Original Article HEF, Hintereisferner; NR, non-stationarity ratio; HEFEX,
Hintereisferner experiment; TKE, turbulence kinetic energy; EC, eddy-
covariance [1]Equally contributing authors. Brigitta Goger, Department of
Atmospheric and Cryospheric Sciences, University of Innsbruck, Innrain 52,
6020 Innsbruck, Austria<EMAIL_ADDRESS>BG acknowledges Austrian
Science Foundation (FWF) grant number: I 3841-N32; IS acknowledges FWF grant
number: T781-N32; TS acknowledges the Deutsche Forschungsgemeinschaft (DFG)
grant number: SA 2339/7-1;

# Large-eddy Simulations of the Atmospheric Boundary Layer over an Alpine
Glacier: Impact of Synoptic Flow Direction and Governing Processes

Brigitta Goger  Ivana Stiperski  Lindsey Nicholson  Tobias Sauter

###### Abstract

The mass balance of mountain glaciers is of interest for several applications
(local hydrology or climate projections), and turbulent fluxes can be an
important contributor to glacier surface mass balance during strong melting
events. The underlying complex terrain leads to spatial heterogeneity and non-
stationarity of turbulent fluxes. Due to the contribution of thermally-induced
flows and gravity waves, exchange mechanisms are fully three-dimensional,
instead of only vertical. Additionally, glaciers have their own distinct
microclimate, governed by a down-glacier katabatic wind, which protects the
glacier ice and interacts with the surrounding flows on multiple scales. In
this study, we perform large-eddy simulations with the WRF model with $\Delta
x=48$ m to gain insight on the boundary-layer processes over an Alpine valley
glacier, the Hintereisferner (HEF). We choose two case studies from a
measurement campaign (August 2018) with different synoptic wind directions
(South-West and North-West). Model evaluation with an array of eddy-covariance
stations on the glacier tongue and surroundings reveals that WRF is able to
simulate the general glacier boundary-layer structure. Under southwesterly
airflow, the down-glacier wind is supported by the South-Western synoptic wind
direction, a stable boundary layer is present over the ice surface, and local
processes govern the turbulence kinetic energy production. Under northwesterly
airflow, a cross-glacier valley flow and a breaking gravity wave lead strong
turbulent mixing and to the subsequent erosion of the glacier boundary layer.
Stationarity analyses of the sensible heat flux suggest non-stationary
behaviour for both case study days, while non-stationarity is highest on the
NW day during the gravity-wave event. These results suggest that the synoptic
wind direction has, in addition to upstream topography and the atmospheric
stability, a strong impact on whether a local glacier boundary layer can form
or not, influencing whether a glacier is able to maintain its own
microclimate.

###### keywords:

boundary layer, glacier, complex terrain, land-atmosphere exchange, gravity
waves, large-eddy simulation, WRF

##  1 Introduction

Mountain glaciers are an essential part of the global climate system and
monitoring their mass balance is required for a large number of applications,
such as sea level rise estimates [41], freshwater availability [35], or
natural hazard warnings [34]. Glacier mass balance, at any point on a glacier,
is a result of energy, mass, and momentum fluxes at the glacier-atmosphere
interface [29]. While the largest part of melt energy stems from the radiation
flux, the turbulent fluxes of sensible and latent heat can be equally large
over shorter time intervals (e.g., hours), especially during strong ice
melting events. Driven by the wind shear as well as thermal stratification and
moisture gradients, these turbulent fluxes are important vertical exchange
mechanisms coupling the surface and the atmosphere. However, mountain glaciers
are not isolated from their environment. The complex interaction with the
surrounding topography causes the turbulent fluxes to be spatially variable
and this heterogeneity has a relevant impact on glacier mass balance [59].
In general, the strength of surface fluxes is connected to surface
characteristics and the atmospheric boundary layer (ABL) structure, which is
spatially heterogeneous in mountainous environments [57, 36, 62]. Mountain
boundary layers are influenced by dynamically-driven topographic flows such as
gravity waves [e. g., 81] and foehn winds [27], but also by thermally-induced
circulations such as slope flows and valley winds that form due to
differential heating/cooling of the surface compared to the overlying
atmosphere [88]. Thermally-induced flows interact on multiple scales and are
not isloated from each other; e.g. slope flows can be eroded by the larger-
scale up-valley wind [55], while the up-valley wind can be superimposed or
eroded by the larger-scale synoptic flow, dependent on its strength, the
synoptic flow direction, and the local topography [e. g., 87, 61]. Over
glaciers, daytime thermal contrasts result in down-slope katabatic winds (also
called glacier winds) that govern the glacier microclimate and protect the
glacier ice from warm-air intrusions from aloft [76, 66, 50]. The specific
vertical structure of katabatic winds with a pronounced jet maximum, as well
as large horizontal variability due to the interaction with other complex
terrain flows leads to a three-dimensional glacier boundary-layer structure,
so that common boundary-layer assumptions, e.g. those used in Monin-Obukhov
similarity theory (stationarity, homogeneity, flatness, constant fluxes, and
no subsidence), do not hold [e.g., 56, 18, 47].
Our understanding of the glacier ABL and microclimates stems from a few field
campaigns. Thetersonde observations during the PASTEX experiment conducted on
the Pasterze glacier in the Eastern Alps [76] showed that the katabatic wind
layer can be up to 30 m deep and its strength depends on interactions with
other thermally-induced flows, such as the up-valley wind, or the ambient
synoptic flow [65, 75]. On cloudy, overcast days, katabatic winds are fairly
weak, while on fair weather days, a well-developed down-glacier wind can be
found over large valley glaciers [66] and even over small perennial ice fields
[44]. An observational study over the Vatnajökull glacier in Iceland revealed
that the local persistent katabatic winds are only disturbed during strong
passing storms [49]. More recent eddy-covariance (EC) observations over
glaciers show that synoptic patterns have a strong impact on the turbulence
and surface flux structure over Alpine glaciers [37, 47]. Furthermore,
katabatic winds can be enforced or eroded by mesoscale circulations [8],
revealing complex flow structures where the underlying atmospheric processes
are still not fully understood. The observations from an array of EC towers in
the Hintereisferner experiment (HEFEX) over the Hintereisferner glacier
(Ötztal Alps, Austria) showed that the glacier tongue is mostly dominated by
down-glacier winds stemming from katabatic forcing, but these katabatic winds
are frequently disturbed by lateral flow from the North-West [43]. These two
situations (katabatic and disturbed) exhibited different surface flux and
advection patterns, while the processes behind the frequent disturbances
remained unknown, because the observations from the EC stations only give
limited information about atmospheric processes aloft.
Simulations with state-of-the art, high-resolution numerical weather
prediction (NWP) models offer a tool to overcome this knowledge gap. However,
the spatial scale of boundary-layer processes over mountain glaciers require
very fine horizontal grid spacings to resolve the relevant processes,
dependent on the phenomenon of interest: [10] suggests horizontal grid
spacings of less than 10 m for the correct simulation of stable boundary
layers. Idealized large-eddy simulations (LES) revealed that state-of-the-art
models are able to simulate the physical properties of katabatic winds over
glaciers under idealized settings [2, 3], while a semi-idealized modelling
approach with real topography by [59] showed that surface flux patterns over a
mountain glacier are strongly affected by the ambient wind direction and the
local topography. These findings were confirmed by [5] using direct numerical
simulations (DNS) to investigate the impact of small-scale surface
inhomogeneities on the surface flux structure over a debris-covered Himalayan
glacier. All these aforementioned studies still have a semi-idealized set-up,
with a realistic surface, but with an idealized atmosphere (e.g., prescribed
wind conditions), while in reality, quickly changing conditions (e.g., shift
of the synoptic wind direction, increasing/decreasing cloudiness) might have a
relevant impact on the stationarity and heterogeneity of surface fluxes over
mountain glaciers. Real-case fine-scale LES process studies (i. e., $\Delta
x<100$ m) over truly complex terrain are still rare and focus on different
atmospheric processes such as precipitation patterns [19], real-time weather
prediction for sport events [38], or foehn-cold air pool interactions [73].
To our knowledge, no real-case LES of boundary-layer processes over a glacier
are available to-date. In this study, we perform LES with the Weather Research
and Forecasting (WRF) model at $\Delta x=48$ m of two case study days in
August 2018 with two contrary synoptic wind directions: The first day (August
7, 2018), exhibits persistent down-glacier flow under a South-Western synoptic
influence, while on the second day (August 17, 2018), the down-glacier wind is
strongly disturbed by cross-glacier flows under a North-Western synoptic
influence. The simulations aim to show a realistic representation of specific
weather situations over a mountain glacier without idealized simplifications
or assumptions. The LES set-up allows a validation of model performance with
the EC station data, examination of the atmospheric processes leading to the
erosion of the down-glacier wind, and an analysis of the spatial patterns and
stationarity of the sensible heat flux on the glacier surface.
The paper is organized as follows: In Section 2, we introduce the area of
interest, the observational data, and the model set-up; followed by Section 3,
where we provide a model validation of the general meteorological variables
and analyze the wind field; in Section 4 we discuss the temporal and spatial
sensible heat flux structure and the horizontal temperature advection
patterns. After the discussion of the results (Sec. 5), we present the
conclusions (Sec. 6).

##  2 Data and Methods

###  2.1 Area of Interest and Observations

The study area is centered on the Hintereisferner (HEF), a glacier located in
in the Ötztal Alps, Austria. HEF (Fig. 1a) is a approximately 6.3 km long
valley glacier, stretching from its highest point, the Weißkugel mountain
(3738 m a. s. l.), to a height of 2460 m, where the glacier tongue’s end is
located (data from 2018). Tributary glaciers formerly connected to the main
tongue include the Stationsferner (small glacier directly located North of
StHE in Fig. 1a) and the Langtaufererjochferner (small glacier located North-
West of hefex-3 in Fig. 1a). HEF has been a subject of long-term mass balance
studies since the 1952/53 season and is therefore marked as one of the World
Glacier Monitoring Service’s reference glaciers [84]. Furthermore, HEF is part
of the Rofental catchment, a long-term hydro-meteorological monitoring area
[69].
The mass balance observations are accompanied by operational meteorological
stations in the area: The longest dataset stems from the station at Station
Hintereis (StHE, 3026 m a.s.l.), located on the South-West facing slope
observing the general meteorological variables and radiation. Data from StHE
was used together with a now-defunct station close to the glacier tongue for a
study of the prevailing wind conditions at HEF and surroundings [48]. A
permanent Terrerstrial Laser Scanner [80] and an EC tower measuring turbulent
statistics are located on the southern ridge (Im Hinteren Eis, IHE, 3245 m
a.s.l.) since 2016.
In August 2018, the HEFEX campaign was conducted on HEF with a main focus on
studying heat exchange mechanisms over the glacier [43]. During the campaign,
four additional EC stations were employed on the glacier, forming two
transects: a cross-transect downwind of the Langtaufererjochferner, and an
along-glacier transect along HEF’s tongue. The EC stations were equipped with
three measurement levels of 2D sonic anemometers (1.7 m, 1.9 m, and 2.9 m) to
capture the katabatic down-glacier wind, furthermore, temperature and humidity
sensors were installed at 1.9 m. The observed turbulence data were rotated
using double rotation, detrended, and averaged over 15 minutes [for more
details see 1, 68, 43]. The HEFEX campaign provides a dataset of turbulence
data over the glacier for around a month, and an analysis of the time series
shows that HEF’s glacier tongue is mostly dominated by down-glacier winds.
However, during certain situations, the down-glacier wind is disturbed by flow
from the North-West, together with warm-air advection. The reason behind these
disturbances is still unknown after the detailed observational analysis by
[43], therefore we focus our simulations on two specific case study days:
August 7, 2018, where the large-scale synoptic flow is southwesterly and down-
glacier flows dominate (SW day hereafter), and August 17, 2018, when a
northwesterly synoptic flow is present and the wind direction over the glacier
tongue was shifting (NW day hereafter).

###  2.2 Numerical Model

We employ a nested set-up of the Weather Research and Forecasting (WRF) model,
version 4.1 [63] for the two case study days. The ERA5 reanalyses [9, $\Delta
x\approx 30$ km], are used as model boundary data every three hours. The set-
up consists of four one-way nested domains with $\Delta x=6$ km (d01, spanning
Europe), $\Delta x=1.2$ km (d02, spanning the Alps, Fig. 1b), $\Delta x=240$ m
(d03, spanning the Ötztal Alps, red rectangle in Fig. 1b), and $\Delta x=48$ m
(d04, spanning the Rofental catchment with HEF in the center, Fig. 1a and blue
rectangle in Fig. 1b), respectively. All domains have 86 vertical levels in
terrain-following coordinates, where the lowest model level is located at
$z=7$ m. The coarser-resolution domains d01 and d02 mainly serve as boundary
data for the two innermost LES domains. All simulations are initiated at 03
UTC on the respective case study day and are run for 18 hours.
Numerical simulations over complex terrain still face numerous challenges
related to static data [e.g., land-use, soil representation, and topography,
42, 21, 33, 24], therefore we replaced the model’s default static data with
higher-resolution datasets: We use the Harmonized World Soil Database [17] for
soil properties, and ESA-CCI land-use data [15] with a horizontal grid spacing
of 1 km for land-use categories. The Shuttle Radar Topography Mission (SRTM) 1
Arc-Second Global topography dataset [74] is chosen for the model topography,
while three cycles of terrain smoothing with the 1-2-1 smoothing filter [26]
are applied. For the two innermost domains with sub-hectometre resolution, it
is necessary to replace slopes steeper than 30∘ with slopes from the
respective coarser-grid domain to avoid numerical instabilities. This allows
the model to keep a part of terrain complexity by reducing the number of
terrain smoothing cycles.
In all domains, the Thompson microphysics scheme [71], the MM5 revised surface
layer scheme [32], and the NOAH-MP land-surface scheme [86] are employed. For
both long- and shortwave radiation, the RRTMG scheme [30] is used while
topographic shading is activated. The ABL physics in d01 and d02 are
parameterized by the level three Mellor-Yamada-Nakashini-Niino
parameterization [46], because parameterizations of the Mellor-Yamada kind
show a good performance for the simulation of thermally-induced circulations
[82, 20]. For horizontal diffusion a horizontal Smagorinsky first order scheme
is employed [64].
After the mesoscale run (d01 and d02) is finished, we use the ndown routine to
create the 30 minute boundary data for the standalone LES (d03 and d04).
Special adjustments in the static data are made for the LES runs: We use the
CORINE dataset [16] for the two innermost domains, reclassifying the land-use
categories to USGS categories following the procedure of [53]. However, the
CORINE dataset with $\Delta x=100$ m still does not represent HEF and the
surrounding glaciers in a satisfactory way. Therefore, we changed the land use
index of the wrfinput files for d03 and d04 with up-to date glacier outlines
from the Randolph Glacier Inventory [52], and for HEF itself, we use a
shapefile acquired with data from an airborne laser scanning campaign in 2018
(Rainer Prinz, personal communication).
In the LES set-up, no boundary-layer parameterization is employed because we
expect that a relevant part of the turbulence is already resolved. We assume
that turbulence is generated at the inflow boundaries of d04 due to the
heterogeneous terrain and because d03 is also run in LES mode. However, we
regard the first three simulation hours as model-spin-up time and exclude them
from data interpretation. We use for both LES domains a 3D subgrid-scale
turbulence parameterization after [11] including a prognostic equation for the
subgrid-scale TKE. The length scale for the calculation of the eddy viscosity
follows the approach by [60]. Instantaneous model output for the standard WRF
variables is generated every 15 minutes, while 1-minute instantaneous output
is available for selected variables such as wind, temperature, and the surface
sensible heat flux. Additionally, we use the online time averaging tool WRF
LES diagnostics [72] to create 15-minute averaged values of various variables
for better comparability with the observations. Unless stated otherwise, all
model output presented in the next sections are 15 minute averages from the
innermost LES domain (d04, $\Delta x=48$ m). The closest model grid point from
the respective stations is determined via Euclidian distance.

##  3 Temperature and Wind Patterns

###  3.1 Time Evolution of Meteorological Variables

At first, we perform a classical model evaluation of standard meteorological
quantities such as 2 m temperature, as well as wind speed and direction from
the lowest model half-level at 7 m a. g. to determine whether the model
delivers reliable results. The 2 m temperature over the glacier tongue remains
quite constant (around 8∘C) on the SW day (Fig. 2a). Minor changes are visible
for the south-facing slope station StHE, and the model is able to simulate the
2 m temperature with a slight warm bias (around 2 ∘C). The observed horizontal
wind speed (Fig. 2c) shows differences of less than 1 m s-1 between the
glacier tongue (hefex-3 station) and the slope station StHE aloft. However,
the horizontal wind speed is overestimated by the model for both locations by
about 2 m s-1 before noon, while the wind speed increases in the afternoon up
to 8 m s-1 with progressing simulation time. The wind direction at both
locations suggests persistent down-glacier flow during the entire day in both
the observed and modelled time series (Fig. 2e). This down-glacier wind
direction corresponds to both the larger-scale synoptic flow on this day
(South-Westerly), as well as to a possible katabatic glacier wind. However, if
the circulation were purely thermally-induced, the wind direction of StHE
would show an up-slope wind direction after sunrise (around 180∘) indicating
up-slope flows. Since this is is not the case, we conclude that the synoptic
flow erodes the small-scale slope flows, but might support the katabatic down-
glacier wind.
The second case study day is dominated by North-Westerly synoptic flow,
therefore we show, besides the glacier tongue station, timeseries from the
ridge EC tower IHE, since its location is representative of the flow across
the glacier valley. The temperature differences between these two stations are
higher than between hefex-3 and StHE due to the larger height difference (Fig.
2b). Asides from this, the model is able to simulate the 2 m temperature
fairly well, although after 12 UTC, there are rapid changes above the glacier
surface not captured by the model. The wind speed shows no specific diurnal
cycle at both locations, but the model overestimates the wind speed at both
stations as on the SW day (Fig. 2d). However, the wind speed at hefex-3 is
less constant with time and quickly changing, especially between 10 UTC and 12
UTC. This is also visible in the timeseries of the wind direction (Fig. 2f):
At the glacier tongue, both in the model and in the observations rapid changes
in wind direction are present, furthermore, the model’s wind direction has an
offset of about 50 degrees during the day compared to the observations.
According to the model, most of the day, a cross-valley flow is present, while
the observations from hefex-3 suggest a heavily disturbed down-glacier flow
with quickly-changing wind directions. One reason for this might be the
different heights from the observations (around 2 m) and the height from the
lowest model half-level (around 7 m), suggesting that the model is not able to
simulate small-scale processes on the glacier tongue. However, the model
simulates the dominating North-Westerly flow at the ridge top station well,
asides from the wind speed overestimation. This suggests that the model likely
simulates a process related to the cross-glacier flow too strongly over the
glacier tongue. None of the wind directions correspond to possible thermally-
induced circulations, and we conclude that the synoptic flow dominates the
wind patterns over the glacier surface. Since the conditions on this day are
strongly dynamically-driven, it is possible that channeling effects or gravity
waves are present over the glacier valley, eroding the glacier boundary layer
and dominating the small-scale processes.
To summarize, the model is able to simulate the general meteorological
variables on the glacier and its surroundings in a realistic way, although we
have to point out that the wind speed is systematically overestimated and the
fast, chaotic changes in wind direction on the NW day have a directional shift
in the model. We decide to focus for both days on the time period from 06 UTC
to 12 UTC, since during this time frame the model performs the best and this
allows a process-based interpretation of model data. If not stated otherwise,
all results presented in the following sections are from this timeframe of 6
hours.

###  3.2 Horizontal Spatial Patterns of Potential Temperature

The potential temperature provides information about the thermal
stratification and, together with the wind field, the spatial variability of
the glacier boundary layer structure (Fig. 3). On early morning of the SW day,
the southeast facing slopes are already heated, while potentially colder air
is present over the ice surfaces (Fig. 3a). Plumes of potentially warmer air
are transported towards the glacier tongue with the westerly wind, while small
plumes of potentially colder air are visible downwind of the smaller tributary
glaciers. During the next four hours (Fig. 3b,c), the synoptic wind direction
shifts to South-West, supporting the persistent down-glacier wind. However,
when the larger-scale wind direction turns towards southerlies, the body of
potentially colder air over the glacier becomes less pronounced (Fig. 3d) and
weakens in the late afternoon (not shown). In general, the SW case study shows
a heterogeneous potential temperature structure and large horizontal gradients
between the ice surfaces and their surroundings.
The potential temperature structure is entirely different on the NW day.
Although the glacier surfaces are still potentially colder than their
surroundings, the horizontal temperature gradients are weaker (Fig. 3e,f,g,h)
and the potential temperature field is spatially homogeneous. During most of
the time, a strong North-westerly cross-glacier flow is present, perpendicular
to the down-glacier wind direction, thus preventing a small-scale glacier wind
to form. The cross-glacier flow often shifts its wind direction slightly, and
turns towards up-glacier in the afternoon (Fig. 3h). The reason for the fast-
changing wind direction over the glacier tongue is discussed in the following
(Section 3.3).

###  3.3 Vertical Structure

Alpine glaciers are not isolated from their environment, because the
surrounding complex terrain has a strong influence on stationarity,
heterogeneity, and the general turbulence structure. We explore the related
atmospheric processes with vertical cross-sections of potential temperature,
the wind vectors, and turbulence kinetic energy (TKE) across the glacier
valley (Fig. 4). On the SW day at 06 UTC, the the potential temperature field
shows stable stratification directly over the glacier surface with large local
differences (Fig. 4a). The minimum in potential temperature coincides with the
body of potentially colder air in Fig. 3b,c. These local stable layers
directly over the glacier surfaces remain present for the next hours (Fig.
4b,c), but the stratification weakens subsequently, which is also visible in
the spatial structure of potential temperature in Section 3.2. TKE maxima are
present above glacier surfaces, suggesting locally-generated turbulence, but
also at upper levels, related to possible interaction of the larger-scale flow
with the topography. On the NW day the atmosphere in the glacier valley is
strongly stably stratified (Fig. 4e,f). This stable stratification, together
with the NW synoptic flow, favors the formation of a gravity wave in the
vicinity of the ridge, north-west of HEF. The isentropes subsequently steepen,
together with a visible elevated maximum of TKE around 200 m over the glacier
(Fig. 4e,f). Around 12 UTC, the gravity wave breaks (Fig. 4h), and strong
mixing and severe turbulence with TKE values higher than 10 m2 s-2 are present
over the glacier tongue. The non-stationary, breaking gravity wave in the lee
of the upstream steep topography (Fig. 4h), and is the main reason for the
continuous change in wind speed and direction in the timeseries of the NW day
(Fig. 2d,h).
The along-glacier cross-section shows that gravity wave-like structures are
also present on the SW day from the early morning at upper levels (Fig. 5a).
However, the atmosphere aloft is not as stable as on the NW day, and the slope
along the glacier is less steep than the North-Western slope, one of the
factors (asides mountain height and stratification) being less favorable for
gravity wave formation. At 10 UTC (Fig. 5c), gravity wave breaking is visible
at levels 1000 m above the glacier surface, however, HEF is not affected by
these upper-level gravity waves, and the local glacier boundary layer remains
stably stratified with minima of potential temperature over the glacier
surface (Fig. 5a,b,c,d). On the NW day, the along-glacier cross-section
reveals strong stability over the accumulation area of HEF above 3000 m (Fig.
5e,f), which is not present at the glacier tongue. The major reason for this
weakening is likely the strong cross-glacier flow related to the gravity wave,
eroding the local glacier boundary layer at the glacier tongue. When the
gravity wave breaks, the strong mixing entirely dominates the glacier tongue,
while a weak stable layer remains above the accumulation zone of HEF (Fig.
5g). These two case studies show that background flow direction, atmospheric
stability, and the upstream topography have a relevant impact on the formation
and strength of gravity waves over the glacier valley. Furthermore, these
factors determine if the glacier tongue is affected by gravity-wave breaking
and the related severe turbulence.
The cross-sections from the previous section gave an overview of the
atmospheric processes contributing to the glacier boundary layer structure. In
the following paragraphs, we have a more detailed look at the thermal
stratification and wind speed with vertical profiles (Fig. 6) from specific
points over the glacier (highlighted in Fig. 5). On the SW day at 08 UTC (Fig.
6a), the potential temperature profile reveals a stable stratification at the
lowest 20 m at all chosen points, while the upper points on the glacier (p3
and p4) show a stronger stability than the glacier tongue points (p1 and p2).
The stable stratification remains present until 12 UTC at all points (dashed
lines), while a neutral layer is present above the near-surface stable layer.
The vertical profile of horizontal wind speed (Fig. 6a) suggests mainly
constant wind speeds with height, although a very weak local maximum is
present at around 20 m, at the same height as the stable layer in the
potential temperature profile. The synoptic wind direction is the same as the
down-glacier flow, therefore we can assume that the down-glacier wind is
supported by the synoptic flow. The strongly stable stratification and the
very weak jet maximum hint that the down-glacier flow might have partly
katabatic origin. Judging from the vertical profiles, we can not decide
definitely whether the forcing of the local layer above the glacier is
katabatic in the model. The simulated local stable layer is not entirely
comparable to observed katabatic flows during the HEFEX campaign with a wind
speed maximum of 2 m above ground [43, their Fig. 4]. The lowest model half-
level is located at 7 m, while the lowest 100 m of the atmosphere in the model
consist of seven model levels. Thus, it is likely that the model is not able
to resolve shallow katabatic glacier winds with the vertical grid.
On the NW day (Fig. 6d-f), the vertical profiles show a different picture:
According to the potential temperature profile at the two lower points p1 and
p2 (08 UTC, glacier tongue), the atmosphere above the glacier surface is
neutrally stratified, while at the two points in the accumulation area of HEF
(p3 and p4), the potential temperature profiles suggest a stable layer above
the glacier ice as on the SW day. Atmospheric stability decreases with time,
while at 12 UTC, a slightly unstable layer is present above the glacier
tongue. The vertical profiles show that a stable boundary layer over the
glacier (profiles from p3 and p4 at 08 UTC) coincides with a weak jet maximum.
While the stable layer in the accumulation area of HEF remains persistent
until 12 UTC, the gravity wave and the induced cross-glacier flow erode the
glacier boundary layer and strong turbulent mixing leads to a neutral
stratification over the glacier tongue (p1 and p2). This suggests that even
dynamically-induced atmospheric processes such as the gravity wave can be very
localized, and that atmospheric conditions at the glacier tongue are not
automatically representative for the entire glacier.
The vertical structure of resolved turbulence kinetic energy (TKE) and its
budget terms also give insights into the vertical ABL structure over the
glacier tongue at hefex-3 (Fig. 7). The TKE budget equation can be written
after [70]:

$\underbrace{\frac{\partial\bar{e}}{\partial t}}_{\text{local
tendency}}+\underbrace{\overline{U_{j}}\frac{\partial\overline{e}}{\partial
x_{j}}}_{\text{advection}}=\underbrace{{\delta_{i3}\frac{g}{\overline{\theta_{v}}}(\overline{u_{i}^{\prime}\theta_{v}^{\prime}})}}_{\begin{subarray}{c}\text{buoyancy}\\\
\text{production/consumption}\end{subarray}}-\underbrace{{\overline{u_{i}^{\prime}u_{j}^{\prime}}\frac{\partial\overline{U_{i}}}{\partial
x_{j}}}}_{\begin{subarray}{c}\text{shear}\\\
\text{production}\end{subarray}}-\underbrace{\frac{\partial(\overline{u_{j}^{\prime}e})}{\partial
x_{j}}}_{\text{turbulent transport
}}-\underbrace{\frac{1}{\overline{\rho}}\frac{\partial(\overline{u_{i}^{\prime}p^{\prime}})}{\partial
x_{i}}}_{\text{pressure
correlation}}-\underbrace{{\varepsilon}}_{\text{dissipation}}$ (1)

where capital letters with overbars denote mean quantities, while small
letters with primes refer to turbulent fluctuations; $\bar{e}$ is TKE, $U$ is
the mean wind speed, $g$ is the acceleration due to gravity, $\theta_{v}$ is
virtual potential temperature, $\rho$ is air density, and $p$ is pressure. On
the left-hand side (l.h.s.) are the local TKE tendency and advection with the
mean flow, while on the right-hand side (r.h.s.) we find the thermally-driven
buoyancy production/consumption term, the mechanical shear production term,
the turbulent transport, the pressure correlation term, and the TKE
dissipation rate $\varepsilon$. For our analysis, we consider the TKE
advection, the vertical buoyancy production, the shear production, and the
dissipation rate from the averaged model output. We have to note that in
sloping terrain horizontal contributions to the buoyancy production might be
non-negligible [51], but we can not assess them with our present model set-up.
Turbulent transport and the pressure correlation term mainly serve as a
redistribution mechanism of TKE, but we do not consider them in our analysis.
On both case study days, the TKE magnitude increases between 08 UTC and 12 UTC
(Fig. 7a,c). On the SW day, the vertical profile of TKE is almost constant
with height at 08 UTC, while at 12 UTC, a local TKE maximum is present at
around 20 m, coincident with the stable layer (Fig. 6a,b). The corresponding
TKE budget terms suggest that the negative buoyancy term acts as a sink of TKE
close to the ice surface, and that shear production is the major contributor
to the TKE budget, counteracted by the dissipation, implying that the
processes contributing the TKE are mostly local.
On the NW day, the vertical profile of TKE at 08 UTC is also constant with
height and the TKE budget structure is similar to the SW day. However, at 12
UTC the TKE values increase dramatically up to 6 m2 s-2, also at upper levels.
The TKE budget terms suggest again that shear is the dominant production term
with values up to 0.02 m2 s-3, while the buoyancy term is closer to zero.
However, the TKE advection is of almost equal magnitude as the shear
production term at upper levels. During strong dynamically-induced situations
with breaking gravity waves, the TKE advection is a non-negligible term of the
TKE budget [e. g., 79, 77]. The NW day TKE structure is therefore not only
influenced by local processes acting in the vertical, but also by larger-scale
three-dimensional dynamics, visible in the generally high TKE values, but also
in the TKE budget structure with TKE advection with the mean flow being a
relevant term.

##  4 Boundary Layer and Surface Fluxes

###  4.1 Sensible Heat Flux Structure

The previously described meteorological phenomena are spatially heterogeneous,
and especially the wind speed and direction might have an impact on sensible
heat flux variability over the glacier. However, according to the energy
balance, sensible heat flux is mostly determined by the net radiation.
Timeseries of net radiation from the SW day suggest some cloudiness, while the
model simulates an almost cloud-free day (Fig 8a). This also manifests itself
in the sensible heat flux observations, which are generally smaller than the
simulated sensible heat flux. The sign of the sensible heat flux is negative
both in the observations and model output, suggesting that the ice surface is
represented correctly in the model. The net radiation on the NW day shows a
better agreement between the model and observations. The weather conditions
are cloud-free before noon, while clouds establish in the afternoon. The
sensible heat fluxes are smaller than on the SW case study day both in the
observations and the model, but the sign is also negative over the glacier
surface.
The animation from one-minute model output [see additional material] shows a
very high temporal variability of the sensible heat flux. For the SW day, with
increasing daytime turbulence, plumes of local sensible heat flux maxima
travel down the glacier tongue with the mean wind. These plumes prevail for
the rest of the day, suggesting a high spatio-temporal variability. As for the
NW day, the breaking gravity wave is the largest driver of high temporal
variability in sensible heat flux. This raises the question whether this non-
stationarity is also present in the observations, and if it has a diurnal
cycle. For this purpose, we divide the one-minute sensible heat flux time
series (from both model output and observations) into 15-mintue intervals and
calculate the non-stationarity ratio after [40]:

$NR=\frac{\sigma_{k,btw}}{RE_{k}},$ (2)

where $\sigma_{k,btw}$ is the variance of each of the sub-intervals and
$RE_{k}$ is the standard error of the 15-minute averaged flux results. When
the $NR$ is approximately unity, the time series can be assumed to be
stationary, because the variances of the 15-minute averages do not exceed
their standard error. For values higher than 2, non-stationarity can be
assumed. We are aware that the non-stationarity depends on the choice of the
averaging period, but similar averaging choices were made for the $NR$ of
sensible heat fluxes under gravity-wave influence during the T-REX experiment
[78].
Figure 8c,d shows the $NR$ of the sensible heat flux from the two case study
days. One-minute instantaneous values for both days from model and
observations show mainly values around or above 2, suggesting non-stationary
behavior. While the $NR$ gradually increases with increasing daytime
turbulence on the SW day, the $NR$ on the NW day is in general higher without
a diurnal cycle: $NR$ maxima are already present at 08 UTC, possibly related
to the strong gravity-wave activity which continues until 12 UTC (cf. Fig.
4f). Furthermore, since the $NR$ is higher in the model than in the
observations, the model seems to simulate a stronger gravity wave influence.
The higher the non-stationarity, the more mesoscale contributions influence
the surface sensible heat flux. The high non-stationarity in the time series
might partly explain the large differences between observed and modelled
sensible heat flux.
Asides from temperature, the horizontal wind speed also influences the
strength of sensible heat fluxes (Fig. 9e,f): The higher the horizontal wind
speed, the stronger the sensible heat flux; it has to be mentioned at this
point that the model tends to overestimate the horizontal wind speed,
therefore also producing higher sensible heat fluxes than observed. Although
there are differences in absolute magnitude between the model and the
observations, the linear relationship between the wind speed and the sensible
heat flux is similar, suggesting that the model is able to reproduce the
relevant physical processes. To conclude, the magnitude of the sensible heat
flux is strongly governed by the horizontal wind speed.
The observations only show the sensible heat flux at a point, but the model
output suggests that the averaged sensible heat flux over the glacier surface
is spatially highly heterogeneous on both case study days. On the SW day at 06
UTC (Fig. 9a), the spatial sensible heat flux structure is connected to the
horizontal wind speed and direction, while the weak cross-wind with
potentially warmer air from the slopes is also visible with the higher
sensible heat flux over the glacier tongue. This changes at 08 UTC (Fig. 9b),
visible with weaker sensible heat fluxes over the glacier tongue and streaks
in the structure, connected to the body of potentially colder air and the
down-glacier wind (Fig. 3b). At 10 UTC, the streaks are still visible, but the
sensible heat flux is now stronger; this is connected to the weakening
stratification over the glacier tongue. At noon (Fig. 9d), together with the
increasing horizontal wind speed, the sensible heat flux over the glacier
tongue reaches its maximum. On the NW day, the sensible heat fluxes are
generally smaller than on the SW day, but they show an atypical pattern: At 06
UTC, a local sensible heat flux maximum is already present at the glacier
tongue downwind from the south-facing slope (Fig. 9e). This structure is
visible for the next six hours (Figs. 9f-h). When at 12 UTC the gravity wave
breaks and severe turbulence is present over the glacier tongue, the sensible
heat flux is strongest (Fig. 9h and Fig. 9b). While on the SW day the
persistent down-glacier flow leads to a specific spatial structure (streaks)
over the glacier tongue, the strong mesoscale influence with the gravity wave
also leads to localized high sensible heat flux values over the glacier tongue
only.

###  4.2 Temperature Advection Patterns and Heat Budget

The heterogeneous spatial structure of the wind field and potential
temperature determine the spatial patterns of the horizontal temperature
advection (Fig. 10). On the SW day, the body of potentially colder air (Fig.
3) coincides with horizontal cold air advection over the glacier. At 06 UTC,
when the colder air is pushed towards the North-facing slope, the glacier
tongue is under the influence of weak warm-air advection. This changes at 08
UTC, when the down-glacier wind increases and the glacier tongue is under
persistent cold-air advection. The streamlines suggest that the “source” of
the cold air is mainly located at the glacier accumulation area. Until 12 UTC,
the thermal stratification decreases (Fig. 6a), but the glacier tongue remains
under the influence of cold-air advection. This suggests that if the wind
direction is down-glacier, the glacier remains in the presence of cold-air
advection. The NW day shows a different temperature advection pattern: The
cross-glacier circulation leads to advection of warmer air over the glacier
tongue. The absolute values of the warm-air advection over the glacier are,
however, much smaller than the absolute values of the cold-air advection of
the SW day. The wind direction determines the type of advection over the
glacier tongue: The upstream source region is the heated slope, and, supported
by the gravity wave, the glacier tongue is under the influence of, albeit
weak, warm-air advection. On the other hand, the glacier accumulation area,
where local stable stratification is present (Fig. 6d) remains under very weak
cold-air advection.
To explore the relation between the horizontal temperature advection and the
wind speed, we compare the model output with observations from the EC
stations. To examine the impact of cross-glacier flows on horizontal
temperature advection, we calculate the observed horizontal temperature
advection between stations hefex-3 and hefex-2:

$THADV=U\frac{\Delta T}{\Delta x},$ (3)

Where $\Delta x=179$ m is the distance between the stations, $\Delta T$ is the
temperature difference, and $U$ is the average horizontal wind speed. The
observations (Fig. 11a) suggest that the glacier tongue is under the influence
of horizontal cold-air advection. The wind direction is mostly down-glacier at
200∘, but when deviates towards 250∘, the glacier tongue is under weak warm-
air advection, and the same patterns are visible in the model output (Fig.
11c). On the NW day, both observations and the model suggest that the glacier
tongue is under continuous warm-air advection. This supports the idea that if
a down-glacier wind is present (corresponding to a wind direction 200∘),
horizontal cold-air advection dominates, but if the wind direction shifts and
the source area therefore changes, warm-air advection dominates on the glacier
tongue. Asides from the wind direction shift in the model (discussed in Sec.
3), the magnitude of the horizontal temperature advection is similar in the
observations and the model. In general, the cold-air advection connected to
the down-glacier flow on the SW day is stronger than the warm-air advection
under intermittent conditions on the NW day, also observed by [43]. The
relation between the horizontal wind speed and the resulting temperature
advection are shown in Fig. 11b,d. The pattern of the scatter is similar in
the observations and the model, while the overestimated wind speeds in the
model again lead to a shifted patterns towards higher wind speeds. However,
the strength of the advection seems to be related to the wind speed strength,
e.g. strong cold-air advection the SW day is related to higher wind speeds. On
the other hand, the type of advection (cold-air or warm-air advection) is then
rather related to the horizontal temperature gradient.
Horizontal temperature advection is only one term of the temperature tendency
equation in the boundary layer [85, 27]:

$\frac{\partial\theta}{\partial
t}=\underbrace{-U\frac{\partial\theta}{\partial
x}-V\frac{\partial\theta}{\partial y}-W\frac{\partial\theta}{\partial
z}}_{Adv}-\underbrace{\frac{\partial\overline{w^{\prime}\theta^{\prime}}}{\partial
z}}_{vHFD}$ (4)

Consisting of temperature advection with the mean wind in all three directions
(ADVX, ADVY, ADVZ) and the vertical heat flux divergence (vHFD), while the
radiative flux divergence is neglected. Vertical profiles of the three
temperature advection terms (Fig. 12a) from the SW day at 08 UTC and 10 UTC
suggest that cold-air advection from the x- and z- direction dominates over
warm-air advection from the y-direction. Together with the decreasing vHFD
over hefex-3 this results in a net cooling of the atmosphere over the glacier
tongue (Fig. 12b). However, at 12 UTC, the net positive advection contribution
in the heat budget (Fig. 12b), leads to a net warming of the atmosphere over
the glacier. This heat budget analysis shows that a down-glacier wind with
lateral cold-air advection is not a guarantee for general cooling of the
atmosphere over the glacier. On the NW day, cold-air advection dominates the
glacier tongue at 08 UTC (Fig. 12c), with the dominant advection from the
x-direction. As on the SW day, this leads to a net cooling at 08 UTC (Fig.
12d). Two hours later (10 UTC), the advection part of the heat budget turns
positive, leading to an overall warming tendency over the glacier tongue. At
12 UTC, the situation changes: while the overall advection turns positive, the
overall heat budget remains negative. The breaking gravity wave mixes
potentially colder air from aloft (also supported by the potentially colder
air over the large glacier upstream of HEF) into the glacier boundary layer.
This heat budget analysis shows that it is not possible to judge only from the
lateral advection components on the atmospheric warming or cooling above the
glacier, because both the vertical temperature advection and the vHFD are
terms of equal magnitude. Therefore, our numerical modelling approach gives
useful insights to the individual components of the heat budget over the
glacier.

##  5 Discussion

The simulation of boundary-layer processes in complex terrain is still a major
challenge for NWP models [14], due to insufficient terrain representation
[82], too coarse land-surface datasets [24] or turbulence parameterizations
developed based on assumptions for horizontally homogeneous and flat terrain
[20, 22]. These problems can partly be avoided by increasing horizontal and
vertical resolution towards horizontal grid spacings where the largest eddies
can be expected to be already resolved [6]. Our LES set-up at $\Delta x=48$ m
has a realistic representation of the topography surrounding the glacier
(within the scope of numerical stability), and furthermore, the horizontal
mesh size also allows a realistic representation of the land-use and the ice
surface (Fig. 1).
Other studies comparing LES with WRF with high-resolution observations suggest
good model performance, so that the model can be used as a tool for better
process understanding [45, 4, 28, 7]. However, in our complex terrain setting
the model still overestimates the horizontal wind speeds on both days. One
reason for this are the differences in measuring heights of the instruments (2
m) versus the lowest model level at 7 m. Another reason for the overestimated
wind speeds can be attributed to the still insufficient topography
representation, although [82] point out that relevant boundary-layer processes
are resolved when the valley is represtented by at least 10 grid points, which
is the case for the innermost domain in our LES. In general, other WRF-LES
studies over truly complex terrain show a similar bias of overestimated wind
speeds [19, 38, 73]. However, model topography still differs from reality due
to smoothing, because the development and formation of the thermally-induced
circulation, katabatic winds, boundary-layer separation, and gravity waves
also depend on the topography steepness and/or shape [83, 67, 54, 13].
Furthermore, the restriction of model topography not having slope angles over
$40^{\circ}$ also reduces complexity of the ABL flow (e.g. no bluff-body
boundary-layer separation in the lee of very steep mountaintops). This well-
known problem of vertical grids over complex terrain might be solved with the
implementation of the immersed-boundary method in the near future [39].
Our current set-up is not able to resolve all relevant length scales equally
well. For example, on the NW day, the synoptic wind direction is well-
simulated at the ridge station IHE (Fig. 2f), and the model simulates a
strong, breaking gravity wave over the glacier tongue. The gravity wave easily
erodes the glacier ABL in the simulation, while the observations suggest a
weak, but strongly disturbed katabatic wind layer. This hints that the model
simulates a stronger gravity wave influence than found in reality, also
visible in the high TKE values (more than 10 m2 s-2 in Fig. 4h) and the higher
non-stationarity of the sensible heat flux than in the observations (Fig.
11d). The HEFEX stations did not record such high TKE values over the glacier
tongue on the NW day, but longer TKE time series from station IHE reveal that
comparably high TKE values (around 10 m2 s-2) are possible in connection with
NW synoptic flows. Furthermore, aircraft observations by [31] over the Ötztal
Alps suggest that our simulated TKE values (around 10 m2 s-2) are realistic.
The predictability of mountain waves decreases with increasing non-linearity
and terrain steepness [13], and strong gravity waves are often a challenge for
the simulation of dynamically-driven flows over mountainous terrain [23, 73].
One of the largest questions when setting up the model was whether WRF-LES is
able to simulate small-scale glacier boundary-layer processes. [10] states
that a horizontal grid spacing of $\Delta x=5$ m might be sufficient to
simulate processes in the stable mountain boundary layer. Although we use a
coarser grid spacing, our simulations suggest that the representation of the
glacier boundary layer is partly possible: On both days, the model simulates a
stably stratified layer over the ice surfaces, which remains persistent during
the daytime (SW day) or is eroded by the gravity wave at the glacier tongue
(NW day). The outer domain (d03, $\Delta x$=240 m) is not able to simulate the
stable layer over the ice surfaces (not shown), although the vertical grid
spacing is the same. This implies that the horizontal mesh size has an
essential influence on the correct simulation of the the spatial variability
of ABL processes over the glacier.
The different scales in the ABL over the glacier are not isolated from each
other and scale interactions are common in both case study days. Small-scale
processes over the glacier, such as local stable layers, are still
underrepresented in the model, and therefore less resilient towards meso-scale
influence, although they might be more persistent in reality. For example, a
down-glacier katabatic wind during summer might have a jet maximum of only 2 m
above ground [as in 43], which cannot be resolved by the model’s vertical grid
(lowest model half-level at 7 m). However, especially at the SW day, the down-
glacier wind is supported by the synoptic flow direction, resulting in weak
jet maxima at around 20 m. This is partly related to the model’s vertical
grid, but on the other hand [65] also observed deeper down-glacier winds when
the katabatic glacier wind was aligned with the synoptic flow, while low-
frequency disturbances in the turbulence spectra were present. The influence
of the synoptic flow direction on the turbulence structure was also observed
over the Saint-Sorlin Glacier in the French Alps [37]. Our results from the SW
day agree with the aforementioned studies and show that the synoptic flow
direction governs the spatial structure of the glacier boundary layer. Due to
the glacier’s high altitude, synoptic flows interact with the topography and
plunge into the comparably shallow glacier valley, eroding the glacier
boundary layer. This raises the question under which conditions a glacier is
able to maintain its own microclimate. Purely thermally-driven situations
(i.e., with an undisturbed glacier wind) as described in [66], [47], and [43]
are still possible under fair-weather conditions with weak background wind,
but the synoptic wind direction and the local topography are major factors for
the spatial sensible heat flux structure on the glacier and should not be
disregarded.
Asides from the aforementioned shortcomings, the model provides valuable
information about the physical processes contributing to the glacier ABL
structure. The simulation results agree well with the observational analysis
of [43] for various quantities: The wind speeds over the glacier are higher
when a down-glacier wind is present than during disturbed situations, the
sensible heat flux is linearly dependent on the wind speed, and the connection
between the wind direction and the horizontal temperature advection are
present in the simulations. The large benefit of the simulations is, however,
the information of spatial fields (both horizontal and vertical) of bpundary-
layer variables such as the sensible heat flux, TKE, and temperature
advection, which can not be observed even by an array of EC towers. The
spatial field of the sensible heat flux especially shows that the elevation
dependence of the sensible heat flux [25] is only partially true for our
simulation results: Non-linear processes such as gravity waves and the
horizontal wind field over the glacier strongly contribute to non-stationarity
and spatial heterogeneity of the sensible heat flux over the glacier. This
raises questions whether linear relationships, single point measurements, and
flux-profile methods basing on Monin-Obukhov similarity theory are
representative for surface energy balance modelling of mountain glaciers [12,
59].

##  6 Summary and Conclusions

We conducted large-eddy simulations with the WRF model at $\Delta x=48$ m over
the Hintereisferner glacier located in the Ötztal Alps, Austria for two case
studies with different synoptic forcings: On August 7, 2018 South-westerly
flow was present, while on August 17, 2018 North-westerly flow prevailed. The
model results are validated with EC towers on the glacier surface (HEFEX
experiment) and permanent stations on surrounding ridges and/or slopes.
Dependent on the direction of the synoptic flow, different wind patterns are
present over the glacier affecting the spatial structure of the glacier
boundary layer and the sensible heat flux. This leads us to the following
conclusions:

  1. 1.

On the SW day, the model is able to simulate the temperature and wind patterns
over the glacier in a satisfactory way. While the horizontal wind speed is
generally overestimated by the model, the wind direction is simulated well for
the SW day. This allows a further process-oriented analysis of the model
output. On the NW day, the model simulates a strong cross-glacier wind, while
the observed wind direction suggests a heavily disturbed down-glacier wind.
However, the down-glacier wind from the observations is so shallow that the
model can not resolve it with its current horizontal and vertical grid
spacing.

  2. 2.

On the SW day, the simulated potential temperature structure reveals that a
prevailing body of potentially colder air is present over the ice surfaces,
accompanied by persistent down-glacier winds. On the NW day, strong cross-
glacier flow leads to a more homogeneous potential temperature structure
without horizontal temperature gradients between the glacier and surroundings.

  3. 3.

Cross-sections along and across the glacier from the SW day reveal that small-
scale processes such as differential heating are present and sources of TKE
are likely local. Furthermore, the synoptic wind direction supports the down-
glacier flow. On the other hand, on the NW day, a strong gravity wave forms on
the upstream steep slope, resulting in severe shear-driven turbulence and an
erosion of the boundary layer on the glacier tongue, while the accumulation
area of the glacier is less affected.

  4. 4.

Vertical profiles of potential temperature and wind speed reveal that a
stably-stratified layer is present over the glacier surface on the SW day. TKE
values are generally low and weak shear is the only TKE production source. On
the NW day, the layer above the glacier tongue is neutrally stratified without
a distinguishable local layer, and the TKE values are high especially also at
upper levels. This is connected to strong shear production, but also TKE
advection acts as an important contributor to elevated TKE maxima.

  5. 5.

The model is generally able to simulate the net radiation and sensible heat
flux structure over the glacier tongue. Both model and observations suggest
high non-stationarity of sensible heat fluxes during the days. On the SW day
non-stationarity is mostly related to a gradual increase in daytime
turbulence, while on the NW day, the high non-stationarity of the sensible
heat flux is related to the influence of the breaking gravity wave.

  6. 6.

On the SW day, together with the down-glacier wind, mainly horizontal cold-air
advection is present over the glacier tongue, while on the NW day the cross-
glacier flow induces mainly warm-air advection. The source region (i.e.,
either glacier accumulation zone or the surrounding slopes) influences whether
cold-air or warm-air advection is present over the glacier tongue, while the
horizontal wind speed mostly determines the advection strength. However, an
overall analysis of the heat budget suggests that the lateral advection terms
have a small influence on whether overall cooling or heating of the near-
glacier atmosphere is present, because also the vertical temperature advection
and vertical heat flux divergence play a relevant role.

  7. 7.

The synoptic flow, the upstream topography, and atmospheric stratification
have a major influence on whether a local glacier boundary layer is able to
form (SW day) or if it is completely eroded (NW day), while even dynamically-
induced processes can be highly heterogeneous in space due to the underlying
complex terrain.

  8. 8.

The horizontal and vertical resolution of our current model set-up is not yet
high enough to resolve very shallow katabatic down-glacier winds. However, the
model is successful in simulation of a daytime stable boundary layer over the
glacier surfaces and the mesoscale processes which contribute to the glacier
wind’s spatial structure or possible erosion.

The Hintereisferner-LES set-up is a valuable tool to investigate boundary-
layer processes over the glacier. The synoptic wind direction strongly governs
the local glacier ABL formation and therefore it might be able to predict
local conditions on the glacier when only the large-scale wind direction is
known. Based on the findings from the simulations, an updated wind climatology
over the glacier might give more insight on when a katabatic glacier wind is
present or when synoptic winds dominate. Our simulations showed that the WRF-
LES HEF set-up can be used for other case studies, and especially also for
other seasons (i.e., winter) to deliver high-resolution wind fields for the
analysis of wind-driven snow redistribution patterns [80] or for studies of
WRF simulations coupled with energy balance models [58].

## acknowledgements

This work is part of the project "Measuring and modeling snow-cover dynamics
at high resolution for improving distributed mass balance research on mountain
glaciers", a joint project fully funded by the Austrian Science Foundation
(FWF; project number I 3841-N32) and the Deutsche Forschungsgemeinschaft (DFG;
project number SA 2339/7-1). IS acknowledges FWF project T781-N32. The
computational results presented have been achieved using the Vienna Scientific
Cluster (VSC) under project number 71434.

## conflict of interest

The authors declare no conflict of interest.

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egu_plot.pdf

Figure 1: (a) Overview of the innermost model domain: colors and contour lines
show the model topography at $\Delta x=48$ m. The glacier outlines are shown
in light blue, while the area of HEF is highlighted in dark blue. Colored
points show the permanent (stars) and HEFEX stations. The light-green line
shows the cross-section of Fig. 4, while the black line indicates the cross-
section of Fig. 5. (b) The mesoscale domain ($\Delta x=1$ km, where the
locations of domain 3 ($\Delta x=240$ m, blue rectangle) and domain 4 ($\Delta
x=48$ m, red rectangle) are highlighted. Figure 2: Time series of 2 m
temperature (a,b), horizontal wind speed (c,d), and wind direction (e,f) from
August 7 (left column) and August 17 (right column). Connected dots indicate
observations, while straight lines (or plus signs, respectively) indicate
model output. Orange colors show data from the station hefex-3, pink colors
indicate StHE, and blue colors indicate IHE. Figure 3: Averaged model output
from the lowest model level of potential temperature (colors and black contour
lines) and horizontal wind vectors. The top row from August 7, while the
bottom row shows data from August 17, at four different times. Blue lines
indicate the outlines of the glacier as it is represented in the model domain.
Figure 4: Vertical cross-section along the light-green line in Fig. 1 for the
SW day (upper row) and the NW day (lower row). White lines along the
topography indicate glaciated areas. Black contour lines (every 0.25 K) show
the potential temperature, wind vectors indicate the cross-valley wind speed,
and colors indicate turbulence kinetic energy. Figure 5: As Fig. 4, but along
the black line in Fig. 1, and wind vectors indicate the along-valley wind
speed. The vertical dashed lines show the segments of the cross-section and
the points where vertical profiles are extracted for Fig. 6. Figure 6:
Vertical profiles from model output of the SW day (a-c) and the NW day (d-f)
at 08 UTC (full lines) and 12 UTC (dashed lines) of potential temperature
(a,d), horizontal wind speed (b,e), and the Scorer parameter (c,f). The colors
show the four different locations (dashed magenta lines in Fig. 5). The lines
start at 7 m above ground (the lowest model half-level).  Figure 7: Vertical
profiles from model output of the SW day (a,b) and the NW day (c,d) at 08 UTC
(full lines) and 12 UTC (dashed lines) of resolved turbulence kinetic energy
(a,c), and the TKE budget terms (b,d). The lines start at 7 m above ground
(the lowest model half-level).  Figure 8: (a,b) Time series of the net
radiation from StHE (orange lines) and the surface sensible heat flux of
hefex-3 (pink lines) for both case study days, where straight lines show model
output and lines with dots show observations. (c,d) $NR$ of the sensible heat
flux time series of one-minute observations (blue points) and one-minute model
output (orange stars). (e,f) Scatter plots of horizontal wind speed and
sensible heat flux from observations (blue) and model output (orange) between
06 UTC and 12 UTC. Figure 9: Averaged model output of the surface sensible
heat flux (colors and dashed lines) and horizontal wind vectors from the
lowest model level over glaciated surfaces. Sensible heat fluxes over ice-free
surfaces are not shown. The left column shows data from the SW day, while the
right column shows data from the NW day, at four different times. Figure 10:
Averaged model output of the averaged horizontal temperature advection
(colors) and streamlines derived from the wind field from the lowest model
level. The left column shows data from the SW day, while the right column
shows data from the NW day, at four different times. Figure 11: Scatter plots
of the SW day (blue) and the NW day (orange) from observations (upper row) and
model output (lower row) of location hefex-3 for horizontal temperature
advection and wind direction (a,c), and horizontal temperature advection and
sensible heat flux (b,d). Figure 12: Vertical profiles from model output of
the SW day (a,b) and the NW day (c,d) at 08 UTC (full lines), 10 UTC (dashed
lines), and 12 UTC (dotted lines) from hefex-3 of the advection terms (a,c),
and the heat budget (b,d). The lines start at 7 m above ground (the lowest
model half-level).