Balance of longwave radiation employing the rate of solar radiation for Santa Maria, Rio Grande do Sul, Brazil

New coefficients were determined for the weighting term for cloudiness in the Brunt-Penman equation using the rate of solar radiation (R-K) in place of the rate of sunshine duration (n/N). The coefficients in the Brutsaert method proposed for daytime in southern Brazil were also tested and adjusted, and the method was selected which gave the more accurate daily results in relation to the original Brunt-Penman equation, for Santa Maria in the state of Rio Grande do Sul, Brazil (RS). Meteorological data covering 2,472 days obtained from the automatic and conventional weather stations in Santa Maria were used. The coefficients were adjusted by linear and nonlinear regression methods depending on the model, using 2/3 of the data. The adjusted equations were tested with the remaining 1/3 of the data. The Brunt-Penman equation modified by the term for cloudiness weighted both for solar radiation incident on the surface with no cloudiness (R-K,R-R) and for solar radiation incident at the top of the atmosphere (R-K,R-K), were those that resulted in the best statistical indices relative to the original Brunt-Penman equation. In those equations the boundary conditions, 0.3 <= R-K,R-R <= 1 or R-K,R-K >= 0.22, were imposed. Although having similar statistical indices, a sensitivity analysis showed that the Brutsaert equation and other weightings for cloudiness resulted in larger deviations when compared to the original Brunt-Penman equation, in addition to having greater complexity for practical application.