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model glacier retreat. Few studies on local scales have incorporated simple parameter-
izations (Stahl et al. 2008 ; Huss et al. 2010 ) into their glacier runoff models; however,
while there are examples of macroscale models using glacier models for local applications
(Zhao et al. 2013 ), we are not aware of any current global-scale watershed models (e.g.,
Hanasaki et al. 2008 ; Wisser et al. 2010 ) incorporating glacier modeling in macroscale
applications. The Randolph Glacier Inventory will further facilitate the inclusion of glacier
mass changes into global hydrology models.
Many studies on various spatial scales have investigated the effects of glaciers on
hydrology under a warming climate. Generally, annual glacier runoff is found to increase
initially due to increased meltwater, followed by reduced flows as glaciers recede, and their
ability to augment flows diminishes. However, contradictory results are reported with
regard to the importance of glacier runoff relative to total runoff in glacierized catchments
(e.g., Weber et al. 2010 ; Huss 2011 ). While this can at least partially be attributed to
differences in physical factors such as climate regimes, catchment size, degree of glaci-
erization, or glacier mass change rates, these differences also depend on the way the glacier
runoff is quantified. In fact, studies on the relative importance of glaciers for runoff are
difficult to compare, because authors use different concepts to compute the contribution of
glaciers to runoff (Table 3 ). Definitions of glacier runoff fall into two principal categories
(Comeau et al. 2009 ): (1) those that only consider the net mass loss component of a glacier
due to glacier wastage, i.e., runoff is zero (Concept 4) or equal to P l -E (Concept 5, Table 3 )
if the glacier is in balance or gains mass, and (2) those that consider all meltwater origi-
nating from a glacier no matter the magnitude or sign of the mass budget (Concepts 1-3,
Table 3 ). It is obvious that for the concepts in (2), glacier runoff generally is much larger
than for the concepts in (1), and consequently the relative importance of glacier runoff to
total runoff will differ between these two categories.
Concepts based on net glacier mass loss are most useful over annual timescales as
they provide a measure for how much water is added to (or withdrawn from) the
hydrological cycle through glacier volume storage changes. In contrast, concepts con-
sidering all meltwater are useful on seasonal timescales in order to assess the effects of
glaciers on seasonal hydrographs. Precipitation that has fallen as snow is released later
during the melt season and hence modulates the seasonality of flow even if the glacier's
annual mass budget is zero. Such concepts are also useful on longer timescales, for
example when physical properties of the meltwater, such as temperature or conductivity,
are of relevance.
Considering only ice or firn melt (Concept 3, Table 3 ) aims to isolate the effects of
glaciers on seasonal or annual flows compared to non-glacierized catchments. Thus, melt
of snow on the glacier surface is excluded from the glacier contribution because this
component also occurs in unglacierized catchments. However, this approach is not
unproblematic since typically some winter snow remains on the glacier by the end of each
melt season, a necessity for a glacier to survive. Hence, in contrast to unglacierized
regions, snowmelt from the glacier surface occurs over the entire length of the summer
(Fig. 2 ) and therefore is a characteristic feature of a glacier that is eliminated in Concept 3.
The surviving winter snow is also directly linked to the glacier system through subsequent
transformation of snow to ice.
Overall, all concepts found in the literature are legitimate, and the choice of concept
will depend on the purpose of the investigation. It is paramount that glacier runoff is
clearly defined to avoid confusion and allow fair comparison between studies.
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