Hump Day Traditional Cache

There's general agreement that Wednesday is the weekly Hump Day, the day when your workweek is half finished, you're over the hump and can start looking forward to the weekend and all that caching. However, the yearly Hump Day is a matter of heated discussion.

It's generally acknowledged that it should be when we're halfway through the long winter and can start looking forward to spring. For those who are particularly depressed by the lack of light, the winter solstice, i.e. Dec. 21 is their hump day. But most folks are more affected by lack of heat than by lack of light and realize there's about a month's lag until it starts to warm up. So around Jan. 21 is often proposed. Some might say halfway between the winter solstice, Dec. 21, and the spring equinox, March 21, i.e. halfway through a commonly used astronomical definition of winter. But that halfway date of Feb. 2 seems rather late, after all it is Groundhog Day. Using the popular definition of the winter months as being Dec-Feb and halfway through that yields Jan. 15, which seems a tad early. Meteorological winter is defined to be the three month period that runs from Dec 5th to March 5th; midway through that is Jan. 19.

To try to resolve these bitterly cold disputes we consulted the work of our namesake, Carl F. Gauss, who specialized in weather, astronomy and data analysis. Using a sinusoidal model of temperature