Optimal Selection of Empirical Reference Evapotranspiration Method in 36 Different Agricultural Zones of China

Abstract

The Food and Agriculture Organization has proposed the current version of the Penman–Monteith method (FAO56-PM) as the standard for calculating reference evapotranspiration (ET₀); however, high meteorological data requirements limit its application in many areas. There is thus an urgent need to identify the best alternative empirical method to accurately calculate ET₀ in regions that lack sufficient meteorological data. In this study, three temperature-based methods and five radiation-based methods were evaluated using ET₀ values generated using the FAO56-PM method in 36 agricultural zones in China based on meteorological data from 823 stations, measured between 2011 and 2020. The results showed that the optimal temperature-based method and radiation-based method differed for different agricultural zones, and no one temperature method or radiation method could be suitable for all agricultural zones. The eight empirical methods were regionally calibrated to improve the ET₀ calculation accuracy in the different zones. The relationship between the optimal methods and climatic conditions showed that the most reliable empirical method could be selected according to the local annual mean temperature and aridity index. The results provide useful guidance for the selection of reliable empirical ET₀ methods in agricultural zones outside China.

1. Introduction

Evapotranspiration (ET) is one of the most important components of the hydrological cycle, directing approximately 60% of the precipitated water on land back to the atmosphere [1]. Accurate estimations of actual evapotranspiration (ET_a) are highly significant for many fields, such as agronomy, hydrology, climatology, meteorology, ecology, and environmental science [2]. However, direct observations of ET_a remain unavailable in many locations worldwide [3,4], and several methods have been proposed to estimate ET_a in these areas [5]. For example, the product of the reference crop evapotranspiration (ET₀) and crop coefficient is a widely used method worldwide for estimating ET_a [3,6,7,8], and it has been recommended by the Food and Agriculture Organization (FAO) [9] for computing crop water requirements. Accurate ET₀ calculation is a prerequisite for obtaining ET_a and is the fundamental basis for irrigation water requirements and optimizing irrigation schedules, crop quality, and productivity [2,10]. ET₀ also represents ET from a hypothetical reference surface and has been used to express the evaporative demand of the atmosphere [11]. The temporal and spatial variations of ET₀ have also attracted extensive research attention with regard to climate change [12,13].

The ET₀ term was first proposed by the FAO to represent evapotranspiration from a defined vegetated surface [14]. Several methods have since been developed to calculate ET₀ and can be generally classified into three categories: (1) temperature-based methods, (2) radiation-based methods, and (3) combination methods [5,15]. The FAO paper No. 24 by Doorenbos and Pruitt (1977) recommended several methods for calculating ET₀ that provided users with the freedom to match the data to a given method. However, many users expressed dissatisfaction with the ET₀ selection and the differences between the results obtained using different methods [16]. The FAO paper No. 56 by Allen et al. [9] defined the reference surface as a hypothetical grass reference crop with an assumed crop height of 0.12 m, fixed surface resistance of 70 s·m⁻¹, and albedo of 0.23, and recommended the sole use of the Penman–Monteith (FAO56-PM) method to calculate ET₀. The FAO56-PM approach has hence become the standard method for calculating ET₀ in different climate regions worldwide [2,15].

However, the FAO56-PM method requires a large number of weather variables (e.g., air temperature, relative humidity, wind speed, solar radiation) that are not measured in many meteorological stations, especially in developing areas [15,17]. Most studies have concluded that the ET₀ values obtained using combined methods are more consistent with the FAO56-PM method than those from temperature-based or radiation-based methods [18,19,20]. However, this does not solve the problem of how to select a reliable method in data-deficient regions, because the meteorological data requirements of the combined methods are similar to those of the FAO56-PM method. The application of the FAO56-PM method and the combined methods to calculate ET₀ is therefore limited in many regions due to insufficient meteorological data, and other simpler empirical methods based on temperature or radiation are still widely used [21,22,23]. Several studies have evaluated the performance of these ET₀ methods under different climate conditions to verify their accuracy and assist in the process by which the optimal empirical method is selected. The performances of empirical ET₀ methods based on radiation or temperature have been shown to vary in different climate zones. For example, Valle Júnior et al. [24] reported that the De Bruin–Keijman method and Priestley–Taylor method were better for calculating ET₀ in a Brazilian savannah than other radiation-based methods, whereas Pandey et al. [25] reported that the Irmak method and Turc method were the two best radiation-based methods for the northeastern region of India. Tabari et al. [26] found that the Blaney–Criddle method performed better than other temperature-based methods in humid areas of Iran, whereas Bourletsikas et al. [20] reported that the Hargreaves method was the best temperature-based method for grass-covered areas in a Mediterranean forest in Greece. As many ET₀ methods have been developed for specific hydroclimatic conditions, it is highly recommended to evaluate and calibrate these methods when used in climate zones beyond their calibration zones [27,28]. Furthermore, the concept of ET₀ was mainly developed on the basis of the concept of potential evapotranspiration (PET) [2,5]. In the review paper by McMahon et al. (2016), PET is defined as ‘the upper limit of evaporation under constant meteorological and surface temperature conditions from a surface (vegetation, bare soil, or open water) that is saturated and of such extent to negate effects of local advection’, and ET₀ represents evapotranspiration from a defined vegetated surface [5]. This has led to confusion regarding the use of the two concepts and thus resulted in the simultaneous evaluation of PET methods together with ET₀ methods. For example, several studies have evaluated the Penman, Priestley–Taylor, and Turc methods in the context of calculating ET₀ [20,24,29,30]; however, such methods should be used to calculate PET rather than ET₀ [2,5,31].

The weather and climate vary substantially across China, owing to the country’s vast size. In recent years, several studies in China have evaluated different ET₀ methods at specific experimental sites [19,32,33,34] and specific climate regions in China [35,36,37]. On a national scale, Peng et al. [38] evaluated 10 ET₀ methods in seven climate regions in China, and Yang et al. [39] evaluated six ET₀ methods in four climate regions in China. Due to the country’s vast climatic differences, the division of its area into four or seven climate zones is insufficient to distinguish its climate differences. Sensitivity analysis showed significant spatial differences within each of the four defined climatic zones in terms of the dominant meteorological factors that affect ET₀ [40]. Song et al. [41] accordingly divided Northeast China, which is mostly characterized by a temperate monsoon climate, into eight sub-regions. The evaluation of 11 ET₀ methods showed that the optimal choice of empirical method significantly differed between the different sub-regions, even within the same climate zone. Furthermore, due to the confusion regarding the mutual use of PET and ET₀, many PET methods have been used in the above-mentioned studies for comparative evaluation with ET₀ methods in China. It is therefore necessary to evaluate the ET₀ methods, while excluding PET methods, in more detailed area divisions in China to appropriately recommend the most suitable temperature-based/radiation-based methods for the different climate zones.

To systematically address these issues, the objectives of this study are as follows: (1) to evaluate eight empirical ET₀ methods with values obtained using the FAO56-PM method in 36 different agricultural zones in China; (2) to recommend the most reliable empirical ET₀ method in the different agricultural zones; and (3) to calibrate the ET₀ methods in the agricultural climate zones.

2. Materials and Methods

2.1. Study Area

China can be divided into 10 zones on the basis of temperature, or 4 regions on the basis of aridity/humidity. The total area can be further divided into 38 agricultural zones (Figure 1). The boundaries of the 38 agricultural zones are provided by the Resource and Environment Science and Data Center (https://www.resdc.cn/, accessed on 26 November 2020). The two agricultural zones in Taiwan are not considered due to insufficient data availability; thus, 36 agricultural zones are discussed in this study. The code, location, annual mean precipitation, air temperature, ET₀, and aridity index [42] (2011–2020) of the 38 total agricultural zones are listed in

Table 1. Agricultural zones in China and their meteorological conditions (2011–2020).

Temperature Zone	Arid/Humid Region	Code	Location	NMS	Ta (°C)	P (mm)	ET0 (mm)	AI
Cold temperate zone	Humid	CT-HU-1	Northern Greater Hinggan Mountains	5	−1.8	521	568	0.77
Mid temperate zone	Humid	MT-HU-1	Lesser Hinggan Mountains–Changbai Mountains	36	4.9	694	741	0.79
Mid temperate zone	Humid	MT-HU-2	Sanjiang Plain	4	3.8	558	639	0.72
Mid temperate zone	Semi-humid	MT-SH-1	Songliao Plain	39	5.4	567	826	0.58
Mid temperate zone	Semi-arid	MT-SA-1	Eastern Inner Mongolia	26	4.2	385	890	0.37
Mid temperate zone	Semi-arid	MT-SA-2	Northwestern of Northern Xinjiang	9	5.4	209	865	0.21
Mid temperate zone	Semi-arid	MT-SA-3	Western of Northern Xinjiang	5	6.8	263	681	0.33
Mid temperate zone	Arid	MT-AR-1	Northern Xinjiang	15	7.1	178	959	0.16
Mid temperate zone	Arid	MT-AR-2	Central Inner Mongolia	26	7.2	242	1012	0.20
Mid temperate zone	Arid	MT-AR-3	Western Inner Mongolia	6	8.9	73	755	0.08
Warm temperate zone	Humid	WT-HU-1	Liaodong Peninsula	14	10.1	604	872	0.58
Warm temperate zone	Humid	WT-HU-2	Shandong Peninsula	13	13.2	701	1003	0.59
Warm temperate zone	Semi-humid	WT-SH-1	North China Mountains	41	10.4	518	973	0.45
Warm temperate zone	Semi-humid	WT-SH-2	North China Plain	50	14.3	667	986	0.58
Warm temperate zone	Semi-humid	WT-SH-3	Loess Plateau	34	10.8	568	925	0.52
Warm temperate zone	Semi-arid	WT-SA-1	Qinghai	11	4.9	432	810	0.45
Warm temperate zone	Arid	WT-AR-1	Southern Xinjiang	35	10.4	97	1026	0.08
Warm temperate zone	Arid	WT-AR-2	Hexi Corridor	21	8.3	171	1013	0.15
Warm temperate zone	Arid	WT-AR-3	Qaidam Basin	13	3.5	144	791	0.15
Plateau cold zone	Semi-arid	PC-SA-1	Southern Qiangtang	13	0.1	385	734	0.44
Plateau cold zone	Arid	PC-AR-1	Northern Qiangtang	1	5.1	71	743	0.08
Plateau temperate zone	Semi-humid	PT-SH-1	Western Sichuan–Eastern Tibetan	38	6.1	640	838	0.65
Plateau temperate zone	Semi-arid	PT-SA-1	Southern flank of Himalayas	6	4.9	352	899	0.33
Plateau temperate zone	Arid	PT-AR-1	Western Tibetan	2	3.1	118	1042	0.10
North subtropical zone	Humid	NS-HU-1	Upper and middle Han River	25	15.3	910	922	0.85
North subtropical zone	Humid	NS-HU-2	Middle and lower reaches of the Yangtze River	58	16.7	1278	951	1.15
Mid subtropical zone	Humid	MS-HU-1	Southern Tibetan	3	6.4	397	683	0.49
Mid subtropical zone	Humid	MS-HU-2	Yunnan Plateau	31	15.3	890	1026	0.75
Mid subtropical zone	Humid	MS-HU-3	Guizhou Plateau	50	16.3	1197	842	1.23
Mid subtropical zone	Humid	MS-HU-4	Sichuan Basin	22	17.3	1081	834	1.11
Mid subtropical zone	Humid	MS-HU-5	Jiangnan hilly region	103	18.6	1617	953	1.46
South subtropical zone	Humid	SS-HU-1	Southern Yunnan Mountain	8	19.5	930	1020	0.79
South subtropical zone	Humid	SS-HU-2	Fujian and Guangdong hilly region	46	22.1	1618	1049	1.34
South subtropical zone	Humid	SS-HU-3	Northern Taiwan	0	-	-	-	-
North tropical zone	Humid	NT-HU-1	Southern Yunnan valley	6	20.3	1409	1000	1.24
North tropical zone	Humid	NT-HU-2	Leizhou Peninsula and Northern Hainan	2	23.6	1622	1193	1.17
North tropical zone	Humid	NT-HU-3	Southern Taiwan	0	-	-	-	-
Mid tropical zone	Humid	MP-HU-1	Southern Hainan	6	24.4	1816	1085	1.45

Note. NMS, number of meteorological stations; P, annual mean precipitation; T_a, annual mean air temperature; ET₀, annual reference evapotranspiration; AI, aridity index, the ratio of annual mean precipitation to the annual mean potential evapotranspiration calculated by the Penman method (see Supplementary Materials).

.

2.2. Data Collection

Daily meteorological data collected from 823 stations were obtained from the China Meteorological Administration (http://data.cma.cn/, accessed on 19 March 2021). The variables measured by the meteorological stations include air temperature (°C), relative humidity (%) at 2 m height, wind speed at 10 m height (m·s⁻¹), and sunshine duration (h). The wind speed at 2 m height, radiations, and other variables required for calculating ET₀ by using various methods were estimated following the procedure described in the FAO paper No. 56 [9] (seen in the Supplementary Materials). Chinese meteorological stations began observations in the 1950s; however, in the early stages, the observation variables measured at certain meteorological stations were incomplete and there are thus numerous missing periods in the early data records. Although ET analysis ideally requires a 30-year timeline, evaluation of ET₀ methods can be completed on a smaller timeline [17,18,19,20,21]. To include as many meteorological stations as possible, the research period in this study was restricted to 2011–2020. The daily ET₀ values were calculated from the daily meteorological data and then processed into annual values.

2.3. Selected ET₀ Methods

A total of eight empirical ET₀ methods were selected, comprising two categories: three temperature-based methods and five radiation-based methods. The three temperature-based methods are the FAO24 Blaney–Criddle (FAO24-BC), Hargreaves–Samani (H-S), and Valiantzas temperature (V-T) methods. The five radiation-based methods are the FAO24 radiation (FAO24-R), Jensen–Haise (J-H), Jones–Ritchie (J-R), and Irmak and Valiantzas radiation (V-R) methods. The equations of the eight empirical ET₀ methods and the FAO56-PM method are briefly presented in

Table 2. Reference evapotranspiration (ET₀) models selected for this study.

Category	No.	Models	Equation	Reference
Temperature-based	1	FAO-24 Blaney–Criddle (FAO24-BC)	$E{T}_0 = a_0 + b_{0}p(0.46T_a + 8.13)$	[43]
	2	Hargreaves–Samani (H-S)	$E{T}_{\mathrm{o}} = 0.0023R_a(T_a + 17.8){\left(T_{\max } - T_{\min }\right)}^{0.5}/\lambda$	[44]
	3	Valiantzas temperature (V-T)	$\begin{array}{l}E{T}_{\mathrm{o}}\approx 0.00668R_a{[(T_{max} - T_{dew})(T_a + 9.5)]}^{0.5} - 0.0696(T_{max} - T_{dew})\\ -0.024(T_a + 20)(1 - RH/100) - 0.00455R_a{(T_{max} - T_{dew})}^{0.5}\\ +0.0984(T_a + 17)(1.03 + 0.00055T_d^2 - RH/100)\end{array}$	[45]
Radiation-based	4	FAO24 radiation (FAO24-R)	$E{T}_{\mathrm{o}} = b\left(\frac{\Delta }{\Delta + \gamma }{R}_s\right)/\lambda - 0.3$	[43]
	5	Jensen–Haise (J-H)	$E{T}_0 = \frac{C_T(T_a - T_x)R_s}{\lambda }$ $C_T = 1/\left[\left(38 - (2H/305)\right) + 7.3 \times 5/(e_2 - e_1)\right]$ $T_x = -2.5 - 1.4(e_2 - e_1) - H/550$	[31]
	6	Jones–Ritchie (J-R)	$E{T}_0 = {\alpha }_1[3.87 \times {10}^{-3}\cdot R_s(0.6T_{\max } + 0.4T_{\min } + 29)]$ ${\alpha }_1 = \left\{\begin{array}{ll}1.1\hfill & 5 < T_{\max } < 35\hfill \\ 1.1 + 0.05(T_{\max } - 35)\hfill & T_{\max } > 35\hfill \\ 0.01\exp [0.18(T_{\max } + 20)]\hfill & T_{\max } < 5\hfill \end{array}\right.$	[26]
	7	Irmak	$E{T}_{\mathrm{o}} = -0.611 + 0.149R_s + 0.079T_a$	[46]
	8	Valiantzas radiation (V-R)	$\begin{array}{l}E{T}_{\mathrm{o}}\approx 0.0393R_s{(T_a + 9.5)}^{0.5} - 0.19R_s^{0.6}{\phi }^{0.15}\\ +0.0061(T_a + 20){\left(1.12T_a - T_{\min } - 2\right)}^{0.7}\end{array}$	[47]
Standard	9	FAO56 Penman–Monteith (FAO56-PM)	$E{T}_0 = \frac{0.408\Delta \left(R_n - G\right) + \gamma u_2\frac{900}{T_a + 273}(e_s - e_a)}{\Delta + \gamma (1 + 0.34u_2)}$	[9]

Note. ET₀, reference evapotranspiration (mm·day⁻¹); $T_a$ average daily air temperature (℃); $T_{max}$ maximum temperature (℃); $T_{min}$ minimum temperature (℃); $T_d = T_{\max } - T_{\min }$; $u_2$, wind speed at 2 m (m·s⁻¹); $RH$, relative humidity (%); $R{H}_{min}$, minimum relative humidity (%); H, elevation (m); $e_s$, saturation vapor pressure (kPa); $e_a$, actual vapor pressure (kPa); $e_2$, saturation vapor pressure (kPa) at the maximum temperature; $e_1$, saturation vapor pressure (kPa) at the minimum temperatures; $\Delta$, slope of the vapor pressure curve (kPa·℃⁻¹); $R_a$, extraterrestrial radiation (MJ·m⁻²·day⁻¹), which is a function of the station latitude and Julian day; $R_s$, incident solar radiation (MJ·m⁻²·day⁻¹); $R_n$, net radiation (MJ·m⁻²·day⁻¹); $G$, soil heat flux density (MJ·m⁻²·day⁻¹), which can be neglected at a daily time step; $\lambda$, latent heat of vaporization (MJ·kg⁻¹); $\gamma$, psychrometric constant (kPa·℃⁻¹); N, hours of sunshine duration (h); p, percentage of annual daylight hours for any day of the year; $p = N_j/({\displaystyle \sum _{i = 1}^{365}{N}_i}) \times 100$; $a_0 = 0.0043R{H}_{min} - n/N - 1.41$; $b_0 = 0.82 - 0.0041R{H}_{min} + 1.07n/N + 0.066u_2 - 0.006R{H}_{min}\cdot n/N - 0.0006R{H}_{min}\cdot u_2$; $b = 1.066 - 0.13 \times {10}^{-2}RH + 0.045u_2 - 0.20 \times {10}^{-3}RH{u}_2 - 0.135 \times {10}^{-4}R{H}^2 - 0.11 \times {10}^{-2}{u}_2^2$.

, and detailed information can be found in the references listed therein.

2.4. Calibration Method

Allen et al. [9] recommended using linear regression to calibrate the empirical ET₀ methods using the ET₀ values obtained by the FAO56-PM method, and this calibration method has been widely adopted worldwide [35,38,39,48,49,50]. The calibration process uses the following expression:

$$E{T}_{FAO56-PM} = a\cdot E{T}_0 + b$$

(1)

where $E{T}_{FAO56-PM}$ is the ET₀ value calculated by the FAO56-PM method, ET₀ is the ET₀ value calculated by one of the eight empirical ET₀ methods, and a and b are the calibrated coefficients.

2.5. Evaluation Criteria and Statistical Analysis

Statistical indices were used to quantitatively analyze the ET₀ modeling performance. The ET₀ values calculated using the eight methods and standard ET₀ values calculated using the FAO56-PM method were compared using a series of statistical criteria as follows:

$$R^2 = {\left[\mathrm{cov}\left(E{T}_0,E{T}_{FAO56-PM}\right)/\sigma E{T}_0\sigma E{T}_{FAO56-PM}\right]}^2$$

(2)

$$MAE = \frac{1}{n}{\displaystyle \sum _{i = 1}^n\left|E{T}_{0,i}-E{T}_{FAO56-PM,i}\right|}$$

(3)

$$RMSE = \sqrt{\frac{{\displaystyle \sum _{i = 1}^n{\left(E{T}_{0,i}-E{T}_{FAO56-PM,i}\right)}^2}}{n}}$$

(4)

$$NSE = 1 - \frac{{\displaystyle \sum _{i = 1}^n{\left(E{T}_{0,i} - E{T}_{FAO56-PM,i}\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(E{T}_{FAO56-PM,i} - \overline{E{T}_{FAO56-PM,i}}\right)}^2}}$$

(5)

where R², MAE, RMSE, and NSE are the coefficient of determination, mean absolute error (mm·day⁻¹), root mean square error (mm·day⁻¹), and Nash–Sutcliffe efficiency, respectively. n is the number of statistical days, and cov and σ are the covariance and standard deviation, respectively. R² values range from 0 to 1, MAE and RMSE values range from 0 to ∞, and NSE values range from −∞ to 1. The perfect fit method is obtained when NSE and R² are equal to 1, and MAE and RMSE are equal to 0.

Statistical analysis was conducted both for the overall time periods and for each individual month. The analysis was first carried out at each meteorological station, and the average statistical index values of all of the meteorological stations were taken as the statistical indices in the different agricultural zones.

To select the optimal temperature-based or radiation-based empirical ET₀ method in each agricultural zone, referring to the method presented by Silva et al. [51], the following performance index was used to rank the performances of the empirical methods:

$$PI = R^2\cdot NSE$$

(6)

where PI is the performance index of the empirical method. Higher PI values reflect better performance, and when PI < 0, the method is not recommended for calculating the daily ET₀.

The classical statistics of the mean ($\overline{X}$) and coefficient of variation (CV) were obtained according to:

$$\overline{X} = \frac{1}{n}{\displaystyle \sum _{i = 1}^n{X}_i}$$

(7)

$$s = \sqrt{\frac{1}{n - 1}{\displaystyle \sum _{i = 1}^n{\left(X_i - \overline{X}\right)}^2}}$$

(8)

$$CV = s/\overline{X}$$

(9)

3. Results

3.1. ET₀ Values Calculated Using the FAO56-PM and Empirical Methods

The results obtained using the FAO56-PM method indicated that the area-averaged annual mean ET₀ in China between 2011 and 2020 was approximately 893.0 mm. The ET₀ values calculated using the eight evaluated empirical methods showed large discrepancies with the FAO56-PM values, and the CV of annual mean ET₀ values calculated using the nine total methods was 0.14. The maximum and minimum calculated annual mean ET₀ values were obtained using the FAO24-R method and J-H method, respectively, yielding values of 1160.5 and 782.1 mm (Figure 2).

The zones with the highest ET₀ values calculated using the FAO56-PM method were located on Hainan Island and its nearby areas (NT-HU-2 and MP-HU-1), whereas the lowest ET₀ values were obtained from two zones in Northeast China (CT-HU-1 and MT-HU-2) and one zone in Northern Xinjiang (MT-SA-3) (Figure 3a). The CV values of the annual mean ET₀ from the nine total methods exhibited spatial differences across the different agricultural zones (Figure 3b). South China was the region with the lowest CV, indicating minor variability of the annual mean ET₀ values calculated using the different methods. The agricultural zones PC-SA-1 and PT-AR-1 in the Tibet Plateau and CT-HU-1 in Northeast China showed high CV values, indicating substantial variations in the annual mean ET₀ values calculated using the different methods. The above results indicate that there were differences among the ET₀ values calculated using the eight empirical methods and the FAO56-PM method, and the differences exhibited spatial variability in the different agricultural zones. This highlights the need to evaluate the applicability of each method to effectively select the optimal empirical method for each agricultural zone.

3.2. Statistical Criteria of Temperature-Based Methods

During the study period, the mean R² values of the daily ET₀ calculated using the FAO24-BC, H-S, and V-T methods versus the daily ET₀ calculated using FAO56-PM in 36 agricultural zones were 0.95, 0.85, and 0.89, respectively; the mean MAE values were 0.79, 0.58, and 0.57 mm·day⁻¹, respectively; the mean RMSE values were 0.96, 0.76, and 0.72 mm·day⁻¹, respectively; and the mean NSE values were 0.56, 0.73, and 0.75, respectively (Figure 4). Of the three temperature-based ET₀ methods, the FAO24-BC method showed the highest R² in all 36 agricultural zones, followed by the H-S and V-T methods, but the other three statistical indexes showed spatial differences (Figure 5). The agricultural zones where the FAO24-BC method had the lowest MAE, the lowest RMSE, and the highest NSE were mainly located in Southeast China. The agricultural zones that produced the lowest MAE and RMSE and highest NSE values were mainly located in (1) Southeastern China using the FAO24-BC method, (2) the Tibet Plateau and surrounding areas using the H-S method, and (3) North China and Northeastern China using the V-T method.

A comparison of the monthly results indicates that the NSE values obtained using the temperature-based methods and FAO56-PM method showed different seasonality features in the different agricultural zones (Figure 6). The obtained NSE values were greater than 0 in all 12 months in only three zones using the FAO24-BC method (SS-HU-2, NT-HU-2, and MP-HU-1), one zone using the H-S method (NT-HU-2), and six zones using the V-C method (NS-HU-1, NS-HU-2, MS-HU-3, MS-HU-5, SS-HU-2, and NT-HU-2). The NSE values obtained for WT-AR-1, the driest zone in China, with the smallest AI (Table 1), were less than 0 in all months using the three temperature-based methods, with the exception of March using the H-S method. Similarly, the NSE values obtained for CT-HU-1, the coldest zone in China, with the lowest annual temperature (Table 1), were generally less than 0, except for April using the three temperature-based methods, as well as March using the H-S method. The daily ET₀ obtained using the three temperature-based methods and FAO56-PM method showed that the colder and drier months or zones yielded smaller R² and larger MAE and RMSE values (Figures S1–S3). Therefore, the ET₀ calculated using the temperature-based methods showed larger errors in the cold and dry months or zones. The monthly statistics showed that the V-T method performed better in South China, the FAO24-BC method performed better in North China, and the H-S method only performed better in March and April in some agricultural zones in Northeast China.

3.3. Statistical Criteria of Radiation-Based Methods

During the study period, the mean R² values of the daily ET₀ calculated by the FAO24-R, J-H, J-R, Irmak, and V-R methods against the daily ET₀ calculated by FAO56-PM in all 36 agricultural zones were 0.95, 0.88, 0.92, 0.92, and 0.93, respectively; the mean MAE values were 0.91, 0.95, 0.46, 0.49, and 0.50 mm·day⁻¹, respectively; the mean RMSE values were 1.14, 1.16, 0.58, 0.62, and 0.63 mm·day⁻¹, respectively; and the mean NSE values were 0.35, 0.37, 0.85, 0.84, and 0.81, respectively (Figure 4). Of the five radiation-based ET₀ methods, the FAO24-R method showed the highest R² in almost all agricultural zones, except for PT-SH-1, MS-HU-1, SS-HU-1, and NT-HU-1, where the Irmak method yielded the highest R² (Figure 5). The lowest MAE and RMSE and highest NSE values obtained using the five radiation-based ET₀ methods showed a similar spatial distribution, and were mainly obtained in (1) North China and the northern Tibet Plateau using the J-R method, (2) South China and the southern Tibet Plateau using the Irmak method, and (3) the northern and mid tropical zones, three zones in Northeast China, and one zone in Northern Xinjiang using the V-R method. The FAO24-R and J-H methods did not show the lowest MAE and RMSE or highest NSE values in any of the investigated agricultural zones.

Figure 7 shows the monthly variation in the NSE values obtained using the five radiation-based methods, and Figures S4–S6 show the monthly variation in the R², MAE, and RMSE values. Similar to the temperature-based methods, some of the NSE values obtained using the five radiation-based methods were less than 0, particularly in arid and cold months or zones. The monthly statistics indicated that the J-R, Irmak, and V-R methods significantly outperformed the FAO24-R and J-H methods. Among these, the J-R method performed slightly better in the Tibet Plateau, and there was no significant performance difference between the Irmak and V-R methods, which performed better in the remaining regions of China.

3.4. Recommended Empirical Methods in Different Agricultural Zones

The temperature-based and radiation-based methods for empirical ET₀ calculation were ranked separately using the evaluation indexes in Equation (5). Figure 8 shows the highest and lowest performances of the temperature-based/radiation-based methods in 36 agricultural zones of China. Among the temperature-based methods, the H-S method was the optimal choice to calculate daily ET₀ in the Tibet Plateau and its surrounding areas. For the remaining regions in China, the FAO24-BC and V-T methods were the most recommended methods for the south and north, respectively. In contrast, the H-S method showed the lowest performance among the three temperature-based methods in South China, and the FAO24-BC method showed the lowest performance in North China, including the Tibet Plateau, and even was not recommended for calculating the daily ET₀ in CT-HU-1 and two zones in the Tibet Plateau.

Among the radiation-based methods, the Irmak method was the optimal choice to calculate the daily ET₀ in South China, including the southern Tibet Plateau, and the J-R method was the optimal choice in North China, including the northern Tibet Plateau. The V-R method was the most recommended method in the north and mid tropical zones, two zones in Central China, three zones in Northeast China, and two zones in Xinjiang. In contrast, the J-H method showed the lowest performance among the five radiation-based methods in most zones, and even was not recommended for calculating the daily ET₀ in PT-SH-1 and NT-HU-1. The FAO24-R method showed the lowest performance in the Tibet Plateau and two zones in Northern Xinjiang, and was not recommended for calculating the daily ET₀ in some zones in the Tibet Plateau. The Irmak method showed the lowest performance in CT-HU-1.

A cross-comparison of the two categories showed that the highest performance of the radiation-based methods was better than that of the performance of the temperature-based methods in most zones. The recommended temperature-based methods only outperformed the radiation-based methods in three zones (MT-AR-3, NT-HU-2, and MP-HU-1). The lowest performances of the temperature-based methods were worse than those of the radiation-based methods in the northernmost and southernmost zones, and the lowest performances of the radiation-based methods were worse in the remaining zones.

The recommended temperature-based/radiation-based methods for calculating daily ET₀ values in each month and zone in China are listed in

Table 3. The most recommended temperature-based/radiation-based reference evapotranspiration methods for each month in the 36 investigated agricultural zones of China.

Zones	Months
	1	2	3	4	5	6	7	8	9	10	11	12
CT-HU-1	0/0	0/0	2/4	2/7	0/7	0/7	0/7	0/8	0/7	2/0	0/0	0/0
MT-HU-1	0/0	0/0	2/7	1/7	1/8	3/7	3/7	3/7	3/8	3/7	2/4	0/0
MT-HU-2	0/0	0/4	2/7	1/7	3/8	3/8	3/7	3/8	3/8	3/7	2/4	0/0
MT-SH-1	0/0	0/4	2/7	1/6	3/6	3/8	3/7	3/7	3/7	3/7	2/4	0/0
MT-SA-1	0/0	0/4	2/7	1/6	1/6	3/6	3/8	3/7	3/7	3/7	0/4	0/0
MT-SA-2	0/0	0/0	2/7	3/6	3/6	3/6	3/6	2/7	3/7	3/7	2/0	0/0
MT-SA-3	0/0	2/0	2/7	2/7	2/8	2/8	2/8	2/7	2/7	3/7	2/0	0/0
MT-AR-1	0/0	0/0	2/7	3/6	3/6	3/6	3/6	3/6	3/7	3/7	2/0	0/0
MT-AR-2	0/0	0/0	2/7	1/6	3/6	3/6	3/6	3/6	3/7	3/7	2/0	0/0
MT-AR-3	0/4	0/0	3/6	1/0	3/0	3/0	3/0	3/6	3/6	1/6	0/0	0/0
WT-HU-1	0/0	0/0	3/7	1/6	3/6	1/8	1/8	3/8	3/7	3/7	3/4	0/0
WT-HU-2	0/0	3/0	1/7	1/7	1/6	1/8	1/8	1/8	3/7	3/7	3/0	0/0
WT-SH-1	0/0	0/0	1/7	1/6	1/6	2/8	3/8	3/7	3/7	3/7	3/0	0/0
WT-SH-2	0/0	3/7	1/7	1/7	3/6	3/8	1/8	1/8	3/7	3/7	3/7	3/0
WT-SH-3	0/0	2/7	3/7	1/7	1/6	1/8	1/8	1/7	1/7	3/7	3/0	0/0
WT-SA-1	0/0	2/0	2/7	2/7	1/6	1/6	1/7	1/7	3/7	2/7	2/0	0/0
WT-AR-1	0/0	0/0	2/7	0/6	0/6	0/6	0/8	0/7	0/7	0/7	2/0	0/0
WT-AR-2	0/0	2/0	3/6	1/6	3/6	3/6	3/6	3/6	3/7	3/7	2/0	0/0
WT-AR-3	0/0	0/0	0/7	3/6	1/6	1/6	2/6	2/6	1/7	2/7	0/0	0/0
PC-SA-1	0/0	0/0	0/0	0/7	3/6	3/6	3/6	3/6	3/7	0/7	0/0	0/0
PC-AR-1	0/0	2/0	3/7	1/6	1/6	3/6	3/6	3/6	3/6	3/7	2/0	2/0
PT-SH-1	0/0	0/0	2/7	2/7	1/6	1/6	1/7	1/7	1/7	2/7	0/0	0/0
PT-SA-1	0/0	0/0	0/7	3/6	3/6	1/6	3/7	3/7	3/7	2/7	0/7	0/0
PT-AR-1	0/0	0/0	0/7	0/6	3/6	1/6	1/6	1/6	1/6	3/6	0/0	0/0
NS-HU-1	3/0	3/7	1/7	1/7	1/7	1/7	1/8	1/7	1/8	3/7	3/7	3/0
NS-HU-2	3/0	3/7	1/7	1/7	1/8	1/8	1/8	1/8	1/8	3/8	3/8	3/0
MS-HU-1	0/0	0/7	0/7	2/7	2/6	1/6	3/6	3/7	2/7	2/7	0/7	0/0
MS-HU-2	3/7	3/7	1/7	1/6	1/6	1/8	1/7	1/7	1/7	3/7	0/0	0/0
MS-HU-3	3/0	3/7	1/7	1/7	1/7	1/8	1/7	1/7	1/8	1/7	3/7	3/0
MS-HU-4	0/0	3/7	1/7	1/7	1/7	1/8	1/8	3/8	1/8	1/8	3/6	0/0
MS-HU-5	3/7	3/7	1/7	1/7	1/8	1/8	1/8	1/8	1/8	3/7	3/8	3/0
SS-HU-1	0/0	0/7	0/7	1/8	1/8	1/8	1/8	1/8	1/8	3/8	0/0	0/0
SS-HU-2	3/7	1/7	1/6	1/8	1/8	1/8	1/8	1/8	1/8	1/7	3/8	3/7
NT-HU-1	0/0	0/7	0/7	1/7	1/7	1/8	1/8	1/8	1/8	1/8	3/0	0/0
NT-HU-2	3/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	3/7
MP-HU-1	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8	1/8

Note. 0. No recommendation; 1. FAO24-BC; 2. H-S; 3. V-T; 4. FAO24-R; 5. J-H; 6. J-R; 7. Irmak; 8. V-R. The underscore indicates that the recommended temperature-based method outperforms the radiation-based method.

. When recommending a method for each month, no empirical method was recommended for certain months in agricultural zones with extreme climatic conditions (i.e., too cold or too dry). This indicated that these empirical methods must be applied with caution for calculating daily ET₀ values during certain months in these areas.

3.5. Calibration of the Empirical Methods in Different Agricultural Zones

The coefficients in the empirical ET₀ methods can be locally calibrated using the ET₀ values from the FAO56-PM method as standard values.

Table 4. Correction coefficients, a and b in Equation (1), used to calibrate the empirical reference evapotranspiration methods in the 36 different agricultural zones of China.

Zones	Methods
	1	2	3	4	5	6	7	8
CT-HU-1	0.46/1.11	0.66/0.30	0.68/0.35	0.69/0.17	0.77/0.75	0.81/0.18	0.64/0.90	0.84/0.33
MT-HU-1	0.58/1.03	0.79/0.27	0.78/0.41	0.71/0.21	0.79/0.95	0.82/0.31	0.80/0.62	0.85/0.48
MT-HU-2	0.56/1.07	0.86/0.26	0.86/0.35	0.71/0.19	0.87/0.90	0.82/0.30	0.76/0.70	0.86/0.43
MT-SH-1	0.59/1.06	0.89/0.27	0.85/0.39	0.74/0.21	0.85/1.00	0.88/0.32	0.86/0.67	0.91/0.49
MT-SA-1	0.59/1.16	0.87/0.40	0.80/0.53	0.74/0.20	0.77/1.13	0.92/0.36	0.90/0.72	0.93/0.58
MT-SA-2	0.60/0.94	0.98/0.17	0.85/0.34	0.73/0.15	0.81/0.88	0.95/0.19	0.95/0.64	0.98/0.41
MT-SA-3	0.62/0.82	0.93/0.04	0.81/0.32	0.70/0.09	0.73/0.78	0.90/0.11	0.93/0.42	0.92/0.35
MT-AR-1	0.64/0.95	1.06/0.19	0.90/0.35	0.76/0.14	0.81/0.99	1.00/0.24	1.03/0.64	1.04/0.44
MT-AR-2	0.64/1.09	0.96/0.34	0.83/0.55	0.74/0.15	0.70/1.25	0.97/0.30	1.04/0.45	0.96/0.62
MT-AR-3	0.68/1.18	1.10/0.44	0.91/0.65	0.81/0.17	0.74/1.55	1.09/0.41	1.24/0.44	1.09/0.77
WT-HU-1	0.66/0.89	0.92/0.33	0.89/0.43	0.72/0.28	0.83/1.22	0.83/0.40	0.92/0.35	0.86/0.63
WT-HU-2	0.72/0.72	0.93/0.35	0.96/0.19	0.72/0.31	0.8/1.29	0.86/0.31	0.98/0.15	0.88/0.59
WT-SH-1	0.66/0.87	0.83/0.30	0.78/0.43	0.71/0.28	0.67/1.21	0.88/0.30	0.98/0.32	0.88/0.60
WT-SH-2	0.72/0.66	0.89/0.17	0.90/0.10	0.73/0.30	0.74/1.18	0.89/0.21	1.01/0.08	0.89/0.47
WT-SH-3	0.69/0.81	0.87/0.21	0.83/0.30	0.69/0.28	0.65/1.19	0.87/0.26	0.99/0.18	0.87/0.58
WT-SA-1	0.66/1.07	0.84/0.29	0.71/0.66	0.65/0.16	0.54/1.20	0.85/0.29	0.92/0.38	0.85/0.71
WT-AR-1	0.64/0.83	0.93/0.21	0.80/0.38	0.74/0.13	0.64/1.17	0.93/0.27	1.07/0.29	0.96/0.49
WT-AR-2	0.65/1.03	0.95/0.33	0.80/0.62	0.72/0.15	0.62/1.35	0.96/0.29	1.08/0.33	0.94/0.68
WT-AR-3	0.64/1.27	0.92/0.43	0.74/0.81	0.66/0.13	0.55/1.37	0.90/0.43	0.99/0.49	0.91/0.83
PC-SA-1	0.64/1.54	0.86/0.68	0.69/1.15	0.60/0.21	0.50/1.46	0.75/0.83	0.86/0.71	0.83/1.13
PC-AR-1	0.67/1.13	1.04/0.26	0.83/0.62	0.66/0.11	0.54/1.33	0.94/0.37	1.02/0.49	0.97/0.66
PT-SH-1	0.71/1.03	0.79/0.37	0.70/0.64	0.64/0.20	0.47/1.31	0.85/0.28	0.94/0.35	0.86/0.71
PT-SA-1	0.70/1.29	0.86/0.66	0.73/0.98	0.61/0.15	0.48/1.61	0.80/0.53	0.95/0.4	0.82/0.97
PT-AR-1	0.66/1.51	1.02/0.59	0.79/1.06	0.64/0.07	0.48/1.60	0.86/0.71	1.02/0.45	0.91/1.05
NS-HU-1	0.72/0.63	0.81/0.09	0.86/−0.04	0.69/0.39	0.62/1.13	0.83/0.24	0.98/0.01	0.84/0.51
NS-HU-2	0.77/0.56	0.93/−0.02	1.01/−0.19	0.73/0.31	0.73/1.14	0.86/0.16	1.04/−0.20	0.87/0.42
MS-HU-1	0.71/1.06	0.84/0.35	0.71/0.72	0.64/0.12	0.55/1.28	0.84/0.26	0.97/0.17	0.84/0.74
MS-HU-2	0.78/0.62	0.9/−0.04	0.91/−0.10	0.67/0.32	0.56/1.23	0.91/0.07	1.13/−0.40	0.91/0.37
MS-HU-3	0.74/0.68	0.81/0.04	0.88/−0.12	0.69/0.43	0.61/1.10	0.82/0.25	0.97/−0.04	0.81/0.58
MS-HU-4	0.75/0.61	0.85/−0.03	0.91/−0.16	0.71/0.41	0.65/1.10	0.83/0.25	1.04/−0.22	0.85/0.50
MS-HU-5	0.75/0.62	0.88/−0.08	0.98/−0.31	0.71/0.39	0.65/1.14	0.82/0.23	1.04/−0.28	0.84/0.46
SS-HU-1	0.75/0.58	0.93/−0.26	0.91/−0.13	0.67/0.39	0.56/1.20	0.86/0.09	1.20/−0.88	0.90/0.23
SS-HU-2	0.79/0.63	0.93/0.01	1.14/−0.61	0.69/0.56	0.65/1.33	0.80/0.42	1.05/−0.37	0.84/0.53
NT-HU-1	0.73/0.65	0.86/−0.20	0.86/−0.02	0.66/0.43	0.54/1.14	0.82/0.11	1.15/−0.88	0.84/0.29
NT-HU-2	0.84/0.55	1.05/−0.13	1.33/−0.81	0.69/0.55	0.70/1.34	0.79/0.41	1.07/−0.51	0.85/0.45
MP-HU-1	0.85/0.52	0.98/−0.03	1.21/−0.56	0.68/0.55	0.65/1.31	0.77/0.41	1.12/−0.75	0.84/0.41

Note. 1. FAO24-BC; 2. H-S; 3. V-T; 4. FAO24-R; 5. J-H; 6. J-R; 7. Irmak; 8. V-R.

shows the calibrated coefficients for the eight empirical methods in the 36 agricultural zones. Compared with the results obtained using the original methods, the ET₀ values calculated using the calibrated methods better fit with those of the FAO56-PM method. The NSE values from the eight calibrated methods in 36 agricultural zones ranged from 0.64 to 0.97, with a mean value of 0.90, whereas the original methods ranged from −2.03 to 0.94, with a mean value of 0.65 (Figure 9a). In all 36 agricultural zones, the NSE values obtained using the eight calibrated methods were all higher than those obtained using the original methods (Figure 9b). The MAE and RMSE values obtained using the eight calibrated methods were also all lower than those obtained using the original methods (Figure S7). The statistical criteria showed that the calibrated methods with locally calibrated coefficients could be used to more accurately calculate ET₀, with lower MAE and RMSE and higher NSE values. The regionally calibrated methods showed better improvements in the zones where the original methods performed poorly, such as in the Tibet Plateau. The original methods with poor performance (e.g., FAO24-R and J-H methods) showed substantial improvements using the local calibration.

4. Discussion

4.1. Comparison with Previous Studies

Several studies have evaluated the performance of different empirical ET₀ methods in specific climatic conditions to select the most suitable empirical method when data availability is limited. Tabari et al. [26] evaluated 31 ET₀ methods under humid conditions in Northern Iran and found that the FAO24-BC method exhibited the best performance among the temperature-based methods. Mallikarjuna et al. [52] reported that the FAO24-BC method showed more accurate ET₀ values than the H-S method under humid conditions in Southern India. Pandey et al. [25] also considered the FAO24-BC method to be a more suitable temperature-based empirical method than the H-S method for humid Northeastern India. In contrast, the H-S method outperformed the FAO24-BC method in arid regions, such as Doha airport in Qatar [53], and arid and semi-arid areas in Iran [54]. The results of this study are consistent with the previous findings: the FAO24-BC method outperformed the H-S method in the humid regions of South China, and the H-S method outperformed the FAO24-BC method in the arid regions of North China. In this study, the H-S method was the most suitable temperature-based method in the Tibet Plateau, and other studies also confirmed that this method had sufficiently high accuracy in mountainous areas of China [55] and Italy [56]. Some studies also concluded that the H-S method seems to be inaccurate in particularly windy areas [57,58].

Among the radiation-based methods, Tabari et al. [26] reported that the Irmak method performed better than the J-H method under humid conditions in Northern Iran and in other humid regions. Similar results were reported by Pandey et al. [25] in Northeastern India and by Islam and Alam [50] in Bangladesh. The FAO24-R method has been shown to outperform the J-R method in the subhumid valley rangeland of the Eastern Himalayas [59], as well as the J-H method under tropical semi-humid conditions in a Brazilian savannah [24]. The results presented here are consistent with these previous findings. The Irmak method is the recommended radiation-based method in many regions of China, such as South China and the Tibet Plateau, and the J-H method is the least recommended radiation-based method in most of the investigated areas.

4.2. Selection of Reliable Empirical Methods Based on Climatic Conditions

This study and other published reports all concluded that the optimal temperature-based/radiation-based method is sensitive to climate conditions in different regions. Figure 10a,c show the optimal temperature-based/radiation-based method for different annual mean air temperatures and AI values in the 36 investigated agricultural zones. The results show that the FAO24-BC method is the optimal temperature-based method for zones with an annual mean temperature above 12 °C and an AI value larger than 0.5, whereas the H-S and V-T methods are the optimal choices for zones with an annual mean temperature below 12 °C and an AI value smaller than 0.5. For the radiation-based methods, the J-R method is the most recommended for zones with an annual mean temperature below 12 °C and an AI value smaller than 0.75, and the Irmak and V-R methods are suitable for a wider range of climate conditions. The FAO24-R and J-H methods are not optimal methods in any agricultural zone. The relationship between the optimal methods and the climatic conditions based on 823 meteorological stations in China showed similar results based on the agricultural zones (Figure 10b,d). The results presented here can therefore provide useful guidelines for selecting reliable empirical methods in other regions.

5. Conclusions

Reference evapotranspiration (ET₀) values calculated using the FA056-PM method were applied to evaluate eight alternative methods for calculating daily ET₀ values, including three temperature-based and five radiation-based, in 36 agricultural zones in China. Both within the 36 agricultural zones and across China as a whole, the area-averaged annual ET₀ values showed large disparities between models, and the annual mean ET₀ values across China calculated using the nine total methods yielded a CV value of 0.14. The annual mean ET₀ values calculated using the different methods showed minor variability in South China, but large variability in Northeast China and the Tibet Plateau.

The H-S method was determined to be the optimal temperature-based method to calculate daily ET₀ in the agricultural zones in the Tibet Plateau and its surrounding areas. For the remaining regions of China, the FAO24-BC method was the recommended temperature-based method in the south and the V-T method was the recommended method in the north. The Irmak method was the optimal radiation-based method in South China, including the southern Tibet Plateau, whereas the J-R method was the optimal choice in North China, including the northern Tibet Plateau. The V-R method was the recommended method in the north and mid tropical zones and some agricultural zones in Xinjiang and Northeast China. The J-H method was the least recommended radiation-based method in most zones in China. The empirical methods based on temperature/radiation were also recommended separately for each month in the investigated agricultural zones. No empirical method was recommended for certain months in some agricultural zones, owing to extreme climate conditions.

The empirical methods were locally calibrated using ET₀ values calculated using the FAO56-PM method, which improved the model accuracy. The relationship between the optimal methods and climatic conditions showed that the most reliable empirical method could be selected according to the local climatic conditions.

This study makes a crucial contribution to the study of ET₀ in different agricultural zones in China (especially when the meteorological data requirements cannot be fully met) and provides valuable information for policymakers, irrigation managers, and farmers for estimating the irrigation water demand and efficient use of water resources in different agricultural zones. The outcomes of this study also provide important guidance for the selection of reliable empirical ET₀ methods based on local climatic conditions in regions outside of the study area.