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Anderson et al.
2010
). However, the models require detailed meteorological input data,
obtained at a glacier surface, which often are not available. Alternatively, these data can be
obtained by dynamical downscaling of climate reanalysis products, i.e., by running
mesoscale atmospheric models at high spatial resolution (less than 1 km in horizontal) over
a region of interest. This approach has only recently been attempted in studies of glacier
melt over a few summer seasons in Kilimanjaro and Karakoram (M ¨lg and Kaser
2011
;
Collier et al.
2013
). Despite promising results, the applicability of this approach in order to
simulate long-term surface mass balance on regional scale still needs to be investigated. In
addition, the validation of surface mass-balance models should ideally be performed on
sub-annual temporal scales, e.g., comparing modeled versus observed winter and summer
mass balances, rather than only annual net mass balances. However, very few glaciers with
annual mass-balance observations have the seasonally resolved components.
The representation of glacier dynamics using volume-area scaling remains a first-order
approximation that is necessitated by the lack of input and validation data needed for
physically based ice dynamics models. However, as shown by L¨ thi (
2009
), volume-area
scaling has some serious shortcomings in modeling glacier volume evolution. Glacier flow
models of high complexity have been successfully applied on individual mountain glaciers
(e.g., Picasso et al.
2004
; Deponti et al.
2006
; Jouvet et al.
2009
). However, it is chal-
lenging to simulate the flow of a full suite of glaciers within a region of complex topog-
raphy (Jarosch et al.
2012
). Such ice-flow models require detailed information of the
underlying bedrock topography, which has been observed for fewer than 1 % of glaciers in
the world (Huss and Farinotti
2012
). In the absence of abundant measured data on glacier
thickness and volume, various alternative approaches to derive ice thicknesses have
recently been developed (e.g., Clarke et al.
2012
; Huss and Farinotti
2012
; Linsbauer et al.
2012
; McNabb et al.
2012
). In particular, promising is the first globally complete dataset of
glacier bed topographies derived from inverse modeling by Huss and Farinotti (
2012
),
which will open new avenues for modeling glacier dynamics on the global scale.
To our knowledge, none of the current global-scale modeling studies of glacier volume
changes incorporates frontal ablation, i.e., mass loss by iceberg calving or submarine melt
of marine-terminating glaciers. Studies on marine-terminating ice caps have shown that
calving may account for roughly 30 % to the total ablation (e.g., Dowdeswell et al.
2002
,
2008
), a significant contribution if widely applicable. Burgess et al. (
2013
) found that
regional-scale losses by frontal ablation in Alaska are equivalent to 36 % of the total
annual net mass loss of the region. Gardner et al. (
2013
) estimated that the present-day
percentage of glacierized area (excluding the ice sheets) draining into the ocean
is * 35 %. Hence, the projections of volume loss, in which only the loss due to the surface
mass balance is modeled, represent a lower bound. However, estimates of frontal ablation
are scarce and lacking on a global scale. Nevertheless, it may be expected that the fraction
of total mass change due to frontal ablation will decrease as warming and terminus retreat
proceed (McNabb et al.
2012
; Colgan et al.
2012
).
4 Glacier runoff
4.1 Effects of glaciers on streamflow
Glaciers significantly modify streamflow both in quantity and timing, even with low
percentages of catchment ice cover (e.g., Meier and Tangborn
1961
; Fountain and
Tangborn
1985
; Chen and Ohmura
1990
; Hopkinson and Young
1998
; see Hock et al.
