Mathematical modelling of the annual temperature wave based on monthly mean temperatures,and comparisons between local climate trends at seven Norwegian stations

Summary Based on observed monthly mean temperatures, it is possible to construct a simple mathematical model of the annual variation of daily mean temperature, the annual temperature wave. For periods of 15 years, the model gives a good correlation with the observed monthly values. The model may be used as a tool for the generation of daily mean temperatures for the corresponding period. It is continuous, differentiable and strictly monotonous between the unique maximum and the minimum of the curve. Consequently, climate quantities of interest for each period can be calculated by the means of simple mathematical analyses. The model was tested by reproducing values for quantities such as annual mean temperature, winter mean temperature, summer mean temperature and temperature sums. Model calculated values, fit values calculated directly from observed data well. The model was also tested by comparing results from two different but neighbouring stations. There was a good correlation between the results from the two stations. Long homogenised time series with 130 years of monthly mean temperature from seven Norwegian stations were analysed by means of the model. It was found that the Frost Free Season Length and the Growth Season Length had increased for all stations by 10–20 days/100 years in the period 1871–1990. The Summer Half-year Length, even if it was defined relative to the annual mean temperature, also increased for all stations by 4–9 days/100 years. The Hot Season Length showed positive trends as well, and for the five stations in Southern Norway, the trends were as high as 18–29 days/100 years. The Heat Sum had increased by 6–11% for southern stations and 20–22% for the northern stations. The results indicate that the level as well as the shape of the annual temperature wave changed in the period from 1871 to 1990. Some of the results for the period 1990–1999 diverge substantially from the trends, possibly indicating significant changes in the shape of the annual temperature wave in this last period.