Geology Reference
In-Depth Information
Box 2.3
The problem of moraine survival.
Ever since the first synthesis of the record of
alpine glaciation (Penck and Brückner, 1909),
it has been common to recognize three or
four major moraines in glaciated valleys. At
the same time, the global climate record indi-
cates that there have been at least 10 major
glaciations in the past 1 Myr and many more
in the previous 1 Myr (Fig. 2.3). Why is there
such a mismatch between the number of gla-
ciations and the preserved morainal record
of those glaciations? One answer comes from
a statistical analysis of the probability of
moraine preservation (Gibbons
et al.
, 1984).
For example, the probability of two moraines
surviving, if there were four glaciations, is
1
P
(2/4)
=
[
P
(1/1)
+
P
(1/2)
+
P
(1/3)]
4
Because
P
(1/
N
) = 1/
N
, we get
1
⎡
1
1
⎤
1 11
⎡
⎤
P
(2/4)
=
1
+
+
=
=
0.46
⎢
⎥
⎢
⎥
4
2
3
4
6
⎣
⎦
⎣
⎦
The probabilities for differing numbers of
preserved moraines can be quite readily com-
puted (see figure A). Perhaps surprisingly, they
indicate that, for 8-20 glaciations with ran-
domly distributed magnitudes, the most likely
number of moraines to survive is only three!
N (glacial of episodes)
3
5
10
15
20
1.0
0.5
0.0
20
most likely
number of
moraines
157
3
157
3
1
3
5 7
1
3
5 7
1
3
5 7
A
n (number of moraines surviving)
15
A. Examples of the predicted number of moraines
surviving after 3, 5, 10, 15, and 20 glacial advances of
random length. Modified after Gibbons
et al.
(1984).
10
Let us assume that there has been a
succession of 15 glaciations and that, with
respect to other glaciations, the relative magni-
tude of each glaciation and its associated
advance is randomly distributed. What would
happen if the most recent glacial advance were
also the largest? It would wipe out most or all
of the geomorphic record of all previous
advances. If, on the other hand, the glaciations
happened to fall sequentially from the most
extensive at the beginning to the least extensive
at the end, then every single glaciation would
be represented. The question of how many
moraines will survive can be posed statistically
as follows. The probability (
P
) that
n
moraines
will survive, if there were
N
glaciations, is
5
3
2
1
0
0
5
10
15
20
Glacial episodes (N)
B
B. Plot of most likely number of surviving moraines
as a function of the number of glacial episodes.
Modified after Gibbons
et al.
(1984).
Overall, it is clear that a succession of
glacial moraines will typically provide only
a fragmentary record of climate change
(see figure B). Similarly, to the extent that
aggradational terraces are correlated with the
magnitude of glacial advances (as is often
supposed), it is likely that the preserved
aggradational terraces have buried older,
smaller terraces beneath them.
N
−
1
1
∑
=
−
PnN
(/ )
P n
((
1)/ )
N
N
=−
Nn
1
