Deriving Snow Cloud Characteristics from CloudSat Observations
Guosheng Liu
Department of Meteorology, Florida State University, Tallahassee, Florida
Corresponding author address:
Guosheng Liu
Department of Meteorology
Florida State University
Tallahassee, FL 32306-4520
Phone: (850) 644-6298
Fax: (850) 644-9642
email: [email protected]
Manuscript submitted to JGR-Atmospheres (Special Issue – Early Sciences from
CloudSat and CALIPSO), Revised May 14, 2008
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Abstract
There has been so far no global estimate of snowfall. CloudSat has, for the first
time, provided an opportunity for us to conduct such an estimate. The present study
seizes this opportunity and attempts to investigate the global snowfall characteristics
using its cloud radar observations. The retrieval methodology developed in this study
includes two parts: first, determining whether a radar echo corresponds to snowfall
(instead of rainfall), and second, converting radar reflectivity to snowfall rate. The first
part is a snow-rain threshold based on multi-year land station and shipboard present
weather reports, and the second part is based on backscatter computations of nonspherical
ice particles and in situ measured particle size distributions. Using the above retrieval
method, global CloudSat data over one year were analyzed. The results show that: (1) In
the southern hemisphere, there is an almost zonally orientated high snowfall zone
centered around 60ºS, where both snowfall frequency and rate are high. In the northern
hemisphere, however, heavy/frequent snowfall areas are mostly locked to geographical
locations. (2) Zonally and annually averaged snowfall rate has its maximum value around
2 mm day-1, which is about 1/3 of the zonally averaged rainfall values found in the
tropics, signifying the importance of snowfall in hydrological cycle. (3) Vertical profiles
of snowfall rate have the greatest variability in the lowest levels. While near surface
snowfall rate generally increases with cloud top height, there seems to be two prevailing
groups of clouds with very different growth rate of snowfall as cloud top height
increases. (4) The characteristics of the vertical distribution of snowfall rate are quite
similar for over-ocean and over-land snow clouds, except that over-land snow clouds
seem to be somewhat shallower than those over ocean.
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1. Introduction
Although rain and snow are just two different forms of precipitation, their
hydrological-climatological impacts are very different. Over land, accumulated snow
may stay on the ground for months, resulting in different hydrological and radiative
consequences from those by rain [e.g., Barnett et al. 1989; Walsh 1995]. Over ocean,
falling snow has complex interaction with ocean surface because it both freshens and
cools (through snow melting) the ocean surface water. How snowfall impacts on ocean
surface buoyancy in the high latitudes (e.g., North Atlantic), and therefore on deep-water
formation, remains largely unknown [Curry et al. 1996; Liu and Curry, 1997]. Despite
the importance of snow precipitation, there have been no global maps of snowfall amount
produced on the basis of observational data although snowfall frequency maps have been
generated from observations at ground weather stations and from transit ships [Petty,
1995; Dai, 2001]. To measure snowfall globally, satellite observations become inevitable.
Unlike satellite rainfall estimations that have a history of several decades [e.g.,
Smith et al., 1998; Adler et al., 2001; Kummerow et al., 2001], the research on satellite
snowfall estimation is still in a very early stage. There have been very few space-borne
sensors suitable for detecting falling snow. Passive satellite sensors such as highfrequency microwave radiometers have been used in detecting snowfall events [Liu and
Curry, 1997; Chen and Staelin, 2003; Kongoli et al., 2003; Skofronick-Jackson et al.,
2004; Noh et al., 2006]. These studies have resulted in very encouraging results for
moderate and heavy snowfall events. Theoretical studies on the sensitivity of passive
microwave radiation to ice particles and their size distributions have been conducted by
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Bennartz and Petty [2001] and Bennartz and Bauer [2003]. Space-borne active sensors
that can be used to estimate both horizontal and vertical snowfall distributions have not
been available until the Cloud Profiling Radar (CPR) on CloudSat [Stephens et al., 2002],
which was launched in April 2006. Therefore, the CPR observation provides the first
opportunity to survey the horizontal and vertical snowfall structures over a global scale.
Taking advantage of this opportunity, the primary goal of this study is to derive the
statistics of the snowfall horizontal and vertical distributions.
Since CPR does not scan, it only observes a strip of ~ 1.5 km on Earth’s surface
for each passing orbit, which limits the ability of obtaining snowfall distribution by
CloudSat measurement alone. One other possibility is to retrieve snowfall through
measuring the scattering signature of falling snowflakes by high-frequency (>89 GHz)
passive microwave radiometers, which are currently on several satellites. For example,
using Advanced Microwave Sounding Unit – B (AMSU-B) observations, SkofronickJackson et al. [2004] and Noh et al. [2006], respectively, retrieved the snowfall
distributions over eastern United States and over the Sea of Japan; their results are
compared reasonably well with surface radar measurements. To develop such passive
microwave snowfall retrieval algorithms as those based on Bayes’s Theorem, it is
required as a-priori to have a database that relates snowfall profiles to microwave
brightness temperatures. The global coverage of CPR observations makes it possible for
us to build such a diversified database for passive microwave snowfall algorithms.
Therefore, a second purpose of the study is to produce a collection of snowfall profiles,
which later can be used to build a database used in passive high-frequency microwave
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snowfall retrieval algorithms. Future combination of the active and passive satellite
observations will greatly improve snowfall data availability.
The CPR observed quantity is radar reflectivity. Prior to obtaining snowfall
characteristics from CPR data, it is needed first to determine whether the radar return is
from rainfall or snowfall, and then convert the radar reflectivity to snowfall rate if it is
due to snowfall. In this study, the conditional probability of snowfall given a surface air
temperature is evaluated using 10 years of weather reports from both land stations and
shipboard measurements around the globe. The rain-snow threshold is then determined as
the surface air temperature at which the conditional snowfall probability reaches 50%.
Converting radar reflectivity to snowfall rate is based on a newly derived reflectivity (Ze)
– snowfall rate (S) relation. In deriving the Ze-S relation, backscatter by nonspherical
snowflakes is studied using discrete dipole approximation [Draine and Flatau, 1994], and
the snowflake size distributions are based on previous in situ observations [Braham,
1990; Lo and Passarelli, 1982]. The detailed description of the above derivations is given
in section 2. Using the Ze-S relation, snowfall rate is calculated; its characteristics
including horizontal and vertical distributions and their variability are analyzed using one
year of CPR data. The analyzed results will be shown in section 3. Conclusions are given
in section 4.
2. Data and Methods
2.1 CPR Data
The principal data used for deriving snowfall characteristics are the observations
by CPR onboard CloudSat. The CPR is a 94-GHz nadir-looking radar that measures the
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power backscattered by clouds and precipitation as a function of distance from the radar.
Its minimum detectable radar reflectivity factor was designed to be -26 dBZ at pre-launch
although analysis of in-orbit observational data has shown that the sensitivity is better
than the specification at about -30 dBZ. The standard CloudSat product 2D-GEOPROF
(Release version 4) [Mace, 2007] is used, which includes radar reflectivity in 150 bins in
the vertical with a bin size of about 240 m. The footprint size of radar reflectivity profiles
is 1.4 km (cross-track) and 2.5 km (along-track). The bin that corresponds to surface
return is also specified in the product. To remove surface contaminated data, data of the
lowest 4 bins (~1 km) for over-ocean and the lowest 5 bins (~1.2 km) for over-land
observations were excluded in the data analysis. In the following, the snowfall rate
derived from the radar reflectivity at the 5th (6th) bin is called “near surface snowfall” for
over-ocean (over-land) observations. All “near surface” snowfall results derived in this
study are based on radar observations at the 5th or 6th bin, which may have caused some
shallow snowfall events being missed.
In addition, two-meter air temperature from ancillary data product ECMWF-AUX
[Partain, 2007] was used to determine whether surface precipitation is rainfall or
snowfall. The ECMWF-AUX contains atmospheric variables from European Centre
Medium range Weather Forecasting (ECMWF) model analysis, interpolated to the
location of CPR bins.
2.2 Separation of Rain and Snow Profiles
From radar reflectivity alone, it is difficult to separate the radar profiles that are
associated with surface snowfall from those with rainfall. Although a melting layer with a
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bright-band in the radar reflectivity profiles indicates rainfall at surface, there are two
problems preventing this method to effectively separate snow and rain profiles. First, a
bright-band only appears in stratiform precipitations where no significant updraft exists
cross the melting layer, which makes this method unusable for convective clouds.
Second, according to data analysis performed in this study, the lowest altitude where
CPR data are uncontaminated by surface reflections is around 1.2 km above surface.
Therefore, it is hard to detect melting layer if it exists below 1.2 km. To determine
whether the precipitation reaching to the surface is snow or rain, we first studied the
conditional probability of solid precipitation at a given surface air temperature using
present weather reports from land stations and ships. The land station data used here are
from global synoptic weather reports archived at the National Center for Atmospheric
Research (NCAR) [DS464.0, http://dss.ucar.edu/ datasets/ds464.0]. The same dataset (but
for different time period) has been used by Dai [2001] to study the frequency of global
precipitation. In the datasets, present and past weather is reported every 3 hours in coded
format, as defined by the World Meteorological Organization (WMO) [WMO, 1988].
While this dataset contains present and past weather codes starting from early 1975, only
the present weather data (occurred at the time of observation) for the recent 10 years
(March 1997 to February 2007) were used for the current analysis. A similar dataset from
shipboard weather reports, called International Comprehensive Ocean-Atmosphere Data
Set
(ICOADS),
is
also
archived
at
NCAR
[DS540.0,
http://dss.ucar.edu/
datasets/ds540.0]. The present weather reports in ICOADS dataset for the recent 12 years
(January 1995 to May 2007) were used for the analysis presented here. The same dataset
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(but different time period) has been used by Petty [1995] and Dai [2001] to study oceanic
precipitation frequencies.
From these weather reports, first, those observations that have non-drizzle
precipitation were extracted, of which distinction between liquid (rain) and solid (snow)
precipitations was further conducted according to the weather code. Then the conditional
probability of snow precipitation was calculated as a function of surface air temperature,
as shown in Fig. 1. The figure shows that the probability varies in a similar fashion for
over-ocean and over-land environments with the transition from liquid to solid
precipitation occurring mostly between air temperature of 4ºC to -1ºC. Above 4ºC, some
90% (95%) of land (oceanic) precipitation are rain, while below -1ºC, some 95% of
precipitation are snow. The 50% probability occurs at air temperature around 2ºC
regardless of surface type. In the following, the 2ºC surface air temperature (from
ECMWF analysis) will be used as the threshold to separate between snow and rain radar
profiles. Bennartz [2007] studied the likelihood of solid precipitation in relation to
freezing level height, and found that the likelihood of solid precipitation is 50% for a
freezing level height of 600 m. His result is comparable to the finding of this study.
2.3 Ze-S Relation
Since snowflakes have comparable size to the radar wavelength of CPR (3.2 mm),
the scattering properties of the particles are largely deviated from Rayleigh relations and
can no longer been approximated by those of equal-volume spheres [Liu, 2004, Kim,
2006; Hong, 2007]. Compared to rain cases, the radar reflectivity versus snowfall rate
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(Ze-S) relation is therefore further complicated by particle shape and orientation in
addition to particle size distribution. Matrosov [2007] developed a Ze-S relation for 94
GHz radar by assuming that the snowflakes are oblate spheroids with an aspect ratio of
0.6 and preferably orientated horizontally. To derive a new Ze-S relation based on ice
particle shapes that more closely resemble natural snowflakes, in this study, three particle
types – rosettes (with 3-, 4-, 5- and 6-bullet), sectors and dendrites are designed and used
to represent snowflakes. Assuming random orientation, their backscatter cross sections
are computed using discrete dipole approximation (DDA) method [Draine and Flatau,
1994; Liu, 2004]. The density and area ratio versus maximum dimension relations for
these particles are based on Heymsfield and Miloshevich [2003] and Heymsfield et al.
[2002]. Detailed description of these particles and their scattering characteristics can be
found in Liu [2004].
Snowfall rate (liquid equivalent), S, and (equivalent) radar reflectivity factor, Ze,
may be expressed by the following equations:
S = ∫ N ( D )v ( D )m( D ) / ρ w dD ,
(1)
D
and
Ze =
λ4
π 5 | K |2
∫ N ( D)σ
bsc
( D)dD ,
(2)
D
respectively. In these equations, D is the maximum dimension of the snowflake, N(D) is
the particle size distribution, v(D) is terminal velocity, m(D) is particle’s mass, ρw is the
density of liquid water, λ is wavelength, K is a function of dielectric constant of water,
and σbsc(D) is the backscatter cross section of the snowflake with the maximum
dimension D. Results from in situ observations showed that the snow particle size
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distributions generally follow an exponential form, while the intercept and slope vary,
among other things, with the intensity of snowfall [Gunn and Marshall, 1958; Sekhon and
Srivastava, 1970; Braham, 1990]. The uncertainty of the size distribution is a major error
source for the Ze-S relation. If dual-wavelength [e.g., Matrosov, 1998] and/or additional
Doppler spectrum measurements [e.g., Mace et al., 2002] were available for CPR, this
error could be reduced. However, since CPR is a single wavelength radar without
Doppler measurement, the retrieval error due to the uncertainty in size distribution will
remain. In this study, an exponential form of particle size distribution, N(D)=N0exp(ΛD), was used with the values of N0 and Λ taken from observational data published by
Braham [1990] (his Table 4) and Lo and Passarelli [1982] (their Fig.8). In the Braham
distribution, D was given by the maximum dimension measured by 2D probes in the
direction either along or cross the aircraft flight direction, whichever was larger. For
terminal velocity, the 15 relations given by Locatelli and Hobbs [1974] (their Table 1) for
various types of ice particles are used. To be consistent with their observations, the size
range of ice particles corresponding to these terminal velocity relations are also adopted
from the Locatelli and Hobbs study.
In Fig.2 shown are the Ze-S relations computed using (1) and (2) for rosettes,
sectors and dendrites. The following mathematical expression is derived using leastsquare fitting of the data points in the figure:
Ze = 11.5 S1.25 ,
(3)
where Ze in mm6m-3, and S in mm h-1. The above relation is incidentally quite similar to
that of Matrosov [2007], which is also shown in the figure by dashed line. However, the
spreading of S values is quite large at any given Ze (about an order), indicating that not
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knowing the particle shape and size distribution will contribute large uncertainties
(random error) to the snowfall rate retrievals. On logarithm scale, the correlation
coefficient of the above fitting is 0.92 while r.m.s difference of ln(S) between data points
in the figure and computed by (3) is 0.47. Because of dln(S)=dS/S, it is estimated that the
relative error (ΔS/S) solely due to the spreading of data points around the fitting curve is
then about 50%. Additionally, it should be mentioned that melting snow particles are not
considered in this study. The liquid-coated particles exhibit higher radar reflectivity than
snowflakes, which causes overestimation of snowfall rates, particularly in warmer
temperatures.
3. Results
In deriving global snowfall statistics, CloudSat data from 1 July 2006 through 30
June 2007 (one year) have been analyzed. Figure 3 shows (a) the number of CPR radar
reflectivity profiles, (b) the number of profiles that correspond to 2-m air temperature
colder than 2°C (hereafter they are called “cold samples” or “cold profiles”), and (c) the
number of “snow profiles” that are defined here to have near surface radar reflectivity
greater than -10 dBZ and 2-m air temperature colder than 2°C in 5° (latitude) x 5°
(longitude) boxes observed during the one year period. The number of profiles ranges
from ~70,000 to ~100,000 within each 5° x 5° box with more observations in the high
latitude boxes than in the low latitude ones, except for outside 85° latitudes where the
satellite does not reach. The distribution of the number of cold samples depends on both
latitude and surface type. In general, except for a few mountain areas, cold samples do
not exist in latitudes lower than ~30°. In the northern hemisphere, the number of cold
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samples is distributed in a similar shape of the continents. In particular, there is a local
maximum of the number of cold samples over the Tibetan Plateau. In the southern
hemisphere where the distribution of the number of cold samples is largely zonal, a sharp
polarward increase of cold samples occurs near 60°S. Here, a threshold of -10 dBZ at the
lowest uncontaminated (5th bin for over ocean and 6th bin for over land) radar reflectivity
is used for identifying snow profiles. The selection of the threshold is somewhat
arbitrary, but is corresponding to a very low snowfall rate of ~0.02 mm h-1 when applying
(3). The sample numbers of snow profiles are much lower than the cold sample numbers,
and the maxima (~15,000 within a 5° x 5° box) are not near the poles.
To understand the statistical characteristics of the radar profiles, we computed the
2-dimensional histogram of the radar echo occurrence, which is the number frequency of
observations in each 250 m (height) x 2.5 dBZ (radar reflectivity) bin, normalized so that
the maximum frequency is 100. The results are shown in Fig.4. The data are separated by
2 surface types, i.e., land or ocean, and 3 profile types, i.e., all profiles – all profiles
outside 30°S-30°N latitudinal belt, cold profiles – of the above profiles, those having 2-m
air temperature colder than 2°C, and snow profiles – of cold profiles, those having nearsurface radar reflectivity higher than -10 dBZ. For the land profiles, actual land surface
level (instead of sea level height) was used as reference to measure height. While the
general pattern of the histogram for cold profiles is similar to that for all profiles, larger
frequencies are distributed at lower altitudes for the cold profiles’ histogram than for the
all profiles’ histogram, suggesting that clouds for cold profiles are shallower in general.
However, there is a distinct difference between the over-ocean and over-land histograms.
For over-ocean profiles, there is a persistent occurrence of low level clouds/precipitation
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in addition to a higher level radar return maximum that lowers its altitude as radar
reflectivity increases. For over-land profiles, the double-maxima pattern does not show in
the all profile and cold profile histograms; only a pattern of gradual decrease of frequency
upward. The double maxima pattern is further investigated by plotting the frequency of
occurrence of cold cloud top heights (as defined here by the highest level with radar
reflectivity greater than -24 dBZ) in Fig.5. It is seen that there are two maxima of
frequencies of cloud top height at ~ 6.5 km and near surface for over-ocean clouds while
there is only the near surface maximum for over-land clouds. The double layer nature of
over-ocean clouds will be further discussed later in section 3.2.
For the snow profiles, the over-ocean and over-land histograms have a similar
pattern that indicates maximum frequency occurs at low radar reflectivity at high
altitudes and shifts to higher reflectivity as altitude lowers. However, compared to overland histogram, the maxima in over-ocean histogram occur at higher altitudes for the
same radar reflectivity. For example, at radar reflectivity of -15 dBZ, the maximum
frequency for ocean profiles is at ~ 5 km while it is ~ 3.5 km for land profiles. This
implies that snow clouds are generally shallower over land than over ocean, an opposite
trend to convective rain clouds in the tropics [Liu and Fu, 2001; Takayabu, 2002].
3.1 Horizontal Distribution
Using the snowfall threshold derived in section 2.2 and the Ze-S relation derived
in section 2.3, the snowfall frequency and snowfall rate were computed in each 5° x 5°
box based on the one year CloudSat data. In Fig. 6, we show the global distributions of
(a) frequency of total precipitation (near-surface radar reflectivity greater than -10 dBZ),
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(b) frequency of snowfall (near-surface radar reflectivity greater than -10 dBZ and 2-m
air temperature colder than 2°C), (c) mean snowfall rate in mm day-1 (averaging all
observations including zeros), and (d) conditional mean snowfall rate in mm day-1
(averaging only those pixels with Ze>-10 dBZ). The total precipitation frequency has its
maxima in the mid latitudes (around 60°S or 60°N), with values exceeding that in the
Intertropical Convergence Zone (ITCZ). Similar results have been shown by Petty
[1995]. As can be seen from Fig. 6b, the mid latitude frequency maxima are largely
contributed by snowfall, particularly for the southern hemisphere where snowfall
frequency exceeds 25% at many locations. There is a distinct difference for snowfall
distributions between northern and southern hemispheres. While snowfall (both
frequency and rate) are largely distributed zonally in the southern hemisphere, snowfall
events in the northern hemisphere seem to be more concentrated to several locations,
such as the coastal regions of Gulf of Alaska, east coast of Newfoundland and Labrador
Sea, the large region covering east of Greenland, North Europe and Arctic Ocean, and the
east coast of Siberia. The frequent snowfall occurring at east coast of Newfoundland and
Labrador Sea was earlier reported by Liu and Curry [1997]. A surprising result is the
frequent occurrence and the large rate of snowfall over the southern oceans along the
Antarctic coast, which has not been reported before to the author’s knowledge. Another
feature worth mentioning is that the conditional mean snowfall rate occurs to the
equatorward edges of the snowfall zones, suggesting that while snowfall events are less
frequent in the lower latitudes; but when it snows, it tends to snow heavier than in the
higher latitudes.
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Figure 7 shows the zonally averaged values of the snowfall frequencies and rates,
also distinguished by whether the snowfall events are over land or over ocean. The
asymmetry of the snowfall frequency and rate distributions for the two hemispheres is
clear. The maximum snowfall frequency is about 25% for southern hemisphere (peaks
near 75°S) and ~15% northern hemisphere (at the northernmost latitudes of CloudSat
observations). The mean snowfall rate peaks at 60°S in the southern hemisphere and near
northernmost regions of CloudSat observations in the northern hemisphere. It should be
mentioned that errors in the snowfall rate estimates are large (about 50%) for any
individual profiles due to the scatter of the Ze-S relation (Fig. 2). Therefore, it should be
cautioned when reading the averaged snowfall values where the number of snow profile
samples (Fig.3c) is small.
Groisman and Easterling [1995] analyzed surface gauge-measured snowfall
records for the region south of 55°N in Canada. The time series of annual snowfall (in
mm) of their data are shown in Fig. 8a, along with the latitudinal distribution of our
CloudSat over-land retrievals averaged between the longitudes of 55ºW and 125Wº
(Fig.8b). It is seen from Fig.8a that the annual snowfall in this region is around 225 mm,
or ~0.6 mm day-1 in mean snowfall rate. Referring to Fig.8b, our retrievals show that the
mean snowfall rate between 45°N to 55°N over land regions ranges from 0.4 to 1.0 mm
day-1, suggesting that our retrievals are generally in the ballpark of the climatology. The
maximum of the zonally averaged snowfall rate is about 2 mm day-1 (1.5 mm day-1) in
the southern (northern) hemisphere. According to Tropical Rainfall Measuring Mission
(TRMM) results [Kummerow et al., 2000], the zonal mean rainfall rate at ITCZ is ~ 6
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mm day-1, implying that the maximum of zonal mean snowfall in southern (northern)
hemisphere can be as large as 1/3 (1/4) of that of ITCZ rainfall.
The over-land versus over-ocean difference of zonal mean snowfall frequency and
rate is small and mainly shows in the southern hemisphere. However, the conditional
mean snowfall rates, particularly those within 45°S/N, are very different between over
land and over ocean. The large values of conditional mean snowfall rates over land
suggest that occasional occurrence of heavy snowfall events in the lower latitudes. The
PDFs of snowfall rate (in logarithmic scale, Fig. 9) shows that snowfall rates less than 1
mm h-1 dominate the spectrum. For southern hemisphere, the PDF for ocean is broader
than that for land, manifesting the fact that most oceanic snowfall areas are equatorward
where heavier snowfall occurs more often. For northern hemisphere, the PDFs for land
and ocean are almost identical.
3.2 Vertical Distribution
Using the one year global CPR data, the mean snowfall profile of all data with
near surface radar reflectivity greater than -10 dBZ was first computed, and then EOF
(Empirical Orthogonal Function) analysis was performed to the variances, separating
profiles over land and over ocean. The results are shown in Fig.10, with Figs.10a and b
showing the (conditional) mean profiles of snowfall rates and Figs.10c and d showing the
vertical distributions of the 3 leading EOFs that together explain 93% (95%) of the
variances for ocean (land) profiles. Except that the mean profile for over-land profiles is
somewhat shallower than that for over-ocean profiles, there is not much difference
between over-land and over-ocean profiles in terms of the magnitude and pattern of the
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mean profiles as well as the variances as described by the EOFs. The conditional mean
snowfall rate near surface is about 0.35 mm h-1 and decreases with the increases of height
until it vanishes at around 8 km. The greatest variability of the snowfall rate profiles as
described by the 1st EOF (explains ~75% of the variance) shows a pattern of gradual
increase of the absolute value of amplitude downward, indicating that the magnitude of
variation among profiles has its maximum near surface and gradually decreases with the
increase of height.
Given a fixed near surface snowfall rate, how is the snowfall distributed vertically
on average? To answer this question, all observed profiles were divided into groups
according to their near surface snowfall rate and the mean profile was computed for each
group. The averaged near surface snowfall rate of and the number of profiles in each
group are shown in Table 1 and the averaged snowfall rate profiles are shown in Fig.11.
As can be expected from Fig. 9, the number of profiles in groups with weaker near
surface snowfall rate is much greater than that in groups with heavier near surface
snowfall rate. Again, the averaged profiles for over-ocean and over-land environments
are quite similar except that the over-land profiles are somewhat shallower than overocean profiles when surface snowfall rates are low. From profiles 1 to 7, as surface
snowfall rate increases, the snow layer grows deeper, manifesting that heavier snowfall is
associated with a thicker cloud layer. However, profiles 8 and 9 do not follow the same
trend, indicating that the heaviest surface snowfalls are produced by rather shallow
clouds. The explanation to this exception of trend is not immediately clear to me although
it is speculated that the last two groups may correspond to shallow convective clouds
associated with “lake effect” (cold air passes warm water surfaces creating strong shallow
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convections) [e.g., Aonashi et al., 2007], which, while shallow, often produce heavy
snowfalls. The prevalence of the two different snow cloud regimes is supported by Fig.
12, in which we show the 2-dimensional PDFs of profiles in a cloud top height (as
defined by Ze = -24 dBZ) versus near surface snowfall rate diagram. It is seen that while
near surface snowfall rate increases in responding to the rise of cloud top height, there
seem to exist two groups of clouds that have different growth rate, particularly for those
profiles over oceanic environment. When surface snowfall rate increases to ~ 2 mm h-1,
one group has cloud top height around 10 km while the other group has cloud top height
below 3 km. The existence of the two cloud groups is also an important piece of
information for us to develop snowfall retrieval algorithms using satellite passive
microwave data. In addition to the ice scattering signal in microwave radiometric data,
infrared observations of cloud top height will also be beneficial for the passive
microwave algorithm to arrive at correct snowfall rate retrievals. Another interpretation
of the profiles of No. 8 and No. 9 is that the sharp downward increase of radar reflectivity
may be caused by melting snow (liquid-coated particle), which, as mentioned earlier,
could result in stronger radar reflectivity than snowflakes.
4. Conclusions
This study intends to provide a first look of the global horizontal and vertical
distributions of snowfall rate based on cloud radar data from CloudSat. To accomplish
this goal, a snow-rain threshold based on surface air temperature and a radar reflectivity –
snowfall rate (Ze-S) relation have been introduced. The former is based on multi-year
land station and shipboard present weather reports, and the latter is based on backscatter
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computations of nonspherical ice particles and in situ measured particle size distributions.
A common problem of the single parameter (Ze) algorithm of snowfall (as well as
rainfall) is that it contains large uncertainties as manifested by the broad scatter of points
in the Ze-S relation plot (Fig.2). To reduce random errors associated with the Ze-S
relation, in this study, only large-scale/long-term averaged quantities of the radar
retrievals are examined. The major findings can be summarized as follows.
First, there is an almost zonally orientated high snowfall belt centered around
60ºS, where both snowfall frequency and rate are high. To the author’s knowledge, this
high snowfall belt has not been previously reported. In the northern hemisphere,
however, heavy/frequent snowfall areas are locked to geographical locations, instead of
along latitudinal belt. Second, the zonally and annually averaged snowfall rate has its
maximum value around 2 mm day-1, about 1/3 of the zonally averaged rainfall value
found in the ITCZ, which signifies the importance of snowfall in hydrological cycle.
Third, the vertical profiles of snowfall rate have the greatest variability in the lowest
levels. While near surface snowfall rate generally increases with cloud top height, there
seems to have two prevailing groups of clouds with very different growth rate of snowfall
as cloud top height increases. It is speculated that one group is associated with low
pressure/frontal systems while the other is associated with shallow convections caused by
“lake effect”. Finally, in contrast to tropical rain profiles, the characteristics of the
vertical distribution of snowfall rate are quite similar for over-ocean and over-land snow
clouds, except that over-land snow clouds seem to be somewhat shallower than those
over ocean.
- 18 -
This study is a first attempt to survey the global snowfall characteristics from
satellite observations. While the retrievals are consistent with climatology at least at one
region as shown in Fig.8, many parts of the retrieval algorithm are still in a stage of “ad
hoc”. In particular, the Ze-S relation needs to be further examined and improved in the
future, when appropriate in situ observations become available. In this sense, the author
would like the readers to view the results of this work as a “quick-look”, and to expect
further improved results to follow. Two types of approaches should be considered in the
future for validating the current and future improved snowfall retrievals. One is to collect
quality-controlled historical surface snowfall data at multiple locations, and to compare
whether or not the retrievals are in-line with the “snowfall climatology”. This approach
does not require additional field observations and can verify the retrieval method
qualitatively. The second approach is to use surface areal snowfall observing network
(e.g., densely placed snow gauges) to match CloudSat measurement at the same time and
with comparable spatial coverage under a special designed field experiment. By
measuring such quantities as snow particle shape, size distribution and terminal velocity,
etc. in the special experiment, one can also validate the assumptions used in deriving the
Ze-S relation.
Acknowledgements. CloudSat data are obtained from CIRA of Colorado State
University. Ground station and ICOADS present weather reports are obtained from
NCAR. Valuable comments from three anonymous reviewers are very helpful. This
research has been supported by NASA CloudSat grant NNX07AQ79G and NASA GPM
grant NNX07AD63G.
- 19 -
References
Adler, R. F., C. Kidd, G. Petty, M. Morrissey, and M. H. Goodman (2001),
Intercomparison
of
global
precipitation
products:
The
third
precipitation
intercomparison project (PIP-3). Bull. Amer. Meteor. Soc., 82, 1377-1396.
Aonashi, K., T. Koike, K.-I. Muramoto, K. Imaoka, N. Takahashi, G. Liu, and Y.-J. Noh,
2007: Physical validation of microwave properties of winter precipitation over the
Sea of Japan. IEEE Trans. Geo. Rem. Sens., 45, 2247-2257.
Barnett, T. P., L. Dumenil, U. Schlese, E. Roeckner, and M. Latif (1989), The effect of
Eurasian snow cover on regional and global climate variations. J. Atmos. Sci., 46,
661-685
Bennartz, R. and P. Bauer (2003), Sensitivity of microwave radiances at 85-183 GHz to
precipitation ice particles. Radio Sci., 38, D8075, doi:10.1029/2002RS002626.
Bennartz, R. (2007): Passive microwave remote sensing of precipitation at high latitudes.
pp. 165-178. In “Measuring Precipitation from Space – EURAINSAT and the
Future”. Eds. V. Levizziani, J. Turk, P. Bauer. 745p. Springer Publishing.
Bennartz, R. and G. W. Petty (2001), The sensitivity of microwave remote sensing
observations of precipitation to ice particle size distributions. J. Appl. Meteor., 40,
345-364.
Braham, R. R., Jr. (1990), Snow particle size spectra in lake effect snows. J. Appl.
Meteor., 29, 200-207.
Chen, F. W. and D. H. Staelin (2003), AIRS/AMSU/HSB precipitation estimates. IEEE
Trans. Geosci. Rem Sens., 41, 410-417.
- 20 -
Curry, J. A., G. Liu, and P. J. Webster (1996), Evaluation of the surface fresh water flux
in the North Atlantic Ocean and its impact on the ocean surface buoyancy flux.
Proceedings on the Eighth Conf. on Air-Sea Interaction and Conf. on the Global
Ocean-Atmosphere-Land System (GOALS). American Meteorological Society,
Boston, 235-238pp.
Dai, A. (2001), Global Precipitation and thunderstorm frequencies, Part I: Seasonal and
interannual variations. J. Clim., 14, 1092-1111.
Draine, B. T. and P. J. Flatau (1994), Discrete-dipole approximation for scattering
calculations. J. Opt. Soc. Am. A, 11, 1491-1499.
Groisman, P. Y. and D. R. Easterling (1995), Variability and trends of precipitation and
snowfall over North America. Nation Climate Variability on Decade-to-Century Time
Scales, National Reseach Council, National Academy Press, Washington, DC, p6779.
Gunn, K. L. S. and J. S. Marshall (1958), The distribution with size of aggregate
snowflakes. J. Meteor., 15, 452-461.
Heymsfield, A. J. and L. M. Miloshevich (2003), Parameterizations for the crosssectional area and extinction of cirrus and stratiform ice cloud particles. J. Atmos.
Sci., 60, 936-956.
Heymsfield, A. J., S. Lewis, A. Bansemer, J. Iaquinta, L. M. Miloshevich, M. Kajikawa,
C. Twohy, and M. R. Poellot (2002), A general approach for deriving the properties
of cirrus and stratiform ice cloud particles. J. Atmos. Sci., 59, 3-29.
- 21 -
Hong, G. (2007), Parameterization of scattering and absorption properties of nonspherical
ice crystals at microwave frequencies. J. Geophys. Res., 112, D11208,
doi:10.1029/2006JD008364.
Kim, M.-J. (2006), Single scattering parameters of randomly orientated snow particles at
microwave frequencies. J. Geophys. Res., 111, D14201, doi:10.1029/2005JD006892.
Kongoli, C., P. Pellegrino, R. Ferraro, N. Grody, and H. Meng (2003), A new snowfall
detection algorithm over land using measurements from the Advanced Microwave
Sounding Unit (AMSU). Geophys. Res. Lett., 30, DOI:10.1029/2003GL017177.
Kummerow, C. et al. (2000), The Status of the Tropical Rainfall Measuring Mission
(TRMM) after two years in orbit. J. Appl. Meteorol., 39, 1965-1982.
Kummerow, C., Y. Hong, W. S. Olson, S. Yang, R. F. Adler, J. McCollum, R. Ferraro,
G. Petty, D.-B. Shin, and T. T. Wilheit (2001), The Evolution of the Goddard
profiling algorithm (GPROF) for rainfall estimation from passive microwave sensors.
J. Appl. Meteor., 40, 1801-1820.
Liu, G. (2004), Approximation of single scattering properties of ice and snow particles
for high microwave frequencies. J. Atmos. Sci., 61, 2441-2456.
Liu, G. and J. A. Curry (1997), Precipitation characteristics in the GIN Seas determined
using satellite microwave data. J. Geophys. Res., 102, 13987-13997.
Liu, G. and Y. Fu (2001), The Characteristics of tropical precipitation profiles as inferred
from satellite radar measurements. J. Meteor. Soc. Japan, 79, 131-143.
Lo, K. H. and J. R. E. Passarelli (1982), The growth of snow in winter storms: An
airborne observational study. J. Atmos. Sci., 39, 697-706.
- 22 -
Locatelli, J. D. and P. V. Hobbs (1974), Fall speeds and masses of solid precipitation
particles. J. Geophys. Res., 79, 2185-2197.
Mace, G. (2007), Level 2 GEOPROF Product Process Description and Interface Control
Document
Algorithm
version
5.3.
http://www.cloudsat.cira.colostate.edu/dataICDlist.php?go=list&path=/2B-GEOPROF.
Mace, G. G., A. J. Heymsfield, and M. R. Poellot (2002), On retrieving the microphysical
properties of cirrus clouds using the moments of the millimeter-wavelength Doppler
spectrum. J. Geophys. Res., 107, 4815-4841.
Matrosov, S. Y. (1998), A dual-wavelength radar method to measure snowfall rate. J.
Appl. Meteor., 37, 1510-1521.
Matrosov, S. Y. (2007), Modeling backscatter properties of snowfall at millimeter
wavelengths. J. Atmos. Sci., 64, 1727-1736.
Noh, Y.-J., G. Liu, E.-K. Seo, J. R. Wang, and K. Aonashi (2006), Development of a
snowfall retrieval algorithm at high microwave frequencies. J. Geophys. Res., 111,
D22216, doi:10.1029/2005JD006826.
Partain, P. (2007), Cloudsat ECMWF-AUX Auxiliary Data Process Description and
Interface
Control
Document,
http://www.cloudsat.cira.colostate.edu/dataICDlist.php?go=list&path=/ECMWFAUX.
Petty, G. (1995), Frequencies and characteristics of global oceanic precipitation from
shipboard present-weather reports. Bull. Amer. Met. Soc., 76, 1593-1616.
Sekhon, R. S. and R. C. Srivastava (1970), Snow size spectra and radar reflectivity. J.
Atmos. Sci., 27, 299-307.
- 23 -
Skofronick-Jackson, G. M., M.-J. Kim, J. A. Weinman, and D.-E. Chang (2004), A
physical model to determine snowfall over land by microwave radiometry. IEEE
Trans. Geosci. Rem. Sens., 42, 1047-1058.
Smith, E. A., et al. (1998), Results of WetNet PIP-2 Project. J. Atmos. Sci., 55, 14831536.
Stephens, G. L., et al. (2002), The CloudSat Mission and The A-Train. Bull. Amer.
Meteor. Soc., 83, 1771-1790.
Takayabu, Y. N. (2002), Spectral representation of rain profiles and diurnal variations
observed with TRMM PR over the equatorial area. Geophys. Res. Lett., 29(12), 1584,
doi: 10.1029-2001GL014113.
Walsh, J. E., 1995: Continental snow cover and climate variability. Nation Climate
Variability on Decade-to-Century Time Scales, National Research Council, National
Academy Press, Washington, DC, p49-58.
WMO, 1988: Manual on Codes, Vol.1. WMO Publ. 306, 203pp.
- 24 -
Table 1. Number of profiles in each near surface snowfall rate group
No.
Snowfall Rate
Over Ocean
Over Land
1
0.024
1,446,300
1,013,105
2
0.049
1,432,311
941,259
3
0.10
1,413,011
814,065
4
0.21
1,374,011
650,434
5
0.43
1,172,291
447,016
6
0.86
604,259
188,244
7
1.6
109,041
36,619
8
3.2
3,452
2,518
9
7.6
249
1,208
- 25 -
Figure Captions
Fig.1.
Conditional probability of solid precipitation as a function of surface air
temperature derived from global land station and shipboard present weather reports.
Fig.2 Ze-S relation for three nonspherical snowflakes. A least-square fitting curve and
relation by Matrosov [2007] are also shown.
Fig.3
Number of CPR observations within 5º x 5º boxes for (a) all, (b) cold (2-m air
temperature colder than 2ºC), and (c) snow (cold samples with near surface radar
reflectivity >-10 dBZ) samples during the study period.
Fig.4
The 2-dimensional (height-reflectivity) number frequency histograms of CPR
observations in the latitudes north of 30ºN and south of 30ºS for (a) all samples over
ocean, (b) cold samples over ocean, (c) snowfall samples over ocean, (d) all samples over
land, (e) cold samples over land, and snowfall samples over land.
Fig.5 Frequency of occurrence of cloud top (defined by -24 dBZ) height for cold profiles.
Fig.6 Global distributions of (a) total precipitation frequency, (b) snowfall frequency, (c)
mean snowfall rate (times 5 in order to use the same color scale with conditional snowfall
rate), and (d) conditional snowfall rate.
Fig. 7 Zonally averaged total or solid precipitation (snowfall) frequency (left column),
mean snowfall rate (middle column), and conditional mean snowfall rate (right column).
The top, mid and bottom rows are, respectively, for all surfaces, over ocean only and over
land only observations.
- 26 -
Fig.8
(a) Annual snowfall over stations south of 55ºN in Canada (adapted from
Groisman and Easterling [1995]), and (b) latitudinal distribution of CPR data retrieved
snowfall rate averaged between 55ºW and 125ºW.
Fig.9 Frequency distribution of snowfall rate (in logarithmic scale), separated by
hemispheres and surface types.
Fig.10 Vertical distributions of (a) conditional mean snowfall rate over ocean and (b)
conditional mean snowfall rate over land, (c) 3 leading EOFs over ocean and (d) 3
leading EOFs over land. The EOF analysis is performed to the variance profiles (mean
removed). The percentages shown in diagrams (c) and (d) are the percentages of variance
explained by the corresponding EOFs.
Fig.11 Mean profiles for a given near surface snowfall rate for (a) over ocean and (b)
over land environments. The sample numbers used in the averaging are given in Table 1.
Fig.12 The relation between near surface snowfall rate and cloud top height as expressed
by snowfall profiles frequency distributions. The frequency values are normalized so that
the maximum frequency is 100.
- 27 -
Percent of Solid Precipitation (%)
100
75
50
25
Ocean
Land
0
-10
-5
0
5
10
Surface Air Temperature (oC)
Fig.1. Conditional probability of solid precipitation as a function of surface air
temperature derived from global land station and shipboard present weather reports.
- 28 -
101
Ze =11.5 S1.25
-1
S (mm h )
100
10-1
Rosettes
Sectors
Dendrites
Least-Square Fit
10-2
Matrosov (2007)
10-3
10-2
10-1
100
101
102
103
Ze (mm6m-3)
Fig.2 Ze-S relation for three nonspherical snowflakes. A least-square fitting curve and
relation by Matrosov [2007] are also shown.
- 29 -
(a) Sample Number ( x 10000) in 5 deg. x 5 deg. boxes
90
60
0
6
7
8
9
89
8 8
0
6
7
8
9
9
8 8 8
8
8
0
6
7
8
9
89
8
8
8
8
8
0
6
7
8
9
98
8
0
6
7
8
9
98
8
8
77
7
77
7
7
7
7
7 7
7 7 77 7 7 7
7
7
7
7
7
7
7
7 7 7 77 7
7
7
7
7 7
7
7
7 7 7
7
7
7 7
77 7
7
7
7 7
7
7 7
7 77 7
7 77 7
77
7 77
7
77
77
77 7
7
7
7
7
7
7
7
7
7
7
7
7
7
77
7
7 77 7
77
7
7
7 7
7 7
7 7
77
77 7 7
7 7 7 77
7
7 7
7
7 7 7 7 7 77
7
77
7
7
7
7
77 7
7 7
7
77
7
7 7
7
7
7
77 7 7
7
7
7
7 7 7 7
7
7 7
7
7
7
7
7 7 7
7
7
7 7
7
7 77 7
7
7
7
7
7
7
7
7
7 7
7
7
7 7 7
7
7
7
7 7
77
7
Latitude
30
0
-30
-60
98
9
8
7
6
0
98
9
8
7
6
0
-90
8
9
9
8
7
6
0
8
9
9
8
7
6
0
89
9
8
7
6
0
(b) Cold Sample Number (x 10000) in 5 deg. x 5 deg. boxes
90
0
1
2
3
4
5
6
9
76
5
342
1
1
0
0
60
Latitude
30
0
0
1
2
3
4
5
6
7
8
78
6
5
4
3
2
1 1
0
0
78
8
1
0
0 0
0
-60
-90
98
9
8
7
6
5
4
3
2
1
0
0
0
1
2
3
4
5
76
8
9
9
8
7
6
5
4
3
2
1
0
50
5
0
30
Latitude
12
3
1
0
1
3
4
5
6
87 2
989
7
56
4
33
1
1
0
0 0
0 0 0
0 0
0
0
2
3
4
5
68
7 1
8 67 9
5
4
8
4
5
2 143
0
0 0
0
0
1
0
1
1 1
0
0
0
0
3
2 1
0
0
0
0
0
0
0 0
0
0
0
0
0
0
0
0
1
2
3
4
5
76
1
0
7
1
2
3
4
5
6
0
0
0
8
9
9
8
7
6
5
4
3
2
1
0
8
9
9
8
7
6
5
4
3
2
1
0
0
0
0 0
0
0
0 0
0 0 0
13
2
4
5
6
7
89
9
8
7
6
5
4
3
2
1
0
(c) Snow Sample Number (x 1000) in 5 deg. X 5 deg. boxes
60
0
5
0
0
5
5
10
10 5
10
1510
5 10
15 10
10
10
5
5 5
5 5
5 5 5
10
10
10 5 5
5
00
5
5
5
5 5
0
0
55
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0 0
0
0 0
0
0
5
5 5
5
0
0
510
5
-30
105
15
10
5
0
-90
-180 -150
0
15 10
15
-120
5
10
15
10 5
0
-90
0
0
0
-60
10
10
0
0 0
5
0
0
5
15 10
15
10
10
15
10
5
0
0
-30
0
60
0
0
0
0
10
10
15 1510
0
0
0
5
10
5
0
0
30
5
0
0
0
0
0
10
15
5
0 5
5
10 10
5
5
5
5
5
0 0
0
0
-60
0
0
7
0
1
0
1
2
3
4
5
76
0
1
1
0
0
1
2
3
4
5
6
8
697
5
4
3 1
1 21 1
00
0 0
0
-30
90
8
9
90
120
150
180
Longitude
Fig.3 Number of CPR observations within 5º x 5º boxes for (a) all, (b) cold (2-m air
temperature colder than 2ºC), and (c) snow (cold samples with near surface radar
reflectivity >-10 dBZ) samples during the study period.
- 30 -
Fig.4
The 2-dimensional (height-reflectivity) number frequency histograms of CPR
observations in the latitudes north of 30ºN and south of 30ºS for (a) all samples over
ocean, (b) cold samples over ocean, (c) snowfall samples over ocean, (d) all samples over
land, (e) cold samples over land, and snowfall samples over land.
- 31 -
14
Cold Samples
Ocean
Land
12
Altitude (km)
10
8
6
4
2
0
0
2
4
6
8
Frequency of Occurrence (%)
Fig.5 Frequency of occurrence of cloud top (defined by -24 dBZ) height for cold profiles.
- 32 -
Fig.6 Global distributions of (a) total precipitation frequency, (b) snowfall frequency, (c)
mean snowfall rate (times 5 in order to use the same color scale with conditional snowfall
rate), and (d) conditional snowfall rate.
- 33 -
2.5
(a)
40
(d)
ALL
Precipitation Frequency
30
ALL
Mean Snowfall Rate
Mean Snowfall (mm/day)
2.0
PERCENT (%)
25
20
15
Total
10
(g)
30
Conditional Snowfall Rate (mm/day)
35
1.5
1.0
0.5
5
ALL
10
Conditional Mean Snowfall Rate
Solid
0.0
0
-90
-60
-30
0
30
60
0
-90
90
35
-60
-30
0
30
60
90
-90
2.5
(b)
-60
-30
0
30
60
90
15
Ocean
(e)
(h)
Ocean
30
Ocean
2.0
10
20
Total
15
1.5
(mm/day)
(mm/day)
PERCENT (%)
25
1.0
5
10
0.5
5
Solid
0
0
0.0
-90
-60
-30
0
30
60
-90
90
35
-60
-30
0
30
60
-90
90
2.5
(c)
-60
-30
0
30
60
90
40
(f)
Land
30
Land
30
(i)
Land
2.0
15
1.5
(mm/day)
Total
20
(mm/day)
PERCENT (%)
25
1.0
10
10
0.5
5
Solid
0
0
0.0
-90
-60
-30
0
30
LATITUDE
60
90
-90
-60
-30
0
LATITUDE
30
60
90
-90
-60
-30
0
30
60
90
LATITUDE
Fig. 7 Zonally averaged total or solid precipitation (snowfall) frequency (left column),
mean snowfall rate (middle column), and conditional mean snowfall rate (right column).
The top, mid and bottom rows are, respectively, for all surfaces, over ocean only and over
land only observations.
- 34 -
Annual Snowfall (mm)
(a)
1.2
(b)
Snowfall Rate (mm/day)
1.0
0.8
0.6
0.4
55 to 125 W
0.2
0.0
40
45
50
55
60
Latitude (N)
Fig.8 (a) Annual snowfall over stations south of 55ºN in Canada (adapted from Groisman and
Easterling [1995] ), and (b) latitudinal distribution of CPR data retrieved snowfall rate averaged
between 55ºW and 125ºW.
- 35 -
25
S. Hemsphere, Ocean
N. Hemsphere, Ocean
S. Hemsphere, Land
N. Hemsphere, Land
Frequency (%)
20
15
10
5
0
0.01
0.03
0.1
0.3
1
3
10
Snowfall Rate (mm h-1)
Fig. 9 Frequency distribution of snowfall rate (in logarithmic scale), separated by hemispheres
and surface types.
- 36 -
10
10
(b) Mean Profile - Land
Height (km)
(a) Mean Profile - Ocean
8
8
6
6
4
4
2
2
0
0
0.0
0.1
0.2
0.3
0.4
0.0
0.1
-1
Snowfall Rate (mm h )
0.3
0.4
Snowfall Rate (mm h-1)
10
10
(c) EOFs - Ocean
(d) EOFs - Land
1st (73%)
2nd (14%)
3rd (6%)
8
Height (km)
0.2
8
6
6
4
4
2
2
0
1st (77%)
2nd (13%)
3rd (5%)
0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Amplitude
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Amplitude
Fig.10 Vertical distributions of (a) conditional mean snowfall rate over ocean and (b)
conditional mean snowfall rate over land, (c) 3 leading EOFs over ocean and (d) 3
leading EOFs over land. The EOF analysis is performed to the variance profiles (mean
removed). The percentages shown in diagrams (c) and (d) are the percentages of variance
explained by the corresponding EOFs.
- 37 -
10
(a) Mean Profiles, Ocean
Height (km)
8
6
4
2
1
0
0.001
10
2
0.01
3
4
5
6
0.1
7
8
1
9
10
(b) Mean Profiles, Land
Height (km)
8
6
4
2
1
0
0.001
0.01
2
3
0.1
4
5 6
7
8
1
9
10
Snowfall Rate (mm h-1)
Fig.11 Mean profiles for a given near surface snowfall rate for (a) over ocean and (b)
over land environments. The sample numbers used in the averaging are given in Table 1.
- 38 -
12
1
2
1
2
1
2
Cloud Top Height (km)
3
8
0
0
00
10
3
3
5
1
2
1
5
10
5
6
15
2
20
15
2
15
20
15
5
30
2
0
0.01
2015
5
0
0
0.03
31 2
0
0.1
1
1
0
3
-1
Snowfall Rate (mm h )
10
0
0.01
1
5 3
10
2
1
0
0
0.03
2
15
30
1520
10 2
105 3
0
0
0.3
20
2
0
5 3
30
50
2
3
10
50
30 10
2
520 3115
0
4
1
5
10
15
10
3
15 15
15
1
20
1
4
5 32
10
10
3
10
15
1
5
10
10
0
2
3
3
5
2
15
10
15
8
00
1
1
2
0
5
10
0
(b) over land
0
10
6
12
0
(a) over ocean
0
0.1
0
0
0
0.3
0
1
3
10
Snowfall Rate (mm h-1)
Fig.12 The relation between near surface snowfall rate and cloud top height as expressed
by snowfall profiles frequency distributions. The frequency values are normalized so that
the maximum frequency is 100.
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