Age Models at Quelccaya and Kilimanjaro

The Quelccaya glacier is at a similar latitude to Kilimanjaro and is also receding. It’s a logical point of comparison. Core 1 is 163.6 m deep (Summit Core- 154.8 m) and is attributed a start date of 470 AD (Summit Core: 744 AD). Annual dust layers are a guide to dating in the upper portions. In Core 1, the layer dated to 1800 AD is at 106 m in depth, the layer dated to 1590 AD at 130 m in depth (Summit – 120 m). It is both much younger and much thicker than Kilimanjaro. If you calculate accumulation rates at both glaciers according to a thickening model, it turns out that the assumed accumulation at Kilimanjaro is about 100 times lower than at Quelccaya, which is a young glacier. Precipitation levels appear to be comparable.

Glaciers become increasingly compressed with age. The usual equation linking the total thickness of the glacier H and the annual accumulation a to the age at a given depth z is as follows:

The main sensitivity in this equation is to a. For Quelccaya, the average accumulation is said to be 1.368 m. See footnote at There is an interesting aliasing artifact discussed by Hans Erren here.

Assuming that I’ve done this right – I’ve cross-checked it, but this is a new calculaiton for me – putting H at 165 m, the value of a needed to yield the 1800 AD layer at 106 m is 0.85 m; to yield AD1590 at 130 m is 0.65 cumulatively (i.e. a much lower rate from AD1800 to AD1590) and to yield AD500 at 160 m is cumulative 0.38 m. I’m unaware of any detailed discussion of the reasoning for this at Quelccaya. But, aside from this, the key point here is that the glacier is both much younger and much thicker than Kilimanjaro.

Here are the ages at 50 m under various accumulation rates a for H=55 m and H=80 m. Thompson does H=50 m, which leads to singularity in the equation, for which he does an odd coercion. Thompson concludes that the accumulation rate is 0.0128 m and that the basal layer is 11700 BP through this odd coercion. For the argument here, it doesn’t matter whether a=0.0128 m or a= 0.0067 m. The point here is just how sensitive this age calculation is to the accumulation rate a and just how low the Kilimanjaro accumulation rate is compared with Quelccaya where, in the well-measured period since AD1800, a=0.85.

Accumulation Rate a (m) Age (H=55 m) Age (H=80 m)
0.5 264 157
0.4 330 196
0.3 440 262
0.2 659 392
0.1 1319 785
0.05 2638 1569
0.0128 10303 6130
.0067 19684 11711

Thompson is saying that Kilimanjaro a is about 1% of the value at Quelccaya. Thompson says that precipitation occurs in all months at Kilimanjaro with monthly totals "typically" less than 100 mm. I’m looking for annual precipitation totals at Quelccaya; if the average accumulation is said to be about 1.268 m, it would appear that annual precipitation at both Quelccaya and Kilimanjaro are pretty similar. Ergo, the average annual ablation rate at Kilimanjaro must be pretty nearly equal to the average annual precipitation. Add in some autocorrelation and I cannot imagine how you can get a plausible age model resulting in Kilimanjaro being 11700 years old. I’m not even sure how you can prove that it’s as old as Quelccaya on the information proffered to date.

It would have been nice if Thompson had commented in the original publication on these astonishingly low accumulation rates and how they reconcile with (say) Quelccaya, where he had previously worked.


  1. Paul Penrose
    Posted Oct 24, 2005 at 5:57 PM | Permalink

    Finally a posting from you that I can fully understand! Good luck on getting some answers from Thompson. It doesn’t seem like a simple adjustment of the numbers will reconcile these two sites, so Thompson’s answer would be interesting indeed.

  2. Steve McIntyre
    Posted Oct 24, 2005 at 9:56 PM | Permalink

    Hans (Erren), what do you think of this?

    The two Quelccaya cores look like they area similar distance apart and are dated pretty much in parallel.

  3. Larry Huldén
    Posted Oct 24, 2005 at 11:40 PM | Permalink

    Annual mean temp for Huaraz (Peru) is 17C (+- 1C each month)
    Annual precipitation for Huaraz is 755 mm
    Huaraz is at 9.35S 77.59W, altitude is 2759 m
    Quelccaya is at 13.56S 70.50W, altitude 5670 m
    Huaraz is much closer to the coast than Quelccaya.

  4. Larry Huldén
    Posted Oct 25, 2005 at 12:31 AM | Permalink

    Mean annual precipitation for four locations Ayacucho, Cuzco, Juliaca and La Paz (Bolivia) seems to be very close to or a little lower than for Huaraz (c. 700 mm). These locations goes along a transect close to Quelccaya.

  5. Hans Erren
    Posted Oct 25, 2005 at 12:40 AM | Permalink

    re: #2
    Good work Steve. This emphasises AGAIN the need for full disclosure of all ice core data. I don’t buy Thompson’s old age for Kilimanjaro ice.

  6. beng
    Posted Oct 26, 2005 at 7:19 AM | Permalink

    And if Kilimanjaro is much younger than touted, then it’s prb’ly quite transient, geologically, and any time that it’s growing, or melting & close to disappearing or even gone, won’t necessarily be “unusual”.

  7. Steve McIntyre
    Posted Aug 28, 2006 at 10:33 PM | Permalink


  8. Willis Eschenbach
    Posted Aug 29, 2006 at 2:26 AM | Permalink

    Steve, just started looking at this … one possibility is that there are several values for “accumulation” “¢’‚¬? snow accumulation, ice equivalent accumulation, and water equivalent accumulation. For Huarascaran, Thompson gives accumulation figures of:

    snow “¢’‚¬? 3.3m
    ice equiv. “¢’‚¬? 1.4m
    h2o equiv. “¢’‚¬? 1.3m

    Unfortunately, neither your formula above nor the Quelccaya text file you link to above say what kind of accumulation they’re talking about … I suspect the desired figure is h2o equivalent, but Quelccaya doesn’t say what they’re using … OK, I found it, they do say it’s h20 equivalent.

    I just looked up the Sajama core information. No accumulation information, but I did a Solver solution and got a value of 0.02 to match with their dates/depths … doesn’t make sense. Likely this is because the accumulation rates change over time, as described in TROPICAL GLACIER AND ICE CORE EVIDENCE OF CLIMATE CHANGE ON ANNUAL TO MILLENNIAL TIME SCALES.

    Unfortunately, they do not give absolute accumulation rates for the various dates, just deviations in sigma from zero … I’ll have to read more to figure out why.


  9. Willis Eschenbach
    Posted Aug 29, 2006 at 2:28 AM | Permalink

    Further thoughts. In the Sajama info I found this:

    If changes in ice thickness are ignored, the average accumulation rate a(ij) between the dated depth horizons zi and zj (where i, and j, are any two dated horizons) is given by:

    Aij = {1/dt(ij)} * (Integral from zi to zj) (1 – z/H)^-p dz

    A_{ij} = {\frac{1}{dt_{ij}} \int_{z_i}^{z_j} (1-{\frac{z}{H}})^{-p} dz

    where H is the ice thickness, z is the ice-equivalent depth, p is a constant, and dt(ij) is the
    number of years between zi and zj.

    I’m too tired right now to do the math to see how that relates to your formula above.


  10. Willis Eschenbach
    Posted Aug 29, 2006 at 2:34 AM | Permalink

    Steve, you should appreciate this one. It’s the accumulation rates by year for the two cores at Quelccaya …


  11. Steve McIntyre
    Posted Aug 29, 2006 at 7:03 AM | Permalink

    #10. Yes, that graphic is fun. That was one of the first ones that I noticed in the Mann data set. I corresponded with Hans Erren about it in spring 2003. Hans Erren explained the odd pattern as due to aliasing from rounding. None of this is directly “observed” data. It has all been transformed through an age model to create an observation. At the left end, the layers are squished togethre so that the linear slope represents the inflation of the same measured thickness back to a calculated “accumulation”.

  12. Willis Eschenbach
    Posted Aug 29, 2006 at 10:36 AM | Permalink

    Steve, I think there’s an error in the latex version of the formula in #9, the quantity in parentheses should be to the minus p, not to the p …


  13. John A
    Posted Aug 29, 2006 at 11:03 AM | Permalink

    re #12


    It’s just easier to read in LaTeX than trying to guess from text.

  14. Willis Eschenbach
    Posted Aug 30, 2006 at 12:04 AM | Permalink

    Re 13, thanks, John. Now I just have to figure out how it relates to the other equation above …


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