Geomorphometry.org/2013
1
2
Naruse and Oguchi
Classification and formation environment of glacial
valleys based on morphometric analyses
3
4
5
6
7
Kosuke Naruse
Takashi Oguchi
10
Graduate School of Frontier Sciences
The University of Tokyo
Kashiwa, Japan
Center for Spatial Information Science
The University of Tokyo
Kashiwa, Japan
[email protected]
11
12
13
8
14
9
15
16
17
Abstract—This paper analyzes glacial valleys in the Swiss Alps, the
Himalayan Range, Yosemite, the New Zealand Southern Alps, and
19 Patagonia using DEMs. Transverse and longitudinal profiles of
20 four to six valleys in each region were obtained and the aspect/form
21 ratio (FR) and slope of each small segment of a transverse profile
22 were calculated. Forms of glacial valleys were evaluated using FR
23 and the kurtosis, skewness, and standard deviation of slope. FR
24 tends to converge into 0.28 with increasing valley size, which may
25 correspond to the balance of vertical and lateral glacial erosion as
26 well as a threshold slope angle for slope failure after deglaciation.
27 The transverse profiles were classified into four types based on
28 their geomorphometric properties: 1) U-shaped, 2) V-shaped, 3)
29 plain, and 4) others. The most common type, other than “others”
30 that include various forms, is U-shaped in New Zealand and
31 Patagonia, V-shaped in the Himalayas, and plain in Yosemite and
32 the
Swiss Alps. These differences may reflect regional
33 characteristics of snowfall, mass wasting, tectonics, and the history
34 of glacier advances. FR may also indicate the past location of the
35 glacial equilibrium line.
50
18
51
36
66
37
52
STUDY AREAS AND METHODS
53
The study areas are typical glaciated mountains in the Swiss
55 Alps, the Himalayan Range, Yosemite, the New Zealand
56 Southern Alps, and Patagonia. Four to six deep and wide glacial
57 valleys without large existing glaciers were selected from each
58 area for detailed morphometric analysis. Valleys that underwent
59 glaciation during MIS2 (Last Glacial Maximum) were selected to
60 minimize the effect of postglacial erosion. The names of the
61 selected valleys are shown in Table I. Fig. 1 shows maps
62 illustrating the distribution of the four glacial valleys in Patagonia,
63 adjacent to the Hielo Patagonico Norte Icefield. Like this case,
64 the selected valleys tend to be located near large existing glaciers.
54
65
INTRODUCTION
Glacial valleys or troughs are a major type of glacial
39 landforms, and their transverse sections are widely known as U40 shaped [1]. Although some researchers investigated the form of
41 transverse profiles of glacial valleys, they typically focus on
42 theoretical interpretation of U-shaped form [2, 3] or net volume
43 of erosion [4]. Detailed studies on the actual shape of glacial
44 valleys, including discussion on whether they are really U-shaped,
45 have been limited to a few case studies [5, 6]. The objectives of
46 this paper are: 1) to analyze the detailed morphometric
47 characteristics of glacial valleys in various regions of the world
48 using digital elevation models (DEMs); 2) to classify glacial
49 valleys based on the statistical analysis of the shape of transverse
profiles; and 3) to discuss environmental factors affecting glacialvalley forms.
TABLE I.
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
38
1
67
SELECTED GLACIAL VALLEYS.
Geomorphometry.org/2013
Naruse and Oguchi
94
95
modification such as the entrance of a tributary is observed along
a transverse profile, the profile is not used for further analysis.
Wee computed the aspect/form ratio (FR
(FR;; total height/total
width [[4])) of each transverse profile and slope of each small
148 segment of the profile (30 m interval in horizontal length)
length). From
149 the frequency distribution of the slope values
values,, statistical moments
150 including kurtosis (Kr),, skewness (Sk),, and standard deviation
151 (Sd
Sd) were computed for each profile
profile. Because of large valley
152 sizes and the 30-m
m sampling interval, the number of data for each
153 profile was sufficient for c
computi
omputing the statistical moments.
154 Forms of glacial valleys were evaluated using these moments as
155 well as FR. We did not deal with areas covered with existing
156 glaciers
glaciers. As noted, the selected valleys do not contain any large
157 glaciers.
146
147
68
103
Figure 1. Maps
aps showing the location of the four selected glacial valleys in
70 Patagonia
Patagonia.
69
RESULTS AND DISCUS
DISCUSSION
SION
104
Correlations between any two of the four parameters (FR
FR, Kr,
181 Sd and Sk) were investigated. Considering the correlations and
182 observ
observing the actual form of the transverse sections, we classified
183 the sections into four types according to the combinations of the
184 parameter values: 1) U-shaped,
shaped, 2) V
V-shaped,
shaped, 3) plain (valley
185 width is much larger than depth)
depth),, and 4) others (Table II
II). The
186 “large
large” and “small
small” parameter values in Table II correspond to
187 upper and lower 30% values of e
each
ach parameter, respectively, as
188 illustrated in Fig. 3. One valley often meets more than one
189 conditio
conditions shown in Table II. In such a case, the type with the
190 largest number of conditions met is regarded as the type of the
191 valley. If none of the conditions in Table II is met, the type of the
192 valley is “others”
”.. In addition, if two types share the same largest
193 number of conditions met, the type of the valley is also “others
others”.
194 Fig. 4 shows typical examples of the U
U-shaped,
shaped, V
V-shaped
shaped and
195 plain types.
180
71
121
127
128
TABLE II.
TYPES OF TRANSVERSE SECTIO
SECTIONS
NS AND CORRESPONDING
COMBINATIONS OF PARAMETER
PARAMETERS.
U-shaped
V-shaped
shaped
Plain
large FR, small Kr
large FR
FR, large Kr
small FR,, large Kr
large FR, large Sk
large FR
FR, small Sd
small FR,, large Sk
large FR, large SSd
large Kr
Kr, small Sd
small FR,, small Sd
small Sk, large Sd
large Kr,
Kr small Sk
large Kr,, large Sk
small Sk
Sk, small Sd
large Sk,, small Sd
72
Figure 2. Morphometric measurements of the San Valentin glacial valley in
74 Patagonia. Red points show the bottom of the valley (1 km interval). Green lines
75 through the points show the location of obtained transverse profiles.
73
L
Longitudinal and transverse profiles of each glacial valley
77 were obtained from the ASTERASTER-G DEM, based on the method of
78 Lin and Oguchi [
[77] (Fig. 2). Although the accuracy of the DEM
79 is limited, it allows us to analyze the general characteristic
characteristics of
80 large and deep valleys like those we studied
studied. Both ends of a
81 transverse profile basical
basically
ly follow the drainage divide as shown
82 in Fig. 2. However, if
f there is a marked break of slope below the
83 divide, the break is used as the end. If significant topographic
76
2
134
135
136
127
FR:: form ratio, Kr:: kurtosis of slope, Sd:: standard deviation of slope, Sk:
skewness of slope. large = values belonging to upper 30% of the total population.
small = values belonging to lower 30%.
Geomorphometry.org/2013
Naruse and Oguchi
The classification results for all transverse profiles in the five 162
regions revealed that the most common valley-form type other 163
125 than “others”, is U-shaped in New Zealand and Patagonia, V126 shaped in the Himalayas, and plain in Yosemite and the Swiss
127 Alps (Table III). These observations may be interpreted as
128 follows. In New Zealand, highly abundant snowfall let glaciers
129 create typical U-shaped valleys. In the Himalayas both V-shaped
130 and U-shaped valleys are abundant and they have high FR values,
131 indicating that active glacial erosion, mass movements after
132 deglaciation, and rapid tectonic uplift contributed to valley
133 formation. The high proportion of the plain type in Yosemite and
164
134 the Swiss Alps may reflect smaller precipitation in both regions,
135 a low uplift rate in Yosemite, and marked glacial re-advances in 165
136 the Swiss Alps that led to stepped valley-side slopes. FR of
137 valleys in Patagonia tends to be small because of active lateral
138 erosion by ice sheets; therefore U-shaped valleys there differ
139 from those in the Himalayas and can be referred to as elongated
140 box-shaped. The above discussion indicates that glacial valleys
141 are not necessarily U-shaped, and the variety of their forms is due
142 to the regional characteristics of precipitation, tectonics,
143 glaciation histories, and post-glacial erosion. Therefore, it is
144 important to examine the shape of valleys in relation to the
145 effects of various factors even in glaciated areas [4].
123
TABLE III.
124
PERCENTAGE OF THE TYPES OF TRANSVERSE SECTIONS IN EACH
AREA. THE REST IS CLASSIFIED AS “OTHERS”.
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)
As a common trend for all glacial valleys investigated, FR
tends to converge into about 0.28 with increasing valley size (Fig.
148 5). The value may correspond to the balance of vertical and
149 lateral glacial erosion. The value also roughly corresponds to the
166
150 threshold slope angle of V-shaped valleys with frequent slope
167 Figure 4.
151 failure (ca. 35° [8]), suggesting that erosion after deglaciation
152 also plays a role in determining the convergent value of FR.
168
146
147
Typical examples of three types of valley transverse profiles.
153
154
Figure 3. Relationship between the form ratio (FR) and standard deviation of
slope (Sd) for all transverse sections analyzed. S: Swiss Alps. H: Himalayas. Y.
157 Yosemite. N: New Zealand Southern Alps. P: Patagonia. Color zones are based
158 on upper 30%, intermediate 40%, and lower 30% of each parameter values.
159 Yellow zone: large Sd, small FR. Pink zone: large Sd, large FR. Blue zone: small
160 Sd, small FR. Yellow-green zone: small Sd, large FR. White zone: intermediate
161 Sd, intermediate FR.
155
156
3
169
Figure 5. Relationship between the area of the valley transverse section and the
form ratio (FR) for all transverse sections analyzed. FR tends to converge into
172 ca.0.28 with increasing section area.
170
171
Geomorphometry.org/2013
Naruse and Oguchi
The correlation between the area of each transverse section
and the equilibrium line altitude was also investigated. In each
175 region, FR tends to change according to elevation, and reaches
176 the maximum in an intermediate elevation in the Swiss Alps and
177 areas around Mt. Cook in New Zealand (Fig. 6). The elevation
178 approximately corresponds to the estimated equilibrium line
179 altitude during the Last Glacial Maximum, suggesting a
180 possibility of estimating the past equilibrium line from
181 morphometric analysis of glacial valleys.
173
205
174
206
207
208
209
210
211
212
213
214
215
182
216
217
218
219
220
221
222
223
224
225
226
227
228
183
Figure 6. Relationship between altitude of the lowest point of each transverse
section and the form ratio (FR) for the Fettes and Sefton glacial valleys near Mt.
186 Cook, New Zealand. FR tends to be the highest at elevations around 900 m,
187 which corresponds to the estimated equilibrium line altitude during the Last
188 Glacial Maximum.
184
185
189
Future studies are needed to confirm the results of this paper
and improve the quality of research. For example, whether a
192 valley bottom consists of mostly bedrock or a valley fill may
193 affect the determination of valley types, although this paper does
194 not take it into account because of the lack of detailed
195 information. Sampling of data also deserves future investigation.
196 In this paper we sampled abundant transverse profiles from each
197 valley, but it is also possible to sample less profiles per valley but
198 from more valleys. The latter strategy may be suitable to discuss
199 local- to meso-scale diversity of glacial valley forms.
190
191
200
201
202
203
ACKNOWLEDGMENT
We appreciate Ian Evans and Peter Guth for their constructive
comments on an early draft of this paper.
204
4
REFERENCES
[1] Evans, I., 2013. “Major scale forms”. In Encyclopedia of Quaternary
Science, edited by S. A. Elias, Elsevier, Amsterdam, 847-864.
[2] Hirano, M., and M. Aniya, 1988. “A rational explanation of crossprofile morphology for glacial valleys and of glacial valley development”.
Earth Surface Processes and Landforms, 13, 707-716.
[3] Harbor, J. M., 1992. “Numerical modeling of the development of Ushaped valleys by glacial erosion”. Geological Society of America Bulletin,
104, 1364-1375.
[4] Montgomery, D. R., 2002. “Valley formation by fluvial and glacial
erosion”. Geology, 30, 1047-1050.
[5] Li, Y., G. Liu, and Z. Cui, 2001. “Longitudinal variations in crosssection morphology along a glacier valley: a case-study from the Tien Shan,
China”. Journal of Glaciology, 47, 234-250
[6] Brook, M. S., M. P. Kirkbride, and B. W. Brock, 2004. “Rock
strength and development of glacial valley morphology in the Scottish
Highlands and Northwest Iceland”. Geografiska Annaler, 86A, 225-234.
[7] Lin, Z., and T. Oguchi, 2006. “DEM analysis on longitudinal and
transverse profiles of steep mountainous watersheds”. Geomorphology, 78,
77-89.
[8] Oguchi, T., Z. Lin, K. Katsube, and Y.-G. Chen, 2011.
"Characteristic slope angle of V-shaped valleys in humid steep mountains
with frequent slope failure" In Geomorphometry 2011, edited by T. Hengl,
I. S. Evans, J. P. Wilson and M. Gould, Redlands, CA, 93-96.