Journal of Hydrology 390 (2010) 245–256

Contents lists available at ScienceDirect

Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol

Global-scale modeling of glacier mass balances for water resources assessments:
Glacier mass changes between 1948 and 2006
Yukiko Hirabayashi a,*, Petra Döll b, Shinjiro Kanae caInstitute of Engineering Innovation, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan
Institute of Physical Geography, Frankfurt University, P.O. Box 111932, 60054 Frankfurt am Main, GermanycDepartment of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japanba r t i c l e

i n f oArticle history:
Received 4 March 2010
Received in revised form 10 June 2010
Accepted 4 July 2010
This manuscript was handled byKonstantine P. Georgakakos, Editor-in-Chief,with the assistance of Aiguo Dai
Keywords:
Glacier
Mass balanceIce volume
Global modela b s t r a c t
Glaciers play an important role for freshwater resources, but in global-scale freshwater assessments, theirimpact on river ﬂows has not yet been taken into account. As a ﬁrst step, we developed a global glaciermodel that can be coupled to global land surface and hydrological models. With a spatial resolution of
0.5° by 0.5°, the glacier model HYOGA computes glacier mass balance by a simple degree-day approachfor 50 m sub-grid elevation bands, modeling all glaciers within a grid cell as one glacier. The model istuned individually for each grid cell against observed glacier mass balance data. HYOGA is able to compute glacier mass balances reasonably well, even those of summer accumulation type glaciers. Still,model uncertainty is high, which is, among other reasons, due to the uncertainty of global data sets oftemperature and precipitation which do not represent well the climatic situation at glacier sites. We
developed a 59-yr (1948–2006) time series of global glacier mass balance and glacier area by driving
HYOGA with daily near-surface atmospheric data. According to our computations, most glaciers have lost
mass during the study period. Compared to estimates derived from a rather small number of observed
glacier mass balances, HYOGA computes larger glacier mass losses in Asia, Europe, Canadian Arctic
islands and Svalbard. In accordance with the estimates, average annual mass losses have increased
strongly after 1990 as compared to the 30 yrs before. The sea level equivalent of the melt water from glaciers is 0.76 mm/yr water equivalent after 1990 as compared to only 0.34 mm/yr water equivalent before.
We computed an acceleration of glacier mass losses after 1990 for all world regions except South America, where the number of gauge observations of precipitation is very small after 1980.
Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction
According to the most recent estimate of Dyurgerov and Meier(2005), glaciers and ice caps cover 540,000 ± 30,000 km2 outside ofAntarctica and Greenland, less than 0.4% of the global land area.
Nevertheless, they play an important role in water availability inmany river basins. Seasonal water storage in glaciers and ice caps
is beneﬁcial for downstream aquatic ecosystems and human water
users, as melted ice augments low ﬂows during the warm and dry
season. Hereafter, we use the term glaciers to refer to mountainglaciers and ice caps outside of Antarctica and Greenland.
According to Lemke et al. (2007), most glaciers have been
shrinking mainly due to air temperature increases, many of themalready since 1850. Exceptions are the glaciers in Norway and
New Zealand, where glacier mass increased in the 1990s due to increased precipitation, but since the year 2000, glaciers have been
shrinking there also. Glacier mass development is driven by the* Corresponding author. Tel.: +81 3 5841 0716.
E-mail address: hyukiko@sogo.t.u-tokyo.ac.jp (Y. Hirabayashi).
0022-1694/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2010.07.001

surface mass balance (the gain or loss of snow, ﬁrn and ice overa certain time period) or ice calving, while the mass balance at
the glacier bed (loss due to basal melting) is negligible at global
or regional scales (Lemke et al., 2007). At a rate of 0.63 ±0.18 mm/yr water equivalent during 1991–2004, glacier mass loss
is estimated to have contributed approximately twice as much toglobal sea level rise than the melting of the much larger Antarctic
and Greenland ice sheets (Lemke et al., 2007). Future climatechange is expected to accelerate glacier shrinkage for most glaciers
as precipitation increases cannot balance increased melting due tohigher temperatures (Meehl et al., 2007).
Most global-scale mass balance estimates for glaciers have been
based on direct mass balance observations at about 300 glaciersthat were up-scaled by area-weighted averaging or spatial interpolation (Lemke et al., 2007) whereas more than 70,000 glacier locations are recorded in the World Glacier Inventory (WGI), which iscollected mainly by the World Glacier Monitoring Service (WGMS),
Zurich, and more than 130,000 glaciers are inventoried in Cogley(2009). With a total area of 34,000 km2, these 300 glaciers represent only about 6% of the global glacier area. Cogley and Adams

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Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256(1998) indicated that the method of estimating glacier mass balance by interpolating limited mass balance data lead to a bias. Thisis due to uneven spatial coverage of observations, because measured glaciers are often small and are commonly located at low
elevations due to better accessibility as compared to high elevation
glaciers. The total global volume of glaciers outside of Antarctica
and Greenland is highly uncertain, with estimates ranging from51,000 to 166,000 km3 (Lemke et al., 2007; Radić and Hock, 2010).
Several previous studies estimated current variations and future development of glacier mass using numerical mass balance
models. For example, Radic and Hock (2006) developed a mass balance glacier model of Storglaciären in Sweden and projected future
glacier mass development. Verbunt et al. (2003) applied theirnumerical snow and glacier model to estimate time series of glacier volume in Alpine river basins. Rees and Collins (2006) showed
the effect of climate warming on discharge in glacier-fed Himalayan Rivers, using a three-dimensional glacier model coupled witha hydrological model. Huss et al. (2008) developed a distributed
mass balance and glacier evolution model and applied the model
to assess the impact of climate change on runoff from three highly
glacierized catchments in Switzerland. However, these studies
treated a limited number of glaciers with mostly well-observed
mass balances. In a global-scale study, Raper and Braithwaite(2006) estimated the impact of climate change on glacier mass
by ﬁrst estimating the 1961–1990 average mass balance in 1° gridcells, using modeled glacier mass balances in seven glacier regionswith good mass balance observation and a multiple regression ofgradients of mass balance versus altitude on global gridded estimates of long-term average precipitation and summer temperature. Then they scaled their computed 1961–1990 global massbalance to match the previous estimate, and projected the future
global mass balance using temperature projections from two different climate models. Hock et al. (2009) also used a modeling approach to obtain global and regional scale glacier mass balance
estimates for the period 1961–2004, based on modeled mass balance sensitivities to temperature and precipitation changes as well
as long-term temperature and precipitation trends obtained fromreanalysis.
To estimate the impact of glaciers on river discharge worldwide, it is necessary to determine not only long-term average annual glacier mass balances but daily or monthly time series. Only
such time series will make it possible to better estimate the impact
of climate change on seasonal low ﬂows and droughts in glacierfed river basins. In modeling studies that did not take into accountglaciers, many glacier-fed river basins were projected to sufferfrom increases in drought frequency induced by climate change(e.g. Hirabayashi et al., 2008a; Lehner et al., 2006). To the best of
our knowledge, no numerical mass balance models have beendeveloped up to now that can provide gridded sub-annual timeseries of glacier mass changes for the whole globe.
The aim of the study presented here is to develop a global glacier model for estimating daily gridded time series of glacier massbalances, suitable for supporting global water resources assessments. The output of our new global glacier model HYOGA (‘‘glacier” in Japanese) can be used to drive global hydrological or land
surface models. This will allow us, for the ﬁrst time, to assess theimpact of glaciers on freshwater resources at the global scale, also
under conditions of climate change. Since a high percentage of irrigated areas are located in glacier-fed river basins, HYOGA also has
the potential to improve global food security assessments. Besides,
model results could also be used for estimating the contribution of
glaciers to sea level rise.
In the following section, we ﬁrst describe the model and its input data, and then show how the model was initialized and calibrated such that the time series of glacier mass balance between
1948 and 2006 could be computed. In Sections 3 and 4, modeled

glacier mass changes are presented, and model uncertainties are
discussed. In Section 5, we summarize our work and draw
conclusions.
2. Methods
2.1. Model description
The global glacier model HYOGA is driven by time series of daily
precipitation and near-surface temperature and computations are
performed using daily time steps. The horizontal spatial resolutionof HYOGA is 0.5° by 0.5° as most global hydrological models, andmany climate data sets, share this resolution. All glaciers withineach grid cell are modeled as one equivalent glacier, the area of
which is the sum of the areas of all glaciers within the grid cell.
Volume-area scaling is used to estimate glacier volume from (observed) glacier area, and to update glacier area after the computation of glacier mass and thus volume changes after each time step.
Mass balances of snowpack and glacier ice are determined in
50 m sub-grid elevation bands, using a simple degree-day approach to compute melting. Within each grid cell, the air temperature is assumed to decrease with increasing altitude, with aconstant lapse rate of 0.65 °C/100 m. This value was determinedby comparing 63 modeled and observed glacier mass balances atdifferent elevation bands (observations provided by WGMS). With
this value, which is equal to the value used by Braithwaite and Raper (2007), it was possible to obtain modeled equivalent line altitudes that are similar to observed values. Like temperature,
precipitation varies with altitude, but these variations are very site
speciﬁc, depending, among others, on wind direction and orography. Therefore, it is not possible to use a uniform precipitation
lapse rate, and a suitable approach for determining precipitation
lapse rates for global-scale studies does not exist yet. Thus, precipitation was assumed to be the same in all elevation bands of a gridcell. Potential orographic effects on precipitation amount are however indirectly adjusted via the calibration process explained in
Section 2.3.2.
2.1.1. Mass balances
HYOGA includes two mass balance modules: a snowpack module which simulates the accumulation and melting of snow as wellas the transformation of snow into glacier ice, and a glacier module
which computes the volume of melted glacier ice using a simple
degree-day approach. The mass balance of the snowpack in theith elevation band (Fig. 1) is computed in terms of equivalent liquidwater volume as

Sni ðt þ DtÞ ¼ Sni ðtÞ þ Snfi ðtÞ  Gi  Msi
Msi ¼ ðT i  T 0 Þ  DDF snow if T i > T 0ð1Þ

0 otherwise
where Sni is water equivalent of snowpack, t is time, Dt is 1 day, Snfi
is snowfall, Gi is the volume of water that is transformed from snow
into glacier ice, Msi is volume of melted snow, T0 is a critical temperature for snow melting, Ti is surface temperature at the sub-grid elevation band height and DDFsnow is the degree-day factor of thesnowpack. T0 was set to 0 °C, while DDFsnow was adjusted by calibration (see Section 2.3.2). We assume that only precipitation that falls
as snow affects the snowpack balance. If HYOGA is linked to ahydrological model, rainfall on glaciers immediately becomes runoff. Precipitation is assumed to fall as snow if air temperature of
the elevation band is less than or equal to 2 °C. This threshold
was used because it leads to similar global snowfall amounts as amore sophisticated method that considers humidity (Hirabayashi
et al., 2008c). One year after snowfall is incorporated into the snowpack, it is transformed into glacier ice (Fig. 1). Thus, ﬁrn is not taken

247

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

Snf1

Ms1

Ms2
Ms3
Mg4

Snf2

Sn1
G1

v1
Sn2

Snf3

G2

v2
Sn3

Snf4

G33

v3
v4

ELA
Snfn (when Gi = Mgi)
Mgn

hmax
i=1
i=2
i=3

Sni(t)
Sni(t-1)i=4…..
Sni(t-365)

vn

i=n

Gi

vi

Fig. 1. Schematic of vertical glacier structure and ﬂows assumed in HYOGA. i is number of elevation band, Snf is snowfall, Ms is snow melt, Mg is glacier melt, G is mass ofsnow transformed to ice, Sn is volume of snowpack and v is volume of ice. In this example, snow layers exist only in the three uppermost 50 m elevation bands. The small
diagram on the right represents that snow is assumed to become glacier ice 1 yr after snowfall. The upper left panel shows, as an example, the area-altitude relationship of a
glacier grid located in the Alps (10.25E, 46.75 N), as assumed by HYOGA, with maximum and minimum glacier altitude of 3075 m and 1875 m, respectively, and a total area of
55.41 km2.

into account in HYOGA. The initial value of Sni on January 1st, 1948,
was obtained by a spin-up simulation from 1948 to 1990, startingwith zero snow volume on January 1st, 1948. Sni on December
31st, 1990, as computed by the spin-up simulation, is then used
as initial value of Sni.
The mass balance of the glacier ice in the ith elevation band iscomputed asv i ðt þ DtÞ ¼ v i ðtÞ þ Gi  Mgi
M gi ¼ ðT i  T 0 ÞDDF ice

if T i > T 0 ; and Si ðtÞ ¼ 0

ð2Þ

0 otherwise
where vi is volume of glacier, Mgi is the volume of glacier melt, and
DDFice is the degree-day factor of ice melting. As for the snowpack,T0 is set to 0 °C. Melting of the glacier ice in an elevation band is assumed to occur only if there is no snowpack in this elevation band.
The initial value of vi on January 1st, 1948 was obtained iteratively
based on data on glacier areas and a volume-area relation (comp.
Section 2.1.2) as described in Section 2.3.1.
By summing the computed glacier mass changes of all the elevation bands, the total glacier volumes in each grid are computedfor each day. Volume-area scaling is used to compute the resulting
changes in glacier area (comp. Section 2.1.2). The model was calibrated by ﬁtting the modeled glacier mass balance to observed glacier mass balance data.
2.1.2. Vertical glacier structure
All glaciers within a grid cell are simulated as only one glacierthat is described by the glacier area (and volume) in each 50 m elevation band (Fig. 1). The glacier area in each elevation band is estimated as follows. The maximum possible glacier area at the ith
elevation band amaxi, in km2, is determined using a normal distribution curve which is shifted by one third of the range of glacieraltitudes (hmax – hmin) as

pﬃﬃﬃﬃﬃﬃﬃ
amaxi ¼ r= 2ps  exp½fhmax  hi  ðhmax  hmin =3Þg2 =2s2 ð3Þ

where r is a coefﬁcient, hi is the mean altitude of the ith elevation
band, in m, hmax and hmin are the maximum and minimum glacieraltitude, in m, respectively, and s is a parameter that is set to 2.
Eq. (3) is derived from the vertical glacier area distribution of
the Dongkemadi Glacier in Tibet (Fujita et al., 2007) and the glaciermodel of Rees and Collins (2006) who modeled a hypothetical alpine glacier. We adjusted hmax and hmin by calibration as describedin Section 2.3.2. Initial values were taken from WGI where avail-able; otherwise hmax was set at the maximum cell elevation, whilehmin was assumed to be equal to ELA  (hmax  ELA).
ELA is the long-term average equilibrium line altitude where
glacier accumulation equals ablation (melting), and Braithwaite
and Raper (2007) showed that long-term averages of ELAs andmedian glacier elevations are very similar. Preliminary ELAs werecomputed by a HYOGA model run from 1948 to 1980, with preliminary values of hmax and hmin, and degree-day factors for snow
and ice of 3 and 5 mm/°C/day, respectively. In some grid cells, no
ELA could be computed because modeled mass balances of all elevation bands showed the same sign. Then, initial hmin was set equal
to the lowest grid elevation. As elevation data, we used the 30 arc
sec (approximately 900 m) elevation data of the Shuttle Radar
Topography Mission (SRTM30 data). The coefﬁcient r is adjusted
such that the initial sum of amaxi is equal to the initial glacier area
within the grid cell.
If amaxi is larger than the sub-grid area of the ith elevation band
abandi, the difference between amaxi and abandi is summed to theamax of the next lower elevation band. In order to minimize required disk space and computational cost, abandi of each elevation
band was determined from the cell area with elevations below hiiXabandk ¼ Acell  ðlogðhi Þ  aÞ=b

ð4Þ

k¼1

where Acell is total area of the 0.5° grid cell, in km2. Parameters a andb were obtained by ﬁtting Eq. (4) to SRTM30 elevation data withineach 0.5° grid cell, with the global mean correlation coefﬁcient
exceeding 0.98. Glacier area at the ith elevation band (amaxi) is thenobtained by distributing total glacier area per grid cell (A) startingfrom the highest elevation band and proceeding downward. The
amaxi is ﬁxed except for the lowest glacier elevation band. amaxi
is ﬁxed for the whole HYOGA simulation, except for the elevation
bands located at and below the lowest band with glacier. amaxi inthe lowest glacierized band is calculated as A minus total glacierarea located above the lowest glacierized elevation bands. The values of amaxi at the elevation bands below the lowest glacierizedband are set to abandi. A is updated after each time step based on
the new total glacier volume using the following equation:

A ¼ ðV=ca Þ1=c

ð5Þwhere V is total glacier volume in each 0.5° grid cell, in km3.
c = 1.375 from Bahr et al. (1997) and ca = 0.2055 m32c from Chen
and Ohmura (1990) are used for all glaciers. If A increases, the additional glacier area is allocated to the lowest elevation band up to the248

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

90˚
60˚
30˚
0˚
-30˚
-60˚
210˚

240˚

270˚

-3000 -1000 -500 -100 -10

0

10

300˚

60˚

90˚

330˚

0˚

30˚

100 500 1000 3000
120˚

150˚

180˚

Fig. 2. Difference of glacier areas according to GGHYDRO and WGI: GGHYDRO area minus WGI area in each 0.5° grid cell, in km2.

maximum area of the elevation band (amaxi). Representative glacieraltitude in the lowest elevation band is assumed to be the middle
altitude of the elevation band. If A decreases, glacier area is decreased in the lowest elevation band.
With its approach of daily updating of glacier areas per elevation band, HYOGA takes account of the feedback between changes
in glacier area, glacier elevation and glacier mass balance. Although
the time scale associated with the feedback processes of glaciergeometry is much longer than daily, HYOGA updates glacier areain every daily time step. If the ice in a grid cell shrinks, it persists
only in the higher elevation bands, and melting per unit glacierarea becomes smaller. Since the area and the area-related volumeof glacier at each elevation band are updated every day, the modelaccounts only implicitly for glaciers. The potential positive feedback of a decreasing glacier surface elevation due to glacier thinning is not taken into account.

2.2.1. Climate input
A global 0.5° gridded data set of daily precipitation and near-surface temperature for 59 yrs from 1948 to 2006 (Hirabayashi et al.,2005; Hirabayashi et al., 2008b) was used to drive the glacier model. The precipitation data are corrected for gauge errors (based ondaily meteorological data and information on gauge types, Hirabayashi et al., 2008c). The temperature data set is based on monthly
temperatures of Fan and van den Dool (2008) that are topographically adjusted, and is called H08-FV. An alternative data set of daily
surface temperature, called H08-CRU, which is based on monthly
temperature values of the Climate Research Unit version TS 2.1 dataset (CRU; Mitchell and Jones, 2005), was generated by also using themethod of Hirabayashi et al. (2008b). Since temperature data of
CRU are available up to 2002 only, monthly temperatures during
2003–2006 in H08-CRU were computed from monthly temperature
data of Fan and van den Dool (2008) for this period by scaling withthe mean ratio of monthly temperatures of CRU and Fan and van
den Dool (2008) from 1986 to 2002. This time period was chosen
as both the CRU and Fan and van den Dool data sets are based ona large number of measurement stations during this period.

line from http://www.trentu.ca/geography/glaciology; Cogley,2003). These data sets represent spans of time rather than dates.
They are used to estimate initial glacier areas in 1948 (compare
Section 2.3).
WGI provides observation data of about 70,000 glaciers, including glacier location, area, elevation and observation dates. GGHYDRO provides total area of glacier on a global 1° grid and was
generated based on maps, mainly at the 1:1,000,000 scale, that had
been published over several decades in the mid-20th century. We assumed that the glacier area of GGHYDRO represents glacier area
information before 1977. Glacier area of WGI per 0.5° grid cell ismostly smaller than that of GGHYDRO, probably because WGI does
not cover all glaciers in those cells. Glacier information in WGI is limited to about 30% of global glacier area outside of Greenland and Antarctica. In many grid cells, GGHYDRO indicates glaciers while no
information is available in WGI (Fig. 2). These grid cells are foundin Europe, Central Asia, the Himalaya, Peru, Chile and the southerncoastal glaciers of Alaska. In some cells, WGI glacier area is larger
than GGHYDRO glacier area (e.g. in some parts of Alaska, Peru andChile, and of the Tibetan Plateau) (Fig. 2). A possible reason for thisis that GGHYDRO expresses glacier area as integer percentages of total 1° cell area. Thus resolution is 1% of grid cell areas, and glacierssmaller than that (approx. 100 km2 at the equator) are not included.
We combined these two products by ﬁrst disaggregating GGHYDRO to the 0.5° grid using SRTM30 sub-grid altitude information.
The four sets of 3600 SRTM30 sub-grid elevations per 0.5° cell were
sorted, and the glacier area in each 1° GGHYDRO grid cell was disaggregated to the four 0.5° grid cells by allocating glacier area preferentially to the highest elevations. In the second step, individual glacierarea data of WGI were summed for each 0.5° grid and compared to
GGHYDRO-based 0.5° glacier area. Finally, the greater of the two values for each grid cell was included in our global glacier area data set.
Glaciers on small Arctic islands not covered by the climate data sets
were not taken into account in the glacier area data set.
Among the approximately 60,000 0.5° land cells, only 2613 contain glaciers. Table 1 compares our 0.5° glacier area data set withother published estimates of glacier areas that exclude glaciersand ice sheets in Antarctica and Greenland. Total glacier area of
this study is 534,945 km2, which is similar to other published data
sets. In our data set, glacier areas on North American Arctic Islands
and on Sub-Antarctic islands are smaller than in other data sets,
because 0.5° grid cells with small islands but without data in the
global meteorological data sets we used were excluded from ouranalysis.

2.2.2. Glacier areas
A 0.5° gridded global glacier area data set was created by aggregating glacier area data of the World Glacier Inventory (WGI) and
the Global Hydrological Data (GGHYDRO, Release 2.3, available on-

2.2.3. Glacier mass balance observation
A total of 110 observed time series of annual mass balances forindividual glaciers, from Dyurgerov and Meier (2005) (referred toas DM05) and, for New Zealand only, from Heydenrych et al.

2.2. Data
Input data for HYOGA are time series of gridded daily near-surface air temperatures and precipitation as well as calculated initial
glacier areas. The observed glacier mass balances at speciﬁc points
in time are used for calibration procedures.

c
h
a

d

g

b

e

f

36,612
11
117,1291007
36,298
5000
486,598

33,685n.a.
121,711433
31,521
2646
489,159

576,800

36,612n.a.
121,575n.a.
25,000
5000
486,598

129,300

49,000a74,700a36,600n.a.
119,000a
35,00018,000a

244,500a

153,184
60,7236758
11,160101,505
149,900
55,6965625
10,938109,680

36,61210
129,076860
25,9087000
516,148

151,758
56,1356095
11,260124,342

Svalbard
AfricaFormer USSR and Asia
Australasia
S. America
Sub-Antarctic islands
Total area excluding Greenland andAntarctica

Alaska38,800n.a.
111,900
1000
36,2605000
500,910150,600
56,1006000
11,300125,210
Arctic Canada
Arctic Eurasia
Europe (Mainland)
Iceland
W. Canada and W. US

n.a.: Not available.
aRegions for which regional averages of mass balance by Dyurgerov and Meier (1997) were used for calibration.
b
Aggregated from original values of Table 2 by Radić and Hock (2010); sum totals of their original region 2 and 3 (Europe), 4, 5 and 6 (Arctic Eurasia), 7, 8, and 9 (Asia) and 14 and 15 (South America).

139,92270,6569022
10,671
44,94956,21336,305
11
128,4441158
36,0991497
534,945
14,69056,7816102
11,005
21,48079,26036,506n.a.
118,6291156
36,7003740
518,048
151,800
n.a.
17,286This
study
Radić and Hock(2010)b
Dyurgerov and Meier(2005)
Dyurgerov and Meier(1997)
Braithwaite and Raper(2002)
Oerlemans(1993)
Haeberli et al.
(1989)
Meier(1984)

Table 1Comparison of different estimates of the global distribution of glacier and ice cap area outside of Greenland and Antarctica, in km2, based on Braithwaite and Raper (2002), Dyurgerov and Meier (2005) and Radic and Hock (2009). Alaska
in the table includes glaciers in northwestern Canada. The last column indicates the regions distinguished in Fig. 8.

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

249(2004), were used for the calibration of HYOGA. Two thirds of theabout 300 observed glacier mass balances could not be used forcalibration, because there were several glaciers with observations
within the same 0.5° grid cell. Data for the glacier with the largest
area were selected if there was more than one observed glacier.
Mean length of the available mass balance observations was
13 yrs. The 110 grid cells with observed glacier mass balances
are mainly in Europe (33), USA and Canada (30) and Asia (22). Only
two are located in South America, while the rest are located in
Svalbard (9), Canadian Arctic islands (6) and Sub-Antarctic islands(1). Yearly glacier mass balances averaged over large regions ofSerreze et al. (2000), which provide an update of Dyurgerov andMeier (1997), were also used for model calibration and validation(referred to as DM97). For validation, summer and winter massbalance observations were available for 21 glaciers (it is not always
the same as the 110 glaciers with annual data used for calibration,
as it was sometimes not the largest glacier in a grid cell that hadsummer and winter data available).
The hydrological year starts when glacier melt reaches its minimum. In this study, the hydrological year starts on the 1st of October in the northern hemisphere and on the 1st of April in theSouthern Hemisphere.
2.3. Model initialization and calibration for estimating global glaciermass balance from 1948 to 2006
Glacier areas in 1948 were estimated by HYOGA in an iterative
manner, based on observed glacier areas for which the observation
time varies between grid cells. HYOGA was calibrated against observed glacier mass balances, adjusting four model parameters:
the maximum and minimum glacier altitude hmax and hmin, andthe melting factors DDFice and DDFsnow. Computation of initial glacier areas and calibration had to be done jointly, as initial areas depend on the calibration parameters.
2.3.1. Initialization of glacier area
Since the global glacier area data set (see Section 2.2.2) contains
observations in different years and months, it was necessary toestimate, as initial condition, the glacier area in each grid cell on
the 1st of January 1948, the start of meteorological data. We prepared gridded data sets of the year and month when the glacierarea was observed, using the glacier statistics of WGI. WGI provides information of observed year (about 30,000 glaciers) andmonth (about 26,000), respectively. However, date information of
WGI is rather inhomogeneous, providing, e.g. dates of snowline
observation, of map publication or of areal photography. If there
was more than one glacier with information on observation datewithin grid cell, data of the largest glacier was used. If observation
dates were not available, those of neighboring grids were used. If
there is not even information for the neighboring grids, observation date was set to the 1st of January 1975, because about
24,000 WGI stations were observed during the period 1961 and1980 (compare Fig. 2 of Cogley, 2009). The glacier area on the 1stof January 1948 was then obtained iteratively for each of the2613 grid cells with glaciers, using different initial glacier areas until the HYOGA glacier mass balance led to a glacier area on therespective observation date that did not differ by more than 5%from the observation. Initial glacier area of each grid cell was updated in each calibration round, using the respective values ofthe four calibration parameters. The initial glacier areas that were
ﬁnally adopted were obtained with the calibrated values of the calibration parameters.
2.3.2. Model calibration
HYOGA was calibrated against long-term average annual glaciermass balances observed within the time period 1948–1980, for the250

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

ularly the case in arid and semi-arid Asia. The warm bias of CRU
temperature in summer caused glaciers in High Mountain Asia tohave no snowfall in summer even on the top of mountains. Because
many arid and semi-arid glaciers in Asia show both accumulationand melting in the summer monsoon season (Fujita and Ageta,
2000), glaciers in these regions are particularly sensitive to potential temperature biases. We concluded that the H08-FV temperature product of Fan and van den Dool (2008) is preferable for
estimation in most regions in Asia. H08-FV, however, also leads
to problematic mass balances, outside of Asia (Fig. 3, center). When
HYOGA was calibrated using either the H08-FV or the H08-CRU
precipitation data set, H08-FV led to better calibration results inhalf of the grid cells with glaciers, and H08-CRU in the other half.
In our further analysis, we selected for each of the 2613 grid cellswith glaciers the temperature data set that, after calibration, led toa better ﬁt to the observed mass balances. With this approach, referred to as H08-mix, modeled mass changes are less biased, withan average relative root mean square error of modeled masschange among the 110 observed glaciers of 54% as compared tothat of simulations using H08-CRU (230%) and H08-FV (197%)(Fig. 3 right). These large root mean square errors of H08-CRU
and H08-FV are due to about 30 of the 110 observations where
snowfall is underestimated and glacier melting is overestimateddue to high temperature values. About 1300 of the 2613 grid cells
show differences of less than 5% for both H08-FV and H08-CRU
after the calibration process. In H08-mix, which is used for further
computations, 1485 of the computed grid cell balances differ byless than 5% from the glacier balances of neighboring observed glacier or from the regional averages.
For 21 glaciers, relatively long-time series of summer and winter mass balances were obtained from the World Glacier Monitoring Service (WGMS). These data are compared to summer andwinter mass balances as computed by HYOGA for the respective
grid cells and time periods. We assumed that summer and wintermass changes refer to the periods 1st April–30th September and1st October–31st March, respectively (except for the one observation located in Southern Hemisphere).
Fig. 4 indicates that HYOGA cannot simulate well the observed
seasonality of winter accumulation and summer ablation. It computes smaller summer mass losses than are observed, and barely
computes any winter mass gains. A likely reason for the underestimation of winter accumulation is an overestimation of winter temperature or an underestimation of winter precipitation in the
global climate data set that we used. In a study of glaciological conditions in seven regions, Braithwaite and Raper (2007) found it

available observation period, because glacier mass before 1980 ismore stable than afterwards. The calibration against observed
mass balances of individual glacier is problematic as HYOGA does
not compute the mass balance of individual glaciers but lumps all
glaciers within one grid cell into one equivalent glacier. We thus
assume that all glaciers within each grid cell have the same speciﬁcmass change (mass change divided by glacier area).
Calibration was done in two steps by ﬁrst adjusting maximum
and minimum glacier altitude hmax and hmin in Eq. (3) and then,in a second step, the degree-day factors (DDFsnow and DDFice) in
Eqs. (1) and (2). In each step, the parameters were adjusted against
the cell-speciﬁc long-term average of total glacier mass balance
observed in 110 grid cells, taking into account all available observation periods before 1981. If there were no mass balance observations within 10 grid cells from the target cell, and the glacier gridcell was located within one of the ﬁve regions with available data
(see regions with asterisk in Table 1), average regional mass balances for 1961–1993 of DM97 were used for calibration. These regional balances were obtained as the area-weighted means ofobserved mass balances. A 948 out of the 2613 glacier grid cells
were calibrated against these regional estimates of long-term glacier mass balance. For 190 grid cells in South America, Australasia,
Africa, Sub-Antarctic islands and small arctic islands, the long-term
average mass balance 1948–1980 was assumed to be zero for calibration purposes.
During calibration, variation of hmax and hmin was constrained
only by the maximum and minimum elevation within the grid cell,respectively. The degree-day factor of snow (DDFsnow) was allowed
to range from 1 to 4 mm/°C/day. This range includes the values
that are used in global hydrological models (e.g. Döll et al., 2003)
and numerical glacier models (e.g. Rees and Collins, 2006). The degree-day factor of glacier ice (DDFice) was adjusted between 3 and20 mm/°C/day, until the long-term average yearly mass balance
was as close as possible to the observed mass balance. This range
for DDFice is based on the literature (e.g. Jóhannesson et al., 1995;
Singh et al., 2000; Hock, 2003; Zhang et al., 2006).
Fig. 3 compares modeled and observed long-term average speciﬁc glacier mass changes, considering the whole observation period and not just the calibration period which ended in 1980. Using
H08-CRU temperature data (Fig. 3, left), at least 15 glaciers show
far too negative mass balances even after calibration, i.e. the glaciers shrink much too rapidly in the model. These glaciers are located in High Mountain Asia and in mountainous areas in the US,
Canada, and Alaska, and often in areas where H08-CRU temperatures are signiﬁcantly higher than the H08-FV values. This is partic-

1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

H08-CRU
-4

-3

-2

1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

-1

0

Observation (m/yr)

1

Model (m/yr)

Model (m/yr)

N. America
S. America
Arc. Eurasia
W Europe
Asia+F.USSR

Model (m/yr)

1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

H08-FV
-2

-1

0

1

Observation (m/yr)

mix
-2

-1

0

1

Observation (m/yr)

Fig. 3. Comparisons of modeled and observed average annual glacier mass changes during the respective observation periods, using temperature data of H08-CRU (left), of
H08-FV (center) or a mix of temperature data of H08-CRU and H08-FV temperature data (right). Each symbol indicates glacier mass changes at one of 110 grid cells withobservations by DM05. Observed values relate to the largest glacier within the grid cell, modeled values to the total glacier mass within the grid cell. Open symbols: before thecalibration, ﬁlled symbols: after calibration. The error bars represent the standard deviation of annual mass balance values during the observation periods. Diagonal grey lines
indicate where model and observation are equal.

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

32

Model (m/yr)

1
0
-1
-2
-3
-4
-5
-5

-4

-3

-2

-1

0

1

2

3

Observation (m/yr)
Fig. 4. Comparison of modeled and observed average annual, summer and winterglacier mass (snowpack and ice) changes for 21 grid cells during the respective
observation periods. Observed values relate to either the largest glacier within thegrid cell or, if no data were available, to another glacier within the grid cell, modeled
values to the total glacier mass within the grid cell. Filled circles: annual massbalance, open triangle: summer mass balance, open circle: winter mass balance.

necessary to decrease temperature data of a global data set empirically using observed temperature at the respective glacier sites.
For three example glaciers/grid cells, Fig. 5 shows time series ofobserved and computed annual mass balances. Modeled mass balances show less interannual variability than of the observed balances, even though average annual mass balances are similar due
to the calibration process. Discrepancies between modeled and observed mass balances are, on the one hand, caused by the fact theobserved mass balances are values for single glaciers, while modeled values represent the average over all glaciers located within
the grid cell. Thus, even if the model represented glacier masschanges at the scale of grid cells perfectly, model results would
only ﬁt to the selected observations if all glaciers in the grid cell
had the same speciﬁc mass balances. On the other hand, inadequate climate data and the modeling of glacier distribution within
grid cells are also major causes for the discrepancies.

3. Results
Fig. 6 (top) presents a global map of 0.5° gridded estimates ofglacier area on the 1st of January 1948 as derived by an iterative
spin-up simulation with HYOGA. Glacier area per grid cell is large
in high latitudes (e.g. Canadian and European arctic islands) and in
the Himalayas. Globally, 76% of the 2613 0.5° glacierized cells
show glacier areas below 300 km2 (about one tenth of the cell area)in 1948, while 33% of the glacierized grid cells have a glacier area of251

less than 50 km2. Global glacier area was estimated as 534,893 km2
in 1948, compared to the value of 534,945 km2 in the basic datacompiled for this study which mixes glacier areas from different
points in time (comp. Section 2.2.3; values shown in Table 1). Global glacier area was simulated to have decreased by 0.8% between
1948 and 2006. This corresponds to an average annual value of
areal shrinkage of 0.014%/yr, which is only about a ﬁfth of the rate
derived by extrapolation of repeated measurements of glacierareas (Cogley, 2008).
Fig. 6 (bottom) shows a global map of the average annual speciﬁc mass change from 1948 to 2006, while Fig. 7 provides enlarged views of selected regions. Here, the mass change isderived as mass change of glacier (expressed as volume of liquidwater) divided by the glacier surface area of the particular year,
in mm/yr. It is obvious that most glaciers suffered from mass losses(retreat of glacier) in the last decades, but there is a high spatial
variability, even with glacierized grid cells with mass gains locatednext to grid cells with high mass losses (e.g. in Norway and SouthAmerica). In Norway, for example, such a high spatial variability ofmass loss is reasonable, because there is a steep gradient between
western maritime (gaining) to eastern continental (loosing) glaciers. The amount of decrease of total glacier volume (not shown)is particularly large in High Mountain Asia, the coastal zone of
Alaska and the European Arctic islands. Fig. 8 shows time seriesof annual glacier mass changes as global average and for sevenlarge regions (comp. Table 1) for the time period 1948–2006, comparing modeled values to independent estimates of mass balancesfrom DM05 and DM97. DM05 obtained their regional and global
estimates of by area-weighted averaging time series of observed
mass balances of a total of about 300 glaciers, while DM97 onlyused about 250 glaciers. All regions except South America show
signiﬁcant mass losses for both model estimation and observation.
The differences of the ranges of mass balance variation among different regions as estimated by DM05 and DM97 are fairly well replicated by HYOGA.
Regionally averaged mass losses in South America (Fig. 8) are
relatively small, because there are some grid cells with large glaciers in the southern part of South America, which show a glaciermass increase. However, our model results for South America suffer from a strong decrease in precipitation observations after 1980(see Section 4), which may partly explain discrepancies to DM05
but also satellite-based studies of Rignot et al. (2003) and Chenet al. (2007).
Table 2 compares the modeled global total speciﬁc mass balance and its equivalent sea level rise in mm/yr with values ofobservation-based estimates that are the arithmetic means of estimates by DM05 and two other data sets which together take into
account 221–470 mass balance measurements within each 5-yrtime period analyzed (Lemke et al., 2007, their Table 4.4 and theirFig. 4.14). Global glacier mass loss values as computed by HYOGA

Fig. 5. Examples of annual speciﬁc mass balances of three selected glaciers: Bezengi glacier in the Caucasus (left), Plattalva glacier in the Alps (middle) and Silver glacier in the
Cascades, USA (right). Solid lines indicate observations, and dotted lines indicate HYOGA model results for the grid cells in which the observed glaciers are located.

252

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

Fig. 6. Global map of modeled glacier area per 0.5° grid cell on the 1st of January 1948, in km2 (top), and average annual speciﬁc mass change of glacier during the 59 yrs from1948 to 2006, in mm/yr (bottom).

are similar to the values of Lemke et al. (2007), and within thegiven uncertainty ranges, which do not include uncertainties thatderive from uncertainties in the glacier area inventory (Lemke
et al., 2007). Both observation-based estimates and HYOGA model

results agree that glacier mass losses have accelerated after 1990,
with HYOGA indicating a somewhat stronger acceleration. According to HYOGA, average annual mass losses have increased strongly
after the 1990s as compared to the 30 yrs before, with a sea level

Fig. 7. Enlarged views of average annual speciﬁc glacier mass change 1948–2006 (mm/yr) in South America (a), Norway (b), High Mountain Asia (c), Alps (d) and Caucasus(e). Regions are indicated as rectangles in Fig. 6.

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

253

Fig. 8. Time series of regionally averaged annual speciﬁc glacier mass balances. Black and grey lines are observations of DM05 and DM97, respectively, and red lines aremodeled values. Thick lines are 5-yr moving average. Blue thick lines are 5-yr moving average of mass balance of glacier grid cells where observed mass balances wereavailable within the grid cell. ‘‘110/2613” (in blue in the lower left corner of the global analysis box), for example, means that there are 110 observed mass balance values
taken into account for constructing the blue lines, and 2613 0.5° grid cells with glaciers in total globally. Grey top-to-bottom bars indicate annual numbers of precipitation
gauges used to create daily precipitation input.

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Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

Table 2Global mass balance of glaciers and ice caps outside Greenland and Antarctica. Data of Lemke et al. (2007, their Table 4.4) (LM07) and this study. Assumed glacier area of LM07 is546  103 km2, while in this study, it is 535  103 km2. Values in parentheses are HYOGA estimations using the LM07 glacier area. Ocean surface area is assumed to be
362  106 km2.
Average annual mass balance(kg/m2/yr or mm/yr)

1960/61–2003/2004
1960/61–1989/1990
1990/91–2003/2004

Average annual sea level equivalent (mm/yr)(Gt/yr)

LM07

This study

LM07

This study

LM07

This study283 ± 102
219 ± 92
420 ± 121

285
227
519

155 ± 55
120 ± 50
230 ± 66

153 (156)
122 (124)
277 (282)

0.43 ± 0.15
0.33 ± 0.14
0.63 ± 0.18

0.42 (0.43)
0.34 (0.34)
0.76 (0.78)

rise equivalent of 0.76 mm/yr after 1990, as compared to only
0.34 mm/yr during the 30 yrs before.

4. Discussion
What are possible reasons for the discrepancies between HYOGA results and observed regional averages as shown in Fig. 8 and Table 2? One hypothesis is that the observed regional averages are
based on a number of glaciers which is much smaller than the total
number of glaciers in a region that was taken into account by
HYOGA. Calibration to DM97 regional values did not lead to a close
agreement of HYOGA and DM97 regional averages of speciﬁc masslosses. For neighboring grid cells, HYOGA may compute very different glacier mass changes.
The blue thick lines in Fig. 8 indicate area-weighted mean massbalances of grid cells in which one of the 110 glaciers with observations used for calibration of HYOGA are located, while 2613 grids
are used to obtain mean mass balance in HYOGA (shown in red).
Overall, the blue lines are within a few tenths of a meter of the regional averages computed by HYOGA, which indicates that the discrepancies between the regional averages that are based oninterpolation of observed mass balances and those that are computed by HYOGA cannot be explained by a bias due to the few
observation locations.
Other possible reasons for discrepant regional estimates of glacier mass loss are errors of the HYOGA model results that arecaused by the simplistic modeling approach (e.g. modeling all glaciers within a grid cell as one effective glacier) and by inadequate
climate input data. Because of the non-linearity in the volume-area
relation, inclusion of the glacier area distribution, and possibly different glacier types, within each grid cell rather than treating all
glaciers as one appears to be indispensable. HYOGA is expected
to underestimate shrinkage of glacierized area and to overestimate
glacier volume in regions with many separate small glaciers withina grid cell as it assumes that mass balance of many small glaciers
can be simulated by the mass balance of one effective glacier, thearea of which is the sum of the areas of the individual glaciers.
Including size distribution of glacier area and different glaciertypes within each grid cell is likely to improve the estimated volume and areal change of glaciers. However, there is currently no
inventory that provides such information except for a few grid cells
world-wide. Size distribution can be derived directly from satellite
imagery and glacier inventories and indirectly from topographic
data, using an empirical relationship between size distribution
and relief (steepness of landscape) (Raper and Braithwaite, 2005).
In South America, in particular, the number of precipitation
gauges that were used to create the gridded precipitation data used
as input to HYOGA decreased strongly from about 50–100 before
1980 to less than 10 afterwards (Fig. 8c). With such a small numberof observations, we cannot expect to be able to simulate the temporal development of glacier mass loss. The number of precipitation gauges in Canadian Arctic islands, Svalbard and SubAntarctic islands are almost zero, indicating that the precipitation

input given for these regions is obtained mainly by extrapolatingfrom surrounding grids or climatologies.
Moreover, the process of glacier calving is not taken into account by HYOGA, such that mass changes of glaciers that do notterminate on land but at the ocean (e.g. in Alaska and South America) are not computed correctly if calving is relevant. Anothersource of error may be the neglect of ﬁrn.
The poor simulation of seasonal mass balances (Fig. 4) andinterannual variability (Fig. 5) can partly be explained by the inadequate temperature and precipitation input. Glacier mass changes
computed by HYOGA depend strongly on precipitation and nearsurface temperature. Climate observations at mountain glaciers
are very scarce. Currently, global temperature and precipitation
data sets are not suited well for modeling glacier mass balances
as they do not represent appropriately the climatic conditions at
glaciers. Precipitation stations are rather located in the valleys
and not on the mountains, and surface-air temperature at a glacieris expected to be lower than at an ice-free location at the same altitude (Braithwaite and Raper, 2007). This results in an underestimation of the seasonal glacier dynamics by HYOGA (see Fig. 4).
A limited sensitivity analysis was performed to determine thesensitivity of computed glacier mass changes to the scale parameter c in Eq. (5). (e.g. Radić et al., 2008). When c was varied by ±30%,mass balance within a grid cell changed by less than 1%, after calibration for the individual c values.
The equilibrium line altitude (ELA) of a glacier is deﬁned as thealtitude where accumulation is equal to melting. To validate
HYOGA, ELA data at 63 glaciers were obtained from the Glacier
Mass Balance Bulletin (WGMS, 2007, and earlier issues). ELA observations may be biased, as low-elevation glaciers are more likely tobe observed due to accessibility. The effect of this bias is expected
to be small, because ELA is mainly inﬂuenced by vertical changes ofclimate variables. Observed ELAs were averaged if several ELA data
were available for a grid cell.

N. America
S. America
Arc. Eurasia
W Europe
Asia+F.USSR

5

Modeled ELA [km]Period

4

3

2

1

0

0

1

2

3

4

5

Observed ELA [km]Fig. 9. Correlation between observed and modeled mean equilibrium line altitude(ELA) at 63 locations.

Y. Hirabayashi et al. / Journal of Hydrology 390 (2010) 245–256

Fig. 9 shows a good agreement of observed and modeled ELA.
This indicates that the balance of accumulation and melting at eachelevation band is well captured by the model, and that the vertically distributed glacier mass balance is represented well in HYOGA. As the air temperature lapse rate varies according to humidity,
Schneeberger et al. (2003) suggested, for a number of glaciers, different temperature lapse rates ranging from 0.1 °C to 0.9 °C per
100 m. Nevertheless, due to lack of information at the global scale,a uniform lapse rate of 0.65 °C per 100 m was applied in HYOGA
to estimate temperature at each 50 m elevation band from themean temperature of the 0.5° grid cell. As is shown in Fig. 9, a single lapse rate in HYOGA appears to be sufﬁcient for replicating vertical mass balance change with altitude.
Even though ELA is modeled well, this does not necessarily indicate that the vertical glacier area distribution (Eq. (3)) and the volume-area relation (Eq. (5)) are correctly represented in HYOGA,
and these characteristics are decisive for a successful simulation
mass changes. In reality, volume-area relationships of glacier vary
among glacier types, while a single equation (Eq. (5)) is assumed todescribe the relationship in HYOGA.
The vertical sub-grid glacier structure of HYOGA allows for representing several glacier types in different regions of the globe. A
glacier mass balance model, for example, that estimates accumulation and melting of glaciers using only the temperature value at asingle reference height of glaciers, such as ELA or mean altitude ofglacier (e.g. Braithwaite and Raper, 2007), may be difﬁcult to apply
to glaciers where both accumulation and melt occur at the sametime. HYOGA however, computes mass balances at individual elevation band and thus has the potential to simulate summer accumulation type glaciers (e.g. in High Mountain Asia) that arecharacterized by accumulation at high elevations and melting at
low elevations in the same season.
Using gravimetric data from the GRACE satellites, Matsuo andHeki (2010) estimated glacier mass loss for the Asian high mountain area (Himalaya, Karakorum, Pamir, Tienshan) of 47 ± 7 Gt/yrduring 2003–2009. However, they had to rely on a number ofhighly uncertain assumptions, including a ground water depletion
rate in Northern India. Their value compares well to the HYOGA
estimate for October 2003–October 2006, with an average massloss of 37 Gt/yr. For the time period 1961–2003, average glaciermass loss was only 25 Gt/yr according to HYOGA, which is almost
equal to the value of from DM05 for the Asian high mountain area(comp. Matsuo and Heki, 2010, their Fig. 2).

5. Conclusions
A ﬁrst global glacier mass balance model was developed thatprovides gridded sub-annual (daily to monthly) time series of glacier mass changes, glacier ice melting rates and melting rates ofsnowpack on glaciers for all land areas of the globe except Greenland and Antarctica. With a spatial resolution of 0.5°, HYOGA computes daily snow and glacier mass balance at different elevation
bands, which makes it possible to estimate also mass changes ofsummer accumulation type glaciers where both accumulation
and ablation occur in the same seasons. Compared to glacier models that estimate glacier mass changes by using correlations of historical glacier mass balance (integrated over all elevations) withsurface temperature and precipitation, HYOGA is better suited for
projecting future glacier mass losses. HYOGA has the potential tobe coupled to global hydrological or land surface models such thatthe impact of glacier mass changes on river ﬂow regimes can be taken into account. This will improve the assessment of climatechange impacts on freshwater resources.
In accordance with other studies, HYOGA model results showthat at the regional scale glaciers have been shrinking at least since

255

1948. Equally in accordance with other studies, in particular the recent IPCC report (Lemke et al., 2007), global glacier mass losses
have accelerated after 1990.
Data on glacier volume are available only for a few glaciers. Dueto the simplistic approach for estimating glacier volume, total glacier volumes in HYOGA are not realistic. Therefore, HYOGA cannot
be used to estimate the total fresh water stock stored in glaciers or
the date when glaciers will disappear due to climate change. Suchstudies require more detailed and reliable glacier volume estimates which could be derived from information about glaciertypes, observed glacier thickness, or geomorphological processes.
To improve dynamic glacier mass balance modeling, in particular the simulation of seasonal and interannual mass variations, itwill necessary to correct global-scale temperature and precipitation data, by considering local data, such that they better represent
the speciﬁc conditions at glaciers. Besides, size distribution of glacier area within each grid cell should be included in HYOGA, different glacier types (valley glaciers and ice caps) should be
distinguished, and the effect of debris on the glacier surface should
be taken into account. Regarding the impact of climate change,
inclusion of the impact of radiation on glacier melting may be
important, although some of the change due to radiation is indirectly included in the surface temperature change (Ohmura, 2001).
Acknowledgments
We thank Graham Cogley and three anonymous reviewers fortheir extensive and very helpful comments. This study was partially supported by Grants of Young Scientists A (20686033,
21686045) of the Japan Ministry of Education, Science and Culture
and Core Research for Evolutional Science and Technology (CREST),Japan Science and Technology Agency (JST).
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