New data method: Consistent weather station map

I had a new idea for how to look at the big data set made available by Berkeley Earth Surface Temperature. While I now understand the effects of La Niña and El Niño are not worldwide, they do make a difference over a huge amount of the earth's surface so I will continue to consider eras that start and end with a strong La Niña years (or conversely with a strong El Niño years) to be time periods that are worth comparing.

I took the data set and wrote a C program that is interested only in the weather stations worldwide that reported a temperature for every season from 1955 to 2010, both of which are strong La Niña years.  The earliest La Niña to La Niña era is 1955 to 1975, while the most recent spans from 1999 to 2010.  Complete data for 2011 and 2012 is dribbling in, but neither is measured as strong La Niña or strong El Niño, so these are the time periods I use to avoid cherry picking the data, which will often mean the data is not completely up to date.

Tomorrow, I will start showing the results for these consistent weather stations, looking at the difference of the averages of the early and late eras. Splitting the data into the two hemispheres, the northern hemisphere is much better covered than the south, completely unsurprising given the differences in both land mass and population. There are many ways to look at a data set this big and as the week progresses we will go from the simplest ideas to the more complex.

Six weeks of climate data: Southern Polar Region #2, 30° to 60° East

There were a total of 540 seasonal readings from this slice of east Antarctica from 1955 to 2010 from only 9 stations.

The two black dots show that the bulk of the readings in this region were on the coast and there are no stations near the South Pole in this slice.

The summer trend is very simple. All three ways to measure the trend from interval to interval show that this region is cooling. The peak warm Summers are getting a little colder, while the median and coldest are getting much colder.
 

Falls are much the same, except that the peak high temperatures are bouncing up and down a little.

Winter tells the same story as Fall. This region is getting colder.

The only rebuttal to calling this a region experiencing a cooling trend in Springs were two freakishly cold seasons in the 1960s.

I usually put a scorecard of what time intervals showed the most warm records to most cold records in all three scales, but the count here is obvious. The region is cooling. The only counterargument is a few warm years last decade, but that warm spell appears to have snapped in Fall of 2010, which in the Southern Hemisphere starts in March.

Here's the thing. When I heard Richard Muller of Berkeley Earth Surface Temperature speak last year, he said he was certain about climate change, but his only proof of any human cause was the consensus of the papers he read in the climate journals. Muller is a physicist by trade and I was surprised to hear him make this argument that relied on authority.

This data gives the start of a hypothesis. Antarctica is as far from major human contact as any place on earth. It is cooling. Greenland is also fairly isolated from major population centers. It shows neither a clear warming or cooling trend.

We have only seen 14 of 72 regions so far. I do not know yet if the majority of slices are going to show warming, cooling or no trend at all. But if proximity to humanity has any correlation to the trends seen, that would be strong evidence that humans have an effect.

Tomorrow, two more slices of east Antarctica, including the first with major inlet, which means more readings of the ice sheets than we have seen so far.

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.

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.

The math behind climate change: Part 1

For the past few months since the election, I've been looking for a math project to work on until election prediction becomes a useful thing again. I've decided to take a shot at looking at climate data.

Does this make me a climate skeptic? Why don't I just accept the consensus of professionals?

Politically, I have more in common with the people who accept climate change than I do with those who doubt it or flat-out deny it. What I really want to do is make a set of rules I want both sides to follow. My system is still evolving, but I think I have it defined well enough to start explaining my methods and publishing my results.

To begin with, I'd like to thank the folks at Berkeley Earth Surface Temperature for creating the most complete database of temperature readings available to the public. Richard Muller founded the project with money supplied by the Koch Brothers, who have funded a lot of projects whose goal is to downplay climate change or deny it outright. Muller is a physicist at Cal and was considered a skeptic when he took their money. In point of fact, his skepticism was based on the fact that he is a physicist and the people doing climate science aren't. Physicists think they understand math better than people in other fields do, and they often are right.

When Muller finally published, he was no long skeptical about the numbers. Many people in the denialist community promised they would abide by whatever Muller found, but few have changed their minds.

Okay, why am I making this my new hobby?

I saw Muller speak last year and what interested me most was the database. I wanted to see if I could come up with a simple way to look at the patterns of change over time in regions. Everyone agrees that not all parts of the globe are changing at the same rate. My not very modest goal is to get rid of cherry picking in every case possible. The examples of cherry picking on the denialist side are legion, but both climate scientists and the press who accept global warming are also guilty of presenting the data in the best possible light, sometimes arriving at completely unsupportable conclusions. I want to make a set of rules for what defines a reasonable time period, most especially years that can start and end such periods, and a reasonable way to look at trends.

My software lets me look at any region that can be defined by a high and low longitude and a high and low latitude. (This means circles or arcs of circles if the North or South Pole are included, and rectangles on Mercator projections, which look more like slices of rings when mapped in any area preserving projection system.)

I will be explaining the system over the next several posts and will present my findings once I have defined the rules.

I will end each post on this topic with my motto.

Death to cherry picking and woe to cherry pickers.