The Math behind Climate Change: Part 5A region and its coverage

I have written a series of programs in C to look at the climate data. I took the most complete data set available, published by Berkeley Earth Surface Temperature, and changed it to record the station information as quarterly averages, using the method explained in Part 3.

My program to look at a region over time uses that quarterly data and sets up a time series. It needs a start and end date, a high and low latitude and high and low longitude.  If the latitude does not include either pole, the shape of the region will look like a rectangle in a Mercator projection map, but there will be some curvature in any projection that preserves area. (Mercator makes things near the poles look larger than things near the equator, which is why Greenland and Africa look to be the same size on some maps, when Africa is in fact much larger.)

A famous region that looks rectangular on Mercator is Colorado.

Using all the weather stations that reported any data from 1955 to 2010, we see the state doesn't look quite rectangular. This is because turning longitude and latitude into x and y coordinates factors in the curvature of the earth.

The state is pretty well covered, which is the case for much of the land in the Northern Temperate Zone, the most populated region on earth. The density is greatest around the red rectangle, which corresponds roughly to Denver and its suburbs.

My system imposes a 10×10 grid on the region and each grid point adds in the data per season from the nearby stations, weighted by distance. This is an effort to even out the sampling somewhat. Even so, some grid points will get more data in their sample, so a map to show the relative strengths will be included in any report. What that grid looks like will be the topic of tomorrow's post.