Classification and formation environment of glacial valleys based … · 1 1 Classification and formation environment of glacial 2 valleys based on morphometric analyses 3 4 Kosuke

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

[email protected]

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

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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


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


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


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


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


FR, Kr, the correlations and

we classified according to the combinations of the

(valley II ). The

correspond to ach parameter, respectively, as


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.


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


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

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Classification and formation environment of glacial valleys based … · 1 1 Classification and formation environment of glacial 2 valleys based on morphometric analyses 3 4 Kosuke