Cold‐air pool development in a small Alpine valley

A field campaign in a valley near Seefeld, Austria, well known for the frequent occurrence of cold‐air pools, was conducted to identify the processes leading to the formation and erosion of the cold‐air pool. Here, we focus on a case study in January 2020 that featured cold‐air pool formation interrupted by a wind disturbance. Simulations with the Weather Research and Forecasting model were performed at a horizontal grid spacing of 40 m and compared with measurement results. The model was able to reproduce the intense cooling in the beginning of the night and the cold‐air pool erosion in the middle of the night caused by the wind disturbance, but stronger winds than observed prevented the cold‐air pool from fully re‐establishing in the model after the disturbance. The dominant cooling processes were long‐wave radiative heat loss and turbulent exchange, both of which are parametrized and cool the air locally. Advection was the most important warming contribution during the cold‐air pool disturbances, especially its cross‐valley and vertical components. Owing to numerical constraints and the shallow nature of the cold‐air pool, its extent was limited to the lowest model level. Further improvements to the cold‐air pool's representation in the model would require a finer grid resolution.


INTRODUCTION
A cold-air pool (CAP) is a phenomenon associated with the stably stratified nocturnal boundary layer that forms in valleys and basins during clear-sky conditions and under weak synoptic forcing (Whiteman et al., 2004c).CAPs can persist for multiple days in winter (Zardi & Whiteman, 2013), when the nights are long and low daytime insolation provides favorable conditions.The air within strong CAPs is decoupled from the overlying flows, causing weak winds close to the surface and stronger turbulence generation by shear at the top of the CAP layer than at its bottom (Mahrt, 1999).Dispersion of air pollutants is greatly reduced within such decoupled layers; hence, persistent CAPs are oftentimes associated with episodes of poor air quality (Steyn et al., 2013).Additionally, CAPs can amplify severe frost events and lead to freezing rain, which negatively impact transportation infrastructure and agriculture (Whiteman et al., 2004c).On the other hand, winter tourism regions can also benefit economically from the frequent occurrence of CAPs owing to increased efficiency of artificial snow production at lower temperatures (Steiger & Mayer, 2008).Terrain geometry, surface characteristics, and atmospheric processes contribute to the CAP formation.
De Wekker & Whiteman (2006) calculated the time-scale of the cooling in the boundary layer for different valleys and basins, giving a time constant at which 63.8% of the total cooling occurred during the night.They found that basins and small valleys cooled down much faster than more open terrain did.Kiefer and Zhong (2015), using idealized two-dimensional numerical simulations, showed that CAP formation is less efficient if the valley is either too small or too large, keeping the depth-to-width ratio close to constant.This is also in agreement with Vosper and Brown (2008) and Sheridan et al. (2014); both detected increasing CAP strengths with increasing non-dimensional mountain height until a critical value, above which the CAP strength no longer increased with valley depth.Minimum temperature and diurnal temperature ranges have been shown to be comparable for limestone sinkholes of different sizes, but similar sky-view factors (Whiteman et al., 2004).In addition, dense forest canopies were found to hinder the development of strong CAPs (Kiefer & Zhong, 2013;Kiefer & Zhong, 2015).Furthermore, the presence of snow cover increases the intensity of CAPs by thermally insulating overlying air masses from the warmer ground (Steeneveld, 2014;Whiteman et al., 2004).Owing to the impact of vegetation and snow cover on the CAP strength, accurate land use and snow cover datasets of high enough resolution improved the agreement between numerical simulations and measurements in both the Salt Lake Valley in Utah, United States (Foster et al., 2017), and the Adige Valley, Italy (Tomasi et al., 2017).The dominant atmospheric processes in the formation of CAPs are local long-wave radiative flux divergence and dynamic effects-advection of cold air by thermally driven wind systems (Kiefer & Zhong, 2013) and turbulence associated with such flows (Arduini et al., 2016).The partitioning between these contributions, however, differs significantly from site to site, as these processes depend on terrain geometry and surface cover (Kiefer & Zhong, 2015;Whiteman et al., 2004).The importance of each process even varies significantly between different areas of the same CAP (Burns & Chemel, 2015;Vosper et al., 2014) and is not constant with time (Burns & Chemel, 2014).Sheltering from large-scale flows in narrow valleys, and therefore reduced exchange with the free atmosphere above, was also suggested to contribute to CAP formation (Sheridan et al., 2014).Owing to an almost infinite number of possible terrain and surface configurations, results from numerical simulations and field measurements are hardly transferable to other topographic settings (Zardi & Whiteman, 2013).
Numerical simulations helped to describe how different processes contribute to the CAP formation in valleys and basins of various scales.Burns and Chemel (2014) focused on an idealized, 800 m deep and 8 km wide Alpine valley with uniform land cover and found that cooling was dominated by radiation effects around sunset, whereas dynamic effects became more dominant later during the night.Over the whole night, long-wave radiative cooling had a larger contribution than advection of cold air.Hoch et al. (2011) reported that advection was the main cooling contribution in their simulations for the Meteor Crater in Arizona.For a 1 km wide and 100 m deep valley, Vosper et al. (2014) identified turbulent mixing as the dominant cooling contribution at the valley floor, whereas the cooling contribution by long-wave radiation was smaller and advection contributed to warming.Arduini et al. (2016) examined the influence of down-valley flow on CAPs by comparing results of idealized two-dimensional (2D) and three-dimensional (3D) simulations using a valley geometry similar to Burns and Chemel (2014), but with a plain at one end of the valley in the 3D case.Their separation of dynamic effects into mean advection and turbulence revealed that turbulence had a cooling effect in both cases.Mean advection, on the other hand, resulted in net cooling in the 2D case and net warming in the 3D case once the down-valley flow was fully developed (Arduini et al., 2016).Adding another valley section with a different width between valley and plain resulted in weaker down-valley flows and, in the case of a valley constriction before the plain, higher cooling rates in the initial phase (Arduini et al., 2017).Simulations with realistic terrain confirmed the warming effect of advection on the valley volume and emphasized that advection dominated the temporal variability of the valley-averaged temperature tendency (Arduini et al., 2020).
Most of the aforementioned studies were based on numerical simulations of CAPs in basins and valleys performed with the Weather Research and Forecasting (WRF) model (Skamarock et al., 2021).Most simulations with WRF, however, dealt either with larger scale valleys like the Salt Lake Valley (Foster et al., 2017), Adige Valley (Tomasi et al., 2017), or Arve River Valley (Arduini et al., 2020) in an effort to test the capability of the model to reproduce measurement results or were performed with idealized input parameters (Arduini et al., 2016(Arduini et al., , 2017;;Burns & Chemel, 2014, 2015).Additionally, high-resolution numerical simulations were often performed for locations without snow cover (Arduini et al., 2016;Burns & Chemel, 2014;Sheridan et al., 2014;Vosper et al., 2014), which greatly impacts the CAP formation due to altered surface characteristics compared with bare ground.To our knowledge, Arduini et al. (2020) were the first to analyze the contribution of cooling processes for a snow-covered valley.Similar to modeling studies, the field campaigns so far also focused either on larger scale valleys and basins (Sun & Holmes, 2019) or on secluded locations (Craig et al., 2003;Dorninger et al., 2011).
The region of Seefeld in Tyrol, Austria, is a well-known skiing destination and especially popular for its cross-country skiing facilities.Like many other skiing areas in the Alps, Seefeld relies on artificial snow production to maintain its ski tracks throughout the entire skiing season.CAPs frequently form around the Nordic ski arena in Seefeld.Hence, local authorities use the site to start producing snow earlier in the season, as well as to produce snow at a lower cost than outside the CAP.The processes responsible for the pooling of cold air in that area have, however, not been investigated so far.To further the understanding of the spatial structure of the Seefeld CAP and to identify the mechanisms behind its formation and break-up, the Seefeld Cold-Air Pool Experiment (SEECAP) was conducted between December 2019 and March 2020.The night between January 16, 2020, and January 17, 2020, featuring an ideal CAP formation interrupted by a wind disturbance, was selected to describe how the CAP at Seefeld forms and evolves overnight.In addition, high-resolution numerical simulations with WRF were performed for the selected night to supplement measurement results regarding the physical processes involved in the CAP's evolution.The goals of the field campaign and the numerical simulations were to determine • the spatial distribution of temperature within the valley during CAP periods, • which processes dominate the formation of the CAP and how important advection is during the CAP's life span, and • how the cooling processes in Seefeld compare with published results from idealized simulations.
The article is organized as follows: Section 2 introduces the study area and the instruments deployed during the SEECAP, whereas Section 3 describes the model set-up.Measurement results are analyzed in Section 4, and the results from the numerical simulation are in Section 5. A discussion of our findings and conclusions are presented in Sections 6 and 7 respectively.

STUDY AREA AND SEECAP
The Seefeld Cold-Air Pool Experiment (SEECAP) took place in a small valley on the Seefeld plateau in Tyrol, Austria (Figure 1) between December 2019 and March 2020.The valley is 200-300 m deep and located between Gschwandtkopf to the southeast and Brunschkopf to the northwest, with the villages of Seefeld and Mösern at its northeast and southwest end respectively (Figure 1d).The valley bottom is characterized by two basins (upper basin UB and lower basin LB), separated by a slightly elevated region in between (ridge RI) (Figure 2).GeoSphere Austria has been operating a permanent weather station within the basin (TAWES) since 1997.The station was, however, moved in 2010 and is since located at an elevation of 1182 m a.s.l.SEECAP was designed to analyze the spatial structure of the CAP and identify regions in the valley offering the highest artificial snow production efficiency.Six automatic weather stations were deployed within the CAP and recorded temperature (PT100; Rotronic, Bassersdorf, Switzerland), pressure (Setra 278;Vaisala,Vantaa,Finland), humidity (HT-1; Rotronic), net radiation (NR lite; Kipp & Zonen, Delft, Netherlands), wind speed and direction (WindSonic 2D sonic anemometers; Gill Instruments Ltd, Lymington, United Kingdom) at 1 min intervals.To reduce the noise, measurement data presented here are 10 min averages of the data measured.Four stations were located within UB (M04), LB (M02 and M08), and at the slightly elevated ridge close to UB (M10) (Figure 2).The other two stations were located on the slopes surrounding the valley, at the southwestern end of UB (M07) and at the ski jump southeast of UB (M03).The temperature sensors at the stations were ventilated, apart from M03, M07, and M10.The temperature sensors were mounted 2 m above the ground, and the 2D sonic anemometers 3 m above the ground.The effective height above the surface was lower, however, due to the presence of approximately 25 cm of snow cover during the case described.
Two surface-energy balance stations were collocated with M04 and M08.They measured four-component radiation (CNR4 net radiometers; Kipp & Zonen, Delft, Netherlands) and turbulent statistics with CSAT3 sonic anemometers (Campbell Scientific Ltd, Logan, UT, United States), a Krypton hygrometer at M08 (KH20; Campbell Scientific Ltd), and a closed-path infrared gas analyzer at M04 (EC155; Campbell Scientific Ltd) at a height of 2.3 m above ground (or roughly 2 m above the snow surface).Turbulent flux measurements were rotated into the mean wind direction using double rotation (Aubinet et al., 2012) and processed as 1 min averages, although only the medians of 10 min intervals are shown here to ease the interpretation of the noisy signal.Sensible heat flux was corrected for the frequency response of the sensor (Aubinet et al., 2012), as well as humidity and cross-wind effects on the sonic temperature flux (Schotanus et al., 1983).In addition, unventilated HOBO temperature sensors (Onset Computer Inc., Bourne, MA, United States) were deployed within the CAP to gain insight in its spatial structure (Figure 2).The majority of the HOBO sensors    were located along the valley floor down-valley of M07 and along the ski jump downslope of M03.Nine of the HOBO locations had temperature sensors at two heights (1 and 2 m above the ground), whereas the other locations had only one sensor either at 1 m above ground or at 2 m.The remaining HOBO sensors were used for vertical profiles at the bridge (marked as VP in Figure 2) and at three different levels of a walk-up tower (Tower in Figure 2).Another ventilated PT100 temperature sensor was mounted on top of the walk-up tower.In the absence of radio soundings, pseudo-vertical temperature profiles provided insight into the vertical temperature structure within the valley.These profiles consisted of measurements from M04, M10, M03, the Tower sensors, HOBOs H, G, S1, S2, S3, and S4 at 2 m above ground level.Whiteman et al. (2004b) proved that temperature measurements from the valley sidewalls give valid information about the temperature structure within CAPs during the night and can therefore be used in the absence of radio soundings.

Model set-up
Numerical simulations were conducted with the Advanced Research WRF (ARW) core of the WRF model (Skamarock et al., 2021), version 4.4.To determine the individual terms of the temperature tendency equation, version 1.4.1 of WRFlux (Göbel et al., 2022) was implemented, which modifies and extends the WRF source code.The simulation was initialized at January 16, 2020, 0000 UTC to ensure a spin-up time of at least 12 hr before cooling starts and had a runtime of 36 hr, but the first 12 hr were not analyzed.The model set-up features five one-way nested domains (see Figure 1 for the extent of the individual domains; specifications of the domains are given in Table 1), with the horizontal grid spacing Δx of the innermost domain being 40 m.Domains D1, D2, and D3 were nested online in the same model run, whereas D4 and D5 were nested offline into D3 and D4 respectively, because of the otherwise long runtime.Each domain had 78 vertical levels, ranging from the lowest mass level at 8 m above ground to the model top at 50 hPa.The distance between two model levels Δz was approximately 15 m at the bottom and reached its maximum of about 400 m at 4 km above ground.European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ERA5) data (Hersbach et al., 2020) provided the meteorological fields needed for the initialization and boundary conditions.Snow cover input was modified to depend on WRF model topography rather than the ERA5 topography and was set to zero below 950 m above sea level (a.s.l.), the approximate snow height for the region based on satellite images.Tomasi et al. (2017) and Foster et al. (2017) stressed the importance of an accurate representation of terrain height and land cover.Hence, data with higher resolution than the WRF standard input fields were used for those fields in the region of interest.Model topography was obtained from 1 arcsec (30 m) resolution Shuttle Radar Topographic Mission data for the area of D3, D4, and D5 and 30 arcsec (1 km) Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010) were used for the area outside D3 in D1 and D2 (Figure 1).To ensure numerical stability, the terrain was smoothed in the steepest areas of each domain to avoid slope angles greater than 40 • .The smoothing had little effect in the study area though (not shown).
For D3, D4, D5, and the area covered by D3 in D1 and D2, Corine Land Cover 2018 (CLC2018) data with 100 m resolution were used.United States Geological Survey (USGS) land cover data with 1 km resolution provided land use information for the area outside D3 in D1 and D2.The land-use classes of CLC2018 were transformed to USGS classes according to the transformation of Pineda et al. (2004), which Schicker et al. (2016) found to be suitable to improve simulation results over the Alps with WRF.Two adaptations to their conversion were implemented: Parts of the study area feature the "Sport and leisure facilities" category in CLC2018, which can be associated with ski slopes and would be transformed to the urban category following Pineda et al. (2004).As fluxes associated with such infrastructure differ from those of urban areas, this category was transformed to the more appropriate USGS category of "Grassland".Additionally, an area in LB covered by low or no vegetation that did not feature buildings was digitized from a georeferenced picture.The original classification of "Urban and Built-up Land" or "Evergreen Needleleaf forest" in these grid cells was also changed to "Grassland".A more detailed description of the modification of the snow cover input and the land-use categories is given in Rauchöcker (2022).
The parametrizations employed include the Noah-Multiparametrization (Noah-MP) land surface model (Niu et al., 2011), the Thompson microphysics scheme (Thompson et al., 2008), the Rapid Radiative Transfer Model for long-wave radiation (Iacono et al., 2008), the Dudhia short-wave radiation parametrization (Dudhia, 1989), the Mellor-Yamada 2.5-order closure scheme by Nakanishi and Niino (2004) to parametrize the planetary boundary layer (PBL), and the MYNN surface layer scheme (Nakanishi, 2001).The Kain-Fritsch cumulus parametrization (Kain, 2004) was used for D1 and D2, but not for domains with horizontal grid spacing below 3 km.This set of parametrizations (except for the land surface model) follows the set-up of Sun et al. (2020) that produced the best results for their strong CAP case.We selected the Noah-MP land surface model instead of Noah land surface model used by Sun et al. (2020), because Noah-MP was superior over other land surface models in reproducing nighttime temperatures and the evolution of the inversion for the snow-covered Adige Valley (Tomasi et al., 2017).
We expected that the development of turbulence would be suppressed by the development of a strong inversion in the simulation.Hence, a mesoscale modeling approach was chosen also for the finest domain D5.While mesoscale simulations solve the Reynolds averaged Navier-Stokes (RANS) equations and fully parametrize turbulence, at grid spacings of Δx = 100 m or finer, the largest convective turbulent eddies are assumed to be resolved and large-eddy simulations (LESs) are preferred (Zhong & Chow, 2013).During quiescent nighttime conditions in winter, however, the expected size of the energy-containing eddies significantly decreases, requiring grid spacings of 1 m to resolve them (Couvreux et al., 2020), as large eddies are suppressed by stable stratification (Stull, 1988).It is unlikely that the energy-containing range of the turbulent spectrum is resolved in D5 for undisturbed nocturnal boundary layers in winter, but perturbations on the resolved scale of our finest domain could include very large turbulent eddies during a disruption of the CAP by foehn.In weak wind conditions typical for stable boundary layers, the impact of submeso motions, non-turbulent motions on scales smaller than 2 km, becomes important and a clear distinction between turbulent and non-turbulent motions in stable boundary layers is difficult (Mahrt, 2014).Hence, the resolution of the simulation presented here is in the gray zone (Honnert et al., 2020), where neither RANS equations nor LESs are fully applicable (Wyngaard, 2004).To test the performance of the RANS simulation in the gray zone, an additional sensitivity test was performed for D5 using the 3D turbulent kinetic energy subgrid mixing scheme (SMS-3DTKE), and a comparison of that simulation with measurement results is shown in Section 6.3.The SMS-3DTKE scheme was developed to address the challenges the gray zone poses (Xu et al., 2018).Although it was tested for convective boundary layers, this scale-aware scheme should be the most suitable of all LES schemes available in WRF under stable stratification.
To compare the measurements with simulation results, the grid point closest to the station coordinates according to the haversine function (Sinnott, 1984) was chosen under the requirement that the closest grid point was representative of the measurement site.To be considered representative, it was required that the slope, orientation, elevation, and land-use classification of the cell agreed with the observed characteristics around the measurement station.This was the case for M02, M03, M07, and M08.The grid cell that was selected for comparison with M04 is located two cells to the west of the closest cell because the land-use classification of the closest cell (evergreen needleleaf forest) did not agree with the grassland vegetation present at M04.As the location of the ridge in the model topography was to the northeast of its true position, the measurements at M10 were compared with simulation results from a grid cell 80 m (two cells) further north and 40 m (one cell) further east.

Analysis of cooling processes
Energy conservation is given by the Reynolds-averaged thermodynamic equation (Stull, 1988), since energy is conserved as long as potential temperature is conserved (Markowski & Richardson, 2010).As WRF itself does not include output fields for temperature tendency and its components, WRFlux (Göbel et al., 2022) was employed to compute those values.The sensible heat-flux divergence is split into a resolved, sub-mesoscale (sms) and a subgrid-scale (sgs) contribution in WRFlux, with the importance of the sub-mesoscale contribution expected to increase with increasing resolution.It is important to note that with "sub-mesoscale"" we refer to all resolved motions on scales smaller than the mesoscale rather than specific processes.These include submeso motions like wave-like motions, drainage flows, and microfronts, which explicitly exclude turbulent motion (Mahrt, 2014), but also resolved turbulence.Considering all processes on this scale was necessary because the scales of the largest turbulent motions and submeso motions overlap in stable boundary layers (Mahrt, 2014).The potential temperature tendency equation in WRF can be expressed as where  is potential temperature and the Cartesian coordinates x  (x, y, and z) and the respective wind components u  (u, v, and w) use Einstein notation.Here,  and u  are split into temporal (10 min) means  and u  and the resolved perturbations  ′ , u ′  from the temporal means.For very stable stratification, the resolved perturbations on a 40 m grid are mostly the result of waves and sub-mesoscale motions interacting with the CAP rather than small-scale turbulence.Potential temperature tendency on the left-hand side of Equation ( 1) is therefore governed by the contributions of advection (−u  ∕x  ), sub-mesoscale flows ((u ′   ′ ∕x  ) sms ), subgrid-scale turbulence (Turb), long-wave and short-wave radiation (R LW and R SW ), microphysics (MP), Rayleigh damping (D), and cumulus parametrizations (CU).Except for advection and resolved sub-mesoscale flows, all processes are accounted for by physical parametrizations.
To distinguish between the effects of along-valley flow and cross-valley flow, the advective tendency was rotated by  = −40 • so that the new x-coordinate is oriented parallel to the valley axis.The rotated tendency terms u rot ∕x rot and v rot ∕y rot are and WRFlux does not provide the horizontal temperature gradients ∕x and ∕y, just the horizontal advection terms u∕x and v∕y.Hence, the horizontal advection terms were divided by their respective mean wind components u and v to compute the horizontal gradients.This approach occasionally caused spikes of large amplitude in the rotated advection terms, when the difference between the unrotated mean wind components was at least one order of magnitude.Since the smaller mean wind component was close to zero in that case, the division resulted in very large horizontal temperature gradients, which in turn appeared with opposing signs in both rotated tendency contributions.Time steps with such spikes were excluded from the analysis of the directional components.The sum of all directional components was unaffected, however.
The individual terms of the energy budget were averaged over a reference area representing the CAP's extent in the model.The reference area was determined based on the elevation of the grid cells around M04 and M08, considered to be the center of UB and LB respectively.The station located at the southwestern slope (M07) at 1,200 m a.s.l.frequently recorded considerably higher temperatures than the station at the ridge (M10) at 1,186 m a.s.l.Therefore, every cell below 1,200 m geopotential height was considered to be within the CAP, which corresponded with the coldest region of the valley.To assess whether the CAP formed or not, a criterion based on the vertical temperature gradient at the reference grid point of M04 was implemented.We selected this location because it featured the lowest temperatures in the measurements, was located close to the valley center, and represented the center of UB in the model (see Figure 1d).A CAP was considered to be present at the grid point every time the temperature gradient between the first and the fourth model level (around 8 m and 68 m above ground respectively) was at least 4 K/100 m.This subjective criterion was not used for any analysis, just to highlight the periods that showed the strongest inversion at the station visually in the time series presented in Figures 6, 9 and 11.The chosen temperature gradient provided the best agreement with periods of strong stratification on the valley floor in the model, although lacking a physical justification.

Climatology
A climatology of local temperature patterns and wind regimes between December 2010 and April 2020 at TAWES station in Seefeld is presented in Figure 3.We chose this period for the climatology because TAWES was at a different location prior to 2010.Although standard definitions of the climatological winter only consider December, January, and February, weather patterns associated with CAP formation in the area are also frequent in November and March.Hence, the daily mean temperatures and minimum temperatures of November 2019 and March 2020 are presented here as well.This climatology was crucial for interpreting the data collected during the field campaign against temperature and wind regimes in other winters.Temperature minima at TAWES were frequently lower than at other stations in Austria with similar terrain characteristics.The lowest temperature in the last decade was −28.1 • C, but also temperatures up to 32.7 • C were measured in summer (Figure 3a).The daily mean temperature was often between 0 • C and −10 • C from December to March, and January had the most days with daily mean temperatures below 0 • C. The winter of 2019-2020 was no exception: January featured more days with daily mean temperatures below 0 • C than the other winter months, although the lowest temperatures were measured in February (20 • C).Compared with the previous decade, December experienced higher temperatures due to a period with persistent foehn.There is a noticeable warming trend towards the end of December in the climatology too, but it occurs later and is not as persistent as in 2019.It remains unclear whether this warming trend in the climatology is a persistent feature or a product of the short 10-year period and frequent foehn events happening towards the end of the year during this decade.Apart from this period, daily mean temperatures during the winter of 2019-2020 were generally within the range of daily means of the last 10 winters.Owing to the good agreement between the climatological daily mean temperature and the daily mean temperature of the winter 2019-2020, the data gathered during the measurement campaign can be considered representative for the location.The wind regime is governed by the topography: southwesterly and northeasterly winds are most frequent, corresponding to down-valley and up-valley flow respectively (Figure 3b).Southwesterly (down-valley) flow dominates during nighttime and northeasterly (up-valley) flow is more frequent during the day.Wind from the southwest is generally weak, with wind speeds below 2 m⋅s −1 , whereas wind from the northeast is often stronger than 2 m⋅s −1 .

Temporal evolution
During the night between January 16, 2020, 1200 UTC and January 17, 2020, 1200 UTC, central Europe was influenced by a weak ridge downstream of a low-pressure system centered around the northern British Isles.This low-pressure system shifted the flow direction above Tyrol from west to southwest in the first part of the night, while a cold front approached the region from the west.The change in flow direction caused a prefrontal south foehn in Tyrol around midnight, and warm air was advected to the north of the Alps.Clear and calm conditions, ideal for CAP formation, prevailed in the first half of the night, and a CAP formed in the study area close to Seefeld, before the onset of south foehn in the valley disturbed its evolution around midnight.The measurements at the automatic weather stations indicated four distinct phases in the temperature evolution within the valley during the night (Figure 4a): a strong cooling phase in the beginning, continuous cooling at lower cooling rates, a warming period around midnight, and subsequent re-establishment of low temperatures.The valley was shaded by the surrounding topography already at 1540 UTC, an hour before astronomic sunset (defined as the time when short-wave incoming radiation becomes zero), but the initial strong cooling period started even earlier (at 1350 UTC at M04).The unventilated sensors M07 and M10 recorded temperature decreases already at 1300 UTC, but the earlier onset of cooling at these stations was likely due to heat accumulation inside the unventilated radiation shield.The strong cooling period, during which temperatures decreased at an average cooling rate of 3.0 K⋅hr −1 at M04, lasted until 1700 UTC.The cooling time constant (De Wekker and Whiteman, 2006) for this night was 2.9 hr and compared well to the time constants calculated by De Wekker and Whiteman (2006) for small basins like Grünloch and Peter Sinks (3.2 hr and 3.1 hr respectively).Similar time constants were calculated also for other undisturbed nights at Seefeld (Rudolph, 2022).
The cooling was much less pronounced at the higher elevation stations on the slopes (M03 and M07).At M07, wind speeds up to 2 m⋅s −1 prevented strong cooling rates similar to those observed at the other stations with calmer conditions (Figure 4b).Although calmer conditions prevailed around M03, the temperature did not decrease further at this station.We hypothesize that foehn-induced mixing was the reason for the temperature development there due to the high variability of wind direction at M03 between 1630 UTC and 1930 UTC (not shown).The high variability in wind direction during this time period could be an indication for mixing, since the wind direction at M03 was predominantly downslope before and after that period.The valley continued to cool at lower cooling rates until 2250 UTC.Temperature at M04 reached a relative minimum of −8.2 • C at 2240 UTC, whereas the temperature at the other stations at the valley floor was slightly higher (−5.2 • C to −6.1 • C).Increases in the westerly down-valley winds to around 1 m⋅s −1 at M04 coincided with temperature increases to values similar to the other stations within the LB and UB.M03 (1.9 • C) and M07 (−2.1 • C) again recorded higher minimum temperatures and wind speeds than the less elevated stations (Figure 4b) and were therefore outside the stagnant layer forming the CAP.Southerly flow at M03 suggested that this station was already influenced by foehn after 1900 UTC (not shown).Relative humidity indicated that saturation was reached at M04 between 1530 UTC and 2230 UTC (Figure 4e).Also, the other stations within the valley and M07 at the southwestern slope reached maxima of over 90%, whereas the air around the uppermost station, M03, remained much drier throughout the night.
With sharp temperature increases and wind speeds above 1.5 m⋅s −1 at M04 and M10 after 2250 UTC, the foehn air descended via the slope of Gschwandtkopf into the UB and disrupted further cooling.Temperatures at M10 and M04 increased by 6.8 • C and 12.2 • C respectively, whereas the dry foehn air decreased relative humidity significantly at both stations.The LB stations M02 and M08 were less affected by foehn, with a less pronounced temperature increase, a weaker decrease in relative humidity, and no increases in wind speed.
The disturbance lasted until 0030 UTC, when temperature and wind speed decreased again at M04 and M10.Another disturbance at 0140 UTC affected primarily the UB, whereas the stations in the LB did not measure wind speed increases and remained at low temperatures.A second strong cooling period started at 0320 UTC in the UB and resulted in the minimum temperature of the night at M04 of −9.5 • C at 0520 UTC.Also, the other stations reached their respective minimum of the night after midnight and the minima at the LB and UB stations were comparable in magnitude with −8.2 • C at M02 (0600 UTC), −7.0 • C at M10 (0610 UTC), and −7.7 • C at M08 (0620 UTC).The stations at the slopes had much higher minima (−0.7 • C at M03 and −4.7 • C at M07).Low temperatures and high relative humidity prevailed until 0900 UTC at all stations, while almost the entire valley was still shaded, when the foehn arrived and finally eroded the CAP with wind speeds above 2 m⋅s −1 .
Net radiation remained below −30 W⋅m −2 throughout the night at all stations (Figure 4c) and changed little with time.The lowest net radiation was registered at M03 with a minimum of −74 W⋅m −2 at 0020 UTC.The evolution of net radiation reflected the temperature time series: decreases in measured net radiation correlated with increases in temperature and wind speed.The net radiation at M04, for example, decreased suddenly to −70 W⋅m −2 during the warming event at 2250 UTC and slowly increased again to reach similar values as M02 and M08 towards the end of the disturbance.Incoming and outgoing long-wave radiation were only available at two stations: M04 and M08.At M08, which was less affected by the foehn disturbance, the magnitudes of both incoming and outgoing long-wave radiation followed the temperature curve, reaching their minima together with the temperature minimum (not shown).The evolution of long-wave radiation at M04 only differed from M08 between 1800 UTC and 0300 UTC.Following its sudden drop after sunset, incoming long-wave radiation frequently increased when the temperature rose due to wind speeds above 1 m⋅s −1 (not shown).The strongest increase coincided with the onset of the foehn disturbance in the UB.These oscillations of incoming long-wave radiation suggested that the wind speed increases were associated with the passage of warmer air above the CAP.The net radiation at M04 was hardly affected, as coinciding oscillations in the outgoing long-wave radiation due to temperature increases (not shown) compensated for oscillations of the incoming long-wave radiation.
The sensible heat flux, although just available at two locations, was also influenced by the evolution of temperature and wind speed (Figure 4d).Measurement values at M04 fluctuated around zero during undisturbed periods and increased in magnitude when wind speeds and temperatures were rising.The largest magnitude (−95 W⋅m −2 ) occurred at the beginning of the foehn disruption at 2300 UTC, during which the sensible heat flux frequently decreased to below −40 W⋅m −2 .A sudden rise at 0550 UTC led to a sensible heat flux maximum at M04, but no effect of this maximum was observed in the temperature and wind speed time series.Similar to wind speed and temperature, sensible heat flux measurements at M08 were less affected by the foehn disruption, and the sensible heat flux stayed close to zero.During the final foehn breakthrough after sunrise, however, the sensible heat flux decreased at both stations.
Overall, the temperature evolution correlated with the wind speed at all stations: calmer conditions coincided with periods of strong cooling, and rising wind speeds resulted in rapid temperature increases.Cooling coincided also with increasing relative humidity within the valley, indicating that local cooling rather than cold-air advection was responsible for the temperature decrease.Net radiation and sensible heat flux, although influencing the temperature evolution during CAP disturbances, were not the driving forces behind the disturbances themselves.

Vertical structure
In the absence of a radio sounding, a pseudo-vertical temperature profile along the sidewall of the valley provided information on the vertical temperature structure of the CAP.These pseudo-vertical profiles consist of, from bottom to top, measurement data from M04, HOBOs H and G, M10, all tower sensors, the HOBOs S1 to S4 at the ski jump, and M03.At the onset of cooling on January 16, 2020, at 1400 UTC, only M04 and M03 recorded temperatures below 5 • C (not shown).As the lowest temperatures were measured at the lowest station, an inversion was thus already present at the valley floor before sunset.The sharpest temperature increase with height was observed up to 1,210 m, after which the increase was significantly smaller.The temperatures at the top of the tower showed anomalously low values, due to the influence of the structure.The inversion remained around 30 m deep, and the temperature distribution at the stations above 1,210 m a.s.l.stayed almost isothermal during the period of strongest cooling.In contrast, temperatures below that level clearly depended on altitude during this period, with a vertical gradient around 2 • C/10 m at 1700 UTC (Figure 5a).Temperatures at HOBO sensors were lower than those measured with Rotronics at collocated stations and remained so throughout most of the night.The inversion layer continued to cool until 2250 UTC, but rising wind speeds caused temperatures to rise in the isothermal layer between 1900 UTC and 2100 UTC.The vertical structure varied little before the disturbance: whereas the inversion depth increased slightly with rising wind speeds at 2100 UTC, the temperature gradient within the inversion and the isothermal layer remained constant.By the end of the disturbance at 0030 UTC, the temperature at all stations above 1,200 m had risen above 2 • C, and therefore similar values to those recorded during the warming on the slopes around 2100 UTC (Figure 5b).The unventilated sensors in the UB indicated a weaker, but still existing inversion at 0030 UTC and 0200 UTC.However, the inversion recovered in strength soon after the wind calmed down.The vertical structure did not change much after the disturbance either, as the temperature decrease at the stations within the CAP was relatively constant with height.Also, the stations within the isothermal layer cooled down, although at a slightly lower cooling rate.

Model evaluation
This section focuses on simulation results of one station each in the UB (M04), the LB (M08) and the slope area F I G U R E 6 Same as Figure 4, but for 10-min averaged measurements (dashed) and simulation results (solid) at the reference grid points of M03 (red), M04 (blue), and M08 (green).Gray shading indicates cold-air pooling around M04, as described in Section 3.2.
(M03), since both measurements and simulation results at the reference grid point were representative of other locations with similar terrain configuration (compare stations in the UB, LB, and at the slopes in Figure 4).The model was able to reproduce both the temperature minima before midnight and the temperature maxima during the interruption event (Figure 6a), despite the fact that the temperature in the simulation was lower than measured at the reference grid points before the onset of cooling.Also, the four characteristic phases of the temperature evolution could largely be reproduced in the simulation, although higher wind speeds within the valley led to notable differences compared with the measurements.Cooling started roughly 2 hr later in the simulation (Figure 6a) because the down-valley wind at the UB (M04) was stronger than measured and prevented a strong cooling immediately after local sunset (Figure 6b).As soon as simulated wind speeds were comparable to the observations, cooling rates were similar to those measured.The simulated sensible heat flux at the UB was lower than at the LB, whereas wind speed was overestimated there, but reached similar values to the LB when the wind calmed down (Figure 6d).Still, measurements suggested smaller magnitudes of the sensible heat flux.Relative humidity in the model indicated saturation at all stations within the LB and UB between 1750 UTC and 2230 UTC (Figure 6e); as a result, fog formed at the lowest model level between 2010 UTC and 2210 UTC (not shown).Fog formation was not observed during this period, though.The short duration of fog formation in the model and the fact that it did not cause a response in the incoming and outgoing long-wave radiation suggests that the impact of fog on the temperature evolution was negligibly small.A shallow downslope flow from Brunschkopf into the LB and wave interactions between this flow and the CAP interrupted further cooling in the model between 1820 UTC and 1930 UTC, but cooling continued in both basins as soon as the wind speed decreased again.During the observed period of reduced cooling, the measured horizontal wind speed increased only on the slopes.The modeled minimum temperature at the reference grid point of M04 (−10.0 • C) was reached at 2210 UTC and 1.8 • C lower than measured minimum temperatures before the disturbance.At 2230 UTC, modeled wind speed rose again in the UB and temperatures reached similar values to those at M03 above the CAP.In agreement with the measurements, the sensible heat flux was stronger and more variable during the erosion event in both basins, although this effect was more pronounced in the UB (up to −58 W⋅m −2 ), which was more affected by the disturbance.The simulation also featured a temperature increase at the LB around 2230 UTC, but the values still remained 5 • C lower than at the UB stations and outside the CAP.The magnitude of temperature increases at the UB and less warming within the calmer LB also agreed with measurements.Because of overestimated wind speeds at the LB in the simulation, however, temperature increases at M08 were larger than measured.
In contrast to the temperature evolution up to the erosion event, temperatures after midnight did not agree well with measurements.The discrepancy could largely be attributed to simulated wind speeds, which exceeded measured values at the slopes already towards the end of the first cooling period.After midnight, the wind calmed down only at the valley floor in the simulation.Temperatures at the LB and UB stations decreased to −5C and remained around that level until the foehn breakthrough eroded the cold air at 0450 UTC in the UB and 20 min later at the LB.Less cooling resulted in a dry bias of the model already before the foehn breakthrough, which was amplified by the arrival of the drier air mass (Figure 6e).The simulated sensible heat flux was around 10 W⋅m −2 lower than measured during the second cooling period.Hence, the difference between measured and simulated sensible heat flux was comparable for both cooling periods.After the final CAP erosion at 0450 UTC, sensible heat fluxes between −49 W⋅m −2 and −61 W⋅m −2 in the UB and up to −44 W ⋅m −2 in the LB had similar magnitudes compared with the measurement values after the final erosion, although the CAP was eroded much earlier in the model (Figure 6d).Similar to the measurement results, the net radiation in the simulation was mainly influenced by the temperature evolution: long-wave radiative heat loss was higher at stations with higher temperatures, and its magnitude decreased when temperatures dropped (Figure 6c).Although the evolution of the net radiation throughout the night compared well with measured values, the magnitude of the net radiation remained around 25 W⋅m −2 smaller in the simulation.At M04 and M08, the difference between measured and simulated net radiation was likely due to underestimated outgoing long-wave radiation to a large extent (not shown).To test this hypothesis, we compared the modeled surface temperature with surface temperatures inferred from measured outgoing long-wave radiation via the Stefan-Boltzmann law, as direct measurements were not available.The modeled surface temperatures were lower than those inferred from measured outgoing long-wave radiation and could thus explain why outgoing long-wave radiation was lower in the simulation.
In summary, the simulation captured the measured temperature evolution within the CAP well and could reproduce the characteristic phases in the temperature evolution.Differences from the measurements could be explained with higher wind speeds in the simulation, either above the valley or within.Though the temperature discrepancies were minor during the first half of the night, the strong cooling after the erosion event could not be reproduced.Similar to measurements, the evolution of both simulated relative humidity and sensible heat flux was influenced by the development of temperature and wind speed rather than causing it.Radiative heat loss was underestimated in the model and also reacted to temperature changes rather than causing it.

Spatial distribution
The spatial distribution of temperature and wind is presented in Figure 7 at two key moments: at the CAP's greatest extent at 2200 UTC and during the erosion at 0000 UTC.An animation of the spatial distribution for the entire night is presented in Supporting Information Figure S1.At 2200 UTC, the coldest temperatures within the valley were limited to the area enclosed by the 1,200 m a.s.l.terrain contour (Figure 7a), which coincided with the lowest simulated wind speeds.This area was roughly 200 m wide and 1,000 m long.The calm conditions at the valley bottom were more favorable for CAP formation than the exposed slopes, and cold air accumulated due to the sheltered location.The warmest areas were the valley slopes, whereas temperatures around the peaks were slightly lower.The cross-section through the valley demonstrated that the strongest inversion was limited to a shallow layer above the valley floor (Figure 7b) and rarely extended to the second model level.Strong southeasterly flow above crest height, connected to the foehn flow crossing the northern Alps via the Seefeld Plateau, did not penetrate into the valley yet.The air between the CAP and crest height was characterized by weaker wind and isothermal stratification, as observed in the pseudo-vertical temperature profile (Figure 5).Instead of focusing on a single   pseudo-vertical profile along the sidewall, the temperature at the first model level of all grid cells within the valley was plotted against elevation, as this approach allowed insights into the spatial distribution of temperature stratification (Figure 8).The area considered in this analysis included all grid cells between the cell located 80 m west and 120 m south of M07 and 240 m east and 400 m north of M08.This area includes all the non-forested cells towards Mösern in the southwest and the outflow region over Seefeld in the northeast.Based on these pseudo-vertical temperature profiles, the strongest inversion extended up to 1,200 m a.s.l. in the model (Figure 8a), with a weaker inversion extending another 20 m higher and isothermal stratification above.The strongest inversion layer in the model was therefore less than 20 m thick, which was less deep than the 30 m inversion depth determined from the pseudo-vertical profile from temperature measurements (compare Figure 5).Since the lowest model level was 7 m above the surface, the lowest measurements were around 5 m below the lowest grid point in the simulation.Realistic near-surface temperature gradients induce a bias when comparing 2 m measurements with model results at 7 m above ground, as the intense inversion at the valley floor results in a larger gradient than at locations higher on the slopes.The difference between the model 2 m temperature extrapolated using similarity theory and the simulated temperature at the lowest model level, however, was less than 1.2 • C during undisturbed periods within the inversion and even smaller at the stations outside the inversion (not shown).Hence, we expect the effect of that bias in our simulation to be small.Though isothermal stratification was present throughout the valley between 1,220 and 1,300 m a.s.l., the temperature of the isothermal layer was 1.5 • C higher on the slope of Gschwandtkopf than on the other sidewalls surrounding the valley.This temperature difference is visible in Figure 7a and even clearer in Figure 8a, where the warmer branch consists mostly of cells on the slope of Gschwandtkopf.Wind speeds above 3 m⋅s −1 were also much more frequent on the Gschwandtkopf slope, suggesting that higher wind speeds were related to higher temperatures there.The observations, being positioned on the same slope, agreed better with this warmer layer than with the modeled temperature along other slopes.Interestingly, land use did not impact the temperature or stratification much during either period in this case study (Figure 8b,c).
During the erosion event, the temperature close to the valley floor increased and reached similar values to those on the slopes (Figure 7c).The southwesterly flow below 1,500 m and southeasterly flow above 1,700 m, both connected to the foehn flow, produced shear-induced mixing above the valley.The cross-section depicts two rotor-like formations above the valley: a larger one above the center of the valley and a smaller one above the slope of Brunschkopf (Figure 7d).Warmer air at the downdraft of these rotors indicated that these circulations mixed warm air down into the valley atmosphere.The core of the central rotor had a strong along-valley component, forming a low-level jet with a southwesterly wind direction between the Seefeld Plateau and the crest height of the surrounding topography.By the end of the erosion event, the CAP within the valley was dissolved and temperatures below freezing were limited to the lowest elevation within the LB.The scatter of temperature in the isothermal layer above 1,220 m increased during the entire warming period (Figure 8b), whereas temperatures remained around 0 • C at most cells and 1-2 • C higher on the slope of Gschwandtkopf for the entire night.The modeled temperatures on this slope again agreed best with the observed temperatures.
Similar to the first cooling period, the valley atmosphere above the inversion was isothermally stratified during the second cooling period (Figure 8c).As already discussed in Section 5.1, the valley cooled less than observed, as the wind was too strong in the simulation.Since the valley atmosphere above the inversion continued to cool in reality, simulated temperatures on the Gschwandtkopf slope at 0400 UTC were now too high compared with observations.Temperatures at the valley bottom reached similar values as on the slopes after 0450 UTC, when another foehn breakthrough eroded the remaining cold air.The foehn air that crossed the Seefeld Plateau did not enter via Innsbruck during this event, but crossed the Alps further west and arrived via the Inn valley from that direction.The foehn air pushed the CAP towards the village, where it was eroded around sunrise.
The analysis of the spatial structure of temperature close to the surface revealed that terrain height had the biggest influence on temperature during calm conditions.The lowest regions featured the lowest temperatures and the strongest inversion, whereas the slopes were much warmer.In particular, the valley atmosphere below 1,200 m a.s.l.featured the strongest inversion and was identified as the CAP extent.Wind speed and elevation did not correlate as clearly: weak wind conditions prevailed within the strong inversion layer, but there was large scatter in wind speed in the isothermal layer (not shown).Still, wind speed caused the 1.5 • C temperature difference between the slope of Gschwandtkopf (which was affected by higher wind speeds and warmer) and the other slopes with weaker wind speeds.

Physical processes
The cooling processes within the valley were analyzed as averages over the CAP volume.To identify the average contributions to temperature tendency in the CAP, the spatial area representing the CAP in the model had to be determined first.The averaging volume, as described in Section 3.2, was based on the area of the coldest air at the time of the maximum extent of the CAP at 2200 UTC and its depth of 20 m, which therefore mostly consisted of cells at the lowest model level.The same volume was the basis for averages throughout the night to ease comparison between different time steps, even though the extent of the CAP changed throughout the night.
The average potential temperature tendency throughout the night agreed well with the temperature evolution around M04: negative potential temperature tendencies prevailed before and during periods with strong inversions, whereas positive tendencies indicated the intermittent warming events around midnight and the erosion at 0450 UTC (Figure 9a).Despite an average net tendency of 0.02 K⋅hr −1 over the entire night, the simulation included two strong cooling periods.The temperature decreased by 6.9 K from sunset until 2230 UTC at an average cooling rate of ∼1 K⋅hr −1 and by 3.5 K in total or 0.95 K⋅hr −1 on average between 0030 UTC and 0410 UTC.Measured average cooling rates at M04 were stronger during both periods (1.2 K⋅hr −1 and 1.3 K⋅hr −1 ), but lower values for the spatial averages compared with the coldest station in the valley were not surprising.
The most important cooling contribution during CAP periods came from subgrid-scale turbulence, which contributed on average −3.6 K⋅hr −1 to the temperature tendency during the first CAP period and −4.9 K⋅hr −1 during the second.The contribution of subgrid-scale turbulence increased with larger contributions of advection, as both increased with rising wind speeds.The vertical component of subgrid-scale turbulence was by far the most important (not shown), which highlighted the role of the PBL parametrization in correctly simulating cooling.Also, long-wave radiative flux divergence was an important cooling contribution, because the surface was colder than the air above.The contribution of long-wave radiation fluctuated less and cooled the valley by −2.1 K ⋅hr −1 on average during the cooling periods.Advection contributed 3.7 K⋅hr −1 (first cooling period) and 5.9 K⋅hr −1 (second cooling period) to the temperature tendency, making it the largest warming contribution during the cooling periods.The advection contribution was largest during the cooling interruption between 1820 UTC and 1930 UTC (Figure 6).Sub-mesoscale flows mostly contributed to warming in the valley as well; however, only the horizontal components had a warming effect, and the vertical component was a cooling contribution (not shown).The average warming contribution of sub-mesoscale flows (0.8 hr −1 and 0.3 hr −1 during the first and second CAP periods respectively) was smaller than that of advection, though.When the air was saturated and fog formed during the first cooling period, the microphysics scheme also contributed to warming.Apart from subgrid-scale turbulence and long-wave radiation, it was the only parametrized process contributing to the temperature tendency during the night.Still, the contribution was not significant owing to its small magnitude (less than 0.6 K⋅hr −1 ) and the short duration of the fog period.
Advection was the most important driver of cooling disruptions, and the end of each CAP period was marked by a sharp increase of the warming contribution by advection.Its average contribution was 10.6 K⋅hr −1 during the disruption period and 13.1 K⋅hr −1 between the final erosion and sunrise.The largest individual contributions from sub-mesoscale flows were simulated towards the end of the first cooling period before warming by the mean advection caused the first CAP erosion.The largest warming contributions by advection also occurred before and θ-tendency (K .during erosion events, suggesting that resolved processes were the most important processes triggering the erosion.The first erosion event, associated with warming by the vertical advection and cross-valley components (Figure 9b), was a result of foehn air descending into the valley via the southwestern slope of Gschwandtkopf and eroding the CAP from the top.All advection components contributed to warming during the rotor formation around midnight, with horizontal advection by the along-valley jet described in Section 5.2 and vertical advection due to potentially warmer air from aloft being transported into the valley.The final CAP erosion was initiated by descending air via the slopes from the southeast, before foehn air entering the valley directly via Mösern from the southwest pushed the CAP towards the village and out of the valley.Sub-mesoscale flows contributed 0.5 K⋅hr −1 to warming between CAP periods, but there was a cooling contribution after the final erosion (−0.5 K⋅hr −1 ).Also, during cooling disruptions, subgrid-scale turbulence and long-wave radiation were the most important cooling contributions.The contribution of long-wave radiation was comparable in magnitude to its contribution during the two cooling periods (−2.3 K⋅hr −1 between CAP periods and −2.1 K⋅hr −1 after the second CAP period), confirming that dynamic processes alone were responsible for the disruption.The magnitude of the contribution of subgrid-scale turbulence increased with rising wind speeds and, therefore, was larger during disruptions, amounting to −5.8 K⋅hr −1 on average during the foehn disruption and −9.6 K⋅hr −1 after the final CAP erosion.
The numerical simulation allowed the description of the average contribution of advection for the entire CAP, but results at individual grid points varied too much spatially and temporally to draw conclusions on the spatial pattern of the advection contribution within the valley during undisturbed CAP periods.Information on the spatial variations of advection within the CAP, however, allowed the identification of flow patterns between different regions of the CAP, and therefore the horizontal exchange between the UB, the LB, and the area surrounding them.To this end, the contribution of advection was also calculated from observational data by combining wind measurements from automatic weather stations with the temperature gradient between HOBO sensors located upstream and downstream of the station.This analysis was motivated by observations of fog moving from the UB towards the LB during CAP nights other than the one described earlier herein, and therefore focused on the flow patterns.The advection contribution was only calculated for wind directions corresponding to flow parallel to the two respective HOBOs and for sufficiently large horizontal temperature differences (larger than sensor accuracy) and wind speeds above 0.4 m⋅s −1 .We focused on the region from the UB towards Seefeld due to the lack of HOBO measurements around M07 (Figure 2).The calculated advection contributions were larger than the modeled contributions presented in Figure 9 (not shown), as small gradients from the measured advection were excluded due to measurement uncertainties, and the modeled advection contributions are area averages computed over the whole CAP area.Since the temperature differences between HOBOs were often smaller than the sensor accuracy, a quantitative analysis for single nights was not feasible.Instead, a qualitative summary of the typical flow patterns during multiple CAP nights is presented in Figure 10, whereas we refer to Rudolph (2022) for a detailed description of the calculation and more detailed results.Down-valley (southwesterly) flow was associated with warming at most stations (left arrows at locations 2 and 5 in Figure 10), whereas up-valley flow caused mostly cooling (right arrow at locations 1, 2, 3 and 5 in Figure 10).The exceptions were down-valley flow from the UB into the LB, which generally had a cooling effect (left arrows at locations 1, 3, and 4 in Figure 10), and warm-air advection in the up-valley direction into the UB (right arrow at location 4 in Figure 10), the coldest area of the valley.The observed along-valley flow was weak during undisturbed periods, however, which makes the estimation of the contribution of advection from observations very challenging.Similar to the simulation, advection associated with downslope flow along the ski jump transported warmer air into the CAP (not shown).These patterns were consequences of the centers of both the UB and LB being colder than the surrounding area within the valley.Inflow towards the basin center therefore transported potentially warmer air into the basin, while outflow advected cooler air towards more exposed areas of the valley.
In summary, the dominant cooling processessubgrid-scale turbulence and long-wave radiative flux divergence-were cooling the air locally, whereas advection had a warming effect on average.The directional components of advection could be associated with both erosion events: vertical and cross-valley advection for the first erosion event induced by a rotor, and cross-valley and along-valley advection for the second event caused by foehn air entering the valley from the Inn Valley.Occasional cooling contributions in one directional component were compensated by warming effects by the other directional components, as the sum of all components was a warming contribution for the entire night.Hence, local processes caused the accumulation of cold air in the valley and drainage flows from the slopes did not contribute to the CAP formation.

Model performance
Despite the differences described in Section 5.1, the simulation performed well in reproducing the observed temperature structure until the second cold-air pooling period.This raised confidence that the cooling and warming processes identified in the model were equally important in reality.The temperature evolution in the valley was very sensitive to the presence of snow cover.The impact of snow cover was tested by comparing one simulation with and one simulation without snow cover with otherwise identical boundary conditions.The simulation without snow cover could not reproduce the intense cooling observed before midnight and underestimated the inversion strength.Temperatures above 0 • C at the valley floor throughout the night and less than 2 K difference between the temperature at sunset and the minimum temperature were clear indications that the model cannot adequately reproduce cooling in the valley without snow cover.Moreover, both net potential temperature tendencies and tendency contributions were larger if snow cover was present (not shown).The cooling contribution of long-wave radiative flux divergence in particular was much larger in the simulation with snow cover, leading to stronger cooling at the valley floor.This increased the temperature gradients between the valley floor and warmer areas surrounding it, which resulted in stronger warming contributions of advection.More warming by horizontal advection in the simulation with snow cover also increased the cooling contribution of turbulence, although snow cover had a larger impact on the contribution of long-wave radiative flux divergence.Apart from snow cover, the importance of high-resolution input datasets for terrain and land-use classification also cannot be understated.The most important cooling processes, long-wave radiative heat loss and subgrid-scale turbulence, are heavily influenced by the land-use classification, since surface characteristics significantly differ between different land-use classes (e.g., between urban and grassland cells).A sensitivity test for the same case study with the GMTED2010 terrain data at approximately 1 km resolution, however, highlighted that the use of a high-resolution terrain dataset was even more important.Especially for small valleys like the one analyzed here, the valley structure can only be resolved with a fine terrain dataset.
Using a very fine grid was also a fundamental factor in reproducing such a small-scale CAP.The CAP formed also in D4 with a horizontal grid spacing of 200 m and only 10 grid cells between the opposing peaks of the valley.Its spatial extent (up to three cells wide and 10 cells long), however, was insufficient for resolving flows within the depression.Minimum temperatures within the valley were up to 4 • C too high in D4 before midnight, and the CAP did not reform on the coarser grid after the erosion event.In addition, although the most important structures of the valley were resolved at 200 m grid spacing, many minor features (depressions and hills of below 10 m height difference) important for cold air to accumulate and not be advected away were only present at a finer resolution.Another sensitivity study with coarser vertical resolution tested the impact of the vertical grid spacing.Refining the vertical grid from Δz ≥ 20 m to Δz ≥ 15 m also improved simulation results, but to a lesser extent than the refinement of the horizontal grid and the adaption of finer topography for the model terrain.Although resulting in a slightly lower temperature minimum and reducing the average temperature by around 0.5 • C in the simulation with Δz ≥ 15 m compared with Δz ≥ 20 m, the important phases of the temperature evolution were present in both cases.Owing to the shallow nature of the CAP, only the lowest model level was within the CAP for the majority of the simulation in both cases.A vertical resolution around Δz ≥ 10 m, although still not sufficient to resolve all processes, would allow an additional model level to be included in the inversion and could improve model performance.Numerical instability at reasonable time steps prohibited the implementation of such fine vertical grids for the entire area of D5, though.Future work could expand on these results by performing a sensitivity test with a smaller domain nested in D5, a smaller time step, and finer vertical resolution, but such in-depth sensitivity tests were beyond the scope of this project.
The majority of the contribution of sub-mesoscale flows to the temperature evolution was likely due to non-turbulent motions, since resolving turbulence at a 40 m grid at such stable stratification close to the surface is unrealistic (e.g., Couvreux et al., 2020).During the cooling periods, the resolved perturbations in our simulation can be attributed to wave interactions between the inversion and the atmosphere above rather than small-scale turbulence.A contribution from the largest turbulent eddies could be possible during the foehn disruption, however, when the contribution of sub-mesoscale flows was largest in the simulation.For a different WRFlux averaging interval than 10 min, the contribution of sub-mesoscale flows to the temperature tendency would also be different.Net tendency itself would not change, though.Larger averaging intervals would further increase the contribution of sub-mesoscale flows.Larger scale circulations caused by surface heterogeneity and complex terrain would be accounted for by sub-mesoscale flows instead of advection.This would include warm air sinking in the valley atmosphere to replace cold air flowing down the valley horizontally.Shorter intervals would have required much more memory but would include the contribution of larger scale non-turbulent motions to advection, thus separating non-turbulent and turbulent motions more clearly.Nevertheless, a separation between these processes would still be ambiguous due to the overlapping scales of submeso motions and turbulence in stable boundary layers (Mahrt, 2014).

Cooling processes
To elucidate how our simulation results compare with other CAPs, the simulated temperature tendencies for the Seefeld CAP were compared with The processes contributing to the temperature evolution in Seefeld were the same as identified by Vosper et al. (2014) and Arduini et al. (2020), except for the warming contribution from the microphysics scheme.This contribution was too weak and short-lived to significantly impact the temperature evolution in the valley.The dominant cooling mechanisms-subgrid-scale turbulence and long-wave radiative flux divergence-were local in nature, whereas the resolved contribution of the sub-mesoscale flows and the non-local effect of advection caused warming.Temperature tendency therefore depended on parametrizations, because the main cooling contributions were both from subgrid-scale processes.Turbulence and long-wave radiation were also cooling contributions in Vosper et al. (2014) and Arduini et al. (2020), and advection had a warming effect in both studies.Arduini et al. (2020) further identified advection as the key process driving the variability of the temperature tendency, which was the case in Seefeld as well.
Another similarity between our results and the simulation of Vosper et al. (2014) was that the contributions of advection and turbulence were larger in magnitude than that of long-wave radiation.The evolution and magnitude of the contribution of long-wave radiation was larger in Seefeld and less variable, though.Vosper et al. (2014) reported that the cooling contribution from long-wave radiation decreased at the valley floor during the second half of the night, which they attributed to temperatures at the lowest model level approaching the surface temperature at the valley floor.In our simulation, however, temperatures at the first model level were significantly higher than at the surface throughout the night, and the contribution of long-wave radiation changed little even during CAP disruptions.This difference could be attributed to the presence of snow cover, as snow layers insulate the surface from the ground heat flux that would otherwise counter the radiative heat loss during nighttime, therefore allowing lower surface temperatures if snow cover is present (Whiteman et al., 2004).Also, Sheridan et al. (2014) mentioned the insulation effect of snow cover as a possible reason why a CAP case with snow cover in the Clun valley featured lower temperatures and an exceptionally intense inversion compared with other nights at the same location.
Although the important processes were the same, the magnitude of cooling rates and their relative contributions to total cooling in Arduini et al. (2016) and Arduini et al. (2020) were much smaller than at Seefeld and not as variable in time.The cooling rates of the surface-based inversion in Arduini et al. (2016) reached up to 1.3 K⋅hr −1 in the beginning of the night and decreased to 0.1 K⋅hr −1 towards the morning.The magnitude of temperature tendency in Arduini et al. (2020) also remained below 1.0 K⋅hr −1 during the night and, therefore, also below the average cooling rates of both cooling periods in Seefeld for this case study.The differences in valley scale could explain larger tendencies for Seefeld.Whereas Arduini et al. (2020) focused on a large Alpine valley with multiple tributaries, the valley in Seefeld was more than 10 times shorter and narrower at the valley floor.Apart from stronger drainage flows in larger valleys, outflow from tributary valleys could also perturb the main valley atmosphere, and therefore the CAP evolution (Zardi & Whiteman, 2013).As its depth was greater than the width on the valley floor, the valley in Seefeld was also more sheltered from synoptic flow, which according to Sheridan et al. (2014) would favor the development of a stronger CAP.With cooling rates between 1 K⋅hr −1 and 2.5 K⋅hr −1 during the first 5 hr of the night at the valley floor, the temperature tendency within the Clun valley (Vosper et al., 2014) indeed agreed better with the temperature tendency at the valley bottom in Seefeld.Hence, the temperature tendency in Seefeld compared best with a valley of similar scale, although the surface characteristics differed significantly.
All in all, the differences in cooling rates reported for other valleys were within the limits of uncertainty created by different boundary conditions in the simulations.Specifically, the comparison demonstrated the impact of terrain and surface characteristics on cooling rates in complex terrain.Although the cooling rates in Seefeld were much larger than reported for a large valley, they compared well with cooling rates for a valley of similar scale.Still, the contribution of long-wave radiation was much more important in Seefeld owing to the inclusion of snow cover, which highlighted the importance of representative surface conditions in simulating the evolution of a CAP.This has to be kept in mind when comparing cooling rates of different locations.

Gray zone
As described in Section 3.1, a mesoscale (RANS) simulation was the basis for the results presented here, but a simulation with the SMS-3DTKE scheme for WRF-LES was also performed as a sensitivity test to diagnose whether LESs provided better results.As mentioned in Section 3.2, we do not expect LESs to outperform the RANS results for Δx = 40 m and a wintertime nocturnal boundary layer.Nevertheless, we wanted to elaborate the potential benefits of using LESs for very stable stratification at such a fine grid spacing.To this end, temperature and wind speed for this test simulation were compared with measurement results (Figure 11).Unlike the RANS simulation presented in this work, however, the test run with the SMS-3DTKE scheme could not reproduce the intense cooling within the valley before midnight.The main reason why temperatures in this simulation were higher than in the RANS simulation, and therefore also higher than observed, was higher wind speeds within the valley before the disturbance.Temperature and wind speed during the erosion and the second cooling period after midnight were comparable to the RANS simulation with the PBL parametrization and therefore also underestimated cooling after the foehn breakthrough.An animation of the spatial distribution of temperature and wind speed for that simulation and a comparison of temperature values at the lowest grid level with the measured pseudo-vertical temperature profile are provided in Supporting Information Figures S2 and S3 respectively.Overestimated wind speed was also reported for a WRF LES run above less complex terrain by Noh et al. (2021).Still, whether the overestimated wind speed was the cause or an effect of weaker stability is difficult to determine.Larger warming contributions from advection and less cooling by turbulence in the beginning of the night decreased the stability within the valley in the LES run (Supporting Information Figure S4).Weaker stratification would allow stronger wind close to the surface.At the same time, higher wind speeds could also have prevented stronger stratification.
Another test with WRF-LES and the 1.5-order turbulent kinetic energy closure scheme (Deardorff, 1980) produced similar results (not shown).A discussion about the performance of the LESs compared with the RANS simulations in the gray zone is beyond the scope of this work, and both approaches have their deficiencies for this case.Nevertheless, the flow within the valley was more quiescent for the RANS simulation and the model performance was superior with a PBL parametrization compared with the LES.The results suggest that the resolution of the 40 m grid was too coarse to resolve the energy-containing eddies close to the surface.

Snow production
The CAP in the valley is an important snow production site in Seefeld, and local authorities want to use the most suitable location for producing snow cost effectively.
The results for this case study provide insight into the suitability of different areas of the valley under undisturbed conditions and during wind disturbances induced by foehn.The measurements and simulation results confirmed that the valley floor provides better conditions for artificial snow production than more elevated zones that were exposed to stronger wind.The evolution of temperature and wind speed differed between the UB and LB, though.Both observed and simulated minimum temperatures are lower in the UB.Therefore, the UB would be more suitable for artificial snow production during undisturbed periods, since lower temperatures are reached there, which improve the efficiency of snow production (Steiger & Mayer, 2008).Still, the LB was more resilient against foehn-related disturbances compared with the UB, as temperatures and wind speed remained lower during the disturbance compared with the UB.The behavior of the CAP after the disruption was comparable between the UB and LB, as the CAP was re-established immediately after wind speed had dropped again.Hence, even though producing snow would be more efficient at the UB during ideal CAP conditions, the resilience of the LB against wind disturbances could provide sufficiently low temperatures for snow production for a longer time period there.

CONCLUSION
The Seefeld Cold-Air Pool Experiment (SEECAP) was conducted in a small valley on the Seefeld Plateau, Austria, between December 2019 and March 2020, to investigate the spatiotemporal characteristics and processes contributing to the development of frequently occurring CAPs in the area.The night between January 16, 2020, and January 17, 2020, featured a CAP that was disrupted by a foehn breakthrough and subsequently reformed.High-resolution WRF simulations were performed for that night to determine the spatial extent of the CAP and the dominant cooling processes.WRFlux, a modification of WRF that allows the output of the modeled potential temperature tendency and the individual terms of the tendency equation, provided the basis to analyze the cooling contributions within the valley.
The finest model domain, with a horizontal grid spacing of Δx = 40 m, could reproduce the intense cooling before the foehn disturbance and also the magnitude of the warming during the erosion.Though the lowest temperatures were measured after the disruption, the CAP did not re-establish with a similar strength in the model after midnight and was eroded much earlier.Wind speeds above 1 m⋅s −1 interrupted the cooling both in the observations and in the model, but such high wind speeds were more frequently modeled than observed.The CAP was up to 20 m deep in the model, topped by a weaker inversion and isothermal stratification above.Observations suggested that the inversion was up to 30 m deep and also topped by an isothermal layer, but with no clear indication of a weaker inversion in between.In the simulation, the isothermal layer was warmer over the southwest mountain sidewall, which was more strongly affected by wind and downward motion of a rotor that formed over the center of the valley than the opposing sidewall.Disruptions of the CAP primarily affected the lowest layer of the valley atmosphere, whereas the temperature of the isothermal layer remained constant.LESs for the same period could not reproduce the temperature minima and featured a weaker inversion and larger wind speed within the valley.
Net potential temperature tendency and the individual terms of the tendency equation were analyzed as an average over the whole CAP to identify the dominant cooling processes.The night featured two periods with significant cooling.The most important contributors to cooling during these periods were parametrized processes and local in character: long-wave radiative flux divergence and subgrid-scale vertical turbulent flux divergence.Advection had a warming effect throughout the night, which was strongest during disruption periods.During the foehn disruption, the most important components were the vertical advection and the cross-valley advection, associated with the formation of a rotor and top-down mixing of warmer air from outside the valley.Also, the resolved temporal perturbations of the mean flow, which we called sub-mesoscale motions, had a net warming effect, although its vertical component contributed to cooling.Though the contribution of long-wave radiation fluctuated little throughout the night, advection and both subgrid-scale turbulence and sub-mesoscale flows were responsible for the variability in net tendency.The simulated cooling rates for Seefeld were comparable to a valley of similar scale that had no snow cover described by Vosper et al. (2014).Owing to the inclusion of snow cover in our simulation, however, the contribution of long-wave radiation was larger in Seefeld, especially during the second half of the night.In comparison with a larger scale Alpine valley with snow cover (Arduini et al., 2020), the simulated cooling rates for Seefeld were larger on average, more variable, and featured larger individual temperature forcings.In the future, simulations allowing higher horizontal and vertical resolutions and a first model level closer to the ground could provide improvements of the results presented here.
Extent and topography of model domains (a) D1, (b) D3, (c) D4, and (d) D5 (the topography of D2 is not shown).Black elevation contour lines in (c) and (d) are at 200 m and 20 m intervals respectively.The dashed square in (d) indicates the area considered for the analysis in Figure 8.The vertical grid spacing in the lowest 4 km is shown in (e).
Areal image of the measurement locations used in the analysis.UB refers to the upper basin, RI to the ridge, and LB to the lower basin.Ventilated automatic weather stations are represented by plus signs and unventilated stations by × signs.The orthophoto and the digital elevation model were provided by Land Tirol.
Climatology for measurements at TAWES in Seefeld.(a) Daily mean temperature and (b) wind speed and direction as a wind rose for a period between December 2010 and April 2020.Daily mean (solid black) and minimum temperature (dotted black) for the winter 2019-2020 are also shown in (a).Adapted from Rudolph (2022).

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I G U R E 4 The 10-min averaged measurements of (a) temperature (T), (b) wind speed (WS), (c) net radiation (R NET ), (d) sensible heat flux (SH), and (e) relative humidity (RH) between 1200 UTC January 16 and 1200 UTC January 17 at the six automatic weather stations.The mean over 10-min intervals is shown for all parameters except sensible heat flux, where the median is plotted.Stations in upper basin are shown in blue (M04 solid, M10 dashed), stations in lower basin in green (M08 solid, M02 dashed), and stations on the slopes in red (M03 solid, M07 dashed).

5
Pseudo-vertical temperature profiles (a)  between 1700 UTC and 2250 UTC and (b) between 2250 UTC January 16 and 0600 UTC consisting of the unventilated HOBO (circles), M03 and M10 (plus signs) measurements, and the ventilated temperature measurements at M04 and on top of the walk-up tower (stars).
Temperature and wind barbs at the lowest model level on (a) January 16, 2020, 2200 UTC, and (c) January 17, 2020, 0000 UTC.Wind barbs represent wind in knots (short barb 5 kt, long barb 10 kt), contour lines terrain height in 100 m intervals, and the black cross is the location of M04.The black line indicates the location of the cross-section shown in (b) and (d), where black contour lines represent potential temperature and gray contour lines the along-valley wind component (positive values point into the page).
Scatter plot of temperature at the first model level at (a) 2200 UTC, (b) 0100 UTC, and (c) 0400 UTC in dependence of elevation for all grid points within the valley grouped by land-use class.Black marker edges indicate grid points exceeding 3 m⋅s −1 wind speed.The measured pseudo-vertical profile from HOBO sensors and Rotronic measurements are indicated in dark gray.
U R E 9 (a) Terms of the temperature tendency equation and (b) advection components between 1440 UTC and 0810 UTC at the lowest model level averaged over all grid cells below 1,190 m a.s.l.within the valley.Gray shading indicates cold-air pooling around M04, as described in Section 3.2.

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assessment of the advection during cold-air-pool nights derived from wind speed measurements at the automatic weather stations and temperature gradients between individual HOBO senors.Adapted from Rudolph (2022).

TA B L E 1
Grid spacing Δx, number of grid cells in x and y directions, and time step Δt for the five domains.
Arduini et al. (2020)rface characteristics on the tendency contributions.Temperature tendency contributions for simulations of a valley with similar surface characteristics and comparable in scale to Seefeld were not available, unfortunately.Hence, we included publications focusing on valleys that resembled either the terrain or the surface characteristics of the valley in Seefeld.In contrast to most simulations of CAP cases,Arduini et al. (2020)had snow cover in their model, and therefore surface characteristics representative of our study area.The valley geometry near Seefeld, however, is more similar to the narrow Clun Valley studied byVosper et al. (2014)than the Arve River Valley considered inArduini et al. (2020).In addition, the results ofArduini et al. (2016)are also included in this section to compare cooling rates with snow cover inArduini et al. (2020)with simulations with similar terrain but no snow cover.