The fleeting pause

At WUWT, there is a monthly post (latest here recording the duration of the Pause, which Lord Monckton defines as the maximum time back that a satellite index, RSS, can be found to have trend less than zero. The choice of that index, which measures an average of troposphere temperature by a complex analysis of data from several satellites, is necessary because all of the better known surface temperature indices have rising trends for all recent periods.

So there is lots of cherry picking. You can see what is actually going on in this calculation in the following back trend graph (from this active plotter).



The graph shows, for various indices, the trend from the year on the x axis to present (Dec 2015). You can see the cherry picking in the choice of index. RSS is the lowest green curve. It now has UAH V6 beta for company, but only recently; V5.6, still being published, was up with the surface indices. The Pause starts from the first crossing of the x-axis, which I've marked with a red circle. But you'll see that even so, most of the curve is positive. The excursions below the axis are brief and shallow, and about to come to an end. In fact the shape is not too far from an inverted image of the time series itself. The big temperature peak in 1998 shows as a dip, while the following trough shows as a local peak in trend. That is why the "pause" has persisted - because of the very big 1998 peak which depresses subsequent trends.

I'll show later how the troposphere measures respond strongly but late to an El Nino. So much higher readings are expected in the coming months. But already those curves are rising rapidly, and I expect them to clear the axis within two or three months. In fact, I'll show a fairly easy way of measuring this, in terms of temperatures to come. Specifically:

• If the January anomaly exceeds about 1.3°C, the Pause is gone. This is unlikely.
• If the Jan and Feb anomalies exceed on average about 0.77°C, the curve will be above the axis. For reference, the Dec anomaly was 0.543°C. I think this is quite likely.
• If the first three months exceed 0.59°C on average, that would suffice to extinguish the pause. That is barely above the December value, and I think very likely indeed.
• If Jan-April exceed 0.5°C, that will also suffice.

I'll explain the arithmetic below the fold.

Here is an easy way to see what happens to the trend r of T_n from month d0 when T_1 at month d1 is added. If T_1 actually lies in the trend line, the trend does not change. So the additional trend is what you would get by adding a series which is zero everywhere except at d1, where its value is the residual R1. Trend is a linear function, so the change in trend is the trend of this rather special function added. And that is
r' = R1*6/(d1-d0)/N
where N is the number of months in the trend.
And
R1=T_1 - mean(T) - r*(d1-d0)/2

For two successive months, two such functions, with just one non-zero at the end, are added. They are displaced by a month, but that has small effect. To good approx, the effect on trend is the same as if the sum of residuals applied for just one month. And so on for three or four months (slightly less good approx).

Here is a plot showing for each starting month d0 the temperature required for the added months to bring the trend to zero. For more than one month, it is an average. You can ignore all but the high parts; the plot also shows which cool temperatures will reduce a positive trend to zero. You'll see that, although the trend dips below zero around 2001 and 2008 are bigger now than in 1997, the arithmetic works so that once the dip at 1997 is eliminated, the other dips have already gone.



To show the pattern in 1997/8, which might be followed in 2015/6, here is the monthly anomaly plot



The increase in 1998 is large and sustained, and 2016 starts from a much higher base.