1. Introduction
Recent evidence indicates the Arctic climate, cryosphere, and hydrological cycle are changing (Hinzman et al. 2005; Lemke et al. 2007; Ettema et al. 2009). Long-term temperature observations show warming trends of variable strength throughout the Arctic and Greenland (Serreze et al. 2000; Allison et al. 2009; Box et al. 2010), with an average increase almost twice the global average rate in the past 100 years (Solomon et al. 2007). Fluctuations in mass balance and freshwater runoff from the Greenland Ice Sheet (GrIS), and from glaciers and ice caps peripheral to the GrIS, follow these climate fluctuations (Hanna et al. 2008; Rignot et al. 2008; Ettema et al. 2009). The associated glacial responses have been observed and marked by glaciers retreating and thinning along the periphery of the Ice Sheet (Krabill et al. 2000, 2004; Weidick and Bennike 2007). In general, approximately half of the mass loss from the GrIS originates from iceberg calving. These can be thought of as point sources unevenly distributed along the coastline. For example, the Helheim Glacier in southeast Greenland and Jakobshavn Glacier in west Greenland are two of the most prolific GrIS calving outlet glaciers (Rignot and Kanagaratnam 2006; Lemke et al. 2007). The other half of GrIS mass loss comes from surface melting and subsequent runoff into the ocean. These fluxes are nonuniformly distributed along the Greenland coast (Mernild and Liston 2012). For East Greenland, approximately 60% of the runoff originates from the GrIS, and approximately 40% from the land area and glaciers peripheral to the Ice Sheet (Mernild et al. 2008b). These peripheral ice masses are quite numerous in Greenland, with as many as 5297 glaciers existing in the southwest quarter between 59° and 71°N and 43° and 53°W (Weidick et al. 1992), and many more than that in northwestern, northern, and eastern Greenland (Fig. 1).
Landsat 7 ETM+ mosaic showing examples of peripheral glaciers in East Greenland, from the Mittivakkat Glacier, Ammassalik Fjord region: acquired on 7 Sep 1999 and 15 Aug 2000. The Mittivakkat Glacier is located to the right and below the red dot. Landsat scene identifiers LE72310141999250AGS00 and LE72320142000228AGS00. The inset figure indicates the general location (red dot) in East Greenland.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
Greenland calving and runoff contributions to the surrounding oceans is likely playing a role in controlling ocean salinity, sea ice dynamics, global eustatic sea level rise, and thermohaline circulation (THC) in the Greenland–Iceland–Norwegian Seas (ACIA 2005; Su et al. 2006; Lemke et al. 2007; Allison et al. 2009). Model simulations of future climate scenarios suggest a warmer Greenland overall (Fettweis et al. 2008; Stendel et al. 2008; Mernild et al. 2010a, 2011b), and the associated accelerating runoff and calving could perturb the THC by reducing the ocean density contrasts that drive the circulation (Rahmstorf et al. 2005). Therefore, quantifying melt-related freshwater fluxes from Greenland snow, glacier, and ice sheet surfaces to the surrounding oceans is expected to play an important role in improving our climate system understanding and representations.
Presently, detailed information about the spatial and temporal runoff distribution to the oceans from nonglaciated and glaciated areas of Greenland are limited (Mernild and Liston 2012). Discharge at catchment outlets represents an integrated response of the upstream watershed to precipitation and other hydrometeorologic processes like snow and glacier melt and to glaciohydrologic processes such as englacial bulk water storage and release. For glaciated areas, the physical mechanisms controlling water flow across the glacier and ice sheet surfaces must be accounted for if physically based simulations of the temporally evolving runoff distribution are to be realistic.
The purpose of this study was to develop HydroFlow and verify its performance for glacier, ice sheet, and snow-free and snow-covered land applications, with the ultimate goal of providing a tool that can simulate the linkages between runoff production from land-based liquid precipitation and snowmelt and icemelt processes, and the associated freshwater fluxes to surrounding oceans. To quantify spatial and temporal runoff distributions over a wide range of snow- and ice-covered and snow- and ice-free landscapes, the modeling system needs to account for individual drainage basins and streamflow networks within the entire domain of interest, and to track rain- and meltwater-related flow from snow-covered ice, snow-free ice, snow-covered land, and snow-free land, to the ocean.
After developing the HydroFlow gridded linear-reservoir runoff routing model for application in glaciated and nonglaciated areas, it was applied to a test area in southeast Greenland. This area contains the Mittivakkat Glacier, the local glacier in Greenland with the longest observed time series of mass-balance (since 1995) and ice-front fluctuations (since 1931) (Knudsen and Hasholt 2008; Mernild et al. 2011a). The spatial and seasonal variations in HydroFlow hydrographs were compared with observed discharge data coming from the Mittivakkat Glacier area and draining into the adjacent ocean.
To provide the time evolution of spatially distributed gridcell runoffs required by HydroFlow, a new, multilayer version of SnowModel (Liston and Elder 2006a,b; Mernild et al. 2006b) was driven with observed atmospheric data. SnowModel is a physically based, spatially distributed, meteorological and snow and ice evolution modeling system that has been used, tested, and verified in domains around the world where snow and/or ice are dominant features of the environment. SnowModel simulates the snow and ice cover evolution in response to blowing and drifting snow processes, snowpack growth and densification, snowmelt and icemelt fluxes, variations in liquid and solid precipitation, and other features important for describing seasonal snow evolution in snow-covered, ice-covered, and ice-free landscapes. The SnowModel-produced gridcell runoffs were used as inputs to HydroFlow, which routed the runoffs through the watersheds of interest and into the surrounding ocean.
2. HydroFlow: A gridded linear-reservoir runoff routing model
To assist in verifying gridcell runoffs generated by SnowModel, and to transport water across land and ice to adjacent oceans, a linear-reservoir runoff routing scheme called HydroFlow was developed. Watershed discharge is an important integrator of the hydrologic cycle and is generally measured more accurately than the other moisture budget components. Observed discharge data represent a readily available and valuable contribution for verifying modeled balances between precipitation, snowmelt, icemelt, evaporation, sublimation, soil moisture changes, transpiration, and runoff. A key output of SnowModel (and virtually any land surface hydrology model) simulations is water available for runoff at each grid cell at each model time step. For the case of SnowModel, these are primarily associated with snowmelt and icemelt and liquid precipitation fluxes and moisture redistribution within the snow and ice cover. To relate these gridcell runoffs to watershed hydrographs, a linear-reservoir runoff routing model (HydroFlow) that routes SnowModel-computed gridcell runoffs through the coincident runoff drainage networks is required. The HydroFlow hydrographs can then be compared with observed discharge values, thus providing a measure of model-simulated regional water balances over time scales ranging from individual storms and melt events to seasonal and annual cycles.
A fundamental premise of the HydroFlow linear-reservoir runoff routing model is that the catchment(s) of interest (i.e., the simulation domain) can be divided into a grid of rectangular model cells that cover the entire domain and are linked via a topographically controlled flow network. Each grid cell acts as a linear reservoir that transfers water from itself and the upslope cells to the downslope cell. HydroFlow assumes that there are two transfer components (or transfer functions) within each model grid cell: a slow-response flow and a fast-response flow. Each of these transfer functions have different time scales associated with them and represent the wide range of physical processes associated with the horizontal moisture transport through and across the landscape. The slow time scale accounts for the time it takes runoff at each individual grid cell, usually produced from liquid precipitation or snowmelt and/or icemelt, to enter the routing network. The moisture is then transported through the flow network at a rate associated with the fast time scale. Associated with these slow and fast time scales are different water transport mechanisms: the slow time scale generally accounts for transport within the snow and ice matrices (for the case of glaciers and ice sheets) and soil (for the case of snow-covered and snow-free land), and the fast time scale generally represents some kind of channel flow, such as that represented by superglacial, englacial, or subglacial flow (for the case of glaciers and ice sheets) and river and stream channels (for the case of snow-covered and snow-free land).
Schematic showing the local, SnowModel-generated layer of water available for runoff in a grid cell (Qm), the slow transport of water within that grid cell to the routing network (Qs), inflow from nearby grid cells (Qfi), and the slow and fast transformation functions (ks and kf). The magnitudes of Qs and Qf are provided by Eqs. (11) and (10), respectively.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
Equations (5)–(7) describe a coupled system of ordinary differential equations whose solution yields a discharge hydrograph for each grid cell (e.g., Liston et al. 1994). These model equations typically involve steady-state terms that do not grow significantly with time, together with rapidly decaying transient terms [depending on the magnitude of k(t)]. The steady-state terms typically result from the slow time-scale flow components, while the transient terms are due to the fast time-scale flow. The presence of significantly different time coefficients in the system of equations and, for the case where the total integration time is much greater than the model time coefficients, leads to a class of problems called “stiff systems” of differential equations. In such problems it is critical that the numerical solution be able to resolve the steady-state portion of the system without becoming dominated by errors encountered in resolving the transient part. While this problem can be overcome by a reduction of the time step, frequently the time step must be made so small that round-off errors may dominate the solution and the computational expense becomes unreasonable. Further discussion of stiff differential equation characteristics was provided by Shampine and Gear (1979) and Byrne and Hindmarsh (1987), and an ordinary differential equation solution scheme capable of handling the “stiffness” issue was presented by Brown et al. (1989).
In the Greenland snow, ice, and land system there are four dominant surfaces where runoff occurs: snow-covered ice, snow-free ice, snow-covered land, and snow-free land. For each of these surfaces there are both slow and fast residence-time coefficients or velocities. For the model simulations presented herein, the slow velocities, Vs, were defined to be 0.12, 0.20, 0.10, and 0.08 m s−1, for snow-covered ice, snow-free ice, snow-covered land, and snow-free land, respectively, based on Mittivakkat Glacier field observations (Mernild 2006; Mernild et al. 2006b). Observed snow-free land values are greater than those typically found in porous media flow (Todd 1980), presumably because of the predominance of bedrock and large gravels in this area (Mernild et al. 2006b).
Note that, because of the exp(−Δt/k) terms in Eqs. (10) and (11), the relative magnitudes of Δt and k strongly control the shape of the simulated hydrographs (Δt and k have the same time units). In practice, a Δt/k ratio ≫ 1 produces virtually no time delay in the flow (the transport is instantaneous and each grid cell accumulates all gridcell runoff and flow from all up-network grid cells at each time step), and if this ratio is ≪ 1, then the flow never changes (it always equals the initial conditions). Intermediate ratio values produce an attenuated representation of all runoff and flow from up-network. Therefore, the time step used in the SnowModel integration (i.e., the local runoff time step) should be roughly compatible with, or less than, the time scale of the flow and transport processes represented by the applied residence-time scale.
3. Model simulations
a. SnowModel
Running the HydroFlow runoff routing model requires gridded runoffs over the domain of interest. Because of the length scale dependence in Eq. (12), the model automatically accounts for residence-time adjustments associated with differences in grid size. These gridded runoffs were provided by SnowModel (Liston and Elder 2006a), a spatially distributed snow-evolution modeling system designed for application in all landscapes, climates, and conditions where snow and ice occurs. It is an aggregation of four submodels: EnBal (Liston 1995; Liston et al. 1999) calculates surface energy exchanges; SnowPack (Liston and Hall 1995) simulates snow depth and water-equivalent evolution; SnowTran-3D (Liston and Sturm 1998; Liston et al. 2007) accounts for snow redistribution by wind; and SnowAssim (Liston and Hiemstra 2008) is available to assimilate field and remote sensing datasets (not used in this study).
SnowModel is designed to run on grid increments of 1 m to 200 m and temporal increments of 10 min to 1 day. It can be applied using much larger grid increments (up to 10s of km) if the inherent loss in high-resolution (subgrid) information (Liston 2004; Liston and Hiemstra 2011a,b; Mernild and Liston 2012) is acceptable. In this application, processes simulated by SnowModel include accumulation from snow precipitation; blowing-snow redistribution and sublimation; snow-density evolution; and snowpack ripening and melt. SnowModel incorporates first-order physics required to simulate snow evolution within each of the global snow classes defined by Sturm et al. (1995) and G. E. Liston and M. Sturm (2012, unpublished manuscript). Required SnowModel inputs include time series fields of precipitation, wind speed and direction, air temperature, and relative humidity obtained from meteorological stations and/or an atmospheric model located within or near the simulation domain; and spatially distributed, time-invariant fields of topography and land-cover type.
SnowModel was originally developed for glacier- and ice-free landscapes. For glacier and GrIS surface mass-balance studies, SnowModel was modified to simulate glacier/ice melt after the winter snow accumulation had ablated (Mernild et al. 2006b), and routines were added to account for the time-evolving, spatial variations in snow albedo (Mernild et al. 2010c). In addition, in the application described herein, the role of surface meltwater percolating into, and refreezing within, snow and firn layers, makes an important contribution to the evolution of snow and ice densities and moisture available for runoff. Accounting for this requires a multilayer snow and ice model that simulates refreezing of meltwater as a function of snow and ice permeability and cold content (the temperature below freezing). To account for this, a multilayer snowpack model (SnowPack-ML) was implemented and coupled with the snow and ice temperature model of Liston et al. (1999) (Fig. 3).
Example SnowModel multilayer snowpack (SnowPack-ML) layers and snow density (kg m−3) evolution.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
b. MicroMet
Meteorological forcings required by SnowModel were provided by MicroMet (Liston and Elder 2006b), a quasi-physically-based, high-resolution (e.g., 1-m to 10-km horizontal grid increment), meteorological distribution model. MicroMet is a data assimilation and interpolation model that utilizes meteorological station datasets and/or gridded atmospheric model or analyses datasets. MicroMet minimally requires screen-height air temperature, relative humidity, wind speed and direction, and precipitation data. The model uses known relationships between meteorological variables and the surrounding landscape (primarily topography) to distribute those variables over any given landscape in physically plausible and computationally efficient ways. At each time step, MicroMet calculates and distributes air temperature, relative humidity, wind speed, wind direction, incoming solar radiation, incoming longwave radiation, surface pressure, and precipitation, and makes them accessible to SnowModel.
MicroMet and SnowModel have been used to distribute observed and modeled meteorological variables and evolve snow distributions over complex terrain in Colorado, Wyoming, Idaho, Oregon, Alaska, Arctic Canada, Siberia, Japan, Tibet, Chile, Germany, Austria, Norway, Greenland, and Antarctica as part of a wide variety of terrestrial modeling studies (e.g., Liston and Sturm 1998, 2002; Greene et al. 1999; Liston et al. 2000, 2002, 2007, 2008; Hiemstra et al. 2002, 2006; Prasad et al. 2001; Hasholt et al. 2003; Bruland et al. 2004; Liston and Winther 2005; Mernild et al. 2006b, 2008b, 2010a, 2011b; Liston and Hiemstra 2008, 2011a,b; Mernild and Liston 2010, 2012).
c. Simulation domain, model configuration, and meteorological forcing
The Mittivakkat Glacier (31 km2; 65°42′N, 37°48′W) is a local glacier (peripheral to the GrIS), located on Ammassalik Island in southeast Greenland. The model simulation domain (Fig. 4) includes the glacier and the surrounding area and ranges in elevation from sea level to 973 m MSL. The entire Mittivakkat Glacier complex (ranging from approximately 160 to 930 m MSL) has several river and stream outlets that drain through proglacier valleys into Sermilik Fjord.
(a) The Mittivakkat Glacier simulation domain, in southeast Greenland, with topography (100-m contour interval) and land cover characteristics. Also shown are the two automatic weather stations, Station Nunatak (515 m MSL) and Station Coast (25 m MSL), and the hydrometric station at the A4 catchment outlet (for locations of the different catchment outlets see Fig. 6). The inset figure indicates the general location of the Mittivakkat Glacier region (red dot) in southeast Greenland. The domain coordinates can be converted to UTM by adding 548 km to the west–east origin (easting) and 7281 km to the south–north origin (northing) and converting to meters. (b) September 2005 QuickBird image of the glacier and surrounding landscape.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
Starting in 1931, Mittivakkat Glacier has been observed at regular intervals using aerial photography, and since that time the glacier terminus has retreated approximately 1300 m. Mittivakkat Glacier is the only local glacier in Greenland for which there exist long-term observations of surface mass balance (WGMS 2009). In 1995 an annual surface-mass-balance program for the glacier was initiated (Knudsen and Hasholt 2002). In 13 of the last 15 years, the Mittivakkat Glacier had a negative surface mass balance, with an average of −0.87 ± 0.66 m water equivalent (w.eq.) yr−1, and a cumulative net mass balance of −13.0 ± 1.9 m w.eq. (Mernild et al. 2011a). This corresponds to a 15-yr 11% decrease of the total ice volume determined in 1994 by Knudsen and Hasholt (1999). For the last eight years (2002/03 through 2009/10; corresponding to the study period described herein), the average mass balance was −1.05 ± 0.81 m w.eq. yr−1, with a winter balance of 1.03 ± 0.14 m w.eq. yr−1, and a summer balance of −2.01 ± 0.63 m w.eq. yr−1 (Table 1). At present, Mittivakkat Glacier is significantly out of equilibrium with present-day climate, and will likely lose approximately 70% of its current area and approximately 80% of its volume, even in the absence of further climate changes (Mernild et al. 2011a).
Mittivakkat Glacier surface mass balance observations for the 8-year period 2002/03 through 2009/10 [individual mass balance data for the entire available 15-year observation period can be found in Knudsen and Hasholt (2008) and Mernild et al. (2011a)].
The mean annual air temperature for the Mittivakkat Glacier region (1994–2006) was −1.7°C. Mean annual relative humidity and wind speed were 83% and 3.9 m s−1. The corrected (following Allerup et al. 1998, 2000) mean total annual precipitation (TAP) was 1550 mm w.eq. yr−1 (Mernild et al. 2008a).
SnowModel was used to simulate gridcell snow evolution, surface energy fluxes, snowmelt and icemelt, and runoff, for the 8-yr period 2002/03 through 2009/10. These runoffs were then used to drive HydroFlow to simulate runoff hydrographs spanning the 8-yr simulation period for each grid cell within the simulation domain. The simulation covered an 11-km by 13-km (143 km2) domain centered on the Mittivakkat Glacier, including its coastal zone along Sermilik Fjord (Fig. 4). The model simulation was performed using a 100-m horizontal grid increment (14 300 grid cells) and 1-day time step. Topographic data used in the model simulation were obtained from a digital elevation model (DEM) based on a 1:100000-scale map with a 25-m contour interval (Mernild et al. 2006b). Each grid cell was classified into SnowModel land cover classes (Liston and Elder 2006a) as bedrock, fjord/lakes, or glacier using a QuickBird satellite image acquired September 2005 (Fig. 4).
To solve the HydroFlow coupled system of equations, watershed flow–accumulation networks must be defined over the domain of interest. In this Greenland application, every nonocean grid cell within the simulation domain is part of a defined watershed, and each watershed has a single flow outlet into either the simulation domain boundary (for the case where the boundary is a land grid cell) or the ocean (Fig. 5). The Terrain Analysis Programs for the Environmental Sciences-Grid Version (TAPES-G) (Gallant and Wilson 1996), in conjunction with the 100-m grid increment simulation domain DEM, was used to define the individual watersheds and the associated grid connectivity within each watershed (Fig. 6). The TAPES-G implementation allows the user to define the domain area and grid size.
Example flow network calculated from hypothetical gridded topography and ocean-mask datasets to illustrate the HydroFlow network configuration over the simulation domain. Computational domain boundary cells are black, gray cells are ocean. Other colors represent individual drainage basins, each of which drains either into the domain boundary or the ocean. Basin outlet points are indicated by black dots and the drainage network by black lines.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
Mittivakkat Glacier complex (represented by the bold black line) and simulation domain including individual glacier basins (Area 1 to 11) (represented by different colors), stream/river flow network (represented by white lines), and locations B1, A4, C1, D1, A3, A2, and A1 for the simulated hydrographs.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
Atmospheric data to drive the model simulations were provided by two automatic weather stations within the domain: Station Nunatak (515 m MSL; representative of the glacier) and Station Coast (25 m MSL; representative of the coastal and valley areas). At these stations wind speed, wind direction, air temperature, and relative humidity were recorded at 2-m levels every hour, and resampled to mean daily values. Liquid precipitation (rain) was measured at both stations 0.45 m above the ground; a height equal to the local roughness elements (i.e., rocks) (for additional information about the meteorological stations, see Mernild et al. 2008a). Solid precipitation (e.g., snowfall) was calculated from snow depth sounder observations, assumed to have an accuracy of within ~10%–15%, adjusted according to routines described by Mernild et al. (2006b) and Liston and Hiemstra (2008). SnowModel has been applied and tested within the Mittivakkat Glacier region, and substantial correlations have been found when model outputs were compared with independent in situ observations of meteorological variables, snow depths and distributions, and glacier mass balances (Hasholt et al. 2003; Mernild et al. 2006b, 2010b; Mernild and Liston 2010). In light of the considerable MicroMet and SnowModel modeling work already done in the Mittivakkat Glacier area, we concluded that the combination of MicroMet and SnowModel simulated gridcell runoffs were of sufficient quality, without any additional adjustments, to drive the HydroFlow simulations.
4. Results
The Mittivakkat Glacier complex and its surrounding landscape, including the simulated individual drainage catchments and flow network, are illustrated in Fig. 6. HydroFlow (using TAPES-G) divided the glacier into 11 individual drainage basins (Fig. 6 and Table 2), and the entire simulation domain was divided into approximately 300 individual subcatchments peripheral to the glacier, where approximately 150 of these subcatchments drain directly into Sermilik Fjord. The eleven drainage basins covering Mittivakkat Glacier ranged in size from 0.4 km2 (Area 3, covering 1% of the glacier area) to 13.6 km2 (Area 4, covering 44% of the glacier area), and the three largest basins (Areas 4, 5, and 8) drained approximately 80% of the glacier area into Sermilik Fjord through the watershed outlets A4, C1, and D1 (Table 2, Figs. 6 and 7).
HydroFlow simulated Mittivakkat Glacier basins and catchment areas for the simulation domain (see Fig. 6 for the location of the catchments and catchment outlets). Average specific runoff is shown for the outlets B1, A4, C1, and D1 (2002/03–2009/10).
Catchment outlets to Sermilik Fjord: (a) A4 and (b) D1. The photos were taken looking west toward Sermilik Fjord, and the distances from the foregrounds to the coast is approximately 2 km (photos: S. H. Mernild, August 2010).
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
The size of the HydroFlow-estimated Mittivakkat Glacier watershed was compared with maps and field observations (Mernild and Hasholt 2006; Mernild et al. 2006a; Knudsen and Hasholt 2008). The drainage area upstream of location A4, for example, was previously estimated to be 18.4 km2 with 78% glacier cover (14.3 km2). In HydroFlow, the area upstream of A4 was 19.0 km2 with 72% glacier cover (13.6 km2). Compared to previous observational studies, HydroFlow reproduced the location of the watershed divides reasonably well and, based on the 100-m grid increment DEM, the size of the defined drainage area is assumed to be within an error of a few percent. Even though HydroFlow reproduced the individual catchments, we are aware, based on tracer observations, that glacier subsurface (englacial and subglacial) water flow between neighboring glacier basins (e.g., to/from Areas 4 and 5) occurs due to englacial fractures such as crevasses and moulins (Mernild 2006, Mernild et al. 2006a). The subsurface exchange between neighboring basins is expected to have only a minor influence on the outlet hydrographs (Mernild et al. 2010b).
For the watersheds upstream of locations A4, C1, and D1 (Fig. 6) the percentage of simulated drainage area covered by Mittivakkat Glacier ranged from 21% (6.0 km2, Area 5) to 72% (13.6 km2, Area 4) (Table 2). In this region, watershed runoff is largely an integrated response of snow and glacier melt and liquid precipitation. Previous studies (e.g., Hasholt and Mernild 2008) have shown that it is appropriate to assume an insignificant contribution from subsurface flow occurs in the glacier-free areas of this bedrock dominated landscape (Fig. 7). Therefore, runoff from different catchments was strongly influenced by the fraction of glacier coverage where high runoff volumes were associated with glacier cover at low elevations. In Fig. 8 for example, the 2003 biweekly spatial distribution of seasonal cumulative runoff, produced by SnowModel at each grid cell, for Mittivakkat Glacier and the bedrock peripheral to the glacier, is illustrated for 1 June through 15 August (for 31 August 2003, see Mernild et al. 2008c). At the low lying glacier margins more than 1600 mm w.eq. runoff was simulated, and runoff from snow cover (and some rain) on bedrock was approximately 900 mm w.eq.
Simulated, biweekly, cumulative, SnowModel grid-cell runoff distribution for the Mittivakkat Glacier region for 2003 from 1 June through 15 August. For 31 August (end of the ablation period), the spatial runoff distribution can be seen in Mernild et al. (2008c).
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
As part of the HydroFlow routing of these (Fig. 8) gridcell runoffs, it assumes there are two runoff components within each HydroFlow grid cell: a within-gridcell slow-response runoff and a fast-response runoff associated with the overland flow network. Each of these is associated with a residence or transient time (k) describing how long it takes a fluid element to pass through a model grid cell. To solve the system of equations, grid-specific, time evolving, residence time coefficients, k, were defined using Mittivakkat Glacier field measurements (Mernild 2006; Mernild et al. 2006a). These field observations included tracer measurements for snow-covered ice, snow-free ice, snow-covered land, and snow-free land at the beginning and the end of the ablation period (see the k values listed in section 2). Figure 9 provides the 2003 time evolution of fast-time-scale k values over the simulation domain. Shown are the changes in water residence times resulting from changes in snow- and ice-covered fractions for glacier and glacier-free areas of the domain. As the snow on land melts free, the residence times increase in response to the water flowing through the tortuous rock-debris flow paths (e.g,. Figure 7), and as the glacier surface becomes snow-free, the residence times are reduced.
Biweekly fast-time-scale residence time coefficient (kf) distributions for the Mittivakkat Glacier region, from 15 June through 31 August 2003. Note the different times plotted in this figure and Fig. 8; because of delayed melt in 2003 the 1 June distribution is identical to that on 15 June.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
The seasonal variability in HydroFlow simulated runoff at outlet A4 was compared, in detail, with observed runoff time series for the two years when we have the most observed runoff data: 2003 (the year with the second lowest cumulative runoff of 25.1 × 106 m3) and 2010 (the year with the highest cumulative runoff of 52.8 × 106 m3) (Figs. 10a and 10b), yielding r2 (square of the linear correlation coefficient) values of 0.77 and 0.63, respectively, and Nash–Sutcliffe coefficient (NSC) (Nash and Sutcliffe 1970) values of 0.61 and 0.60, respectively. If the NSC is 1, then the model is a perfect fit to the observations. If NSC is less than 1, decreasing values represent a decline in goodness of fit, where 0 and negative values represent major deviations between the modeled and observed data. Note that these goodness-of-fit measures could be improved with additional calibration of the fast-response and slow-response transfer functions; something we did not attempt. The other years with runoff observations yielded r2 values of 0.59 for 2004 and 0.62 for 2009.
(a) Observed and simulated runoff at location A4 for 2003 (the year with the second lowest cumulative runoff) and (b) 2010 (the year with the highest cumulative runoff) (r2 = square of the linear correlation coefficient), the observation period is shorter than the simulation period; (c),(d) simulated hydrographs at different locations upstream for outlet A4; and (e),(f) simulated hydrographs at outlets B1, A4, C1, and D1 to the Sermilik Fjord (for outlet locations see Fig. 6).
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
In general, the simulated runoff variations and peaks reproduced available discharge observations (r2 = 0.77 and 0.63), both in time and volume. For 2003 and 2010 the difference between simulated and observed runoff was ~12 000 m3 (analog to a mean discharge difference of 0.14 m3 s−1) and ~2200 m3 (0.03 m3 s−1), respectively, where positive numbers mean the model is overestimating observed control values, and vice versa. Further, comparison of simulated and observed peak runoff values indicate a maximum difference of ~267 000 m3 (analog to a maximum discharge difference of 3.10 m3 s−1) for 2003 and ~453 000 m3 (5.25 m3 s−1) for 2010 (Figs. 10a and 10b). Overall, for the two analyzed years HydroFlow is able to reproduce mean and peak control values reasonably well.
Figures 10c and 10d display the within-catchment runoff variability by plotting the hydrographs at locations A1 through A4 for 2003 and 2010. Consistent with the model formulation, the hydrographs for both 2003 and 2010 increased in volume and runoff period downstream as the flow network progressed downbasin from point A1 through A4. This occurs in response to both decreasing elevation and increasing drainage area. Further, seasonal runoff variations were similar for all four locations, with the most pronounced being at the outlet (A4) and the least pronounced being upstream (A1).
The simulated runoff values at the B1, A4, C1, and D1 catchment outlets (Figs. 10e and 10f), display the spatial variation in coastal runoff contributions from these primary catchments that drain into Sermilik Fjord. At regional scales the spatial variation in runoff was closely associated with variations in glacier cover, size of the drainage area, and travel distance within each catchment (Figs. 10e and 10f). The watersheds upstream of outlets A4 and C1 produced the greatest runoff contribution to Sermilik Fjord.
The 2003–10 mean cumulative annual discharge (m3) into Sermilik Fjord from catchment outlets B1, A4, C1, and D1 are illustrated in Fig. 11a. Figure 11b displays the mean cumulative annual discharge (m3) from all of the catchment outlets along the eastern coast of the simulation domain (they all feed into Sermilik Fjord) for 2003 and 2010. The dominance of the B1, A4, C1, and D1 outlets are clear in Fig. 11b. Also shown is the percentage of total annual discharge represented by the B1, A4, C1, and D1 outlets. In 2003 and 2010, 84% and 90%, respectively, of the eastern coastal discharge came from outlets B1, A4, C1, and D1. Averaged over the 2003–10 simulation period, outlets B1, A4, C1, and D1 contributed approximately 90% of the annual discharge (128.9 ± 34.1 × 106 m3 yr−1 with a standard deviation of ±34.1 × 106 m3 yr−1) to Sermilik Fjord. Taken individually, the average contributions from C1 (38.5 ± 22.2 × 106 m3 yr−1) and A4 (40.9 ± 13.7 × 106 m3 yr−1) were each approximately 30% of the total, and contributions from B1 (14.7 ± 5.8 × 106 m3 yr−1) and D1 (22.4 ± 8.0 × 106 m3 yr−1) were each approximately 15% of the total. For the watersheds without glacier cover (these comprised approximately 90% of the catchments) the cumulative annual discharge to the ocean was relatively low, in the range of 1.0 × 104 to 1.0 × 105 m3 y−1. This uneven spatial distribution of runoff to the ocean (Fig. 11b) is expected to occur throughout East Greenland where the strip of land between the GrIS and ocean contains thousands of individual glaciers, ice caps, and ice-free areas peripheral to the Ice Sheet (Fig. 1).
(a) 2003–10 mean and standard deviation of annual simulated cumulative runoff to the Sermilik Fjord from catchment outlets D1, C1, A4, and B1 (106 m3 y−1) and (b) spatial runoff distribution to Sermilik Fjord for 2003 and 2010. The percentages indicate the fraction of annual discharge into Sermilik Fjord from outlets D1, C1, A4, and B1. Note the ordinate logarithmic scale.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
Another way to compare runoff contributions from different catchments is by looking at specific runoff (runoff volume per unit drainage area per time, L km−2 s−1; to convert to mm yr−1 multiply by 31.6). For the Mittivakkat Glacier region the specific runoff averaged from 43 to 68 L km−2 s−1 (Table 2); the highest values were for outlet A4, due to its high percentage (72%) of contributing area glacier cover. Previous independent model simulations presented an average (1994–2004) value of 63 L km−2 s−1 for the catchment upstream of outlet A4 (Mernild and Hasholt 2006); the same order of magnitude as the value simulated by HydroFlow (Table 2). Furthermore, due to the high percentage of glacier cover upstream of location A4, variations in annual Mittivakkat Glacier net mass balance from 2002/03 through 2009/10 had a significant impact on annual runoff variations (r2 = 0.56; p < 0.01, where p is the level of significance), indicating that, on average, approximately 35% of the simulated runoff was explained by the Mittivakkat Glacier net loss. This value is expected to be lower for catchment outlets C1 and D1 due to the lower percentage of glacier coverage upslope of those locations.
For 2003 through 2010 the seasonal runoff distribution was simulated for the four main outlets: B1, A4, C1, and D1 (Fig. 12). Considering all four outlets, the average runoff period was 200 ± 20 days (from approximately mid-May through mid-November). During the 8-yr study, the Mittivakkat Glacier region runoff period increased by approximately 30 days (p < 0.01, estimated from linear regression over the eight year study period). Not only did the runoff period increase for the Mittivakkat Glacier region, but the number of days with runoff volumes greater than average (1.3 × 105 m3 day−1; 2003–10) also increased. The number of days with runoff greater than average increased from approximately 70 days in 2003 to approximately 85 days in 2010 (nonsignificant), indicating, in general, more days with greater discharge to the ocean. More significantly (p < 0.01), the mean annual volume of runoff to the fjord increased by 54.9 × 106 m3 for the period 2003 through 2010. This enhanced runoff, both in number of runoff days and in volume, support the conclusion of Mernild et al. (2011a) that the Mittivakkat Glacier is out of equilibrium with present-day climate, and significant losses in glacier area and volume are expected in the future, even in the absence of further climate changes.
Simulated runoff hydrographs at the outlets D1, C1, A4, and B1 for the period 2003 through 2010 (for outlet locations see Fig. 6). For outlet A4 available observed runoff is included (no data available from 2005 through 2008). Note the different scales on the ordinate.
Citation: Journal of Climate 25, 17; 10.1175/JCLI-D-11-00591.1
5. Discussion and conclusions
Linear reservoir models have been previously applied to simulate glacier runoff discharge (see Jansson et al. 2003; Hock and Jansson 2005). In most recent applications, the glacier of interest is typically divided into two or three reservoirs according to their surface characteristics (e.g., Hock and Noetzli 1997; Hannah and Gurnell 2001; Schaefli et al. 2005; de Woul et al. 2006): one reservoir covers the snow-free area of the glacier; a second reservoir covers the seasonally snow-covered area of the glacier; and a third reservoir (if used) is applied to the area above the previous year’s equilibrium line (the firn reservoir). The areas covered by the first two reservoirs change as the snow melts and exposes the ice below, and typically the coefficients associated with each reservoir’s time scale do not change throughout the simulation period.
In contrast, HydroFlow treats each model grid cell as a linear reservoir, each with its own temporally evolving residence-time coefficients. This means that the runoff routing model is much more general and, through its coupling with SnowModel, is able to take advantage of available information related to the snow and ice evolution. For example, HydroFlow automatically accounts for when (in these simulations, the day) a model grid cell becomes snow free and only glacier ice remains, and the associated time scale changes for that grid cell. In addition, the coupling of SnowModel with HydroFlow automatically accounts for runoff differences in response to the spatial and temporal variations in snowmelt and icemelt fluxes at each grid cell and on each day of the simulation. These can be caused by, for example, variations in slope and aspect, wind fields, albedo, temperature distributions, and elevation differences (all accounted for as part of the SnowModel integrations). A further application of this coupled modeling system is to use MicroMet to downscale atmospheric forcing variables produced by regional climate model (RCM) simulations and use those to drive SnowModel and HydroFlow integrations over catchments with limited meteorological forcing data or as part of climate change studies (e.g., Mernild et al. 2010a, 2011b). It is also possible to drive HydroFlow with gridded runoff data from other land surface hydrology observation and/or modeling systems.
One source of uncertainty in the HydroFlow simulations results from processes occurring within the watershed of interest that are not included in the modeling system. While the improvements included in HydroFlow can be thought of as a step forward in runoff simulations for snowmelt and icemelt on glaciers, ice sheets, and snow-covered land, there are still numerous water-transport-related processes that are not explicitly included in the model simulations. HydroFlow for example, as with most other models, omits processes such as temporal variations in 1) englacial bulk water storage and release, including drainage from glacial surges and drainage of glacial-dammed water (long-term build-up of storage followed by short-term release); 2) melt contributions from internal glacial deformation, geothermal heat, basal sliding, and the internal drainage system as it evolves during the melt season; 3) englacial water flow between neighboring catchments; and 4) open channel streamflow routing. In addition, SnowModel is not a dynamic glacier model, and routines for simulating changes in glacier area, size, surface elevation, and seasonal variations in the internal drainage system, are not yet represented within the modeling system.
Uncertainty in the simulated runoff discharges also occurs as a result of oversimplifications of the processes represented within the modeling system and due to simplified representations of the atmospheric forcing (e.g., air temperature and precipitation). At present, physically based glacier runoff models are simple representations of a complex natural system (e.g., Hock and Jansson 2005). But, with the HydroFlow routines for estimating drainage area, watershed divides, the flow-accumulation network, the time evolution and spatial distribution of different water transport mechanisms, and the runoff transient times, we are now able to provide information about the temporal and spatial variability in runoff at each point within the catchment including the watershed outlet and at every watershed, large and small, within the simulation domain. A further advantage of this spatially distributed modeling approach is that it also allows detailed analyses of within-watershed runoff-related processes such as those associated with solute transport and sediment erosion and accumulation (Hasholt and Mernild 2006). While good model performance at gauging stations does not ensure good performance at sites upstream of those stations (Refsgaard 1997), the nested watersheds within the simulation domain considered herein have similar physical and climatological conditions as the outlets of the main catchments. Therefore, we expect similar behavior in them also. In addition, the physically based representations contained within MicroMet and SnowModel make them appropriate tools to simulate rainwater and snowmelt and icemelt fluxes, and using them to drive HydroFlow, for both gauged and ungauged basin applications. At the largest scale the combination of MicroMet, SnowModel, and HydroFlow provides the ability to estimate the time evolution and spatial distribution of runoff into adjacent oceans.
Over recent decades, transforming glacier meltwater and liquid precipitation into hydrographs by modeling glacier hydrology has improved in parallel with our increased understanding of the role of snow and ice in the hydrological system. A fundamental premise of the HydroFlow runoff routing model presented herein is that the simulation domain can be divided into individual drainage basins, each with its own river/streamflow network that can track rain and meltwater from snow and ice across and through snow-covered and snow-free glaciers, ice sheets, and land to surrounding oceans. The spatial distribution of catchment runoff to Sermilik Fjord from the Mittivakkat Glacier region was strongly influenced by catchment size and variations in glacier elevation range and areal coverage. For the majority of catchments without glacier cover (approximately 90%) the cumulative annual runoff ranged from 1.0 × 104 to 1.0 × 105 m3 y−1, corresponding to approximately 850–1100 mm yr−1. For catchments with glacier cover the annual runoff was as high as 40.9 × 106 m3 yr−1, corresponding to approximately 2100 mm yr−1 (and contributed approximately 90% of the domain runoff to Sermilik Fjord). A similar uneven discharge pattern to the ocean is expected to be present throughout Greenland because, like the Mittivakkat Glacier region, the land area between the GrIS and ocean includes numerous individual glaciers and ice caps peripheral to the Ice Sheet (Fig. 1).
Acknowledgments
The authors thank Jens Christian Refsgaard, Sveta Stuefer, Kazuyoshi Suzuki, Hans Thodsen, and Amy Tidwell for their insightful review of an early version of this paper. This work was supported by NASA Grant NNX08AV21G; Norwegian Research Council Grant 192958/S60, titled Updating Methodology in Operational Runoff Models; a consortium of Norwegian hydropower companies lead by Statkraft; grants provided by the Climate Change Prediction Program and Scientific Discovery for Advanced Computing (SciDAC) program within the U.S. Department of Energy Office of Science; and by the Los Alamos National Laboratory (LANL) Director’s Fellowship. LANL is operated under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy under Contract DE-AC52-06NA25396. We also thank the Department of Geography and Geology, University of Copenhagen, for providing the observed meteorological and runoff data, and Jeppe Malmros, University of Copenhagen, for the graphic design of Fig. 1.
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