Acessibilidade / Reportar erro

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

Evapotranspiração de referência horária e diária pelo modelo ASCE-PM para o Estado do Paraná, Brasil

Abstract

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 Penman-Monteith 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−1 (Cfa climate type) and 0.35 mm h−1 (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.

Keywords:
hydrological cycle; water relations; water resources; models; precision

Resumo

Teve-se por objetivo no presente trabalho verificar a magnitude e tendência da evapotranspiração de referência horária (EToh), bem como associar e analisar as séries diárias de ETo (ETod) e a soma da ETo horária (ETo24h) em 24 h, estimada pelo modelo Penman-Monteith ASCE para o Estado do Paraná (tipos climáticos Cfa e Cfb). Dados de umidade relativa (UR), temperatura (T), radiação solar (Rs) e velocidade do vento (u2) foram obtidos de 25 estações meteorológicas do Instituto Nacional de Meteorologia, entre 01/12/2016 e 08/11/2018. As análises foram realizadas por meio de regressão linear e associações considerando a raiz quadrada do erro quadrado médio, coeficiente de correlação e índice de concordância. A tendência da EToh teve distribuição gaussiana, com valores mais altos entre as 12:00 e 14:00 h, com média máxima de 0.44 mm h−1 (para o clima Cfa) e 0.5 mm h−1 (em clima Cfb). A diferença média entre os valores de ETo24h e ETod foi pequena (5.1% para Cfa e 7.4% para Cfb), resultando em estreitas associações lineares. Os resultados obtidos indicam que a EToh tem bom potencial para ser utilizada no planejamento e manejo na área de engenharia de água e solo, no Estado do Paraná.

Palavras-chave:
ciclo hidrológico; relações hídricas; recursos hídricos; modelos; precisão

1. 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, 2019NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 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. 1994ALLEN, R.G.; SMITH, M.; PERRIER, A.; PEREIRA, L.S. An update for the definition of reference evapotranspiration. ICID Bulletin, v. 43, n. 2, p. 1-34, 1994.; Allen et al. 1998ALLEN, R.G.; PEREIRA, L.S.; RAES, D.; SMITH, M. Crop Evapotranspiration - Guidelines For Computing Crop Water Requirements. Irrigation and Drainage Paper 56. Rome: FAO, 300 p., 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., 1991HOWELL, T.A.; SCHNEIDER, A.D; JENSEN, M.E.; History of lysimeter design and use for evapotranspiration measurements. Repinted from Lysimeters for Evapotranspiration and Environmental Measurements. New York: IR Div/ASCE, p. 23-25, 1991.; Dhungel et al., 2019DHUNGEL, R.; AIKEN, R.; COLAIZZI, P.D.; LIN, X.; BAUMHARDT, R.L.; EVETTI, S.R.; BRAUER, D.K.; MAREK, B.G.W.; O’BRIEN, D. Increased Bias in Evapotranspiration Modeling Due to Weather and Vegetation Indices Data Sources. Agronomy Journal, v. 3, n. 3, p. 1407-1424, 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., 2014NOIA, C.P.Z.; PEREIRA, S.B.; ROSA, D.R.Q.; ALMEIDA, R.A. Evapotranspiração de referência estimada pelos métodos Penman-Monteith-FAO (56) e Hargreaves & Samani para o município de Dourados, MS. Revista Agrarian, v. 7, n. 24, p. 300-308, 2014.; Lopes & Leal, 2016LOPES, I.; LEAL, B.G. Evapotranspiração horária x diária utilizando Penman-Monteith para o polo de desenvolvimento Petrolina-PE/Juazeiro-BA. Revista Brasileira e Agricultura Irrigada, v. 10, n. 5, p. 914-924, 2016.). The models most recommended and used in the literature for this purpose are Penman-Monteith FAO N° 56 (Allen et al., 1998ALLEN, R.G.; PEREIRA, L.S.; RAES, D.; SMITH, M. Crop Evapotranspiration - Guidelines For Computing Crop Water Requirements. Irrigation and Drainage Paper 56. Rome: FAO, 300 p., 1998.) and Penman-Monteith ASCE (ASCE-EWRI, 2005ASCE-EWRI. The ASCE standardized reference evapotranspiration equation. In: ALLEN RG et al. (eds.), Report 0-7844-0805-X. St. Louis: American Society of Civil Engineers, Environmental Water Resources Institute, p. 1- 69, 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, 2005ASCE-EWRI. The ASCE standardized reference evapotranspiration equation. In: ALLEN RG et al. (eds.), Report 0-7844-0805-X. St. Louis: American Society of Civil Engineers, Environmental Water Resources Institute, p. 1- 69, 2005.).

The reference evapotranspiration in hourly periodicity (EToh) can allow higher precision for ETo estimates, and offer better perspectives for water and soil resources planning and management (Treder & Klamkowski, 2017TREDER, W.; KLAMKOWSKI, K. An hourly reference evapotranspiration model as a tool for estimating plant water requirements. Polska Akademia Nauk, Oddział w Krakowie. Infrastruktura i ekologia terenów wiejskich infrastructure and ecology of rural areas, v. 2, n. 1, p. 469-481, 2017.; Althoff et al., 2019ALTHOFF, D.; FILGUEIRAS, R.; DIAS, S.H.B.; RODRIGUES, L.N. Impact of sum-of-hourly and daily timesteps in the computations of reference evapotranspiration across the Brazilian territory. Agricultural Water Management, v. 226, n. 10578, p. 1-10, 2019.; Nolz & Rodný, 2019NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 2019.). In particular, the subtropical region where the Paraná State is located has scarce information regarding hourly reference evapotranspiration (EToh). 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., 2015COSTA, N.F.S.; FONSCECA, E.L.; PACE, L.F.T.D. Mapeamento da evapotranspiração em região de floresta no município de São João do Triunfo-PR utilizando o algoritmo Metric. Anais XVII Simpósio Brasileiro de Sensoriamento Remoto - SBSR, João Pessoa, p. 1431-1438, 2015.; Jerszurki et al., 2017).

In this context, we verify the magnitude and trend (daily and seasonal) of hourly reference evapotranspiration (EToh), as well as associate and analyze series of daily ETo (ETod) and the sum of hourly ETo in 24 h (ETo24h), estimated with the Penman-Monteith ASCE model for Paraná State, considering the predominant Cfa and Cfb climate types.

2. Material and Methods

The present study was carried out for Paraná State, Southern region of Brazil, with an area of 199.307.922 km2, according to Maack (2012)MAACK, R. Geografia física do Estado do Paraná. 4th ed. Curitiba: IBPT, 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., 2013ALVARES, C.A.; STAPE, J.L.; SENTELHAS, P.J.; GONçALVES, J.L.M.; SPAROVEK, G. Koppen's climate classification map for Brazil. Meteorologische Zeitschrift, v. 2, n. 7, p. 11-728, 2013.).

Figure 1
Predominant climate classification in Paraná State and location of meteorological stations.

The estimation of hourly (EToh) and daily (ETod) evapotranspiration was calculated with the standardized Penman-Monteith equation, presented by the American Society of Civil Engineers (ASCE-EWRI, 2005ASCE-EWRI. The ASCE standardized reference evapotranspiration equation. In: ALLEN RG et al. (eds.), Report 0-7844-0805-X. St. Louis: American Society of Civil Engineers, Environmental Water Resources Institute, p. 1- 69, 2005.) (Eq. (1)), using a short crop having an approximate height of 0.12 m:

(1) E T o P M A S C E = 0.408 δ ( R n G ) + γ C n ( T + 273 ) u 2 ( e s e a ) δ + γ ( 1 + C d u 2 )

where EToPM-ASCE is the hourly or daily reference evapotranspiration (EToh in mm h−1 or ETod in mm day−1, respectively); 0.408 is the coefficient equation (m2 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 s3 Mg−1 h−1 and s m−1, respectively); T is the average air temperature in the period considered (°C); u2 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 (ETod) was calculated using the ASCE-PM equation, according to recommendations and coefficients of the ASCE Manual of Practice N° 70 (ASCE-EWRI, 2005ASCE-EWRI. The ASCE standardized reference evapotranspiration equation. In: ALLEN RG et al. (eds.), Report 0-7844-0805-X. St. Louis: American Society of Civil Engineers, Environmental Water Resources Institute, p. 1- 69, 2005.; p.09-26), for soil cover with short grass: Cndaily = 900 K mm s3 Mg−1 h−1 and Cddaily = 0.34 s m−1; The hourly ETo (EToh) was calculated using the ASCE-PM equation, according to recommendations and coefficients of the ASCE Manual of Practice N° 70 (ASCE-EWRI, 2005ASCE-EWRI. The ASCE standardized reference evapotranspiration equation. In: ALLEN RG et al. (eds.), Report 0-7844-0805-X. St. Louis: American Society of Civil Engineers, Environmental Water Resources Institute, p. 1- 69, 2005.; p.09-26), for soil cover with short grass: Cnhourly = 37 K mm s3 Mg−1 h−1; and, Cddaytime = 0.24 s m−1 for daytime period, or Cdnighttime = 0.96 s m−1 for nighttime period.

The 24 hourly EToh values of one day were added, for statistical comparison with the ETod of the respective day (Eq. (2)):

(2) E T o 24 h = h = 1 n = 24 E T o h

where ETo24h is the reference evapotranspiration resulting from the sum of each h-values of hourly reference evapotranspiration of the same day (mm day−1); EToh 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 temperatures (T; °C); incident solar radiation (Rs; MJ m−2 day−1); and wind speed at 2 meters height (u2; 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)INMET. Rede de Estações Meteorológicas Automáticas do INMET. Nota Técnica No. 001/2011/SEGER/LAIME/CSC/INMET. Brasília: Ministério da Agricultura, Pecuária e Abastecimento, 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 (EToh), 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.

The results obtained for ETo estimative equations with hourly (EToh, which added resulted in ETo24h values) and daily (ETod) ASCE-PM model were compared and statistically validated using regression analyzes, and the main indexes and coefficients recommended in the literature (Eq. (3); Eq. (4) and Eq. (5)) (Jacovides & Kontoyiannis, 1995JACOVIDES, C.P.; KONTOYIANNIS, H. Statistical procedures for the evaluation of evapotranspiration computing models. Agricultural Water Management, v. 27, n. 4, p. 365-371, 1995.; Nolz & Rodný, 2019NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 2019.).

(3) R M S E = 1 n i = 1 n ( E T o 24 h i E T o d i ) 2
(4) r = i = 1 n [ ( E T o d i E T ¯ o d ) ( E T o 24 h i E T ¯ o 24 h ) ] i = 1 n ( E T o d i E T ¯ o d ) 2 i = 1 n ( E T o 24 h i E T ¯ o 24 h ) 2
(5) d = 1 i = 1 n ( E T o 24 h i E T o d i ) 2 i = 1 n ( | E T o 24 h i E T ¯ o d | | E T o d i E T ¯ o d | ) 2

where RMSE is the root mean square error (mm day−1); r is the Pearson correlation coefficient (dimensionless); d is the agreement index of Willmott (1982)WILLMOTT, C.J. Some comments on the evaluation of model performance. Bulletin American Meteorology Society, v. 63, n. 11, p. 1309-1313, 1982. (dimensionless); n is the number of hours analyzed (dimensionless); ETo24hi is the each i-value of daily ETo resulting from the sum of each h-value of hourly reference evapotranspiration for the same day (mm day−1); ETodi is the reference evapotranspiration estimated with the standard Penman-Monteith method at each i-day (mm day−1); ET¯od is the average of ETo values estimated with the standard method for all days analyzed in the period (mm day−1); ET¯o24h is the average of each i-daily ETo values of the period, resulting from the sum of each h-hourly reference evapotranspiration value of the same day (mm day−1).

3. Results and Discussion

3.1. Characterization of the input variables in the ASCE-PM model on daily and hourly periodicity

Table 1 shows the seasonal average values of air temperature (T; °C), relative humidity (RH; %), incident solar radiation (Rs; MJ m−2 day−1) and wind speed at 2 meters height (u2; m s−1), of the 25 meteorological stations analyzed in Paraná State, in the period between December 1, 2016 to November 8, 2018. Of the total weather stations analyzed, 15 are in Cfa and 10 in Cfb climate type. Fig. 2 shows the average seasonal trend of the variables (T, RH, Rs and u2), according to Cfa and Cfb climate types.

Table 1
Seasonal average in the year(1) (1) Seasons are considered to occur in the following periods: Summer between December 21 to March 20; Autumn between March 21 to June 20; Winter between June 21 to September 22; and Spring between September 23 to December 20. for air temperature (T; oC), relative humidity (RH; %), incident solar radiation (Rs; MJ m−2 day−1) and wind speed at 2 meters height (u2; m s−1) in 25 meteorological stations in Paraná State, between December 1, 2016 to November 8, 2018.
Figure 2
Seasonal average trend of the climatic variables in Paraná State, between December 1, 2016 to November 8, 2018, for 15 stations in Cfa climate and 10 stations in Cfb climate: a) Air temperature (T; °C), b) Relative humidity (RH; %), c) Incident solar radiation (Rs; MJ m−2 day−1), and, d) Wind speed at 2 meters height (u2; m s−1).

In general, the variables T, RH, Rs and u2 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 u2 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 (EToh) differ considerably throughout the day. Rs and u2 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 u2 (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.

Figure 3
Hourly average trend of the climatic variables in Paraná State, between December 1, 2016 to November 8, 2018, for 15 stations in the Cfa climate and 10 stations in Cfb climate: a) Air temperature (T; °C), b) Relative humidity (RH; %), c) Incident solar radiation (Rs; MJ m−2 day−1), and, d) Wind speed at 2 meters height (u2; m s−1).

3.2. Trend of hourly reference evapotranspiration (EToh) throughout the day

On average, for each weather station analyzed, the maximum values of EToh achieved over the 24 h of the day occurred between 12:00 p.m. and 2:00 p.m. Mean maximum EToh of 0.44 mm h−1 was observed for Cfa climate and 0.35 mm h−1 for Cfb (Fig. 4). During the peak EToh periods, the highest values of T, Rs, u2 and lowest values of RH had occurred (Fig. 3). The trends observed for EToh are quite evident, due to the dependence of evapotranspiration on the variables T, Rs, u2 and RH.

Figure 4
Average trend of the hourly reference evapotranspiration (EToh), in 25 meteorological stations in Paraná State, between December 1, 2016 to November 8, 2018 according to: a) Average EToh of the 15 stations in Cfa climate type, and, b) Average EToh of the 10 stations in Cfb climate type.

Ismael Filho et al. (2015)ISMAEL FILHO, A.; BORGES, P.F.; ARAúJO, L.S.; PEREIRA, A.R.; LIMA, E.M.; SILVA, L.S.; SANTOS JUNIOR, C.V. Influência das variáveis climáticas sobre a evapotranspiração. Gaia Scientia, v. 9, n. 1, p. 62-66, 2015. consider that RH has an inverse relationship to ETo. Thus, as higher the RH, lower the EToh. The authors statement also confirms the results obtained with EToh 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 EToh estimates at night. In the analyzes carried out in the present study, EToh 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)CAIR, M.A.; RICHARDS, J.H.; DONOVAN, L.A. Nighttime Stomatal Conductance and Transpiration in C3 and C4 Plants. Plant Physiology. v. 143, n. 1, p. 4-10, 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 EToh negative values Guimarães et al. (2013)GUIMARãES, P.L.O; SANTANA, M.A.A; VILELA, W.A.; PAES, T.F.; BERNI, L.A.; SILVA, L.F. Avaliação metrológica de um sistema de calibração indoor para piranômetros baseado em um simulador solar. Revista Brasileira de Energia Solar, v. 4, n. 1, p. 17-24, 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 EToh values were negative. Therefore, it is believed that the estimation of negative EToh 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)YILDIRIM, E.Y.; CAKMAK, B.; KOSE, T. Comparison of hourly and daily reference evapotranspiration values for GAP Projects area. Journal of Applied Sciences Research, v. 4, n. 1, p. 53-57, 2004. comparing EToh and ETod in Harran Plain, region of Turkey, also found EToh 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 EToh trend was very similar to that observed by the authors (Fig. 4).

In general, the seasonal trend of hourly reference evapotranspiration (EToh) 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).

Figure 5
Average trend of the hourly reference evapotranspiration (EToh), in 25 meteorological stations in Paraná State, for Cfa and Cfb climate type, between December 1, 2016 to November 1, 2018, considering: a) Spring, b) Summer, c) Autumn, and, d) Winter.

Pereira et al. (2016)PEREIRA, F.F.S.; PAI, E.D.; MONTENEGRO, R.J.V.; ROMáN, R.M.S.; GONZáLEZ, A.M.G.O.; ESCOBEDO, J.F. Estudo comparativo da evapotranspiração de referência entre localidades no Estado de São Paulo e na Província de Habana. Irriga, v. 21, n. 2, p. 395-408, 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 EToh values.

3.3. ETod trend and association between ETod and ETo24h throughout the year, in Paraná State

There was a tendency of the highest ETod 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).

Table 2
Seasonal average in the year(1) (1) Seasons are considered to occur in the following periods: Summer between December 21 to March 20; Autumn between March 21 to June 20; Winter between June 21 to September 22; and Spring between September 23 to December 20. for ETod and ETo24h (mm day−1) in 25 meteorological stations in Paraná State, between December 1, 2016 to November 8, 2018.
Figure 6
Daily trend of the reference evapotranspiration (ETod; mm day−1) over the analyzed period for Paraná State, being: a) Spring, b) Summer, c) Autumn, and, d) Winter.

The daily ETo obtained with the standard ASCE-PM method (ETod) or with the sum of EToh (ETo24h) did not show high variations. However, a trend towards higher ETo24h values was observed in Cfa climate, mainly during spring and summer (Table 2 and Fig 7).

Figure 7
Average values of ETod and ETo24h, in 25 meteorological stations in Paraná State, according to Cfa and Cfb climate types, between December 21, 2016 to November 8, 2018: a) Seasonal trend, and, b) Monthly trend.

As for the magnitude, the analyzes of the present study for Cfa climate indicated ETo24h average values of 3.50 mm day−1 and ETod average of 3.32 mm day−1, resulting in a difference of only 0.18 mm day−1 (5.1%). For Cfb climate, a ETo24h average of 2.69 mm day−1 and ETod 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)NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 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)ALLEN, R.G.; PEREIRA, L.S.; RAES, D.; SMITH, M. Crop Evapotranspiration - Guidelines For Computing Crop Water Requirements. Irrigation and Drainage Paper 56. Rome: FAO, 300 p., 1998. also considers that the presence of clouds in regions with humid climate provides lower ETo values. Dhungel et al. (2019)DHUNGEL, R.; AIKEN, R.; COLAIZZI, P.D.; LIN, X.; BAUMHARDT, R.L.; EVETTI, S.R.; BRAUER, D.K.; MAREK, B.G.W.; O’BRIEN, D. Increased Bias in Evapotranspiration Modeling Due to Weather and Vegetation Indices Data Sources. Agronomy Journal, v. 3, n. 3, p. 1407-1424, 2019. studying evapotranspiration in a BSh (dry semi-arid) climate obtained mean ETod values in a lysimeter ranging from 0 to 12 mm day−1.

Lopes & Leal (2016)LOPES, I.; LEAL, B.G. Evapotranspiração horária x diária utilizando Penman-Monteith para o polo de desenvolvimento Petrolina-PE/Juazeiro-BA. Revista Brasileira e Agricultura Irrigada, v. 10, n. 5, p. 914-924, 2016. observed that the ETod and ETo24h 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 ETod and ETo24h were small (Table 2), resulting in good correlations, errors and “d” index (Table 3). Similarly, Noia et al. (2014)NOIA, C.P.Z.; PEREIRA, S.B.; ROSA, D.R.Q.; ALMEIDA, R.A. Evapotranspiração de referência estimada pelos métodos Penman-Monteith-FAO (56) e Hargreaves & Samani para o município de Dourados, MS. Revista Agrarian, v. 7, n. 24, p. 300-308, 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 (ETod or ETo24h), obtaining low deviations or errors.

Table 3
Seasonal and annual values of the correlation coefficient (r; dimensionless), “d” index (dimensionless) and root mean square error (RMSE; mm day−1) of the associations between ETod vs ETo24h, for 25 meteorological stations in Paraná State, between December 1, 2016 to November 8, 2018.

In general, the results showed a monthly ETo24h trend very similar to ETod (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 ETo24h and ETod in Paraná State were also similar and close, with the Cfad” index equal to 0.97 for spring and summer; and Cfbd” index equal to 0.99 in the spring and 0.98 in the summer. Lopes & Leal (2016)LOPES, I.; LEAL, B.G. Evapotranspiração horária x diária utilizando Penman-Monteith para o polo de desenvolvimento Petrolina-PE/Juazeiro-BA. Revista Brasileira e Agricultura Irrigada, v. 10, n. 5, p. 914-924, 2016. associating ETod vs ETo24h 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 ETod vs ETo24h 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 ETod vs ETo24h. Treder & Klamkowski (2017)TREDER, W.; KLAMKOWSKI, K. An hourly reference evapotranspiration model as a tool for estimating plant water requirements. Polska Akademia Nauk, Oddział w Krakowie. Infrastruktura i ekologia terenów wiejskich infrastructure and ecology of rural areas, v. 2, n. 1, p. 469-481, 2017. associating ETod vs ETo24h 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)NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 2019. also obtained a correction coefficient r = 0.98 in the association between ETod vs ETo24h for sub-humid climate.

Nolz & Rodný (2019)NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 2019. obtained RMSE = 0.27 mm day−1 in the associations between ETod vs ETo24h in sub-humid climate. In the present study the RMSE values were higher. With the exception of Cidade Gaúcha, due to its lower correlations, the values were between: 0.29 ≤ RMSE ≤ 0.71 mm day−1 for the annual period; 0.23 ≤ RMSE ≤ 0.76 mm day−1 in spring; 0.16 ≤ RMSE ≤ 0.53 mm day−1 in summer; 0.26 ≤ RMSE ≤ 1.35 mm day−1 in autumn; and, 0.35 ≤ RMSE ≤ 1.02 mm day−1 in winter (Table 3).

Many studies have pointed out better estimates with ETo24h, in relation to ETod with the ASCE-PM method, when compared to ETo measured by lysimeters (Nolz & Rodný, 2019NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 2019.; Dhungel et al. 2019DHUNGEL, R.; AIKEN, R.; COLAIZZI, P.D.; LIN, X.; BAUMHARDT, R.L.; EVETTI, S.R.; BRAUER, D.K.; MAREK, B.G.W.; O’BRIEN, D. Increased Bias in Evapotranspiration Modeling Due to Weather and Vegetation Indices Data Sources. Agronomy Journal, v. 3, n. 3, p. 1407-1424, 2019.). The analyzes carried out in the present study (Tables 2 and 3 and Fig. 7) showed that the ETod and ETo24h 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.

4. Conclusions

The EToh trend resembles the Gaussian distribution shape, corresponding inversely to relative humidity and directly to temperature, incident solar radiation and wind speed.

The highest EToh values throughout the 24 h of the day in Paraná State occur between 12:00 p.m. and 2:00 p.m. The maximum EToh 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 ETo24h = 3.50 mm day−1 and ETod = 3.32 mm day−1 (difference of 5.1%) for Cfa climate. For Cfb climate, ETo24h= 2.69 mm day−1 and ETod = 2.49 mm day−1 (difference of 7.4%) were obtained.

The ETo24h was very well associated with ETod 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.

References

  • ALTHOFF, D.; FILGUEIRAS, R.; DIAS, S.H.B.; RODRIGUES, L.N. Impact of sum-of-hourly and daily timesteps in the computations of reference evapotranspiration across the Brazilian territory. Agricultural Water Management, v. 226, n. 10578, p. 1-10, 2019.
  • ALLEN, R.G.; SMITH, M.; PERRIER, A.; PEREIRA, L.S. An update for the definition of reference evapotranspiration. ICID Bulletin, v. 43, n. 2, p. 1-34, 1994.
  • ALLEN, R.G.; PEREIRA, L.S.; RAES, D.; SMITH, M. Crop Evapotranspiration - Guidelines For Computing Crop Water Requirements. Irrigation and Drainage Paper 56 Rome: FAO, 300 p., 1998.
  • ALVARES, C.A.; STAPE, J.L.; SENTELHAS, P.J.; GONçALVES, J.L.M.; SPAROVEK, G. Koppen's climate classification map for Brazil. Meteorologische Zeitschrift, v. 2, n. 7, p. 11-728, 2013.
  • ASCE-EWRI. The ASCE standardized reference evapotranspiration equation. In: ALLEN RG et al. (eds.), Report 0-7844-0805-X St. Louis: American Society of Civil Engineers, Environmental Water Resources Institute, p. 1- 69, 2005.
  • CAIR, M.A.; RICHARDS, J.H.; DONOVAN, L.A. Nighttime Stomatal Conductance and Transpiration in C3 and C4 Plants. Plant Physiology v. 143, n. 1, p. 4-10, 2007.
  • COSTA, N.F.S.; FONSCECA, E.L.; PACE, L.F.T.D. Mapeamento da evapotranspiração em região de floresta no município de São João do Triunfo-PR utilizando o algoritmo Metric. Anais XVII Simpósio Brasileiro de Sensoriamento Remoto - SBSR, João Pessoa, p. 1431-1438, 2015.
  • DHUNGEL, R.; AIKEN, R.; COLAIZZI, P.D.; LIN, X.; BAUMHARDT, R.L.; EVETTI, S.R.; BRAUER, D.K.; MAREK, B.G.W.; O’BRIEN, D. Increased Bias in Evapotranspiration Modeling Due to Weather and Vegetation Indices Data Sources. Agronomy Journal, v. 3, n. 3, p. 1407-1424, 2019.
  • GUIMARãES, P.L.O; SANTANA, M.A.A; VILELA, W.A.; PAES, T.F.; BERNI, L.A.; SILVA, L.F. Avaliação metrológica de um sistema de calibração indoor para piranômetros baseado em um simulador solar. Revista Brasileira de Energia Solar, v. 4, n. 1, p. 17-24, 2013.
  • HOWELL, T.A.; SCHNEIDER, A.D; JENSEN, M.E.; History of lysimeter design and use for evapotranspiration measurements. Repinted from Lysimeters for Evapotranspiration and Environmental Measurements New York: IR Div/ASCE, p. 23-25, 1991.
  • INMET. Rede de Estações Meteorológicas Automáticas do INMET. Nota Técnica No. 001/2011/SEGER/LAIME/CSC/INMET Brasília: Ministério da Agricultura, Pecuária e Abastecimento, 2011.
  • ISMAEL FILHO, A.; BORGES, P.F.; ARAúJO, L.S.; PEREIRA, A.R.; LIMA, E.M.; SILVA, L.S.; SANTOS JUNIOR, C.V. Influência das variáveis climáticas sobre a evapotranspiração. Gaia Scientia, v. 9, n. 1, p. 62-66, 2015.
  • JACOVIDES, C.P.; KONTOYIANNIS, H. Statistical procedures for the evaluation of evapotranspiration computing models. Agricultural Water Management, v. 27, n. 4, p. 365-371, 1995.
  • LOPES, I.; LEAL, B.G. Evapotranspiração horária x diária utilizando Penman-Monteith para o polo de desenvolvimento Petrolina-PE/Juazeiro-BA. Revista Brasileira e Agricultura Irrigada, v. 10, n. 5, p. 914-924, 2016.
  • MAACK, R. Geografia física do Estado do Paraná 4th ed. Curitiba: IBPT, 2012.
  • NOIA, C.P.Z.; PEREIRA, S.B.; ROSA, D.R.Q.; ALMEIDA, R.A. Evapotranspiração de referência estimada pelos métodos Penman-Monteith-FAO (56) e Hargreaves & Samani para o município de Dourados, MS. Revista Agrarian, v. 7, n. 24, p. 300-308, 2014.
  • NOLZ, R.; RODNý, M. Evaluation and validation of the ASCE standardized reference evapotranspiration equations for a subhumid site in northeastern Austria. Journal of Hydrology and Hydromechanics, v. 67, n. 3, p. 289-296, 2019.
  • PEREIRA, F.F.S.; PAI, E.D.; MONTENEGRO, R.J.V.; ROMáN, R.M.S.; GONZáLEZ, A.M.G.O.; ESCOBEDO, J.F. Estudo comparativo da evapotranspiração de referência entre localidades no Estado de São Paulo e na Província de Habana. Irriga, v. 21, n. 2, p. 395-408, 2016.
  • TREDER, W.; KLAMKOWSKI, K. An hourly reference evapotranspiration model as a tool for estimating plant water requirements. Polska Akademia Nauk, Oddział w Krakowie. Infrastruktura i ekologia terenów wiejskich infrastructure and ecology of rural areas, v. 2, n. 1, p. 469-481, 2017.
  • WILLMOTT, C.J. Some comments on the evaluation of model performance. Bulletin American Meteorology Society, v. 63, n. 11, p. 1309-1313, 1982.
  • YILDIRIM, E.Y.; CAKMAK, B.; KOSE, T. Comparison of hourly and daily reference evapotranspiration values for GAP Projects area. Journal of Applied Sciences Research, v. 4, n. 1, p. 53-57, 2004.

Publication Dates

  • Publication in this collection
    22 Mar 2021
  • Date of issue
    Apr-Jun 2021

History

  • Received
    12 June 2020
  • Reviewed
    17 July 2020
  • Accepted
    09 Aug 2020
Sociedade Brasileira de Meteorologia Rua. Do México - Centro - Rio de Janeiro - RJ - Brasil, +55(83)981340757 - São Paulo - SP - Brazil
E-mail: sbmet@sbmet.org.br