, and that between H* and H was 0.9079, indicating a better consistency for H compared to LE. The scatter plot of available energy (Rn − G) against the corrected turbulent flux (LE* + H*) for different growth stages obtained an R² value of 0.9559, further suggesting that the EF forced closure method was effective in correcting LE and H.

3.1.3. Field Scale ET Estimated Based on Flux Data and Single-Crop Coefficient Method

The field scale ET results in comparison to the daily measured ET (ET_m), the constant evaporation fraction upscaling method (ET_EC), and the single-crop coefficient method (ET_Kc) are shown in

Table 5. Comparison between measured ET and estimated values.

DOY	Time	LE* (W/m2)	ETECh (mm/d)	ETEC (mm/d)	AEEC (mm/d)	ETKc (mm/d)	AEKc (mm/d)	ETm (mm/d)
212	9:30	337.10	6.92	6.84	−0.40	9.23	1.99	7.24
	11:00	445.10	6.92
	12:30	580.20	6.92
	14:00	518.65	6.51
	15:30	342.42	6.92
236	9:30	438.98	5.60	5.55	−1.03	7.48	0.90	6.58
	11:00	492.07	5.43
	12:30	515.96	5.60
	14:00	335.38	5.54
	15:30	181.19	5.60
244	9:30	371.38	5.27	5.26	−1.07	7.57	1.24	6.33
	11:00	580.99	5.32
	12:30	496.92	5.09
	14:00	359.22	5.32
	15:30	119.83	5.32
260	9:30	381.03	4.22	4.42	−1.74	5.54	−0.62	6.16
	11:00	458.95	4.65
	12:30	448.34	4.69
	14:00	207.25	4.41
	15:30	123.35	4.13

Note: LE* represents the latent heat flux after closure correction, W/m². ET_ECh represents the instantaneous ET, while ET_EC is the average of the ET_ECh values across all observation times, mm/d. ET_Kc and ET_m represent the ET values estimated using the single-crop coefficient method and field measurements, respectively, mm/d. AE_EC and AE_Kc represent the absolute error of estimated ET values with measured ET_m values, respectively, in mm/d.

.

The ET_m peaked at 7.24 mm/d at the tillering stage and gradually decreased to 6.16 mm/d by the milking stage as the growth period progressed. The ET_EC values were consistently lower than ET_m, with values of 6.84, 5.55, 5.26, and 4.42 mm/d, respectively. The discrepancy between ET_EC and ET_m increased throughout the growth stages, aligning with previous studies that concluded that the EC method tends to underestimate LE and ET [37,38]. At five different observation times during the day, though LE accounted for the majority of turbulent fluxes, the EF exhibited a decrease at first before increasing as H peaked in the afternoon. Since the daily available energy (Rn − G) remained constant throughout the day, ET_EC, which was calculated during times with higher EF values, was also higher.

The ET_Kc values estimated using the single-crop coefficient method were higher than the ET_m values during all growth stages except the milking stage. ET_Kc at the tillering stage had the largest overestimation of ET, which was 1.99 mm/d higher. This difference could mainly be attributed to the Kc values obtained. According to the division of rice growth stages, DOY 212, 236, and 244 were classified as peak growth periods with maximum Kc values, while DOY 260 was marked as a transition to the maturing growth stage, with a slightly reduced Kc value. During the experimental period, frequent rainfall might also have caused the actual Kc value to deviate from empirical values, leading to differences between ET_Kc and ET_m. This deviation also indicated that relying on the Kc values of other sites has a certain degree of limitation. Even in relatively close regions with consistent climate types, environmental factors such as the soil’s stratified texture and farming methods may cause changes in Kc, further illustrating the limitations of the application of the single-crop coefficient method.

3.2. Effect of UAV Flight Strategy on Canopy Temperature Difference Identification Capability

3.2.1. Effect of Flight Altitudes on the Identification of Temperature Difference

Table 6. Thermal infrared temperature of rice canopy at different flight altitudes.

Growth Stage	Altitude (m)	W1N1	W1N2	W1N3	W2N1	W2N2	W2N3
Tillering	20	34.53 ± 0.54 abA	34.14 ± 0.75 bcA	33.41 ± 0.47 dA	35.05 ± 0.96 aA	33.61 ± 0.36 cdB	33.23 ± 0.51 dA
	50	34.06 ± 0.41 bB	33.58 ± 0.19 cB	33.51 ± 0.30 cA	34.59 ± 0.52 aAB	34.50 ± 0.24 aA	33.43 ± 0.30 cA
	100	33.78 ± 0.43 aB	32.78 ± 0.24 cC	32.91 ± 0.44 bcB	34.04 ± 0.74 aB	33.26 ± 0.25 bC	32.38 ± 0.26 dB
Jointing–booting	20	32.49 ± 1.10 aB	31.33 ± 0.35 cA	31.83 ± 0.52 abcA	32.49 ± 0.49 aA	32.14 ± 1.02 abA	31.51 ± 0.25 bcA
	50	31.83 ± 0.56 abA	30.53 ± 0.24 bcB	30.68 ± 0.45 bcB	31.57 ± 0.44 aB	30.80 ± 0.24 bB	30.43 ± 0.34 cC
	100	31.36 ± 0.40 aA	31.42 ± 0.52 bA	31.43 ± 0.48 bA	32.08 ± 0.70 aA	31.59 ± 0.66 abA	30.80 ± 0.32 dB
Heading–flowering	20	29.68 ± 1.36 abA	28.93 ± 0.67 cdA	27.68 ± 0.27 eA	30.22 ± 0.55 aA	29.29 ± 0.52 bcA	28.37 ± 0.21 dB
	50	29.04 ± 0.76 bcA	27.92 ± 0.23 dB	27.79 ± 0.18 eA	29.72 ± 0.50 aA	29.11 ± 0.59 bA	28.36 ± 0.16 cdB
	100	28.72 ± 1.10 bcA	28.71 ± 0.27 cA	28.25 ± 0.24 dB	29.73 ± 0.56 aA	29.19 ± 0.52 bA	28.63 ± 0.18 cdA
Milking	20	31.84 ± 0.24 aA	31.24 ± 0.35 bA	31.02 ± 0.12 bA	31.65 ± 0.31 aA	31.60 ± 0.57 aA	31.07 ± 0.27 bA
	50	31.53 ± 0.22 aB	30.78 ± 0.42 bB	30.15 ± 0.30 cB	31.17 ± 0.48 abB	31.13 ± 0.76 abB	30.23 ± 0.27 cB
	100	30.99 ± 0.36 aC	30.45 ± 0.37 bcB	30.83 ± 0.55 abA	30.81 ± 0.45 abB	30.84 ± 0.48 abB	30.27 ± 0.24 cB

Note: The temperature units in the table are in °C. Lowercase letters (a–e) indicate significant temperature differences (p < 0.05) among different treatments at the same flight altitudes, while uppercase letters (A–C) indicate significant temperature differences (p < 0.05) at different altitudes for the same treatment.

shows a comparison of thermal infrared (TIR) temperature obtained under flight altitudes of 20 m, 50 m, and 100 m at different growth stages (at 11:00 am). Two-way ANOVA was used to describe the differences between flight altitude and treatments. Generally, the retrieved TIR temperature showed a decreasing trend with increasing nitrogen application levels (N3 < N2 < N1), and the TIR temperature under shallow frequent irrigation was lower than that under controlled irrigation (W1 < W2).

In addition, the observed TIR temperature of the canopy showed a decreasing trend with the increase in flight altitude. At 20 m, high resolution imagery (30 mm/pixel) captured detailed canopy heterogeneity but masked treatment differences. While, at 50 m (70 mm/pixel), spatial averaging reduced noise while preserving critical contrasts. Conversely, 100 m flights (140 mm/pixel) further obscured variations, particularly under high nitrogen (N3), where temperature differences between irrigation treatments became statistically insignificant. This phenomenon was mainly a result of the resolution of the image decreasing with the increase in flight altitude; the mixed element effect was thus aggravated. Meanwhile, the image resolutions at 50 m and 100 m were consistent with the structure and temperature heterogeneity of the canopy, making it more capable of identifying temperature differences among the treatments compared with the 20 m altitude.

As the growth stage progressed, the temperature differences between nitrogen treatments could still be observed at all three flight altitudes, and the differences under W1 were more evident than under W2. However, the temperature differences between irrigation treatments could be better distinguished only at 50 m and 100 m. Thus, considering both the ground resolution and the capacity to distinguish these differences, a flight altitude of 50 m was recommended as the optimal altitude for obtaining canopy TIR temperatures.

3.2.2. Effect of Flight Times on the Identification of Temperature Difference

Table 7. Thermal infrared temperature of rice canopy at different observation times.

Growth Stage	Time (hh:mm)	W1N1	W1N2	W1N3	W2N1	W2N2	W2N3
Tillering	9:30	32.75 ± 0.36 aD	31.66 ± 0.43 aD	30.80 ± 0.19 cC	32.61 ± 0.68 bD	31.17 ± 0.25 cD	31.76 ± 0.85 bD
	11:00	34.06 ± 0.41 bC	33.58 ± 0.19 cC	33.51 ± 0.30 cB	34.59 ± 0.52 aC	34.50 ± 0.24 aBC	33.43 ± 0.30 cC
	12:30	36.80 ± 0.77 abA	35.82 ± 0.34 cA	34.84 ± 0.36 dA	37.29 ± 0.95 aA	36.22 ± 0.70 bcA	35.09 ± 0.53 dA
	14:00	35.97 ± 0.98 aB	34.87 ± 0.40 bB	33.32 ± 0.30 cB	35.64 ± 1.03 aB	34.69 ± 0.52 bB	33.91 ± 0.54 cBC
	15:30	35.78 ± 0.93 aB	34.90 ± 0.30 bB	33.26 ± 0.20 dB	35.12 ± 0.89 bBC	34.27 ± 0.30 cC	34.31 ± 0.24 cB
Jointing–booting	9:30	31.03 ± 0.46 bC	30.15 ± 0.18 dD	30.86 ± 0.85 bB	31.63 ± 0.43 aC	30.6 ± 0.23 bcD	30.22 ± 0.18 cC
	11:00	31.36 ± 0.40 aC	30.53 ± 0.24 bcC	30.68 ± 0.45 bcC	31.57 ± 0.44 aC	30.80 ± 0.24 bD	30.43 ± 0.34 cC
	12:30	33.06 ± 0.90 bA	31.26 ± 0.34 dB	32.49 ± 1.22 bcA	33.91 ± 1.02 aA	32.07 ± 0.28 cB	30.89 ± 0.29 dB
	14:00	33.38 ± 0.70 bA	31.65 ± 0.30 dA	32.57 ± 0.92 cA	34.01 ± 0.64 aA	32.53 ± 0.16 cA	31.40 ± 0.19 dA
	15:30	32.27 ± 0.78 aB	31.67 ± 0.16 bA	31.53 ± 0.23 bB	32.27 ± 0.40 aB	31.78 ± 0.18 bC	30.95 ± 0.26 cB
Heading–flowering	9:30	27.81 ± 0.91 bD	26.75 ± 0.27 dE	26.59 ± 0.18 dC	28.47 ± 0.39 aD	27.85 ± 0.71 bD	27.61 ± 0.41 bD
	11:00	28.72 ± 1.10 bcBC	27.92 ± 0.23 dC	27.79 ± 0.18 eB	29.72 ± 0.50 aC	29.11 ± 0.59 bC	28.36 ± 0.16 cdC
	12:30	30.43 ± 1.05 cA	29.37 ± 0.33 dA	29.04 ± 0.25 dA	31.99 ± 1.02 aA	31.17 ± 0.98 bA	30.38 ± 0.23 cA
	14:00	29.09 ± 0.91 cB	28.36 ± 0.15 dB	27.71 ± 0.26 eB	30.60 ± 0.76 aB	29.99 ± 0.94 bB	29.27 ± 0.30 cB
	15:30	28.12 ± 0.66 bcC	27.62 ± 0.18 cD	26.92 ± 0.70 dC	29.65 ± 0.50 aC	29.16 ± 0.92 aC	28.18 ± 0.21 bC
Milking	9:30	29.70 ± 0.20 aD	29.32 ± 0.39 bD	29.02 ± 0.21 dC	29.58 ± 0.27 abD	29.60 ± 0.49 abD	29.53 ± 0.20 abD
	11:00	31.53 ± 0.22 aA	30.78 ± 0.42 bA	30.15 ± 0.30 cB	31.17 ± 0.48 abAB	31.13 ± 0.76 abA	30.23 ± 0.27 cAB
	12:30	31.77 ± 0.45 aA	31.01 ± 0.26 bA	30.59 ± 0.25 cA	31.50 ± 0.53 aA	31.04 ± 0.45 bAB	30.36 ± 0.20 cA
	14:00	31.17 ± 0.39 aB	30.74 ± 0.13 bcA	30.22 ± 0.31 dB	31.04 ± 0.41 abB	30.66 ± 0.18 cB	29.84 ± 0.68 eC
	15:30	30.70 ± 0.34 aC	30.13 ± 0.46 cB	30.02 ± 0.26 cB	30.52 ± 0.33 abC	30.26 ± 0.29 bcC	30.00 ± 0.29 cBC

Note: The temperature units in the table are in °C. Lowercase letters (a–e) indicate significant temperature differences (p < 0.05) among different treatments at the same observation times, while uppercase letters (A–E) indicate significant temperature differences (p < 0.05) at different observation times for the same treatment.

shows a comparison of the TIR temperature obtained at the times of 9:30, 11:00, 12:30, 14:00, and 15:30 at the different growth stages (under a flight altitude of 50 m). Two-way ANOVA was used to describe the differences between observation times and treatments. Consistent with the previous section, the canopy TIR temperature generally decreased as the nitrogen application level increased.

In particular, the capacity to distinguish differences in canopy TIR temperature varied relatively significantly across different observation times. At the tillering stage, morning observations (at 9:30 and 11:00) were optimal for differentiating between irrigation treatments, with higher temperatures observed in W2. However, although the average temperature under W2 remained higher than that under W1, there was no significant difference around midday (12:30 and 14:00) when high solar radiation dominated. This might be due to the relatively low crop coverage at this stage, resulting in a larger proportion of exposed soil background. Since the specific heat capacity of water is greater than that of soil, W1 treatment with a water layer covering showed a slower warming rate compared to W2 treatment.

As the canopy developed, the canopy TIR difference between the irrigation and nitrogen treatments was still observed during the morning time, up until the milking stage. Thus, it could be concluded that the morning observation time was optimal for TIR data collection in paddy fields.

3.3. Evaluation of TSEB for ET Estimation in Rice Paddies

3.3.1. Adapting the TSEB Model Based on Prior Energy Flux Characteristics

As shown in Figure 10, the ratio of G to Rn (G/Rn) in paddy fields first increases and then decreases on a typical day at each growth stage. According to the variation pattern of G/Rn during the daytime (7:30–16:00), the maximum value was taken as the amplitude, and the corresponding time was taken as the phase parameter. The parameters for each growth stage in the constructed diurnal variation function (Equation (11)) were listed in

Table 8. Calculated results of soil heat flux based on the cosine diurnal variation model.

Growth Stage	DOY	(G/Rn)d	td	rRMSE (%)	R2
Tillering	212	0.22	13	5.55	0.9298
Jointing–booting	236	0.20		16.28	0.9368
Heading–flowering	244	0.21		7.79	0.9767
Milking	260	0.18		8.71	0.9215

with the corresponding simulation accuracy.

The R² values of the G/Rn fit were all above 0.90 with rRMSE values of less than 10% during most growth stages, indicating that the cosine relationship constructed based on prior knowledge can better describe the daily variation process of G/Rn, thereby improving the estimation accuracy of G in the TSEB model.

3.3.2. Energy Flux and ET Estimated Using the TSEB Model

By integrating canopy TIR and multispectral images obtained from the UAVs with ground meterological factors, the TSEB model was used to estimate the energy flux values at five observation times (9:30, 11:00, 12:30, 14:00, and 15:30) throughout the four growth stages. As shown in Figure 11, the average estimated flux values of the W1N2 treatment at a flight altitude of 50 m were compared with the flux values monitored by the eddy covariance system in order to evaluate the estimation accuracy of the TSEB model.

The results indicate that the TSEB model could generally obtain satisfactory accuracy over most conditions, while there was a slight overestimation and underestimation when the energy flux was relatively lower and higher, respectively. For Rn − G, the TSEB model achieved an R² of 0.8501, with RMSE and rRMSE values of 71.35 W/m² and 16.52%, respectively. Since the available energy and turbulent flux are fully balanced in the TSEB model, the simulated LE + H was equal to Rn − G and also showed good agreement with the calibrated LE* + H* values, reaching an R² of 0.8659. The estimation accuracy for LE was slightly lower but still had an R² value of 0.7503, with RMSE and rRMSE values of 74.15 W/m² and 19.63%. These results indicated that the modified TSEB model could effectively capture the energy flux variations in paddy fields.

The constant EF method was also used to calculate daily ET values based on the simulated LE flux (Figure 11d). It was found that the estimated daily ET values based on instantaneous EF had good consistency at most growth stages, especially during the jointing–booting stage and the heading–flowering stage. However, at the milking stage, the EF varied from 0.82 to 0.97, resulting in the fluctuation range of ET reaching 4.99–5.96 mm/d. The average ET values estimated by the TSEB model at the four growth stages were 6.92 mm/d, 6.01 mm/d, 5.79 mm/d, and 5.53 mm/d, respectively, which showed a slightly better accuracy compared to the ET_EC values but still lower than the practical ET_m (in Section 3.1.3). This result could be attributed to the fact that the TSEB model introduced real-time EF and empirical theoretical Rn, leading to higher daily ET values.

As illustrated in Figure 12, the TSEB model effectively described the spatial and temporal distribution of ET and revealed differences under different treatments. During the tillering stage, due to the relatively poor development of rice under the N1 treatment, ET values in the corresponding plots showed significant differences compared to the N2 and N3 treatments, being 0.10 mm/d (0.50 mm/d lower than those under W1 treatment) and 0.19 mm/d (0.89 mm/d lower than those under W2 treatment). As the rice entered the jointing–booting stage and the heading–flowering stage, the value of ET gradually decreased, and the ET under N1 and N2 treatments gradually approached that of N3 treatment. After the milking stage, the canopy began to senesce gradually; along with decreasing temperature and radiation energy, the ET differences between treatments further diminished.

4. Discussion

4.1. Accuracy Comparison of the TSEB and SEBAL Models on Energy Flux Estimation at Different Resolutions

As introduced in Section 2.4, the single-source SEBAL model is also a commonly used algorithm for field scale ET estimation, which considers the crop canopy and soil–water background as an integrated unit [57]. In contrast, the dual-source TSEB model based on the P–T model separately considers the energy balance processes of canopy and background, theoretically providing better mechanistic accuracy than the SEBAL model. Therefore, this section focuses on discussing the accuracy of the TSEB and SEBAL models for energy flux estimation in the rice paddies. Specifically, based on UAV multispectral and TIR data with different resolutions obtained at flight altitudes of 20 m (10 mm/pixel), 50 m (20 mm/pixel), and 100 m (50 mm/pixel), the accuracy of the TSEB and SEBAL models on Rn−G, LE + H, and LE simulations were compared at five observation times across four growth stages (4 × 5, totaling 20 sets).

The results presented in Figure 13 illustrate that the estimation accuracy of TSEB for each energy flux is higher than that of the SEBAL model. When the measured flux was, respectively, lower and higher, the SEBAL model performed a similar overestimate and underestimate, but with a larger error. Taking the estimated Rn − G as an example, the TSEB model could achieve R² values of 0.7537, 0.8659, and 0.7489, with rRMSE values of 20.27%, 16.42%, and 20.32%, respectively, corresponding to 20 m, 50 m, and 100 m flight altitudes. Meanwhile, the SEBAL model achieved R² values of only 0.4897, 0.5038, and 0.4705, with rRMSE values of only 26.17%, 25.69%, and 26.43%, respectively.

For both the TSEB and SEBAL models, the flux estimation accuracy obtained at a flight altitude of 50 m was significantly higher than that of the other altitudes. The above results were consistent with the conclusions drawn by Li [58] for the effect of spatial resolution on the accuracy of energy balance models, which indicated that the multispectral and TIR resolution obtained at a flight altitude of 50 m could better match the spatial heterogeneity scale of the field. Additionally, the absolute error boxplot of the TSEB model was more compact than that of the SEBAL model. These results were also consistent with those of a previous study in arid areas [59], indicating that the simulation accuracy of the TSEB model for energy flux was higher than that of the SEBAL model. However, it is worth noting that according to the study on the input errors’ sensitivity of the TSEB and SEBAL models [60], when facing the influence of TIR data errors, the TSEB model was more sensitive compared to the SEBAL model, highlighting the necessity of optimizing the TIR data acquisition strategy. Furthermore, the TSEB model was also sensitive to the accuracy of crop coverage input, especially under high vegetation coverage scenarios. In this study, the vegetation coverage at different growth stages was achieved based on NDVI threshold segmentation combined with visual interpretation. However, the relationship between NDVI and LAI or crop coverage exhibited an earlier supersaturation phenomenon [61], which may underestimate the coverage at the heading–flowering and milking stages, thereby introducing errors to underestimate the ET value at this period (TSEB underestimated 0.54 and 0.63 mm/d to the measured value for these two stages). For future research, vegetation indices, such as NIRv [62], that still have a good relationship between LAI and crop coverage in high coverage scenarios are recommended, or a hybrid method based on the radiative transport model can be adopted for inversion to reduce input error.

Supernumerary ET mapping of the entire study is shown in Figure 14 and Figure 15 (taking DOY 212 as an example), which are ET maps under different flight altitudes at 11:00 and different observation times at 50 m altitude, respectively.

4.2. ET Assessment of Rice Paddies Under Different Treatments Based on the TSEB Model

The above results indicated that the TSEB model could be applied to estimate energy flux in rice paddies; therefore, further estimations of ET under other treatments in the experimental area were conducted.

Table 9. Comparison of ET estimated using the TSEB model and practical measurements.

Treatment	Field ID	Tillering		Jointing–Booting		Heading–Flowering		Milking
		ETm	ETTSEB	ETm	ETTSEB	ETm	ETTSEB	ETm	ETTSEB
W1N1	1#	6.98	6.79	6.49	6.02	6.22	5.65	5.88	4.97
W1N1	9#	7.04	6.86	6.35	6.09	6.31	5.81	5.72	5.12
W1N2	3#	7.24	6.93	6.58	6.06	6.33	5.73	6.16	4.99
W1N3	4#	7.27	6.99	6.66	6.03	6.48	5.72	6.55	5.33
W1N3	10#	8.21	7.66	6.85	6.28	6.62	5.88	6.48	5.54
W2N1	2#	/	6.59	/	5.92	/	5.61	/	4.98
W2N1	8#	/	6.73	/	5.87	/	5.78	/	5.18
W2N2	5#	/	6.85	/	5.93	/	5.57	/	4.98
W2N3	6#	/	7.54	/	6.24	/	5.63	/	5.17
W2N3	7#	/	7.55	/	6.21	/	5.71	/	5.25

Note: ET_m and ET_TSEB represent measured ET values of water balance and those estimated by the TESB model, respectively, measured in mm/d.

presents a comparison of the TSEB-estimated ET_TSEB and the measured ET_m value.

Under the same irrigation schedule, the measured ET_m increased with nitrogen application levels. Specifically, during the tillering stage, the average ET_m of the W1N3 treatment was 7.74 mm/d, which was 0.73 mm/d and 0.50 mm/d higher than that of the W1N1 and W1N2 treatments, respectively. After entering the next two growth stages, the daily ET_m of each treatment decreased, and the differences between nitrogen levels also gradually diminished, ranging from 6.42 to 6.76 mm/d and from 6.27 to 6.55 mm/d, respectively. Daily ET_m values further declined at the milking stage, with W1N1 showing the largest reduction and W1N3 demonstrating the smallest reduction.

Compared with ET_m, the TSEB model generally showed good accuracy under the W1 irrigation schedule, but the simulated values were consistently lower than the measured values. Taking the tillering stage as an example, the average ET_TSEB values of W1N1, W1N2, and W1N3 were 0.19 mm/d, 0.31 mm/d, and 0.41 mm/d lower than the measured values, respectively, and the absolute error increased with the nitrogen application levels. As the growth stage progressed, the discrepancy between the ET_TSEB and ET_m values increased, reaching 0.75 mm/d, 1.17 mm/d, and 1.08 mm/d at the milking stage for W1N1, W1N2, and W1N3, respectively. This phenomenon could be attributed to the fact that the vegetation coverage of N2 and N3 tended to be rapidly saturated after the tillering stage, and the treatments with higher nitrogen application levels had larger ET values [56]. As a result, the discrepancy of physiological and biochemical processes among the treatments may not be accurately described in the TSEB model, where the energy balance was sensitive to the crop coverage, resulting in large deviations. Meanwhile, in the high coverage scenario, the TSEB model might underestimate the impedance within each transfer process due to the simplification of impedance calculations [62], thereby increasing the H flux and obtaining a relatively small LE flux value.

For the W2 irrigation schedule without a water layer, the TSEB estimation results showed that the ET_TSEB value of the W2 treatment was lower than that of the W1 treatment, and the difference showed a decreasing trend as the growth stage progressed. Specifically, under the N1 treatment, the daily average ET_TSEB value of W2N1 was 0.17 mm/d, 0.16 mm/d, 0.04 mm/d, and −0.03 mm/d lower than that of W1N1 during the four growth stages, respectively. It should be illustrated that since the soil moisture content of the W2 treatment had not been measured once a day, the ET calculation cannot be carried out based on the changes in effective moist layer depth and moisture content. We will supplement the measurement of soil moisture content in future studies to verify the accuracy of the TSEB model on ET estimation for paddy fields with no water layer but sufficient water supply.

5. Conclusions

In this study, we systematically investigated the diurnal variation of energy fluxes in rice paddies under clear-sky conditions. By introducing prior energy flux constraints, the adapted TSEB model was evaluated for estimating energy flux components and field scale ET. The main conclusions are as follows:

(1)

The process of energy flux variation in rice paddies was dominated by Rn under typical clear-sky conditions with a single-peak diurnal pattern. The G/Rn ratio during the daytime can be accurately described by the constructed cosine diurnal variation model (R² > 0.90), which effectively improved the fixed proportion calculation method of G in the original TSEB model.

(2)

The canopy TIR temperature gradually decreased with increasing altitudes but was consistently higher than the ground-measured values. Observations made at an altitude of 50 m at 11:00 am were more capable of effectively distinguishing temperature differences between treatments.

(3)

The TSEB model enabled the accurate simulation of energy flux and field scale ET in rice paddies, with R² values of 0.8501 and 0.7503 for Rn − G and LE, respectively, with an absolute error ranging from −0.32 to −0.83 mm/d for ET. Comparisons with the SEBAL model further indicated that the TSEB model had a higher accuracy at different observation times and spatial resolutions.

The techniques and results presented in this study could be valuable for paddy field scale ET monitoring, which could assist further water stress detection and irrigation management strategies.