he evapotranspiration is the term used to define the loss of water vapor to the atmosphere by the effect combined of the process of evaporation of water of superficies of soil and the plant and, of transpiration of water by the plant (OLIVEIRA et al., 2011). The study of evapotranspiration is important to the agricultural planning, being increasingly higher the requirement of information about the water requirement of crop to the regional planning and preliminary project. This study becomes more important in regions characterized by the spatial and temporal irregularity of rainfall (MOURA et al., 2013). utilized in all world. This method requires many input parameters like air temperature, relative humidity, solar radiation and wind speed. However, there are a limited number of meteorological stations to the monitoring of this variable of time. This lack of meteorological data leads to the development of simpler approaches to estimate ET0 that requiring only a few input parameters. In this context, various methods have been reported in the literature for this purpose.

Although there a lot models to estimate of ET0, these, however, are utilized in climate and agronomics conditions very different from those that were originally designed and, therefore, is utmost importance evaluate the degree of accuracy of these models before using them to new condition. Given the above, the aim of this work was to evaluate the performance of 30 methods for ET0 estimate, comparing them with the standard method of Penman-Monteith-FAO56, for the Paranaíba city, Brazil.

The meteorological data required for execution of this study were taken from the National Institute of Meteorology (INMET) for the automatic meteorological station in the Paranaíba city, of Mato Grosso do Sul state, Brazil (Latitude 19º 24' 51"S, Longitude 51º 06' 19" W, Altitude 424 m) for six years, from March 2008 to February 2014. The meteorological data used in the research were: average temperature, maximum and minimum (ºC); average relative humidity, maximum and minimum (%); average dew point temperature, maximum and minimum (ºC); average pressure, maximum and minimum (hPa) wind speed at 10 m height (m s -1 ) and global radiation (kJ m -2 ). Data were obtained from a meteorological station that consists of the equipment WAWS 301 (Automatic Weather Station) of the Brand VAISALA, whose composition is described as follows: (1) Pyranometer CM6B; (2) Pressure Sensor PMT16A; (3) Thermometer QMH102; (4) Hygrometer QMH102; (5) Pluviometer QMR102 and (6) Anemometer WAA151. The hourly meteorological data were converted to daily data. In order to make the meteorological variables data more homogeneous, verification was made and, subsequently, the eliminated, aiming to obtain more representative data groupings. The methodologies used in this research to estimate the daily reference evapotranspiration (ET0) are presented in Table 1. The wind speed was corrected to a height of 2 m (Equation 1).

(1)

where: U 2 = wind speed at 2 m height (m s -1 ); U z = wind speed at "z" m above ground surface (m s -1 ); and z = height of wind measurements (m). The net radiation was estimated according to the following equations: After obtaining the daily ET0 through different methodologies it was conducted a regression analysis that correlated the ET0 values estimated by empirical equations with the Penman-Monteith-FAO56 method (ALLEN et al., 1998). It was considered the coefficients "a" and "b" of the respective linear regressions and the coefficient of determination (r 2 ). The best alternative was the one that showed regression coefficient "a" near to zero, coefficient "b" near the unity and higher coefficient of determination, more than 0.60. The precision was measured through the coefficient of determination, which indicates the degree to which the regression explains the sum of the total squared.

The models performance analysis was performed by comparing the daily ET0 values obtained by empirical methods such as the Penman-Monteith-FAO56 (ALLEN et al., 1998). The methodology adopted for comparison of results was proposed by Allen et al. (1989), and is based on the estimate of standard-error (ESE), calculated by Equation 5. The best method to estimate ET0 was the one that presented the lowest ESE.

( ) (5) where: ESE = estimate of standard-error (mm day -1 ); X i = reference evapotranspiration estimated by the standard method (mm day -1 ); Y i = reference evapotranspiration obtained through the tested method (mm day -1 ); and n = number of observations.

The approximation of ET0 values estimated by the method studied, in relation to the values obtained using the standard method, was obtained by an index called concordance, represented by the letter "d" where its values range from zero, where there is no concordance, to 1, for the perfect concordance. The concordance index (d) was calculated using the Equation 6. To validate the model, it was also obtained the Pearson's correlation coefficient (r) through Equation 7and the reliable coefficient or performance (c) through Equation 8. (8) where: d = Willmott's concordance index; X i = reference evapotranspiration estimated through the standard method (mm day -1 ); Y i = reference evapotranspiration obtained through the method tested (mm day -1 ); Y = average values of reference evapotranspiration obtained through the method tested (mm day -1 ); X = average values of reference evapotranspiration obtained through standard method (mm day -1 ); n = number of observations; r = Pearson's correlation coefficient; and c = reliable coefficient or performance.

According to Cohen (1988), the correlation coefficient (r) can be classified as: "very low" (r < 0.1), "low" (0.1 < r < 0.3), "moderate" (0.3 < r < 0.5); "high" (0.5 < r < 0.7); "very high" (0.7 < r < 0.9); and "almost perfect" (r > 0.9).

The reliable coefficient or performance, proposed by Camargoe Sentelhas (1997), is interpreted in accordance with authors such as: "great" (c > 0.85); "very good" (0.76 < c < 0.85); "good" (0.66 < c < 0.75), "average" (0.61 < c < 0.65), "badly" (0.51 <c < 0.60), "not good" (0.41 < c < 0.50) and "terrible" (c < 0.40).

On Figures 1 and 2 are shown the graphs and the resulting linear regression models considering the methods to estimates of reference evapotranspiration (ET0) utilized on the analysis having the Penman-Monteith method standardized by FAO as standard. It is observed, based on regression straight, that Blaney-Criddle-FAO24 method underestimated the ET0 values only when the Penman-Monteith-FAO56 method was accused estimates exceeding 4.5 mm day -1 . The Camargo, Hamon, Abtew and Global-Radiation methods underestimated ET0 when the values of Penman-Monteith-FAO56 were accused estimates above 3.0 mm day -1 and Blaney-Morin above 1.5 mm dia -1 . The methods of Penman-Original, Priestley-Taylor, Hicks-Hess, Lungeon, Turc, Liquid-Radiation, Stephens-Stewart e Thornthwaite-Modified accused good estimate of ET0, presenting curves of regression near relation of 1:1. Of these, the first four methods deserve spotlight, because presented the regression coefficients "a" next to zero and the coefficient "b" near to unit. Have other methods, independent of evapotranspirometrical demand, presenting higher regressions coefficients and overestimated the values of ET0 in relation to standard method.

It is observed also on the Figures 1 and 2 that the methods that presented the better adjustment, according with the determination coefficient (r²), were the methods of Penman-Original (r² = 0.9949) and Penman-FAO24 (r² = 0.9875), that utilize the same input parameters that standard method. However, it is observed that the Penman-FAO24 overestimated the ET0 (Figure 1), corroborating with Barros et al. (2009). These authors affirmed that the simple adoption of r² as the only criterion of definition of quality of methods is not appropriate, once that this method does not establish the type and the magnitude of the differences between a standard value and a provided value by estimate models.

On the