The aerodynamic roughness of glacier surfaces is an
important factor governing turbulent heat transfer. Previous studies rarely
estimated spatial and temporal variation in aerodynamic surface roughness
(z0) over a whole glacier and whole melting season. Such observations
can do much to help us understand variation in z0 and thus variations
in turbulent heat transfer. This study, at the August-one ice cap in the
Qilian mountains, collected three-dimensional ice surface data at
plot scale, using both automatic and manual close-range digital
photogrammetry. Data were collected from sampling sites spanning the whole
ice cap for the whole of the melting season. The automatic site collected
daily photogrammetric measurements from July to September of 2018 for a plot
near the center of the ice cap. During this time, snow cover gave way to
ice and then returned to snow. z0 was estimated based on
micro-topographic methods from automatic and manual photogrammetric data.
Manual measurements were taken at sites from the terminals to the top of the ice cap; they
showed that z0 was larger at the snow and ice transition zone than in
areas that are fully snow or ice covered. This zone moved up the ice cap during the
melting season. It is clear that persistent snowfall and rainfall both
reduce z0. Using data from a meteorological station near the
automatic photogrammetry site, we were able to calculate surface energy
balances over the course of the melting season. We found that high or rising
turbulent heat, as a component of surface energy balance, tended to produce a
smooth ice surface and a smaller z0 and that low or decreasing turbulent heat
tended to produce a rougher surface and larger z0.
Introduction
The roughness of ice surfaces is an important control on air–ice heat
transfer, on the ice surface albedo, and thus on the surface energy balance
(Greuell and Smeets, 2001; Hock and Holmgren, 2005; Irvine-Fynn et al.,
2014; Steiner et al., 2018). The snow and ice surface roughness at
centimeter and millimeter scales is also an important parameter in studies
of wind transport, snowdrifts, snowfall, snow grain size and ice surface
melt (Denby and Smeets, 2000; Brock et al., 2006; McClung and Schaerer,
2006; Fassnacht et al., 2009a, b). Radar sensor
signals, such as Synthetic Aperture Radar (SAR) (Oveisgharan and Zebker, 2007), altimeters and scatter
meters, are also affected by ice and snow surface roughness (Lacroix et al.,
2007, 2008). One of the most important of these influences
is the aerodynamic roughness of z0, which is related to ice surface
topographic roughness in a complex way (Andreas, 2002; Lehning et al., 2002;
Smith, 2014; Smith et al., 2016). Determination of z0 based on
topographic roughness is therefore of great interest for energy balance
studies (Greuell and Smeets, 2001).
Glacier surface z0 has been widely studied through methods such as eddy
covariance (Munro, 1989; Smeets et al., 2000; Smeets and Van den Broeke,
2008; Fitzpatrick et al., 2019) or wind profiling (Wendler and Streten, 1969;
Greuell and Smeets, 2001; Denby and Snellen, 2002; Miles et al., 2017;
Quincey et al., 2017). However, micro-topographic estimated z0 shows
some advantages, such as lower scatter compared to profile measurements
over slush and ice (Brock et al., 2006), and ease of application at
different locations (Smith et al., 2016). Current research has increasingly
used the micro-topographic method to estimate z0. It has also become clear
that it is important to estimate z0 over the entire course of the
melting season and at many points on the glacier surface, as z0 is
prone to large spatial and temporal variation (Brock et al., 2006; Smeets and
Van den Broeke, 2008). This variation is due to variations in weather and
snowfall (Albert and Hawley, 2002). The micro-topographic estimated z0
allows repeated measurement at many points on the glacier surface, which is
not possible with wind profile or eddy covariance methods.
Photogrammetry has been increasingly popular as a method to measure the
aerodynamic surface roughness of snow and ice (Irvine-Fynn et al., 2014;
Smith et al., 2016; Miles et al., 2017; Quincey et al., 2017; Fitzpatrick et
al., 2019). Initially, the micro-topographic method was developed because snow
digital photos were taken against a dark background plate. The contrast
between the surface photo and the plate could then be quantified as a
measure of glacier roughness (Rees, 1998). This method is still widely applied
for quantifying glacier surface roughness (Rees and Arnold, 2006; Fassnacht et
al., 2009a, b; Manninen et al., 2012). A more recent
method, as described by Irvine-Fynn et al. (2014), uses modern
consumer-grade digital cameras to do close-range photogrammetry at plot
scale (small plots of only a few square meters). Appropriate image settings
and acquisition geometry allow the collection of high-resolution data
(Irvine-Fynn et al., 2014; Rounce et al., 2015; Smith et al., 2016; Miles et
al., 2017; Quincey et al., 2017). Such data facilitates the distributed
parameterization of aerodynamic surface roughness over glacier surfaces
(Smith et al., 2016; Miles et al., 2017; Fitzpatrick et al., 2019).
Precision of micro-topographic estimated z0 also became a major concern,
and many comparative studies with the aerodynamic method (eddy covariance or
wind towers measurements) were carried out over debris-covered or non-debris-covered glaciers. The difference was within an order of magnitude for some
studies (Fitzpatrick et al., 2019) or strongly correlated (Miles et al.,
2017).
Previous researchers have performed some long-term systematic studies of
glacier surfaces (Smeets et al., 1999; Brock et al., 2006; Smeets and Van
den Broeke, 2008; Smith et al., 2016). The current study applied such
methods to the study of snow and ice aerodynamic surface roughness during
the melting season at the August-one ice cap. We used both automatic digital
photogrammetry and manual photogrammetry. Automatic methods allowed us to
monitor daily variations in aerodynamic surface roughness, and manual methods
allowed us to characterize aerodynamic surface roughness variation along the
main glacial flow line. We also recorded meteorological observations in order
to study the impact of weather conditions (e.g., snowfall or rainfall) on
aerodynamic surface roughness. This data allowed a further effort to
characterize variation in plot-scale z0 from an energy balance
perspective.
Location of ice cap and study sites. (a) Location of the
August-one glacier. (b) Locations of the AWS, automatic and manual
photogrammetry plots, and shortwave observation platforms.
Measurement specifications for the AWS located at the top of
the glacier (4820 m a.s.l.). The heights indicate the initial sensor
distances to the glacier surface; the actual distances are derived from the
SR50A sensor.
VariableSensorsStated accuracyInitial height (m)Air temperatureVaisala HMP 155A±0.2 ∘C2, 4Relative humidityVaisala HMP 155A±2 %2, 4Wind speedYoung 05103±0.3 m s-12, 4Wind directionYoung 05103±0.3∘2, 4Ice temperatureApogee SI-11±0.2 ∘C2Shortwave radiationKipp&Zonen CNR-4±10 % d total2Longwave radiationKipp&Zonen CNR-4±10 % d total2Surface elevation changesCampbell SR50A±0.01 m2PrecipitationOTT Pluvio2±0.1 mm1.7Data and methodsStudy area and meteorological data
The August one glacier ice cap is located in the middle of Qilian Mountains
on the northeastern edge of the Tibetan Plateau (Fig. 1a, b). The glacier
is a flat-topped ice cap that is approximately 2.3 km long and 2.4 km2 in area. It ranges in elevation from 4550 to 4820 m a.s.l. (Guo et al.,
2015). This study was conducted during the melting season of 2018, a season
characterized by high precipitation. Energy balance analysis indicated that
net radiation contributes 86 % and turbulent heat fluxes contribute about
14 % to the energy budget in the melting season. A sustained period of
positive turbulent latent flux exists on the August one ice cap in August,
causing faster melt rate in this period (Qing et al., 2018).
Researchers had access to meteorological data that had been recorded
continuously since September 2015, when an automatic weather station (AWS)
was sited at the top of the ice cap (Table 1). The AWS measures air
temperature, relative humidity and wind speed at 2 and 4 m above the
surface. Air pressure, incoming and reflected solar radiation, incoming and
outgoing longwave radiation, and glacial surface temperature (using an infrared
thermometer) are measured at 2 m height. Mass balance is measured by a
Campbell Scientific ultrasonic depth gauge (UDG) close to the AWS. An
all-weather precipitation gauge adjacent to the AWS measures solid and
liquid precipitation. All sensors sample data every 15 s. Half-hourly
means are stored on a data logger (CR1000, Campbell, USA). Throughout the
entire melting season (from June to September) researchers periodically
checked the AWS station to make sure that it remained horizontal and in
good working order. During the entire study period, precipitation total was
261.3 mm, as measured at the AWS. Of this precipitation, 172.1 mm was snow or sleet and 89.2 mm was rainfall (Fig. 7a).
The automatic photogrammetry device at the August one ice
cap.
Frames used for automatic and manual photogrammetry. (a)
Wooden frame in situ set up for automatic photogrammetry; four control
points and three checkpoints are shown on the frame. (b) Detrended DEM for
the corresponding snow surface of (a). (c) Manual observation plot, with the
four control points and four checkpoints shown on the aluminum frame. Ice
surface hummock was covered with cryoconites. (d) Detrended DEM for the
corresponding cryoconite surface of (c).
Automatic photogrammetry
The study began with the placement of an automatic close range
photogrammetry measurement apparatus in the middle of the ice cap (4700 m;
39∘1.1′ N, 98∘53.4′ E; see Figs. 1b and 2). It was placed near the existing meteorological station. This was
done on 10 July 2018. A wooden frame, 1.5 m wide and 2 m long, was put on
the ice surface. This frame served as a geo-reference control field (Fig. 3a). Four feature points demarcated the control field; three additional
points served as checkpoints. A Canon EOS 1300D cameras, with an image size
of 5184×3456 pixels was connected to the frame. The camera lens
was set in wide-angle mode (focal length of 27 mm). The f stop was fixed at f25 with an exposure time of 1/320 s. The camera was programmed to
automatically take seven pictures over a period of 10 min. The
photography was repeated at 3 h intervals from 09:00 to 18:00,
Beijing time. During the 10 min photography periods, the camera moved
along a 1.5 m long slider rail. The camera was 1.7 m above the ice surface and
moved along the control frame. The seven pictures taken during this period
were merged to produce a picture of ice surface topography at millimeter
scale (Fig. 3b). This apparatus took pictures over a period of 3 months (12 July to 15 September, the melting season). A total of 64 d of
data were recorded. Each daily photography series produced four sets of
pictures (12 h and 3 h intervals). The best-exposed photo sets
were manually selected and used as that day's data. We also set up
instrumentation to record incoming and reflected solar radiation. Samples
were taken every 15 s; 10 min means were stored on a data logger
(CR800, Campbell, USA) located at a height of 1.5 m. Surface elevation
changes caused by accumulation and ablation were measured by a digital
infrared hunting video camera, which took pictures of ice surface gauge
stakes located near the automatic photogrammetry site.
Manual photogrammetry
Manual close-range photogrammetry was used to survey glacier surfaces at
several different locations of the ice cap. Observations were made on 4 d: 12 and 25 July and 3 and 28 August. It should be noted that
when the July measurements were performed, the ice cap surface was partially
snow covered.
Channels account for only a small portion of the glacier surface area. These
surfaces show extreme variability of z0 (Rippin et al., 2015; Smith
et al., 2016). For that reason, we distributed the manual photogrammetry
study sites over the glacier surface in such a way as to cover most surface
types and topographic regions without including any channels (Fig. 1b). We
photographed a total of 36 sites over the 4 d of observation.
Study plots were demarcated with a 1.1×1.1 m portable square
aluminum frame. A geo-reference of the point cloud was enabled using control
points established by eight cross-shaped screws on the aluminum frame
(Fig. 3c). Photos (convergent photographs, low oblique photos in which
camera axes converge toward one another) were taken at ∼ 1.6 m
distances, covering an area of ∼ 1.75 m2. A total of 7 to 12
of such photos were taken at each survey site and surrounded the target area
from different directions. The camera used was an EOS 6D 50 mm, with a fixed
focal lens and an image size of 5472×3648 pixels. The f stop was
fixed at f22 with an exposure time from 1/25 to 1/125 s.
Data processing
Structure-from-motion photogrammetry is revolutionizing the collection of
detailed topographic data (Westoby et al., 2012; James et al., 2017). High-resolution DEMs produced from photographs acquired with consumer cameras
need careful handling (James and Robson, 2014). In this study, both manual
and automatically derived photographs were imported into a software program,
Agisoft Photoscan Professional 1.4.0. This software allowed us to estimate
camera intrinsic parameters, camera positions, and scene geometry. Agisoft
Photoscan Professional is a commercial package, which implements all stages
of photogrammetric processing (James et al., 2017). It has previously been
used to generate three-dimensional point clouds and digital elevation models
of debris-covered glaciers (Miles et al., 2017; Quincey et al., 2017;
Steiner et al., 2018), ice surfaces and braided meltwater rivers (Javernick
et al., 2014; Smith et al., 2016). In our study, we found that after new
snowfall it was difficult to match feature points in the photo sets. A total of 3 d of automatic data could not be processed. We estimated z0 data
for the missing days based on data from snowfall days at the automatic site.
Aerodynamic roughness estimation
Methods for measuring roughness at plot scale were first developed by soil
scientists (Dong et al., 1992; Smith, 2014). Metrics such as the random
roughness (RR) or root-mean-square height deviation (σ), the sum of
the absolute slopes (ΣS), the microrelief index (MI) and the peak
frequency (the number of elevation peaks per unit transect length) were
used. Later these roughness indices were used to describe snow or ice
surface roughness (Rees and Arnold, 2006; Fassnacht et al., 2009b;
Irvine-Fynn et al., 2014).
Current photogrammetry methods produce high-resolution three-dimensional
topographic data. Earlier two-dimensional profile-based methods for
estimating surface roughness discard much of the potentially useful
three-dimensional topographic data (Passalacqua et al., 2015). Smith et al. (2016) were able to use Eq. (1), developed by Lettau (1969), to make
better use of the topographic data, using multiple point clouds and digital
elevation models (DEMs). Fitzpatrick et al. (2019) also developed two methods
for the remote estimation of z0 by utilizing lidar-derived DEM.
In this method, z0 is quantified as follows:
z0=0.5h*sS,
where h* represents the effective obstacle height (m) and is
calculated as the average vertical extent of micro-topographic variations,
s is the silhouette area facing upwind (m2), S is the unit ground area occupied by micro-topographic obstacles (m2) and 0.5 is an averaged drag coefficient.
Based on the work of Lettau (1969), Munro (1989) simplified Eq. (1)
by assuming that h* can equal twice the standard deviation of elevations in the de-trended profile, with the profile's mean elevation set to 0 m.
The aerodynamic roughness length for a given profile then becomes
z0=fX(σd)2,
where f is the number of up-crossings above the mean elevation in profile, X is the length (m) of profile and σd is the standard derivation of elevations of profile. For manual photogrammetry, we put the aluminum
frame horizontally over the ice surface, the plot is detrended by setting
the control points at the z axis of the same values. For automatic
photogrammetry, the control field of wooden frame was also laid horizontally
over the ice surface, which lowered as the ice melted and maintained a
horizontal position between the control field and ice surface. A DEM-based
approach enables the roughness frontal area s to be calculated directly for
each cardinal wind direction (Smith et al., 2016). The combined roughness
frontal area was calculated across the plot, and the ground area occupied by
micro-topographic obstacles is 1 m2. We used a DEM-based average
(z‾0_DEM) of the four cardinal wind directions to
represent overall aerodynamic surface roughness. Based on the 30 min wind
direction data at the August one ice cap, the daily upward wind direction
DEM-based z0_DEM was also estimated at the automatic
photogrammetry site. Considering that wind direction changed during the day,
in this case we selected the prevailing wind direction to calculate frontal
area s. The prevailing upwind direction DEM-based z0_DEM
was applied to calculate turbulent heat flux. Using the Munro (1989) method,
z0_profile was calculated for every profile (n=1000)
in both orthogonal directions for each plot at the automatic photogrammetry
site.
Control point RMSE for manual and automatic photogrammetry
Ground control points x error (mm)y error (mm)z error (mm)Total error (mm)AutomaticPoint 10.715.836.615.11Point 20.411.140.740.82Point 30.544.552.402.99Point 40.450.761.040.79Average0.543.763.583.01ManualPoint 20.620.430.811.11Point 40.440.270.430.67Point 50.180.470.850.99Point 70.660.392.973.07Average0.520.401.651.78
Checkpoint RMSE for manual and automatic photogrammetry.
Ground checkpoints x error (mm)y error (mm)z error (mm)Total error (mm)AutomaticPoint 52.064.447.705.27Point 60.913.561.952.40Point 70.983.112.602.41Average1.413.744.833.62ManualPoint 10.300.190.390.52Point 30.790.370.691.12Point 60.280.830.901.26Point80.460.450.440.77Average0.520.530.660.99Snow and ice surface energy balance calculation
The temporal variation in z0 at the automatic site was studied from
energy balance perspective. The surface heat balance of a melting glacier is
given by
QM=Qis-Qos+QL+QE+QH+QP+QG,
where QM is the heat flux of melting, Qis is the incoming shortwave
radiation, Qos is the outgoing shortwave radiation, QL is the net longwave radiation, QE is the latent heat flux; QH is the sensible heat flux, QP is the heat from rain and QG is subsurface heat flux.
In a horizontally homogeneous and steady surface state, the surface heat
fluxes QE and QH can be calculated using either the bulk aerodynamic approach or profile method, based on the Monin–Obukhov similarity theory
(e.g., Arck and Scherer, 2002; Garratt, 1992; Oke, 1987). In this study,
30 min observations at 4 m level and daily upward wind direction
DEM-based z0 were used to calculate QE and QH based on the bulk
method. The heat from rain is given by Konya and Matsumoto (2010):
QP=ρwCWTWPr,
where ρw is the density of water (1000 kg m-3), CW is the specific heat of water (4187.6 J kg-1 K-1), TW is the wet-bulb temperature (K) and Pr is the rainfall intensity (mm). The
subsurface heat flux QG is estimated from the temperature–depth
profile and is given by QG=-kT∂t′∂z′, where
kT is the thermal conductivity, i.e., 0.4 Wm-1 K-1 for old snow and 2.2 W m-1 K-1 for pure ice (Oke, 1987).
In order to calculate Pr, we used the air temperatures recorded at the
AWS. There is an elevation difference between the study site (4700 m) and
the AWS (4790 m). Recorded air temperatures were corrected to account for the
elevation difference. A lapse rate of -5.6∘C km-1 was applied
based on observations made nearby (Chen et al., 2014). The ice cap is flat and
open terrain so in this case wind speed and relative humidity at the study
sites were assumed to be close to those observed at the AWS.
Automatic and manual photogrammetry checkpoint errors. Panels
(a), (c) and (e) are automatic photogrammetry standard deviation for the x, y
and z axes, respectively. Panels (b), (d) and (f) are manual photogrammetry standard deviation
for the x, y and z axes, respectively.
(a) Variation in glacier surface aerodynamic roughness
over time at the automatic observation site for the DEM-based and Munro (1989)
profile-based approaches. Panel (b) shows a snow-covered surface on 13 July.
Panel (c) shows a partially snow-covered surface on 23 July with cryoconite
holes. Panels (d) and (e) show a smooth ice surface on 1 and 30 August. Panel (f) shows a rough ice surface on 13 September.
ResultsPhotogrammetry precision
We used 17 plots to analyze the horizontal and vertical accuracy of
our automatic photogrammetry and 31 plots for our manual
photogrammetry. Based on the Agisoft Photoscan processing report, automatic
photogrammetry average point density of the final plot point clouds was over
1 000 000 points m-2. DEMs of 1 mm resolution were generated at plot
scale. The average geo-reference errors fluctuated at around 1 mm
(see Tables 2 and 3). Total root-mean-square error (RMSE) of the automatic control points was
3.0±2.1 mm and for the checkpoints it was 3.62±1.6 mm. Vertical error for
control points was 3.58 mm ± 3.01 mm and for the checkpoints it was 4.83 ± 2.9 mm (Tables 2 and 3). Standard deviation of control and checkpoint
errors are all within 15 mm (Fig. 4a, c, e). Manually measured average
point density of the final plot point clouds was > 6 000 000 points m-2. DEM of 1 mm resolution was generated at plot scale. The RMSE of four control points is 1.78±1.3 mm (Table 1). The control point vertical accuracy of manual photogrammetry is about
1.65±1.3 mm. The total RMSE of manual photogrammetry checkpoints is
0.99±0.3 mm and the vertical accuracy is 0.66±0.3 mm (see Tables 2
and 3). Standard deviation for the x, y and z axes were all within 5 mm (Fig. 4b, d, f).
Note that the control and checkpoint errors are larger for the automatic
measurements than for the manual ones (see Fig. 4). We believe that this
is the case because, rather than using static f stop and exposure times (as
in automatic photogrammetry), researchers engaged in manual photogrammetry
could adjust exposure time based on ice surface conditions. This allowed
production of better quality photos even on cloudy or foggy days. This
difference in survey design also caused more precise results for manual than
automatic photogrammetry. For the automatic measurements, the camera was
moving linearly and the density of tie points was much higher in the
foreground compared to the background. For the manual method, photos were
taken by surrounding the target area. This type of surface provided a much
more robust elevation model and point density.
Aerodynamic surface roughness as measured by automatic
photogrammetry
Data for ice surface roughness was collected by the automatic photogrammetry
camera site from 12 July to 15 September, a period covering the whole melting
season. Profile and DEM data show that z0 estimates vary by 2 orders
of magnitude over the study period (Fig. 5). The upwind DEM-based data
showed a z0_DEM varying from 0.1 to 1.99 mm (mean:
0.55 mm). The average of the four cardinal wind directions' DEM data shows a
z‾0_DEM varying from 0.1 to 2.55 mm (mean: 0.57 mm). The average Munro profile-based z0_profile varied
from 0.03 to 2.74 mm (mean 0.46 mm).
Surface roughness vs. altitude, (a) as observed on 12 July, (b) 25 July, (c) 3 August and (d) 28 August.
At the start of the observation period of 12 July, snow covered the study
site. As the snow melted, the ice cap surface z0 increased. During this
period, z0 dropped to around 0.1 mm due to intermittent snowfall. On 21 July, cryoconites appeared on patches of snow crust, which led to patchy
melt. From 21 to 24 July, overall z‾0_DEM increased
from 0.1 to 1.6 mm. By 29 July, snow had disappeared from the study site, and
z0 fluctuated but trended lower. From 29 July to 5 August bare ice covered the whole field of view; z‾0_DEM ranged from
0.18 to 0.56 mm. From 6 August to 3 September there was intermittent snowfall
followed by melting, and z‾0_DEM ranged from 0.1
to 1.0 mm. From 4 to 14 September z‾0_DEM
showed an overall increase, reaching a maximum of 2.55 mm on 8 September.
There was intermittent snowfall during this period, which temporarily
reduced z‾0_DEM,
which then increased thanks to patchy microscale melting. After
14 September, snow covered the whole surface of the glacier and there was no melting and little fluctuation in z0.
It should be clear that either z0_profile or
z0_DEM and z‾0_DEM varied
following the same pattern during the melting season. There were two peaks
in z0, both of which occurred in periods of transition: snow surface
turning to ice around 24 July and ice surface turning to snow on 8 September. On 24 July and again on 8 and 13 September, glacier surfaces featured
cryoconite holes and snow crust. Both the automatic and manual observations
showed the same pattern: maximum z0 at the snow–ice transition belt during
partially snow-covered periods.
Weather conditions at AWS over study period: (a)
precipitation, (b) air temperature, (c) incident solar radiation, (d)
relative humidity and (e) wind speed.
Surface roughness as measured by manual photogrammetry
No wind direction measurements were carried out during manual
photogrammetry. In this case, we presented an average of the four cardinal
directions to represent ice aerodynamic surface roughness. Analysis
indicated that z‾0_DEM proved to have an
interesting relationship with altitude. z‾0_DEM was
highest in the transition zone between snow cover and ice. This zone moved
up the ice cap during the melting season. On 12 July, ice surface roughness
decreased from 3.2 to 0.25 mm as altitude increased (Fig. 6a; r=0.8429; P=0.0006<0.01). Near the ice cap terminals at 4590 m, the
ice surface featured porous snow and ice and many cryoconite holes. As altitude
increased, the number of cryoconite holes decreased and snow coverage
increased. At 4700 m the ice surface was predominantly snow covered and only
a few small patches were free of snow. On 25 July, ice surface roughness
fluctuated between 0.27 to 0.65 mm at the ice cap terminals (4593 m). At
∼ 4700 m, roughness increased to 1.85 mm. Above that point,
roughness gradually decreased to 0.25 mm at the ice cap top, which was
covered by snow (Fig. 6b).
On 3 August, the August one ice cap was predominantly bare ice and there was
scattered snow crust at the ice cap top. The ice surface (terminal to top)
showed a heavy deposit of cryoconite. Photogrammetric data collected manually
revealed that ice surface roughness increased with altitude (Fig. 6c,
r=0.7). From the terminals to the top of the ice cap, z0 varied from 0.06 to 2.2 mm. On 29 August, the ice cap surface roughness showed no significant correlation
with altitude (Fig. 6d, r=-0.03). z‾0_DEM
varied from 0.2 to 0.98 mm (Fig. 6d). When we compare the results of
the four surveys, we see that ice surface roughness was variable. Maximum
z0 was seen at the snow and ice transition zone, where the ice surface
featured both cryoconite holes and clean snow crust. Snow crust would have
inhibited melting; cryoconite would have increased it. It is thus
understandable that surface roughness would have been greater in such an
area. Bare ice or snow cover both result in comparatively less roughness.
z0 and weather
Figure 7 compared z‾0_DEM and corresponding
meteorological conditions of precipitation, air temperature, downward solar
radiation, relative humidity and wind speed. Detailed analysis indicates
snowfall was recorded from 12 to 24 July. In general, snowfall reduced
roughness if it resulted in a fully snow-covered surface. However, if a
patchy, shallow snow cover was formed, it tended to increase z0 after
a short drop. For example, on 11 and 12 August, two successive sleety days
created a patchy snow cover which soon increased z0. Between 26 July
and 31 August there were 16 rainfall events, which tended to lower ice
surface z0.
Daily temperatures during the study period ranged from -6.5 to
7.1 ∘C (mean: 1.3; Fig. 7c). It was 1.2 ∘C on
11 July. It increased to 3.6 ∘C on 24 July (the date when z0 was highest). It continued increasing until 29 July, when it reached its highest
annual of 7.1 ∘C. During this period z0 continuously
declined. From 28 July to the end of August temperatures fluctuated between -0.3
and 5.7 ∘C with no evident trend. z‾0_DEM
also fluctuated slightly, showing no obvious trend. In September air
temperature quickly dropped from 0.6 to -6.5∘C. There were large
fluctuations in z0 during this period. The largest fluctuations
appeared when air temperatures dropped from positive to negative.
Daily downward mean solar radiation fluctuated dramatically during the study
period due to cloudy and overcast conditions (Fig. 7d). Incident solar radiation
fluctuated between 129 and 753 W m-2 (mean: 469 W m-2).
From 29 July to the end of August, the weather was cloudy, warm, calm, and humid
most of the time (Fig. 7b, c, e, f) and z‾0_DEM was relatively stable, except when there was intermittent
snowfall-induced fluctuation. After September, the weather again
became cold and dry and z0 was quite variable.
Ice surface energy balance at automatic
z0 observation study site
The following section analyzes the changes in surface energy balance at the
automatic site. Meteorological observation records allowed us to study the
factors that control ice surface roughness. Net radiation varied from -9.7
to 260.2 W m-2 (mean: 95.3 W m-2) during the study period. This
constituted the largest energy flux affecting glacier surface energy
balance. It accounted for 84 % of total incoming flux (Fig. 8). Net
radiation was relatively low in the first 13 d of the study period
(mean: 69.3 W m-2), when the glacier surface was covered with snow. In
the succeeding 5 d, net radiation increased to 103.9 W m-2. At
this time the ice surface exhibited a patchwork of snow, ice, and
cryoconite. From 29 July to 5 August the surface of the study site was
composed of ice with a dusting of cryoconite. Net radiation reached a height
of 183 W m-2. There was intermittent snowfall from 6 August to
8 September. Net radiation dropped to a mean 93 W m-2. Snow cover then appeared and net radiation dropped to a low of 46 W m-2.
Daily mean energy balance at the middle of the glacier study
site, which was close to the automatic photogrammetry site.
Ice surface overview at the automatic photogrammetry site
before and after a strong rainfall event captured by an automatic digital
infrared hunting video camera: (a) photograph taken before the rainfall event on
4 August of 2018 and (b) photograph taken after the strong rainfall event on
5 August of 2018.
Comparison of observed daily mass balance and modeled daily mass
balance. Mass balance measurements were taken from 12 July to
29 August. Measurements of surface lowering were converted into water
equivalents using density values.
Bulk-method-estimated results indicate that sensible heat (QH) was the
second largest energy flux component of in surface energy balance during the
study period (Fig. 8). The sensible heat daily mean varied from -7.1 to
66.3 W m-2. It accounted for -28 % to 32 % (mean: 15 %) of the
net energy flux. Latent heat was generally small throughout the study
period. Daily mean of latent heat varied from -80.1 to 11.1 W m-2
(mean: -13.2 W m-2). It accounts for a mere 0.9 % for the total
incoming flux. It was negative from 11 to 26 July when the ice surface was
snow covered. After 26 July the latent heat was mainly positive in the
following 10 d (the ice surface was pure ice or partially snow covered).
From 6 August to the end of the study period (15 September) it was
predominantly negative.
From 25 July to 5 August rainfall energy varied from 0 to 11.7 W m-2
(mean: 0.3 W m-2). Rainfall accounted for a mere 0.2 % of total
incoming flux. One event accounted for much of the total: on 28 July a 31 mm
rainfall event added a flux of 11.7 W m-2, which resulted in visible
smoothing of the ice surface (Fig. 9). Compared to
other energy components, QG was very small, with a daily mean
of -0.65 W m-2 and a maximum and minimum of -0.4 and -2.1 W m-2,
respectively.
Modeled vs. observed surface ablation
Based on the previously listed measurements of energy fluxes, we calculated
the probable surface ablation at the automatic photogrammetry site. We took
into account observed net radiation, bulk-method-calculated turbulent heat
fluxes, heat from rainfall and subsurface heat flux. There was good
agreement between the model and observed results (Fig. 10).
Figure 11 shows the relationship between estimated daily upward wind
direction DEM-based z0_DEM and the main energy flows.
Scatter diagrams showed a positive relationship between z0_DEM and net shortwave radiation (Fig. 11a, r=0.1) and a significant
negative relationship between z0_DEM and net longwave
radiation (Fig. 11b, r=-0.35), Graphing z0_DEM vs.
bulk-method-estimated latent heat showed a significant negative exponential
relationship (Fig. 11d, r=-0.35). The scatter diagram showed no
significant relationship between z0_DEM and the bulk-method-estimated sensible heat (Fig. 11c). The average of the Munro
profile-based z0_profile, DEM-based
z‾0_DEM and the main energy items are also analyzed. Scatter diagrams showed a significant negative relationship
between z0_profile and net longwave radiation (Fig. S1a, r=-0.5). Graphing z0_profile vs. the bulk-method-estimated latent heat showed a significant negative exponential
relationship (Fig. S1d, r=-0.69). The scatter diagram showed no
significant relationship between z0_profile and the bulk-method-estimated sensible heat (Fig. S1c). z‾0_DEM vs. the bulk-method-estimated latent heat showed a significant
negative exponential relationship (Fig. S2d, r=-0.44). In the scatter
diagrams between z‾0_DEM and net shortwave
radiation, the bulk-method-estimated sensible heat showed no significant
relationship.
Because net shortwave radiation and turbulent heat fluxes were the main
energy fluxes affecting ice surface roughness, we calculated a turbulent
heat proportion index:
LS=(QH+QE+QP)/(Qis-Qos).
Note that aerodynamic surface roughness on days when snow fell was strongly
affected by the amount of the snowfall. If we exclude snowfall days and snow-covered period, we see a significant exponential relationship between ice
surface z0_DEM and LS (Fig. 12a, r=-0.34).
The scatter diagrams showed a significant exponential relationship between ice
surface z0_profile and LS and net longwave
radiation (Fig. 12c, r=-0.69). z‾0_DEM vs.
LS also showed a significant exponential relationship (Fig. 12b,
r=-0.46). Scatter diagrams in Fig. 12 also showed z0 did not keep
decreasing when LS was above 0.2. z0_DEM,
z0_profile and z‾0_DEM
were around 0.56±0.21, 0.33±0.03 and 0.6±0.26 mm,
respectively.
The lagged correlation between z0 and
the main energy items during the melting season; the sensible heat and
latent heat were calculated here based on the bulk method.
Daily upward wind direction of DEM-based
z0_DEM vs. energy inputs: (a)z0_DEM vs. net shortwave radiation,
(b)z0_DEM vs. net longwave radiation,
(c)z0_DEM vs. bulk-method-calculated sensible heat and (d)z0_DEM
vs. bulk-method-calculated latent heat.
The z0 (z0_DEM and z0_profilez‾0_DEM) vs. LS graph indicates that when
turbulence and rainfall heat increased, aerodynamic surface roughness
decreased. As soon as LS is above 0.2, the ice surface will not keep
smoothing and z0 sustains its lowest stage. Time series correlation of
all main energy items and z0_profile were performed.
Table 4 shows an example of the lagged correlations between
z0_profile and five variables. The z0 and net
shortwave radiation displayed a positive correlation with 0 to 1 d lag
time. The z0 response to QE with a correlation of -0.6 showed a
lag of 0 to 1 d. The z0_profile also had a negative
relationship with QL with no lag or 1 d lag time. The
z0_profile response to LS with a correlation of
-0.58 was with a lag of 0 to 2 d. A total of 0 to 2 d lag time gives an
indication of the effort limitations of the main energy items over ice surface
z0. In other words, a sunny and cold day facilitates rough ice
surfaces and warm and cloudy days tend to produce a smoother ice surface. When
net shortwave radiation is higher and latent and sensible heat are
smaller, z0 tends to be higher for the next 2 d. When net
shortwave radiation is smaller, as on cloudy days, any snowfall or rainfall
is usually associated with smaller z0 for the following 2 d. Under a
negative QM, the surface z0 would not be affected by melting
process.
Aerodynamic surface roughness vs.
LS. Where LS=(QH+QE+QP)/(Qis-Qos),
in (a)z0_DEM was estimated
based on DEM-based prevailing upwind direction, in (b)z‾0_DEM was the average of the four
cardinal wind directions' z0 in order to represent overall
aerodynamic surface roughness and in (c)z0_profile was the average of two orthogonal directions z0.
DiscussionAutomatic and manual photogrammetric methods
Photogrammetric techniques such as Structure from Motion (SfM) (James and
Robson, 2012) and Multi-view Stereo (MVS) represent low-cost options for
acquiring high-resolution topographic data. Such approaches require
relatively little training and are extremely inexpensive (Westoby et al.,
2012; Fonstad et al., 2013; Passalacqua et al., 2015). We used both
automatic and manual photogrammetric methods to sample spatial and temporal
z0 variation at the August one ice cap. Adjustments to exposure time
based on ice surface conditions and survey design of the area surrounding
the target made the manual photogrammetry more precise than automatic
photogrammetry (Tables 2 and 3). However, precision is not always the major
concern. The glacier surface was a harsh (even punishing) environment for the
researchers doing manual photogrammetry. In addition, manual photogrammetry
took much longer. Automatic methods reduced hours of field work, spared
researchers and produced nearly continuous data. Cloudy or frosty weather
affected automatic photogrammetry exposures, and heavy snowfalls resulted in
a textureless surface. Nevertheless, it is likely that photogrammetry
techniques will continue to improve and that these drawbacks may be
mitigated.
Spatial and temporal variability of z0
Previous studies of glacier surfaces roughness have rarely covered the whole
glacier, from the terminals to the top of the ice cap, in one melting season (Föhn, 1973;
Smeets et al., 1999; Denby and Smeets, 2000; Greuell and Smeets, 2001;
Albert and Hawley, 2002; Brock et al., 2006; Smeets and Van den Broeke,
2008; Smith et al., 2016). This whole-glacier study allowed us to follow the
movement of the transition zone, where snow was melting and exposing ice,
from the terminals to the top of the ice cap. The transition zone moved up as the melting season
proceeded, thus roughening the surface of the glacier and raising z0. At
the start of the melting season, snow cover first disappeared, leaving an
ice surface at the terminal end of the August one ice cap, i.e., at the
lower altitude. This newly exposed surface was rougher (z0 was higher)
than on the upper part of glacier, which was still snow covered (see the
black line in Fig. 6a for z0 distribution at different altitudes). As
the snowline shifted to higher altitudes, ice surface increased, as did
z0 (see the dashed black curve in Fig. 6b). As the melting continued,
the snow and ice transition belt reached the top of glacier (see the dotted
curve in Figure 6c). When the ice cap was completely free of snow, z0 and elevation were no longer correlated (see the dotted–dashed line in
Fig. 6d). In summary, maximum z0 was recorded at the cross-glacier
transition zone between snow and ice. This zone shifted from lower altitude
to higher altitude, from the terminals to the top of the ice cap, during the melting season. The
spatial pattern of z0 distribution affected turbulent fluxes. The
transition zone had maximum z0, and the zone also migrated across much
of the glacier, highlighting the importance of transient surface
characteristics.
Micro-topography, wind profile and eddy covariance methods generate a wide
range of z0 values for snow and ice surfaces (Grainger and Lister,
1966; Munro, 1989; Bintanja and Broeke, 1995; Schneider, 1999; Hock
and Holmgren, 2005; Brock et al., 2006; Andreas et al., 2010; Gromke et al.,
2011). In this study, z0_profile, z0_DEM and z‾0_DEM showed similar variation pattern
during the melting season. The difference of z0_profile,
z0_DEM, and z‾0_DEM were within
1 order of magnitude. The latent and sensible heat calculated byz0_profile, z0_DEM and
z‾0_DEM were highly relevant among these methods.
The automatic photogrammetry estimated z0 for snow-covered surfaces
ranged from 0.1 to 0.55. New snowfall at the snow surface in July formed the
lowest z0 values. Previous studies have shown that freshly fallen snow
is subject to rapid destructive metamorphism (McClung and Schaerer, 2006),
which can dramatically change the roughness of fresh snow surfaces
(Fassnacht et al., 2009b). Our study showed that z0 followed an
increasing trend during the melting season. Intermittent snowfall first
decreased snow surface z0, which then began to increase as the snow
surface deteriorated. In the data from Clifton et al. (2008), snow surface
z0 was estimated at between 0.17 to 0.6 mm in a wind tunnel experiment.
In an analysis of ultrasonic anemometer recorder data over snow-covered
sea ice, Andreas et al. (2010) found z0 values ranging from 10-2
to 101 mm. In a wind tunnel experiment of fresh snow with no-drift
conditions, Gromke et al. (2011) estimated z0 to be between 0.17
to 0.33 mm, with no apparent dependency on the friction velocity. Our snow
surface data showed that z0 values fluctuated between 0.03 to 0.55 mm,
consistent with some of those wind tunnel studies. The scatter of z0
data reported in some studies is quite large, with a range of 10-2 to
101 mm. The result may be attributed to the occurrence of snow drift, a
transitional rough-flow regime and large uncertainties in the estimation of
friction velocities that propagate to the computation of z0 (Andreas et
al., 2010; Gromke et al., 2011). In contrast, the small scatter in our
data was induced only by the natural variability of snow surface roughness.
For patchy snow-covered ice surfaces, z0 varied from 0.5 to 2.6 mm and
ice surface z0 varied from 0.24 to 1.1 mm. During the melting season,
there were no blowing snow events and snow surface z0 was relatively
smaller than in patchy snow-covered surface or ice surface. Ice surface
z0 was generally larger than snow surface and smaller than patch
snow-covered surface. Our results match values reported in studies reporting
results ranging from 0.1 to 6.9 mm in Qilian mountain glaciers (Guo et
al., 2018; Sun et al., 2018). Our results showed that z0 reached its
maximum at the end of the summer melt, which matched wind profile
measurements by Smeets and Broeke (2008).
The aerodynamic surface roughness is influenced by both the boundary layer and
the surface. In this study, the micro-topographic estimated aerodynamic
surface roughness only considers surface topography at plot scale but its
variability is influenced by its surrounding topography and the boundary layer.
Thus, the results of z0 estimated in this study still need to be validated by
wind tower or eddy covariance observations. However, micro-topographic
roughness metrics are a very strong proxy for z0 (e.g., Nield et al.,
2013), so we have much more confidence in the temporal and spatial
variability presented by this work.
Effects of surface energy balance components on aerodynamic
surface roughness
Aerodynamic roughness is associated with the geometry of ice roughness
elements (Kuipers, 1957; Lettau, 1969; Munro, 1989). Surface geometry
roughness develops due to local melt inhomogeneities in melting season. In
earlier works, researchers argued that a variety of ablation forms, such as sun
cups, penitents, cryoconite holes or dirt cones, are formed by the sun
(Matthes, 1934; Lliboutry, 1954; McIntyre, 1984; Rhodes et al., 1987;
Betterton, 2000). These ablation forms develop in regions with bright
sunlight and cold, dry weather conditions are apparently required (Rhodes et
al., 1987). These structures are observed to decay if the weather is cloudy
or very windy (Matthes, 1934; Lliboutry, 1954; McIntyre, 1984).
The August one ice cap dust concentrations are high in the melting season.
Cryoconites are unevenly distributed over the ice surface, leading to
differential absorption of shortwave radiation at microscale. This process
results in the roughening of the ice surface, a process that enhances
turbulent heat exchange across the atmospheric boundary layer–ice interface.
When the air temperature is above 0 ∘C, the ice surface keeps melting.
The turbulent heat smooths the ice surface, increases the cryoconite
concentration over the ice surface and decreases ice surface albedo,
enhancing shortwave radiation absorption (Fig. 9). This roughening and
smoothing process makes ice surface z0 fluctuate at around 0.56 mm
as long as the air temperature is above 0 ∘C. When the temperature drops
below 0 ∘C, bright sunlight and dry weather shutdown the ice surface
smoothing process. The shortwave radiation induces even rougher ice and
larger z0 until snow covers the ice surface. At the August one ice cap,
the turbulent heat contributes a small portion of incoming energy, but the
smoothing ice surface process decreases ice surface albedo and seems to enhance
ice surface shortwave radiation. The z0 fluctuation in the melt season
is similar, with cryoconite holes developing when the radiative flux is
dominant and decaying when turbulent heat is dominant (McIntyre, 1984;
Takeuchi et al., 2018). The glacier surface energy balance components vs.
z0 analysis in this study confirm that the main energy items of net
shortwave radiation and turbulent heat flux affect the same-day z0 and
following 2 d of z0. This study found an exponential relationship
between z0 and LS. The delicate role of z0 played in the ice
surface balance is still not fully known. Further comparative studies are
needed to investigate the z0 variation through eddy covariance and profiling
methods and DEM-based z0 estimation.
Conclusions
Manual and automatic measurements of snow and ice surface roughness at the
August one ice cap showed spatial and temporal variation in z0 over
the melting season. Manual measurements, taken from the terminals to the
top of the ice cap, show that the nature of the surface cover features are correlated with
z0 rank in the following order: transition region > pure ice area or
pure snow area. The transition region forms a zone of maximum z0, which
shifts over the melting season from the terminals to the top of the ice cap. The observed z0
vs. energy items analysis indicated that LS (turbulent heat index) was
also an important determinant of ice aerodynamic surface roughness.
Aerodynamic surface roughness is a major parameter in calculations of
glacier surface turbulent heat fluxes. In previous studies investigators
used a constant z0 value for the whole surface of the glacier. This
study captures a much smaller-scale variation in spatial and temporal glacier
surface aerodynamic roughness through automatic and manual photogrammetric
observations. Such close observation of variation in z0 certainly
enhanced the accuracy of the surface energy balance models developed in the
course of this study.
This study was carried out at an ice cap with a neat ordering of its
annual layers. The August one ice cap moved slowly, no crevasses were
formed over the ice cap and channels were not considered in this study. In
this case, a more moderate variation in z0 was estimated than would be found
for debris-covered glaciers (Miles et al., 2017; Quincey et al., 2017).
Uneven or heterogeneous ice surfaces such as sastrugi, crevasses, channels
and penitents could greatly affect ice surface aerodynamic surface roughness,
and it would be hard to estimate its z0 based on a profile method. SfM
estimation of z0 might be a good choice at a macroscale. In the
accumulation season, more attention would need to be paid to spatial
and temporal variations in z0, as z0 is a key parameter for
sublimation calculation during this period. Studies have indicated that the
Lettau (1969) approach calculated z0 dependent on plot scale and
resolution. In this study, we only select 1 m×1 m scale at 1 mm
resolution to study spatial and temporal variability. Further
comparative studies of z0 are needed at different scales and
resolutions.
Data availability
All of the observation and
model input and output data presented in this study are available upon
request to the corresponding author (Rensheng Chen, crs2008@lzb.ac.cn).
Author contributions
JL and RC designed the
study and wrote the paper. JL and CH carried out field-based manual
photogrammetry observations.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We thank the editor and
the two reviewers for their insightful comments and ideas that improved the
paper.
Financial support
This research has been supported by the National Natural Science Foundation of China (grant nos. 41877163 and 41671029).
Review statement
This paper was edited by Valentina Radic and reviewed by Joshua Chambers and Evan Miles.
References
Albert, M. R. and Hawley, R. L.: Seasonal changes in snow surface roughness
characteristics at Summit, Greenland: implications for snow and firn
ventilation, Ann. Glaciol., 35, 510–514, doi:10.3189/172756402781816591,
2002.
Andreas, E. L.: Parameterizing scalar transfer over snow and ice: A review,
J. Hydrometeorol., 3, 417–432, 2002.
Andreas, E. L., Persson, P. O. G., Jordan, R. E., Horst, T. W., Guest, P.
S., Grachev, A. A., and Fairall, C. W.: Parameterizing turbulent exchange
over sea ice in winter, J. Hydrometeorol., 11, 87–104,
doi:10.1175/2009JHM1102.1, 2010.
Arck, M., and Scherer, D.: Problems in the determination of sensible heat
flux over snow, Geogr. Ann., 84, 157–169, doi:10.1111/1468-0459.00170,
2002.
Betterton, M. D.: Formation of structure in snowfields: Penitentes, suncups,
and dirt cones, Phys. Rev. E, 63, 056129, doi:10.1103/PhysRevE.63.056129,
2000.
Bintanja, R. and Van den Broeke, M.: Momentum and scalar
transfer-coefficients over aerodynamically smooth Antarctic surfaces,
Bound.-Lay. Meteorol., 74, 89–111, doi:10.1007/BF00715712, 1995.
Brock, B. W., Willis, I. C., and Sharp, M. J.: Measurement and
parameterization of aerodynamic roughness length variations at Haut Glacier
d'Arolla, Switzerland, J. Glaciol., 52, 1–17, 2006.
Chen, R. S., Song, Y. X., Kang, E. S., Han, C. T., Liu, J. F., Yang, Y.,
Qing, W. W., and Liu, Z. W.: A Cryosphere-Hydrology Observation System in a
Small Alpine Watershed in the Qilian Mountains of China and Its
Meteorological Gradient, Arct. Antarct. Alp. Res., 46,
505–523, doi:10.1657/1938-4262-46.2.505, 2014.
Clifton, A., Manes, C., Rueedi, J. D., Guala, M., and Lehning, M.: On
shear-driven ventilation of snow, Bound.-Lay. Meteorol., 126, 249–261,
doi:10.1007/s10546-007-9235-0, 2008.
Denby, B. and Smeets, C.: Derivation of turbulent flux profiles and
roughness lengths from katabatic flow dynamics, J. Appl.
Meteorol., 39, 1601–1612, 2000.
Denby, B. and Snellen, H.: A comparison of surface renewal theory with the
observed roughness length for temperature on a melting glacier surface,
Bound.-Lay. Meteorol., 103, 459–468, 2002.
Dong, W. P., Sullivan, P. J., and Stout, K. J.: Comprehensive study of
parameters for characterizing three-dimensional surface topography I: Some
inherent properties of parameter variation, Wear, 159, 161–171, 1992.
Fassnacht, S. R., Stednick, J. D., Deems, J. S., and Corrao, M. V.: Metrics
for assessing snow surface roughness from digital imagery, Water Resour.
Res., 45, W00D31, doi:10.1029/2008wr006986, 2009a.
Fassnacht, S. R., Williams, M., and Corrao, M.: Changes in the surface
roughness of snow from millimetre to metre scales, Ecol. Complex., 6,
221–229, doi:10.1016/j.ecocom.2009.05.003, 2009b.
Fitzpatrick, N., Radić, V., and Menounos, B.: A multi-season investigation of glacier surface roughness lengths through in situ and remote observation, The Cryosphere, 13, 1051–1071, https://doi.org/10.5194/tc-13-1051-2019, 2019.
Föhn, P. M. B.: Short-term snow melt and ablation derived from heat-and
mass-balance measurements, J. Glaciol., 12, 275–289, 1973.
Fonstad, M. A., Dietrich, J. T., Courville, B. C., Jensen, J. L., and
Carbonneau, P. E.: Topographic structure from motion: a new development in
photogrammetric measurement, Earth Surf. Proc. Land., 38,
421–430, doi:10.1002/esp.3366, 2013.
Garratt, J. R.: The Atmospheric Boundary Layer, Cambridge
University Press, New York, 1992.
Grainger, M. and Lister, H.: Wind speed, stability and eddy viscosity over
melting ice surfaces, J. Glaciol., 6, 101–127, 1966.
Greuell, W. and Smeets, P.: Variations with elevation in the surface energy
balance on the Pasterze (Austria), J. Geophys. Res.-Atmos., 106, 31717–31727, 2001.
Gromke, C., Manes, C., Walter B, Lehning, M., and Guala, M.: Aerodynamic
roughness length of Fresh snow, Bound.-Lay. Meteorol., 141, 21–34, doi:10.1007/s10546-011-9623-3, 2011.
Guo, S. H., Chen, R. S., Liu, G. H., Han, C. T., Song, Y. X., Liu, J. F.,
Yang, Y., Liu, Z. W., Wang, X. Q., and Liu, X. J.: Simple Parameterization
of Aerodynamic Roughness Lengths and the Turbulent Heat Fluxes at the Top of
Midlatitude August-One Glacier, Qilian Mountains, China, J. Geophys. Res.-Atmos., 123, 12066–12080, doi:10.1029/2018JD028875, 2018.
Guo, W., Liu, S., Xu, J., Wu, L., Shangguan, D., Yao, X., Wei, J., Bao, W.,
Yu, P., Liu, Q., and Jiang, Z.: The second Chinese glacier inventory: data,
methods and results. J. Glaciol., 61, 357–372,
doi:10.3189/2015jog14j209, 2015.
Hock, R. and Holmgren, B.: A distributed surface energy-balance model for
complex topography and its application to Storglaciären, Sweden, J. Glaciol., 51, 25–36, doi:10.3189/172756505781829566, 2005.
Irvine-Fynn, T., Sanz-Ablanedo, E., Rutter, N., Smith, M., and Chandler, J.:
Measuring glacier surface roughness using plot-scale, close-range digital
photogrammetry, J. Glaciol., 60, 957–969, doi:10.3189/2014JoG14J032,
2014.
James, M. R. and Robson, S.: Mitigating systematic error in topographic
models derived from UAV and ground-based image networks, Earth Surf.
Proc. Land., 39, 1413–1420, doi:10.1002/esp.3609, 2014.
James, M. R., Robson, S., and Smith, M. W.: 3-D uncertainty-based
topographic change detection with structure-from-motion photogrammetry:
precision maps for ground control and directly georeferenced surveys, Earth Surf. Proc. Land., 42, 1769–1788, doi:10.1002/esp.4125, 2017.
James, M. and Robson, S.: Straightforward reconstruction of 3D surfaces and
topography with a camera: Accuracy and geoscience application, J.
Geophys. Res.-Earth, 117, F03017, doi:10.1029/2011JF002289,
2012.
Javernick, L., Brasington, J., and Caruso, B.: Modeling the topography of
shallow braided rivers using Structure-from-Motion photogrammetry,
Geomorphology, 213, 166–182, doi:10.1016/j.geomorph.2014.10.006, 2014.
Konya, K. and Matsumoto, T.: Influence of weather conditions and spatial
variability on glacier surface melt in Chilean Patagonia, Theor.
Appl. Climatol., 102, 139–149, 2010.
Kuipers, H.: A relief meter for soil cultivation studies, Neth. J. Agr. Sci., 5, 255–262, 1957.
Lacroix, P., Legrésy, B., Coleman, R., Dechambre, M., and Rémy, F.:
Dual-frequency altimeter signal from Envisat on the Amery ice-shelf, Remote
Sens. Environ., 109, 285–294, doi:10.1016/j.rse.2007.01.007, 2007.
Lacroix, P., Legrésy, B., Langley, K., Hamran, S., Kohler, J., Roques,
S., Rémy, F., and Dechambre, M.: In situ measurements of snow surface
roughness using a laser profiler, J. Glaciol., 54, 753–762,
doi:10.3189/002214308786570863, 2008.
Lehning, M., Bartelt, P., Brown, B., and Fierz, C.: A physical SNOWPACK
model for the Swiss avalanche warning: Part III: meteorological forcing,
thin layer formation and evaluation, Cold Reg. Sci. Technol.,
35, 169–184, doi:10.1016/S0165-232X(02)00072-1, 2002.
Lettau, H.: Note on aerodynamic roughness parameter estimation the basis of
roughness element description, J. Appl. Meteorol., 8, 828–832, 1969.Lliboutry, L.: The origin of penitents, J. Glaciol., 2, 331–338, 10.3189/S0022143000025181, 1954.
Manninen, T., Anttila, K., Karjalainen, T., and Lahtinen, P.: Automatic snow
surface roughness estimation using digital photos, J. Glaciol.,
58, 993–1007, doi:10.3189/2012JoG11J144, 2012.
Matthes F. E.: Ablation of snow-fields at high altitudes by radiant solar heat, T. AGU, 15, 380–385, 1934.
McClung, D. and Schaerer, P. A.: The avalanche handbook, The Mountaineers
Books, Seattle, WA, 2006.
McIntyre, N. F.: Cryoconite hole thermodynamics, Can. J. Earth
Sci., 21, 152–156, 1984.Miles, E. S., Steiner, J. F., and Brun, F.: Highly variable aerodynamic
roughness length (z0) for a hummocky debris-covered glacier, J. Geophys. Res.-Atmos., 122, 8447–8466, doi:10.1002/2017JD026510,
2017.
Munro, D. S.: Surface roughness and bulk heat transfer on a glacier:
comparison with eddy correlation, J. Glaciol., 35, 343–348,
doi:10.3189/S0022143000009266, 1989.
Nield, J. M., King, J., Wiggs G. F. S., Leyland, J., Bryant, R. G.,
Chiverrell, R. C., Darby, S. E., Eckardt, F. D., Thomas, D. S. G., Vircavs,
L. H., and Washington, R.: Estimating aerodynamic roughness over complex
surface terrain, J. Geophys. Res.-Atmos., 118,
12948–12961, doi:10.1002/2013JD020632, 2013.
Oke, T. R.: Boundary layer climates, Routledge, London, 1987.
Oveisgharan, S. and Zebker, H. A.: Estimating snow accumulation from InSAR
correlation observations, IEEE T. Geosci. Remote, 45, 10–20, doi:10.1109/TGRS.2006.886196, 2007.
Passalacqua, P., Belmont, P., Staley, D. M., Simley, J. D., Arrowsmith, J.
R., Bode, C. A., Crosby, C., DeLong, S. B., Glenn, N. F., Kelly, S. A.,
Lague, D., Sangireddy, H., Schaffrath, K., Tarboton, D., Wasklewicz, T., and
Wheaton, J. M.: Analyzing high resolution topography for advancing the
understanding of mass and energy transfer through landscapes: A review,
Earth-Sci. Rev., 148, 174–193, doi:10.1016/j.earscirev.2015.05.012, 2015.Qing, W., Han, C. T., and Liu, J.: Surface energy balance of Bayi Ice Cap in the middle of Qilian Mountains, China, J. Mt. Sci., 15, 1229–1240, 10.1007/s11629-017-4654-y, 2018
Quincey, D., Smith, M., Rounce, D., Ross, A., King, O., and Watson, C.:
Evaluating morphological estimates of the aerodynamic roughness of debris
covered glacier ice, Earth Surf. Proc. Land., 42, 2541–2553, doi:10.1002/esp.4198, 2017.
Rees, W. G.: A rapid method of measuring snow-surface profiles, J. Glaciol., 44, 674–675, doi:10.3189/S0022143000002197, 1998.
Rees, W. G. and Arnold, N. S.: Scale-dependent roughness of a glacier
surface: implications for radar backscatter and aerodynamic roughness
modelling, J. Glaciol., 52, 214–222, doi:10.3189/172756506781828665,
2006.
Rhodes, J. J., Armstrong, R. L., and Warren, S. G.: Mode of formation of
“ablation hollows” controlled by dirt content of snow, J. Glaciol., 33, 135–139, 1987.
Rippin, D. M., Pomfret, A., and King, N.: High resolution mapping of
supra-glacial drainage pathways reveals link between micro-channel
drainage density, surface roughness and surface reflectance, Earth Surf.
Proc. Land., 40, 1279–1290, doi:10.1002/esp.3719, 2015.
Rounce, D. R., Quincey, D. J., and McKinney, D. C.: Debris-covered glacier energy balance model for Imja–Lhotse Shar Glacier in the Everest region of Nepal, The Cryosphere, 9, 2295–2310, https://doi.org/10.5194/tc-9-2295-2015, 2015.
Schneider, C.: Energy balance estimates during the summer season of glaciers
of the Antarctic Peninsula, Global Planet. Change, 22, 117–130, doi:10.1016/S0921-8181(99)00030-2, 1999.
Smeets, C. J. P. P., and Van den Broeke, M. R.: Temporal and spatial
variations of the aerodynamic roughness length in the ablation zone of the
Greenland ice sheet, Bound.-Lay. Meteorol., 128, 315–338, doi:10.1007/s10546-008-9291-0, 2008.
Smeets, C. J. P. P., Duynkerke, P. G., and Vugts, H. F.: Turbulence
characteristics of the stable boundary layer over a mid-latitude glacier.
Part II: Pure katabatic forcing conditions, Bound.-Lay. Meteorol., 97,
73–107, 2000.
Smeets, C., Duynkerke, P., and Vugts, H.: Observed wind profiles and
turbulence fluxes over an ice surface with changing surface roughness,
Bound.-Lay. Meteorol., 92, 101–121, 1999.
Smith, M. W., Quincey, D. J., Dixon, T., Bingham, R. G., Carrivick, J. L.,
Irvine-Fynn, T. D. L., and Rippin, D. M.: Aerodynamic roughness of glacial
ice surfaces derived from high-resolution topographic data, J.
Geophys. Res.-Earth, 121, 748–766, doi:10.1002/2015JF003759,
2016.
Smith, M. W.: Roughness in the earth sciences, Earth-Sci. Rev., 136,
202–225, 2014.Steiner, J. F., Litt, M., Stigter E. E., Shea, J., Bierkens M. F. P., and
Immerzeel W. W.: The importance of turbulent fluxes in the surface energy
balance of a debris-covered glacier in the Himalayas, Front. Earth
Sci., 6, 144, doi:10.3389/feart.2018.00144, 2018.
Sun, W. J., Qin, X., Wang, Y. T., Chen, J. Z., Du, W. T., Zhang, T., and
Huai, B. J.: The response of surface mass and energy balance of a
continental glacier to climate variability, western Qilian Mountains, China,
Clim. Dynam., 50, 3557–3570, doi:10.1007/s00382-017-3823-6, 2018.
Takeuchi, N., Sakaki, R., Uetake, J., Nagatsuka, N., Shimada, R., Niwano,
M., and Aoki, T.: Temporal variations of cryoconite holes and cryoconite
coverage on the ablation ice surface of Qaanaaq Glacier in northwest
Greenland, Ann. Glaciol., 59, 21–30, doi:10.1017/aog.2018.19, 2018.
Wendler, G. and Streten, N.: A short term heat balance study on a coast
range glacier, Pure Appl. Geophys., 77, 68–77, 1969.
Westoby, M. J., Brasington, J., Glasser, N. F., Hambrey, M. J., and Reynolds,
J. M.: “Structure-from-Motion” photogrammetry: A low-cost, effective tool
for geoscience applications, Geomorphology, 179, 300–314, doi:10.1016/j.geomophy.2012.08.021, 2012.