Solar Minimum 2009, Global Cooling and the Record Breaking Winter

[Akrasia]

Standard Deviation is a measure of the spread or variance around an estimate of a mean value. Mean values of repeated samples have a standard deviation = (standard deviation of the sample measurements)/sqrt(n),when n is the sample size (assumed to be always the same in this case).

I would surmise that the Standard Deviation is decreasing because the error in the estimate is decreasing e.g. (putting it roughly) repeated mean linear measurements of samples of 4 will have standard deviation proportional to 1/sqrt(4)=0.5, while repeated mean linear measure of samples of 100 will have standard deviation proportional to 1/sqrt(100) =0.1, an improvement by a factor of 5.

If you are applying this to temperature measurements, I presume the scientific reason is the improvement in statistical methods of estmation over the years. Another reason is the profusion of measurements (at this point many land, ocean and atmospheric estimates) which has the sam effect as increasing sample size.

CS is wrong on all aspects of his little standard deviation trip.

As he knows, because I've already told him 3 or 4 times, there are now twice as many recorded record High temperatures as there are record lows (study refers to the U.S.)
Record High Temperatures Far Outpace Record Lows Across U.S. - News Release

. The variation from the mean (30 year average) temperature is getting higher as the globe is warming. Measuring standard deviation over the 30 year trend shows that warming is accelerating. It absolutely does not show that the globe is cooling.

[owedtojoy]

Actually, the graphic has nothing to do with standard deviation at all! I found this explanation:

This graphic shows the ratio of record daily highs to record daily lows observed at about 1,800 weather stations in the 48 contiguous United States from January 1950 through September 2009. Each bar shows the proportion of record highs (red) to record lows (blue) for each decade. The 1960s and 1970s saw slightly more record daily lows than highs, but in the last 30 years record highs have increasingly predominated, with the ratio now about two-to-one for the 48 states as a whole. (©UCAR, graphic by Mike Shibao.)

So the key "takeway" is the proportion by which the red bar exceeds the length of the blue bar.

… If temperatures were not warming, the number of record daily highs and lows being set each year would be approximately even. Instead, for the period from January 1, 2000, to September 30, 2009, the continental United States set 291,237 record highs and 142,420 record lows, as the country experienced unusually mild winter weather and intense summer heat waves.

Incidentally, if Alaska was included, it would actually boost the findings, as the Arctic has been warming faster than the the rest of the globe.

[Cassandra Syndrome]

Standard Deviation is a measure of the spread or variance around an estimate of a mean value. Mean values of repeated samples have a standard deviation = (standard deviation of the sample measurements)/sqrt(n),when n is the sample size (assumed to be always the same in this case).

I would surmise that the Standard Deviation is decreasing because the error in the estimate is decreasing e.g. (putting it roughly) repeated mean linear measurements of samples of 4 will have standard deviation proportional to 1/sqrt(4)=0.5, while repeated mean linear measure of samples of 100 will have standard deviation proportional to 1/sqrt(100) =0.1, an improvement by a factor of 5.

If you are applying this to temperature measurements, I presume the scientific reason is the improvement in statistical methods of estmation over the years. Another reason is the profusion of measurements (at this point many land, ocean and atmospheric estimates) which has the sam effect as increasing sample size.

Thank you owedtojoy. You answered my question. In dealing with econometrics, standard deviation is a useful tool say in time related data. For example the explosion in the mean GNP per capita in the 20th century has been accompanied by greater extremes in wealth.

I have noticed that as a mean increases in time related data, while the skewness and SD does not necessarily have to increase the maximum in ranges of the datasets increase.
Personally I prefer the median than the mean, but I will pay attention to the difference between the 2 in a dataset

Here is a interesting website from somebody thats in your profession,

Now, I probably wouldn’t have had to list all those to make the point, but by my count, we have 4 anomalies that moved a value of 48 from one month to the next in the last 68 years. But then look at what the data shows. There were five such occurrences in the decade of the 1930s, 2 occurrences in the 1920s, 3 occurrences in the previous decade (all in 1917), 2 in the decade before that. Then things really go bonkers. There are 9 such anomalies in the 1890s and 18 occurrences in the 1880s, with at least one such occurrence in every year of that decade except in 1889.

Seeing these numbers, I ran a standard deviation by decade of the temperature anomalies. The 1880s had a standard deviation of 32.02. The 1890s show a standard deviation of 26.66. 1900-1909 have a standard deviation of 19.75, and the 1910s a standard deviation of 22.96. Starting with the anomalies of the 1920s, the standard deviation starts too fluctuate from a low of 14.75 in the 1940s to a high of 20.44 in the 1990s, with the most recent ten-year period showing a value of 16.79.

I present this more as a point of interest, rather than to draw any particular conclusion. It seems reasonable to believe that the further back we go, the less reliable the numbers are. This could be due to both an increase in techological ability to measure temperature as well as an increase in coverage (meaning less estimation in more recent data). So, at some level, there must be a certain amount of garbage (I suppose a nicer term is “noise”) in the older data. This directly speaks to how reliable this older data is. And if called into question, it shortens our observed time period of good data. The other possibility is that the data is reliable, but temperatures actually did fluctuate a lot more during that time period. But it has been suggested to me that one of the impacts of climate change is that we can expect more “extremes.” The suggestion that we are undergoing climate change in the more recent period, and the further suggestion that such climate change means a larger swings in “extremes” seem like contradictory positions given the temperature anomaly data.

April 2008 Update on Global Temperature Trends, Part 1 Digital Diatribes

He mentions some of the points you made.

[owedtojoy]

Thank you owedtojoy. You answered my question. In dealing with econometrics, standard deviation is a useful tool say in time related data. For example the explosion in the mean GNP per capita in the 20th century has been accompanied by greater extremes in wealth.

I have noticed that as a mean increases in time related data, while the skewness and SD does not necessarily have to increase the maximum in ranges of the datasets increase.
Personally I prefer the median than the mean, but I will pay attention to the difference between the 2 in a dataset

Here is a interesting website from somebody thats in your profession,



April 2008 Update on Global Temperature Trends, Part 1 Digital Diatribes

He mentions some of the points you made.

It is important to remember that teh data presented by Akrasia and the data in the link you gave are completely diffferent.

The data from Akrasia is discrete, multinomial data. Daily temperature records for each decade were examined at 18,000 weather stations and classified according to to: High, Low, Neither High nor Low. We could used this data to demonstrate a significant difference between the numbers of highs and lows. Under the null hypothesis that there is no climate change, the number of highs and lows should be equal, so a statistical test would reject the hypothesis in this case. I can post the numbers if you like.

The data in the link is raw, temperature data. The author's post is somewhat out of date because some of the numbers in the data set are different from what he states. I need to look at him some more, but at a first glance his technique looks suspect to me.

[Cassandra Syndrome]

9 days now with no sunspots

The K7RA Solar Update

An interesting article about the first couple of days of the new observer. It reports on the quiet sun.

Launched on Feb. 11, SDO is the most advanced spacecraft ever designed to study the sun. During its five-year mission, it will examine the sun's magnetic field and also provide a better understanding of the role the sun plays in Earth's atmospheric chemistry and climate.

http://www.technewsworld.com/story/N...Sun-69837.html

NASA better be impartial this time!

[Cassandra Syndrome]

It is important to remember that teh data presented by Akrasia and the data in the link you gave are completely diffferent.

The data from Akrasia is discrete, multinomial data. Daily temperature records for each decade were examined at 18,000 weather stations and classified according to to: High, Low, Neither High nor Low. We could used this data to demonstrate a significant difference between the numbers of highs and lows. Under the null hypothesis that there is no climate change, the number of highs and lows should be equal, so a statistical test would reject the hypothesis in this case. I can post the numbers if you like.

The data in the link is raw, temperature data. The author's post is somewhat out of date because some of the numbers in the data set are different from what he states. I need to look at him some more, but at a first glance his technique looks suspect to me.

Well he isn't a climatoligist, he is an impartial actuator. Do you know where you can get large temperature databases on .dta files owed? I wouldn't mind running it through my econometrics software.

[owedtojoy]

Well he isn't a climatoligist, he is an impartial actuator. Do you know where you can get large temperature databases on .dta files owed? I wouldn't mind running it through my econometrics software.

I am not a climatologist either. I plotted the standard deviations of the every ten years (1880 - 1889, 1881 - 1890, ... ,2000-2009), 121 points in total.

As far as I can see there has been no significant change in the standard deviations since 1914, except an increase in the 1980s. The average std. dev. among the 10-yearly groups is 18.84 which is close to his most recent value.

So the standard deviation is not really shifting (the mean is, of course, but that is another story). As the writer said himself:

"... the standard deviation starts to fluctuate from a low of 14.75 in the 1940s to a high of 20.44 in the 1990s, with the most recent ten-year period showing a value of 16.79.

I present this more as a point of interest, rather than to draw any particular conclusion."

The best way to analyse these data is probably with suitable time-series models, but you are probably aware of that already. From my own tinkering with time-series models, they confirm an increasing trend in the temperature.

[owedtojoy]

Well he isn't a climatoligist, he is an impartial actuator. Do you know where you can get large temperature databases on .dta files owed? I wouldn't mind running it through my econometrics software.

I missed out on your question. You can find the GISS data he is using here:

http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt

You can copy and paste into Notepad, save & open in Excel.

Plotting the annual temperature anomaly mean and standard deviation i.e. the mean and stdev of the 12 months) gives a better view. You can see it is fluctuating around an average from about 1914 onwards. This means annual temperature readings have had a fairly constant variance since that time.

[Cassandra Syndrome]

I missed out on your question. You can find the GISS data he is using here:

http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.txt

You can copy and paste into Notepad, save & open in Excel.

Plotting the annual temperature anomaly mean and standard deviation i.e. the mean and stdev of the 12 months) gives a better view. You can see it is fluctuating around an average from about 1914 onwards. This means annual temperature readings have had a fairly constant variance since that time.

Cheers for that

[Cassandra Syndrome]

Somee more observations of the sun from the new observer. Btw, owed that data is variances from the global means over a period using log10 -2. I'll play about with it anyway. I wonder you can get mass levels of temperature data?

Sun is frozen in dazzling new detail - Times Online