REFERENCE EVAPOTRANSPIRATION BY PENMAN – MONTEITH FAO 56 WITH MISSING DATA OF GLOBAL RADIATION

The aim of this study was to evaluate the errors generated on the reference evapotranspiration (ET0) estimation by Penman-Monteith FAO 56 (PMF 56) when employed simplified models to estimate the global radiation (HG) are based on the air temperature. We evaluated 28 automatic weather stations (EMA's) belonging to the National Institute of Meteorology (INMET) network, in different biomes of Mato Grosso state. Was evaluated fifteen simplified models of HG estimate calibrated regionally and five models without calibration. It was used as a reference ETo obtained by PMF 56, with HG measure. The statistical performance were employed mean bias error (MBE), root mean square error (RMSE), adjustmentindex (d) and the cumulative numerical order of the different models in each index. The regional calibration models HG estimation models improve the estimates of ETo. Can be used Bristow and Campbell (1984) and Goodin et al. (1999), De Jong and Stewart (1993) models to HGestimates and then ET0 to Amazon, Cerrado and Pantanal, respectively.


INTRODUCTION
Solar radiation can be considered as the primary source of renewable and natural energy to the environment, which are important in many physical, chemical, biological and biophysical processes that occur on Earth's surface, with applications in areas such as agronomy, ecology, solar energy systems, environment, oceanography, architecture, among others (DAUT et al., 2011;CARVALHO et al., 2011;SOUZA & ESCOBEDO, 2013).Specifically in agricultural systems, solar radiation is essential in photosynthetic processes and the availability of energy for heating air and / or ground, as well as changes of water physical state by evaporation, transpiration and / or evaporation, which together define the water culture needs.
According to Carvalho et al. (2015) the evapotranspiration (ET) is the most active variable of the hydrological cycle and the main component of the water balance in agricultural ecosystems.Therefore, it is an important parameter for the planning and management of water resources (RAZIEI&PEREIRA, 2013;FALAMARZI et al., 2014;MANCOSU et al., 2014).
In general, the conceptual developments of potential evapotranspiration refers to the maximum loss of water from a vegetated surface, low size, in full development and without water deficit, in order to reduce the effect of local advective energy.In this context, evapotranspiration can be directly proportional to the availability of solar energy and radiation balance (CHANG, 1968;PEREIRA et al., 1997;ALLEN et al., 1998;ALLEN et al., 2011).

Direct
measurements and/or estimates of solar radiation, specifically global radiation (H G ) are important in many evapotranspiration estimation models, therefore, reliability in recording and/or data estimates predict accurately models for hydroagricultural purpose (EL SEBAII & TRABEA, 2003).The lack of H G measures a generalized manner, it can be considered as a major research limiting and applications for growth simulation models, development and crops yield (HOOK & MCCLENDON, 1992).
According to Souza & Escobedo (2013) routine monitoring of solar radiation was, during a long time, difficult and expensive, because of the high costs limit the acquisition of pyranometers, restricting its use to research centers.And yet, in Brazil, as in many countries, there are several problems in recording weather information for establishment of monitoring networks.Specifically HG, many stations have no pyranometers and/or data acquisition systems, thus making in inconsistent databases with a large number of faults and/or long periods of measurements absence (data loss failures equipment, calibration errors, water accumulation and dirt on the sensor, etc.), which in turn, do not allow seasonality assessments of solar radiation components and/or atmospheric attenuation (WU et al., 2007;ABRAHA & SAVAGE, 2008;ALMOROX et al., 2011).
According to the International Commission on Irrigation and Drainage (ICID) and the United Nations of Food and Agriculture Organization (FAO), when evapotranspiration and solar radiation are not monitored, estimates can be employed by mathematical models.However, it is emphasized that the select method to be used depends on factors such as weather conditions, accessibility to necessary meteorological data, complexity of the method, grouping the considered data and costs (CARVALHO et al., 2007;ZANETTI et al., 2008).Thus, it is recommended that the different estimation models are evaluated and / or calibrated to the local climate.
The Penman-Monteith FAO 56 (PMF) is recognized as the standard methodology for estimating reference evapotranspiration by combining energy and aerodynamic components (SMITH, 1991;ALLEN et al., 1998).However, this method requires a greater number of input variables such as solar radiation, air temperature, relative humidity and wind speed.Knowing the difficulty of using the standard method PMF 56 in many regions due to lack of climate data, suggested procedures for estimating missing variables such as vapor pressure deficit and wind speed (CARVALHO et al., 2015) and solar radiation (GAVILÁN et al., 2007;YIN et al., 2008;SENTELHAS et al., 2010).Such procedures have required the assessment in different weather conditions to test their viability (DORNELAS et al., 2006;CUNHA et al., 2008;CARVALHO et al., 2011;TODOROVIC et al., 2013;ALENCAR et al., 2015).
The evaluated equations are based on air temperature, air humidity and precipitation, these variables are monitored in all EMAs above, and these data are available on climate normal on conventional weather stations (EMC's) from INMET network in the Mato Grosso state (12 stations distributed in different regions).Therefore, this assessment allows applications to obtain the global radiation and evapotranspiration in the historical series of EMC's more reliably.Given the above, and the importance of solar radiation in obtaining evapotranspiration, this work aimed to evaluate the estimate of global radiation influence in obtaining the daily reference evapotranspiration by Penman -Monteith FAO 56, for Mato Grosso State.

MATERIAL AND METHODS
The meteorological data collected by 28 automatic weather stations (EMA's) installed in the Mato Grosso state (Table 1) were obtained from the National Institute of Meteorology (INMET).The EMA's network in Mato Grosso consists of 35 stations; however some had flaws and lack of data, characterized by equipment failure and/or calibration, maintenance periods or disabled, being disregarded in this study.
The data period refers to operational time of this weather station.
The Mato Grosso state is located in the Midwest region of Brazil, between the coordinates 06 ° 00' S and 19 ° 45' S and 50 ° 06' W and 62 ° 45'W, totaling area of 903,357,908 km 2 (Figure 1).In general, Mato Grosso state has two seasons well defined: rainy season (October to April) and dry (May to September).  1) The incident radiation on the atmosphere top (H 0 ) was obtained as a function of latitude and time of year, according to Iqbal (1983).The evaluated estimation models of solar radiation and their source are shown in Table 2.For estimating the solar radiation were used equations with calibrated coefficients for each regional station (Models 1 to 15), whereas the models 16 to 20 have been used the coefficients proposed by the each model authors.)) H 0 b Abraha and Savage ( 2008)  Allen (1995) 18 -KR3 H G =a(T max -T min ) 0.5 H 0 a=0.00185(Tmax -T min ) 2 -0.0433(T max -T min )+0.4023 a kr3 Hargreaves and Samani (1982) Samani (2000) 19 -BCA * ∆Tdaily temperature range, obtained by the difference in Tmax and Tmin ; ∆ ̅̅̅̅averagethermal range; T medaverage air temperature; T min -minimum air temperature; T maxmaximum temperature; es minminimum vapor pressure saturation, using T min ; es maxmaximum saturation pressure, using T max ; Altlocal altitude; Pprecipitation; tnctemperature factor of summer night; P atmlocal atmospheric pressure (kPa); P 0average atmospheric pressure on sea level (101.33 kPa); the saturation pressure e s Was evaluated the influence of estimated H G in obtaining daily evapotranspiration (ET 0 ) by Penman-Monteith FAO method (Allen et al., 1998) (eq.21), with standard measured Hg.This assessment was based on the influence that the net radiation (Rn) presents on ETo estimation, and also that Rn estimate can be simplified by the radiation balance on shortwave (ROC) and longwave (ROL).Therefore, ROC can be defined as the difference between the incident radiation (H G ) and reflected radiation (albedo lawns parameterized 23%) (ALLEN et al., 1998).
In performance assessing the equations of daily estimates on inclined surfaces as the horizontal were employed statistical indicative: determination coefficient (R²), percentage relative error, MBE (Mean Bias Error), RMSE (Root Mean Square Error) and adjustment index "d" Willmott, as recommended by Souza & Escobedo (2013) and Badescu (2013).
It used weighted values (Vp) of statistical indications to classify the best method for estimating ETo.To obtain the Vp value assigned to weights from 1 to "n" for each statistical indicator, "n" being the number of models tested, in which case, given the weight 1 to the best model and the weight "n" to worse, and consequently, the best model is the one with the lowest sum of the assigned weights ie lower amount of accumulated Vp (TANAKA et al., 2016).

RESULTS AND DISCUSSION
The annual variation in ETo values estimated by the PMF 56 method for meteorological stations located at different latitudes and biomes of the Mato Grosso state, presented behavior similar of global radiation seasonality throughout the year, with higher values in summer and lower in winter (Figure 2).This behavior was influenced by the temporal variation in average air temperature, which was similar for all locations under study, with the highest average temperatures occurring from September to April (rainy season) and the lowest between the months of May and August (dry season).According to Carvalho et al. (2015), if there is no water restriction, evapotranspiration is proportional to the availability of solar energy and radiation balance, setting thus the scenarios to evaluate the influence of H G estimates in ETo (CARVALHO et al., 2011;SOUZA et al., 2011).
The average daily ET 0 for the Amazon biome, the Cerrado and Pantanal (considering its transitions) were 3.57; 3.76 mm and 3.31 day -1 , respectively.These results corroborate with Souza et al. (2013), which analyzed 13 normal climate in the Mato Grosso state, found average daily ET 0 of 4.41 and 4.73 mm for Cáceres and Cuiabá (Pantanal), 3.59 and 3.64 for Matupá and Vera (Amazon) and 3.85 and 3.90 mm for Rondonópolis and Canarana (Cerrado).
The seasonality is dependent on the solar radiation and the amount of water vapor in the local atmosphere which, in turn, is related to cloud cover and directly affect the radiation balance; therefore, the estimates for the same model range from humid regions, semi humid or arid.According to Souza et al. (2011), this behavior can be observed for daily averages of ET 0 obtained by H G evaluated models estimation (Table 3).
For models not regionally calibrated (KR1, KR2, KR3, BCA and WEI) were observed average values of ET 0 higher than those obtained with measured H G , independently of evaluated station.
Marti et al. ( 2010) and Carvalho et al. (2015) find it convenient to use the relative error (ER) to infer onperformance quality of ET 0 estimates different models, however, indicate that model as satisfactory ER ≤ 20% and its cumulative frequency distributions.Relative error analysis showed that occurs errors probability up to 20% ranged from 25.2 to 34.7% for H G with ET 0 estimates obtained by GOO calibrated models and ABS, respectively (Table 4).For uncalibrated models, the probability of ER maximum of 20% ranged from 39 to 64.5%.In general, there was a 50% probability of occurrence ER between 10 and 14% for H G calibrated estimation models.
The adjustment index d of Willmott is dimensionless (ranging from 0 to 1) and shows how the estimated values (dependent variable) fit to the measured values (independent variable), or indicates the removal of estimated data of the observed mean (CARVALHO et al., 2015).The minor adjustments were obtained by the models KR3 and WEI (Figure 5).For the calibrated model, "d" values ranging from 0.56 to 0.94, being smaller than the difference between maximum and minimum were 0.75 to 0.92 (17% variation in adjustment) for HAR and ANN models.The worst adjustments were observed in EMA's A906 (Guarantã do Norte), A917 (Sinop) and A928 (Nova Maringá), both in the State of the Amazon region, resulting from the high percentage of data losses (Table 1).
In Table 5 are the cumulative values (Vp) for statistical indicative considered in performance evaluation estimate of ET 0 with different obtaining HG models.The GOO, BRC, MAH, DOC, HU1 and DJS models were framed with smaller total of Vp to 28.6; 21.4; 21.4; 14.3; 10.7 and 3.6% of EMA's, respectively.The best estimates of ET 0 to the Amazon and Cerrado regions, with their transitions were found when applied BRC and GOO models, respectively.The uncalibrated models showed the highest accumulated Vp values indicating the worst statistical indicative regardless of the season, and demonstrating that the local calibration of solar radiation estimation models is essential for obtaining good evapotranspiration estimates.

CONCLUSIONS
The local calibration of simplified models coefficients to estimate the solar radiation has positively influence on daily estimate of reference evapotranspiration.
In the absence of solar radiation data, reference evapotranspiration estimates by Penman-Monteith FAO 56 to the Amazon, the Cerrado and Pantanal region in Mato Grosso State should consider Bristow and Campbell (1984), Goodin et al. (1999) and De Jong and Stewart (1993) methods, with regional calibration of parametric coefficients for each model.

Figure 2 .
Figure 2. Seasonality of global radiation and reference evapotranspiration for the Água Boa station (A908) belonging to INMET network, from 01/2008 to 01/2013 measured values.The indicative MBE is the deviation from the medium and provides information on the model of long-term performance; negative values indicate an underestimation and positive values overestimation.As smaller MBE absolute value, better the performance of the tested model, however,

Figure 3 .
Figure 3. MBE values to ET 0 estimated by PMF 56 method with different H G estimating models use, to 28 EMA's in Mato Grosso State, Brazil vapor pressure (ea) and solar radiation (H G ) can provide low deviations of mean values of ET 0 by PMF 56 for tropical regions.

Figure 4 .
Figure 4. RMSE values to ET 0 estimated by PMF 56 method with different H G estimating models use, to 28 EMA's in Mato Grosso State, Brazil

Figure 5 .
Figure 5. Adjustment index values (d) to ET 0 estimating by PMF 56 method with different H G estimating models use, to 28 EMA's in Mato Grosso State, Brazil.

Table 2 .
Estimating equation of solar radiation, parameters and references

Table 3 .
Daily average of reference evapotranspiration (mm day -1 ) by Penman-Monteith FAO 56 model with different global radiation estimate methods, to different automatic weather stations in Mato Grosso state.

Table 4 .
Cumulative frequency of relative percentage error occurrence of ET 0 estimate with HG estimate by empirical models to PMF 56 method in Mato Grosso state.

Table 5 .
Classification of global solar radiation estimating models on reference evapotranspiration estimate according to performance indicators ordering MBE, RMSE and d.