Four weeks of climate data (reboot):Explaining the new method of data collection.

When I last reported on climate data on Tuesday, I was showing the stats for Antarctic Region 3. Like much of Antarctica, this region is sparsely covered with weather stations.
 

My first way of measuring the data showed this precipitous drop in average temperatures in all seasons in the late 1980s. A change of 8 degrees Celsius over such a short time span looked suspicious to me.

My original method was to take all the data from all the stations and spread it onto points of a 10 by 10 grid. The stations in this regions are marked by the red points.

What happened here is that the interior stations were not online until recently, and when they came in the average was skewed way down.

My new method still looks at all the data, but a grid point has to show consistency, data from at least 75% of the seasons in the time interval.

Following that rule, only two out of 100 grid points are consistent enough to make it to the final averages.  This is going to get rid of data in some places, but it's necessary to do this to get more reliable results.

The blue crosses are the corners of the region. The boxes represent the grid points that are included in our regional average. This sparsely covered region is only represented by the stations at the edges of the Amery Ice Shelf.

 

Using the new method, we still see a modest cooling trend in the median and the low temperatures and a static pattern in the high temperatures. The thing that makes this more believable is that the changes are in the range of 1 to 2 degrees Celsius instead of nearly 8 degrees.

Another advantage of the new system is that I equalized the grid input. In the old system, very heavily covered input points could overwhelm the points with less coverage. Now, if a grid point makes the threshold of consistency, its data is treated equally will all other consistent grid points.

The data analysis begins again tomorrow.

The Math behind Climate Change: Part 6 Superimposing grids on regions

As we saw yesterday, there are a lot of weather stations in Colorado and the tendency is for the number of stations to correlate to the population of an area. The red rectangle with lots of stations is the area around Denver. The sparseness of stations near the far corners of the grid corresponds to those regions being sparsely populated.

I decided to superimpose a 10 × 10 grid on the map to even out the readings somewhat and to show the reader what areas of the map are being sampled the most. The most sampled grid points are in red, the next most in blue, then the white diamond followed by the small black diamonds being least represented.

Tomorrow (finally), we will look at seasonal data and propose a system that will avoid cherry picking the method to look at trends.

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.