Guest Post by Willis Eschenbach
In my previous post I discussed some of the issues with the paper “Climate related sea-level variations over the past two millennia” by Kemp et al. including Michael Mann (Kemp 2011). However, some commenters rightly said that I was not specific enough about what Kemp et al. have done wrong, so here’s what further investigation has revealed. As there is no archive of their reconstruction results, I digitized their estimate of reconstructed global sea level rise as shown in their Figure S2 (A). First, here is their Figure, showing their reconstruction of sea level.
Figure 1. Kemp Figure S2 (A) SOURCE
I digitized the part of their graph from 1650 onwards, to compare it to recent observation. Figure 2 shows those results:
So what’s not to like in these latest results from Kemp and Michael Mann?
The first thing that seems strange is that they are claiming that globally there has been a sea level rise of 200 mm (8 inches) in the last fifty years (1950-1999). I know of no one else making that claim. Church and White estimate the rise 1950-2000 at 84 mm (three and a quarter inches) mm, and Jevrejeva says 95 mm (three and three-quarters inches), so their reconstruction is more than double the accepted estimates …
The next problem becomes apparent when we look at the rate of sea level rise. Figure 3 shows the results from the Kemp 2011 study, along with the MSL rise estimates of Jevrejeva and Church & White from worldwide tidal gauges.
Kemp et al. say that the global rate of sea level rise rose steadily since the year 1700, that it exceeded 3mm per year in 1950, that it has increased ever since, and in 2000 it was almost 5 mm/year.
Jevrejeva and Church & White, on the other hand, say it has never been above 3 mm/year, that it varies up and down with time, and in 2000 it was ~ 2 mm/year. In other words, their claims don’t agree with observations at all.
In addition, the Kemp 2011 results show the rate of sea level rise started increasing about 1700 … why would that be? And the rate has increased since then without let-up.
So we can start with those two large issues — the estimates of Kemp et al. for both sea level and sea level rise are very different from the estimates of established authorities in the field. We have seen this before, when Michael Mann claimed that the temperature history of the last thousand years was very different from the consensus view of the time. In neither case has there been any sign of the extraordinary evidence necessary to support their extraordinary claims.
There are further issues with the paper, including in no particular order:
1. Uncertainties. How are they calculated? They claim an overall accuracy for estimating the sea level at Tump Point of ± 40 mm (an inch and a half). They say their “transfer function” has errors of ± 100 mm (4 inches). Since the transfer function is only one part of their total transformation, how can the end product be so accurate?
2. Uncertainties. The uncertainties in their Figure S2 (A) (shaded dark and light pink in Figure 1 above) are constant over time. In other words, they say that their method is as good at predicting the sea level two thousand years ago as it is today … seems doubtful.
3. Uncertainties. In Figure 4(B) of the main paper they show the summary of their reconstruction after GIA adjustment, with the same error bands (shaded dark and light pink) as shown in Figure S2 (A) discussed above. However, separately in Figure 4(B) they show a much wider range of uncertainties due to the GIA adjustment. Surely those two errors add in quadrature, and end up with a wider overall error band.
4. Tidal range. If the tidal range has changed over time, it would enter their calculations as a spurious sea level rise or fall in their results. They acknowledge the possible problem, but they say it can’t happen, based on computer modeling. However, they would have been better advised to look at the data rather than foolishly placing their faith in models built on sand. The tidal range at Oregon Inlet Marina, a mere ten miles from their Sand Point core location, has been increasing at a rate of 3 mm per year, which is faster than the Kemp reconstructed sea level rise in Sand Point. Since we know for a fact that changes in tidal range are happening, their computerized assurance that they can’t happen rings more than a bit hollow. This is particularly true given the large changes in the local underwater geography in the area of Sand Point. Figure 4 shows some of those changes:
Note the shallows between the mainland and the south end of Roanoke Island in 1733, which are noted on charts up to 1860, and which have slowly disappeared since that time. You can also see that there are two inlets through the barrier islands (Roanoke Inlet and Gun Inlet) which have filled in entirely since 1733. The changes in these inlets may be responsible for the changes in the depths off south Roanoke Island, since they mean that the area between Roanoke and the mainland cannot easily drain out through the Roanoke Inlet at the north end as it did previously. Their claim that changes of this magnitude would not alter the tidal range seems extremely unlikely.
5. Disagreement with local trends in sea level rise. The nearest long-term tide station in Wilmington shows no statistically significant change in the mean sea level (MSL) trend since 1937. Kemp et al. say the rise has gone from 2 mm/year to 4.8 mm per year over that period. If so, why has this not shown up in Wilmington (or any other nearby locations)?
6. Uncertainties again, wherein I look hard at the math. They say the RMS (root mean square) error in their transfer function is 26% of the total tidal range. Unfortunately, they neglected to report the total tidal range, I’ll return to that in a minute. Since 26% is the RMS error, the 2 sigma error is about twice that, or 50% of the tidal range. Consider that for a moment. The transfer function relates the foraminiferal assemblage to sea level, but the error is half of the tidal range … so best case is that their method can’t even say with certainty if the assemblage came from above or below the mean sea level …
Since the tides are so complex and poorly documented inside the barrier islands, they use the VDatum tool from NOAA to estimate the mean tidal range at their sites. However, that tool is noted in the documentation as being inaccurate inside Pamlico Sound. The documentation says that unlike all other areas, whose tidal range is estimated from tidal gauges and stations, in Pamlico Sound the estimates are based on a “hydrodynamic model”.
They also claim that their transfer function gave “unique vertical errors” for each estimate that were “less than 100 mm”. This implies that their 2 sigma error was 100 mm. Combined with the idea that their VLSI error is 50% of the tidal range, this in turn implies that the tidal range is only 200 mm or so at the Sand Point location. This agrees with the VDatum estimate, which is almost exactly 200 mm.
However, tides in the area are extremely location dependent. Tidal ranges can vary by 100% within a few miles. This also means that the local tidal range (which is very local and extremely dependent on the local geography) is very likely to have changed over time. Unfortunately, these local variations are not captured by the VDatum tool. You can download it from here along with the datasets. If you compare various locations, you’ll see that VDatum is a very blunt instrument inside Pamlico Sound.
That same VDatum site give the Pamlico Sound two sigma errors (95% confidence interval) in converting from Mean Sea Level to Mean Higher High Water (MHHW) as 84 mm, and for Mean Lower Low Water as 69 mm.
The difficulty arises because the tidal range is so small. All of their data is converted to a “Standardized Water Level Index” (SWLI). This expresses the level as a percentage of the tidal range, from 0 to 100. Zero means that the sample elevation is at Mean Lower Low Water, 100 means it is at MHHW. The tidal range is given as 200 mm … but because it is small and the errors are large, the 95% confidence interval on that tidal range is from 90 mm to 310 mm, a variation of more than three to one.
Their standardized water level index (SWLI) is calculated as follows:
SWLI = (Sample Elevation – MLLW) / (MHHW – MLLW) x 100 (Eqn. 1)
When adding and subtracting amounts the errors add quadratically. The sample elevation error (from the transfer function) is ± 100 mm. The MLLW and MHHW two sigma errors are 69 mm and 84 mm respectively.
So … we can put some numbers to Equation 1. For ease of calculation lets suppose the sample elevation is 140 mm, MLLW is 0 mm, and MHHW is 200 mm. Mean sea level is halfway between high and low, or about 100 mm. Including the errors (shown as “±” values) the numerator of Eqn. 1 becomes (in mm)
(Sample Elevation – MLLW) = (140 ± 100 – 0 ± 69)
Since the errors add “in quadrature” (the combined error is the square root of the sum of the squares of the individual errors), this gives us a result of 140 ± 122 mm
Similarly, the denominator of Eqn. 1 with errors adding in quadrature is
(MHHW – MLLW) = (200 ± 84 – 0 ± 69) = 200 ± 109 mm
Now, when you divide or multiply numbers that have errors, you need to first express the errors as a percentage of the underlying amount, then add them in quadrature. This gives us
(140 ± 87%) / (200 ± 55%) *100
This is equal to (.7 ± 103 %) x 100, or 70 ± 72, where both numbers are percentages of the tidal range times 100. Since the tidal range is 200 mm, this means that the total uncertainty on our sample is about 72 percent of that, or ± 144 mm. So at the end of all their transformations, the uncertainty in the sample elevation (± 144 mm) is larger than the sample elevation itself (140 mm).
All of that, of course, assumes that I have correctly interpreted their very unclear statements about the uncertainties in their work. In any case, how they get a Tump Point two sigma error of about 40 mm (an inch and a half) out of all of that is a great mystery.
Those are my problems with the study. Both the rate and the amount of their reconstructed sea level rise in the last fifty years are much greater than observations; tidal ranges in the area are varying currently and are quite likely to have varied in the past despite the authors’ assurances otherwise; and their methods for estimating errors greatly underestimate the total uncertainty.
[UPDATE] One other issue. They say regarding the C14 dating:
High-precision 14C ages (8) were obtained by preparing duplicate or triplicate samples from the same depth interval and using a pooled mean (Calib 5.0.1 software program) for calibration.
This sounded like a perfectly logical procedure … until I looked at the data. Figure 5 is a plot of the individual data, showing age versus depth, from Supplementary Tables DR3 and DR4 here. They have used the “pooled mean” of three samples at 60 cm depth, and three samples at 80 cm depth.
Figure 5. Age and depth for the Sand Point samples in the top metre of the core. Red squares show C14 dates. Horizontal black bars show the 2-sigma uncertainty (95% confidence interval).
Look at the 60 cm depth. The three samples that they tested dated from 1580, 1720, and 1776. None of their error bars overlap, so we are clearly dealing with three samples that are verifiably of different ages.
Now, before averaging them and using them to calibrate the age/depth curve … wouldn’t it make sense to stop and wonder why two samples taken from the exact same one-centimetre-thick slice of of the core are nearly two hundred years different in age.
The same is true at the 80 cm depth, where the ages range from 1609 to 1797. Again this is almost a two hundred year difference.
What am I missing here? How does this make sense, to average those disparate dates without first figuring out what is going on?