Klotzbach revisited

Not a perfect title; it's actually my first comment on the 2009 GRL paper by Klotzbach, Pielke's, Christy et al. It was controversial at the time, but that was pre-Moyhu, or at least in very early days. And I hadn't paid it much attention. But it surfaced again today at Climate Etc, so I thought I should read it.

The paper is very lightweight (as contrarian papers can be). It argues that observed surface trends since 1979 actually exceed troposphere trends, as measured by the UAH and RSS indices, which CMIP etc modelling suggests that the troposphere should warm faster.

Now for global you can simply get those trends, and many more, with CIs from the Moyhu trend viewer. You might say, well, figuring out what the models said should be rated substantial. But they way oversimplified, were corrected at Real Climate (Gavin) and had to publish a corrigendum. There has been more discussion then and over the years. Here, for example, is a post at Climate Audit, with Gavin participating. But the audit didn't seem to pick up the CI issue, though other methods were discussed. Later a Klotzbach revisited WUWT post (my title echoes) two years ago; more on that from SKS here. And now another update.

But what no-one, AFAICS, has noticed is that the claims of statistical significance are just nuts. And significance is essential, because they have only one observation period. The claim originally, from the abstract, was:

"The differences between trends observed in the surface and lower-tropospheric satellite data sets are statistically significant in most comparisons, with much greater differences over land areas than over ocean areas."

I've noticed that the authors are quieter on this recently, and it may be that someone has noticed. But without statistical significance, the claims are meaningless.

Update: I think that the CI's they are quoting may relate to a different calculation. They computed the trends in Table 1, with CI's, and in Table 2 the differences. They say in the abstract that these are differences of trends, but the heading of Table 2, which is not very clear, could mean that they are computing the trends of the differences (a new regression) and giving CI's for that. That is actually a reasonable thing to do, but they should make it clear. I have got reasonably close to their numbers for comparisons with UAH, but not with RSS; it may be that the RSS data has changed significantly since 2009.

I'll describe this in more detail below the jump.

Here is their Table 1 of trends in C/decade with 95% CI's

Table 1. Global, Land, and Ocean Per Decade Temperature Trends and Ratios Over the Period From 1979 to 2008
Data Set         Global Tren         Land              Ocean Trend
NCDC Surface     0.16 [0.12-0.20] 0.31 [0.23-0.39] 0.11 [0.07-0.15]
Hadley Surface   0.16 [0.12-0.21] 0.22 [0.17-0.28] 0.14 [0.08-0.19]
UAH Lower Trop   0.13 [0.06-0.19] 0.16 [0.08-0.25] 0.11 [0.04-0.17]
RSS Lower Trop   0.17 [0.10-0.23] 0.20 [0.12-0.29] 0.13 [0.08-0.19]

My own calcs (to 2014) gave CI's comparable to these.

I've been commenting at CE here and here, and I extracted σ values here

NCDC Surface   0.16 [0.12-0.20]  0.04
Hadley Surface 0.16 [0.12-0.21]  0.04
UAH Lower Trop 0.13 [0.06-0.19]  0.06
RSS Lower Trop 0.17 [0.10-0.23]  0.06

 But you don't need them to see that the results in Table 1 are very unlikely to be significant. Virtually all the trends lie within the CIs of the sat indices. Consider a comparison of NCDC 0.16 and UAH 0.13 [0.06-0.19]. There is no way NCDC is inconsistent with the range of UAH, even if it did not have error of its own.

Anyway, what Klotzbach et al did was to show a table of differences with CIs:

Table 2. Global, Land, and Ocean Per Decade Temperature Trends Over the Period From 1979 to 2008 for the NCDC Surface Analysis
Minus UAH Lower Troposphere Analysis and the Hadley Centre Surface Analysis Minus RSS Lower Troposphere Analysis
Data Set               Global Trend (C)    Land Trend (C)     Ocean Trend (C)
NCDC minus UAH           0.04 [0.00- 0.08]  0.15 [0.08- 0.21]    0.00 [-0.04-0.05]
NCDC minus RSS           0.00 [-0.04- 0.04] 0.11 [0.07- 0.15]   -0.02 [-0.07- 0.02]
Hadley Center minus UAH  0.03 [0.00- 0.07]  0.06 [0.02- 0.10]   0.03 [-0.01-0.07]
Hadley Center minus RSS  -0.01 [-0.04- 0.03] 0.02 [-0.02- 0.06] 0.00 [-0.04-0.04]
Trends that are statistically significant at the 95% level are bold; 95% confidence intervals are given in brackets.

So compare, say, Had-UAH global: 0.03 [0.00- 0.07]
But Had was:
Hadley Surface 0.16 [0.12-0.21]
and UAH
UAH Lower Trop 0.13 [0.06-0.19]  0.06

The CI for the difference has about half the range as for RSS alone. This is reflected throughout the table.  But the normal method requires that Ïƒ's  be added in quadrature. The range for the difference must be larger than for each of the operands.

Now it might be possible to construct an argument that dependence would make a lower CI for the difference. But there isn't much data to resolve dependence as well. And this is basically a test for dependence. You can't start off by assuming it. In any case, the paper doesn't say anything about how the difference CI's were calculated. And I have no idea.

Table 3 shows the differences between amplified (x 1.2) surface vs troposphere. It is little different, and again the CI's are far too narrow. Yet that is where the main claim of significance is based. I won't reproduce here; it is muddied by the changes made in the corrigendum. But they do nothing to repair the situation.

I do not believe any of these trend differences are significant.
Update - see above. I think that interpreted as the CI's of a regression on the differences, the original significance claims may be justified.

Update. A commenter at Climate Etc challenged me to calculate a corrected Table 2. He also wanted Table 3, but it's a bit late for that. Here is Table 2. I've shown under each original line, my variance-added numbers. I've worked with rounded data, so there are rounding discrepancies.

Data Set               Global Trend (C)    Land Trend (C)     Ocean Trend (C)
NCDC minus UAH           0.04 [0.00- 0.08]  0.15 [0.08- 0.21]    0.00 [-0.04-0.05]
                          0.03 -0.05 0.11   0.15  0.03 0.27     0.00 -0.08 0.08
NCDC minus RSS           0.00 [-0.04- 0.04] 0.11 [0.07- 0.15]   -0.02 [-0.07- 0.02]
                         -0.01 -0.09 0.07   0.11 -0.01 0.23    -0.02 -0.09 0.05
Hadley Center minus UAH  0.03 [0.00- 0.07]  0.06 [0.02- 0.10]   0.03 [-0.01-0.07]
                         0.03 -0.05 0.11    0.06 -0.04 0.16     0.03 -0.06 0.12
Hadley Center minus RSS  -0.01 [-0.04- 0.03] 0.02 [-0.02- 0.06] 0.00 [-0.04-0.04]
                         -0.01 -0.09 0.07    0.02 -0.08 0.12    0.01 -0.07 0.09

As you can see, there is now only one case that is barely significant - NCDC-UAH on land. But that is at 95% - we could expect it 1 in 20 times. And here are 12 tests.