## Saturday, December 19, 2009 ... /////

### UAH MSU: temperatures for 2009 and ranking

Looking at UAH daily temperatures, one can estimate the temperature anomaly for December 2009.

In average, the first 17 days of December 2009 were 0.10 °C warmer than the same days in 2008. The "2009 minus 2008" differences for the month are

{7, 12, 22, 26, 34, 34, 17, 2, -1, 2, 1, -3, 1, 3, 3, -3, 7, f, f, f, 34, 22, 17, 10, 1, -2, -9, -4, 6, 14, f}
in units of 0.01 °C. Because the December 2008 UAH anomaly was just 0.18 °C, the December 2009 anomaly will be 0.28 °C plus minus 0.05 °C (standard deviation of my estimate).

Update, January 1st, 2010: the rest of the month had the same average anomaly. I expect the final reading for December 2009 to be 0.28 °C plus minus 0.02 °C.

Update, January 5th, 2010: my preliminary Dec 19th calculation 0.28 °C was exactly correct, see WUWT.

To summarize, the 2009 monthly UAH anomalies are
{0.3, 0.35, 0.21, 0.09, 0.05, 0.01, 0.42, 0.23, 0.42, 0.29, 0.5, 0.28}
and their average is 0.263 °C plus minus 0.005 °C which is statistically indistinguishable from 2006.

The annual UAH anomalies from 1995 to 2009 are:
{0.11, 0.02, 0.05, 0.51, 0.04, 0.04, 0.2, 0.31, 0.28, 0.19, 0.34, 0.26, 0.28, 0.05, 0.26}
Among these 15 years, 2009 will be cooler than 1998, 2005, 2002, 2007, 2003, and maybe 2006, so it will be just the 6th or 7th warmest year - pretty much exactly in the middle of the last 15 years' scoreboard. A global warming trend continues to be absent despite the very strong El Nino episode that has been affecting the weather for more than half a year and that may match the 1998 El Nino of the century in the near future.

Similarly but less accurately, we may predict the ranking according to RSS, too. The December 2009 anomaly is predicted 0.10 °C above the December 2008 anomaly, by using the UAH hints. In the RSS case, it's 0.27 °C. (Update: it was 0.243 at the end, pretty good, too.) The 1995-2009 RSS anomalies will be
{0.159, 0.047, 0.102, 0.551, 0.087, 0.082, 0.244, 0.335, 0.358, 0.251, 0.375, 0.278, 0.308, 0.092, 0.262}
where the error of the last entry is something like 0.01 °C. Here, 2009 is cooler than 1998, 2005, 2003, 2002, 2007, 2006, making it the 7th warmest year - even closer to the middle of the last 15 years. Even though the RSS warming trend is generally known to be somewhat higher than that of UAH, you can see that RSS actually produces a cooler 2009 in the ranking (7th instead of UAH's 6-7th).

Similarly, if the December 2009 GISS anomaly is estimated to be 0.10 °C above December 2008, the 2009 monthly anomalies will be
{0.53, 0.44, 0.47, 0.48, 0.54, 0.63, 0.64, 0.53, 0.67, 0.64, 0.68, 0.57}
The error of the last, estimated month is something like 0.05 °C because it's a very different type of measurement than UAH. The 1995-2009 GISS anomalies will be
{0.38, 0.29, 0.4, 0.57, 0.32, 0.33, 0.48, 0.56, 0.55, 0.48, 0.63, 0.54, 0.56, 0.43, 0.57}
That makes 2009 statistically coincide with 1998, being their second warmest year after 2005, unless it will drop below 2002 and 2007 which are at 0.56 °C. (Update: exactly this conclusion of mine was officially confirmed on January 16th, 2010.) Note the dramatic difference in the rankings between UAH/RSS on one side and GISS on the other side.

For the sake of completeness, let me also add our ClimateGate zombie friends from HadCRUT3. Yes, note the CRU inside the acronym. With the 0.10 °C year-on-year increment for December, the 2009 monthly anomalies are gonna be
{0.383, 0.363, 0.371, 0.419, 0.41, 0.511, 0.509, 0.549, 0.459, 0.429, 0.455, 0.419}
Similarly, the 1995-2009 annual temperature anomalies are
{0.275, 0.137, 0.351, 0.546, 0.296, 0.27, 0.408, 0.464, 0.473, 0.447, 0.482, 0.422, 0.405, 0.326, 0.44}
Let me be cautious and estimate the error of the last entry, 0.44, to be 0.02 °C. Ask Harry why I chose such a high error margin. In this table, 2009 is gonna be cooler than 1998, 2005, 2003, 2002, and probably 2004, making it the 5th or more likely 6th warmest year on their record.

You see that the ranking is between 5th and 7th, with the exception of GISS. So I expect the AGW pundits suggest that the 5th warmest year surely means "terribly hot". They will demonize 1998 which was a hellish year (it was a completely normal year, and because we thought that Czechia was too cold in the summer, we went to Spain).

If there were some significant or urgent global warming, you would expect the record to be broken almost every year: that's what increasing functions like to do. However, it's been the 11th year in a row when the record reading wasn't rewritten. And according to UAH, 2009 was 0.25 °C below 1998. Because the 1979-2009 warming trend indicated by UAH is 0.13 °C per decade, we will need roughly 20 more years to return back where we were in 1998, assuming that the warming observed in the last 30 years will continue (it didn't exist between the 1940s and 1970s).

Even if there were a warming issue worth talking about, it doesn't sound terribly urgent given these numbers, does it?

Bonus: linear regression

As a bonus, I will list you the UAH warming trends (recalculated to temperature changes in °C per century) for various intervals:

1995-2009: +0.95 °C/century
1996-2009: +0.89 °C/century
1997-2009: +0.41 °C/century
1998-2009: -0.24 °C/century
1999-2009: +1.22 °C/century
2000-2009: +0.53 °C/century
2001-2009: -0.78 °C/century
2002-2009: -1.56 °C/century
2003-2009: -1.43 °C/century
2004-2009: -1.43 °C/century
2005-2009: -3.70 °C/century
2006-2009: -2.30 °C/century
2007-2009: -1.00 °C/century
2008-2009: +21.0 °C/century

Of course, the last one must be taken with a big grain of salt. ;-)

Otherwise, you can see among these 14 trends, 6 are warming (generously counting the huge 2008-2009 trend as well) while 8 are cooling! ;-) I could be more quantitative but this is roughly what we mean by saying that there has been no statistically significant warming in the last 15 years.

Update: slope error

You can also use the general formula for the error of the slope to determine whether the slope is significant or not. Taking the full 15 years where the slope was 0.95 °C per century, the formula produces the error of this number at 0.88 °C, so the claim that it is positive is only known at a one-sigma confidence level: a complete noise. Mathematica code:
x = Table[i, {i, 1995, 2009}]
y = {0.11, 0.02, 0.05, 0.51, 0.04, 0.04, 0.2, 0.31, 0.28, 0.19, 0.34, 0.26, 0.28, 0.05, 0.26};
data = Transpose[{x, y}]

n = 15
xAV = Total[x]/n
yAV = Total[y]/n
xmav = x - xAV;
ymav = y - yAV;
lmf = LinearModelFit[data, xvar, xvar];
Normal[lmf]

(* http://stattrek.com/AP-Statistics-4/Estimate-Slope.aspx?Tutorial=AP *)

slopeError = Sqrt[Total[ymav^2]/(n - 2)]/Sqrt[Total[xmav^2]]
Given the huge deviation of slope, the 95% confidence interval for the slope will be something like (-1 °C/century, +2 °C/century) although I haven't calculated it exactly. The sign of the slope is not known with any confidence.

Mathematica actually has compact functions that can tell you the confidence intervals:
lmf = LinearModelFit[data, xvar, xvar, ConfidenceLevel -> .95];
lmf["ParameterConfidenceIntervals"]
The 95% confidence interval for the slope is (-0.87, 2.8) in °C/century. Similarly, the 99% confidence interval is (-1.59, +3.49) in °C/century. On the other hand, the 90% confidence interval is (-0.54, 2.44). All these intervals contain both negative and positive numbers. No conclusion about the slope can be made on either 99%, 95%, and not even 90% confidence level.

We can only say that it is "somewhat more likely than not" that the underlying trend in 1995-2009 was a warming trend rather than a cooling trend. Saying that the warming since 1995 was "very likely" is already way too ambitious and the data don't support it.