Introduction
The portion of solar radiation that appears to originate
from a small disk around the sun is called circumsolar radiation or solar
aureole. This radiation arises from near-forward scattering of direct solar
radiation by atmospheric particles with sizes comparable to or larger than
the wavelength (i.e., larger than 1 µm); the larger the particle
compared to the wavelength of radiation is, the more peaked the scattering
phase function P11 is and the more scattering is concentrated at
near-forward angles. Consequently, the amount of circumsolar radiation varies
widely depending on the geographical, seasonal, and diurnal variation of
airborne particles . As ice crystals are typically
much larger than aerosol particles or gas molecules, a considerably larger
part of the direct solar radiation is scattered into the circumsolar region
in the presence of ice clouds. In addition to the phase function, the amount
of circumsolar radiation depends on the single-scattering albedos and
extinction coefficients of atmospheric gases and particles. All these optical
properties depend on wavelength. Furthermore, the ensemble/volume-averaged
optical properties depend on the concentration, composition, and size-shape
distribution of the particles. Although the impact of ice crystal sizes and
shapes on their optical properties has been studied in much detail
,
there is no detailed information on how ice crystals affect the angular
dependence of circumsolar radiances. However, the studies of
and have revealed that differences in the modeled forward
scattering of smooth and roughened ice crystals as well as different shape
distributions of ice crystals lead to differences in the circumsolar
radiation. also noted the impact of ice crystals properties
(roughness and effective radius) on calculated circumsolar radiances.
Circumsolar radiation is widely detected by instruments measuring the direct
radiation (i.e., pyrheliometers) and therefore counted as direct radiation.
Such instruments often have a half-opening angle of 2–3∘, whereas
the half-width of the solar disk is only about 0.27∘ when observed
from the Earth. Depending on the ambient atmospheric conditions, the
near-forward scattered radiation can be a large portion of the total
radiation measured by these instruments, leading to overestimation of the
amount of direct solar radiation. Therefore, retrievals of ice cloud optical
thickness and other properties from the direct radiation measurements can be
biased. There have been some efforts to quantify the amount of circumsolar
radiation in the measured direct radiation and to account for its impact on
the underestimation of cloud optical thickness . For example proposed a new approach to derive ice
cloud optical thickness and effective diameter from sun photometry
measurements by using ice cloud optical property models.
Since the circumsolar radiance distribution is usually nearly radially
symmetric around the sun, it is reasonable to describe it as a function of
the angular position relative to the center of the sun . This
solar radiance profile is also called the sunshape.
presented a method for determining the sunshape using a pair of
pyrheliometers with different opening angles. The amount of circumsolar
radiance and the radial profile of sunshape can also be measured using a Sun
and Aureole Measurements (SAM) instrument. It consists of two solar tracking
cameras: one observing the sun disk and another the aureole. The cameras are
filtered into the 670±5 nm wavelength band. SAM measures the disk and
circumsolar radiances with a very high dynamic range and produces the disk
and aureole radiances as a function of angle from the center of the sun out
to 8∘ with an angular resolution of 0.0148∘.
demonstrated the ability of SAM measurements to derive the effective radius
and optical thickness of ice clouds and used MODIS retrievals of
thin cirrus to calculate solar disk and aureole measurements that were
compared with SAM measurements. have also developed a
method to determine circumsolar radiation from satellite observations. They
noted that the uncertainties in their retrieval due to assumptions on the ice
particle shape can sum up to 50 %, and even larger errors are expected if
instantaneous values are compared against SAM measurements.
suggested that a collection of SAM measurements might provide a useful
template for helping to derive phase functions of ice crystals.
There have been some efforts to account for the impact of circumsolar
radiation and sunshape on concentrating solar energy applications
. These
applications use concentrating solar collectors whose half-opening angles are
typically less than 1∘. Due to the 1–2∘ smaller acceptance
angle than that of a pyrheliometer, these collectors are able to use only a
fraction of the circumsolar radiation measured with a pyrheliometer.
Consequently, if the performance of the solar concentrating system is
predicted based on measurements of direct radiation (including circumsolar
radiation), the energy contained in the circumsolar region at angles from 1
to 3∘ can lead to overestimation of the performance. To better
estimate and optimize the amount of received energy of the concentrating
solar energy systems, the detailed angular distribution of the circumsolar
radiation and how it varies in time and location should be known.
The overarching goal of this research is to understand how ice clouds
influence the downwelling solar radiances within a few degrees from the
direction of the sun. This knowledge could be exploited, in future work, for
developing schemes to correct measurements of direct solar radiation for the
diffuse radiation that is present at the angular range of instruments such as
pyrheliometers. Furthermore, it is crucial for understanding the information
content in measurements with the relatively new SAM instrument and for the
future development of retrieval algorithms based on SAM data. This study is
largely divided into two components, both of which contribute to the
overarching goal. First the parameters that the circumsolar radiance is
sensitive to are identified. In particular, the impacts on circumsolar
radiances due to ice crystal size-shape distribution and roughness, ice cloud
optical thickness, and aerosol optical thickness are simulated. For this
purpose, a forward Monte Carlo radiative transfer model is used.
Monochromatic downwelling radiances for various ice cloud scenarios are
simulated at a wavelength of 0.670 µm. These scenarios are based on
in situ-measured size distributions of midlatitude ice clouds together with
either measurement-based shape distributions or idealized single-habit
distributions. These size-shape distributions of ice crystals are combined
with a database of single-scattering properties of ice crystals
to produce size-shape-integrated bulk optical properties of
the ice clouds as needed for input to the radiative transfer model. The
in situ-based distributions of ice crystals were obtained from aircraft
measurements made over the Atmospheric Radiation Measurement (ARM) program's
Southern Great Plains (SGP) site (36.606∘ N, 97.485∘ W) during
the Small Particles in Cirrus (SPARTICUS) campaign conducted in 2010. In the
second part of this work, case studies are used to determine the degree of
agreement between selected ground-based solar disk and circumsolar radiance
measurements by the SAM instrument at the SGP site and simulated radiances.
It should be noted that the first component (sensitivity studies) provides
important information for designing and interpreting the comparison with
modeled radiances in addition to providing a fundamental understanding on how
ice crystal properties affect circumsolar radiance.
Radiative transfer model
In this study, the angular dependence of solar disk and circumsolar radiances
are simulated with a modified version of the Monte Carlo Model of the
University of Kiel (MC-UniK) developed by . Even though a
plane-parallel horizontally homogeneous atmosphere is assumed in the
radiation calculations (see below), the Monte Carlo technique is applied
because of its flexibility. Specifically, it allows a consideration of the
finite width of the sun and the computation of radiances at an arbitrarily
high angular resolution in the vicinity of the direction of the sun, without
incurring extreme computational costs. In fact, we are not aware of any
deterministic radiative transfer models that would satisfy these criteria.
Technical details
The MC-UniK is a forward Monte Carlo model for efficient calculations of
radiances at discrete directions. It employs the local estimate method
e.g., and has been validated within the Intercomparison
of 3-D Radiation Codes (I3RC) project . The model simulates the
scattering events of photons within the ice cloud/atmosphere using a
non-truncated treatment for the phase functions. The free path length is
based on Beer's law and gives the distance between two successive scattering
processes. The scattering direction is derived using a random number
generator so that the scattering angle s corresponding to a given random
number [0, 1] equals the cumulative phase function from 0 to s, and the
azimuth angle is sampled uniformly in the range [0, 2π]. Absorption is
taken into account by multiplying the photon weight by the local single-scattering albedo. For reasons of variance reduction and computing time,
techniques as proposed by have been implemented. For
calculating the radiance field, the local estimate method is more efficient
than the common Monte Carlo photon counting method because no photons get
lost. Thus, in effect, MC-UniK assumes that a fraction of the photon is
scattered directly into each detector. These photons are attenuated along the
optical path between the scattering location and the detector.
Modifications
We have modified the original MC-UniK to account for the finite width of the
solar disk, i.e., an opening angle of 0.534∘. In addition, a
phenomenon called limb darkening is accounted for. The solar radiation that
reaches the observer originates in the photosphere of the sun peaking at an
optical depth of roughly unity along the line of sight. On average, this
corresponds to a temperature of about 5778 K. However, along a slant line of
sight toward the sun's limb, an optical depth of one is reached at a higher
altitude with a lower temperature. Hence the intensity reaching the observer
from the limb of the sun is lower than that from the center
. In our version of MC-UniK the limb darkening is taken
into account by using the formula
I(β)=I(0,0)[a+bcos(β)+ccos2(β)]
given in , where β is the angular distance from
the center of the sun to the limb (0–90∘). At λ= 0.69 µm (the closest available wavelength to 0.67 µm), the
coefficients have values of a= 0.4128, b= 0.7525, and c=- 0.1761.
The model output is modified to include the direct and diffuse radiances at
the surface (in units of Wcm-2µm-1sr-1) for specified
detector positions. For the mean solar constant at
λ= 0.670 µm, values of 0.1509 Wcm-2µm-1
and 2206 Wcm-2µm-1 sr-1 are used in
the calculation of diffuse and direct radiances, respectively. The latter
value is obtained by dividing the former by the solid angle of the sun.
Detector positions in the MC-UniK model cover angles from 0 to -8 and 8∘from
the center of the sun (0, 0∘). Both horizontal and vertical cross sections are divided
into positive and negative parts (hp, hn, vp, vn). The circle demonstrates the size of the solar disk,
with a diameter of 0.534∘.
Input
The model domain is separated into grid boxes which are characterized by
their bulk optical properties: the volume extinction coefficient Kext,
the single-scattering albedo ω, and the scattering phase function
P11(γ), where γ is the scattering angle. Here the model
domain of MC-UniK is divided into 15 nonuniform vertical layers extending
from the ground up to 50 km. Gas absorption and Rayleigh scattering occur in
all layers, while aerosols are assumed to be confined to the lowest layer
below 2 km. The ice cloud resides between 8.0 and 11.5 km (model layers
5–11) depending on the case (see Sect. ). A plane-parallel
cloud is assumed due to insufficient information on the cloud horizontal
structure. Thus, while the Monte Carlo model can account for 3-D effects, the
effects related to cloud horizontal inhomogeneity are not accounted for.
Furthermore, the solar zenith angle (θ), detector positions, and
surface albedo data are required. A total of 418 detectors pointing to the
sun and its surrounding areas inside the opening angle of 16∘are
positioned so that they cover both the horizontal and vertical cross sections
of the area as illustrated in Fig. . For surface albedo, a
fixed value of 0.2 is used. To achieve sufficient accuracy for the
calculations, 8 million photons are used. At the angles considered here
(0–8∘from the center of sun), the resulting random errors are mostly
below 3 % (6 %) for rough (smooth) crystals, with smaller errors at the
smaller angles.
Optical properties
The optical properties of ice clouds (and atmospheric gases and aerosols)
needed as input to the MC-UniK are based on data collected during ARM's 2010 Small Particles in Cirrus
(SPARTICUS) field campaign . The
aircraft measurements were collected in the vicinity of the ground-based
measurements made at the SGP site. Out of the numerous case days of
SPARTICUS, only two were deemed suitable for the present investigation: 23
March (hereafter flight A) and 24 June (hereafter flight B). During these
flights, there was a visually observable cirrus cloud without lower cloud
layers and all the needed in situ and ground-based measurement data had good
quality.
Optical properties of atmospheric gases and aerosols
To account for Rayleigh scattering and gas absorption, the optical properties
(ω and Kext) of the atmosphere without cloud and aerosols are
calculated using the scheme of . The spectral band of
0.599–0.685 µm is used for gas absorption, with Rayleigh scattering
optical depth scaled to 0.67 µm. The vertical profiles of
temperature and water vapor are based on radiosondes launched at the SGP
site during the case days, complemented by ERA-Interim reanalysis data
in the middle and upper stratosphere. Ozone profiles are taken
from the ERA-Interim data. The phase function for Rayleigh scattering is
P11(γ)=(3/4)(1+cos2γ).
The ensemble-averaged aerosol ω and P11(γ) are taken from
the OPAC (Optical Properties of Aerosols and Clouds) database ,
assuming values for continental average aerosols at λ=0.650 µm computed at a relative humidity of either 70 % (for comparison
with SAM measurements during flight B) or 50 % (for all other
calculations).The aerosol optical thickness τa is estimated from the
AERONET level 1.5 τa retrieval (at λ=0.675 µm) and
from the visible Multifilter Rotating Shadowband Radiometer (MFRSR)
measurements (at λ=0.673 µm) conducted at the SGP site,
which yields τa=0.09 during flight A and τa=0.166 during flight
B. The aerosol Kext is derived from τa assuming that the aerosols
are confined to the lowest 2 km.
Ice crystal size-shape distributions
During SPARTICUS in situ probes were installed on the Stratton Park
Engineering Company (SPEC) Inc. Learjet 25 aircraft. The Learjet conducted
101 missions sampling several cirrus clouds in the midlatitudes of the
United States at temperatures between -70 and -20∘ C.
examined all the size and shape distributions sampled by the
SPEC Learjet during SPARTICUS, establishing the meteorological context of
each cirrus sampled. The two flights analyzed here are unique in that the
cirrus sampled had no underlying cloud layers below. The probes on the
Learjet that are used in this study include the Cloud Particle Imager (CPI)
acquiring high 2.3 µm resolution images of particles, the Fast
Forward Scattering Spectrometer Probe (FFSSP) measuring particles with
maximum diameter (Dmax) smaller than 50 µm from the forward
scattering of light, the two-dimensional stereo (2DS) probe nominally
measuring particles with 10 < Dmax < 1280 µm, and a two-dimensional
precipitation probe (2DP) measuring particles with 200 < Dmax < 6400 µm for flight A
and a High Volume Precipitation Spectrometer (HVPS-3)
measuring particles with 150 < Dmax < 19200 µm for flight B.
The final habit classes of large ice crystals that are created by combining habit classes of the IC-PCA
and further interpreted as habits. In addition to the IC-PCA-based habit distributions, largeA
and largeB, six single-habit distributions are used to describe the shape of large ice crystals.
Habit class
Habits of
Habit classes of IC-PCA
Column
Hollow column
Columns and bullets
Column agg
Column aggregate with eight elements
Column aggregates and bullet rosette aggregates
Bullet rosette
Bullet rosette
Bullet rosettes
Plate
Plate
Plate
Plate agg
Plate aggregate with five elements
Plate aggregate
Irregular
Plate aggregate with 10 elements
Irregular
Large
Fractional distribution of habits from in situ data
Habits classified using IC-PCA
The composite size distributions required to calculate the microphysical and
optical properties were determined using the FFSSP to characterize particles
with Dmax < 50 µm, the 2DS for 50 µm < Dmax < 1200 µm,
and the 2DP or HVPS-3 for larger particles. Concentrations
of small ice crystals (defined as those with Dmax < 100 µm)
are, however, highly uncertain due to a small and poorly defined sample
volume and potential contributions from shattered
artifacts e.g., in both the
2DS and FFSSP. Therefore, four alternative representations of the
concentration of small ice crystals are used to test the sensitivity of the
results to these concentrations. In small100%, the concentration of
crystals with Dmax < 100 µm is taken directly from the FFSSP
and 2DS measurements. In small0%, small50%, and small200%
the measured concentration is multiplied by 0 (i.e., no small ice crystals),
0.5, and 2, respectively.
Flight information. θ is the solar zenith angle during the flights A and B.
Flight A
Flight B
Date
23 March 2010
24 June 2010
Time (UTC)
16:58–17:56
14:35–15:58
θ (∘)
36.5–42.1
42.7–52.3
Cloud altitude (km)
9.5–11.5
8.0–11.5
Model layers with cloud
8–11
5–11
For large ice crystals (Dmax > 100 µm), the size-dependent
shape distributions are based on the CPI images measured in situ.
and show that the detailed shapes of small
ice crystals cannot be identified using the CPI due to its limited image
resolution and blurring of images due to diffraction that renders the shape
classification of small ice crystals unreliable. Due to the lack of reliable
in situ measurements of the shapes of crystals with Dmax < 100 µm, they are assumed to be hollow columns. For large crystals, an
automatic ice cloud particle habit classifier IC-PCA is used
to determine the fraction of different habits as a function of particle size
from the CPI images. The IC-PCA automatically sorts the crystals into eight
classes: bullet, column, column aggregate, bullet rosette, bullet rosette
aggregate, plate, plate aggregate, and irregular. In this study bullets are
classified as columns and bullet rosette aggregates as column aggregates due
to the lack of information about their single-scattering properties. The
final six habit classes listed in Table are named as column,
column agg, bullet rosette, plate, plate agg, and irregular. The
size-resolved shape distributions are created by combining the size
distributions (measured by 2DS and 2DP or HVPS-3) and the relative portions
of the size-resolved shape distributions from CPI/IC-PCA at each layer.
Vertically averaged size-shape distribution of in situ-measured ice crystals during the
flights on 23 March 2010 (flight A) and 24 June 2010 (flight B). These distributions were obtained
by weighting fractional habit distributions at each vertical layer by the corresponding particle size
distribution. The height of each column indicates the total number of particles in each size range
(logarithmic scale on the y axis). The fraction of particles of each habit is shown with different
colors (on a linear scale). Small ice crystals with Dmax< 100 µm are shown
in gray. They were treated as
columns in the calculations.
Based on the stepwise flight path of the aircraft, the measurements of ice
crystals are sorted into 0.5 km vertical layers. In each layer, the particle
concentrations and size distributions are averaged over the time the Learjet
was in the appropriate layer. During flight A the cloud was present in four
of the layers (from 9.5 to 11.5 km) and during flight B in seven layers
(8.0 to 11.5 km; Table ). The vertically averaged size-shape
distributions for flights A and B are shown in Fig. . The habit
distribution, the maximum ice crystal size, and fractional contribution of
small ice crystals are rather different for the two cases. Small ice crystals
with Dmax < 100 µm contribute as much as 79 % to the total
projected area and optical thickness for flight A, as compared with 27 % for
flight B. Considering the large ice crystals only, during flight A the
largest contributions to the projected area come from column aggregates (30 %) and bullet rosettes (29 %), whereas during flight B they come from column aggregates
(46 %) and plate aggregates (31 %). Comparing Fig. against
Fig. 10 in establishes the degree to which the data from
these two flights were representative of those observed during other
SPARTICUS flights: flight A tends to have lower n(D) than the average
observed during other flights whereas flight B tends to have larger n(D) than
the observed averages. Overall, flights A and B represent well the range of
conditions observed during SPARTICUS.
To investigate the impact of ice crystal sizes on disk and circumsolar
radiances, sensitivity tests were also conducted with a log-normal size
distribution:
n(D)=12πlnσgdexp-lnD-lnD022ln2σg.
Here σg is the geometric standard deviation (fixed at σg=1.5)
and D0 is the median diameter, for which values of 50, 100, 200, 400, and
800 µm are considered. The log-normal size distribution covers
particles with maximum diameter from 2 to 10 000 µm. The treatment
of ice crystal shapes in the tests with a log-normal size distribution is
discussed in Sect. , in connection to Eq. ().
Ensemble-averaged ice crystal optical properties
To obtain the ensemble-averaged optical properties of the ice clouds during
flights A and B, the in situ-measured size-shape distributions are combined
with single-scattering properties of individual ice crystals obtained from
the database of . In this database, the optical properties are
given as a function of wavelength and size (Dmax), shape, and roughness
of the particle. The three roughness options are completely smooth (CS; i.e,
homogeneous), moderately rough (MR), and severely rough (SR). The effect
of roughness is simulated by randomly distorting the surface slope for each
incident ray, assuming a normal distribution of local slope variations with a
standard deviation of 0.03 and 0.50 for the MR and SR cases, respectively
(Eq. 1. in ). In fact, this treatment does not represent any
specific roughness characteristics but attempts instead to mimic the effects
due to non-ideal crystal characteristics in general (roughness effects,
irregularities, and inhomogeneities like air bubbles).
For each ice crystal size and shape, the cross-sectional area A, the
extinction efficiency Qext, the single-scattering albedo ω, and
the phase function P11(γ) at λ= 0.670 µm are
obtained from the database, using the closest Dmax available in the
database. The phase function with 498 scattering angles (γ between 0
and 180∘) is interpolated to 2011 scattering angles to obtain
sufficient angular resolution in the near-forward directions. For
single-habit distributions, the in situ-measured size distribution N(Dmax>100 µm) of either flight A or B is combined with the optical
properties of that habit and then integrated over the size distribution to
obtain the vertical profiles of the ensemble-averaged optical properties
Kext, ω, and P11(γ).
Optical thickness and solar zenith angle (θ) as a function of time during the
flights A and B derived from the Sun and Aureole Measurements device at the SGP site.
For the IC-PCA-based habit distributions, the optical properties of each
habit are weighted by the IC-PCA fractions before size integration.
Hereafter, the optical properties based on the in situ-measured IC-PCA
size-shape distributions of flight A and B are referred to as largeA and
largeB, respectively, since small ice crystals were not classified by
shape. Finally, when studying the sensitivity of disk and circumsolar
radiances to the concentration of small ice crystals, largeA and largeB
are combined with the optical properties of the four alternative in situ-based size distributions of small, hollow column crystals (see
Sect. ).
In the radiative transfer simulations, however, the cloud optical thickness
integrated from the in situ-based size-shape distributions
(τc=∫Kext(z)dz, where z is altitude) is not used. Instead,
the same user-specified τc for each size-shape distribution in the
sensitivity tests is used. This overcomes the effects related to different
area ratios of the crystal habits and to enable the comparisons of the
size-shape distributions of flights A and B. By fixing the cloud optical
thickness, the in situ concentrations of the size-shape distributions are
adjusted by a uniform factor across all shapes and sizes. Furthermore, when
comparing the modeled radiances with those measured with the SAM instrument,
τc is adjusted so that modeled radiances in the disk region agree
closely (i.e., within ≈ 3 %) with the measurements. This often leads
to values of τc that deviate from those retrieved from the SAM
(τSAM) during flights A and B. The values of τSAM vary from
0.1 to 2.1 during flight A and from 0.3 to 3.6 during flight B
(Fig. ), indicating that the clouds were not horizontally
homogeneous during the flights. This further justifies the approach of using
a fixed cloud optical depth because variations in τSAM over the
course of a flight show that exact agreement between retrieved and
in situ-based optical depth should not be expected.
Sensitivity of the vertically integrated phase functions to the size-shape distribution
of large severely rough ice crystals. (a) The P11 of in situ-based distributions of
flights A and B and log-normal distributions with D0= 100/200/400 µm . (b, c) The
relative differences in P11 between the six single-habit distributions and the in situ-based distributions
for flight A (left) and B (right).
Ice cloud phase functions
Ice crystal phase functions play a key role in determining
the angular distribution of disk and circumsolar radiances. Therefore, to aid
the interpretation of the radiance comparisons, the impact of ice crystal
size, habit, and roughness on P11 (integrated over the cloud depth and
the size-shape distribution) is considered in Figs and . First, the impact of ice crystal size on P11 is
demonstrated in Fig. a, which shows phase functions for
three log-normal size distributions with D0= 50, 200, and 800 µm
and for the in situ-based largeA and largeB distributions, assuming SR
ice crystals. The phase functions of the log-normal size distributions defined
by Eq. () are calculated as a weighted sum over the six
habits considered in Table :
P11(γ,D0,σg)=∑i=16wiP11i(γ,D0,σg),
where P11i(γ,D0,σg) is the phase function corresponding to
the log-normal size distribution for habit i and wi is the weight factor.
Here, the weight factors wi were chosen to equal the fractional
contributions of each habit to the projected area for the largeA
distribution (see Sect. ). This treatment ensures that,
independent of the value of D0, the fractional contributions by different
habits remain the same, which helps to isolate the effect of crystal size.
Tests were also conducted with wi based on the largeB distribution, and
similar effects of crystal size were found (not shown).
Sensitivity of the vertically integrated phase functions to the roughness of large ice
crystals. (a) The P11 of the in situ-based size-shape distribution of smooth,
moderately,
and severely rough ice crystals of flight A (largeA). (b, c) The
relative differences in P11 between MR and CS ice crystals and between SR and CS ice crystals of flight A and B.
By comparing the P11 for the different log-normal distributions in
Fig. a it is seen that ice crystal size has systematic
effects on the phase function. With increasing D0, the diffraction peak
becomes sharper and narrower, so that the phase function increases at
very-near-forward directions but decreases at larger scattering angles up to
a few degrees. The phase functions computed for the in situ-based largeA
and largeB distributions follow this same pattern. Due to the presence
of larger ice crystals during flight B than during flight A
(Fig. ), the angular slope of P11 is steeper for flight B
than for flight A. The values of P11 decrease by roughly 4 orders of
magnitude from the exact forward-scattering direction γ=0∘ to
γ=10∘ for flight A and by nearly 5 orders of magnitude for
flight B.
The impact of ice crystal habit on P11 is illustrated in
Fig. b–c, which shows the phase function differences
between P11 of single-habit distributions and the largeA and
largeB distributions, respectively. The differences in P11 related to
ice crystal habit are relatively subtle compared to the large angular slope
of P11 in near-forward directions, but not negligible. At scattering
angles of 0 to 0.1∘, plates yield the strongest forward scattering
(over 35 % stronger than that of the observed largeA or largeB habit
distributions) and bullet rosettes or plate aggregates the weakest scattering
(up to 25 % weaker than that of the largeA or largeB distributions).
Furthermore, while the P11 of plates is lower than that of most other SR
habits at angles of 0.3–1∘, it is highest among the habits considered
at angles of 2–10∘. At these angles, plates yield up to 60 and 80 % larger P11 than the observed
largeA and largeB distributions,
respectively, while columns and column aggregates yield ≈ 20 % lower
values. The impact of habit depends somewhat on the assumed ice crystal
roughness; in particular, for CS crystals, P11 of plates exceeds that of
the largeA and largeB distributions by over 80 % in the very-near-forward directions of 0–0.1∘.
Figure a compares the P11 corresponding to the three
roughness assumptions for the largeA size-shape distribution, while
Fig. b–c show the relative differences between the SR and
MR ice crystals and the CS ice crystals for the largeA
and largeB distributions. The P11 for rough ice crystals is lower
than that for CS crystals in very-near-forward scattering directions but
larger at larger angles, starting from ≈ 0.8∘ for MR crystals
and from ≈ 1.7∘ for SR crystals. Furthermore, the P11 of
MR crystals exceeds that for SR crystals up to ≈6∘, but at
larger angles SR crystals yield the largest P11. Quantitatively, the
impact of roughness is very large and clearly exceeds that of ice crystal
habit. The relative difference between MR and CS crystals peaks at
4–5∘, reaching 400 % for largeA and over 700 % for largeB,
while the difference between SR and CS crystals is largest at 7–8∘ (up
to 500 % for largeA and over 600 % for largeB).
The phase function differences seen in Fig. are mainly
related to rays that are transmitted through an ice crystal, entering and
exiting through parallel crystal faces. If the crystal faces are exactly
parallel, the phase function contribution by this process is concentrated at
very small scattering angles (if finite-size effects are accounted for, as in
the database) or even in the exact forward direction (i.e.,
delta transmission), in the limit of geometric optics. However, in the case
of MR and SR crystals, the ice crystal surface slopes are distorted randomly
for each incident ray, which, in effect, eliminates ray paths that pass
through exactly parallel faces. Hence for both MR and SR crystals, P11
is lower than that for CS crystals in very-near-forward scattering
directions but larger at larger angles (see Fig. ).
Furthermore, almost the same amount of scattered energy is removed from the
very-near-forward directions (up to 0.5∘) for MR and SR crystals and
added at larger scattering angles, although with a different angular
distribution. The standard deviation of local slope variations assumed in the
case of MR crystals is σ=0.03, implying that the scattering angle is
typically modified by a few degrees, whereas for SR crystals with
σ=0.50 the scattered energy is distributed over a much larger range
of scattering angles. This explains why the relative difference between MR
and CS crystals in Fig. peaks at smaller scattering angles
than the difference between SR and CS crystals and why P11 for MR
crystals exceeds that for SR crystals up to 6∘.
Disk and circumsolar radiances: sensitivity tests
In the sensitivity simulations, the size-shape distribution and roughness of
ice crystals, ice cloud optical thickness τc, and aerosol optical
thickness τa are varied. When not otherwise stated the following
parameter settings are used: (1) either the largeA or largeB size-shape
distribution of large severely rough ice crystals, with no small crystals
with Dmax< 100 µm; (2) cloud optical thickness τc=1.6; (3) atmospheric and aerosol properties corresponding to flight A; (4) aerosol
optical thickness τa=0.09; (5) solar zenith angle of
θ=40∘. The simulated radiances (in
Wcm-2µm-1sr-1) are shown as a function of the angular
distance from the center of the sun (0∘) out to 8∘ when looking
towards the sun from the ground (see Fig. ).
Impacts of the aerosol and cloud optical thicknesses on the simulated radiances as a
function of angle from the center of the sun out to 8∘. Atmospheric and aerosol properties
are based on flight A with either τa=0.09 or τa=0.166. The cloud is described with the
largeA distribution of large SR ice crystals using two cloud optical thicknesses, τc=0.2 and 1.6.
Sensitivity of radiances to optical path
To demonstrate the impact of aerosol and cloud optical thicknesses on
radiance, Fig. shows the simulated radiances for an aerosol-
and cloud-free atmosphere (i.e., “gases only”) and for cloud-free (with gases
and aerosols) and cloudy (gases, aerosol and ice cloud) atmospheres. The
largeA size-shape distribution is used for the cloud, and two values are
considered both for cloud (τc= 0.2 and τc= 1.6) and aerosol
(τa= 0.09 and 0.166) optical thickness. From Fig. it is
seen that in the “gases only” case there is a huge contrast between the very
strong radiances in the disk area (1000–2400 Wcm-2µm-1sr-1) and the weak and almost constant radiances
(≈ 0.001 Wcm-2µm-1sr-1) in the circumsolar
region. In the presence of aerosols with τa= 0.09 or τa= 0.166, the
disk radiances are 11 and 18 % smaller and the circumsolar radiances are
1 to 2 orders of magnitude greater than in the “gases only” simulation.
While the circumsolar radiances are ≈ 60 % larger for τa=0.166
than for τa=0.09, the relative difference between these cases decreases
to less than 20 % when an ice cloud is included, even for τc=0.2.
In the presence of a cirrus cloud, the circumsolar radiances are orders of
magnitude greater than in the “gases only” and cloud-free cases as seen from
Fig. . The most striking effects, both in the absolute values
and in the angular dependence, are seen in the angular region between the
limb of the solar disk and 1∘, where in the cloudy cases the radiances
are between 100 and 0.8 Wcm-2µm-1sr-1 as compared with
∼0.1 Wcm-2µm-1sr-1 for the cloud-free cases and
∼0.001 Wcm-2µm-1sr-1 for the gases only case. The
increase in diffuse radiance in the presence of a cirrus cloud is due to the
strong forward-scattering peak of ice crystals, whereas the smaller disk
radiances are due to the larger total optical thickness. The disk radiance
decreases monotonically with increasing τc, being 74 % less for
τc=1.6 than τc=0.2. This is due to the decrease in direct solar
radiation; the diffuse radiation in the disk region is, in fact, larger for
τc=1.6 than τc=0.2 (see the insert in Fig. ). In
contrast, the circumsolar radiance is on average 140–170 % larger for
τc=1.6 than τc=0.2, depending on the assumed τa. However,
as demonstrated in Fig. , the increase of diffuse radiance with
τc is not linear, and when attenuation becomes strong enough the
amount of diffuse radiation decreases with increasing τc, in both the
disk and circumsolar regions.
Sensitivity of the disk and circumsolar radiances to cloud optical thickness when the cloud
is described using the largeA distribution of SR ice crystals. Relative differences between radiances
simulated with alternative cloud optical thicknesses (τc of 0.2, 0,4, 0,8, and 3.2)
and τc=1.6 are displayed. The insert shows the relative differences in diffuse radiance
at angles of 0–0.8∘. In these simulations τa=0.09.
Sensitivity of the radiances to ice crystal sizes
The impact of ice crystal size on disk and circumsolar radiances is
illustrated in Fig. , for log-normal size distributions with
habit weight factors based on the IC-PCA habit distribution of flight A (see
the first paragraph of Sect. ). As expected based on previous
research e.g., and the phase functions in
Fig. , the ice crystal size has systematic effects on
radiances in the vicinity of sun. With an increasing median diameter D0,
the radiances increase at very small angles (up to ≈ 0.3–0.4∘
from the center of the sun) but decrease at somewhat larger angles, with
largest effects at ≈ 0.5–2∘ for CS crystals and ≈0.5–1∘ for SR crystals. At angles of several degrees, the impact of
D0 becomes small especially for SR crystals. Decreasing D0 has opposite
effects. For example, doubling D0 from 200 to 400 µm decreases
the radiance at 0.5–1∘ by up to 45 %, while halving D0 from 200
to 100 µm increases it by up to 80 %, for the optical thickness
τc=1.6 considered here. The effects in the solar disk area are somewhat
smaller, ≈ 15 % for SR crystals and ≈ 25 % for CS
crystals. These difference arise, to a large part, from the effect of ice
crystal size on the diffraction peak (see Fig. ).
A related issue is the effect of small ice crystals, for which the
measurements are quite uncertain. To probe the impact of uncertainties in the
measurements of small ice crystals, the effects of their concentration on the
disk and circumsolar radiances are simulated. Simulations are made with the
largeA and largeB distributions together with 0–200 % of the measured
concentration of small column-shaped ice crystals (small0%,
small50%, small100%, and small200%). In these simulations,
ice crystals are severely rough and τc=1.6. The angular dependence of
the total radiances simulated with 0 and 100 % of the measured small-crystal
concentrations are shown in Fig. a at angles of 0 to 4∘
from the center of the sun. Regardless of the small-crystal concentration,
the radiances at angles larger than 5∘ are within 3 % of each other
during flights A and B. Because the same cloud optical thickness is assumed
for all the size distributions, including small ice crystals necessarily
decreases the concentration of large ice crystals. This acts to decrease the
near-forward radiances in the disk region and just around it and to increase
the circumsolar radiances at angles between 0.5 and 5∘ from the center
of the sun. Again, this is due to the wider forward-scattering peak of the
small ice crystals.
Impact of ice crystal size distribution on the disk and circumsolar radiances.
(a) shows, for reference, the radiances for a log-normal size distribution with a median
diameter D0=200 µm for smooth (CS) and severely rough (SR) ice crystals.
(b) and (c) show the relative differences to the case with D0=200 µm
for D0= 50, 100, 400, and 800 µm. In these simulations, τa=0.09 and τc=1.6.
Quantitatively, the impact of the assumed concentration of small ice crystals
is substantial and somewhat larger for flight A than flight B (see
Fig. b–c). Compared to the cases with large ice crystals only,
the relative reduction in radiance due to small ice crystals is largest near
the edge of the solar disk, amounting up to -47 for flight A and -22 % for flight B. The largest relative increases occur at 1–2∘ from
the center of the sun. For flight A, the maximum differences to the case with
large ice crystals only are 95, 111, and 123 %, and for flight B, 33, 55, and 84 %, when assuming 50, 100, and 200 % of the observed
concentration of small ice crystals, respectively. The impacts of size on
diffuse radiation tend to be opposite in the disk and circumsolar regions and
partly cancel each other, leading to smaller differences when averaged from
0 to 3∘. Even so, for a fixed cloud optical thickness of 1.6,
including 100 % of the observed concentration of small crystals, the average
total radiance in this angular range is 26 % larger than in the case with
large crystals only for flight A and 11 % larger for flight B. The amount
of diffuse radiation in this angular range is 44 and 53 % of the total
radiance for largeA and largeB, respectively. The corresponding
fractions in the disk region are 41 and 51 %.
(a) Impact of the concentration of small ice crystals on the disk and circumsolar
radiances. The simulations are made with the largeA and largeB distributions of large ice crystals
including 0–200 % of the measured concentration of small ice crystals assumed to be columns.
(b, c) Relative differences to the case with no small ice crystals.
In these simulations ice crystals are severely rough, τa=0.09, and τc=1.6.
Sensitivity of the radiances to shape and roughness of ice crystals
Sensitivities of the disk and circumsolar radiances to the size-shape
distributions of large ice crystals are addressed by comparing results for
the six single-habit distributions and the measured habit distributions of
flights A and B. The radiances simulated with largeA and largeB
size-shape distributions are compared in Fig. a. For largeB,
the total radiance in the disk region is 10 to 20 % larger than for
largeA, and the circumsolar radiance is smaller by up to 30 %, even
though the same τc is assumed in both cases. This occurs because the
ice crystal population for flight B results in a stronger and narrower
forward-scattering peak in P11 as noted already from Fig. . As the optical thickness is the same in both cases, the
differences in the total radiances arise from differences in the diffuse
component.
The relative differences between the six single-habit distributions and the
largeA or largeB distributions are shown in Fig. b–c for
total radiances. The differences in radiances follow the differences in
P11 of the habit distributions shown in Fig. . In the
disk region the difference between different habit distributions reaches at
most 15 %. The impact of habit, however, differs between flights and
therefore depends on the size distribution. Based on the circumsolar
radiances, the habits can be divided into two groups: column-like (column,
column agg, and bullet rosette) and plate-like crystals (plate, plate agg, and
irregular). Column-like crystals tend to result in a steeper angular slope in
radiances, producing larger diffuse radiances in the disk region and smaller
radiances in the circumsolar region than plate-like crystals do. In the
circumsolar region, plate and column agg tend to differ most from each other
regardless of the size distribution. The relative differences in the
circumsolar region between the single-habit distributions and CPI-based habit
distributions reach up to 60 % for flight A and up to 80 % for flight B,
similarly to the phase functions differences in Fig. . The
impact of ice crystal habit also depends on the cloud optical thickness.
Generally, as τc increases and multiple scattering becomes more
important, the relative differences in diffuse radiances between different
habits are reduced.
Impact of the shape of large severely rough ice crystals on the disk and circumsolar
radiances. (a) The total radiances based on the largeA and largeB distributions.
(b, c) The relative differences of the radiances based on the six single-habit
distributions of flight A or B and the largeA or largeB, respectively. All the simulations are
conducted with τa=0.09 and τc=1.6.
The impact of ice crystal roughness on the radiances is depicted in
Fig. . Consistent with the large phase function differences
in Fig. , the impacts of roughness on the radiances are
substantial: rough crystals yield smaller diffuse radiances than smooth
crystals at angles smaller than 1 to 2.5∘ but larger diffuse radiances
at angles larger than that. In the disk region, SR and MR crystals produce
almost identical radiances, which are within 1 % of each other but 15 to
21 % below those of smooth crystals, depending on the flight. In the
circumsolar region at angles smaller than 7∘, MR crystals produce
larger radiances than the SR crystals, the relative differences being largest
at angles of 2 to 3∘, up to 140 for flight A and 195 % for
flight B. The relative differences between MR and CS crystals are largest at
angles of ∼ 4∘, reaching up to 425 % for flight B.
Correspondingly, the maximum relative differences between SR and CS crystals
occur at angles larger than 6∘, reaching 240 % for flight B. These
angle-dependent radiance differences between different roughness assumptions
follow the P11 differences shown in Fig. . The relative
differences in radiances are, however, not quite as large as those in
P11, and they decrease somewhat with increasing τc (here,
τc= 1.6) due to the effects of multiple scattering. In any case,
roughness has a large impact on both the disk and the circumsolar radiances,
and these differences clearly exceed the corresponding differences between
different SR habits (compare Figs. and ).
A semi-quantitative summary on the strength of the impacts of microphysical parameters to the direct
radiance and four different angular regions of circumsolar radiance. Impacts due to
the ice cloud optical thickness are addressed in the first row and those due to size, shape, and roughness of ice crystals in the following rows. In
parentheses is the parameter value against which the relative differences are calculated. The maximum
relative strength of the impact is given with symbols:
- (impact < 50 %), + (50 % < impact < 100 %), ++ (100 % < impact< 200 %), and
+++ (200 % < impact). It
is based on the conducted sensitivity tests (see Figs. –).
Parameter
Dir 0.0–0.27∘
Diff 0.0–0.27∘
Diff 0.27–1 ∘
Diff 1–3∘
Diff 3–8∘
Optical thickness (τc= 1.6)
+++
+
+
+
+
Median size (D0= 200 µm)
-
+
+++
+++
+
Small crystals D< 100 µm (largeA/B)
-
+
+
++
+
Shape distribution (largeA/B)
-
-
-
+
+
Roughness (CS)
-
-
-
+++
+++
(a) Impact of the roughness (smooth, CS, moderately, MR, and severely rough, SR)
of large ice crystals on the disk and circumsolar radiances in case of the largeA size-shape
distribution. (b) Relative differences between results based on the MR or SR and CS ice
crystals for the largeA and largeB distributions. In these simulations τa=0.09 and τc=1.6.
The roughness and shape of the particles also impact the fractional
contribution that diffuse radiation makes to the total radiance in the range
of 0 to 3∘ typically measured by pyrheliometers. For the cases
considered here, the fractional contribution of diffuse radiation to total
radiation is ≈10 percentage points larger for CS than SR or MR ice
crystals. The impact of shape distribution is somewhat smaller, between four and
seven percentage points.
Summary of sensitivity tests
The results of the sensitivity tests are summarized in Table , where the importance of various ice cloud properties on
the disk and circumsolar radiances in four angular regions is characterized
in a semi-quantitative manner. Trivially, the direct solar radiation depends
only on the cloud optical depth τc through Beer's law. The optical
depth also impacts strongly the magnitude of the diffuse radiance but not so
much its angular distribution in the circumsolar region (see Fig. ). Ice crystal size has a large impact on circumsolar radiance
at angles close to the sun due to the well-known impact of particle size on
the diffraction peak. Assumptions about ice crystal roughness influence the
circumsolar radiation very strongly, especially at angles larger than about
2–3∘. In comparison to the effects of ice crystal size and roughness,
the impact of ice crystal habit is moderate, being most pronounced in the
outermost region (3–8∘) considered in Table .
The effects of particle roughness, size, and habit on the distribution of
diffuse radiation are closely linked to the corresponding effects on phase
function. The impact of particle size on P11 is well known, and it has
been previously discussed in the context of circumsolar radiation
. The impacts on near-forward
scattered radiation due to ice crystal roughness and habit have also been
considered . However, the present study
extends the knowledge gained in previous research as we simulate in detail the angular
distribution of phase function and radiances instead of circumsolar
irradiances integrated over some angular range (as in ).
The potential applications of these results include remote sensing of optical
thickness, ice cloud properties based on the radiance field near the sun, and
the design of concentrating solar energy applications. For example, when
retrieving cloud optical thickness from measurements of direct solar
radiation from ground using instruments with a typical half-opening angle of
3∘, one needs to account for the fact that there can be a substantial
amount of diffuse radiation within the instrument's field of view
. Similarly, when evaluating the potential
of concentrating solar collectors with typical half-opening angles of
≈ 1∘ , one has to
consider the narrower field of view as compared with measurements of
“direct”
solar radiation. Our sensitivity tests reveal that in the presence of an ice
cloud, the diffuse radiation in the angular range from 0 to 3∘ is
especially sensitive to the roughness and size distribution of the ice
crystals, with the shape of ice crystals being less important.
Overall, the sensitivity tests highlight the important role of ice crystal
size distribution and roughness on the distribution of radiances in the
vicinity of the sun. However, in situ microphysical measurements yield no
information on roughness and only very uncertain information on small ice
crystals. This motivates the study of how assumptions related to these
factors impact the comparison between simulated and measured radiances in
Sect. .
The values of solar zenith angle θ and optical thickness of cloud (τc), aerosols (τa),
and gases (τgases) used in the comparison simulations for flight A. The cloud is described with the size-shape
distributions largeA and largeA+small100% of rough (MR and SR) and completely smooth (CS) ice crystals.
The fractional contribution of small ice crystals to cloud optical thickness for the largeA+small100%
size-shape distribution (fsmall) and the total optical thickness (cloud + aerosols) retrieved from the Sun and
Aureole Measurements (SAM) instrument are also listed.
θ (∘)
40.5
38.3
38.6
τgases
0.072
0.072
0.072
τa (AERONET, MFRSR)
0.09
0.09
0.09
fsmall, largeA+small100%
79 %
79 %
79 %
τc, CS, largeA+small100%
0.6
1.05
2.5
τc, MR/SR, largeA+small100%
0.6
1.0
2.4
τc, CS, largeA+small0%
0.75
1.25
3.1
τc, MR/SR, largeA+small0%
0.65
1.15
2.75
τSAM
0.6
1.0
2.1
Cloud scenes based on the total sky imager (TSI) located at the SGP site. Images are shown for the six times corresponding to the times of SAM measurements used in the comparison with simulations (see Tables and ).
Comparison of the simulated and measured radiances
During SPARTICUS, disk and circumsolar radiances were measured with the SAM
instrument of Visidyne Inc. located at the SGP site. For both flights A and
B, horizontal cross sections of SAM measurements from three different times
are selected for comparison. Note that the radiance arriving at different
sensors comes from different parts of the cloud. To assure that the observed
angular dependence of radiance is not due to cloud inhomogeneity, only cases
where the radiance distributions measured to the right and left of the sun
(the “hp” and “hn” curves; see Fig. ) are similar are
considered. The cloud scenes for the times selected for comparing SAM
measurements and simulated radiances are shown in Fig. . The goal
is to reproduce these radiances using the in situ-based size-shape
distributions of ice crystals. The simulations are conducted both with and
without the contribution of small ice crystals, assuming 100 % of the
measured small-crystal concentration in the former case. The atmospheric and
aerosol properties of flights A and B are used in the simulations. Due to the
large-scale inhomogeneity of the clouds, the cloud optical thickness τc
was adjusted separately for each case, based on the criterion that the
simulated radiance averaged over the solar disk should be within 3 % of the
SAM measurements. The resulting values of τc are listed in Tables and for flights A and B, respectively,
along with θ of the selected SAM measurement times and the total
apparent optical thickness (cloud + aerosols) retrieved from SAM assuming
that the disk radiance consists of direct solar radiation only. The derived
values of τc depend not only on the measurement time but also on the
assumptions about ice crystal roughness and small ice crystals. In
particular, for a given optical thickness, stronger disk radiances are
produced by smooth compared to rough crystals (see Fig. ),
and, consequently, larger τc is needed to match the SAM measurements in
the case of smooth compared to the case of rough ice crystals. Further,
τc tends to be larger than that reported by the SAM. This is in line
with , who found that the τSAM needs to be corrected
upward to account for forward scattering of ice crystals.
Comparison of SAM measured (hp and hn for the horizontal profiles to the right and left from the center of the sun) and simulated radiances at three measurement times
during flight A. For the simulations, the largeA distribution with 100 and 0 % of
measured concentration of small ice crystals is used with τ and θ values listed in
Table . Smooth (CS) and rough (MR and SR) ice crystals are considered.
Comparison of SAM measured (hp and hn for the horizontal profiles to the right and left from the center of the sun) and simulated radiances at three measurement times
during flight B. For the simulations, the largeB distribution with 100 and 0 % of
measured concentration of small ice crystals is used with τ and θ values listed in
Table . Smooth (CS) and rough (MR and SR) ice crystals are considered.
The simulated radiances are compared with the selected SAM measurements in
Figs. and for flights A and B,
respectively. Both the simulated and the SAM-measured radiances shown are
horizontal profiles (to the left and right; see Fig. ) from
the center of the sun out to 8∘. As the simulated clouds are
horizontally homogeneous, the profiles to the left and right from the center
of the sun are averaged, whereas for SAM they are shown separately as the
“hp” and “hn” curves. As exhibited in these images, when the aureole
intensity drops below the sensitivity limit of the SAM 300 solar disk imager,
a gap results, starting somewhere at or beyond the disk edge, e.g., ≈0.27∘, and extending out to ≈0.6∘, where the solar
aureole imager begins its measurements. When both the forward scattering and
the optical depth are sufficiently large, the aureole profile can be within
the sensitivity range of the disk imager and the gap disappears.
The values of solar zenith angle θ and optical thickness of cloud (τc), aerosol (τa), and
gases (τgases) used in the comparison simulations for flight B. The cloud is described with the
size-shape distributions largeB and largeB+small100% of rough (MR and SR) and completely smooth (CS)
ice crystals. The fractional contribution of small ice crystals to cloud optical thickness for the largeB+small100%
size-shape distribution (fsmall) and the total optical thickness (cloud + aerosols) retrieved from the Sun and
Aureole Measurements (SAM) instrument are also listed.
θ (∘)
50.4
50.0
44.3
τgases
0.074
0.074
0.074
τa (AERONET, MFRSR)
0.166
0.166
0.166
fsmall, largeB+small100%
27 %
27 %
27 %
τc, CS, largeB+small100%
0.7
1.3
3.5
τc, MR/SR, largeB+small100%
0.6
1.15
3.05
τc, CS, largeB+small0%
0.75
1.45
4.0
τc, MR/SR, largeB+small0%
0.65
1.25
3.3
τSAM
0.6
1.0
2.3
First, it is noted that while (by construction) the average simulated disk
radiances agree closely with the SAM measurements, the angular slope measured
is not quite consistent with the limb-darkening profile used in the
simulations. The reasons for this discrepancy are not clear and should be
scrutinized in future work. Second, considering the circumsolar radiances,
the simulations with SR ice crystals better capture the measured angular
dependence than do the simulations for CS crystals. The use of CS ice
crystals overestimates near-disk radiances and underestimates the radiances
at angles larger than about 3∘. It is further noted from Figs. and that excluding small crystals
decreases the radiances at angles smaller than 3∘ and, by doing so,
tends to improve the comparison of radiances at these angles. Overall, it
appears that the angular dependence produced by large SR crystals is most
similar to the measurements, even though it tends to overestimate the
radiances at angles larger than ≈ 6∘ in most cases.
The systematically better performance of SR than CS ice crystals in
simulating the measured radiances in the circumsolar region suggests that the
SR crystals better approximate the phase function of ice crystals present
during flights A and B, at least in near-forward directions. Furthermore, the
SR crystals are more consistent with the measured radiances than the MR
crystals. The use of MR crystals results in radiances that exceed those for
CS and SR crystals and also the measurements between angles of
≈ 1 and 6∘, even when small ice crystals are not
accounted for. Referring to the discussion in Sect. , the better
performance of SR compared to CS crystals suggests that ray paths passing
through smooth, exactly parallel ice crystal faces are less common in nature
than they would be for idealized ice crystals. However, there is no reason to
expect that the somewhat ad hoc approach employed in the
database to represent ice crystal “roughness” (or rather, non-ideal features
like roughness, irregularities, and inhomogeneity in general) would result in
a perfect description of P11. Even so, these results add to the growing
body of evidence suggesting that the scattering
by natural ice crystals most often differs from their idealized counterparts,
in the near-forward directions as well .
Conclusions
In this study, the amount of diffuse radiance in the solar disk region and in
the circumsolar region up to angles of 8∘ from the center of the sun were
quantified using a modified version of the Monte Carlo radiative transfer
model MC-UniK. The input data for the model were derived from the measured
size-shape distributions of two ice cloud cases observed over the ARM
Southern Great Plains measurement site during the 2010 SPARTICUS campaign.
This work extends and supports the previous studies on the impact of ice
crystals' properties on near-forward scattering and circumsolar radiation
by modeling radiances instead of irradiances
and by conducting systematic sensitivity tests using in situ-based size-shape
distributions of ice crystals.
In the sensitivity tests, it was found that the disk and circumsolar
radiances depend substantially on the ice crystal properties (roughness and
size-shape distribution) through their impact on the phase function, in line
with previous research :
Of all parameters considered, assumptions about ice crystal roughness
(or non-ideal features in general) were found to be most important.
The use of moderately or severely rough ice crystals instead of
completely smooth crystals leads to reduced radiances in the solar disk
region while substantially increasing radiances in the circumsolar region
at angles larger than ≈ 1–2.5∘, with maximum differences
as large as 400 % between MR and CS crystals and 200 % between SR and CS
crystals.
Ice crystal size distribution is also important for the angular distribution of circumsolar radiance. With increasing ice crystal
size, the diffraction peaks becomes sharper and narrower, so that disk
radiances increase but radiances at angles of ≈ 0.5–5∘
decrease. Increasing the portion of small ice crystals has the opposite
effect. In particular, if 100 % of the measured but uncertain concentration
of small ice crystals is included in the calculations, radiances at
≈ 1–2∘ from the center of the sun can be up to
≈ 100 % larger than in the case with only large ice crystals.
Column-like crystals tend to yield radiances with a steeper angular slope than plate-like crystals, as they produce more diffuse radiance in the
disk region and less in the circumsolar region than plate-like
crystals. The relative differences between all single-habit distributions
and the actually measured habit distributions were less than 10 % in the
disk region but up to 80 % at angles larger than 4∘ from the center of the sun.
The quantitative results listed above depend on the cloud optical thickness
and solar zenith angle. In general, an increasing path length through the
cloud acts to reduce the radiance contrast between the disk region and the
circumsolar region and the impact of the phase function. Changes in aerosol
optical thickness also affect the absolute values of the radiances in the
presence of an ice cloud but not significantly their angular dependence.
Simulated radiances were compared with ground-based measurements with the SAM
instrument for three measurement times during both flights A and B. It was
found that SR ice crystals mimicked the measured circumsolar radiances better
than either the MR crystals (which overestimated the radiances at angles of a
few degrees) or the CS crystals (which invariably underestimated the
radiances at angles larger than ≈ 3∘). In some cases, the
agreement was better when crystals smaller than 100 µm were
neglected from the measured size distribution, suggesting that the
measurements may have overestimated the concentration of small crystals.
These results add to the growing body of evidence suggesting that natural ice
crystals tend not to be pristine .
Even though we had detailed information about the size-shape distribution of
ice crystals of the clouds studied, the observed radiances could not be
reproduced perfectly. There are several factors that possibly contribute to
this. Part of the discrepancies can be surely attributed to the
imperfect
spatiotemporal collocation of the in situ and SAM measurements. It is also
quite possible that the simplistic ad hoc scheme employed to mimic the
effects of roughness, non-ideality, and internal structures on scattering is
not entirely realistic or representative of natural ice crystals. Further,
the limb-darkening parameterization may not be entirely accurate, and some
discrepancies might also be due to the aerosol optical properties chosen.
Likewise, there may be some remaining inhomogeneities in the clouds that our
analysis did not reveal. Finally, it is entirely possible that the clouds
sampled had mixtures of ice crystals with varying degrees of deformation, in
which case any one crystal roughness model could not be expected to perform
perfectly, but a combination of differently deformed crystals should be used.
In the future, the version of MC-UniK modified for the present work could be
used for analyzing a wide range of cirrus cloud and aerosol scenarios and
their 3-D effects on near-forward radiances. The unique modeling results might
be of interest for the design of concentrating solar power systems and for
the interpretation of data from instruments intended to measure the direct
solar radiation. The results could also be utilized for evaluating the
contribution of diffuse solar radiation to the disk radiation in SAM
measurements, thereby allowing for a more accurate determination of the
“true” direct solar radiation and hence the optical thickness. Furthermore,
they might be exploited for developing methods to retrieve ice cloud
properties from measurements of disk and circumsolar radiances; in
particular, it might be possible to estimate ice crystal non-ideality from
SAM measurements. Finally, the combination of SAM with sun photometer
measurements (e.g., AERONET) might allow the separation of the contributions of large
and small particles (e.g., ice crystals vs. aerosols) to optical thickness.