Figure 1

The background of harmonic regression. Panels A, B, and C show how changes in the seven coefficients of a harmonic regression (namely A1 to A7) can be used to reconstruct the mean values of a variable and the peak moment of the year can be modelled. In A, the pattern is obtained leaving A1 = 20, A3 = −15, A4 = 2.357, A5 = −0.12, A6 = −0.094, and A7 = −0.237. The value of A2 was varied between −10 and 10 at constant intervals to produce the pattern observed in the series 1–8. In B, values were left constant for A1 (20) A3 (−10) and A4 to A7 (−0.12), while the value of A3 was varied between −15 and −1, at constant intervals to produce the pattern reproduced. It is observed that changes in A2 and A3 account for the seasonality of the complete year, showing the peak of a variable in both its value and moment of the year. In C, A4 was varied between −15 and 15 at constant intervals leaving the other coefficients with fixed values, namely A1 = 20, A2 = −10, A3 = −15, A5 to A7 = −0.12. Charts in A to C show simulated temperature values. Actual data for temperature were obtained from five sites in either the northern or southern hemisphere (D) and then subjected to a harmonic regression (E), which was fitted with the parameters and the equation included in E. Capital letters in the equation refer to the rows in the table for each of the five sites simulated.