Rock glaciers across the United States predominantly accelerate coincident with rise in air temperatures

Domain: earth_science
Published: 2024-08-31
Editorial outcome: accept

Abstract
Despite their extensive global presence and the importance of variations in their speed as an essential climate variable, only about a dozen global time series document long-term changes in the velocity of rock glaciers – large tongue-shaped flows of frozen mountain debris. By analysing historical aerial photographs, we reconstruct here 16 new time series, a type of data that has not previously existed for the North American continent. We observe substantial accelerations, as much as 2–3 fold, in the surface displacement rates of rock glaciers across the mountains of the western contiguous United States over the past six to seven decades, most consistent with strongly increasing air temperatures in that region. Variations between individual time series suggest that different local and internal conditions of the frozen debris bodies modulate this overall climate response. Our observations indicate fundamental long-term environmental changes associated with frozen ground in the study region.

Introduction
Around 11% of the Earth’s land surface (15% for the Northern Hemisphere alone), or around 14 million km2, is characterized by permafrost conditions1–3, meaning that the ground is permanently frozen at depth. Non-polar mountain ranges account for about 30% of this permafrost area4. In these mountain regions, the total area of permafrost is roughly 20 times larger than the area covered by glaciers5. Permafrost, along with its ice content, serves as a critical hydrologic regulator6–8 and impacts on various types of natural hazards4,9. The seasonally thawing active layers of mountain permafrost are becoming deeper, and permafrost temperatures are rising worldwide4,10–12.

Rock glaciers13,14 are often an indicator of past or present mountain permafrost. Active rock glaciers are suggested to be defined as expression of cumulative deformation by long-term creep of ice/debris mixtures under permafrost conditions but other definitions exist14. The results of such long-term slope deformation are distinctive, tongue-like landforms of frozen debris that move with surface rates in the order of centimetres to a few metres per year15–17. Warmer frozen debris typically moves faster than colder material, primarily because of the reduced viscosity of the warming ice core or ice-debris mixture, and due to the effects of infiltrating meltwater18–20.

The variability of rock glacier velocities has recently been acknowledged by the World Meteorological Organization (WMO) as one product of the essential climate variable permafrost. Empirical data confirm the susceptibility of rock glacier velocities to climatic changes16,18–21. However, only a limited number of long-term time series documenting these changes – spanning several decades – currently exist. The majority of time series are located in the European Alps, with only a few in other mountains16,22. Despite the significant presence of rock glaciers in North America23,24 and some velocity measurements available over shorter time intervals25–29, no systematic long-term time series capturing the kinematic behaviour of rock glaciers have been established on this continent.

The mountainous regions of the contiguous U.S., encompassing roughly 15,000 km2 of permafrost1, host about 10,000 active rock glaciers23, which cover a collective area of approximately 1000 km2. These numbers, in comparison to approximately 5000 glaciers5 occupying an area of 670 km2 highlight the importance of rock glaciers and permafrost to the study region8, and motivate the analysis of changes in rock glacier surface speeds.

Developing long-term time series of rock glacier speed (>30 years) is a challenging and laborious task. For a few rock glaciers worldwide, primarily in the European Alps, such series have been created from decade-long geodetic in-situ measurements16,21. However, these measurements cannot be retroactively extended, and accurately reconstructing rock glacier speed requires archived high-precision remote-sensing data. Satellite radar interferometry, currently used to measure seasonal rock glacier speeds, only yields data from the past around 20 years, and its application for decadal-scale time series is compromised by the disturbances from seasonal and inter-annual speed variations17,29,30. The only method to reconstruct >30-year long time series of rock glacier speed is by utilizing historical air photos where they are available and accessible. The challenge lies in the fact that the substantial geo-positional inaccuracies that stem from camera types and calibration, and the resolution, radiometric quality, and distortions of these historic air photos typically surpass the horizontal surface displacements of a few centimetres to metres associated with rock glacier movement31,32.

Here, we digitally processed and analysed historical aerial photos to construct 60–70-year timelines of surface speeds for 16 rock glaciers located across the Rocky Mountains and the contiguous western United States. This type of data has not previously existed for the North American continent and more than doubles the global quantity of available long-term time series of rock glacier kinematics.

Results
Reconstructing rock glacier speeds from historical air photos
A first objective of our study was to test and demonstrate how variations in rock glacier speed can be measured using the waste U.S. Geological Survey (USGS) airphoto holdings. We selected 16 rock glaciers that cover the latitudinal and longitudinal range of rock glaciers in the contiguous U.S. (Fig. 1), have sufficient air photo coverage in the USGS archive, and exhibit clear signs of modern motion in Sentinel-1 radar interferograms17. (One of the 16 rock glaciers investigated, Hyndman, consists actually of two separate streams that are treated here as one system; Supplementary Information). USGS airphotos from approximately the 2000s onward are provided exclusively in ortho-rectified format (topographically corrected and projected to map coordinates). Prior to that time, only the original, non-rectified air photos are available. We ortho-rectified the older air photos from a challenging variety of camera and calibration types to compile a 60–70 year timeline of three to five orthophotos for each rock glacier studied. By exploring a large number of additional airphotos we found that more populated timelines are not feasible due to the limited existence of suitable airphotos with regard to spatial resolution, radiometric detail, and orthoprojection distortions (“Methods” section). We applied digital image matching between pairs of orthoimages to measure horizontal surface displacements between two consecutive air photos31,33. While this method was able to generate hundreds of successful displacement measurements when utilizing modern high-resolution high-precision orthoimages from USGS, the quantity and accuracy of successful displacement measurements significantly decreased for the old photos dating back to 1947 due to their low resolution and radiometric contrast (“Methods” section). To preclude any spatial bias, we retained only those measurement locations that yielded matches for all measurement periods. This still resulted in the creation of numerous individual time series of displacement rates on each rock glacier (n in Fig. 2; avg. 100, min. 9, max. 370). To prevent result dilution from the large variability of absolute surface speeds over a rock glacier, each individual time series was normalized by its average speed before summarization for each rock glacier. We express the uncertainty of our results in three separate manners. Firstly, the notches between time-step median speeds (red in Fig. 2), next, the standard error of stable ground offsets after orthoimage co-registration (light blue), and finally a statistical significance test for changes between time steps (blue; “Methods” section).

Our study finds that and how decadal-scale time series of rock glacier speed can be reconstructed from the USGS archive, the – to our best knowledge – globally largest freely and open available archive of air photos.

Variations in rock glacier speed
The average speeds on the investigated rock glaciers over the study period varied significantly, from 8 cm per year at the Star Peak rock glacier in the Methow Mountains (Washington state), to 70 cm per year at the Ferguson ranch rock glacier on Mount Sopris (Colorado). Maximum speeds at individual measuring points of up to 130 cm per year are found at some locations for Galena Creek rock glacier in the Absaroka Range (Wyoming). Our measurements are consistent with the few photogrammetric and geodetic measurements available on some of the rock glaciers studied (“Methods” section). Twelve out of the 16 rock glaciers showed a statistically significant acceleration over the measurement period, with several rock glaciers exceeding twice their initial speed between the first and final time intervals (Figs. 1 and 2a). One rock glacier (Cardinal Mountain North, California) even tripled its surface speed, from an average of 36 cm per year for 1947–1987 to 110 cm per year for 2016–2022. As per the extent that the availability of suitable orthoimages and thus the temporal density of the time series allows for such conclusions, several accelerating rock glaciers exhibit a consistent speed increase over time (e.g., Cardinal North, or Crater), with some others demonstrating a more hockey-stick like accelerated increase of speeds during the recent decades22 (e.g., Mt. Mears, or Twinsisters; Fig. 2a). Conversely, the decelerating rock glaciers do so only slightly, close at or within the significance level of our measurements, with one even exhibiting acceleration during the more recent periods (Birch Mtn.).

Methods
Selection of sites
We selected 16 individual rock glaciers for our study following a combination of the following criteria. The study sites span the latitudinal and longitudinal range of rock glaciers in the contiguous U.S. in order to let us investigate rock glacier behaviour under climatic and topographic gradients. Where feasible we selected clusters of several nearby rock glaciers within a given mountain range to also consider the variability in rock glacier behaviour under similar regional conditions.

As a crucial criterion, the sites needed to have coverage by suitable air photos in the U.S. Geological Survey (USGS) archive. This criterion encompasses the existence of low-altitude air photos with spatial resolution and radiometric quality sufficient enough to enable the identification of detailed tracking features on the rock glaciers. This criterion affects in particular the first decades of our time series in the mid-20th century. In order to avoid laborious pre-processing steps for rock glaciers that then in the later analysis turn out to have a surface speed below detection thresholds of the old air photos, we ordered and consulted satellite radar interferograms based on recent synthetic aperture radar (SAR) data from the Sentinel-1 mission. Several interferograms with temporal baselines of 12 and 24 days were chosen and ordered from the Alaska SAR Facility (ASF) Vertex service. For compilation of our speed time series, we selected rock glaciers that show clear signs of contemporary motion in the Sentinel-1 radar interferograms through motion-induced interferometric fringes or localized, and thus likely motion-induced, loss of interferometric coherence17,31. Following standard procedures for interferometry-based rock glacier classification, we relied in our assessment of contemporary rock glacier activity on a combination of interferograms from different times and with different temporal baselines17,48. Most interferograms used stem from Sentinel-1 data of 2022 and 2023. In case several rock glaciers appeared to be feasible sites in a region or mountain range following the above criteria, we preferred rock glaciers with earlier investigations available in order to aid the interpretation and validation of our results, and provide background for or motivate forthcoming studies.

Pre-processing of air photos
For times before roughly the 2000s only original non-rectified air photos are available from USGS. These images have been scanned, or are scanned on demand, and stem from a challenging variety of camera and calibration types. We selected suitable images based on metadata (e.g., image scale) and visual inspection of quick-looks or full-resolution data (e.g., checking for lack of snow cover and sufficient radiometric quality and details). For each individual photo, we collected camera calibration protocols either directly attached to the scanned images, or from the USGS calibration protocol archive. We implemented these calibrations in the photogrammetric software PCI Geomatica OrthoEngine to solve for the inner orientation of each photo. To reconstruct the exterior orientation we chose approximately 30–50 ground control points31 from the most recent ortho-rectified high-resolution image provided by USGS for horizontal control, and extract the elevations of these points from the Copernicus global 30 m-resolution digital elevation model (DEM) for vertical control. The bundle adjustment for each photo or set of connected photos from the same flight gave typically residuals well below 1 metre for georeference. We then topographically corrected the photos within PCI Geomatica OrthoEngine and projected them to UTM coordinates with NAD datum using the image orientation parameters obtained and the Copernicus global DEM.

For about the 2000s on, air photos are provided by USGS exclusively in ortho-rectified format. These images need no further pre-processing for our purposes. We selected suitable images from their spatial resolution, radiometric quality and detail, and with sufficiently long temporal baseline to enable statistically significant motion detection (i.e., about 5–10 years). We found that the most recent USGS orthoimages have excellent resolution, positional accuracy and precision, and radiometric quality which makes them very well-suited for our purpose. The older orthoimages are more affected by lower resolution and distortions (see below on error budget).

After building a 60–70 year long time series of three to five orthophotos for each rock glacier, we co-registered these orthophotos locally around the study rock glacier using image matching33 (see next section on displacement measurements). For that purpose, we chose a set of 20–40 points outside of the rock glacier that we assessed to be lying on stable ground, based on our radar interferograms and interpretation of ground cover and geomorphology (e.g., exposed bedrock). The co-registration parameters were stored and applied to correct the raw displacement measurements.

Displacement measurements
We measured displacements for individual targets on the moving rock glaciers between two orthoimages of different timestamps for a given rock glacier (typical intervals between orthoimages from several to about one decade) using automatic image correlation based on the normalized cross-correlation algorithm33,49,50. For the more recent images with high spatial resolution and radiometric detail such measurements would be possible for dense grids of points, but such procedure fails for most locations for the older images that depict much fewer visual targets such as individual boulders, or furrows and ridges, that can be detected and tracked between images. For grid-based matching33, this problem results in a much smaller number of successful matches than mismatches, which cannot be completely removed through filtering and thus result in substantial contamination of the fields of measured displacement vectors by outliers. We therefore manually selected a large number of irregularly spaced locations on the rock glaciers that contain features that can be identified in all orthoimages of a time series and automatically measured displacements there, i.e., we visually prescribe matching positions. These individual locations are in most cases well distributed over the entire rock glacier (Supplementary Information). The image matching software we were using for this purpose33 allows for interactive selection of matching points, and immediate point-wise automatic image matching and display of displacement vectors. Gross outliers can in that way directly be identified visually and interactively removed. For the image matching we used template sizes of between 20 and 25 metres and search areas were determined iteratively to capture the full range of actual displacements. We measured displacements between all subsequent orthoimages of a series. For some rock glaciers where we found particularly uncertain results, we measured displacements also for additional orthoimage pairs spanning two instead of one-time interval.

Speed time series
Once all measurements were conducted for all orthoimages over a rock glacier we built the velocity time series and extracted the vector magnitudes to obtain speeds. Based on the displacement locations of the earliest time interval, which typically contained the least successful measurements due to the lowest image quality, we selected for each initial location the measurement points in all other subsequent displacement fields closest to the initial one, if existing within a radius of 40 m. In other words, the starting points of measured displacement vectors that are closest to a starting point of displacements in the first image pair and in addition within a 40 m radius to this initial starting point are considered to represent the same location on the rock glacier. All other measurements in the image pairs after the first one are disregarded. Choosing this procedure over using a fixed set of measurement locations throughout the time series allows for the selection of optimal measurement locations that contain features of high contrast for each image pair individually. Each initial measurement location within the earliest image pair that has close-by measurements for all other time intervals defines the one-speed time series. To avoid that the large spread of displacement magnitudes over a rock glacier dilutes our results, we normalize each individual time series by its average speed.

Error budget
The largest component of the error budget of our time series are typically the unresolved orthoimage distortions31. Such distortions can stem from distortions within the original air photos (e.g., lens and camera distortions, distortions of the photographic film, or scanning distortions), from distortions of the photogrammetric model, and from distortions within the orthoprojection process. The latter errors come typically from inaccurate DEMs used for orthoprojection. Whereas these distortions can be evaluated for stable ground as the expected ground motion there is zero, they cannot be separated from the actual ground motion on the rock glaciers31,51 and therefore not be corrected for. The other error budget component of concern are matching errors, i.e. the precision with which a matched displacement corresponds to a (typically unknown) real ground displacement31,52. Also this error can be evaluated from stable ground offsets, but on the moving rock glacier, it can only be evaluated from validation data. Both error components affect measurements on the rock glaciers mainly in a random way as systematic offsets are reduced by the image co-registration step. Through choosing ground control points (GCPs), which are necessary to solve the photogrammetric bundle adjustments, from the latest USGS orthoimages and their elevation from the Copernicus global DEM, and through co-registering the orthoimage pairs, effects from absolute geo-reference errors can only have very minor second-order impact on our time series, and only in the presence of strong local spatial gradients in rock glacier speed. A threshold on spatial speed gradients could be employed to mask out measurement locations with strong local gradients. Such procedure was not applied as we avoided to measure displacements close to rock glacier margins and did not encounter break lines in the displacement fields on the rock glaciers investigated, as for instance confirmed by flickering between images of different times.

As a result of the above error processes, we express the uncertainty of our results in several independent ways. First, the speeds for each time interval and each rock glacier are displayed as median, a robust measure that reduces the effect of outliers, including outliers from local distortions and matching errors. The generally small deviations between these medians and the time interval means confirm the absence of large outliers. Based on the medians and the spread of normalized speeds for each series and time interval, notches are computed. Notches53 of subsequent time intervals that do not overlap indicate that their medians are statistically different at a significance level of >95%. Second, we compute and show the estimated standard error from stable ground offsets. For that purpose, we compute the normalized median absolute deviation of stable ground offsets for each time interval and rock glacier, and from this absolute deviation, we derive a robust estimate of the standard deviation of stable ground offsets54. To then estimate from this standard deviation (i.e. dispersion of the offsets) the standard error for stable ground offsets (i.e., uncertainty of the offset mean) we conservatively assume our 20–40 stable ground measurements to represent only 4 independent measurements (i.e., divide the standard deviation by √4). This reduction accounts for the fact that neighbouring stable ground offsets could be affected by the same low-frequency distortions and could thus be partially correlated. Third, we compute the standard error of speed changes between time intervals for a specific rock glacier and statistically test whether the speed changes are statistically significant. For the latter test, we use the Wilcoxon rank sum test (equivalent to the Mann–Whitney U-test), roughly speaking a robust version of the student test.

Climate data
At the decadal time scales considered in this study, air temperature data from a range of sources show similar temporal variations and trends. We collect and assess annual and seasonal air temperature time series for all our mountain ranges studied using the NOAA compilation of measured air temperatures (https://www.ncei.noaa.gov/access/monitoring/climate-at-a-glance/regional/time-series) and measured temperatures at SNOTEL stations as close as possible to the rock glaciers studied (https://nwcc-apps.sc.egov.usda.gov/imap). We also visually check climate re-analyses such as ERA5 as prepared on the University of Maine Climate Reanalyzer (https://climatereanalyzer.org/research_tools/monthly_tseries). The second climate variable that is considered to be able to significantly impact rock glacier speed is snow cover, through insulating the ground in winter and thus potentially reducing seasonal ground cooling. Snow water equivalents at high elevations over our study region show no clear trends and large spatio-temporal variability. We assess the snow water equivalent measured at SNOTEL stations as close as possible to the study rock glaciers (https://nwcc-apps.sc.egov.usda.gov/imap) (Supplementary Information). We also extracted the winter (Oct–Mar) snowfall water equivalents and winter total precipitation from the ERA5 re-analysis55 in two ways. First, we summarize both variables for all elevations above 2000 m (geopotential height) over the western U.S. Second, we extract both variables specifically at the mountain ranges studied.

Measured air temperatures and precipitation, compiled and interpolated by the PRISM group (PRISM Climate Group, Oregon State University, https://prism.oregonstate.edu) were extracted for the locations and elevations of the individual rock glaciers (Supplementary Information).

Comparison to other velocity measurements
There are only few geodetic in-situ measurements available to compare our results to. In-situ total station measurements on Arapaho rock glacier between 1960, 1985 and 2002 for a transect in the middle of the rock glacier (points 1–4 in ref. 27) reveal average speeds of 14.5 cm/yr, our speeds over 1953–1999 for the same location give 13.6 cm/yr. Both measurements agree by far within their uncertainties. The results by ref. 27 also show that no significant decadal-scale speed variation seems to have happened within our 1953–1999 period. Photogrammetric displacement measurements on Arapaho rock glacier32 over 1978, 1990 and 1999 (e.g., 12.8 cm/yr for the above transect) also agree well with our measurements and indicate little change over 1978–1999.

Comparing in-situ geodetic measurements of boulder displacements on Galena Creek rock glacier26,28 over 1997–2015 to displacements at nearby locations from our photogrammetric measurements of 1994–2015 gives a mean absolute deviation of 3 cm/yr, which is well within the notches and error of around 10 cm/yr that we give for this rock glacier and period. The in-situ speed variations between 1997, 2015 and 2022, and photogrammetric measurements 2020–2022, also from ref. 28, agree with our photogrammetric measurements within their error bounds, all consistently indicating a slight increase in speed during the recent years.

Satellite radar-interferometric measurements over 2007–2008 by ref. 29 are difficult to compare to our measurements due to the different temporal and spatial scales, and the different measurement locations involved. Mean radar-interferometric speeds for late summer 2007 for Birch Mountain rock glacier are 45 cm/yr (from ref. 29; our measurements 2005–2022: 35 cm/yr), for Pine Creek 57 cm/yr (our measurements 2005–2016: 41 cm/yr), for Cardinal North 61 cm/yr (our measurements 2005–2016: 94 cm/yr), and Cardinal South 67 cm/yr (our measurements 2005–2016: 61 cm/yr).

Data availability
USGS orthoimages or original air photos and their camera calibrations are openly available from https://earthexplorer.usgs.gov. Derived displacements from the current study are openly available from the Zenodo repository under accession code https://doi.org/10.5281/zenodo.13254373 (ref. 56). Climate data used are openly available from NOAA and the Copernicus Climate Data Store55 (https://cds.climate.copernicus.eu/), SNOTEL data from NWCC, and the PRISM data from Oregon University (https://prism.oregonstate.edu/). The Copernicus global DEM is openly available from the European Union PANDA service (https://panda.copernicus.eu/).

Code availability
PCI Geomatica OrthoEngine is a commercial software. The image matching software used (CIAS) is freely available from https://mn.uio.no/icemass.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "I enjoyed reading this interesting manuscript. The complex behavior of rock glaciers in\nresponse to climate change can only be decoded with more long-term series on rock glacier\ncreep. With this timely study on rock glacier speed and its variation for the contiguous\nUnited States, the global picture of rock glacier kinematics and its temporal changes is\nenhanced significantly. This is urgently needed to properly quantify and assess the new\nproduct “rock glacier velocity” of the Essential Climate Variable “Permafrost”. Many thanks\nfor this important study!\nThe manuscript is very well written, structured and illustrated.\nThe motivation for this original study is clearly elaborated and credit is given to important\nstudies in the context of rock glacier behavior in relation to increasing temperatures. New\nseries on rock glacier speed are provided for 16 landforms in different regions of the\ncontiguous United States, a region that was lacking long-term information so far. The\nconclusion derived from this study is in line with findings from other regions, supporting the\nobservation of general rock glacier acceleration. The fact that some landforms (4 out of 16)\nshow a different trend is also in line with other studies and underlines the need for more\ndetailed analyses of influencing factors on rock glacier creep. As the data series are\ncompiled by a common methodology, they are easily comparable to series from other\nregions (e.g. from the European Alps). For sure, these noteworthy results will be included in\nfuture global assessments.\nThe methodology of processing aerial imagery and deriving time series of rock glacier speed\nis described in a very detailed and concise way, allowing reproducibility. A proper error\nassessment is provided. The additional use of InSAR data for the site selection as well as\ncomparisons with in-situ geodetic measurements from some site shows the full range and\npotential of information on rock glacier movements and the value of complementary data.\nThe outcomes are nicely summarized in two figures showing the spatial and temporal\npatterns of rock glacier speeds.\nFew individual edits are listed below.\nl 52: “…geodetic in-situ measurements” add reference to the most recent study by Kellerer\net al. 2024: Acceleration and interannual variability of creep rates in mountain permafrost\nlandforms (rock glacier velocities) in the European Alps in 1995–2022\n(https://doi.org/10.1088/1748-9326/ad25a4)\nl 70: “insufficient co-registration accuracy”, please provide a reference\nl 174: delete “at”\nFigure 1: The signature for “Rock glaciers” is hardly readable in the legend, please enlarge. If\npossible, be more explicit regarding the decades you compare “mid-end last century” vs\n“recent decade” (= 2010-2020?). How large is the deviation of the time periods you\ncompare?\nFigure 2: Would be nice to be able to read the decades more clearly; please add thin lines\nfor each decade (like in Figure 2b and 2c)\nSupplementary material:\nFigure S1 and S2: provide the years of the “entire measurement period” (possibly in the\ncaptions, as is seems to be the same for all the stations) and add information on the data\nsource (NOAA, NRCS)\nFigure S3 and S4: it is not fully clear whether you show snow-water equivalent or winter\ntotal precipitation; add description and unit of the axes. Provide data source.", "reviewer_2": "The work suggests temporal and spatial displacement signals from a sample of rock glaciers.\nThe study found significant changes in velocities for some of the rock glaciers investigated.\nIn the western part of the study area rock glaciers both accelerated and decelerated. In the\neastern and northern parts mostly, acceleration was observed. Therefore, in my opinion, the\nwork does not fully support what is claimed in the title “Creep of rock glaciers accelerates\nacross the United States”. My advice is that the title should be adjusted accordingly. The\nconclusion (line 129-131) is more in line with the variability in the data “suggesting\nsignificant changes” instead of just acceleration.\nI also miss data and discussion regarding variation in local snow cover and precipitation for\neach rock glacier. It would also be useful if the authors could present mean measured air\ntemperature anomalies closer to the rock glaciers dating further back in time than the\nSNOTEL-data presented in Fig2b. It would also be valuable if the authors could compare the\nobserved displacement patterns to other available long-term studies.\nAll in all, the authors present convincing results, discussions and conclusions based on\nsubstantial data and sound use of methods. The time span covered and details both spatially\nand temporally are impressive and, in my experience, unprecedented and will have a large\nsignificance to the field and similar fields.\nSee my detailed suggestions and comments in the attached annotated manuscript.\nComments/suggestions for Supplementary Information:\nFig S2: Consider naming the RGs that are close to the stations.\nFig S3: Consider adding unit to y-axis.\nFig S4: Consider adding unit to y-axis.\nBest regards,\nHarald Øverli Eriksen", "reviewer_3": "There are several problems with this paper and it should not be published in its present\nform.\nnecessary to communicate. The text is mainly about the techniques involved and data\nextraction. While I have no complaints about the technique, it is novel and useful, indeed, I\nwould like to know more about it and results that can be seen. But this journal is not the\nplace to present this. The technique and basic results should be published elsewhere.\n2. This title is not only misleading in intent but also in fact, some ‘self-evident’ others more\nnuanced. It is not ’creep’ that is necessarily being measured but ‘speed’ or ‘velocity’ and\nthese words are used in the text. Creep is associated here with rock glaciers, as in text and\nas stated but also with glacier ice deformation. Glaciers can slide to give a surface velocity.\n3. The linkage of rock glacier to ‘permafrost creep’ should be abandoned. This has long been\nused as the only mechanism for rock glacier flow, usually following citation of the book Rock\nGlaciers by D. Barsch (here reference number 14). Barsch denies the existence of the ‘glacier\nice cored rock glacier’. In particular the work of Potter at Galena Creek RG where glacier\nice has been shown to be the core of the rock glacier at Galena Creek and at Sulphur Creek RG\nthe recent work by Meng et al (cited in the paper as ref 27) not only gives velocity data (was\nthis compared to that obtained in this paper?). In other words, the authors use rock glacier\nalways as being indicative of permafrost rock glaciers but omit references to evidence from\n‘disproving cases’. This has been a situation for far too long in the literature. Here the glacier\nice formation is blatantly denied but still uses RG that do have glacier cores in the ‘analysis’.\n4. Any body with ice (glacier or cryogenic) can ‘flow’ or ’creep’ but the creep rate (velocity)\ndepends upon more that ‘temperature’. Thickness of the ice mass and surface slope provide\nthe main stress fields. So, a glacier might give the same results as supposed for a\n‘permafrost rock glacier’. But the problem really is that the data analyses are far too\nsimplistic, other site specific conditions should be analysed. Further, if the rock glaciers are\nburied glaciers then sliding, rather than flowing, might be the main driver of the differences.\n6. But what are these differences? Why does Cardinal Mtn N have the largest surface speed\nchange compared with Cardinal Mtn S have one of the lowest? This alone might suggest\nthat there as more in the variability than ‘temperature’. Indeed, several meteorological\nparameters should be used and investigated. This leads to\n7. The data analysis is overly simplistic. In fact, the paper does not comply with any aspects\nof FAIR data principles. Ok, have a graph but what are the data from which the results are\nplotted? Use of median might be more ‘robust’ but there are other descriptive statistics that\ncould be used for the analysis.\n8. Also with respect to FAIR, the locations of rock glaciers are given only by toponyms. A\nproper geolocation is required. Using a decimal latitude-longitude [dLL] identifier for rock\nglacier locations allows the reader to locate the feature in, for example Google Earth. This\nmight help in interpretation, what might the differences be between Cardinal Mountain\nN/S. From the peak at [36.9996,-118.4148], there are several contenders for ‘north’ but I\ncannot see what is meant by ‘south’. This is not presenting data that are findable,\naccessible, interoperable or re-usable. This is required in any transparent data analysis. No\nattempt to be transparent is made in this paper.\nBut fundamentally, it is the continued scientific lack exactitude of the data presented.\nSupport for the contention suggested by the title is not upheld."}, "author_response": "Rock glaciers across the United States predominantly accelerate\ncoincident with rise in air temperatures\nAndreas Kääb, Julie Røste\nResponse to referees and Revisions made\nGeneral response\nWe would like to thank the three referees for their thoughtful and constructive reviews that certainly\nhelped to improve the paper. We implemented all recommended changes and in particular revised the\nmain text and figures, expanded the analyses and discussion, and added substantially more information\nto the Supplement.\nIn general response to ref#3 we want to briefly comment here on the connection between permafrost\nand rock glaciers. This is a long-standing dispute in the scientific community that we are not involved in\nand try to avoid. Our interest lies in the kinematics of rock glaciers and its response to climatic changes.\nWe believe our results are important, irrespective of the view the reader has on the connection between\npermafrost and rock glaciers. Permafrost is solely a thermal definition, glaciers are defined by form,\nmaterial (ice), origin (snow) and movement. Whether rock glaciers are connected to permafrost or\nglacier ice does thus not have to be a contradiction or topic for dispute. When writing about rock glaciers\nin permafrost environments we follow a large body of literature and, for instance, the World\nMeteorological Organization (WMO) that we cannot just ignore. This is confirmed by ref#1 and ref#2\nwho do not criticize our terminology. On the other hand, we also want to acknowledge the existing\nliterature that points to rock glacier like landforms that do not necessarily reflect permafrost conditions,\nor transitional landforms. We tried now to reach a more balanced terminology and discussion of\nprocesses (see also response to ref#3) that we hope can satisfy to some extent both view points on the\nconnection between permafrost and rock glaciers that exist in the literature. We believe it should not be\ndemanded from an article about (undoubted) rock glacier kinematics to solve a many decades old\nscientific dispute that is not the focus of the study.\nSee a more detailed discussion of the topic in Berthling (2011)(see reference list of the paper).\nEditor/referee comments are in italic, and our response in normal font.\nAn annotated version of our revised manuscript with track changes is attached.\nResponse to reviewer #1 ………….. page 2\nResponse to reviewer #2 ………….. page 3\nResponse to reviewer #3 ………….. page 7\nI enjoyed reading this interesting manuscript. The complex behavior of rock glaciers in\nresponse to climate change can only be decoded with more long-term series on rock glacier\ncreep. With this timely study on rock glacier speed and its variation for the contiguous United\nStates, the global picture of rock glacier kinematics and its temporal changes is enhanced\nsignificantly. This is urgently needed to properly quantify and assess the new product “rock\nglacier velocity” of the Essential Climate Variable “Permafrost”. Many thanks for this\nimportant study!\nThe manuscript is very well written, structured and illustrated. The motivation for this original\nstudy is clearly elaborated and credit is given to important studies in the context of rock glacier\nbehavior in relation to increasing temperatures. New series on rock glacier speed are provided\nfor 16 landforms in different regions of the contiguous United States, a region that was lacking\nlong-term information so far. The conclusion derived from this study is in line with findings\nfrom other regions, supporting the observation of general rock glacier acceleration. The fact\nthat some landforms (4 out of 16) show a different trend is also in line with other studies and\nunderlines the need for more detailed analyses of influencing factors on rock glacier creep. As\nthe data series are compiled by a common methodology, they are easily comparable to series\nfrom other regions (e.g. from the European Alps). For sure, these noteworthy results will be\nincluded in future global assessments.\nThe methodology of processing aerial imagery and deriving time series of rock glacier speed is\ndescribed in a very detailed and concise way, allowing reproducibility. A proper error\nassessment is provided. The additional use of InSAR data for the site selection as well as\ncomparisons with in-situ geodetic measurements from some site shows the full range and\npotential of information on rock glacier movements and the value of complementary data. The\noutcomes are nicely summarized in two figures showing the spatial and temporal patterns of\nrock glacier speeds.\nWe would like to thank the reviewer for their positive and encouraging feedback. All their detailed\ncomments have been incorporated as described below.\nFew individual edits are listed below.\nl 52: “…geodetic in-situ measurements” add reference to the most recent study by\nKellerer et al. 2024: Acceleration and interannual variability of creep rates in\nmountain permafrost landforms (rock glacier velocities) in the European Alps in\n1995–2022 (https://doi.org/10.1088/1748-9326/ad25a4)\nNow cited at several locations. Thanks for pointing to this important study that came out in parallel to the\nfirst submission of the present study.\nl 70: “insufficient co-registration accuracy”, please provide a reference\nWe clarified now that this statement is our own finding from exploring a large amount of airphotos and\nwe referred now to more description in the Methods section.\n3\nl 174: delete “at”\nDone\nFigure 1: The signature for “Rock glaciers” is hardly readable in the legend,\nplease enlarge.\nDone\nIf possible, be more explicit regarding the decades you compare\n“mid-end last century” vs “recent decade” (= 2010-2020?). How large is the\ndeviation of the time periods you compare?\nGood point. The spread of time periods is actually quite large. We rewrote to “mid to end of last century”\nand “recent one to two decades”. The first periods range, for instance, between 1947-1987 and 1985-\n1994, the last periods between 1998-2017 and 2016-2022. We now list the periods for each individual\nrock glacier in the Supplement, and now list this spread and its consequences as source for uncertainty\nin our Discussion section.\nFigure 2: Would be nice to be able to read the decades more clearly; please add\nthin lines for each decade (like in Figure 2b and 2c)\nVertical lines included.\nSupplementary material:\nFigure S1 and S2: provide the years of the “entire measurement period” (possibly\nin the captions, as is seems to be the same for all the stations) and add\ninformation on the data source (NOAA, NRCS)\nMeasurement periods and data source now included in the captions of Figures S1 and S2. Also, we\nspecified now which rock glaciers are closest to the SNOTEL stations shown.\nFigure S3 and S4: it is not fully clear whether you show snow-water equivalent\nor winter total precipitation; add description and unit of the axes. Provide\ndata source.\nBoth fixed now.\nResponse to Reviewer #2 (H.Ø. Eriksen)\nThe work suggests temporal and spatial displacement signals from a sample of rock glaciers.\nThe study found significant changes in velocities for some of the rock glaciers investigated. In\nthe western part of the study area rock glaciers both accelerated and decelerated. In the\neastern and northern parts mostly, acceleration was observed. Therefore, in my opinion, the\nwork does not fully support what is claimed in the title “Creep of rock glaciers accelerates\nacross the United States”. My advice is that the title should be adjusted accordingly. The\n4\nconclusion (line 129-131) is more in line with the variability in the data “suggesting significant\nchanges” instead of just acceleration.\nWe modified the paper title to indicate that most but not all rock glaciers accelerated.\nI also miss data and discussion regarding variation in local snow cover and precipitation for\neach rock glacier. It would also be useful if the authors could present mean measured air\ntemperature anomalies closer to the rock glaciers dating further back in time than the\nSNOTEL-data presented in Fig2b.\nIn addition to the snow water equivalent (SWE) and temperature data of SNOTEL stations as close as\npossible to the rock glaciers in the Supplement, we include already average regional temperatures from\nNOAA (1940-2022) (Fig 2b). New, we now include in the Supplement annual/summer/winter time series\nof temperatures and precipitation (1940-2022) interpolated for the individual rock glaciers by the PRISM\nClimate Group. We add now in the main text a figure (Fig 3) that shows speed changes and air\ntemperature changes together. The PRISM data have also been used for the rock glacier inventory by\nJohnson et al. (2021) and are to our best knowledge indeed the best-suited data for our purpose as the\nPRISM group compiled a very large number of station data from a very large set of sources over the US.\nIt would also be valuable if the authors could compare the observed displacement patterns to\nother available long-term studies.\nSuch discussion is now extended on in the Discussion section.\nAll in all, the authors present convincing results, discussions and conclusions based on\nsubstantial data and sound use of methods. The time span covered and details both spatially\nand temporally are impressive and, in my experience, unprecedented and will have a large\nsignificance to the field and similar fields.\nThanks for this encouraging feedback!\nSee my detailed suggestions and comments in the attached annotated manuscript.\nIn the following we list the comments in the pdf (with the line number referring to the original pdf) and\ngive our response:\nLine 62: It would be of great value it you for each RG could give more information/context in\nthe Supplementary Information. This could including maps/orthophotos showing the main\nfeatures and spatial (and if possible temporal) distribution of the displacement. With this\ncontext it would be easier for the reader to relate/interpret the data in the other figures.\nWe added now in the Supplement one sheet for each rock glacier with airphoto and other\ninformation/context.\nL86: From Fig. 1 maximum speed for Galena creek RG looks lower than 130 cm, see Fig 2a.\nThe 130 cm/yr refer to a few individual measuring points, whereas the data in Figs 1 - 3 refer to average\nand median speeds of all measuring points for an individual rock glacier. This is now clarified.\nAs the first measurement period for Arapaho is exceptionally long due to a lack of sufficient airphotos\n(1953-2006) we prefer to not interpret the shape of the speed series and leave the text as is.\nL97: It is hard to interpret significance levels in Fig 2a due to small graphs and symbols.\nThe pdf resolution is now enhanced so that these symbols should now be readable. We enlarged fonts\nwhere possible.\nL111: Consider to add references here.\nDone\nL115: Have you considered the impact increased precipitation as rain would have on the\nacceleration?\nIn the literature air temperature and snow cover are suggested to be the most important potential factors\nfor long-term changes of rock glacier speed. We now show also precipitation time series for the\nindividual rock glaciers in the Supplement and include precipitation effects in the Discussion section.\nL127: Consider to introduce variations in precipitation as rain for the RGs in the study\nModeled data or data from meteorological stations nearby could give a more detailed\nunderstanding of the observed displacement patterns. If you reduce the number of RGs plotted\nin Fig2a as suggested (see details in my comments in the figure label) there will be room for\nplotting precipitation-trends as a line in the plots by adding another a secondary axis\n(preferably with a different color for both line and axis to increase readability).\nRain data are now included, see above. We experimented with showing only a selection of rock glaciers\nin the main text but we really prefer to show all. We believe the strength of the study is both the number\nof rock glaciers studied in one and the variation of responses seen. A selection would not draw this\npicture very well in our view. We added now a figure with simplified speed changes (no error bars etc.)\nand air temperature as the latter clearly shows the largest explanatory power. Precipitation trends are\nnow shown in the Supplement and correlations have been investigated.\nL141: Consider to add change in speed in each circle as suggested for Cardinal Mtn N (see red\narrow). It can be hard, especially for people with reduced color vision (~8% of males!), to\ninterpret only using the color legend.\nWe tested the figure for all kinds of reduced colour vision, and it should be ok, but find the annotation a\ngood idea that we happily implement. We included the change factor. We also simplified Fig. 2 to\ncontain only change factors, not anymore percentage change, as they are redundant.\nfor additional measurement over two time intervals. Suggestions to consider: - Reduce the\nnumber of RGs plotted in Fig2a to maybe 4, leaving the rest for the Supplementary Information.\nOr show larger versions of the plots in the Supplementary Information. If the plots are\nincreased there will be room for plotting precipitation-trends as suggested.\nSee above response to L127.\n- To increase readability and better link the RGs between Fig1 and Fig 2a, in the heading of\neach RG in Fig2a, name the RG than the mountain range. Ex: Thomas Lake W - Mt Sopris.\nDone\nL153: Consider to add some info what the notches show, ex: \"boxplot notches (95% confident\ninterval of the median)\"\nNow explained in the figure caption.\nL173: Consider to define and reference CONUS.\nChanged to contiguous U.S.\nL249: Could it be that you have missed some high-speed parts an RG that have a displacement\nabove 40 m between acquisition of the orthophotos?\nSorry, a misunderstanding. These 40 m do not refer to a maximum displacement threshold but to a\nradius within which exact measurement locations (which differ from image pair to image pair to follow\nlocations of suitable matching features) are considered to represent the same measurement location.\nWe clarified.\nL269: Is it possible to say something about the spatial speed accuracy, or quantify, a spatial\ngradient speed threshold?\nIf a measurement location is wrong in one image pair by some meters the measured displacement\nwould still be very similar to the one some meters away. The stress transfer by ground ice makes the\nvelocity fields on rock glaciers typically quite smooth. Such geolocation errors could only have an\nimpact at the very margins of the rock glacier where a measurement location could jump on/off the\nmoving rock glacier over a very short distance, or in the case of strong break lines in the flow field. We\navoided to measure displacements on the rock glacier margins (see new rock glacier sheets in the\nSupplement) and became not aware of strong breaks in the flow fields of the rock glaciers investigated.\nThese effects would be random. But, yes, a gradient threshold within the displacements of one time\ninterval could help to exclude measurement zones prone to these effects. We added a respective\nsentence in the text.\nFig S2: Consider naming the RGs that are close to the stations.\nDone in the caption of Fig S1\nFig S3: Consider adding unit to y-axis.\nFig S4: Consider adding unit to y-axis.\nDone\nResponse to Reviewer #3\nThere are several problems with this paper and it should not be published in its\npresent form.\nWe significantly modified our text along the referee’s comments and would be happy to learn if there are\nformulations remaining that could lead to confusion and distract from what we believe are the most\nimportant results from our study: the kinematic time series. See in particular the general response at the\ntop of this response letter.\nwhat is necessary to communicate. The text is mainly about the techniques\ninvolved and data extraction. While I have no complaints about the technique, it\nis novel and useful, indeed, I would like to know more about it and results that\ncan be seen. But this journal is not the place to present this. The technique\nand basic results should be published elsewhere.\nWe have now modified the title and the paper significantly, including an extension of the discussion. The\ntechnique used here builds on Kääb et al. (2021; see reference list of the paper) which can be consulted\nfor other photogrammetric details. We hope the technique presented in the current study inspires similar\nstudies elsewhere and gives useful instructions for that. In agreement with referees #1 and #2, we\nbelieve the most novel results from our study are the time series of rock glacier speed themselves.\nThese data double the amount of such time series measured today, reach particularly far back in time,\nand cover a continent without such data available so far. We believe these findings are important\nenough for a number of fields, ranging for instance from the mechanics of frozen materials to climate\nchange impact, to warrant publication in a widely visible interdisciplinary journal.\n2. This title is not only misleading in intent but also in fact, some\n‘self-evident’ others more nuanced. It is not ’creep’ that is necessarily being\nmeasured but ‘speed’ or ‘velocity’ and these words are used in the text. Creep\nis associated here with rock glaciers, as in text and as stated but also with\nglacier ice deformation. Glaciers can slide to give a surface velocity.\nWe now modified the title and avoid the term ‘creep’ throughout the text, unless where citing other\nstudies.\n3. The linkage of rock glacier to ‘permafrost creep’ should be abandoned. This\n8\nhas long been used as the only mechanism for rock glacier flow, usually\nfollowing citation of the book Rock Glaciers by D. Barsch (here reference number\n14). Barsch denies the existence of the ‘glacier ice cored rock glacier’. In\nparticular the work of Potter at Galena Creek RG where glacier ice has been\nshown to be the core of the rock glacier at Galena Creek and at Sulphur Creek RG\nthe recent work by Meng et al (cited in the paper as ref 27) not only gives\nvelocity data (was this compared to that obtained in this paper?). In other\nwords, the authors use rock glacier always as being indicative of permafrost\nrock glaciers but omit references to evidence from ‘disproving cases’. This has\nbeen a situation for far too long in the literature. Here the glacier ice\nformation is blatantly denied but still uses RG that do have glacier cores in the ‘analysis’.\nTo our best understanding the term ‘permafrost’ does not exclude bodies of frozen debris with a core of\nglacier ice and the term is, in contrast to the term ‘glacier’, mainly a thermal term. Still, to avoid\nconfusion we tried now to rephrase our text throughout and to direct the focus on the changes in speed,\nwhich we consider our most important results. See also our general response at the top of this response\nletter.\nWe indeed compared our measurements to the great and openly available ones by Meng et al. (2023),\nsee last subsection of the Method section (‘Comparison to other velocity measurements’). We also\nmake our detailed speed data now accessible in a data repository along with other information in the\nSupplement enabling others to reproduce our results and to perform own detailed comparisons.\n4. Any body with ice (glacier or cryogenic) can ‘flow’ or ’creep’ but the creep\nrate (velocity) depends upon more that ‘temperature’. Thickness of the ice mass\nand surface slope provide the main stress fields. So, a glacier might give the\nsame results as supposed for a ‘permafrost rock glacier’. But the problem really\nis that the data analyses are far too simplistic, other site specific conditions\nshould be analysed. Further, if the rock glaciers are buried glaciers then\nsliding, rather than flowing, might be the main driver of the differences.\nWe formulated now more neutral throughout the text, well acknowledging that we do not know the\ninternal structure and internal kinematics of the rock glaciers investigated.\nOur comment list did not contain a comment #5 and we assume #6 should read #5, etc.\n6. But what are these differences? Why does Cardinal Mtn N have the largest\nsurface speed change compared with Cardinal Mtn S have one of the lowest? This\nalone might suggest that there as more in the variability than ‘temperature’.\nIndeed, several meteorological parameters should be used and investigated. This\nleads to\nWe extended now the respective parts of the discussion, considering the different factors that are\nthought to influence rock glacier speed. We add substantially more meteorological data in the\nSupplement (as also suggested by referee #2). We also add analysis, discussion and figures on the\nrelation between met data and our rock glacier speed.\n9\n7. The data analysis is overly simplistic. In fact, the paper does not comply\nwith any aspects of FAIR data principles. Ok, have a graph but what are the data\nfrom which the results are plotted? Use of median might be more ‘robust’ but\nthere are other descriptive statistics that could be used for the analysis.\nWe make now available the individual point speeds for all rock glaciers and the data of the graph Fig. 2.\nFor analyzing the rock glacier speeds over time and their changes we use period medians (red lines),\nperiod means (middle of light blue areas, as now clarified), notches (which are derived from interquartile\nranges and thus involve percentiles), an estimate of the error of speed changes between periods, and a\nstatistical significance test of the latter. We have experimented with other statistical descriptors (e.g.,\npercentiles, whiskers) but believe the current set of statistical descriptors covers the most important\nstatistical aspects behind our time series while maintaining readability of Fig. 2. In addition, the stable\nground (=co-registration) errors are given.\n8. Also with respect to FAIR, the locations of rock glaciers are given only by\ntoponyms. A proper geolocation is required. Using a decimal latitude-longitude\n[dLL] identifier for rock glacier locations allows the reader to locate the\nfeature in, for example Google Earth. This might help in interpretation, what\nmight the differences be between Cardinal Mountain N/S. From the peak at\n[36.9996,-118.4148], there are several contenders for ‘north’ but I cannot see\nwhat is meant by ‘south’. This is not presenting data that are findable,\naccessible, interoperable or re-usable. This is required in any transparent data\nanalysis. No attempt to be transparent is made in this paper.\nWe now substantially expanded the Supplement, among others with one separate sheet for each\nindividual rock glacier, including airphoto, measurement locations, descriptive data and we provide the\nspeed time series data.\nBut fundamentally, it is the continued scientific lack exactitude of the data\npresented. Support for the contention suggested by the title is not upheld.\nWe hope the modifications made to the manuscript and motivated in our above responses improved the\npaper. See also general response at the top of this response letter.\nEnd of response\nREVIEWERS' COMMENTS\nReviewer #2 (Remarks to the Author):\nThe authors have during the revision taken into account the comments from the reviewers,\nthey have largely increased readability, transparency and reproducibility. They have given\nmore details regarding data analysis and the interpretation.\nThis work is a significant contribution the to the field, and similar fields.\nThe revised manuscript is in my opinion ready for publication.\nBest regards,\nHarald Øverli Eriksen\nReviewer #3 (Remarks to the Author):\nThank you for doing the changes and modifications.\nHiwever, I would ask that you include [dLL] geolocations for the RG used in the analysis in\nthe paper (not just in the Supplementary). Ideally each place name label should have its\n[dLL] below the toponym. However, I see no reason why they should not be given as a list in\nthe caption for Figure 1. This would make the locations both easily identifiable and,\nimportantly, digitallly readable in the MS text.\nfor example Galena Creek: [44.6502,-109.7907]"}]

Decision letter