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and ablation stake measurements (Østrem and Brugman
1991
; Kaser et al.
2002
; Zemp
et al.
2013
), and provides a measure of the surface mass balance. The glacier-wide surface
mass balance is estimated from extrapolation of the point measurements over the glacier
surface. The earliest mass-balance measurements were taken on the Rhˆ ne Glacier, Swiss
Alps, providing intermittent observations during 1874-1908 (Mercanton
1916
). Annual
mass-balance measurements have been taken at two stakes on Claridenfirn in Switzerland
since 1914 (M ¨ller-Lemans et al.
1994
). The longest continuous glacier-wide mass-bal-
ance time series exists for Storglaci¨ren, Sweden, reaching back to 1945 (Zemp et al.
2010
). In situ measurements of mass balance have been obtained for * 340 glaciers
worldwide, of which * 70 glaciers have continuous annual observations longer than
20 years (Dyurgerov
2010
). The records of glacier mass balance are complied and dis-
tributed by the World Glacier Monitoring Service (WGMS, Zemp et al.
2009
).
Dyurgerov and Meier (
1997a
,
b
) provided the first detailed assessment of annual glacier
mass balances on global and regional scales followed by updates in Dyurgerov (
2002
,
2003
), Dyurgerov and Meier (
2005
), and Dyurgerov (
2010
). Global averages were
obtained from area-weighted specific mass balances of smaller subregions whose balances
were estimated from the single-glacier observations. A similar approach was taken by
Ohmura (
2004
), while Cogley (
2005
) used a different approach by applying a spatial
interpolation algorithm, fitting a second-degree polynomial to the single-glacier observa-
tions to extrapolate the mass-balance observations to all glacierized cells in a 1 9 1
global grid. In contrast to Cogley (
2005
) who used only glaciological mass-balance
measurements, Cogley (
2009a
,
b
) also included geodetic observations (Sect.
3.2
) from
more than 250 glaciers in the interpolation. His estimate was about 30 % more negative
than the one derived solely from direct measurements possibly due to a better represen-
tation of marine-terminating glaciers (which, in addition to surface melting, lose mass by
iceberg calving and submarine melting); however, it was questionable whether the dif-
ference represented adequately the global-average ablation by calving and submarine melt
(Cogley
2009a
,
b
).
Three global estimates (Ohmura
2004
; Dyurgerov and Meier
2005
; Cogley
2005
) were
synthesized into a ''consensus estimate'' (Kaser et al.
2006
) that was used in the Fourth
Assessment of the Intergovernmental Panel on Climate Change (IPCC; Lemke et al.
2007
).
Not surprisingly, since they were based on the same observations, the three assessments
agree well with each other. A glacier mass loss rate of 0.50 ± 0.18 mm sea-level equiv-
alent (SLE) year
-1
was found for the period 1961-2004 and an increased rate of
0.77 ± 0.22 mm SLE year
-1
for 1991-2004, thus a considerably higher mass loss rate
than found for both ice sheets together in both periods (Lemke et al.
2007
). Gardner et al.
(
2013
) applied the methods of Cogley (
2009a
,
b
) to all glaciers other than the ice sheets
and found a mass loss rate of 1.37 ± 0.22 mm SLE year
-1
(0.92 ± 0.34 mm SLE year
-1
excluding the glaciers in the Antarctica and Greenlandic periphery) for the period
2003-2009, comparable to the estimate for 2006 by Meier et al. (
2007
) derived from the
interpolation of local glaciological records (1.11 ± 0.26 mm SLE year
-1
, Table
1
).
All these assessments suffer from serious under sampling. Direct observations of glacier
mass changes exist on fewer than 1 % of the glaciers worldwide (* 300 out
of * 200,000). These are geographically biased with more than 60 % of the records
originating from the European Alps, Scandinavia, Western Canada and USA, and parts of
the former Soviet Union (Dyurgerov
2010
). They are also biased toward smaller, land-
terminating glaciers in maritime climates. The assumption that very few benchmark gla-
ciers with observed mass balances over short-term time period (\ 10 years) are repre-
sentative for the region-wide mass balance over * 40 years is a major but inevitable
