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Geomorphometry.org/2013 Naruse and Oguchi
1
Classification and formation environment of glacial 1
valleys based on morphometric analyses 2
3
Kosuke Naruse 4
Graduate School of Frontier Sciences 5
The University of Tokyo 6
Kashiwa, Japan 7
8
9
Takashi Oguchi 10
Center for Spatial Information Science 11
The University of Tokyo 12
Kashiwa, Japan 13
15
16
Abstract—This paper analyzes glacial valleys in the Swiss Alps, the 17
Himalayan Range, Yosemite, the New Zealand Southern Alps, and 18
Patagonia using DEMs. Transverse and longitudinal profiles of 19
four to six valleys in each region were obtained and the aspect/form 20
ratio (FR) and slope of each small segment of a transverse profile 21
were calculated. Forms of glacial valleys were evaluated using FR 22
and the kurtosis, skewness, and standard deviation of slope. FR 23
tends to converge into 0.28 with increasing valley size, which may 24
correspond to the balance of vertical and lateral glacial erosion as 25
well as a threshold slope angle for slope failure after deglaciation. 26
The transverse profiles were classified into four types based on 27
their geomorphometric properties: 1) U-shaped, 2) V-shaped, 3) 28
plain, and 4) others. The most common type, other than “others” 29
that include various forms, is U-shaped in New Zealand and 30
Patagonia, V-shaped in the Himalayas, and plain in Yosemite and 31
the Swiss Alps. These differences may reflect regional 32
characteristics of snowfall, mass wasting, tectonics, and the history 33
of glacier advances. FR may also indicate the past location of the 34
glacial equilibrium line. 35
36
INTRODUCTION 37
Glacial valleys or troughs are a major type of glacial 38
landforms, and their transverse sections are widely known as U-39
shaped [1]. Although some researchers investigated the form of 40
transverse profiles of glacial valleys, they typically focus on 41
theoretical interpretation of U-shaped form [2, 3] or net volume 42
of erosion [4]. Detailed studies on the actual shape of glacial 43
valleys, including discussion on whether they are really U-shaped, 44
have been limited to a few case studies [5, 6]. The objectives of 45
this paper are: 1) to analyze the detailed morphometric 46
characteristics of glacial valleys in various regions of the world 47
using digital elevation models (DEMs); 2) to classify glacial 48
valleys based on the statistical analysis of the shape of transverse 49
profiles; and 3) to discuss environmental factors affecting glacial-50
valley forms. 51
52
STUDY AREAS AND METHODS 53
The study areas are typical glaciated mountains in the Swiss 54
Alps, the Himalayan Range, Yosemite, the New Zealand 55
Southern Alps, and Patagonia. Four to six deep and wide glacial 56
valleys without large existing glaciers were selected from each 57
area for detailed morphometric analysis. Valleys that underwent 58
glaciation during MIS2 (Last Glacial Maximum) were selected to 59
minimize the effect of postglacial erosion. The names of the 60
selected valleys are shown in Table I. Fig. 1 shows maps 61
illustrating the distribution of the four glacial valleys in Patagonia, 62
adjacent to the Hielo Patagonico Norte Icefield. Like this case, 63
the selected valleys tend to be located near large existing glaciers. 64
65
TABLE I. SELECTED GLACIAL VALLEYS. 66
Area Valleys
Swiss Alps Burgli, Heimritz, Kandersteg, Lauterbrunnen, Leukerbad, Schwanden
Himalaya Lachung, Mangan, Pandim, Sikkim
Yosemite Long Mountain, Lyell A, Lyell B, Lyell C, Tower, Yosemite
NZ Southern Alps Dechen, Fettes, Fiordland, Manapouri, Sefton
Patagonia San Rafael, San Valentin, Teresa, Tortel
67
Geomorphometry.org/2013
68
Figure 1. 69
Patagonia70
71
72
Figure 2. 73
Patagonia. Red points show the bottom of the valley (1 km interval). Green lines 74
through the points show the location of 75
L76
were obtained from 77
Lin and Oguchi [78
is limited, 79
large and deep valleys80
transverse profile basical81
in Fig.82
divide, the break is used as 83
Geomorphometry.org/2013
Figure 1. Maps showing the location of the four selected glacial valleys Patagonia.
Figure 2. Morphometric measurements of Patagonia. Red points show the bottom of the valley (1 km interval). Green lines through the points show the location of
Longitudinal and transverse were obtained from Lin and Oguchi [7is limited, it allows us large and deep valleystransverse profile basicalin Fig. 2. However, divide, the break is used as
Geomorphometry.org/2013
aps showing the location of the four selected glacial valleys
Morphometric measurements of Patagonia. Red points show the bottom of the valley (1 km interval). Green lines through the points show the location of
and transverse were obtained from the ASTER-
7] (Fig. 2). Although the accuracy of the DEM allows us to analyze the general
large and deep valleys like those we transverse profile basically follow the drainage divide as
However, if there is a marked break of slope below the divide, the break is used as the end.
aps showing the location of the four selected glacial valleys
Morphometric measurements of the San ValentinPatagonia. Red points show the bottom of the valley (1 km interval). Green lines through the points show the location of obtained transverse
and transverse profiles of each glacial valley the ASTER-G DEM, based on the method of
Although the accuracy of the DEM to analyze the general like those we studiedly follow the drainage divide as
f there is a marked break of slope below the the end. If significant topographic
aps showing the location of the four selected glacial valleys in
the San Valentin glacial valley in Patagonia. Red points show the bottom of the valley (1 km interval). Green lines
transverse profiles.
of each glacial valley based on the method of
Although the accuracy of the DEM to analyze the general characteristic
studied. Both ends of a ly follow the drainage divide as shown
f there is a marked break of slope below the If significant topographic
2
in
valley in
Patagonia. Red points show the bottom of the valley (1 km interval). Green lines
of each glacial valley based on the method of
Although the accuracy of the DEM characteristics of Both ends of a
shown f there is a marked break of slope below the
If significant topographic
modification such as the entrance of a 94
a transverse profile, 95
146
width [147
segment of the 148
the 149
including kurtosis150
(Sd151
sizes and 152
profile was sufficient for c153
Forms of glacial valleys were evaluated using these 154
well as 155
glaciers156
glaciers. 157
103
104
180
Sd 181
observ182
the sections into four types183
parameter values:184
width is much larger than depth)185
“ large186
upper and lower 30% values of e187
illustrated in Fig. 3. 188
conditio189
largest number of conditions met is regarded as the type of the 190
valley. 191
valley is 192
number of 193
Fig. 4 shows typical examples of the U194
plain types.195
121
127
128
large
large
large
small
FR: form ratio, 134
skewness of slope. large135
small = values belonging to lower 30%.136
127
modification such as the entrance of a a transverse profile,
We computed width [4]) of each transverse segment of the profilethe frequency distribution of including kurtosisSd) were computed
sizes and the 30-m sampling interval, the number of data for each profile was sufficient for cForms of glacial valleys were evaluated using these well as FR. We did not deal with areas covered with glaciers. As noted, the selected valleys do not contain any large glaciers.
Correlations between any two of the four parameters and Sk) were investigated.
observing the actual form of the transverse sections, the sections into four typesparameter values:width is much larger than depth)large” and “small
upper and lower 30% values of eillustrated in Fig. 3. conditions shown in Table II. In such a case, the type with the largest number of conditions met is regarded as the type of the valley. If none of the conditions in valley is “others”number of conditionsFig. 4 shows typical examples of the Uplain types.
TABLE II.
U-shaped
large FR, small Kr
large FR, large Sk
large FR, large S
small Sk, large Sd
: form ratio, Kr:
skewness of slope. largesmall = values belonging to lower 30%.
modification such as the entrance of a a transverse profile, the profile
e computed the aspect/form ratio () of each transverse
profile (30 m interval frequency distribution of the
including kurtosis (Kr), skewnesswere computed for each profile
m sampling interval, the number of data for each profile was sufficient for computiForms of glacial valleys were evaluated using these
We did not deal with areas covered with As noted, the selected valleys do not contain any large
RESULTS AND DISCUS
Correlations between any two of the four parameters were investigated.
actual form of the transverse sections, the sections into four types according to the combinations of the parameter values: 1) U-shaped, 2) Vwidth is much larger than depth)
small” parameter values in Table upper and lower 30% values of eillustrated in Fig. 3. One valley often meets more than one
shown in Table II. In such a case, the type with the largest number of conditions met is regarded as the type of the
If none of the conditions in ” . In addition, if two types share the
conditions met, the type of the valley is also Fig. 4 shows typical examples of the U
TYPES OF TRANSVERSE SECTIOCOMBINATIONS OF
V-shaped
Kr large FR
Sk large FR
Sd large Kr
Sd large Kr
small Sk: kurtosis of slope,
skewness of slope. large = values belonging to upper 30% of the total population. small = values belonging to lower 30%.
modification such as the entrance of a tributary is not used for
the aspect/form ratio (FR) of each transverse profile and slope of each small
interval in horizontal length)the slope values
, skewness (Sk), and standard deviation for each profile. Because of large valley
m sampling interval, the number of data for each omputing the
Forms of glacial valleys were evaluated using these We did not deal with areas covered with
As noted, the selected valleys do not contain any large
ESULTS AND DISCUSSION
Correlations between any two of the four parameters were investigated. Considering
actual form of the transverse sections, according to the combinations of the
shaped, 2) V-shaped, 3) plainwidth is much larger than depth), and 4) others (Table
parameter values in Table upper and lower 30% values of each parameter, respectively, as
One valley often meets more than one shown in Table II. In such a case, the type with the
largest number of conditions met is regarded as the type of the If none of the conditions in Table II is met,
. In addition, if two types share the met, the type of the valley is also
Fig. 4 shows typical examples of the U-shaped, V
OF TRANSVERSE SECTIONS AND COMBINATIONS OF PARAMETER
shaped
FR, large Kr
FR, small Sd
Kr, small Sd
Kr, small Sk
Sk, small Sd kurtosis of slope, Sd: standard deviation of slope,
= values belonging to upper 30% of the total population. small = values belonging to lower 30%.
Naruse and Oguchi
tributary is observed along is not used for further analysis.
FR; total height/total and slope of each small
in horizontal length)values, statistical moments
, and standard deviation Because of large valley
m sampling interval, the number of data for each the statistical moments.
Forms of glacial valleys were evaluated using these moments We did not deal with areas covered with existing
As noted, the selected valleys do not contain any large
SION
Correlations between any two of the four parameters (FR the correlations and
actual form of the transverse sections, we classified according to the combinations of the
shaped, 3) plain , and 4) others (Table II
parameter values in Table II correspond to ach parameter, respectively, as
One valley often meets more than one shown in Table II. In such a case, the type with the
largest number of conditions met is regarded as the type of the Table II is met, the type
. In addition, if two types share the same met, the type of the valley is also “others
shaped, V-shaped and
NS AND CORRESPONDING PARAMETERS.
Plain
small FR, large
small FR, large
small FR, small
large Kr, large
large Sk, small : standard deviation of slope,
= values belonging to upper 30% of the total population.
Naruse and Oguchi
is observed along analysis.
; total height/total and slope of each small
in horizontal length). From , statistical moments
, and standard deviation Because of large valley
m sampling interval, the number of data for each moments.
moments as existing
As noted, the selected valleys do not contain any large
FR, Kr, the correlations and
we classified according to the combinations of the
(valley II ). The
correspond to ach parameter, respectively, as
One valley often meets more than one shown in Table II. In such a case, the type with the
largest number of conditions met is regarded as the type of the the type of the
same largest others”.
shaped and
CORRESPONDING
, large Kr
, large Sk
, small Sd
, large Sk
, small Sd : standard deviation of slope, Sk:
= values belonging to upper 30% of the total population.
Geomorphometry.org/2013 Naruse and Oguchi
3
The classification results for all transverse profiles in the five 123
regions revealed that the most common valley-form type other 124
than “others”, is U-shaped in New Zealand and Patagonia, V-125
shaped in the Himalayas, and plain in Yosemite and the Swiss 126
Alps (Table III). These observations may be interpreted as 127
follows. In New Zealand, highly abundant snowfall let glaciers 128
create typical U-shaped valleys. In the Himalayas both V-shaped 129
and U-shaped valleys are abundant and they have high FR values, 130
indicating that active glacial erosion, mass movements after 131
deglaciation, and rapid tectonic uplift contributed to valley 132
formation. The high proportion of the plain type in Yosemite and 133
the Swiss Alps may reflect smaller precipitation in both regions, 134
a low uplift rate in Yosemite, and marked glacial re-advances in 135
the Swiss Alps that led to stepped valley-side slopes. FR of 136
valleys in Patagonia tends to be small because of active lateral 137
erosion by ice sheets; therefore U-shaped valleys there differ 138
from those in the Himalayas and can be referred to as elongated 139
box-shaped. The above discussion indicates that glacial valleys 140
are not necessarily U-shaped, and the variety of their forms is due 141
to the regional characteristics of precipitation, tectonics, 142
glaciation histories, and post-glacial erosion. Therefore, it is 143
important to examine the shape of valleys in relation to the 144
effects of various factors even in glaciated areas [4]. 145
As a common trend for all glacial valleys investigated, FR 146
tends to converge into about 0.28 with increasing valley size (Fig. 147
5). The value may correspond to the balance of vertical and 148
lateral glacial erosion. The value also roughly corresponds to the 149
threshold slope angle of V-shaped valleys with frequent slope 150
failure (ca. 35° [8]), suggesting that erosion after deglaciation 151
also plays a role in determining the convergent value of FR. 152
153
154
Figure 3. Relationship between the form ratio (FR) and standard deviation of 155
slope (Sd) for all transverse sections analyzed. S: Swiss Alps. H: Himalayas. Y. 156
Yosemite. N: New Zealand Southern Alps. P: Patagonia. Color zones are based 157
on upper 30%, intermediate 40%, and lower 30% of each parameter values. 158
Yellow zone: large Sd, small FR. Pink zone: large Sd, large FR. Blue zone: small 159
Sd, small FR. Yellow-green zone: small Sd, large FR. White zone: intermediate 160
Sd, intermediate FR. 161
TABLE III. PERCENTAGE OF THE TYPES OF TRANSVERSE SECTIONS IN EACH 162
AREA. THE REST IS CLASSIFIED AS “OTHERS”. 163
U-shaped V-shaped Plain
Swiss Alps 25.7% (45/174) 12.6% (22/174) 23.4% (41/174)
Himalayas 27.1% (32/117) 28.8% (34/117) 17.8% (21/117)
Yosemite 22.1% (45/203) 9.3% (19/203) 30.9% (63/203)
NZ S Alps 31.9% (45/140) 18.4% (26/140) 9.9% (14/140)
Patagonia 26.4% (23/86) 16.1% (14/86) 11.5% (10/86)
164
165
166
Figure 4. Typical examples of three types of valley transverse profiles. 167
168
169
Figure 5. Relationship between the area of the valley transverse section and the 170
form ratio (FR) for all transverse sections analyzed. FR tends to converge into 171
ca.0.28 with increasing section area. 172
Geomorphometry.org/2013 Naruse and Oguchi
4
The correlation between the area of each transverse section 173
and the equilibrium line altitude was also investigated. In each 174
region, FR tends to change according to elevation, and reaches 175
the maximum in an intermediate elevation in the Swiss Alps and 176
areas around Mt. Cook in New Zealand (Fig. 6). The elevation 177
approximately corresponds to the estimated equilibrium line 178
altitude during the Last Glacial Maximum, suggesting a 179
possibility of estimating the past equilibrium line from 180
morphometric analysis of glacial valleys. 181
182
183
Figure 6. Relationship between altitude of the lowest point of each transverse 184
section and the form ratio (FR) for the Fettes and Sefton glacial valleys near Mt. 185
Cook, New Zealand. FR tends to be the highest at elevations around 900 m, 186
which corresponds to the estimated equilibrium line altitude during the Last 187
Glacial Maximum. 188
189
Future studies are needed to confirm the results of this paper 190
and improve the quality of research. For example, whether a 191
valley bottom consists of mostly bedrock or a valley fill may 192
affect the determination of valley types, although this paper does 193
not take it into account because of the lack of detailed 194
information. Sampling of data also deserves future investigation. 195
In this paper we sampled abundant transverse profiles from each 196
valley, but it is also possible to sample less profiles per valley but 197
from more valleys. The latter strategy may be suitable to discuss 198
local- to meso-scale diversity of glacial valley forms. 199
200
ACKNOWLEDGMENT 201
We appreciate Ian Evans and Peter Guth for their constructive 202
comments on an early draft of this paper. 203
204
REFERENCES 205
[1] Evans, I., 2013. “Major scale forms”. In Encyclopedia of Quaternary 206
Science, edited by S. A. Elias, Elsevier, Amsterdam, 847-864. 207
[2] Hirano, M., and M. Aniya, 1988. “A rational explanation of cross-208
profile morphology for glacial valleys and of glacial valley development”. 209
Earth Surface Processes and Landforms, 13, 707-716. 210
[3] Harbor, J. M., 1992. “Numerical modeling of the development of U-211
shaped valleys by glacial erosion”. Geological Society of America Bulletin, 212
104, 1364-1375. 213
[4] Montgomery, D. R., 2002. “Valley formation by fluvial and glacial 214
erosion”. Geology, 30, 1047-1050. 215
[5] Li, Y., G. Liu, and Z. Cui, 2001. “Longitudinal variations in cross-216
section morphology along a glacier valley: a case-study from the Tien Shan, 217
China”. Journal of Glaciology, 47, 234-250 218
[6] Brook, M. S., M. P. Kirkbride, and B. W. Brock, 2004. “Rock 219
strength and development of glacial valley morphology in the Scottish 220
Highlands and Northwest Iceland”. Geografiska Annaler, 86A, 225-234. 221
[7] Lin, Z., and T. Oguchi, 2006. “DEM analysis on longitudinal and 222
transverse profiles of steep mountainous watersheds”. Geomorphology, 78, 223
77-89. 224
[8] Oguchi, T., Z. Lin, K. Katsube, and Y.-G. Chen, 2011. 225
"Characteristic slope angle of V-shaped valleys in humid steep mountains 226
with frequent slope failure" In Geomorphometry 2011, edited by T. Hengl, 227
I. S. Evans, J. P. Wilson and M. Gould, Redlands, CA, 93-96. 228