Dedicated to the balanced discussion of global warming
This is a totally different type of article and I hope you will indulge me. I typically give my editorial thoughts on an article that is fairly easily referenced on the web but in this case I wanted to explain some basic mistakes of an article that I recently read and then propose my own calculations on the article. I finish this post with some observations. While I try very hard to show arguments on both sides of this complicated issue, by reading this post you will have some idea of my personal stance.
The article in question is on the Deltoid blog and is titled Corrections to the McKitrick (2002) Global Average Temperature Series. It may be valuable for you to click through to that article and read it first before continuing here. Take your time, I will wait.
Now that you have read that article please read my analysis.
First, Mr. Lambert makes a small but forgivable error. He states that you cannot arithmetically average temperatures to find their mean. He then states a thermodynamic experiment for his justification. He is essentially correct in this statement however if the two bodies are of the same thermodynamic mass then you can add them together. Since we are talking about the atmosphere over 10 weather stations and we do not have any other data (such as relative humidity) we have to assume that atmosphere is constant for all stations. It isn’t, of course, so while Mr. Lambert is correct in his statement – he just gives a poor explanation for it. See the bottom of this article for more discussion on this topic.
Now lets dig into the math. Mr. Lambert is critiquing Mr. McKitrick in his article. Basically Mr. McKitrick took weather data for many years for 10 weather stations and made some interpretations of the data. Mr. Lambert correctly points out that some of the years do not have any data and Mr. McKitrick substituted zero for those years which screws up the analysis. This is an extremely big mistake by Mr. McKitrick since he seems to forget that he is using values that are measured in degrees Celsius which is a differential measurement. In reality he was working in degrees Kelvin so all of the values needed to have 273.15 added to them. Surely, Mr. McKitrick didn’t mean to imply that the missing years were actually 273.15 degrees Kelvin! This is a major mistake and I am surprised that some grad student on Mr. McKitrick’s staff didn’t catch it. I am disappointed that Mr. Lambert did not point out why the error was so bad, but I will give him the benefit of the doubt since he did notice the problem.
Mr. Lambert tries to correct the mistake in two different ways, eliminating the months with no data and substituting values into the years with no data. The former method is the correct strategy and the latter method is foolish. There is no value in substituting values from another month in another year. It overly weights that other measurement and we have no reason to believe the value is correct for the given month. It would have been better to assume that the change is linear between months and to average the months on either side of the missing months but even that is not needed. There are 264 months in the sequence, leaving off 2-10 data points is more accurate to the change in temperature of a location over 22 years than substituting a value. I believe that Mr. Lambert knows this since he offered two different methods, however offering a method that is completely wrong is at best confusing to the reader and he should never have put up that suggestion.
Mr. Lambert does do some calculations by leaving out the data, as this is one of his suggestions. When I looked at the conclusions though, it didn’t make sense or at least I couldn’t draw any conclusions from it.
I decided to do my own calculations since the raw data was offered. This required me to remember some of my high school mathematics on vector analysis though. I started the effort by looking for my high school son’s math books but when I opened the door to his room, I decided that trying to find a textbook in that maze of dirty clothes, food wrappers, Gatorade bottles and Sports Illustrated magazines may shorten my expected lifespan. Second choice was a refresher on the web and I found this article (http://www.1728.com/vectutor.htm) that got me back up to speed on the math that I knew when I wasn’t so gray and overweight.
I have provided my calculations in Excel with this post and I invite you to download and critique the math if you will. As I said, it has been some time since I did vector math and I didn’t have the luxury of independent review of my math that Mr. McKitrick and Mr. Lambert should have available to them. I will depend on you are your compassion to point out any error that I may have made.
My conclusion is that using these 10 weather stations and the data that was provided, the average temperature dropped by 0.15 degrees Celsius in the 22 years. So if you take my analysis out of context the press could put in their headlines “THE EARTH IS COOLING BY .07 DEGREES PER DECADE – ICE AGE IS IMMINENT”. Don’t do that since that is NOT what I am saying. Keep reading…
Why all of this doesn’t even matter
All of the above was a fun effort but it really doesn’t matter. There is nothing to be learned by knowing the average temperature change of 10 locations over 22 years.
First, as mentioned above, the thermodynamic profiles of each location are extremely different. Knowing the temperature doesn’t matter if we don’t know a variety of other information such as wind speed, pressure, humidity, and the percentages of other trace gases such as carbon dioxide and methane. What really matters is the ability of the atmosphere at that location to absorb and retain heat. Temperature is just one partial measurement of this but as a stand alone piece of data it offers very little for us to draw conclusions. Arguing about the temperature is inconsequential since what we are worried about is the change in the amount of heat and its consequential effect on other things (e.g. ice, water, land, animals, plants, etc.). This is just one of the reasons that statements by the IPCC on temperature change can be misunderstood. I believe that Mr. Lambert understood this (maybe not my IPCC statement) but he definitely did not explain it well in his article.
Second, it is not statistically significant to discuss 10 locations. If we say that each location is a fairly good representation of a 100 km by 100 km area (and even this may be too big – 10k x 10k is more likely) then we know it represents 10,000 square kilometers. If we believe Wikipedia when it says that Earth has a surface area of 510M square kilometers then we have only sampled 0.00196% of Earth. Coupling this with the knowledge that these locations were not evenly dispersed across the globe and we can conclude that these 10 locations do not statistically prove anything about the global temperature change of Earth.
Third, the data is quite suspect. I have major concerns as to why whole months are missing and worse when multiple months in a row are missing. This causes me to believe that the reading and recording of those temperatures was not important. How could you miss an entire month if that were your job? Also, what day of the month were these temperatures recorded (or are they the average of the entire month)? What time of day were these recorded? The whole concept of looking at months is suspect since month’s are a decidedly human invention. Rather, it makes more sense to record the temperature, relative humidity, wind, concentration of other trace gases, pressure and several other factors every day at a time that is equidistant from sunrise and sunset. The same measurements should be recorded for the high and low temperature of the day. This data can then be used to calculate the amount of heat in the atmosphere at that location at those times. If we did this at enough locations, we would have some idea of the answer to the question at the top of this site: Is it getting warmer?
I have never seen any effort to calculate this information in enough locations to be statistically significant. This why I question the very base assumption of many people that believe the IPCC reports that it is getting warmer by x degrees. How did you come up with your base temperature and how did you measure the temperature of today. We simply do not know enough to make these claims.
Both gentlemen are learned men and probably know more about climate science than I will ever know. However, for both of them to make such basic mistakes of measurement, science, and math makes one question their motives. Did they just make honest mistakes that are isolated to this one instance or did they have some dishonest motive. I will assume the former but will always be on the lookout for the latter when I read any more of their works. They are on opposite sides on many issues and it starts to call into question the fervor of the entire argument. I will give slightly more credit to Mr. Lambert since he at least noticed the gross errors of the original article and tried to call them out.
Okay, I am done. Please stay tuned for my typical posts that try to give balanced exposure to both sides of this issue. Based on this one instance, I will likely avoid the works of Mr. McKitrick and Mr. Lambert, or at the very least, look at them with a skeptical eye.
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