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.

What does a statistically significant trend mean?

ReplyDeleteOne way of defining that considers only empirical uncertainties. Using this definition almost all trends listed above are statistically highly significant.

Other and more common practices refer unavoidably to some models. Expressed more completely the question is, whether the data shows some trendlike parameter of the model in a statistically significant way that, if other assumptions of the model are correct. The other assumptions include a noise model, but may include also systematic variability in the temperatures that's not considered to be trend.

I consider it essential that statements about the statistical significance of the trend are always qualified clearly in the above spirit, because it's common that contradicting statements are otherwise equally justified.

Pekka,

ReplyDeleteYes, I've posted on that here, for example. I try to distinguish between the uncertainty of the trend that was (your empirical) and the trend tha might have been (based on some model). We have a good idea of the trend that was, and people with talk of significance lose sight of that. They are talking about what might have happened if a population of possible decades had been sampled again.

That last significance counts because the future is in a sense resampling. We don't know if present trends are a guide to future trends, but if they are, that apparent randomness would limit predictability.

However I rail against its use here. The fact is that significance failed. You can't deduce anything useful from that. In the examples above, trends of 0.8-0.9 were not significantly different from zero. But they equally could have been 1.6-1.8, in line with model values.

gentlemen, the ''pause'' doesn't exist; same as the phony global warming doesn't exist!

ReplyDeleteThe truth: it will be exactly the SAME temperature overall on the planet earth for thousandths of years, as it is today; because the ''Self Adjusting Mechanism'' (SAM) is brilliant / infallible - get out of the propaganda cloud and lean about the truth: http://globalwarmingdenier.wordpress.com/2014/07/12/cooling-earth/