Esper the non-Archiver is Trouet’s supervisor (see url.), so I’ve taken the liberty here of ascribing this clever April Fool’s prank to Esper, though undoubtedly Trouet deserves some credit for her role in pulling off the prank.
In a recent post, I alluded to the point that the England precipitation index shown in the Trouet Esper graphic below is derived from Figure 4 of Lamb 1965.
The idea that Lamb’s reconstruction should be held out as a key element in their disproof of the Medieval Warm Period is such a pretty prank that it really deserves to be savored a little more than we’ve done so far. It’s almost as good as prank as Mann using Sherwood Idso’s strip bark results to disprove that MWP. Maybe it’s a better prank since it uses a variation of the IPCC 1990 graphic itself: the link between the IPCC graphic and the Lamb-Esper precipitation series being readily seen in the following excerpt from a Lamb graphic – the rounded version is carried forward into the well-known IPCC 1990 graphic while the more angular version is carried forward into the Esper-Trouet Figure (compare to the cyan line in Trouet-Esper graphic):
Anyway, today I thought it would be interesting to report on exactly how Lamb derived his estimate of winter precipitation, as readers should take care to be aware of exactly what’s in Lamb’s winter precipitation estimate so that they can better protect themselves against pranksters like Esper.
Lamb’s original Table II excerpt for rainfall is shown below – the first column is annual, 2nd is high summer (July-August) and the 3rd is the rest of the year (Sept-June), all expressed as percentages of 1916-1950 values.
The high summer rainfall is calculated through a regression relationship with the “Summer Wetness Index” of Lamb and Johnson, 1961 (I don’t know how this Summer Wetness Index was calculated and have no plans at present to investigage this rabbit hole further).
The regression equation for decade values of July and August rainfall (as % of the 1916-1950 average) over England and Wales (R_JA) on the summer wetness index value (W) is: R_JA = 6.52W + 29.1. The standard error of the resulting percentage figure appears to be ± 4.01. (p. 26)
Next the annual rainfall was calculated through a 2nd regression relationship – this time with the famous Lamb temperature reconstruction (which is why the shape ends up being so familiar).
The estimates of average yearly rainfall in Table II and Fig.4 are derived from the yearly mean temperatures given, and from the winter temperatures adjusted to be at their mildest in the medieval warm epoch the equal of the present century, using the appropriate regression equations …
Footnote 2: The regression equation for decade values of average yearly rainfall in England and Wales (Ry) as % of the 1916-1950 average rain on average yearly temperature Ty is: Ry = 9.80Ty + 6.2. The standard error of the percentage estimates so derived appears to be 4.65.
Thus, Lamb’s estimate of annual rainfall is a linear re-scaling of the famous temperature series. (BTW the IPCC 1990 is a little different than the Lamb 1965 version and appears to be taken from a slightly different version in Lamb 1967, as discussed in a post on an earlier occasion.)
Next the Sept-June rainfall is estimated as the difference between the two values:
Finally, the rainfall averages in Table II for the 10-month period that excludes the high summer, were given by the differences between the amounts of rain implied by the other two columns.(page 33)
The reason why the Lamb-(Esper) winter precipitation estimate has the same shape as the famous annual temperature series is that the summer wetness index does not have a lot of “low frequency” variability relative to the annual temperature series, and thus the famous shape carries through to the winter index.
Somewhat inconsistently, footnote 2 on page 33 reports a third regression equation relating Sept-June rainfall to temperature as below (the running text appears to indicate that it was calculated by difference; I haven’t tried to verify which is the case as it doesn’t matter for present purposes):
The corresponding regression equation for values of rainfall over the 10 months September- June (R10) on winter temperature is: R10 = 7.81 T_DJF + 66.6. The standard error of these estimates appears to be 4.29.
As you can see from Table II, there aren’t a lot of degrees of freedom in any of these regression equations.
Here again, Esper has again pulled a very clever prank as he’s smoothed all his data into 50-year bins as well, so that no one can complain about about overly coarse data in Lamb 1965. Esper has done an additional tease by saying that they used 25 year bins even though the merry prankster used 50 year bins as shown in my earlier post.
All in all, even CA readers must grudgingly respect both Esper and Science for pulling off such an inventive and witty April Fool’s prank.