What is a better measure of temperature anomaly, annual average or a rolling 12 month average?

Question

A 12 month rolling average is the average temperature for the previous 12 months.

This is an open question. You can attack it from a statistical, informational, educational or political perspective.

Based in part on this question and my answer to it: http://answers.yahoo.com/question/index;_ylt=AkSQPgu2I8RhP2IKcBH9IA_sy6IX;_ylv=3?qid=20100615115231AAmcAiZ&show=7#profile-info-4090lGkMaa But I don't intend that my answer be ascribed as definitive.

Answer 1

The rolling 12-month average makes more sense. The annual average is just a 12-month average only starting in January and ending in December. It's arbitrary, just because the calendar year coincidentally starts in January.



According to NASA GISS land-ocean data, we've already broken the 12-month running average record 3 times this year.

http://climateprogress.org/2010/06/10/nasa-hottest-spring-on-record/

https://spreadsheets.google.com/ccc?key=0Au57vongYoiAdEQwRWdLT0lRWjFhNGY3NnpKb1J1d0E&hl=en

Answer 2

Seems pretty obvious that the rolling average would be much better. You can pull the annual average out of the rolling average. The time frame of 12 months for the rolling average obviously makes sense in getting rid of the known yearly temp changes, but honestly, averaging over such a large number of observations and still seeing the variation that we see shows the strength of the noise signal in the temp data.



Noise reduction techniques like this are good, but I would like to research the effect of these noise reduction techniques on the analysis, especially the linear analysis that is always done. We currently use the same p-value methods to determine significance, and I wonder if the noise reduction techniques would influence the probability of finding a signal when none is there or not finding a signal when a signal is present.



OTW shouldn't you be changing your name to second grade rocks?

Answer 3

Depends on your goals. MAs force autocorrelation into a series when there is none, and in the case of temperature data, which is already serially correlated, it will screw around with the ACF. This complicates further analysis quite a bit, but I'm not aware of anyone that attempts a OLS linear fit on 12-month MAs (this was just for Jayd/I expel).



On the other hand, a 12-month moving helps to reduce, but not eliminate, interannual variations like ENSO and other non-climatic factors. And it removes the arbitrary borders of the Jan-Dec calendar year.



Trevor,

What are you using to create your graphs? I've been messing around with R quite a bit over the past few months, but can't get anything that looks so nice.



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Farf,

I'm not sure what dataset Trevor uses specifically (I believe he's said it is a weighted average of the different indices), but both PP and ADF tests easily reject the presence of a unit root in the GISS annual temperature series (1880-2009).

Answer 4

In climatic terms temperature anomalies are measured against a 30 year base period mean. For example, NASA’s GISTemp record uses the period 1951 to 1980 whereas the CRU’s HadCRUT3 record used 1961 to 1990; shorter temperature records such as the University of Alabama’s use more recent base periods (1979 to 2008 in the case of the UAH).



Using a 12 month rolling average (RA) or taking the value for a specific year will certainly identify the warmest calendar year or the warmest 12 month period but it takes it somewhat out of context. There are numerous factors that can affect temperatures over such short periods of time, some have a positive influence and others have a negative one.



Currently temperatures are being pushed higher than would otherwise be the case due to the positive effect of the El Nino Southern Oscillation (ENSO). This peaked last December and is now approaching a neutral phase. However, there is a lag with regard to the effect on temperature and barring any other factors (major volcano for example) then the ENSO effect will continue to amplify temperatures for most of the rest of the year.



Making no allowance for extenuating circumstances, then it’s probable that 2010 will be the hottest year on record, certainly all indicators are pointing to this. However, if the effect of the ENSO is removed then 2010 is likely to end up somewhere between the 7th and 12th warmest year on record which would make it the coldest year since 2004.



One year anomalies have a somewhat limited value, unless they can be put into a larger context then they don’t really tell us a great deal. A more accurate expression of how temperatures are fairing is to look at the longer term trend. If instead of a 12 month RA we use a 60 month one then 2010 comes in 2nd place (after 2004), Using any RA in excess of 84 months ranks 2010 as the hottest year on record.



The norm is a 30 year trend, in this respect temperatures have risen every year since 1966. Here’s a graph I ran off a few weeks ago showing the 1, 5, 10 and 30 year mean temps http://www.flickr.com/photos/trevorandclaire/4567517833/sizes/o/



Your previous answer (the one linked to in your question) is very interesting. It uses the NOAA data which I believe is the same as NASA’s GISTemp LOTI record, the difference being than the NOAA uses a 1901-2000 mean (I think) whereas NASA uses 1951-1980. Using multiple global temperature records and performing the same analysis that you did shows the ten hottest 12 month RA’s to be…



01 .......... Sep 1998 .......... 0.580375K .......... (02)

02 .......... Oct 1998 .......... 0.578875K .......... (07)

03 .......... Nov 1998 .......... 0.571542K .......... (17)

04 .......... May 2010 .......... 0.570583K .......... (06)

05 .......... Dec 1998 .......... 0.561667K .......... (--)

06 .......... Aug 1998 .......... 0.559292K .......... (01)

07 .......... Jan 1999 .......... 0.556708K .......... (--)

08 .......... Apr 2010 .......... 0.554500K .......... (13)

09 .......... Jan 2006 .......... 0.551917K .......... (19)

10 .......... Nov 2005 .......... 0.551042K .......... (12)



The figures in brackets are the rankings as per your calculations. Given there are nearly 2000 values in the range there’s a remarkable consistency. The values I obtained are a bit lower than yours due to the different between base-periods. The value for May is still provisional, it could be out by as much as 0.005K.

Answer 5

How does one define an anomaly?



Given only trevor's graph, it's clear that the time series is NOT stationary and needs to be differenced .Whether you use a 30year mean, annual value, etc, doesn't really matter... you should be adjusting it for seasonal variation anyway (since it's a cyclostationary process)



If you were to use standard forecasting methods using seasonal ARIMA models, I bet the predictions for 2010 or 2011 would be spot on (thus not an anomaly?)

Answer 6

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Answer 7

This question is worth more attention

Answer 8

30 years is better



http://en.wikipedia.org/wiki/Climate

Answer 9

they are pretty much the same thing.