Assessment of Hargreaves-Samani Model and Valiantzas Model for Estimating Solar Radiation Using Temperature and Humidity Parameters Under Semi-Arid Conditions in India Ramachandran J1, Rajeswari M1, Sankar GR Maruthi2 1Department of Agricultural Engineering, Agricultural College and Research InstituteTamil Nadu Agricultural University, Madurai624104Tamil Nadu, India 2ICAR-Central Research Institute for Dryland Agriculture (CRIDA)Hyderabad500059Telangana, India Email for correspondence: eeesurya.tnau@gmail.com
Online Published on 12 September, 2022. Abstract A newly developed solar radiation model which is a function of temperature and humidity data was validated for Madurai district of Tamil Nadu. The model was developed by including the relative humidity in the temperature- based Hargreaves-Samani radiation model using daily data of 20 years (2000-2019) obtained from weather station located at Agricultural College and Research Institute, Madurai, Tamil Nadu. A comparison has been made between measured solar radiation and the solar radiation obtained from Hargreaves-Samani model (HS Rs [T]) and the newly proposed Valiantzas’ model (Val Rs [T & RH]). The reference evapotranspiration (ET0) was estimated by using FAO56 Penman-Monteith method (FAO56-PM) by substituting the measured solar radiation, HS Rs [T] and Val Rs [T & RH] and a comparison has also been made. The indices used for comparison were coefficient of determination (R2), standard error estimate (SEE) and long term average ratio (rt). Annual mean of HS R [T] was lesser and annual mean of Val Rs [T & RH] was higher compared to the measured solar radiation. When Val Rs [T & RH] was used in the FAO56-Penman-Monteith method, it indicated a good performance (SEE= 2.243 MJ/m2/day, rt= 1.067 and R2= 0.540) in the estimation of reference evapotranspiration. It is suggested that Val Rs [T & RH] model could be used to determine values of solar radiation when the measured data are unavailable in order to get efficient measurements of evapotranspiration for use in the agricultural water management and related studies. Top Keywords Evapotranspiration, FAO56 Penman-Monteith, Solar radiation, Temperature, Relative humidity, Hargreaves-Samani model, Valiantzas’ model. Top |
Introduction Accurate estimation of reference evapotranspiration is very important in proper scheduling of irrigation water. FAO56 Penman-Monteith (FAO56-PM) (Allen et al 1998) method is a globally recommended method for estimation of reference evapotranspiration (ET0) among the available physical and empirical models. One complication usually faced in FAO56-PM method is that the inputs appear explicitly in the calculation. It would involve maximum and minimum air temperatures (Tmax and Tmin), solar radiation (RS), maximum and minimum relative humidity (RHmax and RHmin), wind speed (u) as well as the latitude and altitude of the location for ET0 estimation. The practical difficulty in developing countries is that all of these input variables may not be available for a given location either due to lack of instrumentation or repair of instruments. |
The high cost of typical sensors required for ET0 automated stations (Valiantzas 2010, 2013d; Exner-Kittridge 2012) is another disadvantage in going for proper instrumentation. In most of the stations the data sets were found to be incomplete and/or didn’t give appropriate quality requirements. |
Solar radiation is either not routinely measured at many weather stations or its measurements are not always reliable. Accordingly it has to be efficiently estimated. Hargreaves and Samani (1982) proposed an empirical model for estimation of solar radiation which require only maximum and minimum daily air temperature (routinely measured parameters). This model could be used in weather stations where solar radiation is not routinely measured or where measurements are not always reliable or when device is under repair. Hargreaves and Samani (1982) solar radiation model has various modifications as presented in Samani (2000) and Samani et al (2011). |
Valiantzas (2017) proposed a new version of Hargreaves-Samani model for places where good quality RH measurements are available for predicting the solar radiation based on daily temperature and relative humidity data. The additional cost of relative humidity (RH) sensors compared to the cost of RS and sensors is extremely low (Exner-Kittridge and Rains 2010). Several studies have provided valuable information on the accuracy of the Valiantzas’reference evapotranspiration equations in different countries like Iran (Valipour 2014), Mediterranean climate (Kisi 2014); Pilbara region of western Australia (Ahooghalandari et al 2016), Senegal (Djaman et al 2015) and Burkina Faso (Djaman et al |
Therefore it is very much desirable to estimate evapotranspiration accurately under limited data condition with good accuracy similar to FAO56-PM method. Hence this study was aimed to evaluate the new version of solar radiation formula proposed by Valiantzas (2017) which includes temperature and relative humidity data. A comparison was made between the ET0 estimated from FAO56-PM method by substituting the RS values obtained from Hargreaves–Samani model and Valiantzas model. The evaluation was done on daily time steps by using the meteorological data (2000-19) obtained from a weather station located at Agricultural College and Research Institute, Madurai, Tamil Nadu. |
Top Methodology Study Area Meteorological data required for estimating the reference evapotranspiration using FAO56-PM method were collected from the weather station located at the Agricultural College and Research Institute, Madurai, Tamil Nadu for a period of twenty years (2000-2019). It is located at 9° 96’ 84” N latitude, 78° 20’ 62” E longitude and 141 m amsl. Estimation of Solar Radiation Hargreaves-Samani RS formula based on T (HS Rs [T]) Hargreaves and Samani (1982) recommended a simple equation to estimate solar radiation: where RA= Extra terrestrial radiation [MJ/m2/day], Tmax= Maximum temperature [°C], Tmin= Minimum temperature [°C] Ra for each day of the year and for different latitudes can be estimated from the solar constant, the solar declination and the time of the year by the following equation: where Ra= Extra terrestrial radiation [MJ/m2/day], Gsc= Solar constant= 0.0820 MJ/m2/min, dr= Inverse relative distance Earth-Sun, ωs= Sunset hour angle [rad], Õ= Latitude [rad], δ= Solar declination [rad] Valiantzas RS Formula Based on T and RH (Val Rs [T & RH]) Hargreaves’ model for estimating the solar radiation as a function of RH (Hargreaves and Allen 2003) is given as follows: where x= An empirical exponent By combining Eq (1) and Eq (3), Rs is considered as function of temperature and RH. Valiantzas (2017) identified the regression coefficients by following a calibration procedure and used globalclimatic data set including monthly data, the FAO-CLIMWAT (Smith 1993) from thirteen countries that essentially cover the typical range and proposed the following simple empirical and mathematical form of equation in which Rs is estimated from the T and RH data. The new version of Hargreaves-Samani model requiring temperature and RH data is as under: In Eq (4) the value of 1.001 was used instead of 1 because of the singularity appearing when RH/100 = 1. Hence the final form of Valiantzas Rs equation is given as: Estimation of Reference Evapotranspiration The FAO56-PM equation for estimating the daily grass-reference evapotranspiration is given by: where ET0= Reference evapotranspiration [mm/day], Rn= Net radiation at the crop surface [MJ/m2/day], G= Soil heat flux density [MJ/m2/day], T= Mean daily air temperature [°C], U= Wind speed at 2 m height [m/s], es= Saturation vapour pressure [kPa], ea= Actual vapour pressure [kPa],es-ea= Saturation vapour pressure deficit [kPa], Δ= Slope of vapour pressure curve [kPa/°C], Γ= Psychrometric constant [kPa/°C]. Comparison of Methods A comparison was made between the measured solar radiation and solar radiation derived under HS Rs [T] model and Val Rs [T & RH] model separately. In addition comparison was made between the reference evapotranspiration estimated from FAO56-PM equation by substituting the measured Rs values and solar radiation derived by using the HS Rs [T] model and Val Rs [T & RH] model separately. In this study, a comparison has been made by using the simple error analysis and linear regression: where S= Regression coefficient (slope of the line), Y= Reference measured values of RS, X= Corresponding estimates of RS by the comparison formula The indices used in the error analysis is standard error estimate (SEE) and long term average ratio (rt): where Yi= Reference measured values at ith data point, Xi= Corresponding estimates by the comparison formula, n= Total number of observations, Xav and Yav= Long term average values of tested models and reference values respectively Top Results and Discussion The solar radiation measured at the weather station located in the study area was found to vary from 12.93 to 23.81 MJ/m2/day. The variation of 20 years daily mean of measured solar radiation for the study area is shown in Fig 1. The mean measured Rs of the study area was around 18.96 MJ/m2/day with coefficient of variation of 0.13 (Table 1). |
The mean solar radiation estimated by using Eq 1 (HS Rs [T]) and 5 (Val Rs [T & RH]) was around 18.82 and 20.24 MJ/m2/day. It was found that the mean solar radiation estimated from both the models was higher compared to the measured solar radiation. |
The results of simple linear regression analysis for Eq 1 (HS Rs [T]) and measured RS and for Eq 3 (Val Rs [T & RH]) and measured RS for the study area are given in Figs 2a, 2b and Figs 4a,4b respectively along with the coefficient of determination (R2) value, slope (S), standard error estimate (SEE) and long term average ratio (rt). The regression equation obtained from the analysis is also presented in the figures. |
The R2, SEE and rt values for HS Rs [T] model were found to be 0.596, 1.634 MJ/m2/day and 0.992 respectively (Fig 2a). The Valiantzas’ model requiring temperature and relative humidity is best suited for the study area with R2 value of 0.540. The SEE of Val RS [T & RH] model was 2.243 MJ/m2/day (Fig 2b) and also it was close to SEE values reported by Valiantzas (2017) for the different stations located at Greece, Florida and California. Both models produced approximately the same bias (rt). |
The reference evapotranspiration estimated from FAO56-PM method for the study area was found to vary from 2.92 to 5.28 mm/day (Table 2). The variation of reference evapotranspiration using FAO56-PM method is shown in Fig 3. The mean reference evapotranspiration estimated from FAO56-PM equation by substituting measured Rs values was lower compared to the ET0 obtained by using HS Rs [T] model and was higher compared to the ET0 obtained by using Val Rs [T & RH]. |
The R2 value obtained while comparing reference evapotranspiration estimated from FAO56-PM equation by substituting measured Rs and Val Rs [T & RH] values was around 0.811 with lower SEE (0.355 mm/day) which indicated that using Rs values obtained from Valiantzas (2017) model gave a very good estimate of reference evapotranspiration similar to FAO56-PM method. Valiantzas (2017) also reported that it would yield better results than the Hargreaves-Samani for the majority of 16 stations that are characterized by an arid or semi-arid climate and remaining 16 are characterized by a humid climate located in California, Greece and Florida. |
Top Conclusion The comparisons showed a good performance of the new version of Hargreaves-Samani model for calculating the solar radiation from temperature and humidity data. It is also suggested that validation of this new version of Hargreaves-Samani model may be explored for different climatic zones of India which will be useful for the researchers to easily calculate reference evapotranspiration during limited availability of data without compromising the accuracy. Using this model in case of missing data, it will be useful for precision agriculture and water management studies. |
Top Figures Tables | Table 1.: Summary statistics of solar radiation
| | Variable | Minimum (MJ/m2/day) | Maximum (MJ/m2/day) | Mean (MJ/m2/day) | Coefficient of variation | | Measured RS | 12.93 | 23.81 | 18.96 | 0.130 | | HS Rs [T] | 13.86 | 22.06 | 18.82 | 0.123 | | Val Rs [T & RH] | 14.99 | 23.34 | 20.24 | 0.127 |
| | | Table 2.: Summary statistics of reference evapotranspiration
| | Variable | Minimum (mm/day) | Maximum (mm/day) | Mean (mm/day) | Coefficient of variation | | FAO56-PM ET0 | 2.92 | 5.28 | 4.21 | 0.138 | | ET0 using HS Rs [T] | 3.06 | 5.06 | 4.19 | 0.136 | | ET0 using Val Rs [T & RH] | 3.19 | 5.31 | 4.42 | 0.144 |
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