Evaluation of FAO-56 Procedures for Estimating Reference Evapotranspiration Using Missing Climatic Data for a Brazilian Tropical Savanna

: The Brazilian savanna (Cerrado) has been heavily impacted by agricultural activities over the last four to ﬁve decades, and reliable estimates of reference evapotranspiration ( ET o ) are needed for water resource management and irrigation agriculture. The Penman–Monteith (PM) is one of the most accepted models for ET o estimation, but it requires many inputs that are not commonly available. Therefore, assessing the FAO guidelines to compute ET o when meteorological data are missing could lead to a better understanding of which variables are critically important for reliable estimates of ET o and how climatic variables are related to water requirements and atmospheric demands. In this study, ET o was computed for a grass-dominated part of the Cerrado from April 2010 to August 2019. We tested 12 different scenarios considering radiation, relative humidity, and/or wind speed as missing climatic data using guidelines given by the FAO. Our results presented that wind speed and actual vapor pressure do not affect ET o estimates as much as the other climatic variables; therefore, in the Cerrado’s conditions, wind speed and relative humidity measurements are less required than temperature and radiation data. When radiation data were missing, the computed ET o was overestimated compared to the benchmark. FAO procedures to estimate the net radiation presented good results during the wet season; however, during the dry season, their results were overestimated because the method could not estimate negative R n . Our results indicate that radiation data have the highest impact on ET o for our study area and presumably for regions with similar climatic conditions. In addition, those FAO procedures for estimating radiation are not suitable when radiation data are missing.


Introduction
Over the last few decades, the hydrological cycle and climate of the Brazilian savanna (locally known as Cerrado) have been heavily affected by human activities, especially by the expansion of irrigation and the replacement of native vegetation by crops [1][2][3][4][5][6]. Due to this irrigated agricultural expansion, it is important to have good management of available water resources. To handle issues involving water requirements and atmospheric demand, the United Nations Food and Agriculture Organization (FAO) recommended calculating crop evapotranspiration (ET c ) from reference evapotranspiration (ET o ) [7]. Water demands and ET c are important considerations to improve water use efficiency in agriculture [8][9][10][11][12][13].
ET o is the evapotranspiration of a defined hypothetical reference well-watered crop with a crop height of 0.12 m, a canopy resistance of 70 s.m −1 , and an albedo of 0.23 [14]. A "real" ET o value can only be obtained using lysimeters or other precision-measuring devices, which require time and are expensive [10,15,16], however, ET o can be computed from weather data, and climatic parameters are the only factors that affect ET o estimates [17,18]. The ET o estimation models available in the literature may be broadly classified as (1) fully physically based combination models that account for mass and energy conservation principles; (2) semi-physically based models that deal with either mass or energy conservation; and (3) black-box models based on artificial neural networks, empirical relationships, and fuzzy and genetic algorithms [19,20]. Several authors [21][22][23][24] have reported different methods to compute ET o , which have been tested in distinct regions and climates [6,[25][26][27][28][29]; however, the Penman-Monteith (PM) method is recommended by the FAO to calculate ET o of any region when the requisite meteorological data are available [17]. The FAO-PM method can be used globally without any regional correction and is well documented and tested, but it has a relatively high data demand [10,30,31].
For daily calculation, FAO-PM method meteorological inputs are the maximum and minimum temperatures, relative air humidity, solar radiation, and wind speed. Allen et al. [17] suggested using the Hargreaves-Samani (HS) method [22] as an alternative when only air temperature data are available. However, the HS method should be verified and compared with the FAO-PM method since it tends to overestimate ET o under high relative humidity conditions and underestimate it under conditions of high wind speed [17,[32][33][34]. FAO also recommends the pan evaporation (E pan ) method, which is related to ET o using an empirically derived pan coefficient (K p ) [17].
For many locations around the globe, there is a lack of meteorological data. In Brazil, it is possible to collect climatic data from automatic stations of the National Institute of Meteorology (INMET). Although these data are public and the stations cover a significant part of the Cerrado region, there is neither a measure of net radiation nor estimates of regional solar radiation. Several studies have evaluated the use of FAO-PM method procedures to estimate ET o when solar radiation, wind speed, and relative humidity data are missing [35][36][37][38][39][40][41]; however, results vary according to the climatic conditions. Recent studies have used machine learning models to estimate ET o [6,[42][43][44][45][46] and E pan [47][48][49] with limited weather data and satellite remote sensing to estimate global and regional real evapotranspiration [20,32], but few studies have reported the effects of meteorological data variability on ET o in the Cerrado, and no studies have addressed the impacts of missing climatic data for estimating ET o in a Brazilian tropical savanna. This research intends to close this gap in the literature.
It is important to evaluate the performance of the procedures and recommendations when ET o is obtained using missing climatic data. Knowing which meteorological data have the highest impact on ET o estimates could guide better investments in measurement instruments and provide a better understanding of the seasonal behavior of weather variables for the Cerrado region. Thus, the prime objective of this study was to assess the guidelines provided by the FAO to estimate ET o when meteorological data are limited for a grass-mixed Cerrado region and discuss the impact of each climatic variable on the ET o estimates. The outcome of this work will help inform water resource managers, irrigation engineers, and other professionals of the possible errors associated with ET o estimates and, thereby, improve water resource management in this vital region.

Micrometeorological Measurements
The measurements were conducted from April 2009 to August 2019. The measurement instruments were installed on a 20 m tall micrometeorological tower. The data collected were net radiation (Rn), solar radiation (Rs), soil heat flux (G), air temperature (Ta), relative humidity (RH), wind speed (u), soil temperature (Tsoil), soil moisture (SM), and precipitation (P). Rn and Rs were measured 5 m above the ground level using a net radiometer (NR-LITE-L25, Kipp & Zonen, Delft, The Netherlands) and a pyranometer (LI200X, LI-COR Biosciences, Inc., Lincoln, NE, USA), respectively. G was measured using a heat flux plate (HFP01-L20, Hukseflux Thermal Sensors BV, Delft, The Netherlands) installed 1.0 cm below the soil surface. SM was measured by a time-domain reflectometry probe (CS616-L50, Campbell Scientific, Inc., Logan, UT, USA) installed 20 cm below the soil surface. Tsoil was measured by a temperature probe (108 Temperature Probe, Campbell Scientific, Inc., Logan, UT, USA) installed 1 cm below the ground level. Ta and RH were measured by a thermohygrometer (HMP45AC, Vaisala Inc., Woburn, MA, USA) installed 2 m above the ground level. u was measured 10 m above the ground level using an anemometer (03101 R.M. Young Company, Traverse City, MI, USA). Precipitation was measured using a tipping bucket rainfall gauge (TR-525M, Texas

Micrometeorological Measurements
The measurements were conducted from April 2009 to August 2019. The measurement instruments were installed on a 20 m tall micrometeorological tower. The data collected were net radiation (R n ), solar radiation (R s ), soil heat flux (G), air temperature (T a ), relative humidity (RH), wind speed (u), soil temperature (T soil ), soil moisture (SM), and precipitation (P). R n and R s were measured 5 m above the ground level using a net radiometer (NR-LITE-L25, Kipp & Zonen, Delft, The Netherlands) and a pyranometer (LI200X, LI-COR Biosciences, Inc., Lincoln, NE, USA), respectively. G was measured using a heat flux plate (HFP01-L20, Hukseflux Thermal Sensors BV, Delft, The Netherlands) installed 1.0 cm below the soil surface. SM was measured by a time-domain reflectometry probe (CS616-L50, Campbell Scientific, Inc., Logan, UT, USA) installed 20 cm below the soil surface. T soil was measured by a temperature probe (108 Temperature Probe, Campbell Scientific, Inc., Logan, UT, USA) installed 1 cm below the ground level. T a and RH were measured by a thermohygrometer (HMP45AC, Vaisala Inc., Woburn, MA, USA) installed 2 m above the ground level. u was measured 10 m above the ground level using an anemometer (03101 R.M. Young Company, Traverse City, MI, USA). Precipitation was measured using a tipping bucket rainfall gauge (TR-525M, Texas Electronics, Inc., Dallas, TX, USA) installed 5 m above the ground level. We considered only data from days without gaps and measurement errors to avoid inconsistent information.

Penman-Monteith Method and FAO Procedures When Climatic Data Are Missing
The Penman-Monteith (FAO-PM) method (Equation (1)) is recommended by the Food and Agriculture Organization (FAO) as the standard method for determining reference  [17]. We considered ET o computed with the full data set as the reference (benchmark) data for comparisons.
where ET o is the reference evapotranspiration (mm.day −1 ), R n is net radiation (MJ.m −2 .day −1 ), G is the soil heat flux (MJ.m −2 .day −1 ), T a is the mean daily air temperature ( • C), u 2 is the wind speed at 2 m height (m.s −1 ), e s is the saturation water vapor pressure (kPa), e a is the actual water vapor pressure (kPa), γ is the psychrometric constant (kPA. • C −1 ), and ∆ is the slope of the water vapor pressure curve (kPa. • C −1 ). We used Equation (2) (Allen et al., 1998) to convert u to u 2 .
where u z is the measured wind speed at z m above ground surface (m.s −1 ), and z is the height of measurement above ground surface (m), which is 10 m in our study.
To test the impact of radiation, relative humidity, and wind speed data, ET o was also calculated by the FAO-PM using estimated meteorological variables, R s , u 2 , and e a , obtained by procedures given by Allen et al. [17] and compared with data collected through measurements.
The FAO recommends two different approaches to estimate R s when climatic data are missing, i.e., using temperature data or linear regression. In this study, we computed solar radiation by linear regression. R s was estimated using Equation (3).
where R s is the solar radiation (MJ.m −2 .day −1 ), n is the actual duration of sunshine (h), N is the maximum possible duration of daylight hours (h), R a is the extraterrestrial radiation (MJ.m −2 .day −1 ), and a s and b s are local regression constants. To estimate R a , we used Equation (4).
where R a is the extraterrestrial radiation (MJ.m −2 .day −1 ), G sc is the solar constant of 0.0820 MJ.m −2 .min −1 , d r is the inverse relative Earth-Sun distance, ω s is the sunset hour angle (rad), ϕ is the latitude of the meteorological station (rad), and δ is the solar decimation (rad). The values of d r and δ were computed using Equations (5) and (6).
where J is the number of the day in the year between 1 (1 January) and 365 or 366 (31 December). ω s was estimated using Equation (7).
N was estimated using Equation (8). where N is the maximum possible duration of daylight hours (h), and ω s is the sunset hour angle (rad) computed by Equation (7). An estimate of clear-sky solar radiation (R so ) (Equation (9)), net shortwave radiation (R ns ) (Equation (10)), and net longwave radiation (R nl ) is needed to estimate Rn from Rs (Equation (11)).
where R so is the clear-sky radiation (MJ.m −2 .day −1 ), a s and b s are the parameters from Equation (3), and R a is the extraterrestrial radiation (MJ.m −2 .day −1 ).
where R ns is the net shortwave radiation (MJ.m −2 .day −1 ), α is the albedo, which is 0.23 for the hypothetical grass reference crop, and R s is the solar radiation (MJ.m −2 .day −1 ) where R nl is the net longwave radiation (MJ.m −2 .day −1 ), σ is the Stefan-Boltzmann constant of 4.903 × 10 −9 MJ.K −4 .m −2 .day −1 , T max,K is the maximum absolute temperature during the 24 h period (K), T min,K is the minimum absolute temperature during the 24 h period (K), e a is the actual vapor pressure (kPa), R s is the solar radiation (MJ.m −2 .day −1 ), and R so is the clear-sky radiation (MJ.m −2 .day −1 ). R n was estimated using Equation (12).
where R n is the net radiation (MJ.m −2 .day −1 ), R ns is the net shortwave radiation (MJ.m −2 .day −1 ), and R nl is the net longwave radiation (MJ.m −2 .day −1 ). For locations for which there were no solar radiation data available or no calibration for improved estimates of a s and b s , Allen et al. [17] recommend a s = 0.25 and b s = 0.50. We calibrated a s and b s values using observed R s values from April 2009 to March 2010. Using linear regression, the values of a s and b s were, respectively, 0.192 and 0.506 (R 2 = 0.833; n = 358 observations). Estimations of R s were calculated using both the calibrated and recommended regression constants. Allen et al. [17] suggest considering daily G ≈ 0. e a was estimated using Equation (13), considering the absence of relative air humidity data.
where e a is the actual water vapor pressure (kPa), and T min is the minimum temperature ( • C). Allen et al. [17] recommend the use of the dewpoint temperature; however, when humidity data are lacking, it can be assumed that the dewpoint temperature is near the daily minimum temperature.
For estimates of wind speed at 2 m height, Allen et al. [17] suggest the use of the average of wind speed from a nearby weather station over a several-day period. Therefore, u 2 was considered a constant value estimated using the daily mean value of wind speed during the period of measurements (April 2009 to August 2019).

Hargreaves-Samani Method
The Hargreaves-Samani method [22] is recommended by the FAO to compute ET o , in mm.day −1 , when only temperature data are available.
where T mean is the mean daily temperature ( • C), T max is the maximum daily temperature ( • C), T min is the minimum daily temperature ( • C), and R a is the extraterrestrial radiation  Table 1 summarizes the calculation of ET o from April 2010 to August 2019 using limited climatic data. We computed ET o with the following scenarios of estimated data: (a) solar radiation with calibrated parameters (R s -a); (b) solar radiation with recommended parameters (R s -b); (c) relative air humidity (RH); (d) wind speed (WS); (e) R s -a and RH; (f) R s -b and RH; (g) R s -a and WS; (h) R s -b and WS; (i) RH and WS; (j) R s -a, RH, and WS; (k) R s -b, RH, and WS, and (l) using the Hargreaves-Samani method (HS).  (1)); R n (Equation (12)); a s and b s calibrated FAO-PM, no radiation data (using recommended parameters to estimate R s ) (1)); R n (Equation (12)), a s and b s recommended FAO-PM, no relative air humidity data RH ET o (Equation (1)); e a (Equation (13)) FAO-PM. no wind speed data WS ET o (Equation (1)); u 2 calculated by daily mean wind speed Hargreaves-Samani HS ET o (Equation (14))

Performance Evaluation
We compared each ET o estimate with missing data against the FAO-PM benchmark ET o that was calculated without missing data. The comparisons were made by simple linear regression. The performance of each scenario was assessed using Willmott's index of agreement (d) [53] (Equation (15)), correlation coefficient (r) (Equation (16)), root mean square error (RMSE) in mm.day −1 (Equation (17)), and mean bias error (MBE) in mm.day −1 (Equation (18)).
where P i is the estimate value of the i-th day (mm.day −1 ), O i is the observed value of the i-th day (mm.day −1 ), P is the mean of estimated values (mm.day −1 ), O is the mean of observed values (mm.day −1 ), and n is the number of observed values. Willmott's index of agreement (d) was used to quantify the degree of correspondence between P i and O i , where d = 1 indicates complete correspondence and d = 0 indicates no correspondence between measured and modeled values [53]. The root mean square error (RMSE) was used to quantify the amount of error between the observed and estimated values [53].

Seasonal Variation in Micrometeorological Condition
The climate in the study area showed a distinct seasonal variation ( Figure 2). The dry season, which was defined as the period with a rainfall depth lower than 100 mm/month [4,54,55], occurred from April to October, and approximately 25% of the rainfall was Water 2021, 13, 1763 7 of 17 recorded during this period ( Figure 2F). Mean yearly accumulated rainfall (±sd) was 941 ± 297 mm during the study period, which is 34% lower than the expected rainfall for this region.  Higher ETo values were observed during the wet season (November to March). When compared to the meteorological variables in Figure 2, ETo estimates behaved similarly to Rn. Valle Júnior et al. [6] pointed out that ETo models based on Rn perform better than different methods based on other variables for the campo sujo Cerrado conditions. Variations in air and soil temperatures (Figure 2A) were higher during the dry season compared to the wet season, due to frequent cold fronts from the south [56]. The mean (±sd) temperature during the study period was 26.4 ± 2.9 • C. The month with the highest average air temperature was September (28.3 ± 3.4 • C), while the month with the lowest air temperature was July (23.5 ± 3.7 • C). The maximum air temperature was 42.0 • C, and the minimum was 6.3 • C. Relative humidity ( Figure 2C) also varied seasonally, with the highest average values observed during the wet season and the lowest observed during the dry season. Average monthly gravimetric soil moisture (mass water/mass dry soil) ( Figure 2C) ranged between 4% and 5.5% during the wet season, while soil water content reached 2.4% during the dry season when rainfall was scarce.
Wind speed at 2 m height ( Figure 2B) showed a small seasonal variation during the study period, with an average value (±sd) of 1.2 ± 0.5 m.s −1 . We found relatively large daily variation, due to the sporadic nature of the wind in the study area [50]. Allen et al. [17] classified mean wind speed below 1 m.s −1 as light wind and wind speed between 1 and 3 m.s −1 as light to moderate wind.
Net radiation ( Figure 2D) was higher during the wet than the dry season; however, we found a larger standard deviation of R n in the wet season because of frequent cloud cover [57]. The dry-season decline in net radiation may be due to changes in vegetation and a decline of greenness during this season when soil moisture values were lower [57,58]. On the other hand, R s did not show a notable seasonal pattern like R n ( Figure 2D).
Seasonal variations of soil heat flux are represented as G ( Figure 2E). Mean monthly values (±sd) varied from −0.11 ± 0.54 MJ.m −2 .day −1 , in January, to 0.97 ± 1.37 MJ.m −2 .day −1 , in September. From July to November, mean monthly and standard deviation values for G were higher than 0.5 and 0.9 MJ.m −2 .day −1 , respectively. During the dry season, vegetation leaf area declined due to the low soil water availability [58], causing an increase in uncovered area, and consequently, higher values of G. According to Rodrigues et al. [4], during September, G accounts for about 30% of the energy balance of the campo sujo Cerrado. The contribution of G in other tropical ecosystems, such as transition and tropical forests, accounts for about 1-2% of the available energy due to the more closed canopy and greenness during the dry season [1], which is in contrast with our study area since its vegetation is sparse [50]. Figure 3 shows monthly mean ET o calculated using the Penman-Monteith method with observed meteorological data. The average ET o (±sd) was 3.49 ± 1.13 mm.day −1 . Higher ET o values were observed during the wet season (November to March). When compared to the meteorological variables in Figure 2, ET o estimates behaved similarly to R n . Valle Júnior et al. [6] pointed out that ET o models based on R n perform better than different methods based on other variables for the campo sujo Cerrado conditions.

ETo Estimates with Limited Climatic Data
For ETo values computed using limited meteorological data (Figure 4), the value for Willmott's d ranged between 0.64 and 0.99, r between 0.68 and 0.98, RMSE between 0.21 and 1.56, and absolute MBE values ranged from 0.01 to 1.29 mm.day −1 , respectively (Table 2, Figure 5).

ET o Estimates with Limited Climatic Data
For ET o values computed using limited meteorological data (Figure 4), the value for Willmott's d ranged between 0.64 and 0.99, r between 0.68 and 0.98, RMSE between 0.21 and 1.56, and absolute MBE values ranged from 0.01 to 1.29 mm.day −1 , respectively (Table 2, Figure 5).     Our results indicate that wind speed and relative humidity and their variatio throughout the year have a small effect on ETo estimates in the Cerrado region studi here. Investments in accurate air temperature sensors instead of investments in relati humidity probes would be a good option to estimate RH when the budget is limite Moreover, use a constant value of u2 is also viable to estimate ETo.
The methods without observed radiation data (Figure4A,B,E-H,J,K) showed the lo est values of r, i.e., the model results do not indicate a good linear correlation with ref ence data, when comparing ETo using FAO-PM method. However, when the benchma values are close to the average ETo value, those results with estimated radiation were si ilar to ETo with full data. In addition, ETo computed with estimates of Rs showed high RMSE and MBE values than ETo computed when only wind speed and/or relative hum ity were the missing variables. ETo calculated using radiation data computed with ca brated parameters were closer to the benchmark values than ETo calculated with Rs es mates using regression constants recommended by Allen et al. [17].
When radiation values were missing, the resulting estimates of ETo consistently ov estimated ETo when the benchmark values were low. Since the Penman-Monteith mod (Equation (1)) uses Rn − G as the radiation data input and Allen et al. [17] suggests G on a daily basis when there are no G measurements, we compared Rn estimates from Equ tion (12) with observed Rn − G values. Similarly, we compared estimates of ea calculat The methods with relative humidity and/or wind speed as missing data ( Figure 4C,D,I) showed better performance than the other methods, with high r and Willmott's d values that were close to 1.0 (Table 2), which indicate a perfect positive linear correlation and model performance. When using only average annual wind speed as estimated data, we obtained the lowest RMSE and the closest to zero MBE, with values of 0.21 and −0.01 mm.day −1 , respectively. When relative humidity was the only missing climatic data, we obtained RMSE and MBE values of 0.28 and −0.07 mm.day −1 , respectively. ET o estimates calculated when both relative humidity and wind speed data were missing had low RMSE and MBE values of 0.37 and −0.06 mm.day −1 , which indicate that the estimations of ET o using observed R s , e a computed from T min , and u 2 from average values performed very well.
These findings were expected for missing humidity data since under humid conditions there is a high probability of T dew = T min [17]. Several locations presented similar results with e a estimated from minimum temperature [37,38,59]. Sentelhas et al. [60] reported R 2 values from 0.76 to 0.96 when comparing ET o computed with actual vapor pressure to that computed from T min . This method may not be suitable to estimate ET o in humid climates since there are overestimations in VPD values [17,61].
Allen et al. [17] also suggest using a wind speed value of 2 m.s −1 when wind speed data are not available; however, 93% of data from measurements showed wind speed values below 2 m.s −1 . Since wind speed for the Cerrado's conditions does not vary greatly throughout the year, it is possible to use a constant value of wind speed for estimating ET o . Sun et al. [62] found similar results regarding the impact of wind speed on ET o in a mountainous region in China. Similar results were found by Popova et al. [38] and Córdova et al. [61], with the RMSE and MBE values near 0 when u 2 = 2 m.s −1 . Djaman et al. [59] presented unsuitable FAO-PM performances in dry conditions when wind speed was considered as 2 m.s −1 ; however, using daily average wind speed in the same conditions, the results presented MBE values between −0.05 to 0.04.
Our results indicate that wind speed and relative humidity and their variations throughout the year have a small effect on ET o estimates in the Cerrado region studied here. Investments in accurate air temperature sensors instead of investments in relative humidity probes would be a good option to estimate RH when the budget is limited. Moreover, use a constant value of u 2 is also viable to estimate ET o .
The methods without observed radiation data ( Figure 4A,B,E-H,J,K) showed the lowest values of r, i.e., the model results do not indicate a good linear correlation with reference data, when comparing ET o using FAO-PM method. However, when the benchmark values are close to the average ET o value, those results with estimated radiation were similar to ET o with full data. In addition, ET o computed with estimates of R s showed higher RMSE and MBE values than ET o computed when only wind speed and/or relative humidity were the missing variables. ET o calculated using radiation data computed with calibrated parameters were closer to the benchmark values than ET o calculated with R s estimates using regression constants recommended by Allen et al. [17].
When radiation values were missing, the resulting estimates of ET o consistently overestimated ET o when the benchmark values were low. Since the Penman-Monteith model (Equation (1)) uses R n − G as the radiation data input and Allen et al. [17] suggests G ≈ 0 on a daily basis when there are no G measurements, we compared R n estimates from Equation (12) with observed R n − G values. Similarly, we compared estimates of e a calculated when humidity data were lacking (Equation (3)) to measure e a . Figure 6 presents the linear regression results, while Figure 7 shows RMSE and MBE values for the linear regressions of Figure 6 classified by seasons.
R n estimates were always >0 and overestimated net radiation values during the dry season when negative R n − G was observed ( Figure 6A-D). R n using the calibrated parameters presented lower absolute RMSE and MBE values, especially during the wet season ( Figure 7A,B) when RH had smaller daily variation ( Figure 2C) and errors in estimating e a were the lowest. ET o computed when radiation data was missing did not consider G, which was high in this Cerrado grassland; therefore, the suggestion by Allen et al. [17] to consider daily G ≈ 0 is not suitable for our study area.
Our estimates of ET o when R s was missing were less accurate than those calculated with estimated wind speed and/or relative humidity, especially during the dry season when R n values are above the average. Different studies [63][64][65] observed good results for R s estimates using Equation (3); however, there is a lack of studies about solar radiation estimates in the Brazilian Cerrado. Other authors reported better performance of ET o calculated with estimated R s [36][37][38]61,[66][67][68] than observed here, and ET o highly correlated with solar radiation in several different locations [25,27,69,70]. More research is needed to find a better model for estimating R s and R n .
The daily ET o values computed from the Hargreaves-Samani model ( Figure 4L) showed the worst correlation with the reference values. The RMSE and MBE values were 1. 56  regression results, while Figure 7 shows RMSE and MBE values for the linear regressions of Figure 6 classified by seasons.
Rn estimates were always >0 and overestimated net radiation values during the dry season when negative Rn − G was observed ( Figure 6A-D). Rn using the calibrated parameters presented lower absolute RMSE and MBE values, especially during the wet season ( Figure 7A,B) when RH had smaller daily variation ( Figure 2C) and errors in estimating ea were the lowest. ETo computed when radiation data was missing did not consider G, which was high in this Cerrado grassland; therefore, the suggestion by Allen et al. [17] to consider daily G ≈ 0 is not suitable for our study area.  However, the quality control of the dataset utilized for ET o computation with the FAO-PM or the HS equation is vital for the precision of estimates. Therefore, quality control of site and weather datasets is certainly needed, as it is essential to the appraisal of the quality of satellite-based and reanalysis datasets when applied to compute FAO-PM. Future studies along this line are needed. The data-driven model in this vital agricultural region can also be used for estimating ET o in future studies. The outcome obtained from our study can be seasonal-climate sensitive. This also deserves further examination. The main implication of this study is that the availability of precise models and datasets for quantifying ET o is significant for agricultural managers and irrigation engineers in a region with a similar climatic condition. In addition, it is important to explore different solar and net radiation models, since the guidelines provided by the FAO are not suitable for similar Our estimates of ETo when Rs was missing were less accurate than those calculated with estimated wind speed and/or relative humidity, especially during the dry season when Rn values are above the average. Different studies [63][64][65] observed good results for Rs estimates using Equation (3); however, there is a lack of studies about solar radiation estimates in the Brazilian Cerrado. Other authors reported better performance of ETo calculated with estimated Rs [36][37][38]61,[66][67][68] than observed here, and ETo highly correlated with solar radiation in several different locations [25,27,69,70]. More research is needed to find a better model for estimating Rs and Rn.
The daily ETo values computed from the Hargreaves-Samani model ( Figure 4L) showed the worst correlation with the reference values. The RMSE and MBE values were 1.56 and 1.29 mm.day −1 . Thus, while the Hargreaves-Samani equation was found to provide adequate estimates of ETo in a variety of climates, especially arid ones [39][40][41]71], it does not appear to be adequate for estimating ETo in the Cerrado. There are many different models to estimate ETo; however, the FAO does not recommend any equation other than the Penman-Monteith and Hargreaves-Samani models.
However, the quality control of the dataset utilized for ETo computation with the FAO-PM or the HS equation is vital for the precision of estimates. Therefore, quality control of site and weather datasets is certainly needed, as it is essential to the appraisal of the quality of satellite-based and reanalysis datasets when applied to compute FAO-PM. Future studies along this line are needed. The data-driven model in this vital agricultural region can also be used for estimating ETo in future studies. The outcome obtained from our study can be seasonal-climate sensitive. This also deserves further examination. The main implication of this study is that the availability of precise models and datasets for

Conclusions
The overarching goal of our study was to evaluate the Penman-Monteith method's performance in a grass-dominated part of the Cerrado when climatic data are limited. We used ET o computed with a full data set of micrometeorological measurements as the reference data and tested the Penman-Monteith method when data for radiation, wind speed, and relative air humidity were missing.
We found better results for ET o calculated with estimated relative humidity and wind speed. Using average annual wind speed showed excellent results, with an almost perfect linear correlation and the lowest errors. The use of T dew = T min proved to be a great alternative to estimate ET o when RH data are missing, especially during the wet season.
ET o computed with solar radiation estimates performed worse than estimates when the other variables are missing. R n estimates could not compute negative values and G ≈ 0 may not be appropriate for the campo sujo Cerrado conditions. ET o estimates were not suitable when solar radiation data were missing. The Hargreaves-Samani method consistently overestimated ET o and did not perform well compared to the other methods.
The results presented here can help us better understand which meteorological data have the largest impact on ET o estimates of regions with similar climate and vegetation characteristics. Since the Cerrado is the main agricultural region in Brazil, our results could lead to new studies regarding algorithms and alternatives to estimate solar and net radiation in similar weather conditions. Improvements and investments in solar radiation measurements would provide more adequate ET o estimates and a better understanding of crop water demands.
Author Contributions: L.C.G.d.V.J. and T.R.R. analyzed the data and wrote the paper. L.F.A.C., R.d.S.P., J.d.S.N., and F.d.A.L. provided the data and interpreted the results. G.L.V. and A.R.M.T.I. reviewed the paper. All co-authors contributed significantly to this paper. All authors have read and agreed to the published version of the manuscript. Data Availability Statement: Data will be available upon request from the corresponding author.