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Rock glaciers of the contiguous United States: GIS inventory and spatial distribution patterns

Abstract. Continental-scale inventories of glaciers are available, but no analogous rock glacier inventories exist. We present the Portland State University Rock Glacier Inventory (n = 10,343) for the contiguous United States, derived from the manual classification of remote sensing imagery (Johnson 2020, https://doi.pangaea.de/10.1594/PANGAEA.918585). Individually, these rock glaciers are found across widely disparate montane environments, but their overall distribution unambiguously favors relatively high, arid mountain ranges with sparse vegetation. While at least one rock glacier is identified in each of the 11 westernmost states, nearly 88% are found in just five states: Colorado (n = 3889), Montana (n = 1813), Idaho (n = 1689), Wyoming (n = 850), and Utah (n = 834). Mean rock glacier area is estimated at 0.10 km2, with cumulative rock glacier area totaling 1008.91 km2. Rock glaciers are assigned to a three-tier classification system based on area thresholds and surface characteristics known to correlate with downslope movement. Class 1 features (n = 7052, average area = 0.12 km2) appear to be highly active, Class 2 features (n = 2416, average area = 0.05 km2) appear to be intermediately active and Class 3 features (n = 875, average area = 0.04 km2) appear to be minimally active. This geospatial inventory will allow past rock glacier research findings to be spatially extrapolated, help facilitate further rock glacier research by identifying field study sites, and serve as a valuable training set for the development of automated rock glacier identification and classification methods applicable to other large regional studies.


Rock Glacier Identification
Because glaciers and rock glaciers are often co-located (Jones et al. 2019a, Knight et al. 2019, Millar and Westfall 2019), we used two GIS inventories that identify relevant features to inform target areas for our initial search for the rock glaciers; the Randolph Glacier Inventory (RGI) v6.0 (RGI Consortium 2017, Fountain et al. 2017) and the National Land Cover Database (NLCD) 2011 (Homer et al. 2015). The RGI is focused only on glaciers, whereas the NLCD identifies any perennial snow or ice feature. From this initial effort and our growing expertise in locating rock glaciers, we expanded our search areas to explore alpine regions far from any inventoried glaciers or perennial snow or ice features, but that could potentially host rock glaciers.
Rock glaciers were identified manually by their distinct surface characteristics (Aoyama 2005, Haeberli et al. 2006). These characteristics include ridge and swale surface banding resulting from differential flow rates and terminal and lateral slopes over-steepened beyond the angle of repose, presumably cemented by interstitial ice. Common mass wasting processes responsible for individual fragments of regolith traveling downslope result in accumulations at or below the angle of repose.
Similar approaches to rock glacier identification, focusing on surface topography characteristics identified from aerial and satellite imagery, have been applied in other previous research (Eztelmuller et al. 2007, Janke 2007, Degenhardt 2009, Janke et al. 2015, Millar et al. 2019.
We focused our inventory efforts on identifying rock glaciers that, surficially, appear to contain appreciable internal ice fractions and are presently or were recently flowing downslope. We follow previous studies that omit features with expansive bare glacial ice in their accumulation zones as those are clearly debris-covered glaciers, but make no attempt to discriminate rock glaciers from fully mantled debris-covered glaciers , Berthling 2011, Perucca and Angillieri 2011. After the exponentially larger study area than any previously investigated, a second major distinction between our rock glacier inventory and classification system and other previous U.S. rock glacier inventory efforts is that we intentionally attempt to exclude relict rock glaciers. We ignored potential candidate features lacking over-steepened terminal slopes and/or present evidence of advanced surficial soil development, such as expansive vegetation growth, both of which imply the rock glacier has a small internal ice fraction and/or has not flowed downslope recently.
When identifying a candidate rock glacier, plan-view images were initially viewed at 1:2000 scale or better. Once suspected ridge and swale flow banding and over-steepened terminal and lateral slopes were identified, image scale was greatly increased. All available clear sky images of the same scene were then evaluated, with plan views being replaced by oblique views from multiple angles and multiple scales and three-dimensional topography exaggerated by 50%. The perimeter of individual rock glaciers were manually delineated using Google Earth Pro. Usually, sharp changes in slope were evident, indicating a perimeter boundary between the thickened ice-bound regolith of the rock glacier and the surrounding unconsolidated talus of the adjacent slope. Additionally, lower rock glacier margins often abut well-vegetated terrain. The upper margins are often defined by a change in slope, from the steep slopes of exposed bedrock and unconsolidated talus in the rock glacier accumulation zone to the more gentle slope of the main body of the ice-thickened rock glacier.
Understandably, there can be some disagreement between analysts regarding rock glacier classification. To partially address this ambiguity all features identified as rock glaciers were subsequently assigned to a three-tier classification system based on surface characteristics known to correlate with downslope movement motivated by deformation of the internal ice-rock matrix ( Figure 1). Class 1 rock glaciers appear to be highly active, exhibit unambiguous, complex and extensive ridge and swale flow banding, and have substantially over-steepened terminal and lateral boundaries. Class 2 rock glaciers appear to be intermediately active, exhibit some pronounced ridge and swale flow banding, and have somewhat over-steepened terminal and lateral boundaries. Class 3 rock glaciers appear to be minimally active, exhibit sparse ridge and swale flow banding, and have intermittently over-steepened terminal and lateral boundaries.
To characterize the topographic characteristics of the individual rock glaciers identified, elevation data were extracted from the USGS National Elevation Dataset (NED) ⅓ arc-second (≈ 10 m) digital elevation model (USGS 2017). Topographic variables of elevation, slope, aspect, and insolation were determined using Spatial Analyst tools in ArcMap 10.4 (ESRI 2017). Rock glacier area was calculated in km 2 , while slope and aspect were calculated in degrees. Aspect was decomposed to an eastness and northness component (Nussear et al. 2009), and solar insolation was calculated in watt-hours per m 2 . To characterize the climate of the rock glaciers, climate data, including air temperature and precipitation, were also extracted from PRISM 1981 -2010 climate normals (PRISM 2017) using Spatial Analyst tools in ArcMap 10.4. PRISM data were also used to calculate several derivative atmospheric variables, such as fraction of precipitation falling as snow and mean vapor pressure deficit, using the Raster Calculator tool in ArcMap 10.4. These publicly available climate data have a spatial resolution of 800 m, with an average daily accumulated total precipitation bias of less than 2.5% in the western US, 1961-2001(DiLuzio et al. 2008. Rock glacier classification and area clustering analysis using Moran's I-statistics helped further describe rock glacier spatial distributions (Cliff and Ord 1971, Senn 1976, Tiefelsdorf 2002).

Overall Distribution
We identified 10,343 rock glaciers (Class 1 = 7052, Class 2 = 2416, Class 3 = 1021) across the western U.S. (Figure 2, Table   2), after removing 146 small (< 0.01 km 2 ) Class 3 rock glaciers following glaciological convention of area thresholds (Navarro and Magnusson 2017). Average rock glacier area is 0.10 km 2 and the average distance between each rock glacier and its nearest neighbor is 0.69 km. Contiguous U.S. rock glaciers have an average elevation of 3144.8 m, an average slope of 20.50º, an average eastness of -0.007, and an average northness of 0.066. Climatically, the average annual rock glacier precipitation is 350.2 mm, the average air temperature is 0.19 °C, the average dew point temperature is -8.37 °C, and the average vapor pressure deficit is 4.52 hPa. The overall rock glacier centroid (41.5350,-110.7072) is located in the southwest corner of the WNC region ( Figure 2). The centroids of each of the three rock glacier classes (Class 1 = (41.5136, -110.5543), Class 2 = (41.7017, -111.0135), Class 3 = (41.2470, -111.0942)) can be contained by a minimum bounding area circle with a diameter of 57.3 km. Moran's I analysis shows rock glacier classifications and areas are significantly clustered (Table 3 and   Table 4).
Geographically, the average rock glacier size is 0.07 km 2 , and the average distance between each rock glacier and its nearest neighbor is 0.99 km. Topographically, the average rock glacier elevation is 2629.6 m, the average slope is 20.7º, the average eastness is 0.000, and the average northness is 0.109. Climatically, the average annual rock glacier precipitation is 365.4 mm, the average air temperature is 1.06 °C, the average dew point temperature is -7.47°C, and the average vapor pressure deficit is 4.85 hPa. The NW region rock glacier centroid (44.8620, -115.2736) is located in the Sawtooth Mountains of Idaho In the SW region, we identified 4870 rock glaciers (Class 1 = 3291, Class 2 = 1133, Class 3 = 446)( Figure 6). The average SW region rock glacier size is 0.09 km 2 , and the average distance between each SW region rock glacier and its nearest neighbor is 0.59 km. Topographically, the average rock glacier elevation is 3490.35 m, the average slope is 20.70º, the average eastness is -0.013, and the average northness is 0.046. Climatically, the average annual rock glacier precipitation is 335.12 mm, the average air temperature is -0.09 °C, the average dew point temperature is -8.92 °C, and the average vapor In the W region, we identified 817 rock glaciers (Class 1 = 552, Class 2 = 181, Class 3 = 84) (Figure 7). The average W region rock glacier size is 0.12 km 2 , and the average distance between each W region rock glacier and its nearest neighbor is 0.68 km. Topographically, the average rock glacier elevation is 3412.2 m, the average slope is 20.9 º, the average eastness is -0.001, and the average northness is 0.082. Climatically, the average annual rock glacier precipitation is 367.79 mm, the average air temperature is 0.61 °C, the average dew point temperature is -9.52 °C, and the average vapor pressure deficit is

Inventory Accuracy
The completeness and accuracy of the inventory were qualitatively and quantitatively supported by numerous field observations and remote sensing classification verification by multiple GIS analysts familiar with the alpine cryosphere generally and rock glaciers specifically. The lead author personally visited more than 50 rock glaciers during field campaigns for related research, and more than 150 rock glaciers with precise coordinates listed in past peer reviewed research were examined remotely when developing our classification criteria. While developing the inventory, dozens of test areas 7 195 200 205 210 measuring 500 km 2 or greater in all 11 western states were checked by two other well trained GIS analysts familiar with the alpine cryosphere for "missing" rock glaciers not originally identified by the lead author, and none were found. When considering the three-class rock glacier activity classification scheme, a test subset of 60 randomly selected rock glaciers were classified in isolation by five GIS analysts familiar with the alpine cryosphere generally and rock glaciers specifically.
Classifications were then compared, yielding no significant differences between analyst interpretations. Class 1 rock glaciers showed a 92% agreement between analysts, Class 2 rock glaciers an 87% agreement between analysts, and Class 3 rock glaciers a 79% agreement between analysts.
As this rock glacier inventory is of unprecedented spatial extent, no analogous previous inventories exist for us to make direct and detailed GIS comparisons to over the entire study region. While smaller regional-scale rock glacier inventories have been compiled in the past, none of these inventories are publicly available as geospatial data sets. Coarse scale comparisons, however, were completed based on reported findings and figures published in previous studies presenting the aforementioned smaller regional rock glacier inventories. To compare our rock glacier inventory and previous regional rock glacier inventories we created polygons using the corner coordinates of low resolution regional study maps from peerreviewed articles highlighting one Colorado rock glacier inventory (Janke 2007) and two California rock glacier inventories Westfall 2008, Liu et al. 2013). Polygons representing the extents of maps from the smaller regional inventories were then used to select simple counts of rock glaciers identified in our inventory and compare them to counts of rock glaciers reported in the aforementioned studies. The 2007 Colorado inventory reported 28 "active" rock glaciers, the category in that study most similar to our Class 1 classification criteria, in and around Rocky Mountain National Park, while we identified 29 Class 1 rock glaciers in the same region. The 2008 California study reported 184 rock glaciers in the central Sierra Nevada, but used a more inclusive "rock-ice feature" definition, that deliberately includes relict rock glaciers, than our rock glacier classification criteria, while we identified 116 rock glaciers of any class in the same region. The 2013 California study (Liu et al. 2013) reported 67 "active" rock glaciers, a subset of features identified in the 2008 study and the category in that study most similar to our Class 1 classification criteria, while we identified 88 rock glaciers in largely the same study region. These three comparisons, and the agreement between the aforementioned inventories and our findings, greatly bolster our confidence in the overall accuracy of the PSURGI.

Data Availability
The PSURGI geospatial data (Johnson 2020 We present the most spatially extensive geospatial rock glacier inventory in the world to date, a powerful tool informing a wide range of research and management applications. The PSURGI exposes, for the first time at such an expansive spatial scale, what an ubiquitous component of the contiguous U.S. alpine cryosphere rock glaciers truly are. Despite their ubiquity, rock glaciers remain an under-studied and under-appreciated element of the alpine cryosphere (Duguay et al. 2015). The deeper understanding of where rock glaciers form and persist where provided by this inventory will aid ongoing refinement and future implementation of truly automated rock glacier detection methods. The ability to quickly, accurately and objectively identify rock glaciers from presently available remote sensing imagery, without relying on skilled visual image analysts or needing to address the inevitable interpretation disagreements between those analysts, would be an invaluable tool for climatologists, ecologists, water resource managers and many others (Brenning 2009).