TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-10-3043-2016Near-surface snow particle dynamics from particle tracking velocimetry and
turbulence measurements during alpine blowing snow stormsAksamitNikolas O.n.aksamit@usask.cahttps://orcid.org/0000-0002-2610-7258PomeroyJohn W.https://orcid.org/0000-0002-4782-7457Centre for Hydrology, University of Saskatchewan, Saskatoon, S7N 5C8, CanadaNikolas O. Aksamit (n.aksamit@usask.ca)16December20161063043306220April20163May201615November201615November2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/10/3043/2016/tc-10-3043-2016.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/10/3043/2016/tc-10-3043-2016.pdf
Many blowing snow conceptual and predictive models have been based
on simplified two-phase flow dynamics derived from time-averaged
observations of bulk flow conditions in blowing snow storms. Measurements
from the first outdoor application of particle tracking velocimetry (PTV) of
near-surface blowing snow yield new information on mechanisms for blowing
snow initiation, entrainment, and rebound, whilst also confirming some
findings from wind tunnel observations. Blowing snow particle movement is
influenced by complex surface flow dynamics, including saltation development
from creep that has not previously been measured for snow. Comparisons with
3-D atmospheric turbulence measurements show that blowing snow particle
motion immediately above the snow surface responds strongly to high-frequency turbulent motions. Momentum exchange from wind to the dense
near-surface particle-laden flow appears significant and makes an important
contribution to blowing snow mass flux and saltation initiation dynamics.
The more complete and accurate description of near-surface snow particle
motions observable using PTV may prove useful for improving blowing snow
model realism and accuracy.
Introduction
Wind transport of snow influences the variability of alpine
summer runoff (Pomeroy et al., 2012; Winstral et al., 2013) is a large
contributor to the growth or ablation of small mountain glaciers (Dyunin and
Kotlyakov, 1980) and can contribute snow loading to avalanche-prone areas
(Schweizer et al., 2003). Time-averaged blowing snow field measurements often
present an oversimplified view of a highly variable and unsteady natural
phenomenon. Physical snow trap mechanisms only provide mass flux averages
over prolonged collection periods (Budd et al., 1966). Snow particle counters
only recently began providing point measurements of particle speed (Nishimura
et al., 2014) along with particle size and number flux values (Schmidt, 1984;
Brown and Pomeroy, 1989; Kinar and Pomeroy, 2015). Snow traps and particle
counters can neither measure the mechanisms of transport initiation nor
provide continuous vertical profiles of particle concentration or transport.
However, most current blowing snow model development has been informed from
time-averaged measurements from such devices. Accordingly, simplified models
of blowing snow persist in the literature that do not contain self-consistent
wind–snow momentum balances, as demonstrated by Andreotti (2004) for sand. As
well, there is a current lack of detailed measurements of particle–surface
interactions in natural conditions.
Recent progress in blowing snow research has been accelerated by novel
applications of high-speed imaging systems. Kobayashi (1972) pioneered
blowing snow recordings with outdoor, 0.125 s shutter speed images. This was
the first visual evidence of particle mechanics in the snow saltation layer
and was extremely informative in the development of saltation theory (Pomeroy
and Gray, 1995), but the photographs consisted of blurred snow particle
streaks or were saturated with particles, disguising individual particle
motions. More recently, Gordon and Taylor (2009) designed a novel and
effective halogen backlit camera system to effectively obtain particle size
and shape parameters in the Arctic, but they were limited to an imaging area on
the order of 9 mm2. In a further study, Gordon et al. (2009)
modified this technique to image an area of 124mm×101mm with a black and white binarization algorithm to obtain
continuous particle density profiles. Unfortunately, particle velocity
measurements were unavailable from either study.
In laboratories, several wind tunnel studies have examined drifting snow with
particle image velocimetry (PIV) (Lü et al., 2012; Tominaga et
al., 2012), shadowgraphy (Gromke et al., 2014), and shadowgraphic particle
tracking velocimetry (PTV) (Groot Zwaaftink et al., 2014; Paterna et
al., 2016), providing valuable insights into saltating snow velocity
distributions, average relative wind and saltating snow velocities, particle
size distributions, qualitative comparisons to transport driven by large eddy
simulation, and equilibrium wind-blowing snow decoupling. Blowing snow
transport model development continues to address small-scale variability
(e.g., Nemoto and Nishimura, 2004; Groot Zwaaftink et al., 2014) and requires
advanced measurement techniques to understand the physics driving such
multiscale heterogeneities as well as evaluate the uncertainties and
assumptions inherent in proposed models.
Of the multitude of blowing snow models that have been developed, many
implement components of earlier aeolian saltation or initiation models, e.g.,
the work of Bagnold (1941), Owen (1964), Schmidt (1980), Pomeroy and Gray
(1990), and Nishimura and Hunt (2000). In what follows, effort has been made
to refer only to the original work containing the model component or
measurement campaign under discussion, but comments generally apply to all
derivatives. Following the work of Bagnold (1941), current theory often
represents blowing snow in two layers, saltation and suspension, with a
neglected and poorly understood creep mechanism at the lower boundary of
saltation (Pomeroy and Gray, 1990; Nishimura and Hunt, 2000; Doorschot and
Lehning, 2002). Once the wind surpasses a transport threshold velocity,
saltating particles follow ballistic trajectories and rebound off the
surface, rising no higher than 10 cm. As wind speeds increase,
saltating particles become suspended by turbulence and disperse upwards.
Closely following wind streamlines, suspended particles rarely encounter the
ground (Pomeroy and Male, 1992; Bintanja, 2000).
The two most commonly modeled modes of saltation initiation are “aerodynamic
lift”, the direct drag-induced ejections of grains, and “splash”, the
ejection of grains by rebounding saltating particles (Doorschot and Lehning,
2002; McElwaine et al., 2004). However, there are substantial disagreements
about these mechanisms; Schmidt (1980) calculated that direct aerodynamic
lift was not possible under average flow conditions over a level snow surface
due to strong snow particle bonding. Doorschot et al. (2004) argued the
fragile dendritic snow in their study resulted in aerodynamic lift dominance.
It is likely that both mechanisms are possible and that the prevalent
mechanism depends on the wind conditions and snow surface structure and
cohesion. There is a growing pool of blowing snow models parameterizing these
two initiation mechanisms, including the work of Doorschot and Lehning
(2002), Nemoto and Nishimura (2004), and Groot Zwaaftink et al. (2014), all
adapting the blowing sand initiation model of Anderson and Haff (1991)
through wind tunnel measurements.
In contrast to representing saltation as a layer of particles moving with
uniform trajectories (e.g., Owen, 1964) as is common in snow saltation studies
(Pomeroy and Gray, 1990; Tabler, 1991; Doorschot and Lehning, 2002), recent
wind tunnel studies and numerical simulations of wind transport of sand have
shown the benefit of representing saltation with continuous grain velocity
distribution functions (Creysells et al., 2009; Ho et al., 2012, 2014). From
these observations, two populations of saltating particles are
distinguishable by kinetic energy rather than by physical properties such as
grain size. High-energy particles have higher and longer trajectories that
are influenced by changes in wind strength. However, these particles only
constitute the long tails of velocity distribution functions (Ho et
al., 2012). The bulk of sand saltation observed in these studies consists of
low-energy splashed “ejecta” and tractating (bed transport) grains
undergoing very short hops. These grains generate the majority of mass flux
and govern the mean properties of equilibrium saltation (Ho et al., 2014).
As saltation develops, transport mechanics evolve. For instance, in sand,
saltation and creep transport
modes are often coupled when saltation begins (Willets et al., 1991): as
low-energy surface particles accelerate, they begin feeding upper regions of
saltation. Allowing variability of motion in blowing snow saltation models
permits consideration of additional mechanisms of saltation initiation and
momentum transfer to the snow surface.
It remains unknown how well recent advances in conceptualization of blowing
sand transport can improve descriptions of blowing snow because detailed
observations of outdoor blowing snow particle transport processes near the
snow surface have not been conducted. Perhaps due to this, current theories
of snow saltation are inconsistent with each other and conceptualize a
limited range of snow motions and initiation mechanisms. To improve the
physical theory of blowing snow initiation and transport, this study
demonstrates PTV as a tool for measuring short timescale blowing snow
surface motions in an outdoor environment. The objectives of this study are
to examine the mechanics of snow particle motion initiation, the detailed
interactions between wind speed fluctuations and snow particle dynamics, and
the role of turbulent burst mechanisms that are common in mountain
environments in generating shear stress to modify snow saltation. In doing
so, the potential for adapting a continuum sand transport model for
describing snow saltation particle motions is assessed.
Methods
Fieldwork was conducted during blowing snow events in March 2015 and
February–March 2016 at the Fortress Mountain Snow Laboratory (FMSL),
Kananaskis Valley, Alberta, Canada. FMSL receives at least 800 mm water
equivalent of snowfall each winter, can sustain wind speeds exceeding
35 ms-1, and is home to several well-instrumented high-altitude,
windswept observation sites. The blowing snow site (2000 ma.s.l.)
was located in an open base area of the Fortress Mountain ski area (Fig. 1).
The area was lightly used, allowing for a 350 m upwind fetch of undisturbed
open snowfield, with the foot of a moderate ridge flanking the west
200 m away. The ground was snow-covered and shrub vegetation buried
for the duration of the experiment with snow depths fluctuating from 60 to
120 cm. Two Campbell Scientific CSAT3 three-dimensional ultrasonic
anemometers positioned at varying heights depending on snow depth on a single
mast (10–40 and 140–200 cm) measured wind speed at 50 Hz in
three axes.
A unique aspect of this experiment was the implementation of
laser-illuminated high-speed videography for outdoor nighttime snow particle
tracking observations. A portable rigid frame equipped with a Megaspeed MS85K
high-speed camera and a 445 nm wavelength 1.5 W continuous-wave laser was
situated on the snow surface less than 1 m downwind from the anemometer mast
(23 March 2015) or 33 cm away perpendicular to the flow (3 February,
3 March 2016). Dennis and Nickels (2008) suggest reasonable application of
Taylor's hypothesis up to downstream distances of up to 6 times the
boundary-layer depth δ. While there are no measurements of δ
for the present data set, it is safe to assume an extreme value of
1 m is less than 6δ which is often O(10–100 m) in
the atmospheric surface layer (ASL). Thus, using Taylor's frozen turbulence
hypothesis and mean wind speed of the two anemometers as a surrogate for
convection velocity, the effect of the downwind separation on the
representativeness of anemometer mast turbulence statistics for the actual
location of snow transport is assumed negligible with lag times
< 0.25 s. Similarly, for the crosswind orientation, the size of
energy containing eddies (discussed in Sect. 3), even over short recordings,
are large compared to the separation. Lags between instantaneous wind and
particle velocities are mentioned in the Sect. 4.
Blowing snow instrument setup and location of field site, Fortress
Mountain Snow Laboratory, Alberta, Canada.
The frame was positioned on the snow surface allowing the camera a
perpendicular 30×140mm view of the flow of saltating snow.
Laser light was projected through a cylindrical lens to create a 2 mm wide
plane orthogonal to both the snow surface and the view of the camera
(Fig. 1). The light plane illuminated a 2-D projection of saltating snow
particles. This allowed recordings in the lowest 5 cm of the
atmosphere, with minimal foreground shadowing and no background reflection.
PTV measurements were calculated by DaVis 8 (LaVision) software and estimated
individual snow particle velocities using tracking algorithms that match
discrete particles in subsequent frames imaged by the high-speed camera.
Particle velocimetry techniques are normally used for wind tunnel studies
(e.g., Zhang et al., 2007; Creyssels et al., 2009; Ho et al., 2011, 2012;
Lü et al., 2012; Tominaga et al., 2012; Groot Zwaaftink et al., 2014;
Paterna et al., 2016), with few applications, in any discipline, in an
outdoor setting (e.g., Morris et al., 2007; Zhu et al., 2007; Rosi et
al., 2014; Toloui et al., 2014). This is the first known application of PTV
for boundary-layer blowing snow studies in a natural environment.
The high-speed saltation recordings provided a great degree of visual
distinction of surface particle motion and the use of 2-D laser illumination
minimized particle overlap (e.g., Kobayashi, 1972). As the camera was focused
close to the snow surface, hundreds of thousands of rebound and splash events
were recorded over the winter field seasons. In addition to PTV, videos were
later reviewed with playback reduced 40–70 times, providing qualitative
insight to the mechanics of near-surface saltating particle motion and bed
interactions.
Sparse snow particle velocity vector field during 1 s of recording
on 23 March, vector colors scaled according to total particle speed. The
dashed line shows reference below which particles are influenced by
microtopography.
Figure 2 displays an example of velocity vectors calculated from 1 s
of 23 March 2015 (recording no. 3). The stationary snow surface was masked
out. The dashed black line indicates the height (h0) of the upper limit of
particles whose velocities were heavily influenced by surface microtopography
and contributed uncharacteristic velocity and concentration profile
statistics. In order to account for gradual changes in surface topography, an
orthogonal terrain-following coordinate system, in which y=0 is always at
the snow surface and the y direction is parallel to gravity, was adopted to
calculate vertical profiles of mean projected horizontal particle velocity
up and particle number flux concentrations Fz:
Fz=nz*upz∑znz*upz,
where n(z) is the number of particles identified at height z. This
allowed a consistent reference frame along subtle inclines like that found in
Fig. 2. Immersed boundary coordinates based on the camera frame
(xf, yf) are not representative of height above the
complex surface (e.g., (xf,yf)=(5,100) is below the
surface whereas (xf,yf)=(1,5) is above the snow)
and caused statistical values to become increasingly dubious as one
approaches the roughness layer. This can result in misrepresenting surface
fluxes. For example, immersed boundary coordinates indicate a flux maximum of
7 mm for Fig. 2 because of the lack of vectors present below this
height on the right side of the frame. Additionally, the height of surface
microtopography varied as recordings were made over hours of active erosion
and deposition, changing the surface structure and subsequently the relative
height of measurements with an immersed coordinate system. Terrain-following
coordinates allowed observations to be made over a natural snowpack, crucial
for improving the realism of blowing snow measurements, while still
accurately defining the near-surface region.
The improved realism afforded by PTV over a natural snowpack in the ASL was
counterbalanced by increased difficulty in obtaining valuable data from this
methodology and from sonic anemometry during blowing snow storms. Ultrasonic
wind speed measurements sometimes included spikes, “NaN” readings or were
flagged for skewness/kurtosis (Vickers and Marht, 1997); these concurrent
video recordings were used only for qualitative comparison. Spanwise
fluctuations in wind caused snow particles to travel transverse to the plane
of light, and the streamwise wind direction usually varied at the blowing
snow site over the course of an evening's observations. PTV relies on
particles to remain in the plane of light for illumination and tracking
through multiple frames. While the frame could be adjusted for slow
variations in wind direction, directional variations during wind gusts were a
significant complication. To reduce particle mismatch errors and improve
velocity calculation accuracy, initial visual quality controls were
implemented, discarding video that contained particles obviously moving
transverse to the plane of light.
Post-processing required individual particles to be evident in at least five
subsequent frames and limitations were imposed on velocity vector tracks to
discard physically unrealistic acceleration or direction change from one
frame to the next. The camera depth of field and light plane thickness
limited out-of-plane particle velocity components to
±0.5 ms-1. Further uncertainty derives from the limited
ability of PTV software to match individual snow particles at high wind
speeds (> 9 ms-1 at 40 cm height). The particle matching
interrogation area becomes larger as wind speeds increase and particles
travel further from one frame to the next. This exponentially increases the
number of particles that may be incorrectly matched.
Descriptions of the snowpack for each night of recording including a
description of the condition of the snow surface and concurrent
precipitation, bulk density of the top 5 cm of grains, mean air
temperature at the upper anemometer, snow surface temperature, hand surface
hardness, and hand hardness index (HHI) values following Fierz et al. (2009), as well as snow grain
size as determined from the blowing snow video. * Density and snow
surface temperature not available on 23 March with density estimated from
Pruppacher and Klett (1997).
DateSnow surfaceDensity of loose2 m air/snowSurface hardnessBlowing snowconditions andsurface grainssurface(HHI)grain sizeweathertemperature(µm)23 March5 cm graupel over old∼ 350* (kgm-3)-1 ∘C/(–)*Fist over melt–freeze crust263snow with light flurries(1–4)(Max: 1200)3 FebruaryFine decomposing grains228 (kgm-3)-10 ∘C/-10 ∘C1 Finger–pencil258on wind slab/sastrugi(3–4)(Max: 850)No precipitation3 MarchFresh snow.156 (kgm-3)-2 ∘C/-5 ∘CFist276No precipitation(1)(Max: 2500)
To verify particle enumeration, a dual-threshold black and white binarization
technique adapted from Otsu (1979) was used to estimate particle
concentration in each frame. This complimentary method of particle
identification used algorithms that, unlike PTV, are not affected by
transverse particle motion or particle matching limitations in gusty
conditions. Binarization estimates of blowing snow concentration profiles
were in sufficient agreement with concentration profiles generated by PTV,
lending confidence to the measurements of particle trajectories.
Additionally, with the binary image and PTV time series, it was possible to
use a flood-fill algorithm to identify the connected components of blowing
snow particles. Making an assumption of grain sphericity and constant density
(917 kgm-3) and using instantaneous mean particle velocities,
the equivalent diameters of the particles were used to estimate blowing snow
volume fractions and instantaneous density flux Qs
(kgm-2s-1). Particle diameter measurements generated
gamma distributions of particle size (Fig. 3) consistent with other blowing
snow literature (Budd, 1966; Schmidt, 1982).
PTV measurements in exceptionally high wind speeds
(> 10 ms-1) were not possible because the laser light became
blocked by particles. Therefore the data set used in this analysis is focused
on observations taken during relatively low mean wind speeds for blowing snow
(mean 4–7 ms-1, Table 2); these sometimes included periods of
intermittent turbulent bursts and intermittent snow transport. After all
post-processing, three nights of recording satisfied all quality controls
requirements. This included 12 recordings spanning 266 s of raw
video and 470 000 frames.
Results
Examination of data calculated from 23 March 2015, 3 February 2016, and
3 March 2016 demonstrated the value of PTV measurements over varying wind
speeds during periods of natural variation in saltating grain shape, type,
and size. Descriptions of the snowpacks following the designations of the
International Classification for Seasonal Snow on the Ground (Fierz et
al., 2009) for each night can be found in Table 1, with particle size gamma
distributions for each recording in Fig. 3. Sample videos from each night can
also be found in the Supplement. During all three nights, transport was
highly intermittent, implying wind speeds were near threshold conditions.
This was a necessary condition for accurate particle tracking in aeolian
systems as images can become easily saturated (Ho et al., 2014).
Two-parameter Gamma distributions of particle diameters from each
recording. Diameter measurements were obtained through black and white video
binarization and equivalent diameter calculations of flood-fill identified
connected components.
Wind characteristics: mean wind speed u‾, friction
velocity u*, aerodynamic roughness height z0, turbulence intensity
I, and Shields parameter S for recordings on 23 March 2015, 3 February,
and 3 March 2016. Average values from the 15 min surrounding each recording
(and recording-only period in parentheses) are shown for the two measurement
heights. Estimates of blowing snow flux Qs in
kgm-2s-1 are included for recording only periods.
Near-neutral (slightly stable) stability conditions were found during all
nights using flux- and gradient-based methods (Figs. S1–S3 in the
Supplement); however, steady-state wind conditions ∂U∂t=0 did not occur during the field campaign. The less
strict steady-state requirements of Foken and Wichura (1996) were also tested
to further confirm steady-state conditions were not evident. Recording and
wind characteristics encompassing the three nights are displayed in Table 2.
Mean wind speed u‾, friction velocity u*2=u′w′‾2+v′w′‾21/2 (Stull,
1988), and covariance-based roughness length z0=ze-0.4u‾/u*, calculated over 15 min periods surrounding
recordings as well as solely the recording time, are shown for both
anemometer measurements as they are the parameters most often used in blowing
snow models. Additional values of turbulence intensity I=u′2‾+v′2‾+w′2‾/u2‾+v2‾+w2‾
and Shields number S=ρairu*2/ρicegd
(based on mean particle size for each video) over both time periods are
provided, as well as mean blowing snow flux (Qskgm-2s-1) for the recordings.
If wind measurements are close to the surface, such as during the 3 March
2016 recordings, the physical path length of the sonic anemometers can result
in losses of high-frequency turbulence. Following the guidelines of van Boxel
et al. (2004), the Nyquist frequency (25 Hz) is a limiting factor for
mean wind speeds greater than 3 ms-1, and may also contribute to
some discrepancy of low and upper anemometer turbulence measurements.
Additionally, the lower anemometer measurements during recording no. 2 on
23 March 2015 appears to have been contaminated as there is a significant
change in covariance derived u* and z0 values between the two
heights.
The ASL fit a Prandtl–von Kármán logarithmic-law profile poorly
during the storms, most likely due to violations of horizontally homogeneous and flat terrain and stationarity requirements. Recording period
log-law-based roughness lengths z0=eu1ln(z2)-u2ln(z1)u1-u2 and friction velocities u*=κu‾(z)ln(z/z0) were loosely comparable to lower
anemometer fluctuation-based measurements with z0 errors less than
±100 % (except 3 March no. 9), and u* errors less than
±70 %, often slightly underestimating.
The 15 min roughness lengths that were generated by covariance methods
resulted in inaccurate log-linear wind profiles that indicated a zero
velocity zone for the wind well above the snow saltation layer and often at
extremes values of tens to hundreds of mm (Table 2). High roughness lengths
appear characteristic of this mountain region. At a nearby site 14 km
northeast and 600 m lower in elevation, Helgason and Pomeroy (2005)
attributed similar large covariance derived z0 values at varying heights
to the effects of surrounding topography and the nonstationary and
non-steady-state nature of the wind. The modified “focal-point” log-linear
wind profile proposed by Bagnold (1941) for aeolian transport was not
recognized in this study, with estimates of focal lengths fluctuating from
several mm up to 6 m.
The wind was characterized by brief moments of intense gusting separated by
periods of relatively calm conditions as also noted at the Helgason and
Pomeroy (2005) research site. 15 min turbulence intensity ranged from 26 to
113 %, consistently higher than the recording period values where short
time series preclude larger fluctuations around mean values. As a result,
values of u‾, u*, and z0 consistently differ between
video recording-averaged (7.3–28 s) and 15 min averaged values.
Turbulent gust-driven snow transport events dominated the nights. Eleven out
of 12 15 min averages present lower wind speeds than the recording
period with the long averages often below thresholds of transport.
Figure 4 shows varying Reynolds stress (RS =uw) generation during
recording specific periods following the language of quadrant hole analysis
(Willmarth and Lu, 1972). Sweep and ejection events (Q2 and Q4) often
contributed the majority of RS at both anemometers, with a more pronounced
role closer to the ground, indicating changes in the snow surface influence
on wind mechanics. Q2 and Q4 stress also occupied a disproportionately small
amount of time near the surface, as can be seen in the impact factors inset
in the bar graphs (IF = (% Reynolds stress) / (% time)) that
are greater than unity. Therefore, when strong events are captured during the
recordings, RS values can be much larger than long time averages. The
presence of a single pronounced sweep event in recording no. 3, 23 March
(discussed in Sect. 3.3) contributed to a high recording period turbulence
intensity (40–45 %) and a much higher recording friction velocity than
the 15 min values (0.48 and 0.24 ms-1 respectively) and will be
discussed in detail in Sect. 3.3.
Percentage of Reynolds stress distributed by quadrants analysis
during 12 blowing snow recordings with impact factor
(% stress / % time) inset in Q2 and Q4 events. Note dominance of Q2
and Q4 generated stress. For 23 March – no. 2, the low anemometer measurement
are contaminated.
Plots (a) and (b) compare Reynolds shear stress
signals from 3 February 2016 and Paterna et al. (2016) wind tunnel blowing
snow studies. Triangles indicated sweep and ejection events larger than 1
standard deviation of Reynolds stress. (c) Normalized power spectral
density for streamwise velocity for the two time series.
(a–c) Average ascending snow particle horizontal
velocities in lower saltation layer (triangles) with best-fit linear profile
for the first 10 mm. u* values are calculated from 200, 25, and
10 cm for 23 March, 3 February, and 3 March respectively.
(d–f) Friction velocity vs. particle velocity gradient (γ)
for each recording. (g–i) Friction velocity vs. particle slip
velocity (u0) for each recording.
Understanding the changes in the quadrants generating RS helps illuminate the
differences in u* values at the two measurement heights over these short
recording timescales. The recordings with the largest discrepancy in u*
(besides 23 March no. 2, where low height wind measurements are questionable)
are 3 February no. 3 (u*=0.30, 0.45ms-1) and 3 March no. 2 (u*=0.26, 0.43ms-1). This was the result of a significant decrease
in the magnitude of mean RS at the lower measurements (0.27 vs.
0.11 m2s-2 and 0.22 vs. 0.09 m2s-2, 3 February
and 3 March respectively), while the turbulence intensity remained nearly
constant (Table 2). The reduced presence of Q1 and Q3 at the lower heights
and increased impact factor of Q2 and Q4 (Fig. 4) indicated a complex shift
in boundary-layer dynamics towards the snow surface that is beyond the scope
of this paper. Other recordings exhibited much closer friction velocity
and roughness length values at the two anemometers, indicating similar
turbulent motions were captured.
As also seen by Bauer et al. (1998), sweeps and ejections did not immediately
follow one another; rather there were prolonged clusters of sweeps and
ejections with gaps in between (Fig. 5a). The gaps may be a result of point
measurements' inability to capture a full 3-D motion (Bauer et al., 1998),
but nevertheless the measurements showed a significantly different RS
generation than that typically found in wind tunnels. For example, Fig. 5a
and b compare RS values in a recent blowing snow wind tunnel experiment of
Paterna et al. (2016) with RS found on 3 February 2016 at FMSL at similar
friction velocities (0.25 and 0.27 ms-1 respectively). A sweep
signal of magnitude greater than 1 standard deviation of RS is indicated
above the given RS time series by a blue triangle, while similar ejections
are marked by brown triangles. Visually, there is a noticeable shift toward
clustered sweep and ejection events at FMSL (Fig. 5a), in which clustered
pockets of sweeps alternated with ejections, while the sweep–ejection cycle
and turbulent energy occurred at much a higher frequency in wind-tunnel-based
measurements by Paterna et al. (2016) (Fig. 5b). This is further confirmed in
the power spectral density plots of streamwise wind speed (Fig. 5c) and in
the discussion by Paterna et al. (2016). Reconciling these differences
between motions in atmospheric boundary layers and wind tunnel flows is
challenging (Hutchins et al., 2012) and the substantial differences in
Reynolds number must be kept in mind when comparing blowing snow studies in
wind tunnel and outdoor environments.
Vertical PTV profiles
Figure 6 shows profiles of ascending particle horizontal velocity for the
three nights of recording with linear regressions based on the lower
10 mm. Profiles were designated by their recording-specific low
anemometer u* values except for 23 March, when the lower wind
measurements for recording no. 2 were contaminated. Thus, all 23 March
recordings were compared using 2 m wind.
Particle motions begin with an initial ejection velocity at the surface and
then accelerate due to fluid drag in the wind. Therefore the height of an
ascending saltating particle should be a function of the time spent
accelerating. The profiles of horizontal velocities of ascending particles
confirmed this acceleration in Fig. 6. The average momentum transfer from
wind to grain was estimated from the inverse slope of the plots and indicated
the ability of the wind to entrain and accelerate particles. For all three
nights there is a near constant particle velocity gradient immediately above
the surface, ∂up∂z=γ,γ∈R+. Above ∼ 8–12 mm, depending
on the night, mean particle velocities deviate from the linear profile as
seen in Fig. 6 and confirmed by normalized root mean square error (NRMSE)
changes from the order of 0.01 to 0.1 above and below 10 mm
respectively. It must be noted that this did not indicate a discrete
transition height from creep to saltation but is rather evidence of a
continuous spectrum of particle velocities (Anderson, 1987; Ho et al., 2012)
transitioning to a higher energy population away from the surface. As these
recordings captured intermittent transport, saltation is in constant
readjustment to the turbulent wind, with particles falling in and out of the
higher levels of saltation (discussed further in Sect. 3.3). This prevented a
consistent adherence to the linear profile as seen by Ho et al. (2011),
though both studies found linear profiles overestimate particle velocity at
greater heights.
The velocity gradient (shear rate) γ was estimated by linear
regression and varied from 35 to 98 s-1. Variations in wind speed
and Qs during each recording period indicate blowing snow
transport never attained equilibrium. However, γ values are comparable
to wind tunnel PTV sand velocity gradients (39.0–150 s-1)
measured below 30 mm by Zhang et al. (2007) and the range of
20–60 s-1 found by Ho et al. (2011). For each night, γ
increases with increasing friction velocity (Fig. 6d, e, f). The Ho et
al. (2011) rigid bed experiments were conducted at comparable Shields numbers
to the high hand hardness index (HHI), wind-hardened
3 February experiments (Ho et al., 2011: [0.013, 0.043]; this study: [0.026, 0.061])
and shared several trends discussed here and below. For example, as for Ho et
al. (2011), the night of 3 February had on average the lowest γ values
(mean 44 s-1 vs. 69 s-1 for the erodible beds) and the
least variation in γ though transport occurred during comparable
friction velocities, as well as higher Shields parameters than many 23 March
and 3 March recordings (Table 2). The erodible bed studies were performed at
consistently higher Shields parameters for the Ho experiments (Ho et
al., 2011: [0.07, 0.14], Aksamit and Pomeroy: [0.01, 0.12]), yet both studies
also found increases in γ with friction velocity for the erodible
beds. Ho et al. (2011) found less variance in γ over all friction
velocities as could be expected from consistent equilibrium conditions.
As with wind tunnel sand studies (Zhang et al., 2007; Creyssels et al., 2009;
Ho et al., 2011), large nonzero particle slip velocities were observed. The
influence of surface microtopography and density of the flow prevented an
exact measurement of particle slip velocity u0, because it becomes
difficult to enumerate all grains at the surface (Creyssels et al., 2009).
However, by extrapolating the linear regression plots of constant shear rate
dup/dz=γ one can estimate u0. As
found in the same Ho study, our 3 February “rigid bed” experiments
exhibited a nearly linear increase in u0 with u* (Fig. 6h). While our
u0 measurements had a larger range for the “erodible bed” nights of 23
March 2015 and 3 March 2016 (Fig. 6g, i) than that of Ho et al. (2011) and
Creyssels et al. (2009), who found a near constant slip velocity, no
definitive trend with u* could be identified either. A purely constant
slip velocity over erodible beds most likely depends on equilibrium transport
conditions as has been theoretically explained by Ungar and Haff (1987) and
may explain the ambiguity in these results.
Figure 7 shows the vertical profile of the normalized particle number flux
calculated as Eq. (1). A normalized number flux profile was chosen instead of
the volume fraction (e.g., Ho et al., 2011) or mass flux density profile
(Creyssels et al., 2009) because of computational limitations of the PTV
package in DaVis 8 and the nonequilibrium transport during the
recordings. Since it is impossible to control the rate of transport in
nature, and volume fractions will change with rates of transport, wind
fluctuations, and snow surface conditions, it was informative to compare
number flux concentrations between periods of diverse mass transport to
determine differing transport mechanics over varying snow and wind
conditions. As the study was focused on the dynamic role of surface
transport, and not measuring mass flux, each concentration profile was
renormalized by the amount of flux that occurred during a recording to
compare what proportion of total particle transport occurs at each
height at suggested by Ellis et al. (2009) for aeolian transport profiles in
nature. This allowed observation of changes in the relative importance of
regions of transport.
The fractional number flux fits an exponential decrease of the form νz=ν0exp(-z/lv) with increasing accuracy as
one approaches the densest flow at the surface, similar to sand and snow
saltation profiles seen elsewhere (e.g., Maeno et al., 1980; Nishimura and
Hunt, 2000; Creyssels et al., 2009; Ellis et al., 2009; Ho et al., 2011;
Lü et al., 2012), with ν0 and lv being fitted
parameters, the latter referred to as the decay length. The number flux decay
length lv indicated how quickly the number flux concentration
approached zero (Fig. 7d, e, f), but because there were large variations in
the surface concentration ν0 in the present study, more consistent
trends can be observed with the momentum deficit height hv, the
height below which 75 % of particle flux occurred. As seen in the right
inset of Fig. 7, there is a nonlinear increasing relationship between
friction velocity and hv for the 3 February and 3 March
recordings. After disregarding 23 March (discussed below), values of
hv followed an approximate power law relationship
(au*b+c,R2=0.77) with asymptotic-like behavior towards
the top of the region of interest (∼ 11 mm). At low friction
velocities, near-surface saltation was dominated by transport below
7 mm, with transport becoming gradually more uniform as
hv approached the top of the camera frame at higher friction
velocities.
Plots (a–c) are mean horizontal flux measurements (Fz)
and best-fit exponential decay. Plots (d–f) are friction velocity
vs. decay length for each night. Friction velocity vs. hv (height
below which 75 % number flux occurred) for all nights with power law
curve fitting is seen in the right inset. Values of hv from
23 March 2015 are marked in red.
Horizontal particle velocity histograms for near-surface and upper-region descending particles for each recording over the three nights (each
colored differently). Near-surface residual highlighted for 3 March no. 5.
The two-region delineation was set at 3 mm for 3 and 23 March, and
4 mm for 3 February. Bottom left: surface residual to total momentum
ratios for each recording.
23 March exhibited very little change in hv and ν0 with
only a slight decrease in lv. Thus, concentration was largely
invariant with wind strength. This is remarkably similar to the erodible bed
findings of Ho et al. (2011). Only one recording had comparable Shields
numbers to Ho, but the noncohesive graupel bed and spherical snow grains most
similarly represented sand grains and an erodible sand bed out of the three
nights.
The near-surface location of the maximum of Fz found over all recordings
in Fig. 7 is in disagreement with models using Bagnold's focal height
(Bagnold, 1941) to predict a peak mass flux at some distinct height above the
surface (e.g., Pomeroy and Gray, 1990). This stemmed from the earlier lack of
high-resolution measurements of near snow surface processes outdoors, as
results were in agreement with later wind tunnel observations (Sugiura et
al., 1998; Nishimura and Hunt, 2000) and numerical studies (Nemoto and
Nishimura, 2004) of snow flux profiles as well as the recently measured
blowing snow density profiles that Gordon and Taylor (2009) and Gordon et
al. (2009) found over natural snow covers in Churchill and Franklin Bay,
Canada, respectively.
For the time series investigated, mean particle diameters had small temporal
variance over any given recording (0.01 mm on 23 March,
0.05 mm on 3 February, and 0.02 mm on 3 March). For a given
time step, mean particle diameters tended to decrease with height in the
field of view, typical of saltating snow studies (e.g., Sugiura et al., 1998;
Gromke et al., 2014), with the most extreme variations on the order of
60 µm. From this it can be inferred that particle number
concentrations were closely related to particle volume fractions through mean
diameters, and one can neglect variations in particle size with wind speed
changes while admittedly underestimating the relative volume concentration
close to the surface.
Particles moving in the densest region of the flow, immediately above the
surface, are in a zone where particle tracking by optoelectronic snow
particle counters becomes impossible but PTV provides new information. Close
to the surface, it is possible to observe the whole spectrum of saltating
particle velocities including those considered to be moving via creep.
Similar to the high- and low-energy saltating grain populations theory of Ho
et al. (2014), terrain-following height bands were chosen such that two
end-case populations could be delimited. Unique descending particles were
separated into upper and lower regions according to a variable boundary
(2–5 mm) so that they appear at most once in each region. Then,
particles were binned into 20 equivalent size horizontal velocity bins.
Figure 8 shows one example of histograms generated by these bins for a given
height separation (3 mm for 3 and 23 March, 4 mm for
3 February). Assuming that most descending particles tracked in the lowest
30 mm (frame size) will impact the surface, then most descending
grains in the upper region will also be present in the lower region. This
behavior appears in Fig. 8, where the upper-region population is a subset of
the lower-region population, showing that high- and low-energy populations coexist
as part of a continuous spectrum of motion at the surface. This is indicative
of an inherent coupling of the creep and saltating grain motions. There is
sensitivity to the selection of upper and lower regions. With a separation
threshold below 2 mm, numbers of high-velocity, low-region particles
are underestimated because tracking is increasingly difficult. With the
separation threshold above 5 mm, the low density of particles and
sensitivity to out of plane wind fluctuations made measurements of
representative fluxes inaccurate. Thus, the separation threshold was
restricted to the 2–5 mm range.
For every recording and each separation threshold chosen, there was a denser
surface flow whose mean statistics are dominated by slow-moving particles.
This is to be expected from the particle velocity and number flux profiles in
Figs. 6 and 7. The upper-region histograms show saltating particles starting
to transition towards higher-energy trajectories, with transport dynamics
dominated by larger horizontal velocities. The increasing proportion of
high-energy particles with distance from the surface is likely due to the
need for a greater velocity to reach greater heights on a ballistic
trajectory from the surface and the subjection to higher wind speeds with
increasing distance above the surface.
Subtracting the upper-region particle bin numbers from the lower-region bins
permits an estimate of the number of particles at given velocities present
solely in the lower region, hereon termed the surface residual. The
sensitivity analysis showed that for nearly every separation threshold at
least as many high velocity particles existed in the upper region as in the
lower. This allows conceptualization of the surface residual as the slower-moving surface grains, though not necessarily creep. An example of this is
shown in histograms of descending lower-region, upper-region, and surface
residual particle horizontal velocities for 3 March recording no. 5 in Fig 8.
Assuming a fixed particle diameter for all particles in each recording as the
mean from Fig. 3, spherical snow grains, and a grain density of
917 kgm-3, snow transport momentum for each region could be
estimated as the sum of momentum of particles in each velocity bin. Varying
upper- and lower-region separation thresholds from 2 to 5 mm, the
surface residual constituted 2–82, 0.07–35, and 5–49 % of total
transport momentum below 30 mm, on 23 March, 3 February, and 3 March
respectively. Ranges of momentum contribution for individual recordings are
indicated on the respective histograms in Fig. 8 as “Surf Res” and are
plotted in the bottom left panel. Surface residual momentum values compliment
the profiles of Fz (Fig. 7) as near-surface Fz values also include
high velocity particles that impact the surface.
In the near-surface region, the ability of the snowpack to redistribute
impact momentum was estimated from PTV data derived from each recording. Mean
snow particle rebound efficiency varied from night to night and was
quantified by the restitution coefficient, exz‾=sr‾/si‾, where sr‾ and
si‾ are mean ejection and impact
speeds of particles, respectively, at 6mm±2mm, such
that the lower bound of the measurement band corresponds with the upper bound
of the surface band generating Fig. 8 histograms. Because of the density of
the particle flow, and transverse components of travel, a bulk statistical
approach must be used to quantify momentum redistribution into the particle
bed. Therefore particle ejection speeds of both the rebounding grains and the
splashed grains that reach ∼ 20 particle diameters above the surface
were averaged. Over the course of the campaign, exz‾ varied
from 0.58 to 0.84, within the bounds of the previous wind tunnel blowing snow
study of Sugiura and Maeno (2000), who used a complimentary particle by
particle approach, separating individual rebounding and splashed grains. The
mean restitution coefficient was 0.69 for the graupel grains on 23 March,
0.79 for fresh snow on 3 March, and 0.73 for old snow on 3 February. This
suggests rebound efficiency was dependent on time-sensitive saltating snow
crystal and bed mechanical–material properties, as also noted in a blowing
snow wind tunnel study by McElwaine et al. (2004).
Turbulent event transport
The initiation mechanisms observed at the surface during the onset of
transport events differ from those proposed in single threshold velocity
models (e.g., Schmidt, 1980), suggesting multiple thresholds with the dense
surface flow playing a crucial role. All three transport thresholds
recognized during video playback were crossed during 23 March recording no. 3
(Fig. 9), when an isolated gust was captured with minimal antecedent
transport. Thus, it will be used as an example for further discussion.
Concurrent streamwise wind measurements at 200 and 40 cm are plotted
in Fig. 9a, showing penetration of a turbulent sweep to the surface that is
responsible for snow transport. In Fig. 9a, filled circles indicate sweep
events with RS exceeding 1 standard deviation of total RS (colors
corresponding to measurement heights), while triangles indicate similar
moments of strong ejections. Figure 9b and c show time series of spatially
averaged particle velocities and total particles tracked, respectively, in
three height bands: 1<z<4mm (near-surface), 4≤z<8mm
(middle), and 8≤z<30mm (high). These three heights were chosen to
demonstrate the subtle differences in particle transport and the continuum of
motion as grains began motion and began bouncing to greater heights as wind
speeds increased. These are not hard thresholds of “creep” vs.
“saltation” regimes. Figure 9d shows the time series of instantaneous
blowing snow flux Qs in kgm-2s-1. These
binarization-based flux measurements compliment PTV calculations in intense
gusting when enumerating all particles through tracking became difficult.
Recording no. 3 time
series for 23 March: (a) 50 Hz streamwise wind speed at 40 and
200 cm above snow surface; (b) 50 Hz snow particle
velocities obtained by binning particle vectors in three height bands (1<z<4mm, near-surface; 4<z<8mm, middle; 8<z<30mm, high), then temporally averaged over 25 frames;
(c) number of tracked particles in same height bands per 25 frames;
(d) instantaneous blowing snow flux rates Qs
(kgm2s-1) (1250 Hz).
At the end of a strong ejection event (2.5–4.5 s) at wind speeds
near 4 ms-1, snow particle motion began with tumbling surface
movement where aerodynamic drag was barely able to directly break weak
surface crystal bonds and initiate rolling (5 s in Fig. 9b, c, d).
Particle–bed collisions were concurrently responsible for breaking surface
snowpack matrix structures at these wind speeds, though they were not yet able to
initiate a splash regime. The Mar23-15 video in the Supplement for 23 March
begins at 5 s in this time series. The bonds broken by low-energy
grains at low wind speeds enabled more grains to be freely available for
entrainment. During this time, horizontal particle velocities remained low
and in the near-surface region (Fig. 9b), with no particles being tracked
above 4 mm (Fig. 9c) and total mass transport remaining low
(Fig. 9d). At this stage, the only particles in motion were those classically
termed creep.
As the wind speed increased (> 6 s), another threshold was crossed
(∼ 4.5–5 ms-1), above which tumbling near-surface
particles were sufficiently accelerated so that they could regularly bounce
off the uneven surface and out of the creep layer. This initiated what is
classically described as saltation, evidenced by the increasing presence of
particles tracked in the “middle” and “high” regions in Fig. 9c (above
4 mm), though snow mass flux remained moderate at this time
(Fig. 9d). A continuum of motion is evidenced here as all mean particle
velocities increased and velocities steadily increased away from the surface.
At 8 s, a strong sweep is present at 2 m that penetrates to
the surface by 8.5 s when the last critical wind velocity threshold
was crossed (∼ 6 ms-1), at which saltating particles
were sufficiently accelerated to initiate an active splash regime upon
rebounding. At this point snow mass flux increased exponentially (Fig. 9d),
abruptly saturating the recording frame with snow particles and limiting
illumination for successful PTV (discussed below). Similar exponential
increases of sand flux during gust onset and splash commencement have been
documented (Willetts et al., 1991). The increased snow mass flux (Fig. 9d)
persisted for the duration of the gust, (until 10 s) after which both
high and low streamwise velocities decreased. From 11 s onwards, the
decreasing wind speed was no longer able to sustain the mass transport and
particle counts dropped in the “middle” and “high” regions of flow. A
combination of inertia and wind drag prolonged transport in the creep layer,
maintaining rolling crystals that continued breaking surface bonds and were
available for transport during the next gust.
High region particle velocity spikes occurred with some delay after
8.5 s due to the intense snow particle density blocked the laser
light illumination, making particle tracking difficult. At 9 s, the
number of particles tracked in the upper region increased as particles
tracked near the surface decreased. This is likely a measurement error due to
the dense granular flow attenuating light penetration to the snow surface. As
the gust began to subside after 9 s, PTV-observed velocities and
particle numbers increased because tracking became more successful. Then, as
wind speed decreased further, observed velocities and particle numbers
decreased as expected. The Otsu (1979) binarization thresholds were
determined over short subperiods (0.085 s) of recording no. 3
(Fig. 9d), allowing the thresholding technique to adapt to different levels
of illumination and overcome these saturation issues.
Particle impact dynamics evolved as snowpack surface conditions varied during
the season with multiple melt–freeze cycles, periods of wind hardening and
the appearance of mixed grain types. Warm (Air Temp: +1 ∘C)
February 2015 snowstorms precipitated enormous aggregate and rimed crystals
that expanded the role of near-surface particle dynamics. Large (4 mm
diameter) tumbleweed-like aggregate grains, termed here “tumblons”, eroded
many smaller crystals from the surface or shattered themselves and
immediately became saltating grains, depending on impact velocity. Overlain
PTV vectors can be seen in tumblon PTV video in the Supplement, where an
impacting tumblon shatters at the surface at 7 s, with an impact
velocity of approximately u,v= (2.46,
-0.43) ms-1. At 35 s in the PTV video, a comparably
sized tumblon with velocity u,v=0.6, 0.1ms-1 tumbles across the screen without collapse. This
type of particle motion has not been described before and would seem to be a
distinctive feature of blowing snow during or shortly after snowfall of large
dendritic flakes in relatively warm conditions. Uniquely large grains can
also be found in the Mar3-16 video in the Supplement, though shattering
dynamics do not appear prevalent on that night as large grains resulted from
riming and not wet grain aggregation. Decomposing and aggregate grains of
extreme size have not been reported for saltating sand. This may limit the
application of sand bed momentum balances and wind tunnel studies where there
are no contributions of falling snow to saltation.
Discussion
Choosing the appropriate timescale to characterize turbulent energy for snow
transport is vital. From Table 2 and Figs. 6 and 7, it is clear that
recording specific particle velocity gradients γ and flux
concentration profiles did not scale with 15 min u* or z0 values
as is assumed on average for many existing snow saltation models (Pomeroy and
Gray, 1990). Part of this lack of concurrence was due to intermittent
transport and large-scale atmospheric motions generating high shear over
short periods (Fig. 4). Also, the limited Reynolds numbers possible in wind
tunnel blowing snow experiments cannot replicate the complex eddy structure
of the ASL. Thus kinetic energy is contributed to mass transport at much
higher frequencies in wind tunnels (Paterna et al., 2016) and the full
spectrum of motion can be measured over shorter timescales. Moreover, with
the influence of surrounding topography, capturing the relevant range of
energy containing eddies to predict snow transport in the alpine is less
straightforward. The 15 min mean wind speeds were often below any snow
transport thresholds reported in the literature (Li and Pomeroy, 1997). The
significant errors arising when applying time-averaged values in a u*
driven transport model (i.e., Bagnold, 1941) in intermittent winds have been
well examined for sand (Sørenson, 1997) and equally apply for snow
saltation. Pomeroy and Li (2000) accounted for the inapplicability of
steady-state theory in near-threshold conditions by using a probability of
occurrence function to reduce transport fluxes at lower mean wind speeds, but
it is unclear whether this empirical correction can account for the complex
interaction of turbulence and particle flux near the threshold. Disagreements
between u* and z0 values at the two measurement heights, large
15 min z0 values, and disagreement between log-law-based and
covariance-generated u* values reinforces the notion that all required
assumptions must be met before log-law profiles should be applied for blowing
snow models (George, 2007), especially in complex terrain.
Blowing snow PTV transport profiles were clearly more related to
recording-specific u* than 15 min values because of the
non-steady-state nature of the wind. As found in several wind tunnel sand
studies (Creyssels et al., 2009; Ho et al., 2011), particle velocity
gradients adhered to linear profiles below ∼ 8–12 mm depending
on the night. The low-energy near-surface population of particles was less
affected by fluctuations in wind strength (Ho et al., 2014), which resulted
in more temporally consistent periods of near-surface low-energy transport
and lower NRMSE values. Recent blowing snow wind tunnel experiments found
log-linearity present in the horizontal velocity profile (Tominaga et
al., 2012), though this was not observed in the present study because of a
lack of presence of a log-law for the wind.
For all recordings, the velocity gradients γ increased with increasing
friction velocity estimates (Fig. 6d, e, f). Thus even in the dense
low-energy population of grains, there was noticeable adaptation to changing
wind speeds. However, the role of low-energy grains diminished as surface
grains became less available with increasing surface hardness. As with the
rigid bed experiments from Ho et al., (2011) at similar Shields parameters,
there was a much smaller variability in γ for the wind-hardened bed on
3 February than for the two nights with lower HHI and lower overall γ
values. The momentum deficit height hv was also highest for
3 February (Fig. 7 inset) with relatively low Shields numbers (0.026–0.061),
indicating a muted role of creep and a more uniform saltation layer.
On the same night, a linear increase in particle slip velocity u0 was
observed for wind-hardened beds, similar to the findings over rigid beds by
Ho et al. (2011) for sand. This showed a general acceleration of all grains
in saltation when there are fewer new grains to be entrained in the flow. In
comparison, there was much less variability for slip velocity for 3 and
23 March over a wider range of Shields parameters and no clear increasing or
decreasing trend. A constant slip velocity is characteristic of erodible beds
in equilibrium sand transport experiments (Creyssels et al., 2009, Ho et
al., 2011). Presumably, as increasing concentration compensates for
increasing friction velocity, u0 returns to mean values over time. Snow
transport observed to be in constant readjustment to changes in wind speed,
and equilibrium was never reached in the experiments, though reduced
variation in u0 may be indicative of early stages of the equilibrium
process as theorized by Ungar and Haff (1987).
Particle number flux concentration profiles fit an exponential decrease model
with increasing accuracy as height decreased and flow density increased, as
predicted in many other sand and snow studies (Maeno et al., 1980; Nishimura
and Hunt, 2000; Creyssels et al., 2009; Ellis et al., 2009; Ho et al., 2011;
Lü et al., 2012). A direct comparison of decay length (lv)
between recordings and other experiments was impractical because large
variations in surface concentration (ν0) skewed the decay length, making
it a poor analogue for saltation height. Instead, it was found that the
momentum deficit height hv increased for most recordings with
increasing friction velocity. Lower hv values require more
particle transport momentum nearer the surface. The presence of low-energy
near-surface particles at low friction velocities served as a reservoir for
the transition to saltation with subsequent increases in wind speed. As the
wind speed accelerates, more particles are accelerated and transported to
greater heights where they are further accelerated, resulting in a more
uniform vertical distribution of mass flux. This occurs gradually with
increasing wind speed rather than involving discrete transport threshold
velocity values for separate modes of transport.
The notable exception for this trend in hv were the events of
23 March (Fig. 7, inset – red dots) where hv, lv,
and ν0 values remained constant as was predicted by Ho et al. (2011) for
erodible beds. This difference in behavior can be physically justified as
spherical graupel grains over a noncohesive bed are the conditions most
closely resembling sand, and so the number flux profiles behaved more
similarly to sand than for the other two nights of blowing snow.
Histograms of horizontal velocity further supported the relevant and dynamic
role of the low-energy surface population of blowing snow (Fig. 8), and the
decreasing importance of near-surface mass flux with increasing surface
hardness. The bottom left plot in Fig. 8 shows that for the nights with
erodible beds and lower HHI (3 and 23 March), the ratio of surface residual
to total momentum is largest for low friction velocity. This is not sensitive
to the separation threshold height chosen. During low wind speeds, particle
transport for the erodible beds was largely confined to the lower region with
few high-energy surface impacts. The ratio of surface residual to total
momentum, and therefore number flux, was much higher over erodible beds than
over the wind-hardened rigid bed recordings on 3 February (Figs. 7, 8). This
complimented the fact that the low-energy surface transport on 3 February had
the smallest contribution to total number flux. Thus particle type and snow
bed properties played a significant role in the surface momentum balance,
changing the uniformity of saltation profiles and wind momentum lost to
surface transport. Mean particle diameters remained relatively similar over
all recordings and thus snow transport models need to account for snow bed
hardness or erodibility as there is a connection to a variable near-surface
transport momentum sink.
Analyzing the instantaneous wind speeds in Fig. 9a helps to explain the short
timescale roles of gusts, high friction velocity, and turbulence intensity
for snow transport in recording no. 3. The turbulent sweep event (u>0,
w<0) from 8 to 9 s generated considerable RS; this turbulent
structure is widely reported to be involved in initiating aeolian sediment
transport (Grass, 1971; Jackson, 1976; Sterk et al., 1998; Chapman et
al., 2012). The 1 s sweep accounted for 29 and 25 % of total absolute RS
at 40 and 200 cm, respectively, and contributed 56 % of total
snow particle flux below 30 mm, but occupied only 8 % of the
time. Turbulent ejections (u<0, w>0) generated 39 % of total absolute
shear stress during the recording and contributed the same direction of RS
values to friction velocity calculations but only resulted in 3 % of
total snow particle flux. Varying the lag time between wind and snow
measurements from 0 to 1 s to determine the resultant snow flux had
no significant effect on these calculations.
In this gusty alpine environment, periodic turbulent gusts generated the
majority of momentum flux as seen by impact factors greater than unity at the
surface for Q2 and Q4 and small contributions from Q1 and Q3 (Fig. 4). More
importantly, recording no. 3 showed that the sweep event with strong positive
u fluctuation resulted in particle entrainment and transport, whereas the
large ejection event was ineffective at generating snow transport. As
suggested by Sterk et al. (1998), instantaneous wind speed is a potentially
better predictor of snow transport than friction velocity. However, during
each night, the mass flux scaled with
increasing friction velocity (Table 2). This resiliency may help explain some
of the robustness of u*-based time-averaged uniform trajectory blowing
snow models, but it requires further investigation. The role of sweep events
such as this for initiating snow saltation is potentially important for
developing models that couple turbulence to snow erosion, entrainment, and
mass flux and may help resolve current uncertainty in estimating threshold
conditions for transport. The importance of understanding snow response to
instantaneous wind speed is further increased in complex terrain where the
300 m of clear upwind fetch or 60 s of constant wind
suggested by Takeuchi (1980) for saltation to fully develop is not always
available. For a more general application, this requires further
investigation of turbulent snow transport over longer time series and other
snow conditions.
Designating creep as distinct from saltation as originally done by Bagnold
(1941) is not only unnecessary but also physically inaccurate as snow
transport displays a continuous spectrum of motions, similar to that proposed
for sand by Anderson (1987), and individual particles can easily transition
from one form of motion to another over their trajectories. However, two
populations of motion in this spectrum could be identified in the analysis of
Figs. 6–9. While undergoing wind speed fluctuations, the region of
near-surface flux has the most temporally consistent transport (Fig. 9). This
was also the region of largest velocity variance (Fig. 8), yet the consistent
presence of the slow particle flow allowed the best fit of particle number
flux and mean particle velocity to profiles suggested in the equilibrium sand
transport literature. The worst fit of both gradients always occurred at the
upper regions dominated by high-energy particles (Fig. 8). These high-energy
particles constituted the population of fast-moving grains that was most
susceptible to changes in wind speed (Ho et al., 2014) and most temporally
intermittent (Fig. 9).
The lower boundary condition for momentum transfer is complex due to creep
and dependent on instantaneous wind speed and turbulent motions near the
surface. As a result, equilibrium conditions were never found in the field
observations reported here. Nonequilibrium saltation–wind interactions
cannot be described with simple uniform trajectories. The majority of
particle trajectories in saltation consist of short hop lengths and times,
resulting in high frequencies of particle collisions that break surface bond
structures and create dense quasi-fluidized bed characteristics. The
complexity of conservation of mass, momentum, and kinetic energy in blowing
snow in natural environments, such as measured here, cannot be understated,
especially when the large rimed, aggregate tumblons were present. In the
alpine snowpacks investigated, variable particle restitution coefficients
contributed to this complexity. While high HHI wind-hardened surfaces
exhibited similar behavior of slip velocity and particle velocity gradients
as rigid bed sand studies, complexities over a natural snowpack prevented
conclusive bimodal “erodible” vs. “nonerodible” scale relations that
appear to be viable for sand (Ho et al., 2011). Blowing snow is a distinctive
two-phase flow.
Despite arguments to the contrary for other materials (e.g., Sterk et
al., 1998), saltating snow models relate mass flux to surface shear stress
estimated from air motions well above the surface. These estimates are often
based on a momentum deficit derived from the total number of particles in
transport, neglecting the vertical heterogeneity of particle concentration
and momentum within the snow saltation layer (Doorschot and Lehning, 2002).
As all panels in Figs. 6 and 7 show, uniform descriptions of surface shear
stress calculations based on concentration and flux measurements above 10 mm
overlook the substantial wind momentum transferred into the creep layer
(i.e.,
Zhang et al., 2007; Creyssels et al., 2009; Ho et al., 2011, 2012, 2014).
Disregarding this flux prevents calculation of the full momentum balance.
Accounting for variability in saltation trajectories would also allow for a
dense surface flow to be represented that can feed upper regions (e.g., Nemoto
and Nishimura, 2004) and create a self-consistent momentum balance. Andreotti
(2004) wrote a further discussion of self-consistency errors of wind feedback
in single trajectory saltation models.
The wide variety of snow saltation initiation mechanisms observed in this
experiment is in contrast to classic initiation models that assume that a
temporally constant fraction of saltating grains begin motion through either
aerodynamic entrainment or splash (e.g., Pomeroy and Gray, 1990). As seen in
Fig. 9 and the video in Supplement, in intermittent conditions this
variability is magnified, as splash regimes themselves are intermittent and
depend on sufficient wind speed for adequate particle acceleration upon
ejection from the snow surface.
Conclusion
This is the first investigation to measure outdoor
snow particle flux and velocity immediately above the snow surface. It
provides an opportunity to test certain observations of saltating particle
flux trajectories measured in wind tunnels. Though observations were
restricted to moderate wind speeds and intermittent transport, they show the
importance of creep to the initiation of blowing snow transport and the
transition to full saltation. Being able to relate high-frequency turbulent
wind speed to snow transport (e.g., Guala et al., 2008) is critical in the
alpine environment (Naaim-Bouvet et al., 2011) and this study makes a
contribution to understanding these dynamics.
PTV has proven to be a viable avenue for exploring complex wind–snow
interactions at millisecond timescales in natural, non-steady-state, high
Reynolds number wind conditions. These results support the need for further
conceptual advancement of models of snow particle movement, including
initiation, rebound, multiple types of motion, and the interaction of
turbulent sweeps with particle erosion and entrainment. Over short
timescales, snow particle motion is influenced by complex wind-speed-dependent initiation and rebound dynamics, including a dense near-surface
flow whose presence and variation cannot be described by scalar aerodynamic
entrainment and splash parameterizations. Wind-to-snow and snow-to-snow
momentum transfer in the first few mm above the surface is critical for
driving mechanisms of transport initiation and providing lower boundary
conditions for two-phase atmospheric flows.
The results show a wide spectrum of particle motions exist with near-surface
and upper-level snow particle transport intrinsically linked through
momentum and mass balances. The relative contributions of near-surface and
upper-level transport depend on wind strength and snowpack properties. Sand
saltation velocity distribution models do not comprehensively describe
transport of complex snow crystal structures such as the previously
undescribed tumblon motions or snow particle shattering and sintering.
Low-energy near-surface particles contributed significantly to snow
transport as high near-surface particle concentrations compensated for
reduced particle speeds and sustained a layer of peak particle momentum and
mass flux. The low-energy grains also contributed considerably to saltation
by being a reservoir of particles bouncing into saltation and by breaking
snow bed matrix bonds, thus making particles more available by reducing the
wind drag required for splash and entrainment.
The ability of the snowpack surface to absorb wind and particle momentum in
the dense near-surface region of particle transport appears variable and
substantial. The role that low-energy near-surface particles play in the
wind–snow momentum balance and mass flux appeared dependent on snow surface
hardness. Wind-hardened surfaces shared several trends similar to that of
rigid sand beds, though not all wind tunnel observations could be
replicated. As saltation dynamics are dependent upon creep particle motions,
which mediate exchange between the snow surface and blowing snow, creep
dynamics changes over varying surface hardness also result in changes in
saltation, such as changes in velocity gradients, particle concentration,
and rebound dynamics. Therefore the near-surface snow transport has far more
intricate dynamics and greater flux relevance than previously described.
In the present study, the near-surface particle velocities reflected
instantaneous wind speed fluctuations and never achieved equilibrium. As the
snow transport was in constant readjustment to changes in wind velocity, and
short timescale turbulence characteristics did not scale with long time
averages, further characterizations of the timescale of relevance or
relevant turbulence scaling relations in alpine terrain need to be performed
before a steady-state equilibrium type saltation model (e.g., Pomeroy and
Gray, 1990; Doorschot and Lehning, 2002) can be deemed appropriate for these
situations. Furthermore, as contributions of shear stress from different RS
quadrants are spatially and temporally variable and the mechanics of
transport vary during gusts as seen in Sect. 3.3, the need to account for
variable shear stress in high-resolution modeling (Doorschot et al., 2004;
Groot Zwaaftink et al., 2014) is reinforced.
It could be very useful to compare modeled entrainment and splash ratios with
PTV data sets, but longer recording times over a larger variety of snow
types would be necessary to obtain statistically significant comparisons.
Specifically, whether longer time-averaged statistics can account for periods
of varying initiation during intermittent saltation, or can only apply in
more nearly steady-state environments, would be a useful finding for high
temporal resolution applications (e.g., Groot Zwaaftink et al., 2014). PTV
shows potential to answer many open questions in blowing snow research
through quantification of momentum redistribution in very near-surface
particle motions. The use of high temporal-resolution outdoor PTV
measurements may prove useful in future work for understanding how turbulence
influences blowing snow processes in natural settings.
Data availability
Data are available upon request directly from the authors at
john.pomeroy@usask.ca.
The Supplement related to this article is available online at doi:10.5194/tc-10-3043-2016-supplement.
Acknowledgements
The authors acknowledge funding from the Canadian Foundation for Innovation,
the Natural Sciences and Engineering Research Council of Canada, the Changing
Cold Regions Network, Canada Research Chairs, the Global Institute for Water
Security, and Alberta Agriculture and Forestry. The assistance of the Fortress
Mountain Resort in logistics is gratefully noted, as are the suggestions from
Nicolas Leroux and Florence Naaim-Bouvet to improve the manuscript.
Edited by: G. Chambon
Reviewed by: F. Naaim and one anonymous referee
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