Torturing Data

nor·mal·ize

 [ náwrm'l z ]   

1. make something normal: to make something normal or return something to normal, or become or return to normal
2. make something or somebody conform: to make something or somebody conform to a standard
3. heat steel: to heat steel above a specific temperature and then cool it in order to reduce internal stress.  

 A time series can be Normalized by dividing the elements of the time series by the standard deviation of some period of the time series.  The chart above is for the University of Alabama -Huntsville (UAH)  Microwave Sounding Unit (MSU), Lower Troposphere (LT), Mid-Troposphere (MT) and Lower Stratosphere (LS) temperature anomaly data for the Northern Hemisphere (NH) land only, region.  The LS has a (-) minus sign in front meaning it is inverted. 

By forcing the data for the three layers of the atmosphere into a "normal" form, you can more easily compare the data.  The first rule of time series analysis should be look at your data.  Normalizing allows a closer look.

The LS data is inverted because its response is inverse to the response of the LT and MT data.  There is a similarity, but there are differences.

cor·re·la·tion

 [ kàwrə láysh'n ]   

1. mutual or complementary relationship: a relationship in which two or more things are mutual or complementary, or one thing is caused by another
2. act of correlating: the act of correlating, or the condition of being correlated
3. relatedness of variables: the degree to which two or more variables are related and change together

-LS to LT correlation, 0.424,  _LS to MT correlation 0.204, LT to MT correlation 0.894

Perfect correlation is 1 or 100%.  LT to MT correlation is very strong, -LS to LT is weak but may be significant depending on the number of points in the time series, -LS to MT correlation SUCKS.  That is a technical Redneck engineering term.  Any decent spread sheet program will have a correlation function.  For these I used the OpenOffice, CORREL()

This chart compares the Southern Hemisphere (SH) Ocean inverted LS with NH LT and MT for land only.  There is a small difference in the "eyeballed" correlation.  According to OpenOffice, the (-LS) to LT correlation is 0.472, the (-LS) to MT correlation is 0.338.  The 0.338 sucks less than 0.204 in the first chart even though the SH Ocean LS is half a world away.

By shifting the SH Oceans (-LS) forward by 12 months, the correlations improves to 0.558 and 0.404 respectively which in both cases suck significantly less.  Some might consider that the SH oceans LS temperature might indicate that something has more influence on land surface and mid troposphere temperatures than CO2 forcing during this portion of time known as the satellite era.  Since warming in the SH appears to lead warming in NH land regions, that could be natural variability or CO2 forcing uses a time shifting mechanism.

The data is available at NOAA- National Climatic Data Center under Upper Atmospheric Temperature Data.  There is another upper atmospheric temperature data set commonly used, RSS, but unfortunately RSS doesn't provide as many regional options.

In any case, feel free to torture data, er... look into different ways of looking at the data.  :)