Plotter for seasonal variation
Seasonal variations in mortality are pronounced, with elevated mortality in winter and reduced mortality in summer. The seasonal adjustment to log(mortality) at calendar time y is:
exp(SeasonalExcess)*cos(2π(y-SeasonalPeak)).
Only two parameters are required for this simple model of seasonal variation:
- SeasonalPeak, the point in the year when mortality peaks, and
- SeasonalExcess, the log(amplitude) of the mortality peak.
Note that this parameterisation ensures that we always identify the winter mortality peak addition of exp(SeasonalExcess). This will usually occur around at a fraction 0-0.1 of the year after January 1st in the northern hemisphere, and 0.5-0.6 in the southern hemisphere.
An optional third parameter controls the sharpness of the winter peak:
- SeasonalShape, the shape parameter according to Richards, Ramonat, Vesper and Kleinow (2020).
where the following equation is used when SeasonalShape is non-zero:
exp(SeasonalExcess)*2[(exp(SeasonalShape/2*(1+cos(2π(y-SeasonalPeak))))-1) / (exp(SeasonalShape)-1)]-1.
| Parameters: | |||
|---|---|---|---|
| SeasonalPeak | Fraction of year after January 1st when mortality peaks. | ||
| SeasonalExcess | Seasonal excess winter mortality (log scale). | ||
| SeasonalShape | Seasonal shape parameter. | ||
A future development might be an optional parameter to permit SeasonalExcess to increase with age.