Daily average temperatures: modeling and generation with a Fourier transform approach

A mathematical model has been developed to generate daily average temperatures (DATs) on a yearly basis for any climate. The model contains a complete description of the patterns and variations in the DATs for a given location using a set of 29 descriptor values, the magnitudes of which are determined using a Fourier frequency analysis of physical weather data. The model was tuned to imitate the climates at three Canadian sites--Montreal, Winnipeg, and Vancouver. Daily average temperatures were then synthesized for all three locations and these were compared with the physical weather data from which the descriptor values had been derived. A number of evaluation methods were used to assess the effectiveness of the model in reproducing realistic DAT values. First, the model's ability to imitate patterns in the physical data was judged by comparing the distributions and statistics of the DATs at three granularities daily, weekly, and monthly. Second, variability in the data sets was compared by considering the pattern in the differences between consecutive daily average temperatures. Thirdly, a number of characterization measures, such as the heat units for a given crop (e.g., degree-days for corn), were calculated. Lastly, a set of DAT values from Halifax was used to tune the model, and its ability to predict temperature patterns for that climate was assessed. Overall, the model effectively captured the essence of real temperature patterns. Synthetic DATs were similar to the physical data for all three sites studied, at all three granularities. They also showed similar day-to-day variation. Values of the characterization measures were also comparable. The model is conceptually simple, and allows for the rapid generation of unlimited temperature data representative of a given climate. Furthermore, the model descriptors have physical meaning so that it is easy to compose a purely hypothetical climate and synthesize data. The Fourier approach proved to be a practical method of analyzing and reproducing temperature data, and should be widely applicable to the modeling of other natural phenomena as well.