13

Bulletin of Glaciological Research ,. (,**1) +-ῌ,,ῌJapanese Society of Snow and Ice

ArticleSpatial distribution of thermal properties on debris-covered glaciers in the Himalayas
derived from ASTER data
Ryohei SUZUKI, Koji FUJITA and Yutaka AGETA
Graduate School of Environmental Studies, Nagoya University, Nagoya .0.ῌ20*+, Japan(Received August -+, ,**0; Revised manuscript accepted November +-, ,**0)

Abstract
The present study investigates thermal resistances on debris-covered glaciers around Mt. Everestand in the Lunana region of Bhutan, using satellite images taken by ASTER and NCEP/NCAR
reanalysis data. The thermal resistance is deﬁned as the thickness divided by the thermal conductivity of a debris layer, and is an important index to the evolution of glacial lakes through the melting
process. This index is obtained from surface temperature and heat balance on the debris layers.
Since the net radiation is a dominant energy source on the Himalayan glaciers, thermal resistances arecalculated by neglecting turbulent heat ﬂux in heat balance. We evaluate errors of thermal resistances using ﬁeld meteorological data and multitemporal ASTER data. The result shows that above
errors are unlikely to a#ect the spatial pattern of thermal resistances. About half of ,/ target glacierswithout moraine-dammed lakes have larger thermal resistances than 1 glaciers with the lakes.
Spatial distribution of thermal resistances shows the large increases toward glacier termini on theglaciers without lakes, whereas relatively small and uniform values on those with lakes. These
results imply that the di#erence in magnitudes and distribution of thermal resistances on debriscovered glaciers are related to di#erent evolutionary stages of the glacial lakes in the Himalayas.
The present study demonstrates the possibility that ASTER data provide thermal resistance distribution over many glaciers for glacial lake studies without simultaneous ﬁeld observations.

+.

Introduction

Many studies have reported that debris-covered
glaciers generate moraine-dammed glacial lakes(Yamada, +332; Ageta et al., ,***; Richardson andReynolds, ,***; Komori et al., ,**.). The potential
hazards of Glacial Lake Outburst Flood (GLOF) in the
Himalayas are attributed to the rapid retreat of glaciers in this region (e.g., Yamada, +332; Ageta et al.,,***; Komori et al., ,**.; Quincey et al., ,**/). However, physical processes controlling expansion of themoraine-dammed glacial lakes are still uncertain.
Revealing what determines the presence of glaciallakes is particularly crucial and practical for hazard
assessment. Thus, investigation of the di#erences
between debris-covered glaciers with lakes and those
without lakes is needed.
Reynolds (,***) suggested that a glacier’s surface
gradient is a controlling factor in the formation of
supraglacial ponds. He mentioned that ice melting is
also an essential controlling factor because it interacts
with the glacier’s surface gradient and is a source of
meltwater itself. Regardless of such a direct link, theextensive spatial characteristics of glacier melting under debris layer have never been studied in relation to
the presence of glacial lakes in the Himalayas.
Here we focus on thermal properties of supraglacial debris as another possible controlling factor indi#erent evolutionary stages of glacial lakes in the
Himalayas, as ice melting depends on the thermal
properties (e.g., Fujii, +311; Lundstrom et al., +33-;
Mattson et al., +33-; Diolaiuti et al., ,**-). However,
the thermal properties such as thickness and thermal
conductivity of debris layers are so heterogeneouseven on a glacier that ﬁeld observation is not practical. Satellite remote sensing is an e#ective techniquefor mapping surface characteristics regarding glaciermelting. Rana et al. (+331) and Nakawo and Rana(+333) demonstrated a method to estimate the melt
rate of a debris-covered glacier in the Nepal Himalayas using Landsat TM images. They applied the ideaof thermal resistance which was deﬁned by Nakawo
and Young (+32+; +32,) as thickness divided by thermal conductivity of a debris layer. The thermal resistance at a speciﬁc site can be regarded as constantusually in a melting season. Rana et al. (+331) proposed this parameter for runo# modeling and showed

14

Bulletin of Glaciological Researchthat the modeled runo# was in good agreement withthe observed value. The advantage of this methodology is that heterogeneous thermal resistances on a
debris-covered area can be smoothed by moderate
resolution of satellite images as a mixed pixel value(Nakawo et al., +33-). Supraglacial ponds which are
distributed on debris-covered areas play a signiﬁcantrole in evolution of glacier lakes (e.g., Sakai et al.,,***). Mapping their distributions and estimating
their contribution to ice melting is not easy without
remote sensing techniques. Utilization of satellite
images providing moderate resolution and multispectral bands, such as Advanced Spaceborne Thermal
Emission and Reﬂection Radiometer (ASTER), has
proved to be quite valuable in glaciology (e.g., Wessels
et al., ,**,; Kargel et al., ,**/; Quincey et al., ,**/).
The aim of the present paper is to show that extensive
distribution of thermal resistances can be obtained
from ASTER data independently from ground observations. Relationship between thermal resistanceson debris-covered glaciers and the presence of moraine-dammed glacial lakes with an area larger thanthat corresponding to a pixel size (approximately *.*+km,) around the Mt. Everest region of Nepal andChina are shown to demonstrate that ASTER data areuseful for study on processes of glacial lake formation.
Thus, spatial comparison of the thermal resistances
distributed on multiple glaciers over this extensive
area is important for our purpose rather than absoluteor high-detailed spatial resolution measurements on alimited number of glaciers.

,.

Methods

Thermal resistance of a debris layer
The thermal resistance of a debris layer has beenutilized as a useful index for ice melting of individualglacier so far. Thermal resistance is deﬁned as
,.+

R῏

h
ῌ
l

C῏Rn῍H῍Eῌ

(-)

where Rn, H and E are ﬂuxes for net radiation, andsensible and latent heats, respectively. The unit ofall variables is W m῎,. All components are positive
when ﬂuxes are directed towards the debris surface.
Turbulent heat ﬂux, which is composed of H and E,
can be usually estimated using the bulk aerodynamic
method (e.g., Rana et al., +331; Kayastha et al., ,***).
Mattson and Gardner (+33+) observed energy exchange on a debris-covered glacier in Karakoram andfound a negligible contribution of the turbulent heat
ﬂuxes to the total energy exchange on a clear sky day
in melting season. The same characteristic that radiation is a main energy exchange source is also reported in the Himalayas by Ohata and Higuchi (+32*),
Kayastha et al. (,***), Takeuchi et al. (,***), among
others. For the present analysis it is shown that
turbulent heat ﬂuxes on glaciers do not signiﬁcantly
a#ect the relationship between heat balance and ther
mal resistances from analyses using data in the Lunana
region of Bhutan. Based on the analyses, spatial distribution of thermal resistances around Mt. Everestis calculated by neglecting turbulent heat ﬂuxes.
Uncertainties in thermal resistances due to neglecting
turbulent heat ﬂuxes are discussed in section -.+.
Meteorological data
The relation between heat balance components
and thermal resistances was investigated using ﬁeld
meteorological data which correspond to ASTER dataacquisition. Such data sets are available only in the
Lunana region of Bhutan (Fig. +). Hence, the groundmeteorological data which were obtained from an
automatic weather station (AWS) at ./,. m a.s.l. on
the terminal dead ice zone of Lugge Glacier (Yamada
et al., ,**.; Suzuki et al., ,**1) were used in our analysis. Table + shows the mean meteorological compo,.,(+)

where R, h and l are thermal resistance (m, K W῎+),
the thickness (m) and thermal conductivity (m῎+ K῎+W) of a debris layer, respectively (Nakawo and Young,+32+; +32,). Because conductive heat into glacier ice
is negligible on temperate glaciers, a thermal resistance can be derived from the following equation
based on the assumptions that the temperature proﬁlewithin a debris layer is linear and bottom temperatureis *ῐ due to ice melting:
C῏

Ts῎*
ῌ
R

(,)

where C is heat conducted into a debris layer (W m῎,)and used for ice melting, and Ts is surface temperatureof the debris layer (ῐ). The C is calculated by theheat balance equation

Fig. +. False color composite image of Lunana region,
Bhutan taken by ASTER VNIR band +, ,, -N on ,+November ,**+. Names of objective glaciers arealso shown. Two crosses denote locations ofstations with AWS and air temperature sensor.
Violet and black solid lines denote entire target
areas in ,**, and ,**-, respectively.

Suzuki et al.

15

Table +. Input meteorological data to calculate thermal resistances on three glaciers in Lunana
region of Bhutan. Data were obtained from AWS installed at ./,.m a.s.l. on terminal
moraine-covered ice zone of Lugge Glacier. All data shown are mean values from +*: -* to ++: **in local time, during which ASTER data were acquired. Ws: wind speed; Wd: wind direction;
Ta: air temperature; rh: relative humidity; SD: downward shortwave radiation; SU: upward
shortwave radiation; Rn: net radiation; Ts: surface temperature.
Date

Ws
m sῌ+

Wd
deg.

Ta
῍

rh
ῌ

SD
W mῌ,

SU
W mῌ,

Rn
W mῌ,

Ts
῍

,* September ,**,,+ July ,**-

+41
,41

,3,40
-,140

24+
+,4,

.*4./43

3-2
+*1.

+20
+21

0--42
0/,4.

,*4.
,143

Table ,.

ASTER data description.

Year

Date

Path/Row

Target

Level

Usage

,***
,***
,**+
,**,
,**,
,**,
,**,**,**,**.
,**.

,2 September+. October,1 June,* September. October,+ November+ June,+ July,- October
3 October+* November+.*/++0+.*/++0+.*/++0+-2/++/+.*/++0+.*/++0+.*/++0+-2/++/+.*/++0+.*/++0+.*/++0

Nepal
Nepal
Nepal
Bhutan
Nepal
Nepal
Nepal
Bhutan
Nepal
Nepal
Nepal

+B
+B
+B
+B
+B
-A*+
+B
-A*+
+B
+B
-A*+

VNIR, TIR
VNIR, TIR
VNIR, TIR
VNIR, TIR
VNIR, TIR
DEM
VNIR, TIR
VNIR, SWIR, TIR
VNIR, TIR
VNIR, TIR
DEM

nents at every -* minutes for two ASTER data acquisitions in ,**, and ,**-. The meteorological data are
extrapolated to the whole target areas to solve theheat balance equation for the thermal resistances.
The observed air temperatures were corrected foreach altitude using an averaged lapse rate of 0.+῍kmῌ+ obtained from ﬁeld observations which werecarried out from ,3 September to 2 October in ,**(Suzuki et al., ,**1). On the other hand, products ofsurface downward radiation ﬂuxes for clear sky at*0**Z from National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis (Kalnay et al., +330), whichcorresponds to the nearest time and location to each
ASTER data acquisition, were used to calculate thermal resistances on glaciers around Mt. Everest.
ASTER data
ASTER data are composed of visible and nearinfrared (VNIR), shortwave infrared (SWIR) and thermal infrared (TIR) bands. Table , provides a description of ASTER data that were used for the present
calculations. Because of the assumption that the bottom temperature of a debris layer equals *῍ (Eq. ,),we chose the data taken in glacier melt seasons except
for producing the digital elevation model (DEM). In
addition, data with cloud or snow cover on debriscovered areas were not used. Due to these con,.-strained conditions, the number of available images
was limited to ++ (Table ,).
All images were rectiﬁed based on the orthorectiﬁed product Level -A*+ of ASTER and resampled
by the nearest-neighbor method. Only the glacierized areas above *῍ were extracted from each data
because debris surfaces are warmed on a clear sky
morning. Altitudes at the extracted pixels were obtained from DEM which were appended to the Level A*+ product. The DEM data, which are generatedusing the instrument and the spacecraft ephemeris
parameters only without referring to ground control
points for individual images, is produced by the
ASTER Ground Data System (ASTER GDS) at the
Earth Remote Sensing Data Analysis Center (ERSDAC)
in Japan using specially developed DEM software(Fujisada et al., ,**/).
Average brightness temperature was calculated
from ﬁve TIR bands at each acquisition time and usedas surface temperature on glaciers. Spectral reﬂectance at the top of atmosphere in VNIR bands wasaveraged to estimate broadband albedo. Downward
spectral irradiances were varied according to solar
angles at each ASTER acquisition time and location.
Pixel size of all images was uniﬁed to 3* m of TIR
bands, and thermal resistances were calculated using
the same resolution.
Band . (+.0ῌ+.1 mm) in SWIR was combined with

16

Bulletin of Glaciological Researchband , (*.0-ῌ*.03 mm) in VNIR to calculate the Normalized Di#erence Water Index (NDWI) on glaciers in the
Lunana region of Bhutan. This index can show thepresence of water surface based on a spectral characteristic of water that corresponds to stronger absorption in the wavelength of SWIR bands than those in
VNIR bands (McFeeters, +330). NDWI is deﬁned as
NDWIῐ

Band,῎Band.
ῌBand,῍Band.

(.)

where positive NDWI indicates the presence of open
water surface including melting surface of snow, iceand debris saturated with water.

Results and discussion-.

Uncertainties in thermal resistances
In this section, uncertainties in thermal resistances due to neglecting turbulent heat ﬂuxes (section,.+) and total errors are identiﬁed and discussed. Inorder to address the issue, three debris-covered glaciers in the Lunana region of Bhutan (Fig. +) were thefocus. The areas covered with cloud on the target
glaciers in ,**, were extracted manually and eliminated from calculation.
Figure , shows two type calculations of thermal
resistances; one is calculated from all components inheat balance equation (Eq. -) and the other is approximated from only net radiation term. The former isobtained in two ways under water saturated and dry
surface assumptions. Sensible heat term is not important because thermal resistances based on dry surface assumptions nearly equal those from only net
radiation. In contrast, large di#erences are found in-.+

Fig. ,. Relations between thermal resistances calculated from only net radiation and from all components of the heat balance equation at same pixel.
Two curves indicate ultimate values depending on
moisture di#erence on debris layers.

wet condition between approximation and analytic
solutions. Since surface temperature of a debris
layer increases in association with larger thermal resistances, saturated vapor pressure on the debris layer
also increases under the water-saturated condition.
Thus, such large di#erences in thermal resistances
can be caused by the increase of latent heat ﬂux.
As the presence of water a#ects the magnitude ofa thermal resistance, water saturated areas were estimated using NDWI, which was calculated from band ,and band . of ASTER data. Figure -a shows transverse proﬁles of NDWI and surface temperatures thatwere obtained from ASTER images of Thorthormi
Glacier in Lunana region. The moisture dominant
ranges such as central ogive and lateral ponds (Fig. b, Fig. -c), where low surface temperatures near *ῑ
appear, are identiﬁed by positive NDWI, while NDWI
in debris-covered areas and lateral moraines, wherehigh temperature appears, are negative values. Figure . shows the relationship between NDWI and thermal resistances on three debris-covered glaciers in
Lunana region (Fig. +). Thermal resistances in thepositive NDWI range are found to be less than ,.*῏+*῎, m, K W῎+, which produces negligible di#erences
between dry and wet surface assumptions (Fig. ,).
This is because the low temperature surroundings ofmelting ice generate only small di#erences in vapor
pressures between atmosphere and debris. On theother hand, a thick debris-covered area is generally
dry on a clear sky morning in the Himalayas (Mattson
and Gardner, +33+). It is plausible assumption thatthe water-saturated case in Fig. , hardly occurred in
the debris-covered area on a clear day of ASTER dataacquisition. As mentioned above, neglected turbulent heat ﬂuxes do not contribute signiﬁcantly to thethermal resistance calculation.
On the other hand, total errors are also evaluatedby comparing independent observations in ,**, and,**- (Tables + and ,) of the three glaciers. Figure /shows a comparison of thermal resistances calculated
from only net radiation. Note that the thermal resistance at a speciﬁc pixel may be a#ected by the ice
movement and deposition of supraglacial debris between two ASTER data acquisitions, because surface
ﬂow speeds on the analyzed area of Thorthormi Glacier range from .* to +** m a῎+ (Yamada et al., ,**.;
Kääb, ,**/), while the pixel size is 3* m square.
Hence, the error shown in Fig. / is composed of systematic error due to ice movement as well as random
error propagated through each measurement.
Thermal resistance in 1-ῌ of the terminal area of
the Ngozumba Glacier in Nepal (see the next section)
was calculated from 1 independent ASTER data
(Table ,) and corresponding NCEP/NCAR reanalysis
data. The residual area was not available for the
calculation due to cloud cover. The averaged thermal resistance equals -.+῏+*῎, m, K W῎+, while theSuzuki et al.

17

Fig. -. a) Transverse proﬁles of NDWI (solid line) and surface temperature (broken line) obtained from ASTER data on
Thorthormi Glacier in Lunana region of Bhutan. b) Image taken by ASTER-VNIR. White solid line indicateslocation of transverse proﬁle shown in a). c) Corresponding photograph shows glacier surface. Upper right in photoshows right-bank side moraine, and lower left reveals thickly debris-covered area. Thick white line drawn indicateslocation of transverse proﬁle.

Fig. .. Relation between NDWI and thermal resistances on three debris-covered glaciers in Lunana
region of Bhutan.

Fig. /. Relation between thermal resistances in ,**,and those in ,**- at same pixels for three debriscovered glaciers in Lunana region of Bhutan.

18

Bulletin of Glaciological Researchstandard deviation equals *.-/῍+*ῌ, m, K Wῌ+. This
result means that thermal resistances from independent data are not biased signiﬁcantly, because the deviations are less than those shown in Fig. / despite theabovementioned change in surface condition. Because available data can be obtained from ASTER
only on a clear sky morning, the reanalysis data underclear sky conditions were chosen as input radiation
ﬂuxes. Additionally, the density of air is relatively
thin due to the high altitude of the target areas.
These conditions cause less variation in atmosphericconditions such as the amount of water vapor andsmall turbulent heat ﬂux at each acquisition of ASTER data. Thus, the net radiation obtained by combining reanalysis data with ASTER data is considered
to be useful for deriving thermal resistance distribution, because neglecting turbulent heat ﬂux in theheat balance equation does not pose a serious problem
for our study. In the following section, thermal resistances on multiple debris-covered glaciers are calculated using net radiation obtained from these data andneglecting turbulent heat ﬂux.
Spatial distribution of thermal resistances
Figure 0 shows a mosaic image of thermal resistance around Mt. Everest. The western and easternparts of the image were calculated from ASTER datataken in ,2 September ,*** and ,- October ,**-, respectively. In addition, thermal resistances on threedebris-covered glaciers in the Lunana region of Bhutan (Fig. +) were derived using NCEP/NCAR reanalysis data inputs. Totally, -, debris-covered glaciers
were analyzed in this study. Figure 1 shows thefrequency distribution of thermal resistances averaged for each debris-covered area. Means of two groups were obtained from the data; 1 glaciers with lakes
had a mean thermal resistance of +.0῍+*ῌ, m, K Wῌ+,
while ,/ glaciers without lakes had ,..῍+*ῌ, m, K Wῌ+.

-.,Fig. 0.

Fig. 1. Frequency distribution of areal mean thermal
resistances on glaciers with and without lakes.

Distribution of thermal resistances on debris-covered glaciers around Mt. Everest.

Suzuki et al.

The errors discussed in the previous section make it
di$cult to distinguish exactly the thermal resistancesamong all the target glaciers with and without lakes(Fig. 1). However, we found that +, glaciers withoutlakes having a larger thermal resistances than the
maximum of glaciers with lakes. This means that ice
melting on these glaciers is more strongly controlled
by the debris cover than on glaciers with lakes. The
higher surface temperature will be generated in case adebris layer has higher thermal resistance. A negative energy balance through the increase of upward
longwave radiation can occur under such a conditioneven if the climatic condition is uniform. Thus, theice melt rate decreases with the increase in thermal
resistance.
The residual +- glaciers without lakes such as
Khumbu Glacier (Fig. 0) do not show a deﬁnite di#erence in areal mean thermal resistances compared tothose with lakes. Complex surfaces that are composed of supraglacial ponds, ice cli#s and bare ice
areas as well as debris cover resulted in relatively
small thermal resistances, because such various surfaces with low temperature are mixed in pixels of
ASTER images. Therefore, the thermal resistance isreduced and appropriate conditions for ice melting is
produced. In fact, Sakai et al. (,***) found that theamount of energy absorption on a supraglacial pond
is more than several times that on debris-covered areaand suggested that the rapid ice melting accelerates
evolution of supraglacial ponds. Iwata et al. (,***)
reported that the area with a rough uneven surface
with large relative relief had extended both upglacierand downglacier recently. This fact leads to lowering of thermal resistance on the glacier, which willcause a depression in the lower ablation area as predicted by a numerical simulation (Naito et al., ,***).
Figure 2 shows the relation between distributionsof thermal resistance and debris thickness on the
Khumbu Glacier in Nepal. Conway and Rasmussen(,***) reported a thermal conductivity of +.,2 W mῌ+
Kῌ+ of the debris layer ,./ m thick on this glacier.
The data resulted in a thermal resistance of ,.* m, K
Wῌ+, about hundred times as large as shown in Fig. 2.
Such low thermal resistance obtained from Landsat
TM data was also reported in other studies (e.g., Ranaet al., +331). This discrepancy is caused because surfaces of ice cli#s and small ponds as well as debris areobserved as a mixed pixel value of satellite data,
whereas Conway and Rasmussen (,***) observed only
debris in the ﬁeld observation. Thickness of debris isin proportion to thermal resistance as described in Eq.
+. This relation can be seen in Fig. 2. The decreaseof thermal resistances on the eastern side of the glacier in the area several kilometers from the terminus
can be explained by the areas of expanding ponds anddeveloping ice cli#s as reported by other studies (e.g.,
Iwata et al., ,***). If only the eastern part of this19

Fig. 2. Distributions of a) thermal resistances and b)
debris thickness (reprinted from Nakawo et al.,+320 by permission of International GlaciologicalSociety) on Khumbu Glacier in Nepal, respectively.

glacier was shaded in the morning of ASTER dataacquisition, surface temperatures in this area would
be lower than those on the western part. This apparently generates a similar pattern of thermal resistances. In this case, surface temperatures outside of
the glacier would also decrease from west to east.
However, only negligible di#erences of surface temperature can be recognized outside of the glacier itself
along the side moraines. Thus, shading of solar insolation by surrounding mountains may not cause thedecrease of thermal resistances. Thermal resistances
increase gradually along ﬂow directions as a thickness pattern. As Fig. 0 shows, a similar pattern canbe found on the other glaciers without lakes.
In order to investigate spatial characteristics ofthermal resistances, relations with altitudes areshown in Figs. 3 and +* in terms of glaciers withoutlakes and with lakes, respectively. The glaciers in
Fig. 3 were selected based on areal mean thermal resistances which range from +./῍+*ῌ, to ,.1῍+*ῌ, m, K
Wῌ+ as shown in Fig. 1 to represent the glaciers without lakes. Thermal resistances increase toward downstream on ,, glaciers among all the glaciers withoutlakes, whereas di#erent variations that are relatively
uniform magnitudes are found on glaciers with lakes.
Spatial analysis of thermal resistances can be applied
to assessment of glacier lake formation by combining
the other spatial information, for example, ice dynamics and surface slopes, because surface lowering ofglacier is related to mass balances and ice velocity
gradients along ﬂow lines. Multispectral satellite
data are useful for assessment of glacial lake formation.

20

Bulletin of Glaciological Research..

Fig. 3. Relations between thermal resistances andaltitudes of glaciers without lakes; a) Ngozumba, b)
Kangshung, c) Lhotse, d) Barun, e) Kazhen and f)
Nuptse Glaciers in Fig. 0.

Conclusion

Spatial distribution of thermal resistances in the
Mt. Everest region was derived applying extensive
satellite remote sensing to investigate relationshipbetween the magnitudes of thermal resistances andthe presence of moraine-dammed glacial lakes. We
focused on thermal resistances as a relative index ofglacier melting, whereas previous works only aimed
to estimate absolute melt rates for limited glaciers.
Our analysis showed that the errors from neglecting
turbulent heat ﬂuxes in heat balance calculation andusing multitemporal ASTER data are unlikely toa#ect the spatial pattern of thermal resistances. Thismeans that, to clarify the physical processes, the spatial distribution of thermal resistances can be obtained by remote sensing techniques and related tospatial information about the surface gradient and ice
velocity which have also been proved to be importantconditions for glacier lake expansion (Richardson andReynolds, ,***; Quincey et al. ,**0). Thermal resistances on glaciers with lakes tended to be smaller
than on those without lakes. Furthermore, di#erent
altitudinal and ﬂow-line patterns of thermal resistance distribution were identiﬁed in association withthe presence of glacial lakes. These results suggest

Fig. +*. Relations between thermal resistances and altitudes of glacierswith lakes. Letters in these ﬁgures correspond to those in Fig. 0: a)
Lhotse Shar, b) Lower Barun, c) Drogpa Nagtsang, d) unnamed glacieron available map, and e) Trambau Glaciers. Figures f) and g)correspond to Lugge and Thorthormi Glaciers shown in Fig. +, respectively.

Suzuki et al.

that the thermal resistance of debris-covered glaciers
would be a useful index to study glacial lake evolution, and that ASTER data are also useful for suchanalyses. The other dominant processes of glaciallake formation should also be identiﬁed to establish
more general criteria for future hazard assessments.

Acknowledgments
Many people generously cooperated in obtaining
data from the ﬁeld observations for this study. In
particular, we are grateful to the Geological Survey of
Bhutan. The manuscript was much improved by
useful comments from Dr. Nozomu Naito, Dr. Masayoshi
Nakawo and Dr. Howard Conway. The copyright for
ASTER data is reserved by the Ministry of Economy,
Trade and Industry of the Japanese Government.
This study was supported by the Announcement ofResearch Opportunity (ASTER ARO, AP-***0) and a
Grant-in-Aid for Scientiﬁc Research (Project: +--1-**0;+-/1-**.; G-., the ,+st Century COE Program) from
the Ministry of Education, Culture, Sports, Scienceand Technology of Japan. Figure 2b was reprinted
from the Annals of Glaciology with the permission of
the International Glaciological Society.

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