Hourly and Daily Reference Evapotranspiration with ASCE-PM Model for Paraná State, Brazil

The objective of this study was to verify the magnitude and trend of hourly reference evapotranspiration (EToh), as well as associate and analyze daily ETo (ETod) series and the sum of hourly ETo (ETo24h) in 24 h, estimated with the PenmanMonteith ASCE model for Paraná State (Cfa and Cfb climate type). Relative humidity (RH), temperature (T), solar radiation (Rs) and wind speed (u2) data were obtained from 25 meteorological stations from the National Meteorological Institute (INMET), between December 1, 2016 to November 8, 2018. The analyzes were performed by linear regression and associations considering the root mean square error, correlation coefficient and index of agreement. The EToh trend has a Gaussian distribution, with the highest values between 12:00 p.m. and 2:00 p.m., with the maximum average being 0.44 mm h (Cfa climate type) and 0.35 mm h (Cfb climate type). The average difference between the ETo24h and ETod values was small (5.1% for Cfa and 7.4% for Cfb), resulting in close linear associations. The results obtained indicate that EToh has good potential to be used in planning and management in the field of soil and water engineering, in Paraná State.


Introduction
The Evapotranspiration (ET) is the term used to describe the loss of water by the soil surface evaporation and plant transpiration. Evapotranspiration researches are important for water resources planning and management, as well as the understanding of environmental and climate changes (Nolz & Rodný, 2019).
The ET depends on several factors, such as: water supply for plants; interaction between meteorological variables, such as solar radiation, wind speed, relative humidity and air temperature; and physiological issues such as stomatal movement, leaf area and the presence or absence of trichomes. The term reference evapotranspiration (ETo) originated from estimates using a hypothetical reference crop, with a height of 0.12 m, fixed surface resistance of 70 s m −1 and albedo of 0.23. The reference surface closely resembles to an extensive green grass surface, with uniform height, adequate water, in active growth and completely shading the soil surface (Allen et al. 1994;Allen et al. 1998).
The ETo can be measured directly with specific equipment, called lysimeters or evapotranspirometers. These methods are considered accurate and direct, but have high costs, requiring time and specialized labor. Indirect methods are an alternative form to determine ETo, which provide satisfactory results and minimize costs and time, compared to direct methods (Howell et al., 1991;Dhungel et al., 2019).
The time interval considered for ETo calculation may vary according to the purpose of the study. In the literature is common to use monthly, daily or even hourly intervals. The periodicity choice depends on the precision and data availability for use in the models. In areas where there are large changes in wind speed, cloudiness or dew point throughout the day, the calculation of evapotranspiration in hourly periodicity is more accurate (Noia et al., 2014;Lopes & Leal, 2016). The models most recommended and used in the literature for this purpose are Penman-Monteith FAO N°56 (Allen et al., 1998) and Penman-Monteith ASCE (ASCE-EWRI, 2005).
The PM-ASCE method is a modification of the model presented by Food and Agriculture Organization of the United Nations (FAO), which has adjustments that enable even more accurate results. Currently, the PM-ASCE model is considered the standard for estimating ETo. In addition to estimates ETo for daily and hourly periodicity, the model also considers two types of reference surfaces: short grass (low height crop; 0.12 m) and alfalfa (tallest and harshest crop; 0.50 m) (ASCE-EWRI, 2005).
The reference evapotranspiration in hourly periodicity (ETo h ) can allow higher precision for ETo estimates, and offer better perspectives for water and soil resources planning and management (Treder & Klamkowski, 2017;Althoff et al., 2019;Nolz & Rodný, 2019). In particular, the subtropical region where the Paraná State is located has scarce information regarding hourly reference evapotranspiration (ETo h ). In general, studies already carried out deal with ETo only on a daily periodicity, considering few locations and seasons for the predominant Cfa or Cfb climates of the State, which makes its spatialization difficult (Costa et al., 2015;Jerszurki et al., 2017).
In this context, we verify the magnitude and trend (daily and seasonal) of hourly reference evapotranspiration (ETo h ), as well as associate and analyze series of daily ETo (ETo d ) and the sum of hourly ETo in 24 h (ETo 24h ), estimated with the Penman-Monteith ASCE model for Paraná State, considering the predominant Cfa and Cfb climate types.

Material and Methods
The present study was carried out for Paraná State, Southern region of Brazil, with an area of 199.307.922 km 2 , according to Maack (2012). The region is comprised between 22°30'58" S and 26°43'00" S latitude, 48°05'37" W and 54°37'08" W longitude (Fig. 1), with hight variation in altitude, with the locations analyzed in the present study included between 1 and 994 meters. Paraná has a predominance of Cfa and Cfb climate type, according Köppen's climate classification for Brazil. The Cfa subtropical climate has a great rainfall distribution throughout the year, on average 1500 mm year −1 , and average annual temperature of 19°C. The Cfb subtropical climate presents rainfall well distributed throughout the year, being over 1200 mm year −1 , temperate summer and annual average temperature of 17°C (Alvares et al., 2013).
The estimation of hourly (ETo h ) and daily (ETo d ) evapotranspiration was calculated with the standardized Penman-Monteith equation, presented by the American Society of Civil Engineers (ASCE-EWRI, 2005) (Eq. (1)), using a short crop having an approximate height of 0.12 m: where ETo PM-ASCE is the hourly or daily reference evapotranspiration (ETo h in mm h −1 or ETo d in mm day −1 , respectively); 0.408 is the coefficient equation (m 2 mm MJ −1 ); Δ is the slope of the saturated water-vapor-pressure curve to the air temperature in the period considered (kPa°C −1 ); Rn is the net radiation balance in the period considered (MJ m −2 h −1 or MJ m −2 day −1 ); G is the soil heat flux in the period considered (MJ m −2 h −1 or MJ m −2 day −1 );γ is the psychrometric constant (kPa°C −1 ); Cn and Cd are the constants related to the type of vegetation and time scale considered (K mm s 3 Mg −1 h −1 and s m −1 , respectively); T is the average air temperature in the period considered (°C); u 2 is the wind speed at 2 meters height in the period considered (m s −1 ); es is the saturation vapor pressure in the period considered (kPa); ea is the actual vapor pressure in the period considered (kPa).
The daily ETo (ETo d ) was calculated using the ASCE-PM equation, according to recommendations and coefficients of the ASCE Manual of Practice N°70 (ASCE-EWRI, 2005;p.09-26), for soil cover with short grass: Cn daily = 900 K mm s 3 Mg −1 h −1 and Cd daily = 0.34 s m −1 ; The hourly ETo (ETo h ) was calculated using the ASCE-PM equation, according to recommendations and coefficients of the ASCE Manual of Practice N°70 (ASCE-EWRI, 2005; p.09-26), for soil cover with short grass: Cn hourly = 37 K mm s 3 Mg −1 h −1 ; and, Cd daytime = 0.24 s m −1 for daytime period, or Cd nighttime = 0.96 s m −1 for nighttime period.
The 24 hourly ETo h values of one day were added, for statistical comparison with the ETo d of the respective day (Eq. (2)): where ETo 24h is the reference evapotranspiration resulting from the sum of each h-values of hourly reference evapotranspiration of the same day (mm day −1 ); ETo h is the reference evapotranspiration of each h-hour (mm h −1 ); n is the number of hours in a day (dimensionless; n = 24). The hourly and daily reference evapotranspiration were calculated on an electronic spreadsheet developed especially for this purpose, at the Modeling and Agricultural Systems Laboratory -DSEA/SCA -Federal University of Paraná.
We were used data series from 25 automatic meteorological stations (Fig. 1), obtained from the National Meteorological Institute (INMET), between December 1, 2016 to November 8, 2018.
To estimate ETo with the ASCE-PM model, the variables required were: maximum and minimum relative humidity (RH; %); maximum and minimum air tempera-tures (T;°C); incident solar radiation (Rs; MJ m −2 day −1 ); and wind speed at 2 meters height (u 2 ; m s −1 ). The data in meteorological stations are measured in intervals from minute to minute, and after completing one hour, with the average of the measures, the hourly value is generated. Further details about the Automatic Meteorological Station System from National Meteorological Institute (INMET) used in the present study can be verified in INMET (2011), as well as measuring devices, how to install and execute the reading data.
A total of 424,800 hours were analyzed for 25 stations in Paraná State. However, when data failure was detected for some input variable to estimate hourly evapotranspiration (ETo h ), it was decided to exclude the time in question. Thus, 63,720 h (15% of the total) was eliminated. Considering the six input parameters, a total of 2,166,480 data were used.

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Characterization of the input variables in the ASCE-PM model on daily and hourly periodicity
In general, the variables T, RH, Rs and u 2 showed very similar trends among the predominant climates in Paraná (Table 1 and Fig. 2). It was observed that: i) The T was higher in the summer (average of approximately 24°C for Cfa climate and 19°C for Cfb climate) and spring (average of approximately 20°C for Cfa and 18°C for Cfb); ii) The RH showed low seasonal variations for both climates, being between 66% to 80% throughout the year, with winter being the period of lowest RH for Cfa (66%) and summer for Cfb (74.9%); iii) Rs showed a similar trend to T, with periods of higher Rs in the summer seasons (0.95 MJ m −2 day −1 for Cfa and 0.94 MJ m −2 day −1 for Cfb) and spring (0.84 MJ m −2 day −1 for Cfa and 0.75 MJ m −2 day −1 for Cfb); and, iv) The u 2 showed a similar trend to RH, with low seasonal variation, being between 0.95 to 1.45 m s −1 , with highest values observed during autumn (1.45 m s −1 for Cfa and 1.36 m s −1 for Cfb).
The tendency and dispersion of the climatic input variables used to calculate ETo in hourly periodicity (ETo h ) differ considerably throughout the day. Rs and u 2 provided the largest variations observed in the prevailing climates of Paraná State. The Cfa and Cfb climates showed a very similar hourly average trend for T, RH, Rs and u 2 (Fig. 3). For both climatic types it was found that the air temperature showed higher values between 2:00 p. m. and 4:00 p.m. and the RH had an inverse trend, presenting its lowest values between 2:00 p.m. and 4:00 p.m. The Rs showed a peak of solar energy between 12:00 p.m. and 2:00 p.m. In the same way as Rs, the wind speed tended towards the highest values between 2:00 p.m. and 4:00 p.m.

Trend of hourly reference evapotranspiration (EToh) throughout the day
On average, for each weather station analyzed, the maximum values of ETo h achieved over the 24 h of the day occurred between 12:00 p.m. and 2:00 p.m. Mean maximum ETo h of 0.44 mm h −1 was observed for Cfa cli- mate and 0.35 mm h −1 for Cfb (Fig. 4). During the peak ETo h periods, the highest values of T, Rs, u 2 and lowest values of RH had occurred (Fig. 3). The trends observed for ETo h are quite evident, due to the dependence of evapotranspiration on the variables T, Rs, u 2 and RH. Ismael Filho et al. (2015) consider that RH has an inverse relationship to ETo. Thus, as higher the RH, lower the ETo h . The authors statement also confirms the results obtained with ETo h for the analyzed stations ( Fig. 3 and 4).
An interesting aspect when working with the ASCE-PM method in the hourly periodicity refers to the occurrence of positive and negative values in the ETo h estimates at night. In the analyzes carried out in the present study, ETo h values close to zero or negative occurred, on average, between 9:00 p.m. and 4:00 a.m. for Cfa climate, and between 9:00 p.m. and 5:00 a.m. for Cfb climate (Fig. 3  and 4). Caird et al. (2007) considered that some species of plants C3 and C4 do not present complete stomatal closure during the night period due to the recovery of daytime water losses. The amount of water lost by the leaf at night depends on the vapor pressure deficit between air and leaves, resulting in nighttime transpiration up to 30% of the daytime, since the nighttime vapor pressure is lower than the daytime. These aspects show the importance of considering positive nighttime water losses (Fig. 4) to compose accurate ETo analyzes.
Regarding the ETo h negative values Guimarães et al. (2013) report that Rs sensors can have small errors, due to gradual changes in the atmosphere and radiation. In addition, however good the instrument used to measure a physical quantity can be, naturally the measured value will not be equal to the real value, since every measurement process introduces an error. In the present study, 37% of the 351.809 ETo h values were negative. Therefore, it is believed that the estimation of negative ETo h values may result from an error in the sensors measurement. As the values are very small, in the present study they were considered equal to zero. Yildirim et al. (2004) comparing ETo h and ETo d in Harran Plain, region of Turkey, also found ETo h values close to or equal to zero in the nightime hours, with accelerated increase between 6:00 a.m. and 12:00 p.m. Although the climates of Paraná and Harran are different, in the present study ETo h trend was very similar to that observed by the authors (Fig. 4).
In general, the seasonal trend of hourly reference evapotranspiration (ETo h ) indicated that the highest values occurred in summer and spring, and the lowest in winter and autumn ( Figure 5). A similar trend was observed for T and Rs (Fig. 3).
Pereira et al. (2016) note that T and RH are very active in ETo values. As higher the temperature is, higher will be the atmospheric demand for water, indicating the associations between Fig. 3 and 5, and the reasons why the spring and summer seasons have the highest ETo h values.

ETo d trend and association between ETo d and ETo 24h throughout the year, in Paraná State
There was a tendency of the highest ETo d amplitudes during the summer, with the mildest values between spring and autumn and the lowest amplitudes in the winter period (Table 2 and Fig. 6).
The daily ETo obtained with the standard ASCE-PM method (ETo d ) or with the sum of ETo h (ETo 24h ) did not show high variations. However, a trend towards higher ETo 24h values was observed in Cfa climate, mainly during spring and summer (Table 2 and Fig 7).   As for the magnitude, the analyzes of the present study for Cfa climate indicated ETo 24h average values of 3.50 mm day −1 and ETo d average of 3.32 mm day −1 , resulting in a difference of only 0.18 mm day −1 (5.1%). For Cfb climate, a ETo 24h average of 2.69 mm day −1 and ETo d average of 2.49 mm day −1 were obtained, resulting in a difference of 0.20 mm day −1 (7.4%) ( Table 2 and Fig. 7). The Clevelândia weather station was the one with the lowest ETo values and amplitudes. However, this season presented many data  failures, mainly in autumn and winter period for the Rs variable.
Nolz and Rodneý (2019) evaluating the ASCE-PM model to estimate hourly and daily ETo in sub-humid climate in northeastern Australia, obtained values between 0 and 8 mm day −1 . The magnitude differs from the highest values achieved in Parana State (Table 2 and Fig. 7). Allen et al. (1998) also considers that the presence of clouds in regions with humid climate provides lower ETo values. Dhungel et al. (2019) studying evapotranspiration in a BSh (dry semi-arid) climate obtained mean ETo d values in a lysimeter ranging from 0 to 12 mm day −1 . Lopes & Leal (2016) observed that the ETo d and ETo 24h methodologies have different results when taking months or seasons into consideration. When working with a reduced number of data, such as a few months, there is no possibility to analyze ETo considering the changes in meteorological variables throughout the year. The reduced period for analysis can also provide closer correlations, but which do not correspond to the reality of the environment. Long periods, on the other hand, can provide higher variations, since the results will be analyzed through extreme weather changes over the seasons. However, even in a longer period, it was found in the present study that the variations between ETo d and ETo 24h were small (Table 2), resulting in good correlations, errors and "d" index (Table 3). Similarly, Noia et al. (2014) in a study carried out in Dourados city, Mato Grosso do Sul State, Brazil, found that there is a small difference between the two methods of ETo estimation (ETo d or ETo 24h ), obtaining low deviations or errors.
In general, the results showed a monthly ETo 24h trend very similar to ETo d (Fig. 7). This aspect can also be confirmed with the average values (mm day −1 ) of the "d" indexes achieved in the 25 locations in Paraná State (Table 3; "d" ≥ 0.77 for Cfa climate and "d" ≥ 0.82 for Cfb climate). The average seasonal trend for ETo 24h and ETo d in Paraná State were also similar and close, with the Cfa "d" index equal to 0.97 for spring and summer; and Cfb "d" index equal to 0.99 in the spring and 0.98 in the summer. Lopes & Leal (2016) associating ETo d vs ETo 24h for semiarid climate obtained an agreement "d" index ranging from 0.98 to 0.99. In the present study, lower "d" indexes were observed in the autumn and winter periods for Cfa climate. The large number of failures in the input data to estimate ETo in the period may have influenced the differences in the results obtained in both methodologies. In stations with Cfb climate, in which there was a possibility of using more data in the winter period, "d" index ≥ 0.91 was obtained; and for the autumn period, when there were more failures, lower "d" indexes 0.34 ≤ "d" ≤ 0.96 were found (Table 3).
The correlation coefficients of the associations between ETo d vs ETo 24h were very promising. The lowest average value was found for Cfa climate, at Cidade Gaúcha station (r = 0.64), with correlations between 0.80 and 0.99 for other locations with Cfa climate and between 0.85 and 0.97 for Cfb climate. The lowest mean correlation values occurred in autumn and winter, reflected of the low number of data in the periods. Cidade Gaúcha showed considerable failures in the Rs sensor (it showed the same Rs values for day and night in about three months). It is believed that the lowest correlation obtained at the site was due to this reason. The Cfb climate presented excellent average correlations (r ≥ 0.99) for the annual period, and between 0.97 ≤ r ≤ 1.0 in the summer, autumn, winter and spring seasons ( Table 3). The readings failures verified in autumn did not compromise the correlations between ETo d vs ETo 24h . Treder & Klamkowski (2017) associating ETo d vs ETo 24h with the ASCE-PM model, also obtained a correlation coefficient r = 0.99, in humid continental climate, in Poland, in the period of May and September, 2016. In a similar study, Nolz & Rodný (2019) also obtained a correction coefficient r = 0.98 in the association between ETo d vs ETo 24h for sub-humid climate.
Many studies have pointed out better estimates with ETo 24h , in relation to ETo d with the ASCE-PM method, when compared to ETo measured by lysimeters (Nolz & Rodný, 2019;Dhungel et al. 2019). The analyzes carried out in the present study (Tables 2 and 3 and Fig. 7) showed that the ETo d and ETo 24h values had the same trend, were close and well associated in the 25 locations analyzed in the Paraná State. The results obtained are very interesting, as they make possible the development of studies for the planning, design and management of water in Paraná agriculture, considering alternatives for water loss from the soil-plant-system over the hours of the day.

Conclusions
The ETo h trend resembles the Gaussian distribution shape, corresponding inversely to relative humidity and directly to temperature, incident solar radiation and wind speed.
The highest ETo h values throughout the 24 h of the day in Paraná State occur between 12:00 p.m. and 2:00 p. m. The maximum ETo h average of the stations over the hours of the day is equal to 0.44 mm h −1 for Cfa climate and 0.35 mm h −1 for Cfb climate.
The two methodologies tested to obtain daily evapotranspiration in Paraná State resulted in average values of ETo 24h = 3.50 mm day −1 and ETo d = 3.32 mm day −1 (difference of 5.1%) for Cfa climate. For Cfb climate, ETo 24h = 2.69 mm day −1 and ETo d = 2.49 mm day −1 (difference of 7.4%) were obtained.
The ETo 24h was very well associated with ETo d obtained with the standard ASCE-PM method, with the advantage of allowing better understanding and monitoring of water loss in hourly periodicity, as long as climatic data are available in quantity and quality for hourly periodicity. License information: This is an open-access article distributed under the terms of the Creative Commons Attribution License (type CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original article is properly cited.