Differences in sum-of-hourly and daily reference evapotranspiration for a rice–wheat cropping system in Ganga Basin, India

Water moves from the land surface and vegetation to the atmosphere through a physical process called evapotranspiration (ET). It is a key part of the hydrological cycle, has a significant impact on the regional water balance, and is directly related to ecosystem productivity (Lu et al. 2011). ET is an important variable in numerical weather forecasting and simulation of global climate models since it is a measure of the rate of change in the global water cycle (Sun & Wu 2001; Jiang et al. 2009; Wang & Dickinson 2012).

In recent years, much attention has been given to the precise and consistent determination of ET in irrigated agriculture, especially in dry or semiarid regions. In these regions, lack of precipitation typically restricts crop growth and output; therefore, it becomes important to reliably estimate ET for better planning and more effective use of the limited water resources (Allen et al. 1998; Irmak et al. 2005; Maestre-Valero et al. 2017).

As direct measurement of ET is a costly and time-consuming process (Bakhtiari et al. 2017), indirect methods that consider the factors that affect ET including meteorological variables such as solar radiation, air temperature, humidity, and wind speed, and crop factors such as crop type, variety, density, and growth stage, are widely used. However, this increases the sensitivity of ET towards these variables and any uncertainty in these will propagate to estimates of ET as well. Various sensitivity and trend analysis studies have been performed to understand the effect of meteorological variables on ET (Ndiaye et al. 2020; Kejna et al. 2021; Fan et al. 2022; Yonaba et al. 2023; Al Mamun et al. 2024). The ET process is also governed by managerial and environmental factors such as soil characteristics, salinity, fertility, crop diseases, and pests (Allen et al. 1998). Different methods may be used to compute reference evapotranspiration (ET_o) for different regions according to suitability to local conditions (Allen et al. 1989; Katul et al. 1992; Berengena & Gavilán 2005). While most ET_o estimation techniques are empirical and typically rely on statistical correlations between ET_o and one or more meteorological variables, some are based on sound physical principles regulating the process (Sharma 1985).

The Penman–Monteith (PM) equation is recommended by the Food and Agriculture Organization (FAO) for calculating the reference evapotranspiration (Allen et al. 1998). Due to its physical basis, the FAO-PM equation offers an advantage over many other equations and can be applied globally without any local calibrations (Wang & Dickinson 2012). A 24 h period is the basic timestep for this type of calculation (Treder & Klamkowski 2017). However, as more electronic weather stations are being developed and installed around the world, weather data are becoming more and more accessible for computing ET_o at hourly and even more precise timesteps (Allen et al. 2006). Moreover, the information on plant water, a requirement that is determined at hourly timesteps, might help to manage the watering of shallow-rooted plants and plants cultivated in small containers (Treder & Klamkowski 2017).

It is possible to estimate ET from weather data for different time intervals in the range of sub-hour to a month (Suleiman & Hoogenboom 2009; Trajkovic 2010). The timestep choice depends on the available data and the purpose of the study. The computation of ET obtained using different timesteps may not be similar, especially monthly ET computed from monthly average weather data relative to daily or hourly estimates. It is caused by nonlinearities in the equations that are utilized as well as in the algorithms used to calculate meteorological variables like vapor pressure and the slope of the saturation vapor pressure curve (Trajkovic 2010). In areas where hourly weather data are available and when there are considerable diurnal changes in vapor pressure, wind speed, or cloudiness, the calculation of evapotranspiration at an hourly timestep is more accurate (Ortega-Farias et al. 1995; Allen et al. 2000; Irmak et al. 2005; Wang et al. 2012; Treder & Klamkowski 2017). Additionally, some research suggests that hourly estimates of reference evapotranspiration provide more accurate results and provide better planning and management options for water and soil resources (Treder & Klamkowski 2017; Althoff et al. 2019; Nolz & Rodný 2019).

The advent of networks of automatic weather stations has increased the availability of weather data on a sub-hourly basis. This has triggered debate on the appropriate expression and parameterization for the surface resistance (r_s) parameter of the PM equation and the associated coefficient for the reduced form of the FAO-PM equation when applied hourly (Allen et al. 2006). FAO-56 (Allen et al. 1998) recommended a constant surface resistance (r_s) 70 s/m for hourly timesteps as it is used for 24-h timesteps. Due to this constant resistance, hourly ET_o may occasionally be overestimated during the daytime when actual r_s may be somewhat higher and underestimated during the evening when actual r_s may be slightly lower. Following some studies (Walter et al. 2000; Irmak et al. 2005) which showed better agreement between ET_o,d and ET_o,h when hourly ET_o uses a lower value for r_s than that used for the 24-h timestep, Allen et al. (2006) came up with a recommendation to use r_s = 50 s/m during daytime and 200 s/m during night time for hourly ET_o computations.

Meteorological variables like solar radiation, air temperature, vapor pressure deficit, and aerodynamic variables are synced in time during ET_o,h computation. The mean values used for ET_o,d estimation may misrepresent the evaporative power of the environment during parts of the day and may introduce errors in the calculations. These may worsen under conditions where there are significant changes in solar radiation, wind speed, or vapor pressure deficit during the day (Allen et al. 1994; Allen et al. 1998; Bakhtiari et al. 2017; Ji et al. 2017).

Many studies have looked at daily and hourly variation of ET_o using the PM method under different climatic conditions (e.g. abrupt diurnal changes, wet and hot in monsoon and cold in winter, semiarid dry and arid conditions, Sahelian climate, etc.) (Itenfisu et al. 2003; Irmak et al. 2005; Ji et al. 2017; Djaman et al. 2018a, 2018b), land use/landcover (e.g. agricultural areas, grass or natural vegetation) (Gavilán et al. 2008; Perera et al. 2015; dos Santos et al. 2021), and small and large study areas (ranging from point scale to continental scale) (Perera et al. 2015; Bakhtiari et al. 2017; Djaman et al. 2018a, 2018b; Althoff et al. 2019) in different parts of the world including Australia, Brazil, Iran, Spain, Turkey, USA, and Western Africa. These studies have shown that ET_o computed using both daily and the sum-of-hourly calculation methods varies in season, according to the geographical location and climatic conditions. For example, Perera et al. (2015) compared hourly sum and daily ET_o using FAO-PM and ASCE-PM equations for 40 locations across 23 agricultural irrigation areas from nine diverse climate zones over the Australian continent. They observed that ET_o,d is always higher than ET_o,h when it is computed using FAO-PM, and the ratio between ET_o,h and ET_o,d is between 0.96 and 1.04 when the ASCE-PM method is used and this variation depends on location, climatic condition, and season. Bakhtiari et al. (2017) computed ET_o by both methods using meteorological data collected at 10 min intervals from the Kerman branch agrometeorology station, in Iran. They observed that directly computed daily ET_o was consistently greater than ET_o,h for some months. Djaman et al. (2018a) did the comparison between semiarid dry conditions (Senegal) and semiarid humid conditions (the Gambia and Guinea). They reported that the daily timestep overestimated the daily ET_o relative to the sum-of-hourly ET_o by 1.3%–8% for the whole study period. Using datasets collected from 25 automatic meteorological stations across Paraná State, South Region of Brazil, dos Santos et al. (2021) compared hourly sum and daily ET_o. They found a 5.1%–7.4% average difference between daily ET_o and the sum-of-hourly ET_o. They recommended that the hourly sum has a good potential to be used in planning and management in the field of soil and water engineering, in Paraná State.

While these studies offer insightful information on the reliability of using the FAO-PM (Allen et al. 1998) under hourly and daily timesteps in several parts of the world, little is known about the Ganga Plains where irrigated and rainfed rice and wheat productions are predominant. The Ganga Plains account for 50% of India's irrigated areas, but at the same time have the lowest irrigation efficiency (35%–40%). As food security and population growth have increased the demand for water resources, efforts are being made to improve the irrigation efficiency to the maximum achievable (55%–60%) (Central Water Commission, Ministry of Water Resources, River Development and Ganga Rejuvenation 2008). In the Ganga Plains, the variations between the hourly and daily timestep ET_o computations are not known. The prime objective of this study is to quantify differences associated with using 24 h timestep ET_o, as compared with the sum-of-hourly ET_o computations, with the FAO-PM equation in the Ganga Plains. More specifically, it intends to: (i) compare hourly (ET_o,h) and daily (ET_o,d) computed reference evapotranspiration, (ii) examine the seasonal impact on the hourly sum and daily ET_o values, (iii) compare monthly mean hourly sum and daily computed ET_o, and (iv) investigate the effect of diurnal changes in meteorological variables on reference evapotranspiration distribution.

The average farm size on the Indo-Gangetic Plain is less than 0.6 ha and it is decreasing as landholdings increase (Sandhu et al. 2016). Marginal farmers frequently further divide the lands of these farms to support multiple crops during a growing season, which results in farms of a size equivalent to that considered in our study (Monchuk et al. 2010; Deininger et al. 2017). The mean annual precipitation is 801.5 mm, the mean annual temperature is 32.2 °C, and the warmest and coolest months are May and January with a mean temperature of 41.3 and 8.5 °C, respectively (Panwar et al. 2019).

The wheat crop was irrigated five times in varying quantities, and the rice paddy was kept in ponded water at a depth of 5 cm. In consultation with the local farmers, the amount of irrigation water used for the wheat crop was chosen based on local wheat-growing traditions.

Weather data were collected from the Automatic Weather Station (Virtual Hydromet, India) installed at the IIT Kanpur study site at 15-min intervals. Air temperature and relative humidity were measured using digital sensors with an accuracy of ±0.5 °C and ±2%, respectively. A three-cup anemometer was used to measure the wind speed with accuracy better than 0.5 m/s at 3.3 m height. To find wind direction, a smart position pot having accuracy ±3^o was used. A tipping-bucket-type rain gauge was used to measure rainfall with an accuracy of 5% at 25 mm/h rate. The solar radiation sensor, pyranometer, conforming to ISO classification second-class was employed to measure global radiation. The sensor had a nominal sensitivity of 15 μV/W·m⁻² and temperature dependence <0.1%/^oC. A piezo-resistive silicon membrane barometer was used to measure air pressure. A pressure-type sensor was used to measure evaporation having a resolution of 1 mm. The pan was 1,220 mm in diameter and made of non-corrosive material mounted on a timber frame with pan bird gauge (square steel mesh). The instruments were calibrated, and manual inspection of sensors was regularly done at the field site to ensure a good-quality meteorological dataset.

The steps involved in the computation of daily and hourly reference evapotranspiration are provided in the Supplementary Material and have been taken from the FAO-56 manual.

The results obtained agree with observations across the world. Treder & Klamkowski (2017) examined the usefulness of estimating hourly reference evapotranspiration for assessing the water requirements of plants in Skierniewice, Poland. They observed that the hourly PM model produces an average of 11% higher evapotranspiration values than the daily model. Further, they found that the ET_o,h estimates are closer to values measured by lysimeter at the study site. Djaman et al. (2018a) reported up to 16.6% higher annual ET_o estimation by ET_o,h as compared with the daily average approach. The daily timestep overestimated the daily ET_o relative to the sum of hourly by 1.3%–8% for the whole study period in selected semiarid dry and humid regions of West Africa. On the other hand, Irmak et al. (2005) used the standardized ASCE Penman–Monteith (ASCE-PM) model and observed 2%–9% higher ET_o values in daily timesteps than in hourly sum estimates in a range of climates at six out of seven locations in the United States. They observed that the greatest differences between the two approaches were in locations where strong, dry, hot winds cause an advective increase in ET_o, and agreement between the computational timesteps was best in humid regions. Perera et al. (2015) observed that the FAO-PM version of ET_o,h shows a consistent underestimation of ET_o,d across sites, whereas the ASCE-PM hourly equation did not. The diurnal variation in surface resistance (50 and 200 s/m) for the hourly ASCE-PM equation compared with the constant value of surface resistance (70 s/m) used for the FAO-PM hourly equation is the greatest contributor to their difference. A few studies also showed that the difference between the two approaches is not always significant. Ji et al. (2017) assessed ET_o computations in Chinese arid climatic conditions, dry and hot in monsoon and cold in winter, and found that ET_o,d was 5%–7% overestimated when compared with the corresponding ET_o,h. Gavilán et al. (2008) observed an average 2% underestimation in daily timestep in Andalusia, southern Spain. Generally, as Howell et al. (2000) explained, the reference evapotranspiration obtained with the PM method by using hourly climate data provided better results than the values obtained with the same method by using daily data as it keeps solar radiation, air temperature, vapor pressure deficit, and aerodynamic parameters synchronized in time, in contrast to daily calculation. In this case, with the availability of automatic weather stations, the sum-of-hourly evapotranspiration may be more reliable to estimate water consumption values.

In the present study, RMSE and MBD have relatively high values, equal to 0.45 and −0.31 mm/day, respectively. As shown in the figure, a few data points are located between the regression line and the reference line when ET_o is greater than 2 mm/day. This may be related to seasonal or month-wise differences in climatic variables which are reflected in the evaporation estimates. It might be this variation that resulted in higher RMSE and MBD values. The negative MBD tells that daily timestep calculations are underestimating the actual water loss.

There was a good agreement between ET_o,h and ET_o,d at small ET_o values in both seasons. Overestimation of ET_o in daily timestep is observed when evaporation is small in the winter season and it underestimates otherwise and the underestimation increases with increasing evaporation in the monsoon season. The seasonal difference between ET_o estimates in both approaches is 5.04% and 14.94% in the monsoon and winter seasons, respectively.

As shown in Figures 4 and 5, the difference between the two approaches varies monthly and seasonally. The difference ranges from 1.23% to 25.02% which were observed in September and February, respectively. It is quite high but far less than that reported by Bakhtiari et al. (2017) in Iran. They observed that the hourly sum method is 5.8%–44.6% higher than the daily timestep when ET_o is computed using the FAO-56 PM equation and it was 7.6%–47.6% higher when they used the ASCE-PM equation in different months. Generally, RMSE increases as we progress in the winter season, ranging between 0.31 and 0.68 mm/day. It may be related to increasing ET_o. The difference between ET_o,d, and ET_o,h estimates is small when evaporation is low and it increases with increasing evaporation. A general trend is observed in Figure 5. The length of the regression line decreases with time during the months of the monsoon season and increases in the months of the winter season. For example, Figure 5(a) and 5(d) show the maximum and minimum stretches of the regression line, respectively, in the monsoon season. Figure 5(e) and 5(h) show the minimum and maximum stretches, respectively, in the winter season.

The daily standard deviation of temperature, relative humidity, and solar radiation had a positive correlation to the difference between ET_o computed at daily and hourly timesteps in both seasons. However, the standard deviation of wind speed exhibited a negative correlation in the monsoon season and a positive correlation in winter. In monsoon, small standard deviation of temperature is correlated to negative ET_o difference. It is related to the underestimation of ET_o,h. But in the monsoon season, the standard deviation is high and it is correlated to high ET_o differences. Jia et al. (2008) examined the sensitivity of meteorological variables and quantified their impact on reference evapotranspiration of alfalfa (ET_r). They found that a 10%, 10%, and 20% increase/decrease in incoming temperature, relative humidity, and solar radiation, respectively, produces a 10%, 4%, and 14% increase/decrease in ET_r. However, a ±50% change in wind speed results in only a ±5% change in ET_r. They concluded that solar radiation was the most sensitive parameter introducing the largest error in ET_o estimation followed by temperature and relative humidity. Similar observations have been reported by Xing et al. (2016), Poddar et al. (2021), and Yonaba et al. (2023). We did a similar analysis and found 5.67%, 0.58%, and 13.27% increase or decrease in computed ET_o in the monsoon season and a 4.85%, 0.37%, and 9.91% change in that of the winter season for incoming temperature, relative humidity, and solar radiation changes of 10%, 10%, and 20%, respectively. A ±50% change in wind speed results in only a ±1.89% change in ET_o in monsoon and a relatively higher ±4.41% change in the winter season. Similar to seasonal computations, slight changes in computed ET_o values were observed when all months were considered. A 5.25%, 0.47%, and 11.53% increase/decrease in ET_o was observed for 10%, 10%, and 20% changes in incoming temperature, relative humidity, and solar radiation, respectively. A ±3.20% change in ET_o was observed for a ±50% change in wind speed.

It is to be noted that various potential sources of error can be identified in ET_o estimations. Properties of measuring instruments/sensors and their accuracy are one of the major factors influencing the observed data (Beven 1979; Meyer et al. 1989; Ritchie et al. 1996). Another source of error could be due to the estimation of climatic variables from other, less accurate, available meteorological data, like estimation of solar radiation from percent sunshine hours or percent sky cover (Lindsey & Farnsworth 1997). An often overlooked and major source of variation in ET_o estimation is the temporal sampling frequency of the climatic data. Within the framework of agronomical experiments, for instance, the temporal sampling frequency is often less intensive, sometimes reduced to 30 min, hourly or even daily timesteps (Al-Ghobari 2000) based on the available data-logging equipment. However, climatic variables are often prone to large fluctuations at the smaller timescale. The sampling frequency in this study is kept the same at 15 min for both hourly and daily data computations and it was observed that hourly estimates were better able to capture diurnal variations.

It is possible to compare the total daily ET_o for the crop-growing season over the course of a year, which could have some implications for water management in agricultural, hydrological, and environmental studies (Djaman et al. 2018a). For agricultural water management, especially in the Ganga Plains where rainfed crop production is commonly used, the variations in timestep ET_o values during the period from March to November are particularly important. Perera et al. (2015) reported seasonal variation in the agreement between the ET_o,h and ET_o,d techniques in Australia's tropical and arid climates. It is in contrast to what is observed in our study. For example, the ratio of monthly mean ET_o computed with daily time to the hourly sum varies from 1.05 in August to 0.81 in October, i.e. the ET_o,d estimated is 5% higher than ET_o,h in August and 19% lower in October. It is a huge difference considering the climate, farming tradition, and size of the Ganga Plains. Studies showed that the ratio of ET_o,d to ET_o,h varies with climatic conditions, season, and location. For example, Djaman et al. (2018a) found that the differences in estimates by the two approaches on a seasonal basis were 46 and 69 mm for the March–November period at Sapu and Kankan, respectively, while at Fanaye and Ndiaye, it was 104 and 124 mm. It demonstrates that while the seasonal changes at the Fanaye and Ndiaye stations were high, they were very moderate at the Sapu and Kankan stations. According to Itenfisu et al. (2003), during the course of 76 site years, the average ratio for various Penman-type combination equations ranged from a low of 0.81 to a maximum of 1.14. Djaman et al. (2018a) observed that it ranged from 1.01 to 1.08. Walter et al. (2000) also reported 1.07 at Bushland and 1.04 at Champion, and Irmak et al. (2005) as 1.08 at North Platte and 1.05 at Bushland under a semiarid climate when calculations for the April–October (growing season) period were considered.

This study analyses the effects of determining reference evapotranspiration using hourly or daily average meteorological variables. The standard deviation of hourly values for meteorological data has a significant impact on the agreement between ET_o estimates derived under various timesteps. Larger standard deviations relate to abrupt diurnal changes and are likely to result in underestimation of ET_o based on daily averages when compared with hourly timesteps. ET_o,d better agrees with ET_o,h in periods where the standard deviation in hourly meteorological variables is moderate.

There is a good agreement between ET_o,h and ET_o,d for small ET_o values during monsoon and winter seasons. Underestimation of ET_o in daily timesteps is observed in the winter season, and the difference progresses from December to March. During the peak-monsoon season (August and September months), when the standard deviation in meteorological variables at an hourly scale is less, ET_o,h and ET_o,d have very similar estimates; the difference increases during the monsoon withdrawal phase and reduces with the onset of the winter season. The maximum difference between ET_o estimates in both approaches is observed in the winter season. The sensitivity of meteorological variables and their impact on reference evapotranspiration is also quantified. It is observed that the ET_o estimates are more sensitive to changes in solar radiation followed by changes in temperature and relative humidity. Further, the ET_o estimates are more sensitive to changes in these variables in the monsoon months in comparison with winter months. A ±50% variation in wind speed had a very small effect on the estimates of ET_o at the field site, and it was more in the winter season. Unlike the other variables, wind speed did not show a well-defined profile and the standard deviation is high.

The magnitude of monthly average ET_o computed using hourly and daily average meteorological variables and ET_o calculated from mean monthly meteorological variables are compared. The three estimation methods show similar ET_o values in August and September where diurnal variations are low due to high humidity. In addition, the ensemble hourly distribution of reference evapotranspiration is computed for all months to see how it is distributed in the day and to examine the seasonal and monthly variation in the distribution. Though there is a difference in magnitude, the minimum ET_o is observed around midday in all the months. The standard deviation also shows a difference with month and hour of the day, and it is high in months where atmospheric demand is high and at midday except in September. Since there is no or near-zero ET_o at night, the variability is small in this period except in December when there is significant variability even if the evaporation is near zero.

In the end, we would like to emphasize that the findings of this study may lack generality as the analysis is based on data collected at a single station for two seasons. Further, reference ET_o was computed using the FAO-PM equation. It could be of interest to observe how ET_o changes when other methods of estimation are used. The variation of crop evapotranspiration for different crops can help in understanding irrigation requirements and aid in better crop planning. In addition, long-term climatic study of different meteorological variables and their influence on ET_o can give a better understanding of environmental and climatic changes in an area. The sampling frequency and its ensembles are other points toward future research. With the availability of remotely sensed data and advancements in soft computing techniques, the possibilities of exploration are endless.

In India, where irrigation efficiency is low, the use of the hourly approach can help increase the accuracy of estimated ET_o and better planning of irrigation water management. Therefore, it is essential to invest in automated weather stations to guarantee adequate and dependable availability of the necessary meteorological data at the hourly timestep.

E. Y. conceptualized the article, rendered support in data curation, arranged the software, did the formal analysis, validated the data, developed the methodology, and wrote the original draft. N. V. arranged the software, investigated the data, rendered support in formal analysis, wrote the review and edited the article. R. O. conceptualized the article, supervised the article, wrote the review and edited the article, administered the project, and rendered support in funding acquisition.

This research was funded by the Science and Engineering Research Board, Government of India grant number, ECR/2016/000378.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.