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What do glaciers tell us about climate variability
and climate change?
Gerard H. Roe
Abstract
Glaciers respond to long-term climate changes and also to the yearto-year fluctuations inherent in a constant climate. Differentiating
between these factors is critical for the correct interpretation of past
glacier fluctuations, and for the correct attribution of current
changes. Previous work has established that century-scale,
kilometer-scale fluctuations can occur in a constant climate. This
study asks two further questions of practical significance: how
likely is an excursion of a given magnitude in a given amount of
time, and how large a trend in length is statistically significant? A
linear model permits analytical answers wherein the dependencies
on glacier geometry and climate setting can be clearly understood.
The expressions are validated with a dynamic glacier model. The
likelihood of glacier excursions is well characterized by extremevalue statistics, though probabilities are acutely sensitive to some
poorly-known glacier properties. Conventional statistical tests can
be used for establishing the significance of an observed glacier
trend. However it is important to determine the independent
information in the observations, which can be effectively estimated
from the glacier geometry. Finally, the retreat of glaciers around Mt.
Baker in Washington State is consistent with, but not independent
proof of, the regional climate warming that is established from the
instrumental record.
Department of Earth and Space Sciences, University of Washington
2. Much interannual climate
variability is well characterized
by white noise.
Figure 3. (a) Annual mean precipitation recorded at Diablo Dam near Mt
Baker, over the last seventy-five years, equal to 1.89±0.36(1σ) m yr-1; (b)
melt-season (JJAS) temperature at the same site, equal to 16.8±0.78(1σ) oC;
these atmospheric variables at this site are statistically uncorrelated and both
are indistinguishable from normally-distributed white noise with the same
mean and variance. The commonly performed application of a five-year
running mean imparts the artificial appearance of multi-year regimes.
Random realizations of white noise are shown for annual-mean accumulation
(panels (c) and (e)); and for melt-season temperature (panels (d) and (f)). Note
the general visual similarity of the random realizations and the observations.
• The vast majority of the climate variance in the instrumental
is consistent with random year-to-year fluctuation with little to
no persistence (or memory). These fluctuations are integrated
in time by the glacier which responds on longer timescales.
Interannual fluctuations in accumulation and ablation are
intrinsic to a constant climate.
-A constant climate is one in which statistical distributions
of atmospheric variables do not change.
What is the response of a glacier to this natural
interannual variability, and how does it affect the
interpretation of past and current changes?
•
Only when a glacier advance/retreat
significantly exceeds the natural
variability can it be said to reflect a
climate change
Figure 5: A 500 year segment of a 10,000 yr simulation of the glacier response
to interannual climate variability. A standard flowline model calibrated to Mt.
Baker, WA, was used. The lower panels are white-noise realizations of
interannual fluctuations in accumulation and melt-season temperature, and for
which a 30-yr running mean is also shown. The upper panel shows the response
of the two glacier models. Kilometer-scale, century-scale glacier fluctuations
occur in this simulated climate that by construction has no persistence.
A standard test for trend detection is the Student’s t-test:-


DL   2


t =
sL  12 
The challenge here is we have to reply on models to know sL.
Typical numbers for the Northwest if we consider the last 100 years,
(the period of anthropogenic influence on climate): DL=200m,
n=7 (based on a 7-yr response time), t=1.85 for 95% significance.
This would require the natural glacier variability, sL, to be less than
45m for the trend to be declared significant, or nearly an order of
magnitude less than what is modeled in Figure 5. This is very
unlikely.
Issues:
5. What are odds of an advance
or retreat in a given period of
time?
.
3. How does a glacier respond to
this forcing?
Recent retreat trends are stronger, but the shorter record has fewer
degrees of freedom, so the conclusion is the same.
Glaciers are retreating globally. Surely that’s enough to prove
climate change? Almost certainly, yes. But glaciers within a single
region are not independent measures since they experience
generally similar climate. Degrees-of-freedom have to be
carefully calculated.
• Century-scale, kilometer scale glacier fluctuations occur
in a constant climate.
• It is the memory intrinsic to the glacier, not the climate
that is responsible for these fluctuation.
• A climate that has no persistence is equivalent to white noise – its
power spectrum is flat*.
• Glacier dynamics act as a low-pass filter, damping high
frequencies, but admitting low frequencies (illustrated below).
Spectral power
•
Glaciers and trend detection
7. Lessons
1. A classic challenge in signalto-noise detection
•
The climate is warming, and glaciers are retreating because of it,
but are glaciers, by themselves, independent evidence of that
warming? In other words if we threw away all instrumental
data, would the glaciers alone be enough to conclude a climate
change was occurring?
Where:
t is the t-statistic
DL is the linear trend
sL is the standard deviation of natural variability
n is
degrees of freedom = length of record/ (2 ✕ response time)
• It is common to find very little persistence in instrumental records
(see Burke and Roe (2010) for Europe, Huybers and Roe (2009) for
the Pacific Northwest, Stouffer et al., 2000, more generally)
Figure 1: Major Mount Baker glaciers superposed on a
contour map (c.i. = 250 m) Glaciers are shown at their ‘Little
Ice Age’ maxima, 1930, and present positions. What is the
correct interpretation of the cause of these changes?
4. Glaciers undergo
century-scale, kilometer-scale
fluctuations, even in a constant
climate.
6. Are glaciers good detectors of
climate change?
• The interpretation of the cause of past glaciers
fluctuations should factor in the potential role of
interannual variability.
Figure 6: The probability of exceeding a given maximum total excursion
(i.e., maximum advance minus maximum retreat), in any 1000 yr period.
Crosses shows calculations from the dynamic model output. The curves are
calculated from analytical expressions in Vanmarcke (1983).
• Mt. Baker glaciers are not by themselves independent
evident of the warming that is established from the
instrumental record.
• Glaciers are messy thermometers!
Extreme value statistics (e.g., Vanmarcke, 1983) can be used to
predict the likelihood of an excursion in a given period of time.
Such formula are very successful in describing the dynamic
glacier model.
Fig. 2
Frequency
• Therefore a constant climate with no persistence produces low
frequency glacier fluctuations
*n.b. there is equal power at all frequencies, but the phases are random so components different frequencies cancel out, leaving no persistence in the time
series.
•So for the example shown here (Mt. Baker, Wa), in any 1000yr period in a constant climate, you are:
-Very likely (>95%) to see a total excursion of >1.4km
-Very unlikely (<5%) to see a total excursion of >2.2km
References
Burke, E.E., and G.H. Roe, 2010: The persistence of memory in the climatic forcing of European glaciers.
In preparation.
Huybers, K.M., and G.H. Roe, 2009: Glacier response to regional patterns of climate variability. J.
Climate, 22, 4606-4620.
Roe and O'Neal, 2009: The response of glaciers to intrinsic climate variability: observations and models of
late-Holocene variations in the Pacific Northwest. J. Glaciol., 55, 839-854.
Roe., 2010: What do glaciers tell us about climate variability and climate change? Submitted, available at
http://earthweb.ess.washington.edu/roe/GerardWeb/Publications.html.
Stouffer, R.J., G. Hegerl and S. Tett, 2000: A comparison of surface air temperature variability in three
1000-yr coupled ocean–atmosphere model integrations. J. Climate, 13(3), 513-537.
Vanmarcke, E., 1983: Random Fields: Analysis and Synthesis. The MIT Press, Cambridge, 382 pp.