Halo displays, in particular the 22∘ halo, have
been captured in long time series of images obtained from total sky imagers
(TSIs) at various Atmospheric Radiation Measurement (ARM) sites. Halo
displays form if smooth-faced hexagonal ice crystals are present in the
optical path. We describe an image analysis algorithm for long time series
of TSI images which scores images with respect to the presence of
22∘ halos. Each image is assigned an ice halo score (IHS) for
22∘ halos, as well as a photographic sky type (PST), which
differentiates cirrostratus (PST-CS), partially cloudy (PST-PCL), cloudy
(PST-CLD), or clear (PST-CLR) within a near-solar image analysis area. The
color-resolved radial brightness behavior of the near-solar region is used
to define the discriminant properties used to classify photographic sky type
and assign an ice halo score. The scoring is based on the tools of
multivariate Gaussian analysis applied to a standardized sun-centered image
produced from the raw TSI image, following a series of calibrations,
rotation, and coordinate transformation. The algorithm is trained based on a training set for each class of images. We present test results on halo
observations and photographic sky type for the first 4 months of the year
2018, for TSI images obtained at the Southern Great Plains (SGP) ARM site. A
detailed comparison of visual and algorithm scores for the month of March 2018 shows that the algorithm is about 90 % reliable in discriminating the
four photographic sky types and identifies 86 % of all visual halos
correctly. Numerous instances of halo appearances were identified for the
period January through April 2018, with persistence times between 5 and 220 min. Varying by month, we found that between 9 % and 22 % of
cirrostratus skies exhibited a full or partial 22∘ halo.
Introduction
Modeling and predicting the Earth's climate is a challenge for physical
science, even more so in light of the already observable changes in Earth's
climate system (Fasullo and Balmaseda, 2014; Fasullo et al., 2016; IPCC,
2013, 2014). Global circulation models (GCMs) describe the atmosphere in
terms of a radiative dynamic equilibrium. The Earth receives solar shortwave
(SW) radiation and discards energy back into space in the form of terrestrial
long-wave (LW) radiation. The radiation balance of the Earth has been
subject to much study and discussion (Trenberth et al., 2014;
Fasullo and Kiehl, 2009; Kandel and Viollier, 2010; Trenberth et al., 2015).
Global circulation models describe the influence of various parts of
the Earth system in terms of radiative forcing factors (Kandel and
Viollier, 2010; Kollias et al., 2007). Clouds may restrict the SW flux
reaching the surface, but they also influence the LW emissions back into
space. While low stratus and cumulus clouds exhibit a net negative radiative
forcing, high cirroform clouds are more varied in their radiative response,
varying between negative and positive forcing depending on time of day,
season, and geographical location (Campbell et al., 2016).
The Fifth Assessment Report from the IPCC in 2013 (IPCC,
2013) identified ice and mixed clouds as major contributors to the low
confidence level into the aerosol and cloud radiative forcing. The uncertainty
in the aerosol and cloud forcing has implications for the confidence in and for
the variance of the predictions of global circulation models (Fu et al.,
2002; Trenberth et al., 2015). Closing the radiation budget of the Earth
hinges on reliable cloud data (Hammer et al., 2017; Schwartz et al.,
2014; Knobelspiesse et al., 2015; Waliser et al., 2009). Traditionally,
cloud radiative forcing is modeled using a cloud fraction based on sky
images (Kennedy et al., 2016; Kollias et al., 2007; Schwartz et al.,
2014). Cirrostratus clouds, lacking sharp outlines, pose a challenge to this
approach (Schwartz et al., 2014). The uncertainty about the role
of cirrus in the global energy balance has been attributed to limited
observational data concerning their temporal and spatial distribution, as
well as their microphysics (Waliser et al., 2009).
Cirroform clouds, at altitudes between 5000 and 12 000 m, are effective LW
absorbers. Cloud particle sizes can range from a few microns to even
centimeter sizes (Cziczo and Froyd, 2014; Heymsfield et al., 2013).
Methods to probe cirrus cloud particles directly involve aircraft sampling
(Heymsfield et al., 2013) and mountainside observations
(Hammer et al., 2015). Ground- and
satellite-based indirect radar and lidar measurements (Hammer et al.,
2015; Hong et al., 2016; Tian et al., 2010) give reliable data on altitudes,
optical depths, and particle phase. Even combined, these methods leave gaps
in the data for spatial and temporal composition of ice clouds. The analysis
of halo displays as captured by long-term total sky imagers may provide
further insight and allow one to close some of the gaps.
Optical scattering behavior is influenced by the types of ice particles,
which may be present in very many forms, including crystalline hexagonal
habits in the form of plates, pencils and prisms, hollow columns, bullets and
bullet rosettes, and amorphous ice pellets, fragments, rimed crystals, and
others (Bailey and Hallett, 2009; Baran, 2009; Yang et al., 2015). Only
ice particles with a simple crystal habit and smooth surfaces can lead to
halo displays (Um and McFarquhar, 2015; van Diedenhoven, 2014). Usually,
this will be the hexagonal prism habit, which we can find in plates,
columns, bullet rosettes, pencil crystals, etc. If no preferred orientation
exists, a clear telltale sign for their presence is the 22∘ halo
around a light source in the sky, usually sun or moon. More symmetry in the
particle orientations will add additional halo display features such as
parhelia, upper tangent arc, circumscribed halo, and others (Greenler,
1980; Tape and Moilanen, 2006). As shown in theoretical studies (van
Diedenhoven, 2014; Yang et al., 2015), halos form in particular if the ice
crystals exhibit smooth surfaces. In that case, the forward-scattered
intensity is much more pronounced as in cases of rough surfaces, even if a
crystal habit is present. If many of the ice particles are amorphous in
nature, or did not form under conditions of crystal growth – for example by
freezing from supercooled droplets, or by riming – the forward scattering
pattern will be weaker and similar to what we see for liquid droplets: a
white scattering disk surrounding the sun, but no halo. In turn, roughness
and asymmetry of ice crystals influence the magnitude of backscattered solar
radiation, thus influencing the radiative effect of cirrus clouds
(van Diedenhoven, 2016). If the particles in the cirroform cloud are
very small, e.g., a few microns (Sassen, 1991), diffraction
will lead to a corona. We believe that a systematic observation of the
optical scattering properties adds information to our data on cirrus
microphysics and cirrus radiative properties. The authors observed the sky
at the University of Minnesota Morris, using an all-sky camera, through a
5-month period in 2015, and found an abundance of halo features.
There are a few studies pursuing a similar line of inquiry (Forster et
al., 2017; Sassen et al., 2003). The study by Sassen et al. (2003) showed a prevalence of the
22∘ halo, full in 6 % and partial in 37.3 % of cirrus periods,
based on a 10-year photographic and lidar record of midlatitude cirrus
clouds, also providing data on parhelia, upper tangent arcs, and other halo
display features, as well as coronas. The photographic record was taken in
Utah and based on 20 min observation intervals; cirrus identification
was supported by lidar. The authors found an interesting variability in halo
displays, related to geographical air mass origin, and suggest that optical
displays may serve as tracers of the cloud microphysics involved. Forster
et al. (2017) used a sun-tracking camera
system to observe halo display details over the course of several months in
Munich, Germany, and a multiweek campaign in the Netherlands in November 2014. A carefully calibrated camera system provided high-resolution images,
for which a halo detection algorithm was presented, based on a decision tree
and random forest classifiers. Ceilometer data and cloud temperature
measurements from radiosonde measurements were used to identify cirrus
clouds. The authors report 25 % of all cirrus clouds also produced halo
displays, in particular in the sky segments located above the sun. The
fraction of smooth crystals necessary for halo display appearance is at a
minimum 10 % for columns, and 40 % for plates, based on an analysis of scattering phase functions for single scattering events
(van Diedenhoven, 2014). While this establishes a lower
boundary, it is correct to say that the observability of a halo display
allows one to conclude that smooth crystalline ice particles are present and
single scattering events dominate. The consideration of the percentage of
cirrus clouds that display optical halo features allows therefore, upon
further study, inferences about the microphysical properties of the cloud.
This raises interest in examining existing long-term records of sky images.
Long-term records of sky images have been accumulated in multiple global
sites. The Office of Science in the US Department of Energy has maintained
Atmospheric Radiation Measurement (ARM) sites. These sites, among other
instruments, contain a total sky imager (TSI) and have produced multiyear
records of sky images. In this paper, we introduce a computational method to
analyze these long-term records for the presence of halo displays in the
images. We are introducing an algorithm to analyze long sequences of TSI
images. The algorithm produces a time record of near-solar photographic sky
type (PST), differentiated as cirrostratus (PST-CS), partly cloudy
(PST-PCL), cloudy (PST-CLD), and clear (PST-CLR) sky types, as well as
assigns an ice halo score (IHS). The resolution and distortion of the TSI
images restrict the halo search to the common 22∘ halo. Other
halo features, such as parhelia, can occasionally be seen in a TSI image
but often are too weak or too small to reliably discriminate them from
clouds and or 22∘ halos. If present they would be classified by
this algorithm as part of a 22∘ halo. Coronas are obscured by the
shadow strip and often also by overexposure in the near-solar area of the
image. The algorithm offers an efficient method of finding 22∘
halo incidences, full or partial. Since ARM sites also have collected
records of lidar and radiometric data, the TSI halo algorithm is intended to
be compared to other instrumental records from the same locations and times.
This will be addressed in future work.
Section 1 describes the TSI data used in this work.
Section 2 presents the details of the image
analysis algorithm, including subsections on algorithm goals, image
preparation, and sky type and halo scoring. Section 3 applies the algorithm to the TSI data record of the first 4 months of 2018 and examines the effectiveness and types of data
available for this interval. Summary and outlook are given in Sect. 4.
TSI data set properties. Seed images for the algorithm were taken
from all three locations. Data source: ARM (2000).
LocationDates and times (UTC) Image intervalResolution (pixels)Southern Great Plains2 Jul 2000 0:35:0015 Aug 2011 01:17:3030 s288×35236∘ 36′18′′ N, 97∘ 29′6′′ W15 Aug 2011 22:17:3019 Apr 2018 01:02:0030 s480×640North Slope of Alaska25 Apr 2006 21:44:002 Nov 2010 21:31:0030 s288×35271∘ 19′22.8′′ N, 156∘ 36′32.4′′ W9 Mar 2011 01:08:3011 Apr 2018 18:59:3030 s480×640Eastern North Atlantic1 Oct 2013 08:13:0028 May 2018 21:04:0030 s480×64039∘ 5′29.76′′ N, 28∘ 1′32.52′′ WTSI images
Images used in this paper were obtained from Atmospheric Research
Measurement (ARM) Climate Research Facilities in three different locations:
Eastern North Atlantic (ENA) Graciosa Island, Azores, Portugal; North Slope
of Alaska (NSA) Central Facility, Barrow, AK; and Southern Great Plains (SGP)
Central Facility, Lamont, OK (ARM, 2000). The
ranges and dates vary by location, as listed in
Table 1. The images were taken with total sky
imagers, which consist of a camera directed downward toward a convex mirror
to view the whole sky from zenith to horizon. A sun-tracking shadow band is
used to block the sun, which covers a strip of sky from zenith to horizon.
Images were recorded every 30 s. The longest series was taken at the
Southern Great Plains location, reaching back to July 2000. The
images, in JPEG format, have been taken continuously during daytime. Aside
from nighttime and polar night, there are some additional gaps in the data,
perhaps due to instrument failure or other causes. Camera quality, exposure,
mirror reflectance, image resolution, and image orientation varies over time
as well as by location. For example, an image from SGP taken in 2018 has a
size of 488 pixels by 640 pixels. The short dimension limits the radius of the view
circle to at most 240 pixels. A pixel close to the center of the view circle
corresponds to an angular sky section 2.8∘ wide and
0.24∘ tall. At SGP, the solar position never reaches this point.
Close to the horizon, 1-pixel averages a sky section that is
0.24∘ wide and 1.24∘ tall. Best resolution is achieved
at zenith angle 45∘, in which case every pixel represents a sky
region of 0.33∘ by 0.33∘. The perspective distortion is
largest for sky segments close to the horizon due to perspective distortions
of the sky. We used a sampling of 80 images taken from across the TSI
record and across all available years to initiate the training set (ARM, 2000). This included images visually classified from
the images as photographic sky types CS, PCL, CLD, CLR, and halo-bearing.
Descriptions of the PST are provided in Table 2.
The 80 sample images were used to develop the algorithm and define a
suitable set of characteristic properties for PST score (PSTS) and IHS. This set will be
referred to as seed images since they also initialize the master table
described below.
Descriptions of the photographic sky types (PST).
Sky type Visual descriptionCirrostratusPST-CSMuted blue, no sharp cloud outlines; solar position clearly visible, bright scattering disk or halo may be present; changes are gradual and slow (several minutes).Partly cloudyPST-PCLVariable sky with sharply outlined stratocumulus or altocumulus; variations between sky quadrants; sun may be obscured; changes are abrupt and fast (less than 2 min).CloudyPST-CLDSun is obscured; low brightness; low blue intensity values; stratus, nimbostratus, altostratus, or cumulonimbus; changes occur slowly (order of hours).ClearPST-CLRBlue, cloud-free sky; sun clearly visible and no bright scattering disk around it; changes are slow (order of hours).No dataN/AThis may occur at low sun positions for the bottom quadrants of the LSM, or due to overexposure in the near-solar region of the image; it is the default at night.AlgorithmGoal and strategy
The algorithm aims to process very large numbers of images and return
information about the presence of 22∘ halos, as well as the
general sky conditions. The program is written in C++ and uses the
OpenCV library for image processing. If given a list of image directories,
the algorithm proceeds to sequentially import, process, and score TSI images
compared to training sets gleaned from representative images for each scored
class. We define four classes of photographic sky types, listed in
Table 2, and a halo class. The factors that
determine these choices are discussed in Sect. 2.3.1 and 2.3.3. The
algorithm assigns a numeric photographic sky type score (PSTS) and a numeric
ice halo score. For all image classes, sets of discriminant image
properties have been defined which differ between 10 distinct properties
for PST classes and 31 distinct properties for the halo class.
Multivariate analysis is one of the standard methods in image analysis,
applied in a wide variety of problems. Numerous
text books provide introductions to this method in a theoretical background
(Harris, 1975; Gnanadesikan, 1977) as well as in an application-oriented
manner (Alpaydin, 2014; Flury, 1988). A set of
Np discriminant properties of the image is chosen, selected to be
characteristic for a particular sky type or the presence of a halo. Let this
set of properties be the observation vector
X=xiiNp.
For each class, a training set is created. The training set is a set of
Nt observation vectors for images that have been visually assigned to
the class. A training set defines an ellipsoidal centroid in the property
space of X, centered at the mean observation vector
2M=μii=1Np,3μi=1Nt∑k=1Ntxik.
The centroid's extent is described by the Np×Np covariance
matrix
Σ=X-MX-MT‾=σ11σ12…σ21σ22…………,
with elements
σij=1Nt∑k=1Ntxikxjk-μiμj.
The observation vector of any further image X′ will then be referenced with
M and Σ in the form of a multivariate normal distribution:
F=C0exp-12X′-MTΣ-1X′-M,
in which the quadratic form in the exponent is known as the square of the
Mahalanobis distance in property space. The closer an image places to the
centroid of a class, the higher its score Eq. (6) will be. The Mahalanobis
distance is expressed in units of standard deviations, eliminating the
influence of the units of the discriminant properties and the need for
weights. It is interesting to note that the average Mahalanobis distance for
a class is equal to the number of discriminant properties. The prefactor
C0 in Eq. (6) is different for the photographic sky type scores
and the ice halo score since the dimensionality of the observation
vectors for these two class types is different. It is chosen to place the
values for F into a convenient number range. The value F for each class
of images is akin to a continuous numerical probability that the image is
located close to the centroid of this particular class.
Flow chart of the algorithm for the analysis of TSI images.
The algorithm is outlined in Fig. 1, together with
the respective references to this text. Both M and Σ-1 are
computed a priori from the training sets via Eqs. (2) and (4). In order to
score a time series of property vectors X, one only needs to import M and
Σ-1 for each class once at the start of the analysis run. The
training sets for each class of images are started using the set of 80 images described in Sect. 1 and are expanded as needed. This allows one to
continually train the algorithm toward improvement of scoring. This basic
algorithm structure is used on a standardized local sky map, described in
Sect. 2.2. The details of PSTS and IHS will be described
separately below. The code and accessories can be accessed at a GitHub
repository (Boyd et al., 2018).
Image preparations and local sky map (LSM)
The goal of the image preparation is to create a local sky map (LSM) centered at
the sun, in easy-to-use coordinates, after a minimal color calibration and
after extraneous image parts have been masked. The image preparations
include the following steps: (1) a color correction, (2) an alignment
calibration, (3) a removal of the perspective distortion, (4) masking and
marking of the solar position, and (5) rotation and crop to create a local
sky map. Some sample steps in the image preparation are illustrated in
Fig. 2. The figure includes the original image,
the image after preparation step (4), and the LSM after preparation step (5). The two sample images in Fig. 2 were taken at the Southern Great Plains
ARM site in March and April 2018 (SGP, 2018). One
of the images contains a solar 22∘ halo, and the other one is a partly
cloudy sky without any halo indications.
Two examples for image preparation. The left column develops an
image from SGP 17 April 2018 17:45:00 UTC, and the right image was taken on SGP
3 April 2018 19:09:30 UTC. (a, b) Original image; (c, d) image after
color correction, distortion removal, masking of horizon and equipment, and
sun mark were applied; (e, f) final local sky map with sun at center
and a width of about 80 LSM units.
Step (1) is a color correction. Both original images in Fig. 2 have a
slightly green tinge, which is typical for images from the TSI at this
location, in particular after an instrument update in 2010. This is
noticeable in particular if images are compared to earlier TSI data from the
same location, and it can become a problem for the planned analysis, especially
for the use of relative color values. Since the algorithm is intended for
multiple TSI locations and records taken over a long time, including device
changes, it is necessary to consider the fact that no two camera devices
have exactly the same color response, even if of the same type
(Ilie and Welch, 2005). The color calibration used in this
algorithm is based on sampling of clear-sky color channels to define
weighed scaling factors for a whole series of images. Every pixel in a TSI
image exhibits a value between 0 and 255 for each of the three color
channels blue (B), green (G), and red (R). The color values represent the
intensity of the color channel registered for the particular pixel, varying
between 0 (no intensity) and 255 (brightest possible). In a discolored
series, measurements of BGR were taken in clear-sky images (indexed
PST-CLR), and a scaling factor and weight for each color channel were defined
based on this information:
βB=1.00βG=GrefGCLR×BCLRBrefβR=RrefRCLR×BCLRBrefwithBref,Gref,Rref=180,120,85.
The reference values are based on color values for clear sky images from
the TSI records listed in Table 1. Near-zenith,
clear blue sky provides a reproducible color reference in all the
locations. Once these color-scaling factors were determined for a series,
every image was then tinted by generating an average color B‾,G‾,R‾ for a small near-zenith sky sample and
applying
B′=B+αβBB‾-BG′=G+αβGG‾-GR′=B+αβRR‾-R
to each color channel and pixel, respectively, followed by a simple scaling
to preserve the total brightness of the pixel I=B2+G2+R2. For the series SGP 2018, these factors were β=(0.9,0.78,1)
and α=0.4. The coefficient α regulates the strength of the
tinting such that α=0 leads to no tint, and α=1 produces
an image of a single color. This tinting is minimal, and linear color
behavior is a reasonable assumption.
Step (2) is a stretch-and-shift process that identifies the horizon circle.
Occasionally, a slight misalignment of the camera and mirror axis leads to an
elliptical appearance of the sky image. A calibration is necessary in such
cases to stretch the visible horizon ellipse to a circular shape and to
center the horizon circle as close to the zenith as possible. A north–south
alignment correction may also have to be applied. Both calibrations will
ensure successful identification of the solar position in the next step.
These calibrations become necessary if the TSI was not perfectly aligned in
the field. They need to be readjusted after any disturbances occurred to the
instrument, such as storms, snow, and instrument maintenance. Typically,
this can be once every few months, or sometimes several times per month. It
is important to check the calibrations regularly by sampling across the
series whether the solar position was correctly identified after
calibration. In addition, the horizon circle is placed at a zenith angle
smaller than 90∘, often between 85 and 79∘,
to eliminate the strong view distortion close to the horizon and, in some
cases, objects present in the view. As explained earlier, the zenith angle
resolution per pixel exceeds 1.2∘ close to the horizon. The
information value for a solar zenith angle (SZA) larger than 80∘
is diminished. These pixels are excluded from the analysis. Practically,
this is a very thin ring cut from the original image but does help eliminate
false signals at low sun angles. The current process requires one to find these
calibrations for a small sampling of images in a series and to then
apply them to all images in the series.
Step (3) removes the perspective distortion. The projection of the sky onto
the plane of an image introduces a perspective distortion, as described in
Long et al. (2006). A coordinate transformation
is performed to represent the sky within the horizon circle in terms of
azimuth and zenith angle. The azimuth is the same in both projections.
Zenith angle θ relates to the radial distance r in the original
image from the center of the horizon circle as r=Rsinθ. While R is
not determined, image horizon radius RH and horizon zenith angle
θH provide one known point to allow for proportional scaling. The
coordinate transformation represents the sky circle in a way in which radial
distance from zenith sz scales with zenith angle θ as
sz=RHsinθH×θ.
Long et al. (2006) discuss a further image distortion
introduced by the particulars of the optics of the system of convex mirror
and camera. The authors give an empirical correction curve for the SZA
transformation. This correction is small; it has been omitted in this
algorithm. One of the visible effects of this transformation concerns
22∘ halos: in the original TSI image, a halo appears as a
horizontal ellipse; after the transformation it will have a shape closer to
a circle.
Step (4) identifies the solar position and masks nonsky details. The
position of the sun is marked based on the geographical position of the TSI
and the Universal Time (UTC) of the image. Extraneous details, such as the
shadow strip, the area outside the horizon circle, the camera, and the
camera mount, are masked. Figure 2c and d show the image
produced by all these adjustments up to step (4). Since often the position
of the sun is detectable in the image, the marked sun position serves to
refine the calibrations described above.
In step (5), the standardized local sky map is created. A sketch of
the layout of the LSM is provided in Fig. 3. The
LSM provides a standard sky section, centered at the sun, oriented with the
horizon at the bottom, and presented in the same units for all possible TSI
images (independent on the resolution of the original). Units of measurement
in the LSM are closely related to angular degrees but do not match
perfectly due to a zenith angle dependence of the azimuth arc length. The
LSM is generated by rotating and cropping the image from step (4) to
approximately within 40∘ of the sun, with the sun at its center.
Layout of the local sky map (LSM). The LSM is divided into four
quadrants, named according to their position as TR – top right, BR –
bottom right, BL – bottom left, and TL – top left. The RAI is the radial
analysis interval for which PST and IHS properties are evaluated. The
approximate position of the halo maximum is sketched in light gray. Shadow
strip and camera are excluded from analysis.
The side length of the LSM in pixels scales with the previously determined
horizon radius RH in pixels and the corresponding maximum zenith angle
θH in ∘ as
wLSMpixels=RH(pixels)θH(degrees)×40∘.
Equation (10) provides a unit transformation between pixel positions and LSM
units. For a TSI image of size 480pixels×640pixels, the LSM will have a
size of approximately 240pixels×240pixels. For the earlier, smaller TSI
images, the LSM has a size of approximately 140pixels×140pixels. The
unit scaling includes the calibration choices RH and θH;
hence, there is a slight variation in LSM side lengths. We eliminate the
influence of the LSM sizes by performing all algorithm operations in
standardized LSM units, which roughly correspond to angles of 1∘.
In other words, all LSMs are equivalent to each other in terms of their LSM
units but not in terms of pixel positions. At θ=45∘, the arc length
of azimuth angle ϕ is equivalent to the arc length of θ of
same size; however, if θ > 45∘, the azimuth arc is stretched, requiring an
additional horizontal compression to ensure equivalence of horizontal and
vertical angular units. The LSM is divided into quadrants, shown in
Fig. 3, which are analyzed and classified
separately by the algorithm described in the next section.
Computing photographic sky type and halo propertiesAverage radial intensity (ARI)
Halos, as sun-centered circles, are creating a brightness signal at a
scattering angle of 22∘. We found it useful to analyze the radial
brightness I(s), with s being the radial distance from the sun in the image plane,
similar to the halo detection algorithm by Forster et al. (2017). The term intensity refers to the
color values of any of the color channels and varies between 0 and 255.
There is a physical reason for using I(s) in PST and halo assessment. The
presence of scattering centers in the atmosphere influences the properties
of sky brightness in the near-sun sky section. A very clear atmosphere, for
example, exhibits an exponential decline, but with relatively high intensity
values in the blue channel due to Rayleigh scattering. In the case of
cirrostratus, the increased forward scattering of larger particles (in this
case ice crystals) leads to a decreased gradient of radial brightness, with
more evenly distributed intensities in the red, green, and blue channels. In
a partially cloudy sky, we would find sharp variations in I(s), varying with
color channel. An overcast sky, on the other hand, may exhibit no decline
in radial brightness and will generally have low intensity values across
all color channels. A sketch of the LSM is given in
Fig. 3. The radial intensity I(s) is computed using
the color intensity values of the image (0 to 255), separated by color
channel. The LSM is divided into four quadrants: TR represents top right, BR represents bottom right, BL represents bottom left, and TL represents top left, analyzed separately for
quadrant scores, and then recombined for the image scores. The division into
quarters allows one to accommodate partial halos, low solar positions, and the
influence of low clouds in partially obstructing the view to cirrostratus.
The algorithm uses various properties of I(s) to assign numeric PSTS and IHS, as
detailed below.
Average radial intensity of the red channel is shown versus radial
distance s, measured in LSM units, for the two images of Fig. 2, halo at
left. (a) includes the average intensity Is, a linear fit, and the running average I‾6s as averaged over a width of 6 LSM units. (b) shows the
radial intensity deviation ηs. The
halo signal is visible as a minimum at 17 LSM units, followed by a maximum
at 21 LSM units in the left column.
The average radial intensity I(s) is computed as an average over pixels at
constant radial distance s from the sun. Due to the low resolution of the
LSM, and due to some noise in the data, we average I(s) over a circular ribbon
with a width of 4 pixels, centered at s. Computing I(s) over a thin ribbon
addresses issues encountered when averaging over a circle in a coarse square
grid, allowing continuity where otherwise pixelation may interrupt the line
of the circle. Figure 4 shows the radial intensity
of the red channel (R) in the bottom right quadrants of the LSMs featured in
Fig. 2. Panel a includes I(s), a linear fit, as well as the running average
I‾6, plotted versus radial distance s. The running average is
taken as the average of I(s) over a width of 6 LSM units centered at s:
I‾6s=1N∑s-3LSMunitss+3LSMunitsIs.
The clear-sky image exhibits a lower red intensity overall than the halo
image. The halo presents as a brightness fluctuation at about 21 LSM units.
The analysis of I(s) is undertaken in an interval between 15 and 26 LSM units,
called the radial analysis interval (RAI). The RAI is marked in
Fig. 3. A linear fit yields a slope and intercept
value used for the PSTS. We define the radial intensity deviation as
ηs=Is-I‾6s.
Panels b in Fig. 4 show η(s) for both
situations. The details of the halo signal in η(s) contribute in
particular to the computation of the IHS.
Discriminant properties used to classify the photographic sky type.
Averages and standard deviations for the training set of each class are
listed. All units are based on color intensity values and LSM units. The number of records for each sky type is indicated in parentheses.
1 Areal standard deviation. 2 Average color ratio.
Photographic sky type properties. Slope and intercept (a, b)
for the radial fit; areal standard deviation (ASD) of brightness (c); average color ratio (ACR) (d). Sky types were assigned
visually.
Photographic sky type (PST)
The training sets for the properties of I(s) were started for the set of 80 seed
images mentioned in Sect. 1. Twenty images for
each sky type were divided further by sky quadrants, yielding between 60 and
80 property sets for each sky type to initiate the training sets. Some
quadrants were eliminated by near-horizon sun positions. The training
quadrants were used to apprise the utility of I(s) in making sky type
assignments, with focus on the radial analysis interval between 15 and
26 LSM units. The 10 image properties used to compute the numeric PSTS are
listed in Table 3. Also listed are the components
of M together with their standard deviations, computed from a later and more
complete version of the training sets. The 10 image properties include the
slope and intercept of the line fit to I(s) for each color channel, where the
slope characterizes a general brightness gradient, and the intercept gives
access the overall brightness in the RAI. The line fit alone will not allow
one to differentiate partially cloudy skies from other sky types. However, the
presence of sharply outlined clouds leads to a larger variation in intensity
values, even for the same radial distance from the sun. The areal standard
deviation (ASD) is an average of the standard deviation of I(s) for each radial distance s, averaged over all radii separated by color channel. To set
apart clear skies, the average color ratio (ACR) in the analysis area is
computed as
ACR=B2‾GR.
In Fig. 5, the PST property set is represented
graphically, including means, standard deviations, and extreme values as
observed for the completed training set. Clearly, no single property alone
will suffice to assign a PST reliably. There is overlap in the extreme
ranges. Relations between the color channels are influential as well. We
are using the mechanism described in Sect. 2.1,
Eqs. (1) through (6). The training sets for each class are collected in a
master table, where M and Σ-1 for each PST are computed.
As a new image is processed, and its PST property
vector X is computed for each sky quadrant. Subsequently, a numeric score is
computed for each sky type using Eq. (6). The coefficient C0 in Eq. (6) for the PSTS computation is chosen as 103, which places a rough
separator of order 1 between images that match closely a particular sky
type and those which do not. The raw values of Fimage in Eq. (6) vary
greatly even between similar looking images; hence the PSTS is computed as a
relative contribution between 0 % and 100 % for each sky type and each
quadrant. For the PST-CS score this would mean
PST_CS=FCSFCS+FPCL+FCLD+FCLR×100%
and equivalent for all other PST classes. A single image quadrant can carry
scores of 45 % for PST-CS, 35 % for PST-PCL, and 20 % for PST-CLD. The
dominant sky type then is PST-CS for this quadrant, since it contributes the
largest score. The PSTS for the image is assigned as the average over all
quadrants. If the raw scores F for all PSTs were smaller than 10-8, the quadrant is classified as N/A. It simply means that its properties are not
close to any of the PST categories. Such conditions may include overexposed
quadrants, near-horizon sun positions, a bird sitting on the mirror, and
other conditions that produce images very different from the PST sought
after. Also classified as N/A are quadrants in which the average radial
intensity lies above 253 (overexposure) or contains a large fraction of
horizon (bottom quadrants in low sun positions). A 1 d sample of sky
type data is shown in Fig. 6, for 10 March 2018.
The day was chosen for its variability, including periods of each of the
PST, as well as clearly visible halo periods. The central panel tracks the
PSTS for all photographic sky types through the day, taken for all four LSM
quadrants combined. It is important to note that the PST only can be
representative of the section of sky near to the sun. Some of the late-day
images in Fig. 6 contain quadrants that were
eliminated due to overexposure. The white scattering disk around the sun
near the horizon does not allow for analysis, which is exemplified in the sample
image at 22:53:00 UTC included in Fig. 6. For large portions of the day, the
dominant sky types have been classified as PST-CS and PST-PCL, and the
images corroborate this. The 14:36:00 image shows a thicker cloud cover, and
the algorithm correctly responds by increasing the PST-CLD score. At
21:00:00, the algorithm indicates an increased PST-CLR score, consistent
with the visual inspection of the TSI image at the time. Given the
simplicity and physical relevance of this photographic sky type assessment,
we believe that a radial scattering analysis around the sun has the
potential to address some of the challenges that have been encountered using
a simple photographic cloud fraction in radiation modeling (Calbó
and Sabburg, 2008; Ghonima et al., 2012; Kollias et al., 2007). The
variation in radial intensity gradient as scatterers are present along the
optical path can provide an alternative assessment for the presence of
cirroform clouds, solving problems of classifying near-solar pixels using a
color ratio and/or intensity value only (Kennedy et al., 2016; Long
et al., 2006). That will be a direction to discuss and explore in the
future.
The 1 d example for PSTS and IHS (SGP 10 March 2018). Sample TSI
images are included. The middle panel shows PSTS versus time of day (N/A
excluded). Bottom panel shows the IHS versus time; w=3.5 min. All times in
UTC.
Ice halo score (IHS)
The 22∘ halo is a signal in the image that can be obscured by many
other image features, including low clouds, partial clearings, inhomogeneous
cirrostratus, regions of overexposure, and near-horizon distortions. The
appearances of 22∘ halos span a wide variety of sky conditions,
ranging from almost clear skies to overcast altostratus skies, with the
majority of halo phenomena appearing in cirrostratus skies. The challenge to
extract the halo from such a wide variety of sky conditions is formidable.
While the statistical approach described in Sect. 2.1 will again form the core of the approach, the
challenge shifts to defining a set of suitable discriminating properties of
the image. In addition to the properties used in sky type assignment, the
halo scoring must seek features in η(s), Eq. (12), that are unique in
halo images, such as a minimum followed by a maximum at halo distance from
the sun. The absolute values of η(s) are dependent on various image
conditions. Due to the variety of sky conditions, and variations in
calibration and image quality, the values of maximum and minimum alone are
not sufficient to reliably conclude the presence of a halo. We have found
instances in which η(s) does exhibit the halo maximum but does not dip
to negative values first. However, the upslope–crest–downslope
sequence is consistently present in all cases of 22∘ halo. The
halo search is undertaken for a sequence of upslope–crest–downslope in
terms of radial positions and range of slopes. All three characteristics
present clearly in the derivative of the η(s), the radial intensity
deviation derivative η′(s). This derivative of the discrete series η(s) is approximated numerically by a secant method as
η′i≈ηi+1-ηi-1si+1-si-1.
Discriminant properties used for the ice halo score. Averages and
standard deviations for a training set of 188 quadrant records are listed.
All units are based on color intensity values and LSM units.
IHS propertyBGRSlope a-3.3±1.5-3.3±1.6-3.8±1.8Intercept b279±35278±37268±45ASD12.6±4.714.8±6.016.2±6.4Maximum upslope ηup′2.1±1.32.1±1.42.5±1.6Maximum downslope ηdown′-1.6±1.0-1.6±1.0-1.8±1.1Upslope location sup17.5±1.917.8±2.317.5±2.1Maximum location smax18.9±1.919.1±2.318.8±2.1Downslope location sdown20.0±2.120.2±2.419.9±2.2Number of maxima nmax2.42.62.5BGR consistencyσBGRsup=0.8σBGRsmax=0.8σBGRsdown=0.9ACR1.2±0.3
Radial markers used in halo scoring. The data belong to the green
channel of the TSI image from SGP, 17 April 2018; see Fig. 2. (a) shows the radial intensity deviation ηs; (b) shows its derivative η′s. Units are color value units (0 to 255) for the
intensity and LSM units for the radial distance. The sequence of radial
locations used in halo scoring is indicated, as well as the interpretation
of the up- and downslope markers.
In Fig. 7, both η(s) and η′(s) are shown for
the bottom-right quadrant of the green channel of the halo image in
Fig. 2. The sequence of radial halo markers is
illustrated in Fig. 7. The algorithm computes
η′(s) and seeks the positive maximum and the subsequent negative minimum,
plus the radial position of the sign change between them. This produces a
sequence of radial locations sup, smax, and sdown which basically
outline the halo bump in width and location. There are often multiple maxima
of η′(s) contained in the RAI. A halo image typically has fewer maxima
than a nonhalo image but of larger amplitude. Therefore, the number of
maxima as well as the upslope value ηup′ and downslope derivative
ηdown′ join the set of halo indicators. If multiple maxima are
found, the dominant range is used. Lastly, a radial sequence should be
consistent across all three color channels. The resolution of the TSI
images only allows one to resolve 0.4 to 1.2∘ with
certainty; in addition, variations in calibration and SZA do influence
deviations from the expected 22∘ position. The separation of
colors observed in a 22∘ halo display is not resolved with
statistical significance; therefore this was not used as a criterion for
halo detection. The standard deviation of all three radial positions across
the three color channels was added to the halo scoring set of properties.
We arrive at a set of 31 properties for the computation of the IHS, listed
in Table 4, together with their means and standard
deviations. The mean value vector M and the inverse covariance matrix
Σ-1 are computed in the master table and then imported by the
halo searching algorithm for use in Eq. (6). The coefficient C0 in Eq. (6) is arbitrary. In the IHS computation, a value of 106 was chosen for
C0, which places a rough separator of order 1 between image quadrants
that do have a halo and those which do not. While the scoring of individual
images works very well for true halo images, it does trigger the occasional
halo score for images that do not exhibit a halo. This may occur due to
inhomogeneities in a broken cloud cover or other isolated circumstances.
These false halo scores often occur on isolated images. We utilize the
factor of residence time of a halo to address this. In a 30 s binned series
of TSI images, the halo will appear usually in a sequence of subsequent
images, often in the order of minutes or even hours. We added a Gaussian
broadening to the time series of halo scores Fi, taken at times ti
with a broadening w:
IHSt=∑ti=t-3wti=t+3wFtiexp-ti-t22w2.
This de-emphasizes isolated instances and enforces sequences of halo
scores, even if they individually exhibit weak signals or gaps. This
procedure reduced the false halo identifications significantly. Just as for
the PSTS, the training set for the IHS in the master table is being
complemented as more images are analyzed. The raw halo score F is computed
for each of the four quadrants of an individual image; their average is used
to assign the raw score for the whole image. The broadening in Eq. (16) was
chosen as w=7 images throughout, corresponding to
3.5 min. In Fig. 6, the clear 22∘
halo between 19:00 and 20:00 UTC produces a strong IHS. There are a few
weaker halo signals, and upon inspection of the images we find that these
correspond to partial halos (like at 17:07:00), or halos in a more variable
sky.
Results for January through April 2018
We chose the record of the month of March 2018 at the SGP location for a
thorough comparison of algorithm results to visual image inspection, as well
as an expansion of the training set. The complete month TSI record, starting
at 1 March 2018 00:00:00 UTC and ending at 31 March 2018 23:59:30 UTC,
contains 44 057 images. Only 31 398 were classifiable in terms of their
PST. Exclusions occur due to large SZA, overexposure, or low PSTS.
The algorithm and the current training set (starting with the 80 sets
discussed above) are used to assign an image IHS and a set of four image
PSTS, averaging over the quadrant IHS and PSTS values. Both of these score
sets are continuous numerical values, resulting in a time-resolved scoring
for all PSTS and IHS values as shown in Fig. 6,
across the month of March. In order to manage comparison to a visual
classification of these images, and to learn how both score sets behave in
terms of numerical values, the following two procedural steps are added in
the postprocessing: (1) for the PST, the sky type with the maximum
contribution is taken as the image sky type; (2) an IHS discriminator is
used to assign a halo/no halo designator to an image. This IHS discriminator
is arbitrary, not part of the image analysis algorithm, and dependent on
factors such as w and C0, the quality of the calibration, and the
quality and relevance of the training set. The algorithm assigns a
continuous IHS to every image as a number varying between 10-10 and
106, with fluid continuous change in consecutive images. The decision
on the value of the discriminator is based on the behavior of the timeline.
Halo images generate a significant peak above a population of low-level
peaks. The discriminator is placed to exclude about 75 % of the low peaks
when analyzing for a count of halo incidences. Our testing, minimizing false
negatives and maximizing correct positives, places it at around 4000 for the
month of March.
Visual image classification for so many images poses a considerable
challenge, which we approached in the form of an iteration. For each of the 31 d of March, an observer assigned sky classifications to segments of the
day by inspecting the day series as an animation. This can easily be done by
using an image viewer and continuously scrolling through the series. Then,
the day would be subjected to the algorithm. The sections of the record in
which visual and algorithm differed were inspected again, at which point
either the visual assessment was adjusted or samples of the misclassified
images were added to the training set. Adjustment to visual classifications
often occurred at the fringes of a transition. For example, when a sky
transitions from cirrostratus to altostratus to stratus, the transitions are
not sharp. The observer sets an image as the point in which the sky moved
from PST-CS to PST-CLD, but the criteria in the algorithm would still
indicate PST-CS. This can affect up to a hundred images at transition times,
which then were reclassified. On the other hand, if a clearly visible halo
was missed by the algorithm in the form of a low numerical IHS, a couple of new
lines were added to the training set, selected from the few hundred quadrant
cases in which this particular halo had scored low. The IHS discriminator is
not part of the algorithm itself, but follows in the postprocessing from
the general behavior of the IHS across the month. It is a tool to allow a
comparison but not an ultimate answer to halo strength. Halo strength could
be assessed by the IHS. After each change to the training set, the algorithm
would be repeated, and recalibrations to the visual record, as well as to
the training set, were made. The process was repeated several times until no
more gains in accuracy were observed. The training sets at the end of this
process contained between 93 and 188 property records, of which up to 50 %
were taken from March 2018. Compared to the number 31 398 of classifiable
images in March (after exclusion of high-SZA, overexposure, and other), and
considering that each of these images contributes up to four individual
property sets, the number of training sets is indeed diminutive. These
adjustments were done by SB.
The resulting time lines for PSTS and IHS for the month of March are plotted
in Fig. 8. Many of the images exhibit strong
indicators for multiple PST. The largest PSTS is used to assign a PST to an
image. As expected, the high halo scores coincide with strong PST-CS
signals. Noteworthy is also that there are a number of days in which PST-CS
does not carry a 22∘ halo, indicated by very small IHS values.
Algorithm versus visual classifications for SGP March 2018. (a) shows the percentage of visual assignments corresponding to algorithm
assignments; (b) shows the percentage of algorithm assignments and how
they distribute among the visual assignments. For example, 88 % of all
visual CS skies are classified as PST-CS by the algorithm, but only 86 %
of all algorithm PST-CS skies also identify as visual CS. Agreement
combinations are shown in bold. A halo was assigned to an image if IHS > 4000.
(a)Percentage of visually assigned sky type which corresponds to algorithm-assigned PST CS PCL CLD CLR N%N%N%N%PST-CS667588683113813974PST-PCL182255138617631912PST-CLD61147161299700PST-CLR641813620010 52995N/A12 597 (40 % of all images) Percentage of visually assigned halos which corresponds to the algorithm assignment 22∘ halo No 22∘ halo N%N%22∘ halo1996852721No 22∘ halo3491541 40999(b)Percentage of algorithm-assigned PST which corresponds to a visually assigned sky type CS PCL CLD CLR N%N%N%N%PST-CS6675866839 3803975PST-PCL182355139117631914PST-CLD61147161299800PST-CLR641613610010 52993N/A12 597 (40 % of all images) Percentage of algorithm-assigned assigned halos which corresponds to a visual assignment 22∘ halo No 22∘ halo N%N%22∘ halo19968827212No 22∘ halo349141 40999
PSTS and IHS versus time for TSI images from SGP March 2018. Left
panel shows the PSTS. Right panel: IHS broadening w=3.5 min.
In Table 5, visual and algorithm results of the sky
type assignments are cross-listed for SGP March 2018. It is worth reminding
the reader that PSTs are assigned only for the radial analysis interval
indicated in Fig. 3.
Table 5a lists the percentage of visually assigned
sky types that correspond to the algorithm-assigned PST; Table 5b lists the
percentage of algorithm-assigned PSTs that also have been identified as a
visual sky type. For example, the algorithm correctly identifies 88 % of
all visual CS skies as PST-CS (part A); 86 % of the images classified as
PST-CS by the algorithm also have been visually classified as CS (part B).
PST-CLD is reliably identified by the algorithm. A small percentage (3 %)
of visual PST-CLD skies trigger a PST-PCL signal, mostly due to
inhomogeneities in cloud cover. The algorithm classifies 95 % of all
visual PST-CLR skies correctly. Differentiating between PST-CS and PST-PCL
is successful. However, these two sky types pose some difficulties. For
example, 8.5 % if visual PST-CS skies scored a PST-CLR signal and 10 % of images classified as PST-CS were visually assigned a PST-PCL sky type. In
these cases we often found that the algorithm assignment might be more
persuasive than the visual assignment – a visual assignment is a subjective
call and open to interpretation of the observer. Combined with image
distortion and resolution limits, it is quite possible that the visual
assignments carry a considerable uncertainty. Some of the visual PST-CS
skies, for example, present to the eye as PST-CLR but reveal the movement
of a thin cirrostratus layer if viewed in the context of time development
(animation). Similarly, cirrostratus may present as an inhomogeneous layer
in transition skies, triggering a PST-PCL assessment in the algorithm. Low
solar positions are prone to larger image distortion, which may lead to
misinterpretation. It is worth noting that every image quadrant receives a
PSTS for all classes of PST. In cases of mismatch, we often find that the
two sky types at conflict both contribute significantly to the PSTS of the
image quadrant. If SZA > 68∘, no PST assignments were
made. Most of the 397 PST-CLR images that presented as PST-CS to the
algorithm were taken at very low sun, with a significant overexposure disk
in near-solar position. Table 5 also lists a
comparison of visual halo identifications with the algorithm scores.
According to this assessment, the algorithm correctly calls 85 % of
visual halo images while not diagnosing 15 % of them. On the other hand,
12 % of all halo signals do not correspond to a halo in the image. One
can improve the correct identification rate by lowering the cutoff score,
at the cost of an increase in the signal from false identifications.
Balancing the false positive and false negatives yields a reliability of
about 12 % to 14 %. Some of the false negatives arise from altocumulus
skies, in which the outlines of cloudlets may trigger halo signals by their
distribution and size. These are very difficult to discriminate from visual
halo images. Some images were flagged with an IHS by the algorithm, and the
presence of a weak halo revealed itself only after secondary and tertiary
inspection of the image. Caution is advised in relying heavily on visual
classifications of TSI images alone. The visual sky type and halo
assignments themselves have an uncertainty due to subjectivity. While it is
easy to distinguish a partially cloudy sky from a clear sky, this may become
difficult for the difference between thick cirrostratus and stratus. Their
visual appearances may be quite similar. Sometimes, an assignment can be
made in the context of temporal changes. Some clear-appearing skies reveal a
thin cirrostratus presence if viewed in a time series instead of in an
individual image. It is therefore a future necessity to combine the visual
assignments of sky types with lidar data for altitude, optical thickness,
and depolarization measurements to make an accurate assessment of the
efficacy of the PST identification, following closely the processes
described by Sassen et al. (2003) and
Forster et al. (2017).
PST and 22∘ halo formations during the months of January
through April 2018 (SGP). Percentages are with respect to all classifiable
images. Times are in UTC.
Jan 2018Feb 2018Mar 2018Apr 2018*Total number of images 36 63236 01144 05727 741Number with valid PST 21 23823 60431 39820 436Begin date of record 1 Jan 2018 13:47:001 Feb 2018 13:36:001 Mar 2018 0:00:001 Apr 2018 0:00:00End date of record 31 Jan 2018 23:50:0028 Feb 2018 23:59:3031 Mar 2018 23:59:3019 Apr 2018 1:02:00PSTPST-CS20 %18 %25 %34 %PST-PCL24 %24 %19 %19 %PST-CLD11 %33 %20 %25 %PST-CLR45 %25 %36 %22 %22∘ halosNumber of separate26453446halo incidentsMean duration16 min22 min34 min21 minMaximum duration62 min136 min171 min208 minTotal halo time411 min998 min1160 min963 min% halo instances with4/4 22∘ halo29 %42 %77 %42 %1/3 22∘ halo38 %31 %13 %40 %1/2 22∘ halo32 %25 %10 %18 %1/4 22∘ halo1 %1 %0 %0 %Relations% halo instances of allsky type instancesPST-CS9 %16 %18 %22 %PST-PCL6 %7 %6 %9 %PST-CLD4 %5 %10 %12 %PST-CLR0 %0 %0 %0 %All PSTSs3.9 %8.5 %7.4 %9.4 %% sky type of allhalo instancesPST-CS49 %60 %87 %78 %PST-PCL42 %33 %9 %14 %PST-CLD2 %5 %3 %5 %PST-CLR0 %0 %0 %0 %N/A7 %2 %1 %3 %
* Incomplete month.
Distribution of observed 22∘ halo durations for the
first 4 months of 2018 at the SGP ARM site.
We applied the algorithm to the TSI record for the first 4 months of 2018
for the SGP ARM site. It is worth noting that this paper is not intended to
present a complete exploration of the ARM record concerning 22∘
halos. We are, however, including a demonstration of capacity of the
algorithm presented here. Table 6 summarizes our
findings. It lists the percentages for the PST by month. A portion of the
images has not been assigned with a PSTS. The conditions under which this
occurs have been described earlier and include near-horizon sun
positions, images with overexposure in the RAI, and images for which the
raw PSTS for each sky type was numerically too low to be considered a
reliable assessment. Therefore, PST percentages refer only to all identified
images. January and March exhibited a large fraction of clear skies.
February was dominated by cloudy skies, while April registered a high
percentage of PST-CS. Only a partial month of images was available for
April. Cloud types depend strongly on the synoptic situation. That means
that no further conclusions should be made from these data without expanding
the data set. The 22∘ halo statistics in
Table 6 lists data on the 22∘ halo,
including duration, number of incidents, and data on partial halos. The
partial halo data are based on the individual quadrant IHS for an image,
while the image score is used for duration and incidence information. The
number of separate halo incidences counts sequences of images for which the
IHS did not fall below the cutoff value of 4000. While it is worth noting
that the number of incidences lies in the order of magnitude of the number
of days in a month, it is certain that the halo instances are not evenly
distributed. Figure 8 does demonstrate this
behavior. However, even on a day of persistent cirrostratus with
22∘ halo, interruptions of its visibility can occur. Sometimes low
stratocumulus may obscure the view of the halo, and sometimes the cirrus layer
is not homogeneous. This may lead to a large number of separate halo
incidences in a short time, while none are counted at other times. The mean
duration of a halo incident lies between 16 and 34 min, depending on
month. We listed the maximum duration found in each month as well. The
longest halo display in the time period occurred in April 2018, with nearly
3.5 h. Mean values are easily skewed by a few long-lasting displays.
Figure 9 shows the distribution of 22∘
halo durations for the 4 months. The most common duration of a
22∘ halo lies between 5 and 10 min, followed by 10 to 15 min. Due to the time broadening applied via Eq. (16), the display time
cannot be resolved below 3 min. We consider the fraction of images in
which a halo was registering. That marker varied between 3.9 % for January
and 9.4 % for April. In accord with findings in Sassen
et al. (2003), we find a low amount of halo display activity in January.
However, this may be influenced by the large SZA in January. The closer the
sun to the horizon, the more TSI images have been excluded from the
analysis, and the stronger the influence of distortion.
Occasionally, only partial halos will be seen, depending on positioning of
the cirroform clouds and on obstruction by low clouds. The division of the
LSM into quadrants allows one to assess the possibility of fractional halos, as
indicated in Table 6. The overwhelming portion of
halo incidences shows full or 75 % halo. This means that, in four or three
of the quadrants, the IHS has exceeded its minimum cutoff. Quarter halos
have only rarely registered in the algorithm. Many of the half halos can be
found for images taken close to sunrise or sunset. That explains their
relative frequency in January and February.
We started the project with the goal to find information on cirrostratus
composition, in particular with respect to assessments of variation of
smooth versus rough crystals. Forster et al. (2017) discuss that the necessary fraction of smooth crystals for a halo
appearance lies between 10 % and 40 %. The bottom part of
Table 6 investigates the relation between sky type
and 22∘ halo incidences. The first set of data in the “Relations”
section of Table 6 gives the fraction of each sky
type, as it produced a 22∘ halo incident. For example, in January
we found that 9 % of PST-CS were accompanied by a 22∘ halo. In
the data for April, this fraction increased to 22 % of PST-CS. We also
have registered halos for a portion of PST-PCL and for PST-CLD. No halos
have been registered in any of the PST-CLRs. The April data are consistent with
the observations of Forster et al. (2017), who report a 22∘ halo for 25 % of all cirrus clouds for a
2.5-year photographic record taken in Munich, Germany. Differences exist,
however, in that the Forster observations verified ice cloud with lidar and
IR measurements, while this current record compares to a photographically
assigned sky type. We must consider reasons for the PST-PCL and PST-CLD halo
incidences. Upon random sampling of these combinations we find the
following: the PST-PCL indicator has been assigned to images that have a
highly varied cirroform sky, including halo appearances. In a few instances,
low clouds triggered the PST-PCL indicator; however, a cirroform layer at
higher altitude still contributed a halo score above the threshold. Many of
the halo scores in PST-CLD skies belong to images with an overcast
appearance; however, they most likely belong to a thickening and lowering cirro-
or altostratus as is often found in warm front approaches. These are not false scores but conditioned by the limitations of the PST classification. The
second set of numbers in Table 6 shows the fraction
of all halos associated with the various PST. In January, 49 % of all halo
incidences occurred in PST-CS skies, while in March this number was 87 %.
As for the overall frequency of halo displays, we can refer to
Table 6, in which the observed halo frequency for
all PST combined is listed. It varies from 3.9 % in January 2018 to
9.4 % in April 2018. The closest comparison is the number given by Sassen
et al. (2003), who report a full 22∘ halo at 6 %
of the 10-year record of hourly images, while any halo feature was observed
at 37.3 % of the time. For such a comparison, Forster et al. (2017) is cautioning that a statistic
like this may strongly depend on the binning interval.
With this image analysis algorithm used on TSI images to identify the PST
and the appearance of 22∘ halos, the next useful and logical step
will be to relate these data to other instrument records: lidar for
altitude, particle density, and particle phase (solid or liquid),
as well as photometric measurements to glean information on radiative flux. ARM sites
have accumulated such instrumental data. The algorithm proposed here will
make such data investigation possible.
Finally, it is worth discussing the general approach of the TSI algorithm in
comparison to the halo detection algorithm developed by Forster et al. (2017). Both algorithms utilize features
found in the radial intensity I(s), such as the sequence of minimum–maximum at the expected radial positions in order to find halos in an image.
The random forest classifier approach described in
Forster et al. (2017) is a machine learning approach
that arrives at a binary conclusion for an image in the form of halo/no halo.
Their algorithm was trained on a visually classified set of images in order
to construct a suitable decision tree. In addition to 22∘ halos,
the Forster algorithm also identifies parhelia and other halo display
features in images taken by a high-resolution, sun-tracking halo camera. The
algorithm presented here for TSI data must work with a much less specialized
set of images, notably of lower resolution. It does not characterize halos
in a binary decision but rather assigns a continuous ice halo score to an
image, in addition to photographic sky type scores for four different types
of sky conditions. Similar to the Forster algorithm, the TSI algorithm also
was trained on a visually classified set of images. For the algorithm
presented here, further training sets are easily added. Both algorithms have
overlap. The TSI algorithm makes extensive use of the radial brightness
gradient (slope) for the sky type assignments. The relation of this gradient
to the physical presence of scatterers along the optical path makes this an
attractive approach.
Summary
ARM sites have produced long-term records of sky images. We developed an
algorithm that assigns sky type and halo scores to long-term series of TSI
images with the goal of using these long-term image records to provide
supporting information on the presence of smooth, hexagonal ice crystals in
cirrus clouds from observations of 22∘ halos. We described this
algorithm in this paper, including the image preparation to generate a
standardized image section centered at the sun, called the local sky map
(LSM). A multivariate analysis of selected LSM properties, as supported by a
master table, allows the assignment of scores with respect to photographic
sky type and 22∘ halo presence in the near-solar section of the
sky. In particular, we focus on the properties associated with the radial
brightness behavior around the sun. Physically, the number and type of
scattering centers in the atmosphere do influence the radial brightness
gradient, thus giving us access to an assessment of cloud type and cloud
cover. The brightness fluctuation associated with the 22∘ halo
provides a further set of properties specific to the presence of a
22∘ halo. We analyze all four quadrants adjacent to the sun
separately and then combine the scores into a raw image score. For the ice halo
score, we also apply a Gaussian broadening across the time series. The
algorithm has been found to be about 90 % in agreement with the visually
assigned sky type and 85 % in agreement with the visually identified ice
halo score. The application to the first 4 months of the TSI records from
the SGP ARM site indicates periods of halo displays, with a most common duration
of about 5 to 10 min but lasting up to 3 h. It allowed us to identify
the fraction of PST-CS skies that do produce halo displays, as well as find
such data for other PST. In the future, the algorithm will be applied to
deliver 22∘ halo data for the long-term TSI records accumulated in
various geographical locations of ARM sites, as well as allow further
investigation into correlations with other instrumental records from those
sites. In particular, lidar data for altitude and optical thickness
measurements, as well as depolarization analysis, will be a useful
combination with this photographic halo display record. It is reasonable to
expect that the reference set for sky type determination will improve with
the support of lidar data. The method described here may be suitable to
expand to other types of sky analysis on TSI images.
Code availability
Code and accessory files are made available at GitHub under 10.5281/zenodo.2226125 (Boyd et al., 2018).
Author contributions
SB is the main author of this paper and the code. The four
coauthors worked on the algorithm as undergraduate researchers. SS decided on the use of C++ and OpenCV3.2 for image manipulation
and initiated the program code. SR worked out the details of the
radial intensity computation and properties. MK and MG contributed algorithm parts to eliminate optical distortions and
low-cloud obstruction, as well as input management. SR, MK, and MG all contributed
to data collection and analysis.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Data were obtained from the Atmospheric Radiation Measurement (ARM) Program
sponsored by the U.S. Department of Energy, Office of Science, Office of
Biological and Environmental Research, Climate and Environmental Sciences
Division. The work was supported by The Undergraduate Research Opportunities
Program (UROP) at the University of Minnesota, as well as a grant to the
University of Minnesota Morris from the Howard Hughes Medical Institute
through the Precollege and Undergraduate Science Education Program. Sylke Boyd
wishes to thank the University of Minnesota Morris for the generous
one-semester release from teaching obligations, allowing for the completion of
this work.
Review statement
This paper was edited by Andrew Sayer and reviewed by two anonymous referees.
References
Alpaydin, E.: Introduction to machine learning, third edition, Cambridge,
Mass, MIT Press, Cambridge, Mass, 2014.Atmospheric Radiation Measurement (ARM): Climate Research Facility. updated hourly. Total Sky Imager (TSISKYIMAGE). 2013-10-01 to 2018-05-28, Eastern North Atlantic (ENA) Graciosa Island, Azores, Portugal (C1). 2006-04-25 to 2018-04-11, North Slope Alaska (NSA) Central Facility, Barrow AK (C1). 2013-08-30 to 2018-05-24, ARM Mobile Facility (OLI) Olikiok Point, Alaska; AMF3 (M1). 2000-07-02 to 2018-04-19, Southern Great Plains (SGP) Central Facility, Lamont, OK (C1), compiled by: Morris, V., Atmospheric Radiation Measurement (ARM) Climate Research Facility Data Archive: Oak Ridge, Tennessee, USA, 10.5439/1025309, 2000.
Bailey, M. P. and Hallett, J.: A Comprehensive Habit Diagram for Atmospheric
Ice Crystals: Confirmation from the Laboratory, AIRS II, and Other Field
Studies, J. Atmos. Sci., 66, 2888–2899, 2009.
Baran, A.: A review of the light scattering properties of cirrus, J. Quant. Spectrosc. Ra., 10, 1239–1260, 2009.
Boyd, S., Sorenson, S., Richard, S., King, M., and Greenslit, M.:
Haloloop-Search TSI record for ice halos, Zenodo,
doi.org/10.5281/zenodo.2226125, 2018.
Calbó, J. and Sabburg, J.: Feature Extraction from Whole-Sky
Ground-Based Images for Cloud-Type Recognition, J. Atmos.
Ocean. Tech., 25, 3–14, 2008.
Campbell, J. R., Lolli, S., Lewis, J. R., Gu, Y., and Welton, E. J.: Daytime
Cirrus Cloud Top-of-the-Atmosphere Radiative Forcing Properties at a
Midlatitude Site and Their Global Consequences, J. Appl.
Meteorol. Clim., 55, 1667–1679, 2016.
Cziczo, D. J. and Froyd, K. D.: Sampling the composition of cirrus ice
residuals, Atmos. Res., 142, 15–31, 2014.
Fasullo, J. T. and Balmaseda, M. A.: Earth's Energy Imbalance, J.
Climate, 27, 3129–3144, 2014.
Fasullo, J. T. and Kiehl, J.: Earth's Global Energy Budget, B.
Am. Meteorol. Soc., 90, 311–324, 2009.
Fasullo, J. T., von Schuckmann, K., and Cheng, L.: Insights into Earth's
Energy Imbalance from Multiple Sources, J. Climate, 29, 7495–7505, 2016.
Flury, B.: Multivariate statistics: a practical approach, London,
New York: Chapman and Hall, London,
New York, 1988.Forster, L., Seefeldner, M., Wiegner, M., and Mayer, B.: Ice crystal characterization in cirrus clouds: a sun-tracking camera system and automated detection algorithm for halo displays, Atmos. Meas. Tech., 10, 2499–2516, 10.5194/amt-10-2499-2017, 2017.Fu, Q., Lohmann, U., Mace, G. G., Sassen, K., and Comstock, J. M.:
High-Cloud Horizontal Inhomogeneity and Solar Albedo Bias, J.
Climate, 15, 10.1175/1520-0442(2002)015<2321:HCHIAS>2.0.CO;2, 2002.Ghonima, M. S., Urquhart, B., Chow, C. W., Shields, J. E., Cazorla, A., and Kleissl, J.: A method for cloud detection and opacity classification based on ground based sky imagery, Atmos. Meas. Tech., 5, 2881–2892, 10.5194/amt-5-2881-2012, 2012.
Gnanadesikan, R.: Methods for statistical data analysis of multivariate observations, New York, Wiley, New York, 1977.
Greenler, R.: Rainbows, Halos, and Glories, Cambridge University Press,
Cambridge, 1980.Hammer, A., Monahan, A. H., Schmidt, T., and Heinemann, D.: Simulating
clear-sky index increment correlations under mixed sky conditions using a
fractal cloud model, Sol. Energy, 150, 10.1016/j.solener.2017.04.048, 2017.Hammer, E., Bukowiecki, N., Luo, B. P., Lohmann, U., Marcolli, C., Weingartner, E., Baltensperger, U., and Hoyle, C. R.: Sensitivity estimations for cloud droplet formation in the vicinity of the high-alpine research station Jungfraujoch (3580 m a.s.l.), Atmos. Chem. Phys., 15, 10309–10323, 10.5194/acp-15-10309-2015, 2015.
Harris, R. J.: A primer of multivariate statistics, New York, Academic Press, New York, 1975.Heymsfield, A. J., Schmitt, C., and Bansemer, A.: Ice Cloud Particle Size
Distributions and Pressure-Dependent Terminal Velocities from In Situ
Observations at Temperatures from 0∘ to -86∘ C, J. Atmos. Sci., 70, 4123–4154, 2013.
Hong, Y., Liu, G., and Li, J.-L. F.: Assessing the Radiative Effects of
Global Ice Clouds Based on CloudSat and CALIPSO Measurements, J.
Climate, 29, 7651–7674, 2016.
Ilie, A. and Welch, G.: Ensuring color consistency across multiple cameras,
Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1, 1262, 1268–1275, 2005.
IPCC: Climate Change 2013: The Physical Science Basis, Contribution of
Working Group I to the Fifth Assessment Report of the Intergovernmental
Panel on Climate Change, Cambridge, UK and New York, USA, 1535
pp., 2013.
IPCC: Climate Change 2014: Synthesis Report. Contribution of Working Groups
I, II and III to the Fifth Assessment Report of the Intergovernmental Panel
on Climate Change Geneva, Switzerland, 151 pp., 2014.
Kandel, R. and Viollier, M.: Observation of the Earth's radiation budget
from space, Observation du bilan radiatif de la Terre depuis l'espace, 342,
286–300, 2010.
Kennedy, A., Dong, X., and Xi, B.: Cloud fraction at the ARM SGP site:
reducing uncertainty with self-organizing maps, Theor. Appl.
Climatol., 124, 43–54, 2016.Knobelspiesse, K., van Diedenhoven, B., Marshak, A., Dunagan, S., Holben, B., and Slutsker, I.: Cloud thermodynamic phase detection with polarimetrically sensitive passive sky radiometers, Atmos. Meas. Tech., 8, 1537–1554, 10.5194/amt-8-1537-2015, 2015.Kollias, P., Tselioudis, G., and Albrecht, B. A.: Cloud climatology at the
Southern Great Plains and the layer structure, drizzle, and atmospheric
modes of continental stratus, J. Geophys. Res.-Atmos.,
112, 10.1029/2006JD007307, 2007.
Long, C. N., Sabburg, J. M., Calbó, J., and Pagès, D.: Retrieving
Cloud Characteristics from Ground-Based Daytime Color All-Sky Images,
J. Atmos. Ocean. Tech., 23, 633–652, 2006.
Sassen, K.: Corona-producing cirrus cloud properties derived from
polarization lidar and photographic analyses, Appl. Opt., 30, 3421–3428,
1991.
Sassen, K., Zhu, J., and Benson, S.: Midlatitude cirrus cloud climatology
from the Facility for Atmospheric Remote Sensing. IV. Optical displays,
Appl. Opt., 42, 332–341, 2003.
Schwartz, S. E., Charlson, R. J., Kahn, R., and Rodhe, H.: Earth's Climate
Sensitivity: Apparent Inconsistencies in Recent Assessments, Earth's Future,
2, 601–605, 2014.
Tape, W. and Moilanen, J.: Atmospheric Halos and the Search for Angle X,
Am. Geophys. Un., 2006.
Tian, L., Heymsfield, G. M., Li, L., Heymsfield, A. J., Bansemer, A., Twohy,
C. H., and Srivastava, R. C.: A Study of Cirrus Ice Particle Size
Distribution Using TC4 Observations, J. Atmos. Sci.,
67, 195–216, 2010.
Trenberth, K. E., Zhang, Y., and Fasullo, J. T.: Relationships among
top-of-atmosphere radiation and atmospheric state variables in observations
and CESM, J. Geophys. Res.-Atmos., 120, 10074–10090,
2015.
Um, J. and McFarquhar, G.: Formation of atmospheric halos and applicability of geometric optics for calculating single-scattering properties of hexagonal ice crystals: Impacts of aspect ratio and
ice crystal size, J. Quant. Spectrosc. Ra., 165, 134–152, 2015.
van Diedenhoven, B.: The prevalence of the 22 deg halo in cirrus clouds,
J. Quant. Spectrosc. Ra., 146, 475–479, 2014.
van Diedenhoven, B.: The effect of roughness model on scattering properties
of ice crystals, J. Quant. Spectrosc. Ra., 178, 134–141, 2016.Waliser, D. E., Li, J.-L. F., Woods, C. P., Austin, R. T., Bacmeister, J.,
Chern, J., Del Genio, A., Jiang, J. H., Kuang, Z., Meng, H., Minnis, P.,
Platnick, S., Rossow, W. B., Stephens, G. L., Sun-Mack, S., Tao, W.-K.,
Tompkins, A. M., Vane, D. G., Walker, C., and Wu, D.: Cloud ice: A climate
model challenge with signs and expectations of progress, J.
Geophys. Res.-Atmos., 114, 10.1029/2008JD010015, 2009.
Yang, P., Liou, K.-N., Bi, L., Liu, C., Yi, B., and Baum, B. A.: On the
radiative properties of ice clouds: Light scattering, remote sensing, and
radiation parameterization, Adv. Atmos. Sci., 32, 32–63,
2015.