Estimation of monthly solar radiation from measured air temperature extremes

Solar radiation (Rs), a very important variable in agricultural meteorology, is measured at a very limited number of meteorological stations worldwide. However, a number of methods are reported in the literature for estimating Rs from routinely measured air temperature extremes, the accuracy of which needs to be tested. Rs was thus estimated by different methods for 29 stations distributed throughout India. The methods compared were Hargreaves [Hargreaves, G.H., 1994. Simplified coefficients for estimating monthly solar radiation in North America and Europe. Dept. Paper, Dept. Biol. and Irrig. Eng., Utah State Univ., Logan, Utah], Annandale et al. [Annandale, J.G., Jovanovic, N.Z., Benadé, N., Allen, R.G., 2002. Software for missing data error analysis of Penman–Monteith reference evapotranspiration. Irrig. Sci. 21, 57–67], Allen [Allen, R.G., 1995. Evaluation of procedures for estimating mean monthly solar radiation from air temperature. Rep., Food and Agriculture Organization of the United Nations (FAO), Rome, Italy], Samani [Samani, Z., 2000. Estimating solar radiation and evapotranspiration using minimum climatological data. J. Irrig. Drain. Eng., ASCE, 126(4), 265–267], Allen [Allen, R.G., 1997. Self-calibrating method for estimating solar radiation from air temperature. J. Hydrol. Eng., ASCE, 2 (2), 56–67], and Bristow and Campbell [Bristow, K.L., Campbell, G.S., 1984. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agric. Forest Meteorol., 31, 159–166]. The estimated Rs values were then compared to measured Rs (or Rs estimated from measured sunshine hours with locally calibrated Ångström coefficients), to check the suitability of these methods under Indian conditions. Three statistical indicators were used for comparing the performances of different methods, namely, modelling efficiency (ME), coefficient of residual mass (CRM), and root mean squared error (RMSE) expressed as a percentage of the arithmetic mean of observed values. To understand the effect of Rs estimation on reference evapotranspiration, ET0, the internationally accepted FAO-Irrigation and Drainage Paper 56 Penman–Monteith based method (Allen et al. [Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration—guidelines for computing crop water requirements. Irrig. and Drain. Paper 56, Food and Agriculture Organization of the United Nations (FAO), Rome, Italy]), employed using both measured Rs and estimated Rs, were also compared. The methods performed differently for different stations. In general, the original Hargreaves methods, both with [Annandale, J.G., Jovanovic, N.Z., Benadé, N., Allen, R.G., 2002. Software for missing data error analysis of Penman–Monteith reference evapotranspiration. Irrig. Sci. 21, 57–67] and without [Hargreaves, G.H., 1994. Simplified coefficients for estimating monthly solar radiation in North America and Europe. Dept. Paper, Dept. Biol. and Irrig. Eng., Utah State Univ., Logan, Utah] altitude correction, performed better. The choice of method to obtain Rs estimates was found to have a relatively small effect on the resulting ET0 estimates. In conclusion, under Indian conditions where no Rs measurements are available, the Rs estimation methods from air temperature extremes were ranked as (in order of descending suitability): Hargreaves [Hargreaves, G.H., 1994. Simplified coefficients for estimating monthly solar radiation in North America and Europe. Dept. Paper, Dept. Biol. and Irrig. Eng., Utah State Univ., Logan, Utah] > Annandale et al. [Annandale, J.G., Jovanovic, N.Z., Benadé, N., Allen, R.G., 2002. Software for missing data error analysis of Penman–Monteith reference evapotranspiration. Irrig. Sci. 21, 57–67] > Samani [Samani, Z., 2000. Estimating solar radiation and evapotranspiration using minimum climatological data. J. Irrig. Drain. Eng., ASCE, 126(4), 265–267] > Allen [Allen, R.G., 1995. Evaluation of procedures for estimating mean monthly solar radiation from air temperature. Rep., Food and Agriculture Organization of the United Nations (FAO), Rome, Italy] > Allen [Allen, R.G., 1997. Self-calibrating method for estimating solar radiation from air temperature. J. Hydrol. Eng., ASCE, 2 (2), 56–67] > Bristow and Campbell [Bristow, K.L., Campbell, G.S. 1984. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agric. Forest Meteorol., 31, 159–166], for estimates of monthly means.