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Supervised classification of landforms in Arctic mountains

Erosional and sediment fluxes from Arctic mountains are lower than for temperate mountain ranges due to the influence of permafrost on geomorphic processes. As permafrost extent declines in Arctic mountains, the spatial distribution of geomorphic processes and rates will change. Improved access to high‐quality remotely sensed topographic data in the Arctic provides an opportunity to develop our understanding of the spatial distribution of Arctic geomorphological processes and landforms. Utilizing newly available Arctic digital topography data, we have developed a method for geomorphic mapping using a pixel‐based linear discriminant analysis method that could be applied across Arctic mountains. We trained our classifier using landforms within the Adventdalen catchment in Svalbard and applied it to two adjacent catchments and one in Alaska. Slope gradient, elevation–relief ratio and landscape roughness distinguish landforms to a first order with >80% accuracy. Our simple classification system has a similar overall accuracy when compared across our field sites. The simplicity and robustness of our classification suggest that it is possible to use it to understand the distribution of Arctic mountain landforms using extant digital topography data and without specialized classifications. Our preliminary assessments of the distribution of geomorphic processes within these catchments demonstrate the importance of post‐glacial hillslope processes in governing sediment movement in Arctic mountains.

permafrost, it is important to understand how the spatial distribution of potentially hazardous surface processes (and their rates) may change.
Mapping of the distribution of geomorphic processes and landforms is not new in Arctic mountains. Since   7 first mapped Kärkevagge, there has been considerable effort to constrain the distribution of Arctic geomorphic processes and rates. At a landform scale, systematic mapping and measurement of process rates has occurred in blockfields, 8 solifluction, 9,10 and scree (talus) slopes. 11,12 Much of this effort has involved manual mapping, which remains the method that produces the most accurate maps, although the time-consuming nature of this method restricts its utility to local-and regional-scale maps. The reliance on expert interpretation subjects this method to varying degrees of accuracy. 13 Remotely sensed methods provide an alternative and there is a significant body of work dedicated to the study of geomorphometry as reviewed by Romstad and Etzelmüller (2012). 14 This work is supported by improvements in the quality of remotely sensed data that have allowed more detailed analysis into remote areas and at regional scales. 13,[15][16][17] These automated classification methods allow for larger areas to be mapped more quickly while reducing human error (although introducing machine error), and facilitating comparable results and model transferability. 13,18 At regional scales, topographic parameters derived from digital elevation models (DEMs) are shown to be one of the primary predictors of landforms in periglacial environments, 13,19,20 particularly in high-Arctic environments because of the low abundance of vegetation. 19 Statistical analyses of remotely sensed topographic, optical and/or climate data landform classifications 21 use a range of multivariate and simple statistical techniques including generalized linear methods such as linear discriminant analysis (LDA), 13,22 logistic regression, 17 and artificial neural networks. 13,23 Reported comparisons of different suites of statistical modeling suggest that simple models such as LDA and logistic regression perform equally when compared to more complex machine-learning techniques. 24,25 The inclusion of optical remotely sensed data or climate data can improve fine-scale differentiation of geomorphic features with similar topography but different levels of activity (such as differentiating active and less active talus sheets).
However, due to the strongly variable nature of Arctic vegetation, optical solutions are difficult to translate across landscapes. Optical remote sensing may have more traction in vegetation-free areas, such as hyperspectral, 26 thermal inertia mapping 27 or texture filters applied to high-resolution optical imagery. 28 In addition, highresolution cloud-free optical imagery and climatic data for remote areas of the Arctic are difficult to obtain 29 whereas topographic data for the entire Arctic are readily accessible. 30 We develop a technically simple classification of geomorphic features that can be applied across the Arctic. The purpose of geomorphic classification is to improve our ability to understand, to a first order, the spatial distribution of important sources and sinks of sediment within mountainous Arctic catchments. To achieve this goal, our classification must pass two key tests: (a) that it can be implemented using regionally available digital terrain data, and (b) it must classify landforms that clearly relate to processes of either erosion or deposition in the current climate. For example, erosion of till or moraine by solifluction processes would be defined as a solifluction sheet. To achieve the balance of technical simplicity and geomorphic process focus, we settled on a pixel-based statistical landform classifier that uses LDA. We demonstrate the potential utility of this model for cross-Arctic mapping of landforms by comparing classifications in Svalbard and Alaska.

| Western Svalbard
We investigated two catchments in western Svalbard, Endalen and Ringdalen ( Figure 1a). The study area is a high-Arctic semi-arid desert, with a mean annual temperature of −6.8°C and a mean annual precipitation of 190 mm (1961 to 1990, Svalbard Airport). 9 Permafrost is continuous outside of the glacier-covered areas and is typically 100 m thick in valley bottoms and 400-500 m thick at higher elevations. 31 The dominant geology is early Cretaceous to Eocene nearhorizontally bedded sandstones, siltstones, shales and coal. 32 The landscape is mountainous with 400 m of relief. Summit areas are typically flat plateaus composed of blockfields and patterned ground.
Shallow (5°-25°) concave slopes of solifluction sheets are found at the base of many hillslopes (Figure 1c)  Blockfields were flat areas found on summit plateaus with individual angular blocks observed in the satellite imagery. Bedrock outcrops tend to be found at the margins of summit plateaus bounded by scree slopes. In imagery, bedrock is darker in color and often contains significant shadow due to the steep nature of outcrops and low sun angle. Allochthonous material is defined simply as material that has moved downslope from its point of origin (such areas are generally termed as debris-mantled slopes), and we identified these regions to be in the transition zone from active (gray in imagery) to less active material (yellow-green in imagery). Tolgensbakk et al.
(2000) 42 used this term to indicate material that was found on side slopes that could not obviously be tied to a specific landform or process. 42 We have continued to use this definition. Scree (talus) slopes are planar or slightly fan-shaped, are non-vegetated, contain blocky material and are typically located mid-slope below exposures of bedrock. Solifluction sheets are found at the base of hillslopes, are vegetated and contain lobate deposits. 10

| Classifier development, training and testing
We trained an LDA classifier 43 using mapped landforms from Adventdalen ( Table 1)  During training of the model, we extracted the range of pixel values obtained from a 5-m photogrammetry-derived DEM for each mapped landform. We calculated ArcGIS-derived 44 slope aspect, slope gradient, planform curvature, profile curvature, total curvature, topographic wetness index, 45 topographic openness 46 and landscape roughness using a 3 × 3 pixel square window and the SR1 eigenvalue ratio. 47 We call SR1 the ratio of ln(S1/S2) where S1 is from McKean and Roering (2004). 47 Their study noted that the SR1 ratio can pick out other rough elements of the landscape such as roads, channels and bedrock outcrops. SR1 describes the tendency for vector data to be clustered such that braided rivers and alluvial fans have a greater landscape roughness or lower SR1 values because they are highly dissected with channels, and have high sediment loads of gravels, cobbles, boulders and sand banks. We used an elevation-relief ratio (ERR), 48 where ERR = (xx min )/(x maxx min ) for a 5-km-diameter moving window. The size of the window was consistent with other measures of local relief 49 consistent with the typical width of a glacial valley.
We performed a recursive feature elimination analysis on our mapped landform dataset from Adventdalen to determine which topographic parameters contribute the most to the predictive power of the classifier. We found that the combination of ERR, landscape roughness and slope gradient returned the highest accuracy score during the recursive feature elimination analysis.
To assess the classifier's performance, we split the landform dataset into a 70% training set and a 30% testing set, and evaluated the classification using model accuracy metrics defined below. We repeated this train/test split procedure ten times on different segments of the landform dataset and took the average accuracy score. We used this test to ensure that the classifier did not perform differently after being trained on different segments of the landform dataset. Our classifier is trained using only 70% of the Adventdalen dataset, namely the 70% training set. From this point onward, we will call this our "trained classifier." Despite choosing a relatively small, but representative area (n < 10 for some features), the training and testing datasets were accurate at >80%, suggesting that these metrics capture these features well.

| Classifier application
We applied the trained classifier to the Endalen, Ringdalen and

| LDA classifier results
The LDA results show that more than 95% of the separation (the  Figure 2).
For each landform we used a Pearson correlation test to determine the correlation between topographic parameters (Figure 3)   Our receiver operating characteristic (ROC) analysis on the training dataset shows that a combination of ERR, slope gradient and landscape roughness produces the highest area under the curve ( Figure 5).

| Classifier implementation: Endalen
The classified map for a 10-km 2 area of Endalen (Figure 6d) has an overall accuracy of 88.91%. The confusion matrix (Figure 6a,d)

| Classifier implementation: Ringdalen
The classified map for Ringdalen had an overall accuracy of 80.15%

| Classifier implementation: Saviukviayak
The accuracy of the LDA model trained in Svalbard and applied to the Brooks Range is 81.54% ( Figure 10). An interesting result of the classifier was the identification of blockfields (1.08% of the area), which we did not observe from our geomorphological mapping using satellite imagery. Upon re-analysis of the imagery it is evident that a flat plateau exists at the top of the narrow ridgeline. Colluvium occupies 73.02% (Figure 7b) of the study area, the largest proportion when compared to our sites on Svalbard. Bedrock is confined to the midand upper slopes, primarily north-facing slopes, and covering a relatively large area of 6.34% compared to our sites on Svalbard.

| DISCUSSION
We have developed a technically simple classification of geomorphic features that relate to processes of either erosion or deposition in the current climate and can be applied across Arctic permafrost.
Technically simple methods for classifying landscapes were originally developed for implementation using contour maps of topography. 49,52,53 Our model uses a three-parameter LDA chosen on the basis of a recursive elimination. Although we have achieved technical simplicity with our classification, there are questions as to whether our classification is too simplistic, particularly as there are alternative methods that include object-oriented 18 (rather than pixel-based) classification and those that incorporate readily available optical remote sensing data. 28 Our pixel-based classification is strongest where the landform shape is simple and separated by clear breaks in slope gradient, ERR or landscape roughness (Figure 8). Hence, the classifier does best at determining blockfields, solifluction sheets and bedrock out- delineating floodplains, 57 or zero-order drainage basins. 58 By limiting ourselves to available >20-m-resolution topography, we are working at the limit of most process-based methods for topographic analysis. 59 We experimented with the inclusion of hydrologic parameters within our classifications, and found the extensive summit plateaus and planar side slopes in our field area led to anomalous positioning of channels relative to mapped channels. Alternatively, simple landform classifications using a small number of parameters have been used generically to distinguish areas by shape (rather than process). 60 These methods have proven extremely useful for landscape ecology and for regional-or continental-scale mapping. Yet, their deliberately generic nature does not allow for a simple relationship to geomorphic process.
Object-oriented landform classifiers have shown considerable promise as potential methods for identifying landforms. 18 Objectoriented analysis segments landscapes by grouping pixels into areas of consistent morphology that are separated by boundaries. 18 The essential difference between this and pixel-based methods is that context, landform shape and geometric signature can be accounted for in defining a landform. 61 Currently, object-oriented landform segmentation methods, for example geomorphon analysis 62 or elementary forms, 61 have been applied relatively locally at a catchment or smaller scale, or applied generically (i.e., identifying form only rather than form and process) across large areas. There is considerable discussion within the literature about the role of spatial scale, particularly the potential desire to create multi-scale object-oriented landform analysis, 63 and this has been resolved through, for example, hierarchical algorithms. 54 The issue of scale in this context reflects a This debate is well exemplified by the curvature scaling in soilmantled landscapes that reflects the transition from pit and mound topography to hillslope diffusion. 64 Given the challenges with the implementation of these methods across wide spatial scales, we adopted the simpler, more parsimonious pixel-based characterization of landscape form.
Arctic landform classification has often included a combination of digital topography and optical remote sensing analysis. Spectral ratios that identify vegetation have been included in classifications of differential landforms with similar topographies. 28,54 The strength of this process is that it strongly differentiates landform disturbance rate, such that more active landforms cannot grow significant vegetation. In our field area, areas mapped as allochthonous slopes cannot be differentiated from scree slopes using topographic data alone. Instead, during the manual mapping of these landforms, they are differentiated using the total amount of vegetation. As a signifi-

| Relationship between form and process
We sought to create a classification that reflected the underlying geomorphic processes governing the spatial distribution of landforms is low in our study areas. This is also evident across the Arctic because sediment yield from Arctic rivers is low when compared to their temperate counterparts. 1 Sediment production and transport are negatively impacted by low temperatures in the Arctic, 75 where freezethaw cycles occur less frequently, the active layer is frozen for most of the year, much of the annual precipitation falls as snow, and when it does rain its intensity is low. 1 However, studies show that the Arctic is warming at twice the global average, 76 causing ground to freeze later and thaw earlier, the active layer to deepen, 77 and more precipitation to fall as rain. 78 This is thought to increase the frequency and rate of mass-wasting processes that remobilize sediment on Arctic hillslopes such as debris flows 69 and solifluction. 9 Hillslope-channel connectivity related to solifluction is thought to be low because of its slow movement rates (<1 mm year −1 ). 10 However, solifluction monitoring sites on Svalbard have shown an increase in movement rates due to a deepening active layer caused by higher air temperatures. 9,79 In addition, regions of solifluction experience active layer detachment failures where shallow translational landslides move sedimentary material from the hillslope to adjacent channels. 80 Therefore, with solifluction being one of the most extensive landforms in our study areas, it has the potential to remobilize sediment (colluvium) locked on Arctic hillslopes.

| CONCLUSION
We developed a landform classification model that can be applied across Arctic mountain ranges using readily available topographic data.
The model estimates the distribution of geomorphologically significant landforms using a combination of three topographic parameters: slope gradient, ERR and landscape roughness. We trained our classifier in the Endalen catchment of Svalbard, then applied the trained classifier to another Svalbard catchment (Ringdalen) and one in Alaska (Saviukviayak). The classifier is internally accurate (88.91%) when applied to landforms with strong differences in topography, such as scree slopes and solifluction sheets. Bedrock, blockfields and solifluction sheets were identified with a high degree of accuracy, with bedrock outcrops modeled at a greater resolution than was possible to map using satellite imagery. Classification accuracy did not change significantly between sites, suggesting that this method can be readily transferred between geographic locations. The process-oriented nature of our classification method allows for an improved understanding of the spatial distribution of key geomorphic processes in Arctic mountains.