The Decaying Near‐Surface Boundary Layer of a Retreating Alpine Glacier

The presence of a developed boundary layer decouples a glacier's response from ambient conditions, suggesting that sensitivity to climate change is increased by glacier retreat. To test this hypothesis, we explore six years of distributed meteorological data on a small Swiss glacier in the period 2001–2022. Large glacier fragmentation has occurred since 2001 (−35% area change up to 2022) coinciding with notable frontal retreat, an observed switch from down‐glacier katabatic to up‐glacier valley winds and an increased sensitivity (ratio) of on‐glacier to off‐glacier temperature. As the glacier ceases to develop density‐driven katabatic winds, sensible heat fluxes on the glacier are increasingly determined by the conditions occurring outside the boundary layer of the glacier, sealing the glacier's demise as the climate continues to warm and experience an increased frequency of extreme summers.

Recent works have highlighted this problem in increasing detail with examples from on-glacier data sets around the world (Ayala et al., 2015;Carturan et al., 2015;Conway et al., 2021;T. Shaw et al., 2021;T. E. Shaw et al., 2017;Troxler et al., 2020;Yang et al., 2022). Several of those works have also identified the presence of warm air processes that generate increases in Ta toward the terminus of mountain glaciers (Ayala et al., 2015; T. E. Shaw et al., 2017;Troxler et al., 2020). Various hypotheses have been raised as to the cause of this behavior (e.g., debris warming, convergent and divergent air flows, valley winds). Moreover, detailed eddy-flux measurements , atmospheric model simulations (Potter et al., 2018), and large eddy simulations (Goger et al., 2022;Sauter & Galos, 2016) have highlighted those potential interactions of air masses with distinct trajectories for fine atmospheric conditions. Ultimately, the governing processes of on-glacier Ta variability will likely evolve as mountain glaciers continue to shrink and their boundary layers further diminish (Carturan et al., 2015;Jiskoot & Mueller, 2012). As such, the empirical relationships between temperature and ice melt rate may change as a result (e.g., Bolibar et al., 2022).
Due to the lack of long-term, distributed observations, however, no study to the authors' knowledge has explored the evolution of the on-glacier Ta through time and its response to atmospheric warming and glacier changes. Here we compile six distinct years of meteorological datasets on the Swiss Haut Glacier d'Arolla to explore the changing air temperature and wind patterns spanning 2001-2022. We aim to explore the following questions: 1. how variable is on-glacier Ta in space and time? 2. how has Ta responded to changing surface and meteorological conditions as the glacier diminishes? 3. what do these changes imply about the boundary layer development of decaying mountain glaciers?

Study Site
Haut Glacier d'Arolla (45.97°N, 7.52°E) is a small mountain glacier located in the southwestern Swiss Alps at the head of Val d'Herens, Canton Valais ( Figure 1a). As of 2022, the glacier area was approximately 3.3 km 2 , with supraglacial debris covering around 22% of the total surface area. The area of the glacier has reduced by ∼35% since 2001, with more rapid frontal retreat and tributary separation since ∼2005 (Figures 1a and 1b, Figure S1 in Supporting Information S1). Since the early 1990s, the glacier has been subject of numerous studies exploring surface conditions and energy balance (e.g., Brock et al., 2000;Carenzo, 2012;Strasser et al., 2004), subglacial hydrology and morphology (e.g., Nienow et al., 1998;Sharp et al., 1993), and glacier mass balance (e.g., Arnold et al., 1996;Dadic et al., 2008;Willis et al., 2002). Since 2010, distributed measurements of Ta and other energy balance variables have been used to explore some of the common assumptions regarding Ta distribution in melt modeling (Ayala et al., 2015;Petersen et al., 2013).

Data
The meteorological setup consists of on-and off-glacier air temperature stations (hereafter "T-Loggers") and automatic weather stations ("AWS"). T-loggers are free-standing, 2 m tripods that support an Onset Tidbitv2 temperature logger (accuracy 0.2°C) housed in a naturally ventilated radiation shield. The type of radiation shield is distinct between the 2010 campaign (see Petersen and Pellicciotti (2011)) and that of 2021 and 2022 (see Section S3 in Supporting Information S1). AWS sensors vary given the year of study (see Table S3 in Supporting Information S1) but typically provide a full array of meteorological variables, including aspirated air temperature and humidity, wind speed and direction and radiative fluxes.
Before 2010, one pro-glacial AWS was operated by the Grand Dixence hydropower company ("OFF1" in Figure 1a-2,507 m a.s.l.), with an additional upper AWS available in 2010 ("OFF3"-2,985 m a.s.l.). In 2021 and 2022, a T-Logger was installed near to site "OFF3" at high elevation and in the pro-glacial zone ("OFF2"-2,531 m a.s.l.). OFF1 and OFF2 were >700 m from the terminus of the glacier in the respective year, suggested to be close to the limit of katabatic wind intrusion into the glacier forefield (Oke, 2002). Therefore, we use data from OFF1 (2001-2010) and OFF2 (2021 to provide an indication of off-glacier, "ambient" air temperature (hereafter Ta OFF ). Data from the other off-glacier AWS were not available after 2010. Full details on AWS and T-Logger specifications are given in Table S3 in Supporting Information S1.
Station data are filtered for obvious errors and extreme values are manually removed (e.g., when T-loggers fell over due to strong differential ablation or heavy storms- Figure S3 in Supporting Information S1). Due to the potential for naturally ventilated radiation shields to overheat and bias Ta measurements under high insolation, low wind speed conditions (Carturan et Table S2 in Supporting Information S1) stations are provided and referred to in the main text. (b) The area of the glacier given by the available historic outlines (Table S1 in Supporting Information S1) and recently digitized extents (colored circles) and the debris cover percentage (hollow squares), as derived from Landsat imagery. naturally and artificially aspirated Ta observations that were recorded at the same location (2010 and 2022). We utilize a multivariate-regression to estimate the hourly Ta differences (natural-aspirated) from hourly wind speed and incoming shortwave radiation measurements ( Figure S4 in Supporting Information S1) and use this to correct the naturally ventilated Ta observations. Details on data corrections and uncertainties are described in Section S2 in Supporting Information S1. Spatial information related to glacier extent and hypsometry ( Figure 1) are taken from historic and newly digitized data as described in Section S1 in Supporting Information S1.

Temperature Sensitivity
In order to estimate the state of the glacier boundary layer and its change through time, it is useful to consider the sensitivity of on-glacier Ta to the equivalent off-glacier Ta at a given elevation. This "temperature sensitivity" (TS) is defined as the ratio of the on-glacier observed Ta at each station (Ta obs ) to the above-zero estimated, off-glacier Ta at the same elevation (Ta est ) derived from the slope of the regression equation: Where ß is the regression intercept and Ta est is derived following: where Γ refers to the hourly variable temperature lapse rate derived from all available off-glacier Ta records or the literature (see Section S2 in Supporting Information S1) and Z obs and Z OFF are the respective elevations of the on-glacier observation and OFF1/OFF2. A sensitivity of 1 indicates that a change in Ta obs is equal to a change Ta est and that no cooling in the glacier boundary layer (Carturan et al., 2015) is detectable (i.e., the air temperature on-glacier is equal to the one off-glacier at the same elevation). Conversely, a sensitivity of 0.5 would indicate that, on average, for every 1°C change in the off-glacier Ta, a 0.5°C change in observed on-glacier Ta is evident (an example is given in Figure S5 in Supporting Information S1). This is the same as presented by earlier works (Greuell & Böhm, 1998;J. Oerlemans, 2001) and similar to the statistical estimation framework presented by Shea and Moore (2010), which divides relative temperature changes on the glacier by a threshold event for the onset of katabatic conditions.

Data Subsets
To assess the influence of the valley wind system on Ta obs , we define an up-valley/glacier wind index (UWI) that follows the form: where DIR is the wind direction (°) for a given hour and φ is the up-valley/glacier orientation (°). Accordingly, a value of one indicates that the wind direction is precisely up-valley/glacier and a value of negative one states that it is precisely down-valley/glacier. Changes in average UWI through time provide an indication of a wind regime switch at our study site. To emphasize the changes in on-glacier wind through the years, we compare selected stations on the glacier that have similar flowline distances (white box in Figure 1a-hereafter our "comparative AWS location").

Energy Balance Calculations
To explore the impact of katabatic boundary layer decay on the glacier, we calculate the point-based energy balance at the comparative AWS location (Figure 1a) using the cryospheric component of the land surface model Tethys-Chloris (T&C) (Fatichi et al., 2012(Fatichi et al., , 2021Fugger et al., 2022). The model is run at an hourly resolution for the entire period of observation in each year ( Figure S3 in Supporting Information S1) using a reconstructed meteorological time-series (see Section S5 in Supporting Information S1) and evaluated against ablation stake data ( Figure S9 in Supporting Information S1).

Patterns of Temperature and Temperature Sensitivity
There is evidence of increasing mean on-glacier Ta ( Figure 2) consistent with warmer ambient conditions over the last decade ( Figure 1c). While mean Ta has only slightly warmed at the glacier terminus between 2010 and 2021 (0.4°C increase >2,000 m along the flowline), 2022 temperatures are ∼2.5°C warmer on average than 2021 and ∼3°C warmer than the average pre-2010 Ta at 2,000-2,500 m flowline distance (Figure 2a). On-glacier Ta at the comparable AWS location (gray box in Figure 2a) have increased more relative to Ta OFF in recent years.
Irrespective of the year, temperature sensitivities (TS) typically decrease or remain stable until ∼2,000 m along the glacier flowline, followed by increases toward the terminus of the glacier (Figures 2c and 2d). For a common off-glacier temperature range (4°C-12°C), TS typically lowers to a minimum of ∼0.6 before gently rising toward 3,000 m along the flowline (Figure 2c), with slightly higher TS (0.75) in 2021 and 2022. For warmer atmospheric conditions (Ta OFF > P50), the contrast between earlier and later years is stronger (Figure 2e) with a more pronounced decrease of TS toward the mid-glacier for earlier years, followed by a relative increase in TS beyond 2,000 m in the later years. Comparing observations from 2010 onward, TS on the lower terminus has increased, by >0.07 on average between 2010 and 2021, and by >0.09 on average between 2010 and 2022 ( Figure 2e). Although observations do not extend to the glacier terminus for 2001 (Figure 1a), comparable observations at 2,000-2,400 m (gray boxes in Figure 2) demonstrate a clear change in the relationship of TS to the glacier flowline. Given a normalized flowline distance between the headwall and glacier terminus in each year, TS closely relates to the proximity of observations to the glacier terminus (Figure 2f).

Evolution of Glacier and Valley Winds
Observations  Figure S6 in Supporting Information S1).

Relation of Temperature Sensitivity to Wind
Considering the comparable AWS on the glacier (Figure 1a-white box, Figure 2a-gray box, Table S3 in Supporting Information S1) a clear change in the relation between warm conditions and the occurrence of katabatic winds is evident (Figures 3c-3h).  (Figure 3i). Up-glacier wind occurrence produces consistently higher TS across the glacier for all years and across most of the flowline (Figure 3j), highlighting the expected erosion of the katabatic boundary layer for warm, up-glacier winds (e.g., Petersen & Pellicciotti, 2011;T. Shaw et al., 2021). In 2022, up-valley winds notably establish a decreasing TS with distance up-glacier (Figure 3j), likely due to a combination of adiabatic cooling and sensible heat loss as air moves up-glacier to the highest elevations. This also acts to re-establish the elevation-dependence of on-glacier temperatures for 2022, such that a lapse rate could appropriately describe on-glacier temperature variability under warm atmospheric conditions ( Figure S8 in Supporting Information S1). Wind mixing events (coincident down-glacier and up-valley winds) result in a similar pattern to completely down-glacier/down valley wind events (Figure 3k), though most years have too few observations to robustly test the resulting TS.

Relevance of Decay to Surface Energy Balance
Since 2010, up-valley winds have become the dominant contributor to sensible heat fluxes on the glacier (Figure 4). Prior to 2021, the majority of up-valley winds occurred only under cooler ambient conditions (Figures 3c-3e), though contributed similarly to the sensible heat flux on the glacier due to stronger winds (Figures 4a and 4b).
In  Figures 4e and 4f). 2022 was characterized by record breaking warm weather, following a dry winter (Cremona et al., 2022), resulting in large fluxes of sensible energy to the surface given strong up-valley winds under a range of ambient temperatures (Figure 4f, Figure S10 in Supporting Information S1). During 2022, mean sensible heat flux under up-glacier wind conditions is 43% greater than that which coincided with down-glacier winds, while sensible heat flux is 54% less on average during up-glacier winds pre-2010 ( Figure 4, Table S4 in Supporting Information S1).

Discussion
A tendency toward more physically based modeling of glaciers (e.g., Y. Wang et al., 2021) increases the dependence on accurate forcing data (Gabbi et al., 2014), as forcing data errors are less able to be compensated during parameter calibration. Within the context of glacier meteorology, much work has been done to explore the spatial and temporal variability of near-surface air temperature and wind fields and its role in the decoupling of the glacier boundary layer with its surroundings (Ayala et al., 2015;Conway et al., 2021;Greuell & Böhm, 1998;Shea & Moore, 2010;Yang et al., 2022). However, while the key physical processes determining katabatic development are well understood (e.g., B. J. Oerlemans & Grisogono, 2002;Van Den Broeke, 1997), most studies have only provided a perspective at individual points on a glacier ablation zone and often for an individual year. A key finding of our study is the increased incursion of up-valley winds into the glacier boundary layer, accompanied by increased frequency of warmer conditions on the glacier. In the past, warm conditions generated down-glacier katabatic winds (Strasser et al., 2004), whereas now warm conditions are mostly associated with external up-valley winds. In line with the hypotheses of Carturan et al. (2015), our observations have demonstrated for the first time, to the authors' knowledge, the increasing sensitivity of the above-ice air temperatures to external climate as a mountain glacier shrinks and fragments. This has interesting implications for future glacier modeling (e.g., Figure 4) given the expected feedback of an increased sensitivity to external warming due to a lack of boundary layer development that is further diminished due to glacier mass loss and retreat. Under the same ambient temperature range, the increase in sensitivity at the same distance down-glacier is modest (Figure 2c), though as the glacier retreats and debris cover expands, more area is exposed to the presence of warm air (Figure 2d). Moreover, as the katabatic activity ceases to develop on a glacier of such size (Carturan et al., 2015;T. Shaw et al., 2021), the dependency of temperature on elevation (and the applicability of a lapse rate) is restored ( Figure S8 in Supporting Information S1), emphasizing a further non-linearity of glacier response to climatic warming.
Given that negligible differences in topographically induced convergence/divergence of down-glacier air would be expected between the years (Munro, 2006) and that turbulence driven by wind interactions from down-glacier and up-valley source regions are uncommon (Figure 3k), the dominant source of this increased sensitivity appears to be linked to the increase in up-valley/glacier winds ( Figure 3) entraining warmer air which passes over snowfree terrain and an expanding debris-covered area (Figure 1b). While there is clearly an increasing temperature deficit between the atmosphere and near-surface required to generate katabatic winds (Figure 1c), the glacier fetch is seemingly no longer sufficient to overcome the valley circulation and slope winds generated by warm and dry conditions in recent years (Greuell & Böhm, 1998;Potter et al., 2018).
The variability in temperature sensitivity for down-glacier wind events under warm conditions (Figure 3i) suggests the role of heat advection from snow-free slopes (Haugeneder et al., 2022;Mott et al., 2018Mott et al., , 2020 in drier years such as 2010 and 2022. For those snow-dominated years (2001, 2006, and 2021), cold air drainage was seemingly more efficient, producing the less temperature sensitive conditions at lower elevations (Figure 3i), and adhering to the patterns described for larger glaciers in earlier works (Greuell & Böhm, 1998;Shea & Moore, 2010). However, the absolute differences in temperature sensitivity at the shortest flowline distances (Figures 2e and 3i) remain to be explained and could likely implicate many local effects (T. E. Shaw et al., 2017;Strasser et al., 2004) that are not resolved here.
Previous work addressing air temperature distribution on multiple glaciers (Carturan et al., 2015;T. Shaw et al., 2021;Shea & Moore, 2010;Yang et al., 2022) have highlighted the need to account for different glacier characteristics (principally glacier length) when forcing fully distributed, physically based or intermediate complexity (ETI) models of snow and ice melt (Carturan et al., 2015;Petersen & Pellicciotti, 2011;T. E. Shaw et al., 2017). Our analyses are limited due to the variable location of on-glacier stations and due to a short total observational period, despite a notable retreat of the Arolla Glacier in the last 20 years (Figure 1). Nevertheless, our work presents novel evidence as to the necessity of an appropriate temperature distribution parameterization that explicitly accounts for the non-linear changes in sensitivity of the glacier through time (e.g., Bolibar et al., 2022). The inclusion of feedbacks related to reduced katabatic wind speeds ( Figure 4) and adjustment of vapor pressure gradients (Shea & Moore, 2010) would also be of great relevance for future glacier and glacio-hydrological modeling at local/sub-regional scales. Further work to establish critical length scales associated with this shift in wind regime would be beneficial, particularly because as much as half of the world's mountain glaciers are expected to disappear by the end of the century based upon recent modeling estimates (Rounce et al., 2023).

Conclusions
We have demonstrated novel instrumental evidence as to the decay of katabatic winds on a small, shrinking Alpine glacier by exploring on-and off-glacier meteorological data for six years in the period 2001-2022. The glacier lost ∼35% of its area since 2001, coinciding with notable frontal retreat post 2005, warming temperatures on the glacier and an increase in the occurrence of up-valley/glacier winds on the glacier. An increase in up-valley slope flows permitted by the decay of the katabatic boundary layer has promoted an increased intrusion of warm air flowing up the glacier during the summer, increasing the sensitivity of on-glacier air temperatures to external climate and reestablishing the applicability of lapse rates to describe its variability. Moreover, the retreat of the glacier terminus and increased presence of supraglacial debris cover acts to increase the area of the glacier that is sensitive to off-glacier temperature changes. Accordingly, sensible heat fluxes to the glacier are increasingly determined by the conditions occurring outside the boundary layer of the glacier. Ultimately, the enhanced sensitivity of on-glacier near-surface temperatures to external environmental conditions implies an accelerated negative response of glacier melt to climate warming, partly explaining the observed non-linear decay of alpine glaciers.

Acronyms
Ta Near-surface air temperature TS Temperature sensitivity OFF(n) An off-glacier observation location Ta OFF The off-glacier Ta at the off-glacier station of the given year Ta obs Observed Ta at station locations on the glacier Ta est Ta estimated for the elevation of Ta obs based upon observations from OG and a calculated lapse rate Z OFF The elevation of the OFF station Z obs The elevation of the on-glacier station observations Ta obs P50 The 50th percentile of Ta at the off-glacier station

Data Availability Statement
The meteorological data used in this analysis (T. E. Shaw et al., 2023) are made publicly available at the following repository: https://doi.org/10.5281/zenodo.7554648. The source code of the T&C model is available at https:// doi.org/10.24433/CO.0905087.v2. This work was funded by the EU Horizon 2020 Marie Skłodowska-Curie Actions Grant 101026058. The authors acknowledge the dedicated collection of field data by many parties since 2001, including those acknowledged for the cited works on Arolla Glacier. The authors would like to thank Fabienne Meier, Alice Zaugg, Raphael Willi, Maria Grundmann, and Marta Corrà for assistance in the field for the summers of 2021 and 2022. Off-glacier data provided by Grand Dixence SA (Arolla) and MeteoSwiss are kindly acknowledged. Simone Fatichi is thanked for the provision and support in the use of the Tethys-Chloris model. We thank Editor Mathieu Morlighem and two anonymous reviewers whose comments have helped to improve the quality of the manuscript.