## Sunday, February 17, 2008

### Tamino's Bet - Month One

Tamino has recently made a well-designed, easily tractable "bet" on the future direction of global temperatures. Tamino asks a simple question, "Is global warming continuing?" and bases the wager and ultimate answer on whether or not the 1975 to 2007 upward trend continues into the future. Since there is considerable volatility in the global temperature anomaly, Tamino takes this into consideration and bases his measurement of this volatility on the temperature record over the 1975 to 2007 period. The actual "bet" is therefore the following:

If annual average global temperature anomaly (land+ocean) from GISS exceeds 0.735 deg.C for two (not necessarily consecutive) years before it falls below the value $0.277455 + 0.018173 (t-1991)$ (where t is the year) for two (not necessarily consecutive) years, then the still-warming side wins; if it falls below the above equation for two years before it rises above 0.735 for two years, then the not-warming side wins.
Looking back over his post, it seems that the above equation represents the mid-point of his trend line rather than the lower two standard deviation bound of his trendline (which is his intention). I think, therefore, that the above equation should be changed to:

0.277455+.018173(t-1991)-.1918

This would produce the following series of lower bound values through 2015:

2008 .4035
2009 .4217
2010 .4399
2011 .4580
2012 .4762
2013 .4944
2014 .5125
2015 .5307

Remember that the upper bound value is fixed at .7350 degrees throughout the "bet".

That is, if the average GISS annual anomaly value falls below the above values in a given year, then that year is considered to be a year meeting the lower bound criterion. We can therefore monitor the "bet" on an ongoing basis and will do so going forward.

I would have to say that this is a very fair and, indeed, generous wager. Tamino's confidence in the trend continuing is evident in the conditions he has made in this wager. I personally would have considered a wager that the average global anomaly would fall below .3853 degrees (or two standard deviations below the trend for 2007) for two years against the .7350 degrees figure as very reasonable.

As the reader may know, this wager was placed before the GISS January anomaly of .12 degrees was released. One may be interested to know the average temperature trend for the remainder of 2008 that would result in an average anomaly temperature above 2008's .4035 degrees lower bound. This minimum average figure would be .4293 degrees. Since all but one month of 2007 recorded anomalies greater than .43 degrees, the probability the average anomaly in 2008 would be below .4035 degrees appears to be relatively small at this point. Stay tuned, we'll be checking the progress of his "bet" going forward . . . .