Lingering the pause

As I predicted, the Pause, as measured by periods of zero or less trend in anomaly global temperature, is fading. And some, who were fond of it, have noticed. In threads at Lucia's, and at WUWT, for example.

Now I don't think there's any magic in a zero trend, and there's plenty of room to argue that trends are still smaller than expected. Lucia wants to test against predictions, which makes sense. But I suspect many pause fans prefer their numbers black and white, and we'll hear more about periods of trend not significantly different from zero. So the pause lingers.

We already have. A while ago, when someone objected at WUWT to Lord M using exclusively the RSS record of long negative trend, Willis responded
"Sedron, the UAH record shows no trend since August 1994, a total of 18 years 9 months."
When I and Sedron protested that the UAH trend over that time was 1.38°C/century, he said:
"I assumed you knew that everyone was talking about statistically significant trends, so I didn’t mention that part."

And that is part of the point. A trend can fail a significance test (re 0) and still be quite large. Even quite close to what was predicted. I posted on this here.

I think we'll hear more of some special candidates, and the reason is partly that the significance test allows for autocorrelation. Some data sets have more of that than others. SST has a lot, and I saw HADSST3 mentioned in this WUWT thread. So below the fold, I'll give a table of the various datasets, and the Quenouille factor that adjusts for autocorrelation. UAH and the SSTs do stand out.

Here is a table of cases you may hear cited (SS=statistically significant re 0):

Dataset	No SS trend since...	Period	Actual trend in that time
UAH	June 1996	18 yrs 4 mths	1.080°C/Century
HADCRUT 4	June 1997	17 yrs 3 mths	0.912°C/century
HADSST3	Jan 1995	19 yrs 9 mths	0.921°C/Century

These trends are not huge, but far from zero.

So here is the analysis of autocorrelation. If r is the lag-1 autocorrrelation, used in an AR1 Arima model, then the Quenouille adjustment for autocorrelation reduces the number of degrees of freedom by Q=(1-r)/(1+r). Essentially, the variance is inflated by 1/Q. Put another way, since initially d.o.f. is number of months, all other things being equal, the period without statistical significance is inflated by 1/Q.

So here, for various datasets and recent periods, is a table of Q, calculated from r=ar1 coefficient from the R arima() function:

Dataset	1990-2013	1995-2013	2000-2013	2005-2013
HadCRUT 4	0.1078	0.1711	0.269	0.3092
GISS Land/Ocean	0.1378	0.2155	0.2907	0.3244
NOAA Land/Ocean	0.121	0.1949	0.3186	0.3396
UAH5.6	0.0789	0.1132	0.1538	0.1837
RSS.MSU	0.0978	0.142	0.2	0.1814
TempLS grid	0.1349	0.1959	0.3298	0.3748
BEST Land/Ocean	0.1201	0.1799	0.2326	0.3081
Cowtan/Way krig	0.1032	0.1642	0.2215	0.2939
TempLS mesh	0.1266	0.1862	0.2698	0.3165
BEST Land	0.2923	0.3953	0.4608	0.4835
GISS.Ts	0.1465	0.2351	0.342	0.3978
CRUTEM Land	0.2041	0.31	0.4614	0.5105
NOAA Land	0.3451	0.4795	0.6438	0.6319
HADSST3	0.036	0.0504	0.0736	0.0888
NOAA SST	0.0178	0.0251	0.0387	0.0514

Broadly, SST has low Q, land fairly high, and Land/Ocean measures, made up of land and SST, are the expected hybrid. The troposphere measures, especially UAH, have lower Q, and so longer periods without statistically significant non-zero trend.