Impact of sum-of-hourly and daily timesteps in the computations of reference evapotranspiration across the Brazilian territory

Agricultural Water Management 226 (2019) 105785

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Impact of sum-of-hourly and daily timesteps in the computations of reference evapotranspiration across the Brazilian territory

T

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Daniel Althoffa, , Roberto Filgueirasa, Santos Henrique Brant Diasb, Lineu Neiva Rodriguesc a

Department of Agricultural Engineering, Federal University of Viçosa (UFV), Av. Peter Henry Rolfs, s.n., 36570-900, Viçosa, Minas Gerais, Brazil Department of Soil Science and Agricultural Engineering, State University of Ponta Grossa (UEPG), Av. General Carlos Cavalcanti, 4748, 84030-900, Ponta Grossa, Paraná, Brazil c Brazilian Agricultural Research Corporation (EMBRAPA) Cerrados, BR-020, Km 18, 73310-970, Planaltina, DF, Brazil b

A R T I C LE I N FO

A B S T R A C T

Keywords: ASCE standardized Irrigation management Penman-Monteith Water resources

Estimating reference evapotranspiration (ETo) in 24 h timesteps has been considered sufficiently accurate for a long time. However, recent advances in weather data acquisition has made it feasible to apply the hourly procedures in ETo computation. Hourly timesteps can improve ETo estimates accuracy, for data averaged daily may misrepresent evaporative power during parts of the day. Only a few studies have assessed vast databases, yet, studies considering tropical regions are basically inexistent. The objective of the present study was to assess the differences between daily ETo computations performed on 24 h (ETod) and hourly (EToh) timesteps for the Brazilian territory. Daily and hourly ETo computations were performed according to the standardized ASCE (American Society of Civil Engineers) Penman-Monteith equation. Large daily weather variations of meteorological parameters resulted in ETod generally underestimating EToh, while lower variations resulted in ETod overestimating. Overall, ETod overestimated EToh in 0.7%, with monthly percentage bias ranging from -3.9% to 2.9%. This study considered one year of data from 567 automatic weather stations and, despite acknowledging the existence of interannual climate variability, findings strongly agreed with relevant literature. ETod predominantly overestimated EToh during wet periods in warm regions. Thus, this behavior is observed almost yearround for the tropical monsoon and rainforest climate, in the Amazon and Pantanal biome. For the tropical savannah and semi-arid climate, ETod overestimated EToh during wetter periods (main crop harvest) but underestimated along the dry season (second harvest). On the other hand, ETod predominately underestimated EToh for colder regions, such as the Pampa (humid sub-tropical climate), regardless of rainfall. The Cerrado and Caatinga are likely to be affected most, for EToh is underestimated in periods of lower water availability, making adequate irrigation techniques fundamental.

1. Introduction Crop evapotranspiration is considered one of the major components of hydrological cycle (Djaman et al., 2018b). Over recent decades, evapotranspiration increases due to climatic change have been observed in many regions across the globe (Zhang et al., 2016). These trends are responsible for further increasing conflicts among water users, especially in agricultural areas (Pires et al., 2016). To reduce future conflicts over water use in such areas, water should be used precisely (Dinpashoh et al., 2019). Irrigation activities need to be more efficient, which can be achieved through irrigation management techniques (Chukalla et al., 2015; Geerts and Raes, 2009) that depends on more reliable evapotranspiration estimates. A popular irrigation management technique is the deficit irrigation,

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which consists on irrigating during the growth stages that the crop is sensitive to water deficit and limiting water in the other phenological stages. Many researchers have found that deficit irrigation techniques are decisive to increase water use efficiency and achieve sustainable water use (Fabeiro et al., 2001; Geerts and Raes, 2009; Goldhamer and Fereres, 2017; Tari, 2016). However, to obtain the correct values of crop water demand has long been a challenge, especially due to the fact that direct crop evapotranspiration measuring is not only costly but laborious and difficult to implement in real management. In order to surpass these limitations, evapotranspiration has been estimated indirectly based on climatic data. In this context, computing reference evapotranspiration (ETo) in 24 h timesteps has been considered sufficiently accurate for designing, planning and managing irrigation. Yet, advances in data acquisition from weather stations in

Corresponding author. E-mail address: daniel.althoff@ufv.br (D. Althoff).

https://doi.org/10.1016/j.agwat.2019.105785 Received 30 May 2019; Received in revised form 22 August 2019; Accepted 7 September 2019 0378-3774/ © 2019 Elsevier B.V. All rights reserved.

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in its 6 biomes (Fig. 1): Amazon rainforest (49%), Atlantic rainforest (13%), Savanna (Cerrado) (24%), Caatinga (10%), Pantanal (2%) and Southern plains (Pampa) (2%). The Amazon, Cerrado and Pantanal present predominant tropical climate, while Caatinga presents predominant semi-arid climate, Pampa is within humid subtropical climate zone and Atlantic rainforest is divided in tropical and humid sub-tropical climate zones.

recent years have made it feasible to apply evapotranspiration procedures on an hourly basis. The difference associated to ETo computation using daily or hourly averaged data is unpredictable and varies with location and weather conditions (Irmak et al., 2005). For instance, some studies have reported on the differences between ETo estimates for different timesteps under different climatic conditions. Irmak et al. (2005) assessed 9 sites in humid coastal and semiarid temperate climates and observed daily to sum-of-hourly ratios ranging from 0.97 to 1.09. Ji et al. (2017) assessed ETo computations in the Chinese arid climatic conditions and found the daily ETo to overestimate their corresponding sum-of-hourly ETo from 5% to 7%. Djaman et al. (2018b) reported sum-of-hourly ETo estimation to have from -0.2% up to 16.6% higher annual ETo in arid and semi-arid regions of New Mexico. Itenfisu et al. (2003) presented a study performed in 45 sites, but mostly for arid, semi-arid and humid sub-tropical climates. The only study found considering tropical climatic conditions was performed by Perera et al. (2015), where only two of 40 sites were classified within this climatic zone. According to Allen et al. (2000), hourly or shorter timesteps have the advantage of improving ETo estimates accuracy in locations where large diurnal changes in meteorological parameters present different patterns than for the locations in which they were developed. In arid and semi-arid regions, where diurnal temperature amplitude is large, daily ETo computations are well-documented to overestimate sum-ofhourly ETo (Djaman et al., 2018a, b; Irmak et al., 2005; Ji et al., 2017). Tropical regions have climatic conditions very distinct from arid and semi-arid regions, but have also been documented to present substantial differences in diurnal cycles (Yang and Slingo, 2001). Despite the diversity of studies, the improvements of calculating ETo in hourly timesteps has not been thoroughly investigated for the tropical regions. In this context, Brazil, one of the world’s largest country and food producers, has its climatic conditions classified as tropical across most of its territory (Alvares et al., 2013) and, despite of its economic importance, studies assessing the differences of sum-of-hourly and daily ETo for extensive areas under tropical climate are basically inexistent. Understanding the differences between daily and hourly ETo estimates across the Brazilian territory can contribute to improve irrigation water use and reduce water conflicts in some strategic regions of Brazil. Thus, the objective of this study was to investigate differences between sum-of-hourly and daily ETo estimates in the Brazilian territory.

2.2. Data sources and integrity The reference evapotranspiration computations were performed using hourly meteorological data obtained from the Brazilian National Institute of Meteorology (INMET). Networks of automatic weather stations has increased in Brazil in the last years, but the available quantity of meteorological data is still low and varies a lot among regions. Due to this fact, this study was conducted for the period from 01/ 02/2018 to 31/01/2019 and focused on the regional variability of ETo instead of its temporal variation. The Brazilian’s climates and biomes heterogeneity provide a broad variability of meteorological conditions, which will further increase the knowledge of sum-of-hourly and daily ETo estimates agreement over different conditions. The INMET adopts the model MAWS-301 as the standard surface automatic weather station (AWS), a station provided by the Finnish company Vaisala and installed according to the World Meteorological Organization standards (INMET, 2011). INMET’s network contemplates 567 AWS across the Brazilian territory (Fig. 2), recording hourly data of temperature, relative humidity, wind speed, solar radiation, atmospheric pressure and rainfall. The quantity of AWS is lower in the northwest region of Brazil. 341 AWS are located inside climatic zone A, 36 in B and 190 in C. The stations density within biomes is higher in the Atlantic rainforest (0.187 stations/1,000 km2) and Pampa (0.142 stations/1,000 km2), intermediate for Caatinga (0.095 stations/1,000 km2) and Cerrado (0.081 stations/1,000 km2), and lower for Pantanal (0.027 stations/1,000 km2) and Amazon (0.020 stations/1,000 km2). Hourly weather data that presented days with missing or faulty data were eliminated. Screening procedures to eliminate faulty data were: relative humidity values outside the range 5–100% were flagged and corresponding daily data eliminated (Gavilán et al., 2008); solar radiation measurements above global radiation had corresponding daily data eliminated (Allen, 1996); stations with equal values for maximum and minimum temperature were also eliminated (Shafer et al., 2000). Final results of evapotranspiration estimates were also assessed in order to eliminate stations with unreasonable spatial incoherence between its neighbor stations. After data screening, stations reliability was assessed by the percentage of time they presented data considered fit for further analysis in the study period, that is, passing the criteria used in screening procedure (Allen, 1996; Gavilán et al., 2008; Shafer et al., 2000).

2. Materials and methods 2.1. Study area With a population of almost 210 million people, Brazil is the largest country in South America (Fig. 1) and fifth largest in the world, covering approximately 8.52 million km2. Brazil has an average surface water discharge of approximately 260,000 m³ s−1, and accounts for 12% of the world’s fresh water reserves (ANA, 2017b). Its agriculture covers about 0.65 million km2 of its territory (Miranda, 2018), being the world’s largest cattle, sugarcane, orange, coffee and fibre crops producer, second largest soybean producer, and standing out in the production of a diverse number of other fruits and grains (FAO, 2019). With an irrigated area of approximately seven million hectares, irrigation is responsible for 67% of Brazil’s total consumptive water use. Also, irrigated areas are expected to expand up to 45% until 2030, which would represent a rise of 42% in consumptive water use (ANA, 2017a). Disputes over water use are fairly common in many regions of Brazil (Carvalho and Magrini, 2006) and are expected to further increase due to climate changes (Chou et al., 2014; Pires et al., 2016) and increase in water demand. Alvares et al. (2013) has classified Brazil, according to the Köppen climate classification (Köppen, 1936), into three climatic zones: A zone – tropical climate (81%); B zone – semi-arid climate (5%); and C zone – humid sub-tropical climate (14%). Brazil also presents rich biodiversity

2.3. Reference evapotranspiration computation Hourly and daily reference evapotranspiration computations were performed according to the methodology presented by Allen et al. (2006), known as the standardized ASCE (American Society of Civil Engineers) Penman-Monteith. Allen et al. (2006) recommended the use of a different parametrization of surface resistance when the FAO56 Penman-Monteith ETo equation is applied to hourly or shorter basis computations. The ASCE’s reference evapotranspiration is calculated as follows: Cn

ETo =

0.408 (Rn – G) + γ T+273 u2 (es – ea ) Δ + γ (1 + Cd u2)

(1) −1

−1

or mm hr ); where: ETo = reference evapotranspiration (mm d Rn = net radiation (MJ m-2 d−1 or MJ m-2 hr−1); G = soil heat flux, 2

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Fig. 1. Localization of Brazil in the context of South America (A), its biomes (B) and altitude (C). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

positive if soil is warming (MJ m-2 d−1 or MJ m-2 hr−1); T = average daily or hourly mean air temperature (°C); u2 = average daily or hourly wind speed at 2 m height (m s−1); es = saturation vapor pressure (kPa); ea = actual vapor pressure (kPa); Δ = slope of saturation vapor pressure curve (kPa °C−1); γ = psychrometric constant (kPa °C−1); Cd = denominator constant for grass-reference surface dependent on calculation timestep (equal to 0.34 s m−1 for 24h time step, and equal to

0.24 and 0.96 s m−1 for hourly timesteps during daytime and nighttime, respectively and Cn = numerator constant for grass-reference surface dependent on calculation timestep (equal to 900 °C mm s3 Mg−1 d−1 for 24h time step, and equal to 37 °C mm s3 Mg−1 h−1 for hourly timesteps). Wind speed values were measured at 10 m height and were converted to values at 2 m height (u2) (Allen et al., 1998). All the other

Fig. 2. Brazilian climatic zones according to Köppen and weather stations spatial distribution in its latitude and longitude (marginal histograms). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 3

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assessment of ETod. The reason for selecting the EToh method as the basis was because several studies have pointed out that diurnal changes in meteorological parameters can cause 24 h means to misrepresent the daily ETo (Allen et al., 1994; Pruitt and Doorenbos, 1977; Snyder and Pruitt, 1985) and recommended the use of hourly data for its estimation (Allen et al., 2000; Gavilán et al., 2007; Irmak et al., 2005; Pruitt and Lourence, 1966; Tanner and Pelton, 1960). The statistical indices used to quantify the agreement between equations were the mean bias deviation (MBD), percentage bias (PBIAS), mean absolute deviation (MBD) and root-mean-squared deviation (RMSD).

Table 1 Statistical description of meteorological parameters and reference evapotranspiration. Variables

Xmin

Xmax

− X

SD

Skew

Kurt

Rf-h Rf-d T-h T-d RH-h RH-d Rs-h Rs-d u2-h u2-d EToh ETod

0.00 0.00 −4.70 1.84 7.00 7.50 0.00 2.60 0.00 0.00 0.23 0.38

88.20 197.20 44.40 37.08 100.00 100.00 5.30 41.70 15.56 11.64 10.16 10.17

0.13 3.24 23.48 23.48 72.04 72.04 0.76 18.16 1.40 1.40 3.89 3.92

1.21 9.61 5.39 4.02 19.60 13.43 1.07 6.03 1.20 0.88 1.46 1.43

19.58 5.37 −0.35 −1.14 −0.68 −0.77 1.22 −0.22 1.12 1.18 0.05 0.13

569.30 42.21 0.49 1.85 −0.41 0.36 0.18 −0.22 1.94 3.07 −0.35 −0.35

n

MBD =

1 ∑ (ETodi – ETohi) n i=1

PBIAS =

Xmin = minimum observed value; Xmax = maximum observed value; X̄ = mean observed value; SD = standard deviation; Skew = Skeweness; Kurt = Kurtosis; Rf = rainfall (mm); T = mean air temperature (°C); RH = relative humidity (%); Rs = solar radiation (MJ m−2 hr-1 or MJ m−2 d-1); u2 = wind speed at 2 m height (m s-1); P = atmospheric pressure (kPa); EToh and ETod = reference evapotranspiration based on hourly and daily timesteps (mm d-1); -h and -d indicates whether variable refers to mean hourly or mean daily values.

MBD 100 mean(ETo h )

(2)

(3)

n

MAD =

1 ∑ |ETodi – ETohi| n i=1

(4)

n

RMSD =

variables were also assumed or calculated according to FAO56. The Stefan-Boltzmann constant was taken as 4.901 10−9 MJ K-4 m-2 d-1 and 2.043 10-10 MJ K-4 m-2 hr-1 for 24 h and hourly time step, respectively. The specific heat at constant temperature was set to 1.013 10-3 MJ kg1 °C-1, latent heat of vaporization was equal to 2.45 MJ kg-1 and the ratio of molecular weight of water vapor to dry air equals to 0.622. Though soil heat flux is simplified for ETo calculations in 24 h time step (Gd ≈ 0), it is important for hourly calculations and should not be overlooked. For hourly timesteps, Ghr was considered equal to 0.1 Rn during daylight (defined as when Rs > 0) and 0.5 Rn during nighttime. The ratio between solar radiation and clear sky solar radiation (Rs/Rso) was used to represent cloud cover in the Rn computation and was limited to less than or equal to 1.0 during all periods. During nighttime, Rs/Rso calculated between 2–3 hours before sunset was adopted. ETo computations performed in hourly timesteps were summed over 24 h periods and is denominated EToh, whereas ETo computations performed on 24 h time step is named ETod.

1 ∑ (ETodi – ETohi )2 n i=1

(5)

where n = the number of observations. RMSD indicates the variance from 1:1 line and is commonly used to judge the accuracy of methods. MAD is an indication of how widely the ETod values diverged from EToh on average, while MBD and PBIAS provide a general overview whether ETod over (> 0) or underestimates (< 0) EToh. The fit line between both estimates was also plotted along with the 1:1 line in order to assess if systematical under or overprediction would occur for lower or higher values of ETo. 3. Results 3.1. Data After the quality and integrity analysis of the weather data obtained from INMET the final dataset was composed by 3,769,440 pairs of hourly meteorological observations. The AWS network covers a diverse number of regions and ecosystems which are subject to different terrain, environmental and climatic settings, providing a very rich database for a broad evaluation (Figs. 1 and 2). The statistical description of all meteorological parameters and evapotranspiration is presented in Table 1. Hourly mean air temperature ranged from -4.70 to 44.40 °C, a difference of 49.10 °C, while daily mean air temperature showed a difference of only 35.20 °C. Wind speed presented a range of hourly values up to 33.7% larger than for daily averages. Relative humidity (RH) showed similar range for both time periods. EToh ranged from 0.23 to 10.16 mm a variation similar to ETod (0.38 to 10.17 mm). The T, Rs and u2 were positively correlated with EToh while RH was negatively correlated. The correlation coefficients obtained were 0.59 (T), -0.62 (RH), 0.92 (Rs) and 0.29 (u2); The correlations with ETod were equal to 0.60 (T), -0.64 (RH), 0.91 (Rs) and 0.28 (u2). The variability and amplitude of meteorological parameters across the months is presented for each climatic zone in the Appendix 1. In this supplementary material, a brief description is given for the meteorological parameters as well as reference evapotranspiration and monthly rainfall. It is also observed in the Figure A.1 the wet seasons periods, which was established for months when rainfall was greater than 60 mm (Peel et al., 2007). Meteorological stations reliability was also assessed (Fig. 3) by computing the percentage of time they provided complete daily data during the studied period. Overall reliability was 84%, with approximately 78% (442) of stations presenting reliable data over 75% of the

2.4. Effect of meteorological parameters diurnal changes on different evapotranspiration timesteps Rainfall occurrence may directly relate to diurnal changes in wind speed, cloudiness and vapor pressure, which in its turn interfere directly on how well ETod and EToh agrees (Allen et al., 2000). In order to better understand these interactions, the relations between rainfall, diurnal changes of meteorological parameters and differences between ETo estimates (ETod – EToh) were assessed. The diurnal changes of meteorological parameters were represented by the standard deviation of its hourly values. These standard deviations directly relate to the range of within-day observations, which has a strong influence in ETo estimation and may not be well represented by daily averages. For example, a high standard deviation of relative humidity for a given day would indicate a large range between minimum and maximum relative humidity values. This means that, at some point during that day, relative humidity has registered values much larger and/or much lower than the average, which could result in high evaporative power. Thus, adopting daily averages would lead to the misrepresentation of ETo. 2.5. Performance and statistical analysis The ASCE EToh computations were used as basis for comparison and 4

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Fig. 3. Automatic meteorological stations reliability for study period in Brazil (A), reliability histogram (B) and boxplot (C). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

indicates that ETod tends to overestimate lower values of EToh. MAD and RMSD presented low values, equal to 0.17 and 0.22 mm d−1. Although with good agreement, ETod showed a small tendency to overestimate EToh across the Brazilian territory, with MBD equal to 0.03 mm d−1 and PBIAS equal to 0.7%. Such overestimations are more noticeable in the semi-arid region and most of the tropical region, in the Amazon. Stations where ETod tended to underestimate EToh were mostly located in the humid sub-tropical region and, more specifically, in the Pampa. In a more detailed analysis, monthly average MBD for each station is

time and 57% (321) over 90% of the time (Fig. 3B and 3C). 3.2. Evapotranspiration timesteps comparison An initial evapotranspiration analysis and comparison between hourly and daily calculations considering the entire study period is presented in Fig. 4. EToh presented its higher values in the semi-arid, with similar annual averages for the tropical and humid sub-tropical regions. In general, EToh and ETod presented good agreement, with R2 and slope of fit-line near 1; the positive intercept and slope just below 1

Fig. 4. Evapotranspiration annual average (A) and comparison between sum-of-hourly and daily (scatterplot (B), mean bias deviation (MBD) (C) and percentage bias (PBIAS) (D). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 5

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Fig. 5. Sum-of-hourly and daily reference evapotranspiration monthly mean bias deviation (MBD) and monthly accumulated rainfall. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

Despite showing larger deviation from 1:1 line, Amazon showed overall better agreement between ETo estimates when compared to Pampa and Pantanal, for its MAD and RMSD were lower. Pampa and Pantanal presented the least favorable agreement between ETo estimates, with MAD equal to 0.20 and 0.21 mm d−1, and RMSD equal to 0.25 and 0.26 mm d−1, respectively; the agreement observed for all the other biomes presented MAD ranging from 0.17 to 0.18 mm d−1, and RMSD ranging from 0.21 to 0.22 mm d−1. The monthly averages percentage bias for Brazil and its biomes are shown in Table 2, where it is possible to have a better understanding of evapotranspiration regional deviations. In general, ETod overestimated EToh (average PBIAS = 0.7%); monthly PBIAS ranged from -3.9% in July to 2.9% in November, with higher underestimations from May to August, which corresponds to, in a large part of Brazil, the dry season. The Cerrado biome presented overall good agreement between ETo estimates (average annual PBIAS = 0.2%), followed by Atlantic rainforest (average annual PBIAS = 0.3%), Caatinga (average annual PBIAS = 0.7%), Pampa (average annual PBIAS = -1.6%), Pantanal (average annual PBIAS = 2.9%) and Amazon (PBIAS = 3.9%). The low PBIAS observed in the Cerrado and Atlantic rainforest biomes, representing both almost 66% of the Brazilian AWS network, attenuated the bias between ETo estimates when considering the entire territory.

shown in Fig. 5. In general, ETod in the Amazon region showed steady overestimation of EToh; Pantanal, Caatinga, Atlantic rainforest and Cerrado regions presented similar behavior, with ETod underestimating EToh during the dry season and overestimating during the wet season; In the Southern region ETod moderately underestimated EToh throughout the year, with only few weather stations presenting overestimates by the end and in the beginning of the year. It is also noted in Fig. 5 for the tropical and semi-arid regions that periods with higher volumes of rainfall coincide with ETod larger overestimations of EToh. For the humid sub-tropical regions this is not necessarily true. Colder regions, like the Pampa in the South, seem to underestimate EToh despite the rainfall incidence. These observations strongly relate with what was discussed on topic 2.4, where rainfall patterns in certain regions are expected to interfere on how well EToh and ETod agrees. The regression between ETo estimates for each biome (Fig. 6) presented strong agreement, with coefficient of determination (R2) values close to 1 and low metrics for MAD and RMSD. The Amazon presented the least desired fit line relation, with intercept equal to 0.41 and slope with 0.92; although slope values were fairly close to 1 for the other biomes, intercept positive values for the scatterplots between ETo estimates is evidence that ETod tends to overestimate lower values of EToh. 6

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Fig. 6. Scatterplot between daily (ETod) and sum-of-hourly (EToh) reference evapotranspiration for each biome.

almost exclusively on irrigation and crop water productivity relies on providing the right amount of water at certain stages. Regarding the biomes (Table 2), Pampa presenting larger values of monthly PBIAS has low relevance for irrigation management purposes. The Pampa’s rainfall is well-distributed throughout the year and low EToh values were observed during the months with higher underestimation. On the other hand, underestimating becomes extremely relevant in other biomes, such as the Caatinga and Cerrado. Caatinga presents semi-arid climate with irregular rainfall distribution, while Cerrado presents tropical savannah climate with two well-defined seasons (rainy and dry). A number of regions within these biomes present high agricultural contribution to economy and strongly rely on irrigation practices (Rodrigues and Domingues, 2017; Tabarelli et al., 2017). Thus, as previously discussed, underestimating EToh in larger magnitudes may result in inadequate water supply to crop at specific stages, reducing its water productivity and profitability. Even recognizing the interannual climate variability that exists, the results reported here strongly relate to many other relevant studies. For instance, ETod generally overestimating EToh in the semi-arid is a similar result to what was reported by Irmak et al. (2005) and Djaman et al. (2018b) in semi-arid regions in USA, and by Djaman et al. (2018a) for the semi-arid in Senegal. Irmak et al. (2005) also reported better agreement between daily and sum of hourly ETo for humid regions, which was observed in most of the Brazilian humid sub-tropical region (Atlantic rainforest and southern Cerrado) (Fig. 4 and Table 2). As for the tropical region, Perera et al. (2015) has reported good

3.3. Causes for differences between evapotranspiration estimates Fig. 7 presents the influence of rainfall on daily standard deviation of meteorological hourly values and, in Fig. 8, the role of these standard deviation on possible differences between ETo estimates. Rainfall had a negative correlation to daily standard deviation of Rs, T and RH hourly values (Fig. 7), that is, as rainfall values increase, the within-day range of meteorological parameters are expected to decrease. In consequence, a lower range between daily maximum and minimum values resulted in ETod overestimating EToh, while higher standard deviations resulted in ETod underpredicting EToh (Fig. 8). Overall, diurnal changes in Rs, T, RH and u2 presented a correlation to differences between ETo estimates of -0.30, -0.48, -0.42 and -0.18, respectively. 4. Discussion It was observed in Fig. 5 that EToh is overestimated by ETod in a large part of Brazil during its main crop season (October to April). Despite of this season coinciding with the rainy season, drought periods may occur, and irrigators might not only supply crop a larger amount of water than needed, but increase their electric energy expenses. It was also observed in Fig. 5 that ETod has generally underestimated EToh during periods with low rainfall occurrence, such as dry seasons. This increases the relevance on the difference between ETo estimates because, during these periods, satisfying crop water demand depends

Table 2 Monthly average reference evapotranspiration estimates and percentage bias within biomes and Brazil for the studied period.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Annual

AM

CA

CE

SP

PA

AF

Brazil

ETod 3.5(6.5%) 3.3(7.2%) 3.6(5.9%) 3.3(5.3%) 3.3(2.5%) 3.4(0.6%) 3.6(0.2%) 4.0(2.0%) 4.3(2.7%) 4.3(3.8%) 3.7(5.5%) 3.4(6.6%) 3.7(3.9%)

ETod 5.3(1.1%) 4.6(2.7%) 4.6(2.1%) 3.9(1.4%) 3.9(-1.0%) 3.9(-2.4%) 4.2(-2.1%) 5.0(-0.9%) 5.8(0.8%) 5.9(2.4%) 5.8(2.2%) 5.0(1.3%) 4.9(0.7%)

ETod 5.0(1.9%) 4.1(3.3%) 4.1(2.8%) 3.7(0.0%) 3.5(-3.3%) 3.2(-5.2%) 3.6(-5.5%) 4.1(-1.8%) 4.7(0.1%) 4.5(2.8%) 4.1(3.8%) 4.7(2.4%) 4.1(0.2%)

ETod 4.5(2.2%) 5.0(-1.3%) 3.9(-1.9%) 2.9(-1.6%) 1.8(-6.2%) 1.2(-7.9%) 1.3(-4.9%) 1.9(-6.6%) 2.7(-2.0%) 3.8(-2.1%) 5.0(-0.5%) 5.0(0.3%) 3.3(-1.6%)

ETod 5.0(3.9%) 4.0(7.1%) 4.5(4.9%) 2.9(3.7%) 2.3(1.8%) 2.4(-0.2%) 2.9(-4.2%) 3.3(-0.3%) 3.8(2.5%) 4.0(5.1%) 3.7(6.0%) 4.5(4.1%) 3.7(2.9%)

ETod 5.1(1.6%) 4.2(1.5%) 3.9(1.8%) 3.3(-0.9%) 2.6(-3.3%) 2.1(-3.2%) 2.5(-5.0%) 2.8(-1.8%) 3.5(0.5%) 3.6(2.5%) 4.2(2.2%) 4.8(1.5%) 3.6(0.3%)

ETod 4.9(2.0%) 4.1(2.6%) 4.0(2.4%) 3.5(0.4%) 3.1(-2.2%) 2.8(-3.3%) 3.2(-3.9%) 3.7(-1.2%) 4.3(0.7%) 4.3(2.6%) 4.4(2.9%) 4.6(2.1%) 3.9(0.7%)

EToh 4.8 4.0 3.9 3.4 3.2 2.9 3.3 3.7 4.3 4.2 4.3 4.6 3.9

ETod = reference evapotranspiration in 24 h timesteps (mm d−1); EToh = reference evapotranspiration in hourly timesteps summed over 24 h periods (mm d−1); AM = Amazon; CA = Caatinga; CE = Cerrado; SP = Pampa; PA = Pantanal; and AF = Atlantic Forest. 7

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Fig. 7. Influence of rainfall on the daily standard deviation of meteorological parameters hourly values. The blue line represents the fitted linear model. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

tropical regions of the world as long as their conditions are close to the observed. As also pointed out by Djaman et al. (2018b), the majority of differences between ETo estimates observed outcomes from variables 24 h averages misrepresenting ETo under conditions of considerable daily weather changes. For instance, in Fig. 8, larger amplitudes of mean air temperature seem to have a stronger effect on ETod underestimating EToh in the semi-arid region. On the other hand, larger diurnal changes in solar radiation and relative humidity have stronger effect in underestimating EToh for the tropical regions. The humid sub-tropical region seems to be less sensitive to diurnal changes in wind speed. This

agreement for two stations assessed in the Australian tropical region. The region assessed by these authors present savannah climate with dry winter (Aw), and showed similar results as seen for the northern Cerrado, also Aw climate type. On the other hand, the Amazon, covering most of the Brazilian territory, presents tropical monsoon (Am) and tropical rainforest climate (Af) types which, to the authors knowledge, have no studies reporting on the difference between their ETo estimates. Looking at Fig. 4 and Table 2, the conclusion that may be drawn is the clear tendency of ETod to overestimate EToh in such tropical regions. Given the bioclimatic diversity of the Brazilian territory, the findings of this study are strong indicators of the ETo behavior in other

Fig. 8. Influence of daily standard deviation of meteorological parameters on the difference between ETo estimates (ETod – EToh). The blue line represents the fitted linear model. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article). 8

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Acknowledgments

behavior in humid sub-tropical may result from higher relative humidity (Figure A.4) mitigating the aerodynamic effects on evapotranspiration, rendering ETo changes more susceptible to changes in radiation. Aside the weather variation throughout the day, characterized by the standard deviation of hourly values, the period of the day when higher or lower values occur may also interfere on how ETo estimates deviate. For instance, high values of wind speed occurring during nighttime will have a different impact on EToh calculations when compared to high values occurring during daytime. ETod overall overestimating EToh has an awfully large impact on environmental studies. For instance, Zhang et al. (2016) have shown a significant ETo trend for a large part of South America (and Brazil) over past decades, where transpiration from vegetation represents more than 70% of total evapotranspiration. However, ETo computations in environmental and climate change studies is, in most cases, based on daily or longer periods averages (Chou et al., 2014; Coulibaly et al., 2018; Oliveira et al., 2017), which is intended to reduce the already large amount of time invested in processing such extensive database. This type of study is reasonable for planning, but not for daily management purposes, specifically for irrigation. Irrigation plays a key role in matching expected food demand by 2050 (Godfray et al., 2010). However, increasing irrigation may rise water demand in critical regions, that can intensify water conflicts. Thus, it is necessary to improve management techniques and evapotranspiration estimates. For instance, the main crop is sowed during November in some regions of the Cerrado, when ETod overestimates EToh by 3.8%. This overestimation represents an exceeding volume equal to 155.8 m³ d−1 for one center pivot system covering an area of 100 ha. In order to reduce uncertainties and avoid the introduction of unnecessary error in ETo estimation, adopting hourly timesteps computation is a must (Djaman et al., 2018b; Gavilán et al., 2008; Irmak et al., 2005). Also, for irrigation systems to achieve the socio-economic benefits of its investment, effective use of irrigation management practices is fundamental, for it increases sustainable production and profitability, as well as reduces the need to expand agriculture over new areas.

This study was financed in part by the Coordination of Improvement of Higher Education Personnel (CAPES) - finance code 001, and by the National Council for Scientific and Technological Development (CNPq) - scholarship grant 142273/2019-8. We thank the data provided by the Brazilian National Institute of Meteorology (INMET) and the help provided by AgriSensing in processing the data.. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:10.1016/j.agwat.2019.105785. References Allen, R.G., 1996. Assessing integrity of weather data for reference evapotranspiration estimation. J. Irrig. Drain. Eng. 122, 97–106. https://doi.org/10.1061/(ASCE)07339437(1996)122:2(97). Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. FAO Irrigation and Drainage Paper 56, Crop Evapotranspiration - Guidelines for Computing Crop Water Requirements. Food and Agriculture Organization of the United Nations, Rome. 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5. Conclusion The present study, based on a vast and heterogenous database, reports on the implications of computing reference evapotranspiration adopting hourly or daily average meteorological parameters. In summar, using daily averages resulted in consistent ETo overestimation for the tropical monsoon and tropical rainforest climate types (Amazon), while for the tropical savannah (Cerrado) daily averages showed better agreement to sum-of-hourly estimates. Along the year, adopting daily instead of hourly timesteps for estimating ETo will lead to overestimations during Brazil’s main crop season, while to an expressive underestimation during the drought periods. Regions where agriculture presents high relevance in the Brazilian economy, such as the Cerrado and Caatinga, are likely to be affected most by these underestimations. Agreement between ETo estimates computed under different timesteps largely depends on the standard deviation of meteorological parameters hourly values. Larger standard deviations relate to abrupt diurnal changes and are likely to result in underestimations from ETo based on daily averages when compared to sum-of-hourly ETo. ETo based on daily averages will better agree to sum-of-hourly ETo in periods of moderate standard deviation of meteorological parameters hourly values, or overestimate in conditions of lower standard deviation, conditions which are related to rainy seasons. Declaration of Competing Interest None. 9

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