Weekly to monthly terminus variability of Greenland’s marine-terminating outlet glaciers

. Seasonal terminus-position variability of Green-land’s marine-terminating outlet glaciers is superimposed on multidecadal trends of glacier retreat. To characterize this seasonal variability, we manually digitized terminus positions for 219 marine-terminating glaciers in Greenland from January 2015 through December 2021 using Sentinel-1 synthetic aperture radar (SAR) mosaics. We digitized at a monthly frequency for 199 glaciers and at a 6 d frequency for 20 glaciers. We found that nearly 80 % of glacier termini in Greenland vary signiﬁcantly on a seasonal basis. For these seasonally varying glaciers, on average, seasonal re-treat typically begins in mid-May, and seasonal advance generally commences in early October. The timing of the initiation of the retreat period may be related to the timing of the onset of ice-sheet surface melt. The rate of retreat events peaks in late summer and reaches a minimum in late winter and early spring. The median magnitude of terminus-position seasonality, the difference between glacier length at the dates of peak advance and retreat, is about 220 m. We ﬁnd a stronger correlation between this magnitude and glacier velocity than between magnitude and glacier width. Terminus-position seasonality can inﬂuence longer-term glacier dynamics and, consequently, ice-sheet mass balance. This study contributes to our understanding of terminus-position sea-sonality

Previous studies have suggested that seasonal terminus-position variability is driven by the effect of proglacial mélange or meltwater runoff on calving rates. In front of some glaciers, a rigid mélange tends to form in the winter as sea ice freezes and binds icebergs together. At several glaciers in Greenland, the presence of a rigid mélange in front of a glacier terminus has 40 been shown to inhibit calving and promote glacier advance, and similarly the clearing out or weakening of mélange is associated with glacier retreat (Carr et al., 2013;Cassotto et al., 2015;Fried et al., 2018;Howat et al., 2010;Joughin et al., 2008a;Kehrl et al., 2017;Kneib-Walter et al., 2021;Moon et al., 2015;Todd and Christoffersen, 2014). However, there is not always a clear relationship between mélange and terminus position (Carr et al., 2013;Sakakibara and Sugiyama, 2019).
Other work suggests that there is a relationship between seasonal terminus retreat and the timing and duration of meltwater 45 runoff (Fried et al., 2018), or relatedly, above-freezing air temperatures (Carr et al., 2013). Runoff can drive subglacial upwelling, which increases terminus-face melting and calving due to undercutting . Alternatively, runoff may increase seasonal retreat via hydrofracture-induced calving (Nick et al., 2010;Sohn et al., 1998). Other studies, however, have found little or no relationship between seasonal terminus positions and runoff or its proxies such as air temperature Schild and Hamilton, 2013). 50 Glacier flow is highly sensitive to changes at the terminus (Howat et al., 2008;Joughin et al., 2008b;Meier and Post, 1987;Nick et al., 2009;Schoof, 2007), so short-term terminus-position variability may influence longer-term trends in glacier dynamics and, consequently, ice-sheet mass balance. Omitting terminus seasonality from numerical models can lead to both over-and under-estimated mass change projections on decadal time scales for individual glaciers, depending primarily on the magnitude of terminus seasonality (Felikson et al., 2022). Therefore, it is important that the terminus seasonality of 55 individual glaciers be well-characterized.
To maintain a tight focus, we limit this investigation primarily to characterizing seasonal terminus-position variability for marine-terminating outlet glaciers around the entire Greenland Ice Sheet. Given the number of processes contributing to seasonal variability (e.g., surface melt, ocean temperatures, and mélange) a more detailed investigation of the causes of seasonal variability is beyond the scope of this paper. 60 Our methods capitalize on the capabilities of the Sentinel-1A/B synthetic aperture radar (SAR) satellites, which typically imaged Greenland at a repeat interval of six days when both satellites were operating, and 12 days when only Sentinel-1A was operating. For the period from January 2015 through December 2021, we manually digitized monthly terminus positions for 199 glaciers around Greenland, and six-to twelve-day terminus positions for an additional 20 glaciers in central-west and https://doi.org/10.5194/tc-2022-176 Preprint. Discussion started: 8 September 2022 c Author(s) 2022. CC BY 4.0 License.
northwest Greenland. We use these terminus position data to characterize the magnitude and trends of seasonal terminus-65 position variability, and to estimate the frequency and seasonality of glacier retreat events at a six-day level.

Data
We used a total of 373 Sentinel-1A/B SAR mosaics (Joughin, 2020) to digitize glacier terminus positions at monthly and six or twelve-day intervals from January 2015 through December 2021. We chose this time period based on the availability of Sentinel-1 mosaics at the time that we digitized the glacier termini (late 2021 and early 2022) and in order to capture 70 complete years of data. The monthly glaciers are located around the full margin of the ice sheet, while the six-day glaciers are concentrated in central-west and northwest Greenland ( Figure 1).

Satellite images
SAR mosaics of the Greenland Ice Sheet were generated from images taken by the Sentinel-1A/B satellite pair (Joughin, 2020). These satellites are able to image the ice-sheet surface regardless of cloud conditions or solar illumination, making 75 them valuable for capturing changes in glacier behavior throughout the year. Since Version 3, the SAR mosaic product has 25 m image resolution; earlier versions had 50 m resolution. The mosaics cover 12-day intervals from 1 January 2015 through 27 September 2016, during which time only Sentinel-1A was in orbit. After the launch of Sentinel-1B, the mosaics cover six-day intervals, up until the failure of Sentinel-1B on 23 December 2021, after which the mosaics returned to 12-day intervals. Occasionally, missed acquisitions produce intermittent spatial gaps (missing swaths) in the SAR mosaics, with 80 corresponding temporal gaps in terminus position data for the affected glaciers.

Terminus positions
We manually digitized glacier terminus positions from Sentinel-1A/B SAR mosaics using ArcGIS. All digitizing was performed by a single analyst to reduce potential differences in interpretation of imagery. The error associated with these manually-digitized terminus positions is typically comparable to the image resolution (i.e., 25 m for most SAR mosaics used 85 in this study)  and often results from difficult interpretation conditions arising from poor image contrast, such as extensive proglacial mélange cover.
We digitized terminus positions for a total of 219 marine-terminating outlet glaciers (Figure 1), 199 of which were digitized at monthly intervals (Table S1), and 20 of which were digitized at six-day intervals (Table S2). For the monthly glaciers, we used the first SAR mosaic entirely within each month (e.g., for the month of May, we may use 5-10 May, but not 29 April-4 90 May), from January 2015 through December 2021. For the 20 six-day glaciers, we chose to focus on central-west and northwest Greenland, where outlet glaciers have been changing rapidly King et al., 2020), and selected glaciers with clear seasonal variations in the monthly data that we wanted to capture at higher temporal resolution.
As part of this set, we selected all five glaciers in Upernavik Icefjord to include a local grouping of glaciers. For comparison https://doi.org/10.5194/tc-2022-176 Preprint. Discussion started: 8 September 2022 c Author(s) 2022. CC BY 4.0 License.
to those with clear seasonal variations, we included one glacier (Yngvar Nielson Gletsjer, no. 65) that did not show strong 95 seasonal variability in the monthly data. For these six-day glaciers, we digitized terminus positions in all available SAR mosaics from January 2015 through December 2021 at 12-day intervals before October 2016 and six-day intervals thereafter.
For simplicity, we refer to metrics associated with this dataset as "six-day" (e.g., "six-day glaciers").

Methods
We digitized 23,333 glacier terminus positions representing January 2015 through December 2021, with an average of 82 100 per glacier for the monthly glaciers and 353 per glacier for the six-day glaciers. We calculated glacier area and length change and used these data to identify the significance, timing, and magnitude of terminus-position seasonality for each glacier. We also summarized these characteristics for all glaciers around the ice sheet, as well as for individual regions of the ice sheet (IMBIE, 2022;Rignot and Mouginot, 2012). Finally, we identified the timing and magnitude of individual retreat events for the six-day glaciers. 105

Glacier area and length change
We used the box method (Moon and Joughin, 2008) to calculate glacier area over time. For each glacier, we defined an open-ended reference box with sides approximately parallel to ice flow and the back perpendicular to ice flow and upstream of the range of observed terminus positions. The box may be complex in shape (i.e., composed of more than three line segments) as it follows glacier flow around obstacles and up fjords, particularly if the glacier has retreated substantially. 110 Each terminus position intersects both sides of the box, forming a polygon from which we calculate the area. We calculated a proxy length over time by dividing each area measurement by the mean box width at the terminus, following the methods of Black and Joughin (2022).

Presence of terminus-position seasonality
In characterizing terminus-position variability, one of our main objectives was to determine if there is a seasonal component 115 to the pattern of terminus variation. To do this, we used the Lomb-Scargle periodogram, a tool for detecting periodicity in unevenly sampled data (Lomb, 1976;Scargle, 1982;VanderPlas, 2018). We chose this method due to the random temporal gaps in our time series associated with occasional missed satellite image acquisitions. For each glacier's set of terminus positions, we computed the length time series, linearly detrended the length, and calculated the Lomb-Scargle periodogram for the detrended time series. We determined the power for cycles with a period of one year and compared this to the Lomb-120 Scargle false-alarm level at probability p=0.05. This is the threshold at which, if there were no periodic signal in the data, there could still be a peak at this frequency 5% of the time. If a glacier's length periodogram had a peak at annual frequency that exceeded the false-alarm level (i.e., p<0.05), we classified it as having significant annual terminus-position seasonality. Note that this classification only applies during our observation period (January 2015 through December 2021) as terminusposition seasonality can change over time (e.g., Joughin et al., 2008a). 125

Timing and magnitude of terminus-position seasonality
For glaciers with significant annual terminus-position seasonality (as determined with the Lomb-Scargle periodogram), we identified peaks and troughs in the glacier length time series to determine the timing and magnitude of seasonality (see example in Figure S1). First, we used a peak-finding algorithm to identify all peaks and troughs in the length data. Next, the data were detrended and we found the resulting detrended glacier length at each peak and trough. We then found the date and 130 detrended length of the highest peak and lowest trough for each year. In cases where retreat continued into the following year, we paired the associated trough with the peak in the previous year (i.e., the peak from which the retreat initiated). We differenced the peak and trough lengths to find the magnitude of the terminus-position seasonality for each year. Finally, for each glacier, we determined the median annual dates of greatest advance and retreat, the median duration of retreat, and the median magnitude of terminus-position seasonality. We used these values to compute the Greenland-wide and regional 135 timing and magnitude of terminus-position seasonality.

Timing and magnitude of retreat events
For the six-day glaciers, we used each glacier's length time series to determine the timing and magnitude of retreat events (integrated over six days) for individual glaciers and cumulatively for the entire group of six-day glaciers. To do this, we differenced the glacier length time series to find all potential retreat events (negative differences). To exclude small events 140 within the range of terminus digitization uncertainty, we filtered the retreat events to retain only those with magnitudes greater than a threshold value of 50 m. In this process we do not account for glacier velocities, and so this method does not capture any retreat events that are smaller than the advance that occurred in the same time frame, i.e., cases where there is net advance that is smaller than would be expected based on glacier velocity.

Results 145
We found that most glaciers in Greenland undergo annual cycles of advance and retreat. Figure 2 shows the relative monthly glacier length as a function of time for each of the 219 glaciers in our study. A pattern of annual cycling between relatively advanced terminus positions (blue) and relatively retreated terminus positions (red) is visible for many glaciers, illustrating terminus-position seasonality. The overall shift from blue to red over the entire duration illustrates an interannual retreat trend. Selected length time series are shown in Figure S2 and Figure S3 to illustrate what terminus-position seasonality (or 150 lack thereof) can look like for a subset of glaciers, including all of the six-day glaciers.

Prevalence of terminus-position seasonality
To better isolate the annual signals in glacier length, we computed Lomb-Scargle periodograms for the detrended data for each glacier to identify significant annual peaks. We found that between 2015 and 2021, 73.5% (n=161) of Greenland's marine-terminating outlet glaciers exhibited significant annual terminus-position seasonality at the 95% confidence level. 155 For many of the other glaciers, annual peaks were visible in the Lomb-Scargle periodograms but below the 95% confidence level, suggesting some weak seasonal variability may be present. Table 1 illustrates that glaciers with pronounced seasonality are more common in western Greenland (80.9 to 94.1%) and slightly less so in the east (64.0 to 69.3%).
Seasonality is least common in the north (46.2%), where several glaciers have floating ice tongues, such as Petermann (no. 93 following the MEaSUREs Glacier ID system of Joughin et al. (2015)) and Ryder (no. 96) which do not vary seasonally. 160

Timing and magnitude of terminus-position seasonality for all glaciers
We characterized the timing of terminus seasonality for the glaciers that had significant seasonality by finding the peaks and troughs in each glacier's length time series as described above. Figure 3 shows that these seasonally-varying glaciers tended to be at their most advanced state in late spring to early summer, and their most retreated state in autumn. Across all of these seasonally-varying glaciers, the median date of maximum advance ranged between May 6 and June 8, with a median of May 165 12. Retreat initiated immediately after the time of greatest advance, and the median date of maximum retreat ranged between September 4 and November 6, with a median of October 8. After this time, the glaciers began advancing again. The duration of the ice-sheet-wide retreat period, the time between the median dates of greatest advance and retreat, varied between 118 and 184 days, with an average of 145 days.
We calculated the amplitude of the seasonal signal in order to determine the typical annual range in detrended terminus 170 positions. For the 161 glaciers with significant terminus seasonality, the magnitude of the terminus-position seasonality is the difference between its detrended lengths at the dates of greatest advance and retreat. Figure   To look at regional variations, we organized the glaciers into six groups defined by the regional drainage basins shown in northeast. The timing and magnitude of terminus-position seasonality for individual glaciers is presented in Table S3.

Timing and magnitude of retreat events for six-day glaciers
We digitized 20 glaciers in central-west and northwest Greenland at six-day resolution rather than monthly resolution (Table   S2). The greater temporal resolution of the six-day dataset allowed us to explore the number and magnitude of retreat events for this subset of glaciers in northwest and central-west Greenland. Note that we use the term 'retreat events' rather than 190 'calving events' because our method cannot detect calving that did not offset advance between observations, and because the calving that we did detect is integrated over a six-day period. Figure 5 shows that both the number and the magnitude of retreat events were greatest in July and August, and were lowest in January through March. The timing and magnitude of retreat events for these 20 glaciers, individually and combined together, are shown in Figure S4 and Figure S5.

Discussion 195
The data reveal several interesting points about the prevalence (Table 1) (Table 2), and at individual glaciers (Table S3). In the following we discuss each aspect separately.

Prevalence of terminus-position seasonality
Our observations show that terminus-position seasonality is widespread throughout Greenland ( Figure 4b) and is especially 200 common in western regions of the ice sheet (Table 1). We expect that the presence or absence of terminus-position seasonality is related to ice velocity because advection of ice is necessary for the advance phase of the seasonal terminus position cycle. For instance, a glacier flowing at 50 m a -1 could not sustain annual terminus-position seasonality of larger than 50 m, because it is not flowing fast enough to replenish the ice lost each year to complete the seasonal cycle. To estimate representative velocities, we calculated the mean velocity along the most-retreated terminus position for each 205 glacier, using a 2020 annual velocity map (Joughin, 2021;Joughin et al., 2010). We chose the most-retreated terminus position to ensure that it would be covered in the velocity map. Glaciers with significant terminus-position seasonality tended to have a much higher velocity (median velocity of 840 m a -1 ) than glaciers without significant terminus-position seasonality (median velocity of 200 m a -1 ). For a glacier flowing at an average of 840 m a -1 , a seasonal retreat of 220 m (the median magnitude of terminus-position seasonality) represents removal of a quarter of the annual advection. Applying this 210 relationship to the median velocity of glaciers for which we did not detect significant terminus-position seasonality, we find that these glaciers could have a magnitude of terminus-position seasonality of about 50 m, which would be difficult to detect in the Sentinel-1 SAR mosaics that we used. We also explored whether our classification of the presence or absence of terminus-position seasonality aligned with other classifications of glaciers in Greenland. Vijay et al. (2021) classified glaciers based on their seasonal velocity patterns 215 following Moon et al. (2014), which may indicate variations in subglacial hydrology. Their classification includes glaciers that both speed up and slow down during the melt season ("type 2"), glaciers with high winter and spring velocities and a longer period of slowing ("type 3"), and glaciers with no classification. We compared our terminus-position seasonality classification with their seasonal velocity classification and found that most glaciers in most velocity categories showed significant terminus-position seasonality. We also compared our seasonality classification with the glacier bathymetry 220 classification of Wood et al. (2021), who sorted glaciers into six categories based on their bathymetry at the terminus (e.g., calving on a ridge, or calving in deep fjords). Again, we found that most glaciers in most bathymetry categories showed significant terminus-position seasonality. Thus, the lack of a clear relationship with either of these classifications suggests that the presence or absence of terminus-position seasonality is likely not related to the type of seasonal velocity variations or to bathymetry types. We have not established, however, whether the type of seasonal velocity variations or terminus 225 bathymetry have an effect on the magnitude of terminus-position seasonality.

Timing of terminus-position seasonality
We established that, ice sheet-wide, seasonal glacier advance tends to peak (and retreat begins) in May or early June each year, and retreat tends to peak (and advance begins) in October to early November (Figure 3), with regional variations in timing ( Table 2). The timing of peak advance and retreat that we observe is generally consistent with regional studies of 230 glacier terminus seasonality (Carr et al., 2013;Fried et al., 2018;Seale et al., 2011). In cases where there are differences in the timing of terminus-position seasonality, it appears to be related to the number of glaciers sampled (Sakakibara and Sugiyama, 2019). The only difference in Greenland-wide compilations is with King et al. (2018), who found that ice-sheetwide retreat commenced about a month earlier (early April through late September) than our findings (mid-May through early October; Table 2). However, in calculating the timing of retreat, King et al. (2018) weighted each glacier by its 235 contribution to total discharge; some of the highest-discharge glaciers begin retreating earlier in the year, which would bias the weighted timing of retreat earlier in the year as well. We do find that the number and magnitude of retreat events, which typically peaked in July and August (Figure 5), matches well with the seasonal peak discharge in mid-July reported by King et al. (2018). sheet. We examined cumulative annual melt area (Mote, 2014;Mote and Anderson, 1995) and found that melt started relatively early (mid-April) in 2016, 2018, and 2019, and relatively late (early May) in 2015 and 2017. The 2020 result appears to be an outlier as early-season melt followed a similar trajectory to 2018 and 2019, but 2020 had the shortest observed retreat period. The timing of the onset of melt may control the initiation and duration of retreat through the effects 250 of increased melt on early mélange breakup, hydrofracture-induced calving, and terminus undercutting through enhanced subglacial discharge. The timing of the onset of melt appears to be more important to retreat duration than the total melt, as 2015 and 2020 ultimately had moderate cumulative melt (more than 2017 and 2018), but also had the shortest retreat durations in our record. The duration of the retreat period also does not appear to correspond strongly with annual net mass balance or surface mass balance on an ice sheet-wide scale (Fettweis et al., 2017;Shepherd et al., 2020;Simonsen et al., 255 2021).
Our findings about the timing and magnitude of terminus-position seasonality provide some insights into previous studies. Fried et al. (2018) found that glaciers with terminus-position seasonality of a magnitude less than 500 m tended to be more sensitive to runoff. We found that 78% of glaciers in our study had a seasonal magnitude less than 500 m (Figure 4), so it is possible that runoff dominates seasonality for most glaciers in Greenland. However, a number of the glaciers in our study 260 start advancing very late in the season (e.g., December, January) and/or start retreating very early in the season (e.g., February, March) (Figure 3), which suggests that the timing of their seasonality is not entirely controlled by runoff. Instead, the timing of seasonality for these glaciers seems more likely to be controlled by the formation of proglacial mélange, which tends to lag the end of runoff and can facilitate glacier advance (Carr et al., 2013;Howat et al., 2010;Joughin et al., 2008a;Kehrl et al., 2017;Kneib-Walter et al., 2021;Todd and Christoffersen, 2014), and by mid-winter episodes of mélange 265 clearing, which can help initiate early glacier retreat (Cassotto et al., 2015;Joughin et al., 2008a). The conditions under which each mechanism may dominate remain unclear.

Magnitude of terminus-position seasonality
The magnitude of seasonal terminus variations tends to be small relative to the multi-decadal retreat, with 55% of glaciers having a magnitude less than 250 m, and only 22% having a magnitude greater than 500 m (Figure 4). Many prior studies of 270 glacier terminus seasonality used MODIS daily imagery to capture terminus positions at a higher temporal resolution than we could achieve with Sentinel-1 (Joughin et al., 2008b;Schild and Hamilton, 2013;Seale et al., 2011). However, the spatial resolution of MODIS imagery at best is limited to 250 m, so the terminus-position seasonality of many glaciers in Greenland would not be detectable in MODIS imagery. Studies using higher-resolution imagery have been focused on western Greenland (Carr et al., 2013;Fried et al., 2018;Moon et al., 2015). Fried et al. (2018) found seasonal terminus position 275 cycles ranging in magnitude from 150 to 1000 m in central-west Greenland, which is consistent with our findings for the same subset of glaciers, with magnitudes ranging from 80 to 880 m. The only glacier in central-west Greenland with a larger magnitude was Sermeq Kujalleq (Jakobshavn Isbrae, no. 3), with a magnitude of 2600 m, but this glacier was not included in Fried et al. (2018). In northwestern Greenland, previous estimates of magnitudes of terminus-position seasonality ranged https://doi.org/10.5194/tc-2022-176 Preprint. Discussion started: 8 September 2022 c Author(s) 2022. CC BY 4.0 License.
from 600 to 800 m (Carr et al., 2013;Moon et al., 2015), which is three to four times higher than our median magnitude of 280 220 m for this region. These studies looked at small subsets of glaciers in northwestern Greenland; applying approximately the same subsets to our data, we found median magnitudes ranging from 340 to 470 m and mean magnitudes between 530 and 550 m, which are still below the previously reported magnitudes. These differences in magnitude may reflect differences in methodology, as we remove the interannual length trend before calculating the magnitude of the terminus-position seasonality. Alternatively, the differences between our study and previously reported values could reflect the evolution of 285 terminus-position seasonality over time, as the data from Carr et al. (2013) were taken from 2004 through 2012, and those from Moon et al. (2015) were from 2009 through 2014, both of which predate our study period (2015)(2016)(2017)(2018)(2019)(2020)(2021).
Some previous studies have found a strong relationship between the magnitude of terminus-position seasonality and glacier width (Schild and Hamilton, 2013;Seale et al., 2011). We examined the relationship between magnitude and width for the glaciers in our study and found that, while there was a significant correlation (p=0.004), width alone could not explain the 290 variance in the data (R 2 =0.051). This correlation was improved somewhat (p=0.000, R 2 =0.178) by removing Sermersuaq (Humboldt Glacier,no. 92), which at ~32 km wide was a substantial outlier ( Figure S6). Seale et al. (2011) also found that glaciers with magnitudes of terminus-position seasonality of less than 1 km were typically less than 2 km wide. However, we found that of 148 glaciers with magnitudes of terminus-position seasonality less than 1 km, 107 were actually wider than 2 km. 295 We instead found a stronger correlation between the magnitude of terminus-position seasonality and mean annual glacier velocity (p=0.000, R 2 =0.479; Figure S7). The stronger correlation between terminus-position seasonality and glacier velocity makes sense when considering how much a glacier would have to calve to balance its velocity. For instance, at a glacier that is flowing at several kilometers per year at the terminus, our median magnitude of terminus-position seasonality of 221 m would be a relatively small signal. However, above we showed that this terminus-position seasonality would remove a 300 quarter of the annual advection for a glacier flowing at the median observed annual velocity. Because our data are detrended, the magnitude of terminus-position seasonality is separated from interannual terminus position trends. Our measured magnitude of terminus-position seasonality also only captures the period of seasonal retreat and does not include calving events that may happen outside of that period. Therefore, there is likely to be additional retreat each year to offset the annual advection and generate the widespread interannual retreat that has been observed. 305

Comparisons with select individual glaciers
The spatial breadth of our study allows us to make comparisons to data on several individual large glaciers reported in previous studies (Table 3). At all of these glaciers, we find that the differences in the timing and magnitude of terminusposition seasonality reported by our study compared to others are relatively small (approximately a month) Joughin et al., 2008a, b;Kehrl et al., 2017;Schild and Hamilton, 2013). In a few cases we found larger differences in 310 timing, typically compared to the data reported by Schild and Hamilton (2013), who studied several of these glaciers from 2001 to 2010. For example, at Daugaard-Jensen (no. 120), they reported that seasonal retreat began in late May, whereas we https://doi.org/10.5194/tc-2022-176 Preprint. Discussion started: 8 September 2022 c Author(s) 2022. CC BY 4.0 License. found that retreat began over a month earlier, in early April. At Kangerlussuaq (no. 153), Schild and Hamilton (2013) reported that it typically retreated from July through late September; we found that it instead retreats from mid-July until December, which is consistent with the more recent findings of Kehrl et al. (2017). Finally, at Helheim, we found that the 315 timing of the initiation of retreat was shifted a month earlier than Schild and Hamilton (2013) and Joughin et al. (2008b), who found that Helheim typically began retreating and calving in May. All of these differences can likely be explained by interannual variations in terminus-position seasonality and the different time periods covered by these studies. Our data are insufficient to rule out potential longer-term trends in the timing of terminus-position seasonality.

Conclusions 320
We used Sentinel-1 SAR images to characterize terminus-position seasonality for 219 marine-terminating glaciers around Greenland from January 2015 through December 2021. We found that terminus-position seasonality is common, with 74% of glaciers expressing significant seasonality. The glaciers that do not have significant terminus-position seasonality tend to have large floating tongues or relatively low ice velocities. Of the glaciers with significant terminus-position seasonality, retreat typically begins in mid-May and advance typically begins in early October, with some variation in different years and 325 in different regions of Greenland, and substantial variation among individual glaciers. The number and timing of retreat events peaks in July and August and is lowest in January through March. The average annual peak-to-trough magnitude of terminus-position seasonality is nearly 400 m, although this is skewed by a few glaciers with very large seasonal cycles; the median magnitude is about 220 m. We found a stronger relationship between the magnitude of terminus-position seasonality and glacier velocity than between magnitude and glacier width. Because glacier dynamics are sensitive to conditions at the 330 terminus, understanding terminus-position seasonality is important for projecting future glacier change. This study provides an important step forward by extending characterizations of terminus-position seasonality from individual glaciers and regions to the entire ice sheet. The terminus positions digitized for this study may also serve as a valuable training data set for artificial intelligence-based detection of terminus positions in SAR imagery, to reduce the time and labor necessary to produce similar data in the future. 335

Code and data availability
Data analysis and visualization code are available at https://github.com/tarynblack/greenland_terminus_seasonality. The terminus positions are being prepared for submission to NSIDC. Sentinel-1 mosaics are from MEaSUREs Greenland Image Mosaics from Sentinel-1A and -1B, Version 4 (https://nsidc.org/data/nsidc-0723/versions/4 (Joughin, 2020)).   Table S1 and Table S2. The color scale is logarithmic with a linear threshold at ±10 -1 to account for values approaching zero. Terminus positions that are advanced relative to the mean length appear in blue, and terminus positions that are retreated relative to the mean length appear in red. No-data values are gray and are due to either spatial or temporal gaps in the SAR mosaics used for digitizing terminus positions.