COMPARISON BETWEEN ESTIMATION METHODS OF REFERENCE EVAPOTRANSPIRATION IN

1 Agronomist, Master Science student in Agriculture Engineering, Federal University of Viçosa, Viçosa, Minas Gerais, Brazil. taiarasouzacosta1@gmail.com 2 Doctorate student in Agriculture Engineering Post-Graduation Program at Federal University of Viçosa, Viçosa, Minas Gerais, Brazil. argolo.agro@gmail.com 3 Doctorate student in Plant Science Post-Graduation Program at Federal Universtiy of Viçosa, Viçosa, Minas Gerais, Brazil. ramonamarodesales@gmail.com 4 Agronomy undergraduate student, State Universtiy of Feira de Santana, Feira de Santana, Bahia, Brazil. niranina@hotmail.com 5 Associated Professor at State University of Feira de Santana and Weather Station coordinator, Feira de Santana, Bahia, Brazil. rosangela.leal@gmail.com


INTRODUCTION
Irrigated farming activities imply in a large consumption of water. Moreover, its scarcity has become more and more worrying, so, efforts have been used in the development of studies that make possible its economy through the rational use. The municipality of Bom Jesus da Lapa in the State of Bahia presents itself with zoning and classification for investment in agricultural production, where irrigated production is found in large areas as it is located in the São Francisco Basin.
Farming activities are highly dependent on meteorological elements, which make them determining factor for agriculture (Sales et al., 2018a). Through these elements, it is possible to obtain knowledge of the evapotranspiration of the agro-ecosystem, whether for irrigation design and / or management, assuming fundamental importance.
One alternative for rationalize the use of water in farming projects is to estimate the crop evapotranspiration (ETc), based on the reference evapotranspiration (ETo) and on the crop coefficient (Kc), so, the water depth needed by the crop can be correctly applied (COSTA et al., 2019). Thus, the determination of ETo is imperative to make a water calculation of a crop, and as a result, it may assist in irrigation and river basin management strategies depending on the climatic conditions of each region (Sales et al., 2016).
There are several models for determining ETo such as the direct ones, which are represented by lysimeters, and the indirect ones, consisting of empirical mathematical equations. Because of the difficulties of direct measurement of evapotranspiration, as well as its importance in the management of water resources, the choice of a method that estimates it accurately and based on climatological variables available at the study site is essential, because both the climatological variables and the precision of the models factors that restrict their use (FANAYA JÚNIOR et al., 2012).
Therefore, before choosing the method to be used to estimate ETo, it is necessary to know which climatic elements are available and, based on that, to check which methods can be applied. This is necessary, since the use of different methods for a particular place of interest depends on these variables and their precision (ARAÚJO et al., 2007). Food and Agriculture Organization of the United Nations (FAO) establishes Penman-Monteith parameterized equation as standard model in the Bulletin 56 of the institution. This physical-physiological model estimate ETo with adequate accuracy, but requires a greater number of meteorological variables, which may not be available in some regions (CONCEIÇÃO, 2013).
Thus, the objective of this work was to evaluate the efficiency of the methods of Camargo, Benevides and Lopes, Hargreaves and Samani and Priestley and Taylor to estimate the daily ETo in the period from 2010 to 2017 for the conditions of Bom Jesus da Lapa (BA), compared to the standard Penman-Monteith method.

MATERIAL AND METHODS
The study was carried out using meteorological data from the municipality of Bom Jesus da Lapa (13º15'18" S and 43º25'05" W and 436 m above sea level), which has a total territorial area of 4,115,511 km² and located in the state of Bahia, in the Northeast of Brazil ( Figure 1).
The average annual rainfall index is 833 mm, occurring most intensely between October and March (spring-summer). The climatic type of the region, according to the Köppen-Geiger climatic classification, is the tropical climate with dry winter season (INMET).
For the calculation of ETo, daily climatological data of maximum, minimum and average temperature, relative humidity, solar radiation and wind speed were required. These data were obtained from the automatic meteorological station owned by the National Institute of Meteorology (INMET) from January 1, 2010 to December 31, 2017.
Prior to the calculations of ETo, an analysis was carried out to verify the quality of the data and to exclude possible measurement errors in the field. Based on the methodology proposed by Sales et al. (2018b), data inconsistent with the following parameters were excluded: minimum temperature below 0°C, maximum temperature above 39°C, maximum temperature less than the minimum temperature for the same day, global solar radiation equal to zero and global solar radiation greater than extraterrestrial solar radiation. Consequently, after these analyses, 2,633 days remained with consistent measurements, corresponding to 90.17% of the data.
Then, the equations used to calculate ETo for the different estimation methods are shown.

Camargo (CM)
The Method of Camargo (1971) is a simplification of the Thornthwaite method. The main advantage of this method is the use of only the daily average air temperature data and the extraterrestrial solar radiation, which can be easily estimated from equations or obtained from specific tables (Equation 2).   (2) In which, Ra = extraterrestrial solar radiation, MJ m -2 d -1 , and T average = air average temperature, ºC.

Benevides and Lopes (BL)
It can be seen in Equation 3 the method developed by Benevides and Lopez (1970), which is based on data of average temperature and relative humidity of the air.
In which, T average = average air temperature, ºC, and RH = air relative humidity, %.

Hargreaves and Samani (HS)
The model proposed by Hargreaves and Samani (1985) is an alternative to estimate ETo in places where data on solar radiation, relative humidity and wind speed are not available (Equation 4).

Priestley and Taylor (PT)
The Priestley and Taylor Method (1972) is a simplification of the Penman and Penman-Monteith method. Thus, this model has the advantage of requiring less climatological data (Equation 5).
For comparative analysis and indication of the best ETo estimation methods for the municipality of Bom Jesus da Lapa, the following statistical indices were used: Willmott's "d" agreement index (WILLMOTT et al., 1985), root of the mean square error (RMSE in mm d -1 ), systematic error (BIAS in mm d -1 ), determination coefficient R², "r" correlation coefficient and confidence coefficient or performance "c", in addition to the classification of the confidence coefficient (Equations 6,7,8,9,10). The "d" values may range from 0 to any agreement, to 1, for a perfect concordance. Table 1 shows the confidence coefficient, proposed by CAMARGO & SENTELHAS (1997), which is obtained by the product between the correlation coefficient (r) and the Willmott index (d). For all statistical calculations, it was used the Microsoft Office Excel ® software in order to assist in the organization of data and also the R open source software (R core team, 2016).

RESULTS AND DISCUSSION
The statistical indicators RMSE, BIAS and R² for the estimation of daily ETo are shown in Figure  2. The analysis of coefficient of determination R² allowed to observe that it varied from 0.34 to 0.66, where the PT method indicated the highest value. However, analyzing R² as the sole criterion for selecting the ETo model is not convenient, as this parameter does not indicate the range of differences between a standard value (PM FAO-56) and a value predicted by the alternative models (BARROS et al. , 2009).
One of the reasons PT had shown the highest R² among the methods under study is because this model uses solar radiation as a predictor variable as this meteorological element is one of the most important in ETo estimate (PANDEY et al., 2016). According to Allen et al. (1998), the evapotranspiration process is conditioned to the amount of energy available for water evaporation. Also, according to the authors, solar radiation is the most important energy source of the plant and influences the physical processes of water, transforming liquid water into vapor.
Based on the root of the mean square error (RMSE), the methods were ranked in the following order: HS <PT <CM <BL. The HS method obtained an RMSE value of 0.66 mm d -1 , while the BL showed an RMSE of 2.98 mm d -1 , which is very high in comparison to the others. Such result may be linked to the environmental conditions of the study area, since HS was developed in semi-arid California, with conditions similar to those found in the municipality under study.
The BIAS systematic error shows the underor overestimation of a model, thus it is possible to observe that HS and BL overestimated, being more accentuated for BL with a systematic error of 2.68 mm d -1 while the PT and CM methods underestimated it ( Figure 2). These results are in agreement with Santos et al. (2017), as when studying ETo in Feira de Santana, state of Bahia, found values for HS overestimating PM FAO-56 in all the months. The authors Borges Júnior et al. (2017), when estimating the daily ETo for Sete Lagoas, state of Minas Gerais, found that the original HS has an overestimate tendency.
It is evident that the BL had the greatest overestimation of the standard method PM FAO-56 (Figure 2), in addition to presenting R² of 0.44. The trend line of this model is further away from the line 1:1, together with the CM. Therefore, it was evident that BL and CM showed the worst adjustments for the municipality of Bom Jesus da Lapa, State of Bahia. Table 2 shows the correlations between the ETo estimated through PM FAO-56 and the ETo estimated by means of the other models for Bom Jesus da Lapa, Bahia. Smaller dispersions were found for the HS and PT models, and worse correlations for the estimates obtained using CM and BL models, with respective values of 0.58 and 0.65. The low correlation found for CM and BL was followed by a lower agreement between the data, thus impairing their performance, since it is a product between the correlation and the concordance.
These results are in agreement with those found by Borges , when estimating the daily ETo using different methods in Garanhuns, Pernambuco state, in which a poor performance was observed for CM. It should be highlighted that the method of Camargo was initially proposed to determine ETo for periods from seven days onwards, and for regions with temperate and humid climates, which contributed to its low accuracy (PAZ & THEBALDI, 2018).
According to Araújo et al. (2010), when working with ETo in the city of Crateús, state of Ceará, found unsatisfactory results for the BL method, which showed a poor performance. This result was also found in this study, and can be explained by the semiarid climate in the municipalities.
The correlation and concordance values found through HS and PT are close to those obtained by Tagliaferre et al. (2012) by evaluating ETo on a daily scale in the municipality of Piatã, state of Bahia, with a correlation of 0.70 and 0.86 respectively, and with concordance between the data of 0.82 for HS and 0.87 for PT. Studies conducted by Oliveira et al. (2010), for the region of Juazeiro, BA showed that the HS method had a performance considered Good.
It is possible to observe in Figure 3 the annual accumulated ETo estimate among the different methods analyzed in the study. The annual sum of ETo estimates by means of BL was 2,889.70 mm   (Figure 2, 3), being much higher than the PM-FAO56 standard method during the eight analyzed years.
When observing the HS model, it can be seen that ETo has always approached the PM-FAO56. However, although CM has presented values closer to that of PM-FAO56 when accumulated annually, their statistics show that it cannot be recommended for the region (Figure 2). This is due to the lower concordance and correlation between the data, thus showing greater variability between them, that is, on specific days, it overestimated very much and on others, it underestimated.

CONCLUSION
• According to the adopted statistical criteria, the methods of Hargreaves and Samani and Priestley and Taylor showed the best performance for daily estimation of ETo, when compared to the PM FAO-56, being recommended to be used in the region under study.
• The methods of Benevides and Lopez and Hargreaves and Samani overestimated reference evapotranspiration.
• Camargo and Benevides and Lopes models are methodologies not recommended for calculating ETo in Bom Jesus da Lapa, Bahia, and require regional calibration of their coefficients so to be used.