Introduction
Due to a variety of ice particle types and shapes,
representation of winter precipitation in models
and in ground, airborne and satellite remote sensing retrievals
is a topic of continuous interest.
Both models and retrieval algorithms rely on a prior knowledge of snowflake
mass (or density), shape and fall velocity, which are typically expressed as
functions of a characteristic particle size .
Furthermore, information on possible particle size distributions (PSDs) is also
required. Even though some of the microphysical properties of ice particles
are not independent, e.g., fall velocity can be computed from particle mass
and shape
, the
remaining degrees of freedom are rather numerous.
Historically, measurements of snowflake properties have been carried out on a
particle-by-particle basis e.g.,. While
we may still regard such measurements as the more precise and detailed, these studies are limited to a relatively small number of
observed ice particles due
to the sheer amount of time needed for such experiments and corresponding
data analysis. After the introduction of robust optical instruments
capable of measuring particle size, shape and in some cases fall velocity,
e.g., 2-D-video disdrometer 2-DVD;,
particle size velocity (Parsivel) laser-optical disdrometer
, hydrometeor velocity size detector
HSVD;, snow video imager SVI;
and multi-angle snowflake camera MASC;, continuous
recording of ice particle properties became possible. It should be noted that, in
comparison to surface-based observations, aircraft measurements have a much
longer history in determining ice particle microphysical properties and were
carried out in different types of clouds and climate regimes
. A typical limitation of automatic observations of ice
particle properties, however, is that only a subset of needed parameters is
directly measured.
By combining optical disdrometer observations with other measurements, e.g.,
by radar or precipitation gauge, physical properties such as mean snow
density can be derived. have used a C-band weather radar
observations of equivalent reflectivity factor, Ze, in combination
with a 2-DVD to derive a snow density–dimensional relation and to infer more
consistent Ze–snowfall rate relations. Another method for snow
density retrieval is based on solving aerodynamic equations to derive
particle mass from observed fall velocity and particle effective projected
area as proposed by and applied by and
more recently by and . ,
hereafter referred to as B07, used a combination of a weighing gauge and a
2-DVD to derive a relation between mean bulk density and median volume
diameter and to document relations
between PSD parameters for Colorado winter storms. Their approach is similar
to the one used by , who have combined aircraft PSD and
ice water content observations to derive mean snow density and average
mass–dimensional relations for ice particles. Albeit using slightly different
definitions, both B07 and derive effective ice
densities for ensembles of ice particles, but there is a difference in
terminology. and many others have used the term
(particle) bulk density to refer to the density of individual ice or snow
particles defined as the ratio of mass of a particle with a size D to its
assumed volume: ρ=ρ(D). In most of such cases, the word “bulk” is
used to emphasize the inclusion of hollows within particles. The term
“(mean) bulk density” is sometimes used also when referring to the mean
density of an ensemble of particles representing the whole PSD, i.e.,
ρ‾=ρ‾(D0) (e.g., B07), whereas
used the term “population-mean effective density”.
In this study we derive the volume flux weighted snow density, similar to,
e.g., B07, and refer to it as ensemble mean density, ρ‾, to
avoid possible confusion.
This paper documents the connection between ensemble mean density and other
microphysical properties of snow as observed in Southern Finland. Using the
estimated ρ‾, average mass–dimensional relations
characteristic to studied snowfall events are defined. In order to derive
ensemble mean density, a method proposed by B07 was used. However, instead of
a 2-DVD, a new generation of the SVI is employed. It is shown that, despite
simpler construction compared to the 2-DVD, this instrument's data are
suitable for such studies.
Even though this study is based on retrieval of ensemble mean snow density
and not mass–dimensional relations directly, which could be more easily
applied to radar retrievals and numerical weather prediction (NWP), there are
a number of applications of such relations. used
ρ‾(D0) to convert PSD observations to
precipitation rate. , , , and used
mean snow density–median volume diameter relations for characterizing winter
precipitation microphysics by radar. showed a connection
between mean snow density and multi-frequency radar observations.
used the density relation by B07, and
applied a similar density retrieval method to improve parametrization of snow
microphysics in NWP models, for example.
Liquid water equivalent precipitation accumulation measured with
Pluvio2 200 and 400, change in snow depth and maximum and minimum
temperature, maximum and minimum relative humidity, mean and maximum wind
speed and mean wind direction of the studied snow events. Events before the
horizontal line are recorded during the BAECC campaign.
LWE (mm)
ΔSD
Temp (∘C)
RH (%)
Wind (m s-1, ∘)
Event
200
400
(cm)
min
max
min
max
mean
max
mean dir.
2014 Jan 31 21:00–Feb 01 06:00
7.4
7.3
5.1
-9.8
-8.9
84
91
1.6
2.9
138
2014 Feb 12 04:00–1:00
1.0
0.9
1.8
-1
0
96
98
0.6
2.0
170
2014 Feb 15 21:00–Feb 16 03:00
2.6
2.6
2.5
-2.1
-1
86
97
1.9
2.7
140
2014 Feb 21 16:00–Feb 22 05:00
5.5
5.2
3.6
-2.7
0
88
98
2.1
3.4
138
2014 Mar 18 08:00–19:00
4.4
4.0
7.3
-3.8
-1.8
76
96
1.2
2.7
155
2014 Mar 20 16:00–23:00
6.1
5.9
4.8
-4.3
-1.3
89
97
2.0
3.4
146
2014 Nov 06 19:00–Nov 07 14:30
10.5
–
10.3
-2.44
-1.6
95
97
0.8
1.9
238
2014 Dec 18 14:00–19:00
2.6
2.2
3.9
-2.3
-0.8
97
98
1.0
1.8
134
2014 Dec 24 08:30–13:00
1.3
1.2
1.2
-9.2
-8.9
90
91
0.7
1.5
204
2014 Dec 30 00:30–14:00
6.3
5.3
4.9
-10.4
-0.6
91
98
–
–
–
2015 Jan 3 09:00–23:50
7.3
7.3
11.9
-3.9
0
96
98
2.6
5.2
318
2015 Jan 7 01:00–20:10
5.4
4.8
2.2
-6.5
-0.8
92
97
1.3
2.8
181
2015 Jan 8 06:00–13:30
2.6
2.7
1.6
-1.9
0
97
99
1.0
2.2
155
2015 Jan 9 18:00–Jan 10 06:00
3.1
3.1
4.6
-3.7
-0.2
95
98
1.0
3.0
286
2015 Jan 10 22:00–Jan 11 09:00
0.7
0.6
0.7
-12.6
-4.4
88
95
1.6
3.4
207
2015 Jan 12 21:00–Jan 13 08:30
12.8
10.9
9.6
-15.7
-9.0
88
94
1.3
3.1
181
2015 Jan 13 22:00–Jan 14 07:00
–*
2.2
1.9
-8.0
-0.3
94
98
0.5
1.9
134
2015 Jan 16 01:30–07:30
–*
5.8
5.2
-1.3
-0.6
92
98
1.9
3.4
154
2015 Jan 18 16:00–21:00
1.9
1.9
2.7
-2.4
-0.3
95
97
1.2
2.6
300
2015 Jan 22 21:00–Jan 23 04:30
2.1
2.0
2.3
-13.3
-12.5
87
90
–
–
–
2015 Jan 23 15:00–23:00
1.4
1.2
1.4
-10.1
-8.8
91
93
0.3
1.0
205
2015 Jan 25 09:00–16:00
2.8
2.5
1.9
-2.4
-1.7
96
97
0.7
1.7
170
2015 Jan 31 12:00–Jan 31 23:15
7.0
6.6
5.7
-1.9
-0.4
92
97
1.2
2.6
175
* Pluvio2 400 was used because data from Pluvio2 200
were unavailable.
Measurements
Measurement setup
Measurements were made at the University of Helsinki Hyytiälä
Forestry Field Station, Finland (61∘50′37′′ N,
24∘17′16′′ E), during the Biogenic Aerosols Effects on clouds
and Climate (BAECC) field campaign and during the
consecutive winter of 2014/15. BAECC was a joint experiment between the
University of Helsinki, the Finnish Meteorological
Institute (FMI) and the United States
Department of Energy Atmospheric Radiation Measurement (ARM) program. From 1
February through 12 September 2014 the second ARM Mobile Facility (AMF2) was
deployed to the measurement site. The measurement setup was designed for
snowfall intensive observation period of BAECC, called BAECC Snowfall Experiment (SNEX), which
was undertaken from 1 February though 30 April 2014 and focused on
measurements of snow microphysics. However, in order to extend the dataset,
the measurements were continued upon completion of BAECC. In total, 23
snowfall cases from winters 2013/14 and 2014/15 were used in this study as
summarized in Table . The snowfall cases were selected based
on measurements of liquid water equivalent (LWE) precipitation accumulation
by a weighing gauge, snow depth using a laser sensor and temperature measured
by the automatic weather station of the FMI located 500 m distance from the measurement site. Only
precipitation cases, where temperature was below or equal to 0 ∘C,
were chosen, and the data were omitted when occasionally the temperature
during the event rose above 0 ∘C.
The experiments in both winters were organized in collaboration with the
National Aeronautics and Space Administration (NASA) Global Precipitation
Measurement (GPM) mission ground validation program. The surface
precipitation measurements are carried out using a number of collocated
instruments, such as NASA Particle Imaging Package (PIP), two OTT Pluvio2
weighing gauges, two Parsivel2 laser disdrometers , a 2-DVD
and a laser snow depth sensor by Jenoptik. To minimize effects of wind, a
Double-Fence Intercomparison Reference (DFIR) wind protection
was build on site as shown in
Fig. and discussed in more detail in
. Inside of the DFIR, the 2-DVD, one of the OTT
Pluvio2s and one of the Parsivel2 disdrometers were placed. In addition
to the precipitation sensors, 3-D anemometers were deployed. The wind
measurements were carried out at the heights of precipitation instrument
sampling volumes. In this study data from the NASA PIP disdrometer and both
OTT Pluvio2 gauges are used.
Particle Imaging Package
The NASA PIP is the new generation of the SVI. The PIP,
like the SVI, consists of a halogen lamp and a charge-coupled device
full frame camera with sensor resolution of 640×480 pixels. The main
differences between PIP and SVI are the camera and improved software. The
camera is now capable of imaging with a frame rate of 380 frames per second,
enabling measurements of particle fall velocities. The distance between the
lamp and the camera lens is approximately 2 m. The lens focus is set at
1.3 m, where the field of view (FOV) is 64×48 mm, and the image
resolution thereby 0.1×0.1 mm. The main advantage of PIP, as well
of SVI, over other disdrometers is the open particle catch volume, which
minimizes effect of wind on quantitative precipitation measurements
.
Snow precipitation instruments on the measurement field in
Hyytiälä. The Pluvio2 200 is inside the wind protection on a
platform and the PIP lamp can be seen at right on the ground. The view of the
picture is to southwest and the distance from the platform to the treeline
behind is approximately 20 m.
![]()
The instrument records shadows of particles as they fall through the
observation volume. Given the camera frame rate, multiple images of a
particle are recorded and used to estimate its fall velocity. The depth of
field (DOF) is determined by the processing software either rejecting or not
detecting particles that are out of focus. Thus, the observation volume is
defined by the FOV and the DOF. The expected particle size error due to the
blurring effect is 18 % . From the recorded particle
images a number of parameters describing particle geometrical properties are
calculated with National Instruments IMAQ software. The measured diameter is
given as the equivalent area diameter, which is the diameter of a circle with
the same area as the area of a particle shadow. Other parameters, such as
particle orientation, and bounding box width and height are also recorded.
The aspect ratio of a particle is derived by fitting an ellipse to the
bounding box utilizing the orientation of the particle. The aspect ratio is
the minor axis in respect to major maxis of the fitted ellipse. The major
axis also defines the minimum circumscribing disk, and the area ratio is
defined as total area of shadowed pixels in respect to area of the
circumscribing disk.
Weighing gauges and anemometers
The measurement setup includes two OTT Pluvio2 weighing gauges, one inside
and one outside the DFIR, with orifices of 200 and 400 cm2, respectively.
There are differences in wind shielding as well. The Pluvio2 200 is
equipped with a Tretyakov wind shield and the Pluvio2 400 with a
combination of Tretyakov and Alter wind shields, as seen in the forefront in
Fig. .
The gauges output several products of precipitation rate and accumulation. In
this study, a non-real-time accumulation product is used as it is filtered
for various sources of errors such as changes in the bucket mass due to
evaporation, and as such should yield the most precise precipitation rate
estimate among the output products. Because of the filtering, there is a
5 min delay in the recorded time series, which needs to be taken into account
when comparing to other instruments. The precipitation accumulation values
are recorded with a resolution of 0.001 mm, but non-real-time accumulation is
output with a resolution of 0.05 mm.
The 3-D anemometer manufactured by Gill is located approximately at the
height of the PIP on the field, respectively. The wind parameters, horizontal
and vertical speed and horizontal direction, of Gill anemometer are measured
every 10 s and averaged over 60 s. The mean and maximum of the 60 s wind
speed averages and the mean wind direction for each event are given in the
Table .
Snow depth sensor
The laser snow depth sensor, Jenoptik SHM30, is located on the measurement
field, next to Pluvio2 400. It is an optical sensor, which measures the
snow depth by comparing signal phase information of the modulated visible
laser light. It is a point measurement, and hence the piling of wind driven snow
or random branches and leaves drifting on the snow pack can cause
misreadings. To reduce this we have sheltered the measurement spot with a
small wind fence and the instrument structure excluding the measurement pole
is buried under the ground to prevent the piling of snow. The data are
recorded every minute.
Retrievals of ensemble mean density, velocity–dimensional relations and PSD
Observations from the PIP and one of the weighing gauges are combined to
retrieve snow ensemble mean density. Typically the gauge located inside of
the DFIR, the Pluvio2 200, is used for this retrieval. On a couple of days
this gauge was not operational and data from the Pluvio2 400 located
outside of the DFIR were used instead. These dates are marked in
Table with asterisks in the LWE precipitation rate column. As
seen in the Table the differences in accumulated LWE recorded
by the two Pluvio2s are small, the largest being 15 %. Pluvio2 200
inside the DFIR is typically measuring higher accumulations, which is
expected because of the better wind protection. However, the observations do
not show a clear indication that the observed precipitation accumulation
difference depends on the wind speed. However, the difference seems to
increase in respect to certain wind directions. There are two openings from
the measurement field, one to a road crossing (approx. 130∘) and the
other to small field (approx. 180∘). If the wind is blowing from
these directions the difference between the two gauges seem to increase.
The retrieval procedure is described below and is similar to the one
presented by B07, but with notable modifications. Prior to retrieval of
ρ‾, PSD and velocity–dimensional relations are estimated. It
was found, however, that the density retrieval is highly sensitive to the
integration time. To minimize this, a variable integration time determined by
the precipitation accumulation is used. The same integration time was applied
to compute PSD parameters and v–D relations.
The ratio of the diameter observed by PIP, DPIP, to
volume equivalent diameter D.
![]()
Particle size distribution
The PSDs are calculated from the PIP records of particles that fell through
the observation volume. The observed distributions are defined with respect
to equivalent area diameter DPIP, which is different from the
apparent diameter of the 2-DVD and maximum particle dimensions used in other
studies e.g.,. studied differences
between diameter definitions and found that the diameter recorded by SVI is
approximately 0.82 of maximum particle dimension. We performed a similar
study by examining mean dimensions of rotated ellipsoids on a single
projection, as shown in Fig. . The ellipsoids were defined by
a long dimension a and a short dimension b lying nominally in the
horizontal plane along the x and y-axes, respectively, and a short
vertical dimension c lying nominally along the z-axis. The particle
orientation was defined by Gaussian distribution of canting angles with a
standard deviation of 9∘ and a uniform
distribution of azimuth angles. The equivalent area diameters
DPIP of simulated particles were estimated from their projected
areas onto the x–z plane and the resulting values were averaged over all
orientations. The ratios of mean DPIP to the particle volume
equivalent diameter, i.e., the diameter for which the particle volume
V(D)=π6D3, for a number of combinations of vertical and
horizontal aspect ratios are shown in Fig. . Assuming
spheroids and taking the typical vertical aspect ratio
c/a=0.6 , we found that
DPIP is roughly equal to 0.92 of a volume equivalent diameter.
As can be seen, the conversion factor varies between 0.8 and 1. For ice
particles with axis ratios smaller than 0.4, i.e., pristine ice crystals, this
factor could approach 1.2. From this analysis we can conclude that the
largest expected error is associated with observations of ice crystals.
Dimensions of snowflake aggregates and graupel like particles are expected to
be captured with a smaller error. In this study the same conversion factor of
0.92 is used for all the cases. As can be seen in
Fig. the median area and aspect ratios of the
particles are 0.65 and 0.72, respectively. These observations also support
our choice of a mean particle shape and the corresponding diameter
transformation. Therefore, the results presented in the rest of the
paper are using this volume equivalent diameter proxy.
The distributions of snowflake (a) aspect ratio and
(b) area ratio as observed using PIP with interquartile ranges
visualized and median values shown.
![]()
Prior to calculations of PSD parameters, recorded PSD data are filtered to
remove spurious observations of large particles. Following the procedure
described in , records of large particles were ignored if
there was a gap of more than three consecutive PSD diameter bins. The bin
size was set to 0.25 mm during the BAECC experiment and it was reduced to
0.2 mm for the winter 2014/2015. The PIP resolution is 0.1 mm and the
minimum detectable particle diameter is approximately 0.3 mm
. The smallest diameter bin used in calculations is 0.25 to
0.5 mm during BAECC and 0.2 to 0.4 mm in the following winter.
The PSD parameters were calculated using method of moments and assuming that
PSD follows gamma functional form; see for example and
citations therein. The normalized gamma distribution N(D) in
mm-1m-3 was adopted
following , and :
N(D)=Nwf(μ)DD0μexp(-ΛD),f(μ)=63.674(3.67+μ)μ+4Γ(μ+4),Λ=3.67+μD0,
with Nw in mm-1m-3 being the intercept parameter,
D0 the median volume diameter in mm, Λ the slope parameter in
mm-1 and μ the shape parameter. Using the second, fourth and
sixth moments for the non-truncated gamma PSD, M2, M4 and M6, the
PSD parameters were estimated as follows:
η=M42M6M2,μ=7-11η-η2+14η+12(η-1),Λ=M2Γ(μ+5)M4Γ(μ+3),D0=3.67+μΛ.
Ensemble mean density retrieval
The integration time, τ(t), of the ensemble mean density retrieval is
driven by precipitation measurements of the Pluvio2. The step of the
non-real-time accumulation output is 0.05 mm, causing the output interval to
be on the order of several minutes even at moderate snow rates. With a short
fixed integration time in timescales of minutes or tens of minutes, the
produced ensemble mean density estimation would hence be more unstable,
the lower the precipitation rate. Therefore, variable length time intervals
driven by the gauge output are used with a selected threshold value of
0.1 mm. This corresponds to a τ(t) of 6 min for a LWE precipitation
intensity of 1 mm h-1. Effectively, the temporal resolution of the
ensemble mean density retrieval is increased with increasing precipitation
intensity, and in the analysis of the snowfall events in
Table the median τ(t) was 5 min.
As the integration time τ(t) is effectively driven by precipitation
intensity, there is less variation in number of particles between intervals
compared to a fixed time interval approach. With the selected accumulation
threshold there are typically between 103 and 104 particles within a
given integration time interval. However, with low precipitation
intensities, τ(t) increases up to 1 h and retrieved
ρ‾ becomes less representative for the time interval in
question. With LWE precipitation rates lower than 0.2 mm h-1, the
resolution of Pluvio2 LWE measurements is insufficient and calculations of
ρ‾ become overly sensitive to recorded number concentrations.
Correspondingly, similar unwanted sensitivity to LWE precipitation
accumulation occurs when the number of particles observed by PIP within
τ(t) is less than 800. Therefore, time intervals with precipitation
rates or particle counts lower than these thresholds are excluded from our
analysis.
Given a population of solid precipitation particles with volume equivalent
diameters D over the integration time τ(t), the liquid equivalent
precipitation accumulation in millimeters is approximately
G(t)≈π6×10-6ρ‾ρw∫tt+τ(t)∫DminDmaxD3v(D,t)N(D,t)dDdt,
where ρ‾ is the volume flux weighted population mean snow
density in g cm-3, ρw=1 g cm-3 is the density of
liquid water, N(D,t) is mean particle number concentration over the
integration time in mm-1 m-3, v(D,t) is particle velocity
relation in m s-1 and Dmin,Dmax is the size
range of snowflake observations from a disdrometer. From Eq. ()
we can estimate volume flux weighted snow density for each observation time
interval as
ρ‾(t)≈6π×106ρwG(t)∫tt+τ(t)∫DminDmaxD3v(D,t)N(D,t)dDdt,
using liquid equivalent precipitation accumulation G(t) as measured by the
Pluvio2 gauge, and retrieving averaged N(D,t) and volume flux using
fitted v(D,t) based on measurements by the PIP as described in the
following sections. It should be noted that, unlike in the retrieval of PSD
parameters where gamma PSD was assumed, ρ‾ was retrieved
without making any assumptions on the shape of the PSD distribution and
instead measured PSDs are used in the calculations.
Comparison of derived mean density to snow depth observations
The definition of ensemble mean density here is the same as for mean bulk
density in B07. They determine the densities for 5 min precipitation volumes
derived with a 2-DVD disdrometer observations together with precipitation
mass measured by a weighing gauge. B07 defined the volume of a single
particle by summing coin-shaped sub-volumes together, estimated separately for
both orthogonal projections and taking geometrical mean. As the diameter used
in our study is the estimated volume-equivalent diameter, our results are
comparable to B07. In , the volume of a single particle
is defined as a function of circumscribing maximum diameter, and the
population mean effective density is determined from ice water content.
The estimated ensemble mean snow density is volume-weighted and expected to
have lower values than the velocity-weighted snow density. The difference is
not generally prominent especially with low-density aggregates, whose
velocity–dimensional dependence is weak.
It should be noted that the derived density is inversely proportional to the
snow ratio, Rs, assuming that issues related to packing of
snowflakes on the ground can be ignored. The snow ratio
is used by operational weather services to
estimate change in snow depth from LWE observations and can be defined as
follows:
Rs(t)=1P⋅Cρwρ‾(t),
where ρ‾(t) is the volume flux weighted snow density derived
as shown in Eq. (), P is the packing efficiency of
snowflakes and C is the snow compression. Assuming that the packing and
compression terms, or their product, are close to unity, the derived density
can be tested against the commonly used assumption that 1 mm of LWE
accumulation corresponds to 1 cm change in snow depth. In
Fig. the combined distribution of estimated snow ratios
on temporal scales defined by the gauge accumulation for all the 23 events
analyzed in this study is shown. It can be seen that the mean and median
values, equal to 10 and 9, respectively, are very close to the commonly
assumed value.
Distribution of snow ratios, ratio of snow depth change to LWE,
calculated from retrieved ensemble mean densities with interquartile range,
and median and mean values.
![]()
This analysis assumes that packing efficiency of snowflakes is 100 % and
compression of snow on the ground can be ignored or that snow compression
counteracts reduction in snow density due to packing. The packing efficiency
of snowflakes on the ground is not known. Random packing of the same size
spheres has density of 64 % and dense packing of such spheres uses
74 % of the volume, corresponding to P=0.64 and 0.74, respectively.
Packing efficiency of equal spheroids depends on axis ratios, exceeding that
of spheres, and could exceed 77 % . It is not
unreasonable to expect that irregular shaped particles of variable sizes,
such as snowflakes, would pack more efficiently than equal spheroids. At
least, packing efficiency in excess of 90 % can be expected for spheres
of several radii . The packing efficiency of 70 % would
mean that density of freshly fallen snow would be 30 % lower than that of
falling snowflakes. The packing efficiency of 80 % would correspond to
20 % bias in estimated snowflake density from snow depth measurements or
in 25 % underestimation of the snow depth change by using
ρ‾(t). We do not know the exact value of the snow packing, but
we could expect that in the worst case scenario it is about 70 % and
probably closer to 80 % or even higher. It should also be noted that the
snow compression would counteract this, but we are considering only freshly
fallen snow and expect that the compression factor C is very close to
unity.
One of the major uncertainties in the density retrieval is the assumption
about particle volume. In this study we have assumed that snowflakes are
spheroids with axis ratios of 0.6. Given this assumption, a conversion factor
relating volume equivalent and observed disc equivalent diameters was
defined. Figure shows that for a reasonable range of
ellipsoid axis ratios this conversion factor can range between 0.8 and 1.
This range of values implies that the uncertainty in the density estimation
can range from an overestimation by as much as 50 % to an underestimation
by about 20 %. This range of uncertainty is much larger than what is
expected from a comparison of the retrieved volume-flux weighted density and
snow depth measurements, as was discussed previously. Therefore, by comparing
the PIP derived and the directly measured snow depths, the validity of the
derived values of ρ‾, and assumption of particle shape, can be
checked. In Fig. hourly change in the snow depth
measured by the Jenoptik SHD30 is compared to the PIP derived snow depth. It
can be seen that the agreement is good, with RMSE of 0.30 cm, linear
correlation coefficient of 0.88 and normalized bias as low as -0.06. This
comparison also gives confidence about the validity of the derived ensemble
mean densities.
Scatterplot of the hourly change of snow depth measured with
Jenoptik SMH30 and estimated from volume flux using PSD and fall velocities
as measured by PIP. The data include all the studied cases except
10–11 January 2015.
![]()
Effect of PSD truncation on derived ensemble mean snow density
The observed PSDs are truncated on left and right sides .
They are truncated on the right side because of the instrument finite
sampling volume and because natural sizes of hydrometeors do not extend to
infinity. The truncation on the left, on the small-diameter side, is due to
instrumental limitations and possible wind effects .
have presented a comprehensive analysis on how the
right-side truncation affects the derived gamma PSD parameters. A similar
study on the effects of the left-side truncation and other instrumental
effects was presented by . Here we apply the method
presented by to estimate impact of PSD truncation on the
derived mean snow density.
To investigate the impact of the PSD truncation on retrieval of mean snow
density, a simulation study was performed. To initiate the simulation, the
PSD parameters Nw, D0 and μ, together with parameters of
m–D and v–D, are used. During the study it was found that the
density estimation error is most sensitive to D0 and μ and virtually
independent of the other input parameters. Therefore, the results presented
here assume that Nw is constant and equal to
104 mm-1 m-3. Further, only one m–D relation
representative of all BAECC cases, as presented in Sect. ,
is selected, and v–D representative of the snowfall with mean density
ranging between 100 and 200 g cm-3 is utilized. The D0 values were
varied between 0.5 and 4 and μ values between -0.9 and 3.
At the first stage of the simulation, the number of observed particles was
computed, assuming a Poisson distribution, with the expected number of
particles being determined by PIP sampling volume and
τ(t). Given this number of
particles, their diameters were found by sampling a gamma probability density
function, parameters of which are determined by the input PSD. To simulate
the left-side truncation all particles with diameters smaller or equal to
0.25 mm, the PIP sensitivity threshold, were rejected. The right-side
truncation was achieved by rejecting particles with sizes exceeding 3D0.
For each D0 and μ pair, 50 simulated PSDs were computed. Given the
simulated truncated PSD the density is estimated in the same way as was
presented above. This estimated density is compared to the one that is
directly derived from the simulation input parameters and the results of
their comparison is shown in Fig. . As one can
see, the derived ensemble mean snow density is biased. The bias is largest
for small D0, which is explained by the left-side PSD truncation. For
D0 larger than 1 mm, the bias decreases and approaches 2 %. Given
that the error associated with PSD truncation is rather small for D0>
1 mm, and that most of the observations fall within this range, the
truncation error is not corrected in this study.
Computed normalized bias and standard deviation of estimated mean
snow density as a function of μ and D0. The shaded area indicates data
that are not included in the analysis because derived D0 is smaller than
0.6 mm. The increased values of bias at low D0 values is due to left side
truncation of the observed PSD, which is caused by the instrument
sensitivity. At larger D0 values the bias approaches value of 0.02.
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Velocity–dimensional analysis
For the retrieval of volume flux weighted snow density, velocity–dimensional
relations of falling snow need to be estimated. For each integration time
interval, v(D)=avDbv is fitted for velocity–diameter
data from the PIP. The v(D) power-law fits to unfiltered data tend to be
strongly biased by outliers. To address this problem, Gaussian kernel density
estimation KDE; is used to find the most probable
velocity for each diameter bin, and only observations with velocities within
half width at half maximum from the bin peak KDE value are included in
calculating the fit. Using the linear least squares method, a fit is
performed for the data points in log–log scale to derive a power-law
relation. It should be noted that using linear regression in log–log space
does not optimally minimize residuals in linear space, but the method is used
here as it does not overly emphasize the large end of the size spectrum. The
retrieved velocity fits are shown for selected integration time intervals of
the 18 March 2014 and the 22–23 January 2015 cases in the bottom of
Figs. and , respectively.
It should be noted that the power-law model, albeit widely used, may not
necessary represent correctly velocities of ice particles over the complete
range of diameters . In many cases the fit can also be
uncertain either because of narrow PSD or in presence of multiple particle
types.
Conclusions
Microphysical properties of snow in Southern Finland were documented using
observations from PIP and a weighing gauge. The data were collected during US
DOE ARM funded BAECC campaign and the consecutive winter. It is shown that
there is a detectable difference in measured snow properties between
consecutive winters. Snow observed during BAECC is denser than during the
next winter. The derived m–D relations from two winters are also
different, and the difference is namely in the prefactor of the power-law
relations.
It is found that D0 and Nw parameters of gamma PSD are
correlated with ρ‾. While the relation between ensemble mean
density and D0 is not surprising, since these two parameters are related,
the correlation between Nw and ρ‾ is interesting.
This correlation arises from the observed connection between Nw and
D0. It should be noted that this observed connection is partially due to
data filtering that removes low precipitation rate data from the analysis.
However, it indicates that for heavier precipitation aggregation is an
important snow growth process. During snow growth by aggregation,
Nw should decrease while D0 increases, as was found by
. The shape parameter of the gamma PSD, μ, does
not seem to depend on ensemble mean density and its average value is close to
0, which is in line with studies reported in literature.
Dependence of v–D relation on ensemble mean density was also studied. It
was found that the prefactor of the v–D power law depends on density. It
is higher for higher densities. This result is in agreement with the
conclusion made by : the coefficient and power terms
increase with riming degree.
The presented study uses the newly developed instrument Particle Imaging
Package, which is a new generation of SVI. It is shown that data collected by
this instrument are adequate for such studies. While the instrument only
observes particle shapes projected to single 2-D plane, as opposed to 2-DVD
or MASC, it has a larger sampling volume and its observations are less
affected by wind . Additionally, the instrument itself is
operationally more robust and requires less maintenance, enabling deployment
in sites with remote locations and harsh field conditions.