In between ideas on climate reports.

People who have been following this blog know that I have spent more than a week talking about how I want to measure climate change in a fair way. I started with Greenland yesterday and promised the Arctic Circle today.

I have had a new idea.

Greenland made some sense as a single island, but my software is designed to look at areas defined by longitude and latitude. What I am going to do is cut the world up into 72 regions and report on them over the time period from 1955 to 2010, the first and last Strong La Niña years in the past 60 years. This map gives us an idea of the straight longitude lines I will use to cut the world into twelve wedges from pole to pole, but my latitude lines will be the Arctic and Tropical lines.

Here is the projection of the Southern Hemisphere from the South Pole. Both the Antarctic Circle and the Tropic of Capricorn are marked.

Here are my six areas defined by latitude.

Northern polar.
Northern temperate.
Northern tropical.
Southern tropical.
Southern temperate.
Southern polar.

To make 72 regions total I slice each latitude region into twelve longitude regions.

0° to 30° West.
30° to 60° West.
60° to 90° West.
90° to 120° West.
120° to 150° West.
150° to 180° West.

0° to 30° East.
30° to 60° East.
60° to 90° East.
90° to 120° East.
120° to 150° East.
150° to 180° East.

Problem #1. Some of these regions are going to be almost entirely ocean and the Berkeley Earth Surface Temperature count stations in a constant position, which is difficult for a seabound weather station. This means some oceanic regions will not get enough coverage to reasonably talk about the numbers being area averages. Tomorrow, we will weed out the areas that can be fairly measured from those that are so sparse we should only look at stations as uniquely representative of their single positions instead of part of a larger chorus.

When I started looking at the data from different polling companies to create the system I now call Confidence of Victory, I had several moments like this when I decided to re-think my measuring system. For most people, the view they have of math is as an unchanging edifice. Mathematicians see it differently, and in this case, you are going to see a story as it is written, draft by draft, instead of a finished product. I hope you enjoy it. it is certainly a lot of fun for me to spend time thinking about it.

Climate Change regional reports #1: Greenland 1955-2010

And so it begins. I am still new to collecting climate data, so my methods may change over time. Right now, the program I've written takes trends by seasons over an area defined by high and low latitudes and high and low longitudes. On a Mercator projection, this means a rectangle unless the North or South Pole is included. Taken from a pole, a Mercator region will look like a circle or a slice of a pie.

I chose not to take all of Greenland because I wanted to exclude Iceland and parts of eastern Canada. Iceland will be measure on it own in a future post.
 

 While the map looks like a rectangle, the slice will actually be a curved shape. The stations have a clump in the mid lower right, which corresponds to the middle south of the map.  Right now, I do not show that not all regions report all the years in the range. Future versions of this graphic will show how strong a station is by the number of reports it gives.

For example, the clump has a lot of stations that were only temporary. The areas that got the most reporting were in the southwest and the southeast, marked on the map in red.  The next strongest regions are the orange marks in the northeast.  If a region is well covered, it will have 100 diamonds on it. Parts of the middle of Greenland are so remote they have no nearby stations, so those grid points do not even appear.

And now to the reporting of the seasons, starting with winter. The jagged line is the year by year reports. The more blocky lines are the high temperature, median temperature and low temperature for an Oceanic Niña Interval, or ONI for short.  We will be using the 1955 to 2010 range for our work until there is another Strong La Niña or Strong El Niño. The intervals are

1955-1975
1975-1988
1988-1999
1999-2010

 And now the answers to The Two Questions when looking at Greenland Winters.

The trend is Greenland Winters are getting warmer, both the warmest and the coolest.

The most recent interval shows that warming trend in Greenland Winters is not slowing down.

And now the data for Spring.


The trend is Greenland Springs are getting warmer, both the warmest and the coolest, though the rise in the coolest is not as dramatic.

The most recent interval shows that warming trend in Greenland Springs is not slowing down.

And now the data for Summer.

The trend is Greenland Summers are getting warmer, both the warmest and the coolest, though the rise in the warmest is not as dramatic as the Winter increase and the median temperature for 1999-2010 is lower than the median for 1975-1988, the only counterexample in all our measurements for this recent ONI to count as the warmest in more than a half century.

The most recent interval shows that warming trend in Greenland Summers may be alternating. The next Strong La Niña or El Niño year may give us a better idea.

And now the data for Fall.

The trend is Greenland Falls was inconclusive in the first three ONI in our time span, but the most recent showed a dramatic increase in highest temperature, median temperature and lowest temperature.

The most recent interval shows that warming trend in Greenland Falls is not slowing down.


And this brings me to my first important points about terminology. "Global warming" is a bad phrase because not all regions show data as convincing as Greenland. "Climate change" isn't as bad, but it fails to say what the change is.

I propose three categories about regions: Warming regions, static regions and cooling regions. Greenland counts as a warming region.

Tomorrow: The Arctic Circle.

The Math behind Climate Change: Part 8 Trendlines based on Oceanic Niño Intervals (ONI)

We start again with the data for average Winter temperatures in Greenland from 1955 to 2010. The start and end years were not chosen at random. They coincide with strong La Niña years as measured by climate scientists on a system called Oceanic Niño Intervals or ONI for short. The list of strong La Niña years in this range are as follows.

1955, 1973, 1975, 1988, 1999, 2010

The two years in the 1970s are too close together to make a meaningful trend and they have no El Niño between them, since 1974 was a weaker La Niña. I'll remove 1973 from the list and we get 1955, 1975, 1988, 1999 and 2010.

We use the years to create intervals. In each interval, we mark the highest temperature in red, the average in black and the lowest in blue. These trends are easy to read and take no difficult to explain math. (Note: I am not against difficult to explain math. The math of best fitting curves comes from Gauss and is completely legitimate. My complaint against it is how many different curves can be chosen and the possibilities of cherry picking to make a point.

The three trends tell slightly different stories. All agree that the 1988 to 1999 interval saw much cooler winters than any other span and that the recent span from 1999 to 2010 is by far the warmest interval. While the average in the final interval is only slightly higher than the second warmest interval from 1975 to 1988, the high and the low both increase significantly over the second warmest in each of those categories.

Here are the statements I read most often in the papers of climate skeptics and denialists.

1. The climate is not warming.
2. The warming trend is decreasing.

For all the data I will produce, I will end with a statement addressing these questions for all four seasons in a form

Greenland 1955-2010
Winter: getting warmer, trend increasing
Spring:
Summer:
Fall:


Tomorrow, we will see the data for all the seasons from Greenland.

The Math behind Climate Change: Part 7 Trendlines from the best fitting polynomial method

Here is a typical set of data we are going to be looking at, one season in a region over a period of years, this particular graph the winters in Greenland from 1955 to 2010.

As you can see, the temperatures fluctuate a lot. Just eyeballing the situation, it looks like temperatures were dropping from the mid 1980s to the early 1990s, but from that low the trend is going to 2010, the warmest winter 







Here is a best fitting curve, this one the best fitting line. As you can see, it's fairly flat, so it would say that winters in Greenland are not showing a warming trend. Is that the end of the story?

No, we can fit any kind of curve to a set of data. If we are limited to polynomials, the next size up is the second degree, known as a parabola or quadratic equation. Now the curve hits a single lowest point known as the vertex and rises. It's also possible for a parabola to hit a single highest point. In any case, this shows a slight warming trend from the early 1980s on, but still shows little change from 1955 to 2010.

Next is the best fitting third degree polynomial, known as a cubic, which tells us a completely different story, a rising trend until the mid 1960s, a dropping trend until the early 1990s then a strong rising trend.
 









Next is the best fitting fourth degree polynomial, known as a quartic. It tells us the same story as the cubic only more so. If you enlarge the pictures, you'll see the variable R² gets larger as the degree of the polynomial rises. In layman's terms, that means the fit is better.

Next is the best fitting fifth degree polynomial, known as a quintic. The only significant difference is the little downward trend in the mid 1950s before the upward trend.

Next is the best fitting sixth degree polynomial, known as a sextic. This looks significantly different from the quintic, with a little downward trend at the end even though 2010 was obviously the warmest winter on record.

What gives?

Simply put, the polynomial approximations will get better eventually as more degrees are added, but the sequence of polynomials can't be trusted. It allows for cherry picking, which is the thing I want expressly to avoid.

Tomorrow, I will propose another way to look at trends, simpler than best fitting lines and incorporation the Oceanic Nino Intervals (ONI) that I consider vital to the study of the field.

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.

The Math behind Climate Change: Part 4Better data about El Niño and La Niña years

On Friday, I proposed a system for making fair intervals on which to measure climate data. Looking around the Internet, I found a webpage about the Oceanic Niño Index, also known as ONI, that looks to be more thorough and informative. Based on that info, I make a new list of fair intervals.

Here is the list of strong La Niña and El Niño years, written in blue and red respectively.

1955 1957 1965 1972 1973 1975 1982 1988 1991 1997 1999 2010

The list of fair years to start and end has been reduced significantly, so I am going to modify the rules as to what constitutes the fair years to be at the beginning and end of an interval.

1. The beginning and end of a fair interval have to be the same type of years, either both Strong El Niño or both Strong La Niña.

2. There has to be one year between the start and end of a fair interval that is of the opposite type from the type used for the beginning and end year.

Example #1: 1973 and 1975 are both Strong La Niña years, but there was no Strong El Niño between them, so 1973-1975 would not count as a fair interval. The earliest year that would make a fair interval starting in 1973 would be 1988.

Example #2: 1957, 1965 and 1972 are three Strong El Niño years without an intervening Strong La Niña year to break them up. That means 1957-1965, 1957-1972 and 1965-1972 would not count as fair intervals.

Here is a list of what I call the Consistent ONI.

First, the usable La Niña intervals.

Starting in 1955:
1955-1973 1955-1975 1955-1988 1955-1999 1955-2010

Starting in 1973:
1973-1988 1973-1999 1973-2010

Starting in 1975:
1975-1988 1975-1999 1975-2010

Starting in 1988:
1988-1999 1988-2010

And the fair El Niño Intervals.

Starting in 1957
1957-1982 1957-1991 1957-1997

Starting in 1965
1965-1982 1965-1991 1965-1997

Starting in 1972
1972-1982 1972-1991 1972-1997


Starting in 1982
1982-1991 1982-1997

As you can see, if we want to talk about the 21st Century, the shortest Consistent ONI is 1988 to 2010. When the next strong El Niño year is confirmed, it will make 1999 to 20xx a Consistent ONI.

As the proposer of the system, I will admit this is a weakness. Human nature wants to know what is happening now. An option would be to make Moderately Consistent ONI and Weakly Consistent ONI. For example, 2011 was a weak La Niña year and the previous weak La Niña years were 2005 and 2000. Because the weak years are more plentiful, it would make sense not to go back just one previous weak year but two, so 2000-2011 could be called a Weakly Consistent ONI.


I'm not a climate scientist, just a mathematician. I have no standing in the community to make the Consistent ONI the industry standard. El Niño and La Niña patterns have an effect over a vast region in the Indian and Pacific Oceans and the land masses that border them. I will do some research to see if the Atlantic has a similar known warming-cooling trend and if they exist, I will propose fair intervals based on them, which would be of use for regions bordering the Atlantic, including the eastern parts of North and South America, the west coast of Africa and all of Europe.

Tomorrow, we will look at a typical region and the distribution of stations.

The math behind climate change: Part 2What is a "reasonable" span of years to check?

As I stated in yesterday's introduction, it is my hope to create a standard that will be accepted (or at the very least debated) in the climate science community for what constitutes cherry picking and what does not. The place to start is to define what is a reasonable span of years to check for change in climate.

This is a graph of the average temperatures in Spring in Greenland from 1955 through 2011. Spring in Greenland is one of those regions over time where the data is by no means overwhelming in terms of warming. It's easy to see a peak in the mid 1970s, a cooling trend until the early 1990s and a general warming trend since. 2010 was the warmest Spring in over 50 years, but 2011 sunk to the coldest Spring this century.

What gives?

We need to remember that weather is not climate. The peak in 2010 does not prove the planet is getting warmer any more than the plummet in 2011 proves it's all bunk.

I propose that certain start dates and end dates should be accepted by people discussing the data as fair cycles. Showing my California bias, I want to look at the pattern of years that are counted as El Niño or La Niña years, which means warmer or cooler than average respectively over much of the Pacific and Indian Oceans, a substantial percentage of the earth's surface. There are other such patterns around the world and using the same method I propose here for Niño/Niña would be reasonable in those areas. (For example, since Greenland is in the North Atlantic far from the Pacific or Indian Oceans, using Niño/Niña cycles might be less constructive than using a cycle in the oceans closer to the island.)

Here is the list of El Niño and La Niña* years since 1950.

La Niña   El Niño
1950
                1952
                1954
1955
1956
                 1958
1964
                1966
                1969 
1970
1973
1975
                1977
                1983
                1987 
1988
                1992
1995
                1997 
1998
                2002
                2006 
2007
                2009
2010
2011


My proposal is this. To look at a set of years, it is acceptable to start in an El Niño year, but it should be at the beginning of a clump of El Niño years.  The end of a pattern should be the last year of a clump of El Niño years that is at least two El Niño clumps away, which is to say Niño/Niña/Niño/Niña/Niño.

Likewise, a pattern could start in the first year of a La Niña clump, then pass through Niña/Niño/Niña/Niño/Niña. It is also acceptable to look at longer patterns, but always starting at the beginning of one sort of clump and ending at the last year of the same sort of clump.

Here is the list of the acceptable year ranges starting with the La Niña years, written in blue.

1950 to 1964
1950 to 1975
1950 to 1988
1950 to 1995
1950 to 1998
1950 to 2007


1955 to 1975
1955 to 1988
1955 to 1995
1955 to 1998
1955 to 2007

1964 to 1988
1964 to 1995
1964 to 1998
1964 to 2007
1970 to 1995
1970 to 1998
1970 to 2007

1988 to 19981988 to 2007

1995 to 2007
Here is the list of the acceptable year ranges starting with the El Niño years, written in red.

1952 to 1969
1952 to 1987
1952 to 1992
1952 to 1997
1952 to 2006
1952 to 2009

1958 to 1987
1958 to 1992
1958 to 1997
1958 to 2006
1958 to 2009

1966 to 1992
1966 to 1997
1966 to 2006
1966 to 2009

1977 to 1997
1977 to 2006
1977 to 2009

1992 to 2006 
1992 to 2009

1997 to 2009

You will notice that no data pattern allows us to include information past 2009 yet, because we don't have an El Niño year to end the current La Niña clump. This may well go against the grain of people on both sides of climate debate who want to use latest data to prove their point.

My fond but forlorn hope is that these people will get over it.

If it is real, climate change is exactly the kind of problem humans are worst at solving, slow moving catastrophes that require action now to stop disasters in the future. Politically, the climate debate is mostly the left saying "Act now!" and the right saying "Bite me!" When it comes to entitlements and the budget deficit, the political sides are reversed. Neither problem is truly being addressed today.

It's not impossible to address long term problems. The Dutch, who understand their seaside country is largely under sea level, have built a remarkable set of levees and dikes. Americans did a less convincing job of protecting New Orleans. When the ozone layer was showing remarkable change, the aerosol industry was convinced into changing what they used as propellant. Climate data has done nearly nothing so far to change either the petroleum industry or its addicted consumers to change their ways.

How to start effective change if necessary is not the current goal of this series of blog posts. This is just to start a framework that has everyone discussing climate using the same benchmarks.

As I wrote on my Facebook page this morning, I was thinking about bringing peace to the Middle East, but this looked more challenging and more mathematically rich.

Tomorrow: turning lots of data into quarterly average data.

*Note: El Niño was named first and the opposite effect started out named La Niña, but some objected to the sex-based insinuation "boys are hot and girls are cold". Some wanted to call the opposite trend El Viejo, which would translate to the age-based statement "boys are warm and old men are cold". As a no longer young man, I find El Viejo more accurate metaphorically than La Niña, but the names appear to be pretty well stuck by now, more the pity.

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.