The math behind climate change: Part 3Quarterly data

 As I have said before, the data I use are taken from the set compiled by Berkeley Earth Surface Temperature. Richard Muller was considered a climate skeptic when he started his project and the Koch Brothers funded it. He was less skeptical when it was finished and the climate skeptic community has given him the treatment Scientologists give those who leave the fold.

 The important data has a station number a data and a temperature. Stations have a longitude, latitude and altitude associated with them. To deal with altitude, there is a formula called the lapse rate, the simplest version saying temperatures drop as the altitude rises at a linear rate of 6.4 degrees Celsius for every 1000 meters. (For Americans, this means about 11.5 degrees added to a temperature for every 3,281 feet above sea level.)

Stations are not bound by the same standards as to when they take readings, so to level that off I took seasonal averages. I called the seasons year.00, year.25, year.50 and year.75, though the readings actually began on the first days of winter, spring, summer and fall, respectively. (Of course, in the southern hemisphere, that would be summer, fall, winter and spring.) Here is data that covers the third quarter of 1978. The first reading is well before 1978.50 and the last reading is after 1978.75.
  

Using a simple formula, I truncate the first and last line segments to get the pattern we will use to take the seasonal average. While I did not include the scale, all these temperatures were taken from a station in the Arctic Circle, so they are all below 0 degrees Celsius.

Imagine vertical line extending up from each grid point to the x-axis at the top of the picture. This creates trapezoids. The area of a trapezoid is the width times the average of the two heights. We add up all the trapezoids and get a number that will equal the area of the shape.

The red series shows the average height of all the trapezoids and it is that average that is recorded as the temperature for the season.

Tomorrow, a re-definition of "reasonable" time ranges based on more exact data.