Supraglacial meltwater channels are ubiquitous fluvial features in the ablation zones of glaciers and ice sheets (e.g., [1
]). They are of intrinsic interest to researchers as unique fluvial systems as well as for the important roles they play in glacial hydrology. As fluvial systems, researchers have been interested in their morphometrics and controlling processes (e.g., [1
]), and in how their form may encode landscape processes [10
]. Hydrologically, supraglacial meltwater channels influence the spatial and temporal distribution of surface water inputs to en- and sub-glacial hydrological systems [3
], which in turn have been shown to influence glacier and ice sheet dynamics (e.g., [3
]). This recent and growing interest has been concurrent with a growing availability of high-resolution remotely sensed imagery and topographic data of ice surfaces [16
Relatively little is known about the characteristics of these channel networks and their controls, in part because of a dearth of data on their form and behavior through space and time [21
]. Most data pertaining to supraglacial channel form and process come from spatially and temporally limited field studies carried out in the 1970s–1980s [1
]. Recently, remotely sensed imagery of ice surfaces has facilitated various approaches to supraglacial channel delineation. Manual delineation of meltwater channels and lakes has been widely used with imagery from various satellites. Landsat ETM+ has been used to assist with meltwater channel digitization on the Devon Ice Cap [3
] and the Greenland Ice Sheet (GrIS) [6
]. Optical imagery from WorldView-1 has been used to delineate channels on the GrIS [13
]. Landsat-7/8, L-band ALOS-PALSAR, and C-band RADARSAT images were used to detect mainstem reaches of large supraglacial meltwater channels on the southwest GrIS [33
Multispectral methods, in which channels are automatically delineated based on the spectral reflectance of water relative to snow and ice, have also been employed with significant success. Smith et al. (2015) [2
] and Yang et al. (2015) [34
] used multispectral methodologies on high-resolution (~2.0 m) WorldView-2 imagery of the southwest GrIS to produce the most extensive dataset to date, and Yang et al. (2016) [8
] analyzed fluvial morphometry of these supraglacial river networks. With topographic data, Rippin et al. (2015) [4
] used drone imagery to produce high-resolution (0.01 m) surface Digital Elevation Models (DEMs) of an alpine glacier in Svalbard, and identified channels using an iterative elevation threshold. DEMs have also increasingly been used to delineate channels through flow routing methods modified for use on ice surfaces [10
Each methodology has its limitations. Manual digitization is labor-intensive and sensitive to user bias. Multispectral methods have been highly successful [2
]. However, at commercially available multispectral image resolution (~2 m), they underestimate channel density by as much as sevenfold when compared to manually digitized channel networks (spatial resolution 0.5 m) [2
]. Additionally, both methods have been found to be of limited utility at low elevations on the GrIS where supraglacial rivers are smaller, less dense, and more segmented by crevasse fields [6
]. Furthermore, the derived network does not directly contain spatial information on channel network linkages, and requires additional geometric processing to create continuous networks and derive basic connectivity data [6
In terrestrial landscapes, flow routing is a standard and widely accepted methodology for delineating channels from DEMs [38
]. This method assumes an impermeable surface with no storage and requires that sinks (low elevation pixels surrounded by higher elevation pixels) be leveled to force flow routing from drainage boundary to catchment outlet [39
]. This processing step is problematic in ice surfaces, however, where surface water drains via moulins (sinks on the ice surface) to the englacial hydrological system [39
]. Yang et al. (2015) [34
] and Rippin et al. (2015) [4
] both concluded that flow routing overestimates hydrological network extent for this reason. Studies employing flow routing to delineate supraglacial meltwater drainage pathways have employed various approaches to this problem. Banwell et al. (2012) [35
] defined all depressions in moderate resolution (30 m) DEMs as supraglacial lakes, and modeled flow routing over the GrIS by employing a lake filling model. Banwell et al. (2013) [12
] and Arnold et al. (2014) [36
] further assumed these lakes drain through moulins, and therefore preserved all topographic depressions as sinks during flow routing over moderate resolution DEMs (30 and 90 m, respectively). Yang et al. (2015) [34
] tested an automated sink retention size threshold (termed a “depression area threshold”), but advised caution when using flow routing over moderate resolution (30–40 m) DEMs to delineate supraglacial channels. To overcome the limitations of automated moulin detection, non-automated sink preservation has been used by Andrews (2015) [37
] and Karlstrom and Yang (2016) [10
], in which manually identified moulin locations are preserved as sinks during flow routing over moderate- (25 m, resampled from 10 m) and high-resolution (2 m) DEMs, respectively.
Flow routing has many advantages with regard to channel delineation, even in the relatively complicated case of ice surfaces. It is a widely used, relatively simple method of channel delineation, and a basic feature of most GIS platforms (e.g., [42
]). Channel locations are derived based on a physical relationship, i.e., the geometric network relationship between one channel pixel and another is physically interpretable based on their elevation differences and positions in the network. Contrast this to, for example, manually digitized channel networks, in which it can be difficult to distinguish flow direction between pixels, and spatial proximity may not be a good indicator of network connectivity. Network connectivity is implicit in flow routing; no further processing is needed to connect channel segments and order networks. This avoids the complication of shape analysis (e.g., [8
]) or linear feature detection (e.g., [17
]), and facilitates the easy coupling of channel networks with hydrological models and topographically derived morphometrics such as stream ordering, contributing area, and gradient (e.g., [45
]). Furthermore, using flow routing to delineate supraglacial channels provides the opportunity to capitalize on the growing availability of often free, high-resolution topographic data of a variety of glacier and ice sheet surfaces [16
In this paper, we assess the performance of flow routing on high-resolution (2 m) ice surface DEMs [16
] with targeted (non-automated) moulin identification to systematically assess the utility and limitations of flow routing in supraglacial channel delineation. We employ this methodology to assess the performance of flow routing in delineating supraglacial channels without the complicating factor of automated sink detection, i.e., under the assumed conditions of known sink locations. Both crevasses and moulin-type sinks are retained during sink filling, based on manual identification of sinks. The impacts of channel initiation threshold on the flow routing-derived channel network extent and accuracy are investigated. This assessment is made relative to two independent datasets—one manually digitized from Worldview-1 0.5 m resolution panchromatic imagery, and one of channels derived through multispectral analysis, developed by Smith et al. (2015) [2
] (see Table 1
2. Materials and Methods
Supraglacial meltwater channels were extracted from DEM datasets using a flow routing (FR) workflow described in Section 2.2
below. The performance of this workflow is evaluated by comparing the results to two independent datasets: (1) meltwater channels derived from multispectral (MS) imagery by Smith et al. (2015) [2
]; and (2) manually digitized (MD) fluvial channel networks, as described below. A summary of the datasets is provided in Table 1
. The following sections describe the data sources, channel extraction workflow, and error analysis.
2.1. Datasets and Study Area
The spatial and temporal coverage of the study was constrained by the availability of data. As such, this study is focused on Greenland’s southwestern margin where there is a coincidence of multispectral and topographic datasets. The study area displays extensive supraglacial channel development [2
], and has been the focus of previous studies on the GrIS’s surface meltwater systems (e.g., [2
]). A total of seven meltwater catchments were delineated through flow routing on the ice surface. Their characteristics are described in Table 2
and their spatial extents are shown in Figure 1
. Six of the catchments (Catchments 1–6) were above 1000 m in elevation (‘high’-elevation catchments), where the ice surface has a lower slope and the surface topography is generally uniform [6
]. Catchment 7 (‘low’-elevation catchment) was delineated on Russell Glacier, where surface slopes are higher and numerous areas of extensional and compressive ice flow create a rough surface, imparting structural elements to the ice surface. To date, there has been no successful, automated methodology developed for delineating supraglacial channels at low elevation, often heavily crevassed parts of the GrIS [6
]. This seventh location was chosen specifically to assess the performance of flow routing in delineating channels across a range of ice surface morphologies. Only one low-elevation catchment was selected as MS-derived meltwater channel data were not available for low-elevation locations and the comparison was therefore limited to MD channels.
The dataset used to test the channel extraction by flow routing is a 2 m resolution DEM of large parts of the western GrIS. This ‘Surface Extraction with TIN-based Search-Space Minimization (SETSM)’ DEM is derived from overlapping DigitalGlobe Worldview-1 satellite images and has reported root mean square errors of 3.8 and 2.0 m in the horizontal and vertical, respectively [16
]. Experience working with the data suggests that errors in geo-referencing may produce local errors and offsets of several tens of meters between features in the DEM and their real-world coordinates. An offset was similarly observed by Andrews (2015) [37
]. Flow routed (FR) channel networks were delineated using flow routing over the SETSM DEM in all seven study catchments, as described in Section 2.2
The six high-elevation GrIS catchments (Catchments 1–6) extracted from the SETSM DEM using flow routing overlap in space with multispectral-derived meltwater channel networks extracted from 2 m resolution WorldView-2 images dated to July 2012, provided by Smith et al. (2015) [2
] (Table 1
and Table 2
). This MS dataset represents channels containing meltwater at the time of image acquisition, as identifiable at the 2 m resolution. These overlapping FR and MS datasets are used to compare the channels derived with multispectral and flow routing methodologies. The FR dataset for Catchments 1–3 overlaps in time with the MS datasets, and is dated to one month after the MS dataset for Catchments 4 and 5. The FR dataset for Catchment 6 is from August 2011. Data availability and overlapping spatial extent for the MS and FR datasets limit the spatial extent of our study area and restrict the temporal resolution of our data choices. However, numerous observations suggest that supraglacial meltwater channels (particularly high-order, mainstem channels) perennially re-occupy the same spatial location [1
], even as abandoned channels are advected down-glacier [10
]. Furthermore, Lampkin and VanderBerg (2014) [29
] observe that the extent of the supraglacial network on the GrIS, observable at 15 m resolution, did not change significantly between early July and early August 2007. Considering melt on the GrIS in 2012 was higher than in 2007, [49
], it follows that the fluvially incised channel network was sufficiently unchanged between the July and August image acquisition dates to justify comparison between datasets from the two dates. Again, we distinguish here between water-filled channels, which cannot explicitly be delineated by flow routing (the MS dataset) and whose extent is likely sensitive to timing, and the fluvially incised network, which is unlikely to change following peak melt and will persist until erased by either ablation of the ice surface or burial by seasonal snow.
A third and manually digitized dataset (MD) was also developed from 0.5 m panchromatic images from the WorldView-1 satellite, obtained for a high-elevation GrIS location that overlaps with both a MS- and FR-derived catchment (Catchment 5) and the low-elevation GrIS outlet glacier (Russell Glacier, Catchment 7). The channels in these two images were digitized manually for comparison with FR-delineated channels in both Catchment 5 and Catchment 7, as well as with the MS dataset in Catchment 5. Digitized channels were identified as rectilinear features that are darker and appear recessed relative to the surrounding ice surfaces, and were systematically digitized from the terminal moulin up to the smallest channels that could be readily distinguished in the 0.5 m resolution imagery. They may or may not have been actively filled with water at the time of image acquisition—it is not objectively possible to differentiate water from shadow, particularly in small channels, and therefore we assume that this dataset represents the full extent of the fluvially incised channel network, identifiable at 0.5 m resolution, regardless of the presence of meltwater at the time of image acquisition. Although we developed this dataset to represent an objectively mapped channel network, there are a number of errors inherent in manual digitization, including, for example, user bias, the scale of the image, limitations of panchromatic imagery (particularly with regards to illumination and shading), and difficulty distinguishing flow direction and connectedness, particularly for small channels.
The three datasets represent three distinct types of channel networks. The MS dataset represents active meltwater channels and the MD dataset represents channels that are fluvially incised but may or may not actively contain meltwater at the time of image acquisition. The FR dataset represents the likely path that water takes through a landscape, where network extent is set by a user-specified channel initiation condition. Therefore, these datasets are fundamentally different, and comparing them in this context is not intended to suggest that they are equal attempts to represent the same processes. However, the MD dataset represents fluvial incision at times of maximum melt, and therefore by definition should contain the MS dataset. For this current study, then, these datasets provide independent opportunities to assess flow routing for reproducing channel network structure and characteristics, rather than a direct comparison of their abilities to reproduce the same processes.
2.2. Channel Network Extraction
The general methodological workflow is illustrated using the DEM from which Catchment 7 was extracted (Figure 2
). In the flow routing channel extraction method, flow is routed to moulin locations in the SETSM DEM which are preserved as sinks during the sink filling stage of a flow routing workflow. Two types of potential englacial entry locations are included: sinks in crevasse fields (Figure 2
, step 3a) and isolated moulins (Figure 2
, step 3b). Although not all crevasses are necessarily englacial entry locations, preserving them as sinks in flow routing conservatively overestimates the presence of sinks in a DEM and limits the catchment extent (Figure 2
, step 6). Both crevasse fields and isolated moulins were visually identified and mapped from the DEM and hill shade layers, and sinks within (crevasse fields) or at (moulins) those locations were preserved during sink filling and flow routing. Moulins were readily identifiable as places where channels terminated abruptly, or depressions with no outlets (see Figure 2
, step 3b for an example). Crevasse fields were identified as areas with abundant parallel or cross hatched and discontinuous linear depressions. A 1 × 1 km grid was overlain on the DEM, and a grid search pattern was used to assist in the visual identification of sinks (Figure 2
, Steps 2, 3a and 3b).
Flow routing was carried out using the ArcHydro toolbox in ArcGIS 10.3.1 [43
], which allows for sink preservation during sink filling and flow routing using a standard D8 flow routing algorithm [50
]. A multi-directional flow (MDF) routing algorithm was also tested using the MATLAB based TopoToolbox [51
]. Similar to findings by Karlstrom and Yang (2016) [10
], channel networks delineated with MDF were similar to those delineated with D8. We therefore employ only a D8 flow routing algorithm here as it is coupled with sink preservation tools in ArcHydro (‘Fill Sinks’ tool using IsSink field, followed by ‘Flow Direction with Sinks’ tool). Flow was routed over the ice sheet DEM to visually identified sink locations, generating flow direction, flow accumulation, and sink watershed layers (Figure 2
, Steps 4, 5, and 6). Watersheds of interest can then be extracted for further analysis (e.g., Figure 2
, Steps 6 and 7, showing the extraction of Catchment 7). Streams were defined by employing a flow accumulation area threshold (e.g., Figure 2
, Step 7). Choosing an appropriate channel initiation threshold criteria is a pervasive problem for hydrologists and geomorphologists [52
]. It is an unresolved question in alluvial systems, and has not been addressed in supraglacial systems. In this study, we investigate the methodological effects of channel initiation area thresholds on flow routing and meltwater channel delineation as described in the following section.
2.3. Channel Initiation Threshold
Field observations suggest several different mechanisms of channel initiation. At the beginning of the melt season, saturated snow may transition into channelized meltwater flow through the formation of rills [1
], overflow from slush swamps, lakes or hollows [9
], or slush avalanches [57
]. Although these processes have been empirically described, there has been only one numerical description of the hydrodynamic controls on rill-like supraglacial channel initiation [59
]. There is therefore no generalizable and mechanistic methodology for predicting channel initiation points in a flow network. In terrestrial landscapes, inflections in slope/area relationships are often used [60
]; however, it is not yet clear if these relationships can be extended to supraglacial systems [10
], and furthermore channel initiation locations are likely below the resolution of available imagery [5
]. In previous supraglacial research, Karlstrom and Yang (2016) [10
] employed a threshold of 0.02 km2
and noted that the resultant channel networks were sensitive to this threshold. Researchers using flow routing will likely need to make locally based judgements on the initiation threshold they employ. In the present study, we avoid testing a specific initiation area and instead specify a range of 10 channel initiation threshold areas, bounded on the lower end by the high density MD networks, and on the upper end by the lower-density MS network.
We assume that the MS-derived initiation points represent an upper bound for the initiation area threshold of the active meltwater network, and the MD-derived initiation points represent a lower bound on the full extent of the fluvially formed network. We calculate initiation point density based on the density of first-order channel endpoints in the MS and MD datasets (number of initiation points divided by catchment area, giving us the average area per initiation point). An MS-derived initiation point density is available for each of the high-elevation catchments, and MD-derived initiation point densities are available for Catchments 5 and 7. The MD-derived point density is applied as the lower bound on channel initiation densities in the other high-elevation catchments, where there are no MD datasets.
Our objective here is not to suggest that the MD dataset channel head densities are directly generalizable to other parts of the GrIS. Indeed, a generalizable methodology for identifying channel initiation points is a complicated issue that is highly dependent on scale and local governing processes [59
], and is beyond the scope of this work. In this work, we investigate the MD threshold as a suitable and conservative channel initiation area recommendation value during or right after peak melt time. In the absence of process based approaches to mapping channel initiation locations, initiation area thresholds may be useful for the purpose of helping researchers map general surface drainage patterns rather than to reveal the physical processes of channel initiation.
2.4. Quantification of Discrepancy between Datasets
Systematic and local offsets sometimes exist between the channel networks from the different datasets due to stitching and georectification errors, and potentially, in the case of datasets with different acquisition dates, due to ice advection. This makes comparisons of the three flow extraction methodologies difficult. A direct spatial comparison would necessitate a large allowable offset, which would complicate the analysis in such a dense network of channels. Because our interest here is an evaluation of flow routing as a means of delineating supraglacial channels, and not an assessment of the datasets, the datasets were spatially adjusted to ensure spatial overlap and facilitate error quantification. This was done by linear translation using readily identifiable channel junctions as displacement links between datasets.
Many flow routing algorithms, including D8, cannot produce realistic channel segments in the absence of topographic variation, including over lakes, and furthermore cannot capture channel bifurcations. As such, channel lengths in lakes and large bifurcations were removed from the datasets. Lakes were visually identified as areas with multiple adjacent, perfectly straight channel segments in the FR dataset, and large braided sections were automatically identified by building polygons from enclosed areas in the MS dataset.
Similarity between the datasets was determined as follows. (1) The lowest drainage density dataset was identified, hereafter referred to as Dataset A (the MS dataset in Catchments 1–6 and the FR dataset in Catchment 7); (2) A 15-m buffer was applied to Dataset A (buffer size determination is explained below); (3) The comparison dataset (Dataset B) was clipped to the buffer; (4) Before comparing the datasets, we removed any lengths of channel equal to or shorter than twice the buffer width in the clipped Dataset B (i.e., any lengths of channels shorter than 30 m). This was done to avoid artificially high match rates due to inclusion of the ends of tributary channels from Dataset B incidentally clipped to the Dataset A buffer.
Similar to Yang et al. (2015) [34
], two metrics of comparison were employed: (1) the length of the clipped Dataset B relative to the length of Dataset A, which provides a measure of the similarity between Datasets A and B; and (2) the length of Dataset B outside of the buffer relative to the total length of Dataset B, which provides a measure of how much additional channel network is delineated in Dataset B. Yang et al. (2015) [34
] refer to these two metrics of comparison as ‘completeness’ and ‘miscoding’; however, this terminology is not adopted here. As discussed in Section 2.1
, the MS dataset represents the lower-density active meltwater channels and the MD and FR datasets target the fluvially incised network; these are therefore not direct comparisons of the same system, and we therefore avoid the implication of a direct comparison implicit in the terms ‘completeness’ and ‘miscoding’.
Appropriate buffer size was determined by comparing match rates between the datasets over a range of buffer sizes. A 15 m buffer size was chosen because additional increases to buffer size produced only moderate gains in match rate and, because the data had been spatially translated, we wanted to employ as small a buffer size as possible while still allowing for some unavoidable minor offset between the datasets.