The objective of this research was to adjust the harmonic model for the estimation of average monthly air temperature, in 37 locations of Rio Grande do Sul State, Brazil, with data from the period 1931 to 2000. In each locality, data from 1931 to 1990 (60 years) was used to estimate the coefficients of the harmonic model and from 1991 to 2000 (10 years) to validate the model. It was tested the normality and homogeneity of variance among months, estimated trends and incorporated into the models harmonic based in waves annual and semiannual. The coefficients linear, angular, correlation and determination, the root mean square error and the index of WILLMOTT (1981) and CAMARGO & SENTELHAS (1997) were used to validate the models. The coefficient of determination (R²) of the harmonic model, was high in all sites (R²≥0.9867), giving reliability for future forecasts. The harmonic model generated for each of the 37 location in the the Rio Grande do Sul State, Brazil, is adequate to estimate the average monthly air temperature.
time series; modeling; periodic regression
