A review of methods for estimating the contribution of glacial meltwater to total watershed discharge

Abstract

Glaciers store water over a range of temporal scales with important implications for downstream human and natural systems. Assessment of the contribution of glacial meltwater runoff to total watershed discharge is an essential part of climate change risk assessment and sustainable water management in glacierized watersheds. Over the past decade, a range of techniques for quantifying the proportional contribution of glacial meltwater has been presented in the scientific literature. Here we examine five different methodological approaches: direct discharge measurement, glaciological approaches, hydrological balance equations, hydrochemical tracers, and hydrological modeling. After a brief summary of the role of glaciers in watershed hydrology, we evaluate each approach, with regard to their respective data requirements, assumptions, and associated uncertainties. Next, we discuss factors that researchers must consider in deciding upon a particular methodological approach, then conclude with a discussion of future research needs. We underscore the need for expanded meteorological, hydrological, and glaciological monitoring networks in glacierized watersheds worldwide, for more comprehensive assessment of uncertainty and for better integration of research with the specific needs of watershed stakeholders.

Keywords

climate change glacier meltwater hydrological modeling hydrological tracers mountain hydrology water resources

I Introduction

Glaciers store water over a range of temporal scales (Jansson et al., 2003) while providing baseflow for downstream water users during periods of otherwise low precipitation (Kaser et al., 2010; Viviroli et al., 2007; Willis, 2005). With an estimated 119 million people worldwide living in watersheds where glacial meltwater comprises at least 50% of total discharge at least one month per year (Schaner et al., 2012), the water resources implications of persistent glacier retreat are worrisome (Barnett et al., 2005). Glaciers in most of the world’s mountain areas are retreating (Barry, 2006; Zemp et al., 2009) and there have already been noticeable changes in hydrological behavior in many watersheds (Casassa et al., 2009). Ice loss is projected to continue and even accelerate under most plausible climate change scenarios (IPCC, 2007b) and water stress is expected to intensify as a result (Bradley et al., 2006; Huss, 2011; Immerzeel et al., 2010). Because meltwater runoff is essentially a non-renewable resource under extended periods of negative glacier mass balance (Immerzeel and Bierkens, 2012), an accurate assessment of the contribution of glacial meltwater runoff to total watershed discharge is an integral part of climate change risk assessment and sustainable water management in glacierized watersheds (Miller et al., 2012; Schaner et al., 2012; Viviroli et al., 2011).

Quantifying the contribution of glacial meltwater in a watershed is a challenging task. The physical processes involved in glacier ablation and watershed hydrology are complex, and measuring the various stores and fluxes incurs large uncertainties (Braun and Aellen, 1990; Miller et al., 2012; Zemp et al., 2013). Detailed hydrological, glaciological, and climatological data are often limited to a small number of easily accessible, well-studied watersheds and downscaling of global data for use at the watershed scale remains problematic, especially in complex mountain environments (Buytaert et al., 2010; Koboltschnig and Schoner, 2011). Furthermore, attempts to directly compare the volume of water produced by a glacier with the volume of water at some point downstream are confounded by highly dynamic climatic (e.g. evaporation), geologic (e.g. groundwater exchange), and human (e.g. irrigation diversions) factors modulating downstream flow (Kaser et al., 2010). Indeed, the very definition of ‘glacier meltwater’ is viewed inconsistently (Hopkinson and Young, 1998), with some researchers including not only ice melt itself, but also seasonal snowmelt or all runoff, including precipitation quick-flow (e.g. Nepal et al., 2013), generated from glacierized portions of a watershed.

Despite such challenges, multiple approaches for quantifying the proportional contribution of glacial meltwater have been presented. These can be classified into one of five different categories that: (1) compare measured discharge at the glacier snout with measured downstream discharge (direct discharge measurement); (2) estimate the water produced by changes in glacier mass (glaciological approaches); (3) estimate glacier meltwater discharge by solving for other components of the hydrological balance (hydrological balance equations); (4) utilize hydrochemical tracers to solve the hydrological balance; and (5) employ hydrological models. Many studies utilize multiple approaches in order to independently validate their results (e.g. Gascoin et al., 2011; Mark and Seltzer, 2003; Nolin et al., 2010). The earliest such studies date from the 1950s, with much work (in German) focused upon conditions in the European Alps, as reviewed by Koboltschnig and Schoner (2011) and Lambrecht and Mayer (2009). With recognition of climate change and its implication for water resources, there has been a rapid expansion in the scientific literature within the past decade, and scenario-based estimates of future glacial meltwater contribution are also increasingly common. While most major mountain areas have been studied, a particular emphasis on present and future conditions in the Himalaya-Hindu Kush region reflects recent controversy over the impact of glacier retreat on the densely settled river basins originating there (e.g. Barnett et al., 2005; Immerzeel and Bierkens, 2012; Immerzeel et al., 2010; IPCC, 2007b; Miller et al., 2012). The European Alps also continue to be a nexus of research, and enough glacio-hydrological modeling studies have now been completed in Austria that a meta-analysis of the relationship between glacierized area and glacial meltwater contribution to discharge was recently presented (Koboltschnig and Schoner, 2011). Table 1 summarizes the literature discussed within this review and Figure 1 illustrates its geographic distribution.

Figure 1.

Locations of studies discussed in this review.

Table 1.

Literature discussed in this review, grouped by primary methodological approach.

Number	Author(s)	Region	Secondary method^a	Basin scale^b	Glacier cover^c	Multiple basins	Nested basins
Direct discharge measurement
17	Gascoin et al., 2011	Central Andes	Glaciological	Micro^*	Low⁺	Y	Y
59	Thayyen and Gergan, 2010	Himalaya – Hindu Kush	Glaciological	Micro	Low	N	N
Glaciological approach
2	Aizen et al., 2007	Tien Shan	(f*)	Macro	Low⁺	Y	N
10	Collier, 1958	Rockies	–	Meso	Mod	Y	Y
20	Henoch, 1971	Rockies	–	Meso	Mod	N	N
21	Hopkinson and Young, 1998	Rockies	–	Meso	Low	N	N
23	Huss, 2011	Alps	(f)	Macro	Low	Y	N
28	Jiskoot and Mueller, 2012	Rockies	–	Macro	Low	N	N
35	Lambrecht and Mayer, 2009	Alps	–	Meso	Mod⁺	Y	Y
36	Liu et al., 2009	Tibetan Plateau	(f)	Macro	Low	N	N
41	Marshall et al., 2011	Rockies	(f)	Macro	Low	Y	N
48	Pelto, 1992	Cascades	–	Meso	Low	Y	N
49	Pelto, 2011	Cascades	–	Meso	Low	N	N
61	Zhang et al., 2008	Tibetan Plateau	–	Macro	Low	N	N
62	Zhang et al., 2011a	Tien Shan	–	Macro	Low	Y	N
63	Zhang et al., 2012	Quillian Mountains	(f*)	Macro	Low	Y	N
Hydrological balance equations
1	Aizen et al., 1996	Tien Shan	–	Meso	Mod⁺	Y	N
5	Baraer et al., 2009	Tropical Andes	–	Micro	Low	N	N
6	Baraer et al., 2012	Tropical Andes	(f)	Meso	Mod	N	N
55	Singh and Jain, 2002	Himalaya – Hindu Kush	–	Macro	Mod	N	N
56	Singh et al., 1997	Himalaya – Hindu Kush	–	Macro	Mod	N	N
Hydrochemical tracers
8	Brown et al., 2006	Pyrenees	–	Micro	Low	N	N
9	Cable et al., 2011	Rockies	–	Meso	Low	N	N
14	Fujita et al., 2007	Tibetan Plateau	–	Micro	High	N	N
33	Kong and Pang, 2012	Tien Shan	–	Meso*	Low	Y	N
38	Mark and Seltzer, 2003	Tropical Andes	Hydro. bal.	Micro	High	Y	N
39	Mark et al., 2005	Tropical Andes	Hydro. bal.	Micro	Low	N	N
40	Mark and McKenzie, 2007	Tropical Andes	–	Meso	Mod	N	N
42	Maurya et al., 2011	Himalaya – Hindu Kush	–	Macro	Low	N	N
46	Nolin et al., 2010	Cascades	Hydro. modeling (f)	Micro	Low	N	Y
Hydrological modeling
3	Akhtar et al., 2008	Himalaya – Hindu Kush	(f*)	Macro*	Mod⁺	Y	N
4	Alford and Armstrong, 2010	Himalaya - Hindu Kush	–	Meso*	Low⁺	Y	N
7	Boscarello et al., 2012	Alps	–	Meso	Mod	N	N
11	Comeau et al., 2009	Rockies	Hydro. bal.	Meso*	Low⁺	Y	Y
12	Farinotti et al., 2012	Alps	(f*)	Micro*	High⁺	Y	N
13	Finger et al., 2012	Alps	(f*)	Macro	Mod	N	N
15	Gabbi et al., 2012	Alps	(f*)	Meso	High	N	N
16	Gao et al., 2012	Tibetan Plateau	(f)	Micro	High	Y	Y
18	Hagg et al., 2007	Tien Shan	(f*)	Micro*	High⁺	Y	N
19	Hagg et al., 2011	Pamirs	(f*)	Meso	Mod	N	N
22	Horton et al., 2006	Alps	(f*)	Micro*	Mod⁺	Y	N
24	Huss et al., 2008	Alps	(f*)	Micro	High	Y	N
25	Huss et al., 2010	Alps	(f*)	Micro	High	N	N
26	Immerzeel et al., 2010	Himalaya – Hindu Kush	(f)	Macro	Low	Y	N
27	Jeelani et al., 2012	Himalaya – Hindu Kush	(f)	Meso	Low	N	N
29	Jost et al., 2012	Rockies	(f)	Macro	Low	N	N
30	Juen et al., 2007	Tropical Andes	(f)	Micro	High	N	N
31	Koboltschnig et al., 2007	Alps	–	Micro	High	N	N
32	Koboltschnig et al., 2008	Alps	–	Meso	Low	N	N
34	Konz et al., 2007	Himalaya – Hindu Kush	–	Meso	High	N	N
37	Loukas et al. 2002	Selkirks	(f*)	Meso	Low⁺	Y	N
43	Mukhopadhyay, 2012	Himalaya – Hindu Kush	–	Macro	Low	N	N
44	Mukhopadhyay and Dutta, 2010	Himalaya – Hindu Kush	–	Macro	Low	N	N
45	Nepal et al., 2013	Himalaya – Hindu Kush	(f)	Meso	Mod	N	N
47	Pellicciotti et al., 2012	Himalaya – Hindu Kush	–	Macro	High	N	N
50	Prasch et al., 2013	Himalaya – Hindu Kush	(f)	Macro	Low	N	N
51	Rees and Collins, 2006	Himalaya – Hindu Kush	(f*)	Meso*	Low⁺	Y	Y
52	Schaefli and Huss, 2011	Alps	–	Micro	High	N	N
53	Schaefli et al., 2005	Alps	–	Micro*	High	Y	N
54	Shahgedanova et al., 2009	Caucasus	(f)	Meso	Mod	N	N
57	Singh et al., 2006	Himalaya – Hindu Kush	(f)	Micro	High	N	N
58	Stahl et al., 2008	Coast Range	(f*)	Meso	High	N	N
60	Verbunt et al., 2003	Alps	–	Micro*	High⁺	Y	N
–	Schaner et al., 2012	Global	–	Macro	Low	Y	N

^a‘Secondary method’ describes studies where multiple methodological approaches have been taken; (f) indicates an additional scenario-based modeling of future glacier meltwater contribution component; (f*) indicates that scenario-based modeling of future glacier meltwater contribution was the sole study objective.

^b‘Basin scale’ describes the overall average size of watersheds in the study area (micro: <100 km²; meso: 100–10,000 km²; macro: >10,000 km²); the notation (*) indicates that the study includes basins at different scales.

^c‘Glacier cover’ describes the overall average proportion of the total watershed area that is covered by glacier ice (low: <10%; moderate: 10–30%; high: >30%); the notation (+) indicates that the study includes basins with different glacier coverages.

In this paper, we review the different methodological approaches that have been employed to estimate the contribution of glacial meltwater to total watershed discharge. After a brief summary of the role of glaciers in watershed hydrology, we evaluate each approach with regard to their respective data requirements, assumptions, and associated uncertainties. Next, we discuss some of the factors that researchers must consider in deciding upon a particular methodological approach, then conclude with a discussion of future research needs. To delimit this review, we consider only research attempting an explicit quantification of current or future glacial meltwater contribution, although there is much additional literature describing the potential hydrological consequences of glacier change more broadly (Barnett et al., 2005; Casassa et al., 2009; Kaser et al., 2010; Miller et al., 2012). We do not impose a singular definition of glacier meltwater beyond what is presented by published papers to represent the total liquid contribution of melted glacier ice that enters the watershed from the glacier snout. We further limit our review to papers published in English-language journals, acknowledging that similar research has been published in German (see Koboltschnig and Schoner, 2011), Russian (see Sorg et al., 2012), and Mandarin (see Liu et al., 2009). We also exclude non-peer-reviewed technical reports and other gray literature.

II The role of glaciers in watershed hydrology

The presence of glaciers has a number of important consequences for the hydrological behavior of a watershed (Chen and Ohmura, 1990b; Fountain and Tangborn, 1985; Jansson et al., 2003; Kaser et al., 2010; Rothlisberger and Lang, 1987; Willis, 2005). Here, we summarize the most salient points and refer readers to the aforementioned literature for a more detailed discussion.

Glaciers store a proportion of total precipitation and modulate downstream river discharge over daily to multi-century timescales (Fleming and Clarke, 2005; Hock et al., 2005; Jansson et al., 2003). The seasonal and interannual modulation of discharge is of particular importance for water supply. On a seasonal basis glaciers ensure a dependable water supply throughout the dry season, while on an interannual basis this ‘glacier compensation effect’ (Lang, 1986; Rothlisberger and Lang, 1987) mitigates the impact of extended meteorological runoff deficits. The glacier compensation effect is maximized when watershed glacier coverage is moderate (∼30–40%; Fleming and Clarke, 2005; Moore, 1992), since more highly glacierized watersheds tend to be small and with a relatively limited elevation range (Willis, 2005). Climatic regime is also a dominant factor modulating the intensity of the glacier compensation effect and thus the potential hydrological significance of glacial meltwater, especially at the macro-watershed scale (Kaser et al., 2010). The value of the glacier compensation effect to water users is well illustrated by conditions in the European Alps during the exceptionally hot, dry summer of 2003. During August, the proportional contribution of glacial meltwater was as much as 12 times greater than normal (Koboltschnig et al., 2008), permitting normal to enhanced hydroelectric production in glacierized watersheds whereas power production was significantly reduced elsewhere on the continent (Koboltschnig and Schoner, 2011). Tropical glaciers behave somewhat differently from those in temperate regions in that ablation occurs year-round rather than seasonally, and annual maxima in accumulation and ablation may be coincident (Kaser and Osmaston, 2002; Wagnon et al., 1999). Nonetheless, they provide the same seasonal and interannual compensating effects, especially in areas with pronounced dry seasons (Mark et al., 2005). The seasonal effect is diminished in monsoonal climates like those of the eastern Himalaya since the ablation season is coincident with the period of heaviest rainfall (Immerzeel and Bierkens, 2012; Miller et al., 2012). Conversely, glacier meltwater becomes more hydrologically significant when the summer monsoon is relatively weak.

Glaciers modulate discharge at different temporal and spatial scales, so that the proportional contribution of glacial meltwater is highly variable in both place and time. Koboltschnig et al. (2008) quantify the contribution of glacial meltwater to discharge in the upper Salzach watershed (Austria) and find that while the contribution for 1999–2000 hydrological year was only ∼1%, the contribution for August of 2000 was ∼4% and, on 26 August 2000, the contribution was 12%. In the climatically extreme year of 2003, the August contribution was 58%. Glaciers generally contribute a much greater proportion of total discharge than would be expected given the proportion of the watershed that is glacierized, at least on a seasonal basis. Mark et al. (2005) find that glaciers contribute as much as 40% of dry season discharge in the Rio Santa watershed (Peru) despite covering only 8% of the watershed area, while Jost et al. (2012) estimate glacier-derived waters to be 25–35% of August/September inflow to the Mica Reservoir (British Columbia, Canada) despite the watershed having only 5% glacier coverage.

Unsurprisingly, glacial meltwater provides a higher proportion of total discharge as one approaches the glacierized headwaters of a watershed, while input from other water sources such as precipitation and groundwater discharge increase as the watershed area grows larger (Immerzeel et al., 2010). In some areas, the hydrological significance of meltwater may be negligible at the macro-watershed scale despite the presence of large glaciers in the headwaters area (Immerzeel, 2008; Rees and Collins, 2006). Again, this is largely a function of climatic regime. Glaciers in highly arid regions such as the western Himalaya, Central Asia, and the central Andes are a very important component of discharge even at the macro-watershed scale (Kaser et al., 2010). In the densely populated Indus River basin, for example, glacier meltwater contributes an estimated 26% of total annual discharge despite watershed glacier cover being only 2.2% (Immerzeel et al., 2010). The same can hold true even in more temperate climatic regimes during the driest, warmest months. Nearly 4% of the Danube River discharge entering the Black Sea in September is of glacial origin despite 0.06% glacier area coverage (Huss, 2011).

Considering the prognosis for enhanced atmospheric warming in the centuries ahead (IPCC, 2007a), understanding the potential evolution of glacial meltwater contribution in response to extended glacier retreat is an increasingly prominent area of research. Under conditions of net mass loss, discharge from glacierized watersheds will initially increase due to the glacier compensation effect. However, if net mass loss persists, glaciers will at some point pass a critical threshold whereby shrinking ice mass can no longer sustain elevated discharge (Braun et al., 2000). Casassa et al. (2009) analyze discharge data from glacierized watersheds worldwide to determine their state relative to the critical threshold and found that rivers in Central Asia (Tien Shan Mountains and Central Tibet), the Peruvian Andes, the northern Canadian cordillera, and highly glacierized watersheds in the European Alps were generally exhibiting increased runoff, while those in the southern Canadian cordillera, the central Chilean Andes, and more modestly glacierized European watersheds had already experienced diminished discharge. Baraer et al. (2012) incorporate both discharge volume and variability characteristics in identifying four phases of discharge response to extended glacier retreat. During the first phase, annual discharge increases and interannual discharge variability decreases in response to the enhanced input of meltwater. Phase two begins when interannual variability reaches a minimum and begins to increase; while annual discharge continues to increase, the rate of increase begins to slow. The transition to phase three represents the passing of the critical threshold after which discharge begins to steadily decrease while interannual variability continues to increase. The final stage occurs only when glacier retreat ceases (or deglaciation is complete) and both annual discharge and interannual discharge variability reach a new equilibrium state.

III Methodological approaches

We describe five categories of methodological approaches that have been developed for quantifying the contribution of glacial meltwater to watershed discharge. Table 2 summarizes each method, its essential data requirements, controlling assumptions, and key sources of uncertainty.

Table 2.

Summary of methodological approaches for estimating the contribution of glacier meltwater to total watershed discharge.

Approach	Appropriate spatial scale(s)	Appropriate temporal scale(s)	Primary advantages	Primary sources of uncertainty	Measurement type	Dependence on existing data	Differentiates glacier melt from wastage
Direct discharge measurement	Micro	Hourly; other scales possible with repeated measurements or installation of reliable gauges	Simple technique; no existing data needed	Inability to differentiate seasonal snowmelt and precipitation runoff originating above the glacier tongue; difficulty in routing all glacier meltwater past a measuring gauge; measurement error	Discrete	Low	No
Glaciological	Micro to meso (macro if geodetic mass balance approaches used)	Annual to decadal (can be scaled to shorter timescales with climate data)	Potentially the most precise; leverages existing mass balance data	Extrapolation of point mass balance or energy balance measurements across all glacier surfaces (direct and energy balance approaches); DEM error (geodetic approach); accuracy of area/volume scaling equations (geodetic approach); unquantified loss of glacier melt to other hydrological pathways; measurement error	Averaged	High	Yes (if direct mass balance measurements are used)
Hydrological balance equations	Micro to meso (high uncertainty at macro)	Monthly to decadal (longer timescales may be more accurate)	Measurement of some non-glacial terms is relatively simple; existing data may be available	Interpolation of hydrological balance terms from limited point measurements; measurement error (especially with precipitation); difficulty accounting for evaporation, sublimation and groundwater exchange	Averaged	High	No
Hydrochemical tracers	Micro to meso	Daily; other scales possible with repeated measurements	No existing data needed; water sampling easy/inexpensive (though laboratory analysis is required); captures temporal and spatial variations in contribution	Lack of heterogeneity of end-member chemical signatures within watershed; end-member chemistry that is not conservative; inability to differentiate some end-members in certain chemical environments	Discrete	Low	No
Hydrological modeling	Any (depends on input data)	Hourly to decadal	Potentially applicable at a range of temporal/spatial scales; provides hypothesis testing capabilities; can pinpoint areas where additional processes knowledge is needed	Measurement error of input data; interpolation/rescaling of measured input data; equifinality; model simplification of complex processes	Depends on model time-step	High	Yes (depending on model design)

1 Direct discharge measurement

A comparison of streamflow measurements taken immediately downstream of the glacier tongue with those taken simultaneously at points farther downstream (accounting for water transit time) offers the simplest, least data-intensive approach for quantifying glacier contribution to total watershed discharge (Gascoin et al., 2011; Nolin et al., 2010; Thayyen and Gergan, 2010). The presence of existing stream gauge infrastructure and/or the relatively simple and inexpensive installation of small, continuously recording discharge loggers, makes the direct measurement approach a potentially attractive option. However, the logistical requirements of installing and maintaining measuring devices effectively restrict this approach to watersheds where all glaciers have easily accessible tongues. Furthermore, there are multiple factors which combine to produce relatively high levels of uncertainty, thus the application of this approach has been limited to validation of estimates obtained via one of the more complex methods described below.

The direct measurement approach requires two fundamental assumptions: (1) that all of the water draining from the glacier tongue is of glacial origin; and (2) that all of the glacial meltwater within the watershed is measured at the first stream gauge. The first assumption is challenged by the fact that water flowing from glaciers is nearly always some combination of melting ice, melting seasonal snow cover on the glacier surface (i.e. wastage and melt; see Hopkinson and Young, 1998), and direct precipitation runoff, so proportional estimates of glacier contribution made using this approach will typically be unable to isolate true glacial meltwater from other components. Additionally, since some proportion of the surface area upstream from the glacier tongue will be ice-free (e.g. bare moraine slopes, exposed rock faces), the water measured at the tongue will also include surface runoff from these non-glacier areas. For example, Thayyen et al. (2005) estimate that 10–26% of the water measured at the tongue of a glacier in the Indian Himalaya was monsoonal precipitation runoff. Thayyen and Gergan (2010) recommend installing a rain gauge at some point above the glacier tongue during the melt season to help quantify this contribution. The second assumption ignores the potential for infiltration at the glacier bed whereby meltwater reappears at the surface some distance downstream from the glacier tongue (Favier et al., 2008) as well as the possibility that other, non-visible ice bodies such as debris-covered and rock glaciers may also contribute to watershed discharge (Gascoin et al., 2011). Nolin et al. (2010) find significant discrepancies in their estimate of glacial meltwater contribution to one of the sub-watersheds in the Oregon Cascades (31% via direct discharge measurement versus 88% ± 5% via hydrochemical tracer) and speculate that a primary cause was their inability to measure all of the discharge issuing from all of the glacier ice in that watershed.

There is often considerable uncertainty associated with the volumetric measurement of flowing water due to the technical limitations of measuring equipment, the need to interpolate/extrapolate point discharge measurements to create stage-discharge rating curves, and the frequent presence of unsteady flow conditions (Di Baldassarre and Montanari, 2009; Soupir et al., 2009). Furthermore, the highly dynamic channel conditions of the pro-glacial environment – where frequent shifts in course, sudden surges, and high sediment loads are common – may result in an even greater level of measurement error than would occur in non-glacial streams (Nolin et al., 2010). Researchers may be forced to compensate for these conditions by establishing their first gauges at more stable locations hundreds of meters below the glacier tongue (e.g. Thayyen and Gergan, 2010), though doing so increases the uncertainty that all of the water being measured is of glacial origin.

2 Glaciological approach

If the volume of ice melting from glaciers in a watershed can be determined, the volumetric water equivalent can be compared to downstream measured streamflow to determine the proportional contribution of glacial meltwater to total discharge. Some of the earliest attempts at quantifying the glacial meltwater proportion of watershed yield applied this glaciological approach by leveraging existing glacier mass balance, climate, and discharge data (Collier, 1958; Henoch, 1971), and it continues to be employed in watersheds where glacier monitoring programs are well established (e.g. Huss, 2011; Lambrecht and Mayer, 2009; Pelto, 2011).

Three different methods for estimating the volume of melted ice are used. The most common utilizes direct mass balance measurements obtained from ablation stake networks (Lambrecht and Mayer, 2009; Pelto, 1992, 2011). Depending upon the inclusion/exclusion of water-equivalent accumulation data, this approach can be used to quantify the contribution from either glacier ‘melt’ (water generated from melting ice in the ablation area exclusive of glacier mass balance state), or ‘wastage’ alone (water generated by net ice loss only when the glacier is in a negative mass balance state; Hopkinson and Young, 1998). A fundamental assumption is that the mass balance calculation derived from a sample of surface measurements is truly representative of accumulation and ablation rates over the entire glacier (Collier, 1958; Marshall et al., 2011). In reality, glaciers can experience wide variation in point-measured mass balance behavior due to variable topography and patterns of snow distribution (Konz and Seibert, 2010), providing a potential source of notable uncertainty. A dense stake network can ameliorate this uncertainty to some degree (Pelto, 2011), though stake networks are often limited to accessible parts of the glacier surface, giving a potentially skewed estimate of mass balance. Furthermore, because ablation stake networks are typically limited to a small number of glaciers within a region, it is usually necessary to extrapolate these data to represent the volumetric contribution of glacial meltwater at the watershed scale (e.g. Hopkinson and Young, 1998; Huss, 2011; Marshall et al., 2011). Such extrapolation introduces further uncertainty given the highly heterogeneous nature of ablation within individual glaciers as well as between glaciers featuring different headwall elevations, aspects, slope gradients, and basin morphologies (Benn and Lehmkuhl, 2000). Mass balance estimates based on ablation stake data will also be subject to both systematic and random measurement errors (Zemp et al., 2013), which also propagate into uncertainty about the actual volume of glacier meltwater released into the watershed.

Comparison of multi-temporal remote-sensing products such as digital elevation models (DEMs) (Huss, 2011; Jost et al., 2012) or volumetric estimates based on 2D data sources such as imagery or maps (Farinotti et al., 2009; Marshall et al., 2011) offers a second method for estimating changing ice volume, particularly where direct mass balance measurements are unavailable. Assuming complete data coverage, these techniques have the advantage of providing measured volumetric change estimates for all glaciers in the watershed. A limitation of this geodetic approach is that it cannot account for meltwater that is generated when the glacier is in an overall positive mass balance state. High-resolution DEMs can be generated from techniques such as conversion of existing contour maps (Racoviteanu et al., 2007), photogrammetry (Lambrecht and Kuhn, 2007), and airborne or terrestrial laser scanning (LIDAR) (Hopkinson and Demuth, 2006). The free availability of satellite-derived DEMs from the Shuttle Radar Topography Mission (SRTM) and the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) (Paul and Haeberli, 2008) make these coarser DEMs (90 m and 30 m, respectively) a popular option, though coarser resolution limits use to glaciers with relatively larger surface areas. All DEMs will have some quantity of error (Frey and Paul, 2012) that directly influences the uncertainty associated with the resulting estimate of glacial meltwater volume. The relatively poor vertical accuracy of ASTER DEMs (Fujisada et al., 2005), especially over ice and water, makes this product particularly problematic in this regard (Racoviteanu et al., 2007).

Where multi-temporal DEMs of sufficient quality are unavailable, an alternative method for quantifying ice volume change is to estimate initial and final glacier volumes based on 2D representations of glacier area obtained from aerial or satellite imagery or recent large-scale maps. Empirical equations based on the physical relationship between glacier surface area and volume have been developed (Bahr et al., 1997; Chen and Ohmura, 1990a). Variables within the equation adjust for specific conditions such as tropical glaciers or glaciers located on volcanoes. Empirical scaling relationships will introduce a great deal of uncertainty into estimates of ice volume loss on individual glaciers through time (up to 50% error; Marshall et al., 2011), though it is argued that the error is reduced as a greater number of glaciers are considered based on the assumption that the measurement mean will approach the true mean in a normally distributed data set (Comeau et al., 2009; Marshall et al., 2011). Glacier volume has also been approximated using ice thickness-glacier surface slope equations (Farinotti et al., 2009; Huss, 2011; Immerzeel et al., 2012). Nevertheless, Farinotti et al. (2009) find that differences between estimated ice depth using this method and measured ice depth were between 20% and 30% for four Swiss glaciers. Given the cascading uncertainties that result from multiple estimates representing before/after conditions, hydrological conclusions drawn from such a reckoning must be treated with caution (Marshall et al., 2011).

A third approach to estimating the volume of melted ice involves the use of energy balance models (Jiskoot and Mueller, 2012) or temperature-index models (Aizen et al., 1996; Liu et al., 2009; Zhang et al., 2008, 2011a). Energy balance models compute the amount of meltwater generated by a glacier based on the state of controlling variables such as air temperature, humidity, radiative fluxes, wind velocities, and surface albedo (Arnold et al., 1996; Hock and Holmgren, 2005; Oerlemans and Klok, 2002). Such models are useful because output is controlled by the physical conditions that result in ice melt, though they remain limited in their ability to capture all of the complex processes that drive ablation as well as their ability to sufficiently represent the variable conditions that exist across the glacier surface (Jiskoot and Mueller, 2012) or throughout the watershed. Temperature-index (also known as degree-day) models are based on the empirical relationship between atmospheric temperature and glacier ablation (Hock, 2003; Ohmura, 2001). They have the additional advantage of providing information about historic glacier meltwater contributions to discharge, since temperature and discharge are generally the most readily available and highest-quality data over decades past (Liu et al., 2009). Furthermore, because temperature is generally more persistent across large areas than are other energy balance parameters, the uncertainty associated with extrapolation to the watershed scale may actually be reduced using this technique. In several instances, temperature-index models have been used as stand-alone tools for estimating the current (e.g. Zhang et al., 2008, 2011a) and future (e.g. Aizen et al., 2007; Zhang et al., 2012) contribution of glacier meltwater.

Certain assumptions, uncertainties, and limitations are inherent in the glaciological approach regardless of the specific technique used to estimate the volume of water generated by glacier melt. By excluding other components of the hydrological cycle, this approach assumes that all lost glacier mass is converted to water volume that enters and remains in the stream channel as far as the first discharge measurement point. Researchers typically justify this by assuming that sublimation and evaporation in high mountain watersheds are minimal relative to the amount of meltwater generated by a glacier (Jiskoot and Mueller, 2012; Pelto, 2011) and that steep slopes and extensive areas of exposed bedrock limit infiltration while producing rapid runoff (Lambrecht and Mayer, 2009). In arid climates, however, sublimation can be a significant factor in glacier mass balance (e.g. Gascoin et al., 2011), and the turbulent conditions of many alpine streams – a function of their frequently steep gradients and obstructed channels – may enhance evaporation (Hopkinson and Young, 1998). The glaciological approach also assumes that both the measured loss of ice mass and measured discharge are reasonably accurate, though both components are subject to considerable uncertainties as described above (Bamber and Rivera, 2007; Di Baldassarre and Montanari, 2009; Zemp et al., 2013).

Depending upon the method chosen for calculating glacier mass change, the application of the glaciological approach limits some of the conclusions that can be drawn about the contribution of glacial meltwater to total watershed discharge, particularly over varying timescales. If direct mass balance measurements are only obtained on an annual basis, the intra-annual variation of glacier meltwater and its role in buffering seasonal periods of otherwise low flow will be difficult to quantify unless it can be assumed that ablation occurs only during a specific set of months (Pelto, 2011) or some sort of temperature-index ablation scaling relationship can be used (Lambrecht and Mayer, 2009). Multiple mass balance measurements made during the course of the hydrological year will help obviate this weakness; however, such data are typically limited to relatively easily accessed sites where long-term glaciological monitoring programs have been established (e.g. Huss, 2011; Pelto, 2008, 2011). The geodetic approach is even more limited in this regard since the epoch between different ice volume estimates may extend across decades except in a few exceptionally well-studied areas such as the European Alps (e.g. Huss, 2011). This is one area where energy balance models offer a distinct advantage, given that they can quantify glacier meltwater over very short periods of time (hourly or daily) rather than providing only a lumped contribution estimate.

3 Hydrological balance approach

The hydrological balance approach is a relatively simple technique premised on mass conservation in the hydrological cycle. Various components of the water cycle are quantified such that one remaining unknown, typically glacier melt, can be estimated from measured discharge. The basic hydrological balance equation may be stated as:

Q = P + Δ G - G_{W} - E

where Q is total discharge from the glacierized watershed, P is precipitation, ΔG is change in glacier storage, G_W is groundwater flux and E is net evapotranspiration (Mark and Seltzer, 2003). Balance equations may be further simplified if the assumption that evapotranspiration and/or groundwater flux are minimal in high mountain watersheds can be justified (Aizen et al., 1996; Mark et al., 2005). Conversely, the balance equation can be rendered significantly more complex if processes such as sublimation and differential evaporation (as a function of land cover type) are considered (Baraer et al., 2012). The hydrological balance may be calculated for a specific season in which glacier meltwater is expected to be at a maximum, over the entire hydrological year, or even for an aggregated collection of years. Decadal balance calculations are viewed as advantageous based on the assumption that interannual variability in precipitation, groundwater fluxes, and soil moisture status will tend towards zero over an extended period of time (Baraer et al., 2012; Singh et al., 1997).

Accurate watershed-scale quantification of each term in the water cycle is limited by measurement error and the uncertainty of basin-wide extrapolation of point observations. Stream discharge and precipitation are challenging variables to measure accurately (Legates and Willmott, 2006; Wood et al., 2000). Precipitation is also the most difficult component to interpolate since local factors such as elevation, aspect, vegetative cover, and wind patterns result in very high spatial heterogeneity (Mark and Seltzer, 2003; Mark et al., 2005). This uncertainty is compounded by the fact that pertinent data may only be available from meteorological stations located at lower-elevation sites, where hydro-climatic conditions are likely to be considerably different than those farther upstream. The precipitation measurement challenge can make it difficult to differentiate glacier meltwater from seasonal snowmelt (Mark et al., 2005), and some studies report only an aggregated glacier melt/seasonal snowmelt term (e.g. Singh and Jain, 2002; Singh et al., 1997), prohibiting direct comparison with studies that are able to isolate the two.

Evaporation and sublimation are also challenging to quantify in mountain watersheds, where few direct observations are maintained. Some studies exclude them completely (e.g. Baraer et al., 2012), while others use minimal empirical information to estimate them. Given a lack of local data, Mark and Seltzer (2003) apply an evaporation factor to their precipitation measurements based on data obtained at a site hundreds of kilometers away, while Singh and Jain (2002) and Singh et al. (1997) are forced to extrapolate evaporation obtained from a single evaporation pan across seasonal snow-free areas in watersheds of 22,200 km² and 22,305 km², respectively. In the latter two cases, evaporation from snow-free areas is estimated, but sublimation from snow- and ice-covered areas is not. In arid mountain watersheds with strong winds and high solar radiation, sublimation can be a substantial component of the water cycle. In the arid Chilean Andes, Gascoin et al. (2011) estimate that sublimation reduced annual discharge by as much as 10%.

4 Hydrochemical tracer approaches

Waters of different provenance tend to have unique hydrochemical signatures as a result of the specific hydrological, geological, and biological processes to which they have been exposed (Drever, 1997). Thus, it is possible to quantify the proportion of hydrochemical ‘end-members’ to streamflow by analyzing the water chemistry (Christophersen and Hooper, 1992). Conservative chemical constituents in natural waters such as stable isotopes and major solutes can serve as tracers that can be used to reconstruct the hydrological routing of an end-member (Hooper and Shoemaker, 1986). Hydrochemical tracer approaches to quantifying the contribution of glacial meltwater to watershed discharge thus isolate the hydrochemical signature of the meltwater and employ volumetric mixing models to estimate its proportional contribution to streamflow (Mark et al., 2005). The simplest mixing models differentiate two end-members (glacial and non-glacial) in a ‘concentration space’ such as a Piper diagram (Mark et al., 2005), though more complex mixing models that distinguish a greater number of end-members (e.g. glacier melt, surface runoff, and groundwater discharge) are possible using Bayesian and other statistical analysis techniques (Baraer et al., 2009; Cable et al., 2011).

The hydrochemical tracer approach is reliant upon several key assumptions. The most fundamental is that the hydrochemical signatures of various end-members are sufficiently distinct. Similarly, the approach assumes that the tracer being employed is conservative within the study watershed, meaning that no additional isotopic fractionation or solute-altering chemical reaction has taken place along the flow path between source and mixing point (Baraer et al., 2009; Mark et al., 2005). The chemical characteristics of the mixed stream water must solely be a function of the proportions of the respective end-members that have been mixed into it rather than any post-mixing chemical processes, otherwise the mass of the solute in the mix will not be representative of the proportional input from each end-member (Christophersen et al., 1990). Hydrochemical tracer approaches also assume that chemical characteristics defining each end-member capture the range of natural hydrochemical variation that each water source might experience. For example, ‘glacier meltwater’ is typically a mixture of waters originating from different ablation processes and englacial pathways that are subject to differential isotopic fractionation and chemical reactions (Nolin et al., 2010; Sharp et al., 1995), while meltwater derived from different glaciers within a single watershed may be chemically distinct due to factors such as bedrock geology, ice flow rate, and subglacial drainage patterns that can be unique to each glacier (Yuanqing et al., 2001). Groundwater signatures may be similarly variable given that solute concentrations are influenced by the specific geology in the immediate vicinity of the flow paths, something that is often highly heterogeneous in mountain environments (Brown et al., 2006). This assumption of minimized end-member variability can also be a limiting factor in efforts to use hydrochemical tracers to describe the seasonal variation of glacial meltwater contributions to discharge, since any temporal variation in the mixed water chemistry must be assumed to represent changing proportional contributions from each end-member (e.g. Maurya et al., 2011).

Despite the limitations of these assumptions, the hydrochemical tracer approach has a number of notable advantages over other techniques. First, tracer analyses do not require the detailed, often long-term glaciological and meteorological observations needed for each of the other approaches since one sampling suite is sufficient to provide a reasonable snapshot of the watershed if made during baseflow conditions. Second, they do not require an explicit calculation of hydrological parameters that can be very difficult to accurately measure in the field, such as groundwater exchange and evapotranspiration (Kong and Pang, 2012; Mark et al., 2005). Third, obtaining hydrochemical data is easy and inexpensive, even in remote watersheds (Mark and Seltzer, 2003; Nolin et al., 2010), notwithstanding the costs of laboratory analysis that may present financial challenges for researchers/institutions with limited resources. Fourth, depending upon the sampling design and hydrochemical characteristics of the watershed, hydrochemical tracers can be very effective at capturing variation in glacial meltwater contributions at high temporal and spatial resolutions (Brown et al., 2010; Kong and Pang, 2012).

Given the requisite assumptions of this approach, some studies are limited to a simplified partitioning of watershed discharge without explicit terms of uncertainty. For example, Mark and Seltzer (2003), using both isotopes and solutes, only classify water as glacial meltwater or precipitation-derived runoff, while Fujita et al. (2007), using solutes (as measured by electroconductivity), differentiate only glacial meltwater and soil water. It can be very difficult to know with high confidence whether or not the hydrochemical signatures of various components are sufficiently uniform to support the assumption of end-member uniqueness (Nolin et al., 2010), especially when a relatively small number of samples are used to characterize each component within the watershed. It can be similarly difficult to know whether or not a tracer is conservative, especially in highly dynamic, geologically heterogeneous mountain watersheds (Mark and Seltzer, 2003). An additional area of uncertainty is associated with the hydrochemical differentiation of glacier ice and seasonal snow melt (Cable et al., 2011).

Stable isotopes of water (¹⁸O and ²H) (e.g. Cable et al., 2011; Mark and McKenzie, 2007; Nolin et al., 2010) and various solutes (e.g. major ions such as Ca²⁺, Na⁺, Cl^-, and SO₄ ² ^-) (e.g. Brown et al., 2006; Mark et al., 2005) are the tracers most commonly employed in end-member mixing analysis. Stable isotopes are useful because different hydrological components are exposed to different fractionation processes as they transit the water cycle (Kendall and McDonnell, 1998). The relationship between ¹⁸O and ²H within a water sample, known as deuterium-excess, is also a useful tracer since it is strongly controlled by the amount of evaporation to which the water has been exposed (Maurya et al., 2011). Solute concentrations are appropriate tracers because different components of the water cycle tend to be dominated by different ions. For example, precipitation tends to have high proportional concentrations of Cl^-, since atmospheric vapor evaporated from salty oceans will contain this ion, but low proportional concentrations of ions such as Ca²⁺ and Mg²⁺ that are largely derived from bedrock. Because many solute concentrations are controlled by both rock type and residence time in the geologic system, an observed change in the solute concentration is often a strong indication of a change in dominant water source within the watershed (Brown et al., 2006). Because stable isotopes are especially effective for distinguishing glacier meltwater from precipitation and snowmelt while solutes are most effective for differentiating groundwater from other hydrological components, many studies incorporate both tracer approaches in their analyses (e.g. Baraer et al., 2009; Kong and Pang, 2012; Mark and Seltzer, 2003; Maurya et al., 2011). Electrical conductivity has also been used as a tracer, since it reflects the overall ionic concentration of the water (Fujita et al., 2007; Kong and Pang, 2012; Maurya et al., 2011) but there is disagreement about whether or not it meets the requirement for being conservative in the watershed (Moore et al., 2008; Sharp et al., 1995).

5 Hydrological models

Hydrological modeling represents the most frequently applied approach to quantifying the proportional contribution of glacial meltwater. Models generally employ a set of nested equations that solve the water balance while simulating the spatial and temporal variation of various hydrological components such as precipitation, groundwater fluxes, seasonal snowmelt, and ice melt. Because models are designed to use local meteorological, glaciological, and hydrological data to simulate hydrological processes, they can improve our understanding of observed processes within a watershed (Verbunt et al., 2003) and can help pinpoint areas where knowledge is lacking, additional measurements are needed, and uncertainty is greatest (Pellicciotti et al., 2012). Models are also very useful for testing hypotheses such as how discharge responds to changing climate (e.g. Koboltschnig et al., 2007) and/or different water management decisions (e.g. Jeelani et al., 2012).

There are two general classes of hydrological models (Farinotti et al., 2012). Physically based models are based on the governing physical principles that drive hydrological response to climatic and other biophysical conditions. These models often produce results with the highest temporal resolution and the lowest uncertainties; however, they generally require a great deal of input data, are computationally intense (Koboltschnig et al., 2008), and thus are usually limited in application to smaller watersheds where extensive monitoring provides verification (Boscarello et al., 2012; Huss, 2011). Conceptual models use statistical relationships based on past hydro-climatic observations to simulate hydrological behavior without resolving small-scale physical processes (Hagg et al., 2011). This approach simplifies the amount of input data needed (excluding, for example, wind and radiative flux data), making them more appropriate for use in watersheds in remote areas where limited data have been accumulated. Conceptual models are, however, more prone to the problem of ‘equifinality’ (Hagg et al., 2011), the condition whereby different combinations of model parameters produce the same output, that is a primary source of uncertainty in hydrological modeling (Beven, 2006). Furthermore, because conceptual models are developed for specific locations and epochs, they are not transferable in space or time. While some researchers develop new glacio-hydrological models specifically for their study (e.g. Jeelani et al., 2012; Rees and Collins, 2006; Schaefli et al., 2005), most incorporate glacier melt modules into existing hydrological models such as HBV and its variants (Gao et al., 2012; Jost et al., 2012; Shahgedanova et al., 2009), SRM (Immerzeel et al., 2010; Nolin et al., 2010), or PREVAH (Koboltschnig et al., 2007, 2008) (Table 3). Some modeling studies do not explicitly quantify the proportional contribution of glacial meltwater but rather describe only overall discharge patterns (e.g. Mukhopadhyay and Dutta, 2010); these are nonetheless included in this review since they are subject to the same assumptions and uncertainties.

Table 3.

Hydrological models adapted for studies quantifying the contribution of glacier meltwater to watershed discharge.

Model	Model class	Authors^(a)	Spatial discretization^(b)	Time-step	Standard input data^(c)
FEST-WB	Conceptual	Boscarello et al., 2012	Gridded (500 m)	Hourly	Air temperature; precipitation; runoff; snow cover; topography; soil characteristics; glacier area
HBV	Conceptual	Hagg et al., 2007 (HBV-ETH) (f) Akhtar et al., 2008 (f) Stahl et al., 2008 (f) Shahgedanova et al., 2009 (HBV-ETH) (f) Hagg et al., 2011 (f) Gao et al., 2012 (HBV-Light) (f) Jost et al., 2012 (HBV-EC) (f)	HRU	Daily	Air temperature; precipitation; runoff; topography; land cover; glacier area
GERM	Conceptual	Huss et al., 2008 (f) Huss et al., 2010 (f) Farinotti et al., 2012 (f) Gabbi et al., 2012 (f)	Gridded (25 m)	Daily	Air temperature; precipitation; runoff; topography; land cover; glacier volume
GSM-SOCONT	Conceptual	Schaefli et al., 2005 Horton et al., 2006 (f) Schaefli and Huss, 2011	HRU	Daily	Air temperature; precipitation; potential evapotranspiration; runoff; glacier area; glacier mass balance
ITGG-2.0 R	physically-based	Juen et al., 2007 (f)	HRU	Monthly	Air temperature; precipitation; runoff; solar radiation; albedo; atmospheric emissivity; proportion of sublimation to melting; glacier area
J-2000	Conceptual	Nepal et al., 2013 (f)	HRU	Daily	Air temperature; precipitation; sunshine hours; wind speed; relative humidity; soil characteristics; glacier area
OEZ	Conceptual	Hagg et al., 2007 (f)	HRU	Monthly	Air temperature; precipitation; runoff; topography; land cover; glacier area; glacier mass balance
PREVAH	Conceptual	Koboltschnig et al., 2007 Koboltschnig et al., 2008	HRU	Hourly	Air temperature; precipitation; humidity; wind speed; sunshine duration; solar radiation; land cover; runoff; glacier area; glacier mass balance
PROMET	physically-based	Prasch et al., 2013 (f)	Gridded (1 km)	Hourly	Air temperature; precipitation; topography; land cover; glacier area
SNOWMOD	Conceptual	Singh et al., 2006 (f)	HRU	Daily	Air temperature; precipitation; runoff; glacier area
TOPKAPI	physically-based	Finger et al., 2012 (f) Pellicciotti et al., 2012	Gridded (250 m)	Daily	Air temperature; precipitation; snow cover; runoff; solar radiation; land cover; glacier volume
SRM (Snowmelt Runoff Model)	Conceptual	Immerzeel et al., 2010 Nolin et al., 2010	HRU	Daily	Air temperature; precipitation; snow cover; glacier area
TAC^D	Conceptual	Konz et al., 2007	Gridded (200 m)	Daily	Air temperature; precipitation; runoff; topography; glacier area
UBC Watershed	Conceptual	Loukas et al., 2002 (f)	HRU	Hourly	Air temperature (max and min); precipitation; runoff; topography; land cover; glacier area
Variable Infiltration Capacity	physically-based	Schaner et al., 2012	Gridded (0.25°)	3-hourly	Air temperature; precipitation; wind speed; topography; soil characteristics; land cover; glacier area
WaSiM-ETH	physically-based	Verbunt et al., 2003	Gridded (100 m)	Hourly	Air temperature; precipitation; vapor pressure; solar radiation; wind speed; sunshine duration; topography; soil characteristics; land cover; glacier area
WATFLOOD	Conceptual	Comeau et al., 2009	HRU	Daily	Air temperature; runoff; topography; land cover; glacier area

(f) indicates an additional scenario-based modeling of future glacier meltwater contribution component.

HRU = Hydrological Response Units. For gridded spatial discretization, the highest applied grid-cell resolution is given.

Includes data used for model calibration (usually runoff and/or glacier mass balance).

Models can operate at temporal resolutions ranging from hourly (e.g. Koboltschnig et al., 2008; Prasch et al., 2013; Verbunt et al., 2003) to monthly (e.g. Juen et al., 2007; Mukhopadhyay, 2012), and spatial resolutions ranging from as little as 25 m (e.g. Schaefli et al., 2005) to many kilometers (e.g. Comeau et al., 2009; Schaner et al., 2012), both of which greatly influence the nature of the information provided by the model. Models with shorter time-steps require more detailed input data and greater computing power/time (Verbunt et al., 2003), which may be limiting factors as the size of the modeled watershed increases. The coarse spatial resolutions necessary for modeling large watersheds typically require a greater number of simplifying assumptions and more generalized parameters (Schaner et al., 2012).

Model parameters fall into two categories: empirical parameters determined from field measurements or statistical relationships that generally have some physical basis; and calibration parameters determined during the model tuning process (Zhang et al., 2011b). As the number of calibration parameters increases, model uncertainty increases in response to the elevated risk of equifinality (e.g. Gao et al., 2012; Konz et al., 2007). Model performance is thus a function of empirical parameter quality, with uncertainty increasing as data become less temporally or spatially complete (Gao et al., 2012; Mukhopadhyay, 2012; Nepal et al., 2013). A lack of data also leads to increased uncertainty due to necessary reductions in model complexity and increases in calibration parameters. Recent research has focused on improving modeling in otherwise data-poor watersheds by developing techniques for acquiring data via remote sensing and improving downscaling of macro-scale data sets (Konz and Seibert, 2010; Prasch et al., 2013).

As with other methodological approaches to quantifying the contribution of glacier meltwater, researchers must make explicit their key assumptions and simplifications: for example, assumptions about the accuracy of extrapolated climate data, the routing of meltwater through downstream hydrological systems (e.g. Comeau et al., 2009), or the explicit conditions causing ablation (Farinotti et al., 2012). Modeling studies may assume that the data used to calibrate and validate the model are error-free and thus that discrepancies between simulated and measured outputs are due to problems with model parameterization rather than potential measurement error (e.g. Prasch et al., 2013). Conversely, it can also be tempting to overly trust the model rather than field measurements when there are large discrepancies between the two, even when there is no direct evidence that the measurements are erroneous (e.g. Mukhopadhyay and Dutta, 2010).

There are numerous sources of uncertainty in the hydrological modeling approach, including those associated with model structure, those associated with parameterization of the model, and those associated with equifinality. Structural uncertainty is enhanced for conceptual models that are not explicitly constrained by guiding physical processes, such as a glacier evolution model that does not incorporate ice flow mechanics (e.g. Farinotti et al., 2012). Indeed, because different models forced with the same parameter set may produce considerably different results (e.g. Hagg et al., 2007), selection of the most appropriate model remains a key challenge (Huss et al., 2010). One of the most critical structural decisions a researcher using the modeling approach must make is whether to employ an energy balance or temperature-index melt module. The greater simplicity and lower data requirements of the temperature-index approach make it an attractive option, and though temperature does correlate with other important factors such as radiation and wind patterns, their exclusion will increase uncertainty (Gabbi et al., 2012). So-called ‘enhanced temperature-index’ models that incorporate radiative fluxes can mitigate this uncertainty somewhat (Pellicciotti et al., 2012; Verbunt et al., 2003), though it is a lack of this sort of data that forces the use of temperature-index approaches in the first place. It should be noted that the temperature-index approach is generally not applicable in tropical climates since moisture and radiative fluxes control ablation rather than sensible heat (Juen et al., 2007).

Parameter uncertainty is related to the same data measurement uncertainties that plague the direct discharge measurement, glaciological, and hydrological balance approaches: a dearth of weather data collected in the higher elevations of watersheds (Pellicciotti et al., 2012); an inability to accurately measure precipitation, especially snow accumulation (Boscarello et al., 2012; Hagg et al., 2007) and the need to interpolate precipitation measurements across highly heterogeneous mountain landscapes (Koboltschnig and Schoner, 2011); a lack of empirical evapotranspiration data (Horton et al., 2006; Koboltschnig et al., 2008); and uncertainty about the accuracy of stream discharge measurements, especially at higher flows (Nepal et al., 2013). Pellicciotti et al. (2012) suggest that model parameterization may be a larger source of uncertainty than has generally been recognized, while Blöschl and Montanari (2010) argue that uncertainty assessment remains an area of weakness and that this is an area where researchers must make progress. Greater attention to parameter sensitivity has been suggested as one approach to meeting this challenge (Nepal et al., 2013).

Glaciological parameters are a particular source of uncertainty in hydrological modeling approaches. This is partly due to the inherent challenge of trying to resolve both the hydrological balance and glacier mass balances simultaneously (Schaefli and Huss, 2011), but also because existing glacier volumes are often highly generalized, especially in macro-scale modeling applications (Gabbi et al., 2012). Many researchers have concluded that mass balance data are essential for reducing equifinality and improving model performance (Braun and Aellen, 1990; Koboltschnig and Schoner, 2011; Schaefli and Huss, 2011), though the lack of such data is one reason a researcher might employ a hydrological model rather than using a glaciological approach. The ability to incorporate limited mass balance data (as little as a single year) along with just a few days of melt-season discharge information has been shown to greatly reduce uncertainty in model performance (Konz and Seibert, 2010), though Schaefli and Huss (2011) caution that glacier-wide mass balance data derived from a single measurement point are prone to considerable error. The geodetic approach to reconstructing mass balance offers an alternative, but this too is reliant upon the existence of high-quality data covering multiple years. As with other approaches, differentiating between ice melt and seasonal snow melt can also be a challenge, though the existence of remotely sensed data such as the MODIS snow-cover product can help improve parameter sets where they are scale appropriate (Koboltschnig et al., 2008; Pellicciotti et al., 2012).

Equifinality is a troublesome source of uncertainty because it occurs when the model appears to have accurately simulated reality without having actually replicated the true relationship between model parameters. Equifinality is especially common when glacier mass balance processes are poorly parameterized, since other model parameters are likely to be erroneously adjusted in order to better match measured discharge (Konz and Seibert, 2010; Schaefli et al., 2005). Researchers suggest calibrating the model against multiple empirical parameter sets rather than the usual single set (typically discharge), since doing so permits a better assessment of model consistency (Pellicciotti et al., 2012; Verbunt et al., 2003). Various random sampling techniques have been employed to identify the most likely combination of calibration parameter values, with the best parameter set identified using a statistical correlation test (e.g. Finger et al., 2012; Gao et al., 2012; Nepal et al., 2013; Schaefli et al., 2005). However, Pellicciotti et al. (2012) note that different types of correlation tests could yield different ‘best’ parameter sets, thus introducing yet another source of uncertainty.

Many studies employing hydrological modeling incorporate an additional scenario-based component to describe potential future glacier meltwater contributions within a watershed, and some make this their sole objective (e.g. Akhtar et al., 2008; Huss et al., 2008; Loukas et al., 2002). Such scenario-based modeling is subject to additional uncertainties about the future behavior of hydro-climatic systems due to: unanswered questions about the rate and intensity of future climate change (Huss et al., 2010); the response of glaciers to climate change (Immerzeel et al., 2010); and the response of watersheds to glacier change and other shifting climatic conditions (Farinotti et al., 2012).

IV Discussion

Our survey of the literature reveals that the methodological approaches available for a specific study are constrained by both social (e.g. monitoring capacity) and environmental (e.g. climate, geology) conditions in the study area; and that the methodological approach selected for the study limits the nature of the conclusions that can be drawn as a result. Researchers considering potential approaches for their own studies need to be aware of these constraints before settling upon any particular research design.

A fundamental decision that researchers must make at the outset is how they will define ‘glacial meltwater’ (Gao et al., 2012; Jost et al., 2012). Some studies report the contribution from glacierized areas, including both ice melt as well as water generated by seasonal snowpack in the glacier’s ablation zone and on bare surfaces (e.g. Nepal et al., 2013) while others exclude seasonal snowmelt from the estimate (e.g. Stahl et al., 2008). This distinction is important because the volume of water generated by seasonal snowmelt on a glacier surface can be a significant proportion of the discharge generated by the glacierized portion of the watershed (Huss, 2011; Verbunt et al., 2003) and may actually dominate discharge early in the melt season (Pelto, 2008). Though most studies do not differentiate between glacier ‘melt’ and ‘wastage’ (Hopkinson and Young, 1998), this distinction is important because glacial meltwater influences watershed yield at different temporal scales. Wastage represents the hydrological consequence of negative mass balance and thus describes the impact of glacial meltwater on interannual timescales, whereas melt describes both wastage and the water stored and released by the glacier within a single hydrological year and thus the seasonal buffering of watershed yield at intra-annual timescales (Gao et al., 2012; Hopkinson and Young, 1998). Because different techniques have different capabilities for differentiating between ice melt and seasonal snow melt, and between glacier melt and glacier wastage, researchers must decide upon their intent before selecting their methodological approach. These variable definitions for glacial meltwater mean that conclusions drawn from one study may not be directly comparable to those of another.

Researchers should account for the spatial and temporal variability of glacial meltwater contribution in their research design. Given the importance of the glacial compensation effect to watershed hydrology, quantification of seasonal variability is especially important lest the study misinterpret the relative importance of glacial meltwater at key times during the hydrological year (e.g. Jeelani et al., 2012). Glaciological and hydrological balance equation approaches often rely on data representing conditions over an entire year and thus may be limited in their ability to describe these seasonal variations. Direct discharge measurement and hydrochemical tracers approaches provide discrete estimates of meltwater contribution; thus measurements need to be repeated multiple times to capture its seasonal variation. Hydrological models are effective at identifying variation, even when run at monthly time-steps. The proportional contribution of glacial meltwater is also a direct function of the location within the watershed at which total discharge is being measured. While some researchers calculate discharge at a logical watershed pour-point such as a major river confluence, others use locations where there happens to be a stream gauge with discharge data of sufficient quality (e.g. Singh et al., 1997). The problem this presents is that the proportional contribution estimated at that point may not accurately reflect conditions elsewhere in the watershed, particularly at a key location such as a specific irrigation intake canal. Those techniques that depend upon measured downstream discharge data, such as glaciological and hydrological balance approaches and some hydrological modeling approaches, may be particularly prone to this limitation.

Finally, researchers must be cognizant of the other conditions that can limit the range of methodological options available to them. The two most significant constraints guiding the selection of a technique, which are often tightly interwoven, are watershed accessibility and the availability of existing hydrological, glaciological, and climatologic data. Approaches that yield estimates with better spatial and temporal resolution and with less overall uncertainty are almost always limited to readily accessible watersheds where monitoring infrastructure has already been put in place, and data management capacities are more highly developed (e.g. Gascoin et al., 2011; Pelto, 2011; Verbunt et al., 2003). While a number of creative data interpolation techniques have been employed to leverage existing data sets collected from outside the study area (e.g. Juen et al., 2007; Marshall et al., 2011), these data sources will still result in greater uncertainty about actual conditions within the study watershed. The development of techniques that are applicable in ungauged watersheds has been one key area of research (Huss, 2011; Konz et al., 2007;). Hydrochemical tracer methods (e.g. Mark and McKenzie, 2007; Maurya et al., 2011) and hydrological models parameterized from global-scale data sets (e.g. Immerzeel et al., 2010; Mukhopadhyay and Dutta, 2010) present potential opportunities in this regard, though each introduces its own uncertainty to the study.

V Areas for future research emphasis

There will be many sources of uncertainty regardless of the methodological approach taken to estimate the proportional contribution of glacier meltwater to total watershed discharge. Future research must thus address the dual needs of providing information about the glacio-hydrological conditions in specific watersheds where the hydrological impact of glacier meltwater is considerable, as well as identifying new techniques for reducing methodological uncertainties. Miller et al. (2012) suggest several specific lines of research that will help address uncertainty, including improving our ability to quantify the spatial variability of glacial and seasonal snow melt, improving our understanding of current and future streamflow patterns, and continuing to improve the performance of glacio-hydrological models. Sorg et al. (2012) argue that fully distributed, physically-based models are better able to simulate the complexities of watershed hydrology and the transient shifts in hydrological and glaciological conditions that can be expected due to climate change; therefore, further refinement of these models and reductions in computational and data limitations should be priorities. A frequent obstacle to modeling and most other approaches is a lack of high-quality meteorological, hydrological, and glaciological data, underscoring the ongoing need for additional monitoring networks involving both the research community and appropriate water management authorities. Improved dissemination of data collected from short-term monitoring efforts would also benefit the research community, since these data are especially valuable in places where no long-term monitoring program has been established (Pellicciotti et al., 2012). Because predictive modeling of future glacio-hydrological conditions requires well-constrained estimates of current glacier geometry and mass balance behavior, as well as reasonable predictions of future glacier geometry and extent, emphasis on ice-thickness surveys in many mountain regions would also be highly useful (Gabbi et al., 2012; Marshall et al., 2011; Stahl et al., 2008).

There is tension within the literature between the desire to investigate small watersheds, where conditions are more homogenous and thus uncertainty is generally lower, and larger watersheds where studies are relevant to a greater number of people. However, despite the desire to generalize findings from a small sample of watersheds, the high temporal and spatial heterogeneity of mountain climatic, hydrological, and glaciological systems makes necessary the investigation of a wide array of watersheds, especially as these systems respond to global climate change (Baraer et al., 2012). Furthermore, it is worth re-emphasizing that glacial meltwater can be a critical hydrological component in small, headwaters watersheds even when its contribution is negligible at the macro scale (Comeau et al., 2009; Miller et al., 2012) and the water resources implications of glaciers are worth investigating in these areas as well.

Three other areas of potential future research emphasis are worth noting. First, given the signal role of glacial meltwater in buffering stream flow during dry periods – especially during periods of intense heat and/or extended drought – there is considerable value in specifically investigating the contributions of glacial meltwater in these hydrologically significant years (e.g. Koboltschnig et al., 2007). Second, there has been very little research about the relationship between glacial meltwater and nearby groundwater systems. Despite the common assumption that there is minimal infiltration in high, rocky mountain watersheds, there is evidence that groundwater systems can play a substantial hydrological role in glacierized watersheds (Andermann et al., 2012; Baraer et al., 2009; Favier et al., 2008). Given the enhanced melting expected in most mountain areas over the next century, understanding these linkages is important. Third, considering the importance of projecting future discharge under the shifting glacial conditions of global climate change, there will be increasing value in returning to previously investigated watersheds to validate earlier predictions with direct measurements, especially as time progresses.

Finally, echoing the detailed recommendations of Viviroli et al. (2011), we believe that more emphasis should be placed on integrating this area of research with the specific needs of watershed stakeholders. When stakeholders are engaged in the research design and are provided specific results in a useable format, the socio-economic motivations for investigating glacio-hydrological systems are better met (Miller et al., 2012). Given the high spatial and temporal variability of glacial meltwater contributions, we suggest that research should investigate the current and potential future hydrological significance of meltwater at specific locations such as hydro-electric facilities and important water diversions so that managers of this infrastructure can better adapt research results into their planning and operations (e.g. Jeelani et al., 2012). We also wish to emphasize the value of transdisciplinary research in improving our ability to understand watershed hydrology in mountain areas (e.g. Bury et al., 2011; Mark et al., 2010), given the tight coupling of natural and human systems in this environment.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

References

Aizen

Kuzmichonok

(2007) Glaciers and hydrological changes in the Tien Shan: Simulation and prediction. Environmental Research Letters 2: 045019.

Aizen

Melack

(1996) Precipitation, melt and runoff in the northern Tien Shan. Journal of Hydrology 186: 229–251.

Akhtar

Ahmad

Booij

(2008) The impact of climate change on the water resources of Hindukush-Karakorum-Himalaya region under different glacier coverage scenarios. Journal of Hydrology 355: 148–163.

Alford

Armstrong

(2010) The role of glaciers in stream flow from the Nepal Himalaya. The Cryosphere Discussions 4: 469–494.

Andermann

Longuevergne

Bonnet

. (2012) Impact of transient groundwater storage on the discharge of Himalayan rivers. Nature Geoscience 5: 127–132.

Arnold

Willis

Sharp

. (1996) A distributed surface energy-balance model for a small valley glacier. I. Development and testing for Haut Glacier d’Arolla, Valais, Switzerland. Journal of Glaciology 42: 77–89.

Bahr

Meier

Peckham

(1997) The physical basis of glacier volume-area scaling. Journal of Geophysical Research 102: 20355–20362.

Bamber

Rivera

(2007) A review of remote sensing methods for glacier mass balance determination. Global and Planetary Change 59: 138–148.

Baraer

McKenzie

Mark

. (2009) Characterizing contributions of glacier melt and groundwater during the dry season in a poorly gauged catchment of the Cordillera Blanca (Peru). Advances in Geosciences 22: 41–49.

10.

Baraer

Mark

McKenzie

. (2012) Glacier recession and water resources in Peru’s Cordillera Blanca. Journal of Glaciology 58: 134–150.

11.

Barnett

Adam

Lettenmaier

(2005) Potential impacts of a warming climate on water availability in snow-dominated regions. Nature 438: 303–309.

12.

Barry

(2006) The status of research on glaciers and global glacier recession: A review. Progress in Physical Geography 30: 285–306.

13.

Benn

Lehmkuhl

(2000) Mass balance and equilibrium-line altitudes of glaciers in high-mountain environments. Quaternary International 65: 15–29.

14.

Beven

(2006) A manifesto for the equifinality thesis. Journal of Hydrology 320: 18–36.

15.

Blöschl

Montanari

(2010) Climate change impacts – throwing the dice? Hydrological Processes 24: 374–381.

16.

Boscarello

Ravazzani

Rabuffetti

. (2012) Integrating glaciers raster based modelling in large catchments hydrological balance: The Rhone case study. Hydrological Processes In press.

17.

Bradley

Vuille

Diaz

. (2006) Threats to water supplies in the tropical Andes. Science 312: 1755–1756.

18.

Braun

Aellen

(1990) Modelling discharge of glacierised basins assisted by direct measurements of glacier mass balance. In: Lang

Musy

(eds) Hydrology in Mountainous Regions I: Hydrological Measurements – The Water Cycle. IAHS Publication 193. Wallingford: International Association of Hydrological Sciences, 99–106.

19.

Braun

Weber

Schulz

(2000) Consequences of climate change for runoff from Alpine regions. Annals of Glaciology 31: 19–25.

20.

Brown

Hannah

Milner

. (2006) Water source dynamics in a glacierised alpine river basin (Taillon-Gabiétous, French Pyrénées). Water Resources Research 42: W08404.

21.

Brown

Milner

Hannah

(2010) Predicting river ecosystem response to glacial meltwater dynamics: A case study of quantitative water sourcing and glaciality index approaches. Aquatic Sciences 72: 325–334.

22.

Bury

Mark

McKenzie

. (2011) Glacier recession and human vulnerability in the Yanamarey watershed of the Cordillera Blanca, Peru. Climatic Change 105: 179–206.

23.

Buytaert

Vuille

Dewulf

. (2010) Uncertainties in climate change projections and regional downscaling in the tropical Andes: Implications for water resources management. Hydrology and Earth System Sciences 14: 1247–1258.

24.

Cable

Ogle

Williams

(2011) Contribution of glacier meltwater to streamflow in the Wind River Range, Wyoming, inferred via a Bayesian mixing model applied to isotopic measurements. Hydrological Processes 25: 2228–2236.

25.

Casassa

López

Pouyaud

. (2009) Detection of changes in glacial run-off in alpine basins: Examples from North America, the Alps, central Asia and the Andes. Hydrological Processes 23: 31–41.

26.

Chen

Ohmura

(1990a) Estimation of Alpine glacier water resources and their change since the 1870s. In: Lang

Musy

(eds) Hydrology in Mountainous Regions I: Hydrological Measurements – The Water Cycle. IAHS Publication 193. Wallingford: International Association of Hydrological Sciences, 127–135.

27.

Chen

Ohmura

(1990b) On the influence of Alpine glaciers on runoff. In: Lang

Musy

(eds) Hydrology in Mountainous Regions I: Hydrological Measurements – The Water Cycle. IAHS Publication 193. Wallingford: International Association of Hydrological Sciences, 117–125.

28.

Christophersen

Hooper

(1992) Multivariate analysis of stream water chemical data: The use of principal components analysis for the end-member mixing problem. Water Resources Research 28: 99–107.

29.

Christophersen

Neal

Hooper

. (1990) Modelling streamwater chemistry as a mixture of soilwater end-members: A step towards second-generation acidification models. Journal of Hydrology 116: 307–320.

30.

Collier

(1958) Glacier variation and trends in run-off in the Canadian Cordillera. In: IAHS Publication 46, Assemblée Générale de Toronto, 1957, Neiges et Glaces. Wallingford: International Association of Hydrological Sciences, 344–357.

31.

Comeau

LEL

Pietroniro

Demuth

(2009) Glacier contribution to the North and South Saskatchewan Rivers. Hydrological Processes 23: 2640–2653.

32.

Di Baldassarre

Montanari

(2009) Uncertainty in river discharge observations: A quantitative analysis. Hydrology and Earth System Sciences 13: 913–921.

33.

Drever

(1997) Geochemistry of Natural Waters. Upper Saddle River, NJ: Prentice-Hall.

34.

Farinotti

Huss

Bauder

. (2009) A method to estimate the ice volume and ice-thickness distribution of alpine glaciers. Journal of Glaciology 55: 422–430.

35.

Farinotti

Usselmann

Huss

. (2012) Runoff evolution in the Swiss Alps: Projections for selected high-alpine catchments based on ENSEMBLES scenarios. Hydrological Processes 26: 1909–1924.

36.

Favier

Coudrain

Cadier

. (2008) Evidence of groundwater flow on Antizana ice-covered volcano, Ecuador. Hydrological Sciences Journal 53: 278–291.

37.

Finger

Heinrich

Gobiet

. (2012) Projections of future water resources and their uncertainty in a glacierised catchment in the Swiss Alps and the subsequent effects on hydropower production during the 21st century. Water Resources Research 48: W02521.

38.

Fleming

Clarke

(2005) Attenuation of high-frequency interannual streamflow variability by watershed glacial cover. Journal of Hydraulic Engineering 131: 615–618.

39.

Fountain

Tangborn

(1985) The effect of glaciers on streamflow variations. Water Resources Research 21: 579–586.

40.

Frey

Paul

(2012) On the suitability of the SRTM DEM and ASTER GDEM for the compilation of topographic parameters in glacier inventories. International Journal of Applied Earth Observation and Geoinformation 18: 480–490.

41.

Fujisada

Bailey

Kelly

. (2005) ASTER DEM performance. IEEE Transactions on Geoscience and Remote Sensing 43: 2707–2714.

42.

Fujita

Ohta

Ageta

(2007) Characteristics and climatic sensitivities of runoff from a cold-type glacier on the Tibetan Plateau. Hydrological Processes 21: 2882–2891.

43.

Gabbi

Farinotti

Bauder

. (2012) Ice volume distribution and implications on runoff projections in a glacierised catchment. Hydrology and Earth System Sciences 16: 4543–4556.

44.

Gao

. (2012) Modeling the runoff and glacier mass balance in a small watershed on the Central Tibetan Plateau, China, from 1955 to 2008. Hydrological Processes 26: 1593–1603.

45.

Gascoin

Kinnard

Ponce

. (2011) Glacier contribution to streamflow in two headwaters of the Huasco River, Dry Andes of Chile. The Cryosphere 5: 1099–1113.

46.

Hagg

Braun

Kuhn

. (2007) Modelling of hydrological response to climate change in glacierised Central Asian catchments. Journal of Hydrology 332: 40–53.

47.

Hagg

Hoelzle

Wagner

. (2011) Estimation of future glaciation and runoff in the Tanimas basin, Eastern Pamirs. Hydrology and Earth System Sciences Discussions 8: 1507–1540.

48.

Henoch

WES

(1971) Estimate of glaciers secular (1948–1966) volumetric change and its contribution to the discharge in the upper North Saskatchewan River Basin. Journal of Hydrology 12: 145–160.

49.

Hock

(2003) Temperature index melt modelling in mountain areas. Journal of Hydrology 282: 104–115.

50.

Hock

Holmgren

(2005) A distributed surface energy-balance model for complex topography and its application to Storglaciaren, Sweden. Journal of Glaciology 51: 25–36.

51.

Hock

Jansson

Braun

(2005) Modelling the response of mountain glacier discharge to climate warming. In: Huber

Bugmann

HKM

Reasoner

(eds) Global Change and Mountain Regions. Dordrecht: Springer, 243–252.

52.

Hooper

Shoemaker

(1986) A comparison of chemical and isotopic hydrograph separation. Water Resources Research 22: 1444–1454.

53.

Hopkinson

Demuth

(2006) Using airborne lidar to assess the influence of glacier downwasting on water resources in the Canadian Rocky Mountains. Canadian Journal of Remote Sensing 32: 212–222.

54.

Hopkinson

Young

(1998) The effect of glacier wastage on the flow of the Bow River at Banff, Alberta, 1951–1993. Hydrological Processes 12: 1745–1762.

55.

Horton

Schaefli

Mezghani

. (2006) Assessment of climate-change impacts on alpine discharge regimes with climate model uncertainty. Hydrological Processes 20: 2091–2109.

56.

Huss

(2011) Present and future contribution of glacier storage change to runoff from macroscale drainage basins in Europe. Water Resources Research 47: W07511.

57.

Huss

Farinotti

Bauder

. (2008) Modelling runoff from highly glacierised alpine drainage basins in a changing climate. Hydrological Processes 22: 3888–3902.

58.

Huss

Jouvet

Farinotti

. (2010) Future high-mountain hydrology: A new parameterization of glacier retreat. Hydrology and Earth System Sciences 14: 815–829.

59.

Immerzeel

(2008) Historical trends and future predictions of climate variability in the Brahmaputra basin. International Journal of Climatology 28: 243–254.

60.

Immerzeel

Bierkens

MFP

(2012) Asia’s water balance. Nature Geoscience 5: 841–842.

61.

Immerzeel

Van Beek

LPH

Bierkens

MFP

(2010) Climate change will affect the Asian water towers. Science 328: 1382–1385.

62.

Immerzeel

Van Beek

LPH

Konz

. (2012) Hydrological response to climate change in a glacierised catchment in the Himalayas. Climatic Change 110: 721–736.

63.

Intergovernmental Panel on Climate Change (IPCC) (2007a) Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by Pachauri

Reisinger

. Geneva: IPCC.

64.

Intergovernmental Panel on Climate Change (IPCC) (2007b) Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, edited by Parry

Canziani

Palutikof

. Cambridge: Cambridge University Press.

65.

Jansson

Hock

Schneider

(2003) The concept of glacier storage: A review. Journal of Hydrology 282: 116–129.

66.

Jeelani

Feddema

van der Veen

. (2012) Role of snow and glacier melt in controlling river hydrology in Liddar watershed (western Himalaya) under current and future climate. Water Resources Research 48: W12508.

67.

Jiskoot

Mueller

(2012) Glacier fragmentation effects on surface energy balance and runoff: Field measurements and distributed modelling. Hydrological Processes 26: 1862–1876.

68.

Jost

Moore

Menounos

. (2012) Quantifying the contribution of glacier runoff to streamflow in the upper Columbia River basin, Canada. Hydrology and Earth System Sciences 16: 849–860.

69.

Juen

Kaser

Georges

(2007) Modelling observed and future runoff from a glacierised tropical catchment (Cordillera Blanca, Perú). Global and Planetary Change 59: 37–48.

70.

Kaser

Osmaston

(2002) Tropical Glaciers. Cambridge: Cambridge University Press.

71.

Kaser

Groshauser

Marzeion

(2010) Contribution potential of glaciers to water availability in different climate regimes. Proceedings of the National Academy of Sciences 107: 20223–20227.

72.

Kendall

McDonnell

(1998) Isotope Tracers in Catchment Hydrology. Amsterdam: Elsevier.

73.

Koboltschnig

Schoner

(2011) The relevance of glacier melt in the water cycle of the Alps: The example of Austria. Hydrology and Earth System Sciences 15: 2039–2048.

74.

Koboltschnig

Schoner

Zappa

. (2007) Contribution of glacier melt to stream runoff: If the climatically extreme summer of 2003 had happened in 1979. Annals of Glaciology 46: 303–308.

75.

Koboltschnig

Schoner

Zappa

. (2008) Runoff modelling of the glacierised Alpine Upper Salzach basin (Austria): Multi-criteria result validation. Hydrological Processes 22: 2950–2964.

76.

Kong

Pang

(2012) Evaluating the sensitivity of glacier rivers to climate change based on hydrograph separation of discharge. Journal of Hydrology 434–435: 121–129.

77.

Konz

Seibert

(2010) On the value of glacier mass balances for hydrological model calibration. Journal of Hydrology 385: 238–246.

78.

Konz

Uhlenbrook

Braun

. (2007) Implementation of a process-based catchment model in a poorly gauged, highly glacierised Himalayan headwater. Hydrology and Earth System Sciences 11: 1323–1339.

79.

Lambrecht

Kuhn

(2007) Glacier changes in the Austrian Alps during the last three decades, derived from the new Austrian glacier inventory. Annals of Glaciology 46: 177–184.

80.

Lambrecht

Mayer

(2009) Temporal variability of the non-steady contribution from glaciers to water discharge in western Austria. Journal of Hydrology 376: 353–361.

81.

Lang

(1986) Forecasting meltwater runoff from snow-covered areas and from glacier basins. In: Kraijenhoff

Moll

(eds) River Flow Modelling and Forecasting. Dordrecht: D. Reidel, 99–127.

82.

Legates

Willmott

(2006) Mean seasonal and spatial variability in gauge-corrected, global precipitation. International Journal of Climatology 10: 111–127.

83.

Liu

Zhang

. (2009) Estimation of glacier runoff and future trends in the Yangtze River source region, China. Journal of Glaciology 55: 353–362.

84.

Loukas

Vasiliades

Dalezios

(2002) Climatic impacts on the runoff generation processes in British Columbia, Canada. Hydrology and Earth System Sciences 6: 211–228.

85.

Mark

McKenzie

(2007) Tracing increasing tropical Andean glacier melt with stable isotopes in water. Environmental Science and Technology 41: 6955–6960.

86.

Mark

Seltzer

(2003) Tropical glacier meltwater contribution to stream discharge: A case study in the Cordillera Blanca, Peru. Journal of Glaciology 49: 271–281.

87.

Mark

Bury

McKenzie

. (2010) Climate change and tropical Andean glacier recession: Evaluating hydrologic changes and livelihood vulnerability in the Cordillera Blanca, Peru. Annals of the Association of American Geographers 100: 794–805.

88.

Mark

McKenzie

Gomez

(2005) Hydrochemical evaluation of changing glacier meltwater contribution to stream discharge: Callejon de Huaylas, Peru. Hydrological Sciences Journal 50: 975–987.

89.

Marshall

White

Demuth

. (2011) Glacier water resources on the eastern slopes of the Canadian Rocky Mountains. Canadian Water Resources Journal 36: 109–134.

90.

Maurya

Shah

Deshpande

. (2011) Hydrograph separation and precipitation source identification using stable water isotopes and conductivity: River Ganga at Himalayan foothills. Hydrological Processes 25: 1521–1530.

91.

Miller

Immerzeel

Rees

(2012) Climate change impacts on glacier hydrology and river discharge in the Hindu Kush – Himalayas. Mountain Research and Development 32: 461–467.

92.

Moore

(1992) The influence of glacial cover on the variability of annual runoff, Coast Mountains, British Columbia, Canada. Canadian Water Resources Journal 17: 101–109.

93.

Moore

Richards

Story

(2008) Electrical conductivity as an indicator of water chemistry and hydrologic process. Streamline Watershed Management Bulletin 11: 25–29.

94.

Mukhopadhyay

(2012) Detection of dual effects of degradation of perennial snow and ice covers on the hydrologic regime of a Himalayan river basin by stream water availability modeling. Journal of Hydrology 412–413: 14–33.

95.

Mukhopadhyay

Dutta

(2010) A stream water availability model of Upper Indus Basin based on a topologic model and global climatic datasets. Water Resources Management 24: 4403–4443.

96.

Nepal

Krause

Flügel

. (2013) Understanding the hydrological system dynamics of a glaciated alpine catchment in the Himalayan region using the J2000 hydrological model. Hydrological Processes. doi: 10.1002/hyp.9627.

97.

Nolin

Phillippe

Jefferson

. (2010) Present-day and future contributions of glacier runoff to summertime flows in a Pacific Northwest watershed: Implications for water resources. Water Resources Research 46: W12509.

98.

Oerlemans

Klok

(2002) Energy balance of a glacier surface: Analysis of automatic weather station data from the Morteratschgletscher, Switzerland. Arctic, Antarctic, and Alpine Research 34: 477–485.

99.

Ohmura

(2001) Physical basis for the temperature-based melt-index method. Journal of Applied Meteorology 40: 753–761.

100.

Paul

Haeberli

(2008) Spatial variability of glacier elevation changes in the Swiss Alps obtained from two digital elevation models. Geophysical Research Letters 35: L21502.

101.

Pellicciotti

Buergi

Immerzeel

. (2012) Challenges and uncertainties in hydrological modeling of remote Hindu Kush-Karakoram Himalayan (HKH) basins: Suggestions for calibration strategies. Mountain Research and Development 32: 39–50.

102.

Pelto

(1992) Changes in water supply in alpine regions due to glacier retreat. In: Bras

(ed.) The World at Risk: Natural Hazards and Climate Change. New York: American Institute of Physics, 61–67.

103.

Pelto

(2008) Impact of climate change on North Cascade alpine glaciers, and alpine runoff. Northwest Science 82: 65–75.

104.

Pelto

(2011) Skykomish River, Washington: Impact of ongoing glacier retreat on streamflow. Hydrological Processes 25: 3356–3363.

105.

Prasch

Mauser

Weber

(2013) Quantifying present and future glacier melt-water contribution to runoff in a Central Himalayan river basin. The Cryosphere 7: 889–904.

106.

Racoviteanu

Manley

Arnaud

. (2007) Evaluating digital elevation models for glaciologic applications: An example from Nevado Coropuna, Peruvian Andes. Global and Planetary Change 59: 110–125.

107.

Rees

Collins

(2006) Regional differences in response of flow in glacier-fed Himalayan rivers to climatic warming. Hydrological Processes 20: 2157–2169.

108.

Rothlisberger

Lang

(1987) Glacial hydrology. In: Gurnell

Clark

(eds) Glacio-Fluvial Sediment Transfer: An Alpine Perspective. New York: Wiley, 207–274.

109.

Schaefli

Huss

(2011) Integrating point glacier mass balance observations into hydrologic model identification. Hydrology and Earth System Sciences 15: 12–27.

110.

Schaefli

Hingray

Niggli

. (2005) A conceptual glacio-hydrological model for high mountainous catchments. Hydrology and Earth System Sciences 9: 95–109.

111.

Schaner

Voisin

Nijssen

. (2012) The contribution of glacier melt to streamflow. Environmental Research Letters 7: 034029.

112.

Shahgedanova

Hagg

Hassell

. (2009) Climate change, glacier retreat, and water availability in the Caucasus Region. In: Jones

JAA

Vardanian

Hakopian

(eds) Threats to Global Water Security: Proceedings of the NATO Advanced Research Workshop on Natural Disasters and Water Security: Risk Assessment, Emergency Response and Environmental Management, Yerevan, Armenia, 131–143.

113.

Sharp

Brown

Tranter

. (1995) Comments on the use of chemically based mixing models in glacier hydrology. Journal of Glaciology 41: 241–246.

114.

Singh

Jain

(2002) Snow and glacier melt in the Satluj River at Bhakra Dam in the western Himalayan region. Hydrological Sciences Journal 47: 93–106.

115.

Singh

Haritashya

Kumar

. (2006) Hydrological characteristics of the Gangotri Glacier, central Himalayas, India. Journal of Hydrology 327: 55–67.

116.

Singh

Jain

Kumar

(1997) Estimation of snow and glacier-melt contribution to the Chenab River, Western Himalaya. Mountain Research and Development 17: 49–56.

117.

Sorg

Bolch

Stoffel

. (2012) Climate change impacts on glaciers and runoff in Tien Shan (Central Asia). Nature Climate Change 2: 725–731.

118.

Soupir

Mostaghimi

Mitchem

Jr (2009) A comparative study of stream gaging techniques for low flow measurements in two Virginia tributaries. Journal of the American Water Resources Association 45: 110–122.

119.

Stahl

Moore

Shea

. (2008) Coupled modelling of glacier and streamflow response to future climate scenarios. Water Resources Research 44: W02422.

120.

Thayyen

Gergan

(2010) Role of glaciers in watershed hydrology: A preliminary study of a ‘Himalayan catchment’. The Cryosphere 4: 115–128.

121.

Thayyen

Gergan

Dobhal

(2005) Monsoonal control on glacier discharge and hydrograph characteristics, a case study of Dokriani Glacier, Garhwal Himalaya, India. Journal of Hydrology 306: 37–49.

122.

Verbunt

Gurtz

Jasper

. (2003) The hydrological role of snow and glaciers in alpine river basins and their distributed modeling. Journal of Hydrology 282: 36–55.

123.

Viviroli

Archer

Buytaert

. (2011) Climate change and mountain water resources: Overview and recommendations for research, management and policy. Hydrology and Earth System Sciences 15: 471–504.

124.

Viviroli

Dürr

Messerli

. (2007) Mountains of the world, water towers for humanity: Typology, mapping, and global significance. Water Resources Research 43: W07447.

125.

Wagnon

Ribstein

Francou

. (1999) Annual cycle of energy balance of Zongo glacier, Cordillera Real, Bolivia. Journal of Geophysical Research 104: 3907–3923.

126.

Willis

(2005) Hydrology of glacierised basins. In: Anderson

(ed.) Encyclopedia of Hydrological Sciences. Chichester: Wiley, 2601–2631.

127.

Wood

Jones

Moore

(2000) Accuracy of rainfall measurement for scales of hydrological interest. Hydrology and Earth System Sciences 4: 531–543.

128.

Yuanqing

Theakstone

Tandong

. (2001) The isotopic record at an alpine glacier and its implications for local climatic changes and isotopic homogenization processes. Journal of Glaciology 47: 147–151.

129.

Zemp

Hoelzle

Haeberli

(2009) Six decades of glacier mass-balance observations: A review of the worldwide monitoring network. Annals of Glaciology 50: 101–111.

130.

Zemp

Thibert

Huss

. (2013) Uncertainties and re-analysis of glacier mass balance measurements. The Cryosphere Discussions 7: 789–839.

131.

Zhang

Gao

. (2011a) A modified monthly degree-day model for evaluating glacier runoff changes in China. Part II: Application. Hydrological Processes 26: 1697–1706.

132.

Zhang

Gao

Zhang

. (2012) Projection of glacier runoff in Yarkant River basin and Beida River basin, Western China. Hydrological Processes 26: 2773–2781.

133.

Zhang

Liu

. (2008) Glacier change and glacier runoff variation in the Tuotuo River basin, the source region of Yangtze River in western China. Environmental Geology 56: 59–68.

134.

Zhang

Liu

. (2011b) A modified monthly degree-day model for evaluating glacier runoff changes in China. Part I: Model development. Hydrological Processes 26: 1686–1696.