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1. Introduction
Intense convective updrafts often cause cloud tops to penetrate through the surrounding cirrus anvil and
into the upper troposphere and lower stratosphere (UTLS). These “overshooting cloud tops” (OTs) and re-
sulting outflow impact UTLS composition (Smith etal.,2017), and storms with intense updrafts frequently
produce a variety of severe and aviation weather hazards (Bedka & Khlopenkov,2016; Reynolds1980; Yost
etal., 2018). Analysis of geostationary (GEO) satellite imagery collected at 30-s to 1-min intervals by Ge-
ostationary Operational Environmental Satellites (GOES) shows that deep convection cloud tops and OTs
evolve very rapidly, and many OT regions can occur simultaneously (Bedka etal.,2015; Bedka & Khlopen-
kov,2016), making it almost impossible for human analysts to quantify trends in this detailed data across
many simultaneous storms. Automated OT detection algorithms are therefore required to determine when
and where OTs occur, to better understand how convection impacts the UTLS, and to understand processes
associated with hazardous weather conditions. GEO imagers generally observe the tops of deep convec-
tion, while other remote sensors such as cloud and precipitation radars (Cooney etal.,2021; Takahashi &
Luo,2014; Zisper etal.,2006), passive microwave imagers (Liu etal.,2020), and lightning sensors (Rudlosky
etal.,2019) observe processes occurring within convective clouds. Automated OT detection permits accu-
mulation of large samples of co-located remote sensing data to better understand relationships between
cloud top and in-cloud processes (e.g., Bluestein etal.,2019).
Simple approaches for deep convection and OT detection, such as single-pixel processing based on infrared
(IR) temperature thresholds and/or multi-spectral information (e.g., based on 6–7μm water vapor absorp-
tion or 12μm channels, or brightness temperature differences (BTD)), are not effective in all cases because
1) a convective pixel may have an identical spectral signature to cold but ordinary cirrus clouds, and 2)
pixels with cold IR brightness temperature (BT) are widespread throughout an anvil, but no single BT or
BTD threshold is effective for convection detection across a range of latitudes and large-scale environmental
Abstract This paper describes an updated method for automated detection of overshooting cloud
tops (OT) using a combination of spatial infrared (IR) brightness temperature patterns and modeled
tropopause temperature. IR temperatures are normalized to the tropopause, which serves as a stable
reference that modulates how cold a convective cloud should become within a given region. Anvil clouds
are identified using histogram analysis and cold spots embedded within anvils serve as OT candidate
regions. OT candidates are then assigned an OT probability, which can be interpreted as a metric of
storm intensity and an estimate of confidence in a detection for a particular pixel. It is produced using
an original mathematical composition of four factors: Tropopause-normalized temperature, prominence
relative to the surrounding anvil, surrounding anvil area, and spatial uniformity of anvil temperature,
which are calculated from empirically derived sensitivity curves. The shape of the curves is supported
by independent analysis of a large sample of matched IR and radar-derived OT regions. An optimal
sensitivity for each factor was determined by maximizing correlation between the OT probability and
a set of human-identified OT regions. Coarser spatial resolution of GOES-13 data cause OTs to be
less prominent compared to GOES-16, necessitating different sensitivities for each satellite. Detection
performance is quantified for each satellite based on human OT identifications and as a function of how
prominent the OT appeared in visible and IR imagery. Based on analyses of human-identified OTs, OT
detection accuracy, defined by the area under a receiver operating characteristic curve, is determined to be
0.94 for GOES-16 and 0.78 for GOES-13.
KHLOPENKOV ET AL.
© 2021. American Geophysical Union.
All Rights Reserved. This article has
been contributed to by US Government
employees and their work is in the
public domain in the USA.
Recent Advances in Detection of Overshooting Cloud
Tops From Longwave Infrared Satellite Imagery
Konstantin V. Khlopenkov1 , Kristopher M. Bedka2 , John W. Cooney3 , and Kyle Itterly1
1Science Systems and Applications Inc., Hampton, VA, USA, 2NASA Langley Research Center, Hampton, VA, USA,
3NASA Postdoctoral Fellowship Program at NASA Langley Research Center, Hampton, VA, USA
Key Points:
• A new OT detection method
combines tropopause-relative
infrared (IR) temperature, anvil-
relative prominence, anvil area and
its spatial uniformity
• Overshooting cloud tops (OT)
probability derived from spatial
cloud analyses is validated with
human-identified OTs, revealing
improvements over previous
methods
• Differing imagery spatial resolution
necessitates optimization of
sensitivity curves to account for
warmer observed OTs from coarser
imagery
Correspondence to:
K. V. Khlopenkov,
konstantin.khlopenkov@nasa.gov
Citation:
Khlopenkov, K. V., Bedka, K. M.,
Cooney, J. W., & Itterly, K. (2021).
Recent advances in detection of
overshooting cloud tops from longwave
infrared satellite imagery. Journal of
Geophysical Research: Atmospheres,
126, e2020JD034359. https://doi.
org/10.1029/2020JD034359
Received 4 DEC 2020
Accepted 13 MAY 2021
Author Contributions:
Conceptualization: Konstantin V.
Khlopenkov, Kristopher M. Bedka
Data curation: Kristopher M. Bedka,
John W. Cooney
Formal analysis: Konstantin V.
Khlopenkov, Kristopher M. Bedka
Funding acquisition: Kristopher M.
Bedka
Investigation: Konstantin V.
Khlopenkov, Kristopher M. Bedka
Methodology: Konstantin V.
Khlopenkov, Kristopher M. Bedka
10.1029/2020JD034359
This article is a companion to
Cooney et al. (2021), https://doi.
org/10.1029/2020JD034319.
RESEARCH ARTICLE
1 of 25
Journal of Geophysical Research: Atmospheres
conditions (Bedka etal.,2010). Deep convection is a dynamic process occurring at the mesoscale with char-
acteristic patterns in imagery that require spatial analysis. Human perception, by its nature, is designed to
recognize visual patterns within spatially defined objects. With some training, human analysts can easily
recognize distinctive features that indicate the presence of convective cells and OTs. To a computer algo-
rithm, however, this presents a particular challenge, as it requires a rigorous formal description of a process
before it can be analyzed and quantified digitally.
In recent years, there has been increased interest in the development of more advanced satellite-derived IR-
based OT detection algorithms and application of their output for weather and climate analysis. Previous
studies have made it clear that OTs, identified via unique texture in visible imagery, have small and distinct
IR BT minima with temperatures near to or colder than the tropopause that are embedded within convective
anvil cirrus clouds. Key differences in these algorithms are (a) how BT minima (or “cold spots”) are defined,
(b) if/how the temperature difference between a cold spot and the surrounding anvil is computed, and (c)
the methods used to define a detection and to assign detection confidence. Detection methods have been
based on single-pixel processing using multi-spectral temperature thresholding (Mikus & Mahovic2013;
Schmetz etal.,1997), spatial analyses to capture sharp BT gradients typically associated with OTs (Bed-
ka etal.,2010; Bedka & Khlopenkov, 2016), and machine learning (e.g., Berendes etal.,2008; Cintineo
etal.,2020; Kim et al.,2017). The GOES-R Aviation Algorithm Working Group (AWG) was tasked with
developing an objective OT and enhanced-V signature detection algorithm (Bedka etal.,2010,2011) for use
with GOES-R Advanced Baseline Imager (ABI) data (Schmit etal.,2017). This GOES-R AWG algorithm
focused on identification of cold spots colder than the tropopause and used very simple spatial analysis to
compute anvil-relative temperature difference. Improvements to this approach were recently developed at
NASA Langley Research Center (LaRC) based on product feedback from the operational forecasting com-
munity and researchers, where it was suggested that too many true OTs were missed due to strict detection
criteria, and a simple yes/no binary detection mask was undesirable. These updated algorithms use more
advanced spatial analysis to detect and characterize embedded BT minima and adjacent anvil clouds (Bedka
& Khlopenkov,2016). The term “characterize” refers to how cold and prominent a BT minimum is and how
likely it is to be an OT. Such characterizations enable an improved capability to filter detections to include
only those that are most intense and/or confident for weather and climate studies, which is an improvement
over a yes/no binary OT product (e.g., Apke etal.,2018; Clapp etal.,2019).
Despite recent improvements and science applications with the Bedka and Khlopenkov(2016) method (e.g.,
Apke etal.,2018; Sandmael etal.,2019), the launch of GOES-16 and -17 satellites and application of this
method to 1-min ABI data (Schmit etal.,2017) revealed some inconsistencies in detection performance
from image to image, suggesting that further advancements were needed. This paper provides an enhanced
technical description and describes recent advancements to IR-based deep convection and OT detection
algorithms since the version described by Bedka and Khlopenkov(2016). We have sought to (a) make all BT-
based factors and thresholds operate relative to the local tropopause temperature, (b) improve detection of
anvil clouds, (c) improve the temporal stability of OT detection when dealing with 30-s to 1-min super rap-
id scan observations from the GOES-16/17 Advanced Baseline Imager, (d) improve detection consistency
across historical and current imagers, and (e) improve the overall quality of OT detection through statistical
analysis and validation against gridded U.S. Next-Generation Radar (NEXRAD) network data (see Homeyer
& Bowman,2017 and references therein). This paper is the first of a two-part paper, focusing on algorithm
description and quantitative analyses of detection products relative to human-identified OT regions, while
a companion paper, Cooney etal. (2021), focuses on quantitative comparisons of GOES-13/16 detection
products with NEXRAD GridRad OT detections.
2. Satellite Data
The input required by the NASA LaRC OT algorithms is comprised of images from a visible band with
∼0.65μm central wavelength and an infrared (IR) window band with varied central wavelengths from 10.3
to 11.2μm, satellite dependent. This paper will only describe IR-based algorithms, while the brief descrip-
tion of visible processing here will be elaborated upon in a future paper. The original geolocation (longitude
and latitude) data are also required for each satellite pixel and scan line. This imagery is acquired using the
Man computer Interactive Data Access System (McIDAS) software (Lazzara etal.,1999) in this software's
KHLOPENKOV ET AL.
10.1029/2020JD034359
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Project Administration: Kristopher
M. Bedka
Resources: Kristopher M. Bedka
Software: Konstantin V. Khlopenkov
Supervision: Konstantin V.
Khlopenkov, Kristopher M. Bedka
Validation: Konstantin V. Khlopenkov,
John W. Cooney, Kyle Itterly
Visualization: Kristopher M. Bedka
Writing – original draft: Konstantin
V. Khlopenkov, Kristopher M. Bedka
Writing – review & editing:
Konstantin V. Khlopenkov, Kristopher
M. Bedka, John W. Cooney, Kyle Itterly
Journal of Geophysical Research: Atmospheres
proprietary “AREA format,” but in practice these algorithms can be applied to data in other formats, provid-
ed the required VIS, IR, and geolocation information is available.
As the OT detection is not based on per-pixel analysis but uses spatial context and patterns, it is important
that the cloud features preserve their natural shape and appearance. For this reason, the satellite-viewed
images have to be reprojected to any conformal (i.e., preserving object shapes rather than scales) map pro-
jection. We selected a simple equirectangular projection, which uses equally spaced latitude and longi-
tude increments and is quite conformal at low- and mid-latitudes where most convective storms occur.
The equirectangular grid also simplifies any subsequent data aggregation and cross matching against other
meteorological products. Details on the reprojection and processing of data near the edges of valid satellite
data are provided in AppendixA1.
The output spatial resolution of the reprojected data is selected to approximately match the nominal reso-
lution of the input imagery, and the output resolution for VIS data is always made four times higher than
for IR data, in order to streamline the subsequent processing independent of the input data source. For
example, when processing data from the GOES-16/17 ABI or Himawari-8/9 Advanced Himawari Imager
(AHI), which collect VIS data at 0.5km/pixel and IR data at 2.0km/pixel at their sub-satellite coordinate,
the output resolution for VIS data is 224 pixel/degree (which is about 0.5km/pixel) and so for IR data it
is 56 pixel/degree. For other satellites, the output resolution is selected to be two times lower. The input
imagery from the Meteosat Second Generation Spinning Enhanced Visible and Infrared Imager (SEVIRI)
instrument, which provides IR data at 3.0km/pixel, is also reprojected to 112 pixel/degree for VIS data and
28 pixel/degree for IR data.
3. Overshooting Cloud Top Detection Processing
A set of processing steps are used to identify OTs in infrared imagery. IR BT is first converted to a tropo-
pause-relative temperature. Anvil clouds are identified, and then cold spots embedded within the anvils are
detected. A set of spatial analyses are performed in the anvil regions surrounding cold spots to quantify the
tropopause-relative IR BT, prominence of the cold spot relative the surrounding anvil, anvil area, and anvil
temperature spatial coherence, which are combined to derive the likelihood that a cold spot is an OT. The
following sections detail these processing steps.
3.1. IR Image Normalization by Tropopause Temperature
Anvil clouds are typically located somewhere in the altitude range between the level of neutral buoyancy
(LNB, also commonly referred to as “equilibrium level”) and the tropopause, though some anvil clouds are
colder than the tropopause (Bedka & Khlopenkov,2016). The LNB is a challenging parameter to calculate
accurately because it depends on temperature and moisture profiles in the planetary boundary layer, which
are not well known, especially over data poor regions. Though Bedka and Khlopenkov(2016) show that
anvil cloud temperature is correlated with the LNB, spatial inconsistencies or inaccuracies in LNB data,
when compared with observed IR temperature patterns, could yield misleading analyses of storm intensity
and OT detection error.
The tropopause temperature can be estimated more easily across the globe because the UTLS temperature
is better observed by satellites, radiosondes, and commercial aircraft, and therefore provides a more reliable
reference to identify anvil clouds and embedded OT regions based upon their IR temperature. Solomon
etal.(2016) and Xian and Homeyer(2019) show that reanalyses such as ERA-Interim, JRA-55, MERRA-2,
and CFSR identify tropopause altitudes with small bias (typically less than ±150m) and error compara-
ble to the model vertical resolution when compared with tropopause altitudes derived from radiosondes.
Storms in the mid-latitudes, where the tropopause is lower and warmer, will have warmer cloud top tem-
peratures than those in the tropics. For example, an IR temperature of 215K may indicate a very severe
storm in northern mid-latitudes but would correspond to an unremarkable storm in the tropics. Therefore,
to enable accurate convection detection globally, IR BT is converted to a tropopause-relative temperature
using the hourly Modern-Era Retrospective analysis for Research and Applications Version 2 (Bosilovich
etal.,2016) tropopause analysis, contained in the 2days, 1-Hourly, Time-Averaged, Single-Level, Assim-
ilation, Single-Level Diagnostics V5.12.4 (“MERRA2_400. tavg1_2d_slv_Nx”) collection. MERRA-2 data,
KHLOPENKOV ET AL.
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Journal of Geophysical Research: Atmospheres
originally at 0.5°×0.625° spatial resolution, are interpolated spatially to our equirectangular grid (described
in Section2) using Lanczos filtering, and also in time using linear interpolation between the two nearest
available time samples. The MERRA-2 “TROPT” parameters is used in this analysis that represents a blend-
ed estimate of the tropopause temperature based on a combination of the WMO definition of the primary
lapse-rate tropopause (WMO,1957) and equivalent potential vorticity. Such model analyses will be referred
to here generically as numerical weather prediction (NWP) fields. In practice, these methods could be ap-
plied to any NWP tropopause field.
NWP tropopause temperature fields can depict spatial variations that may not be realistic relative to the
actual conditions around ongoing storms. We feel that this is primarily due to the limited vertical resolution
of the analyses compared to radiosondes. At one location the tropopause detection algorithm may success-
fully identify the primary tropopause, while at a nearby location it may fail to detect the primary tropopause,
which causes a higher level to be incorrectly labeled as the primary tropopause. This leads to substantial
overestimates of the tropopause altitude. This is most common near jet streams, where there is commonly
a sharp jump in the tropopause altitude. In addition, the tropopause has details that, when compared to
satellite IR BT, would result in a noisy product not amenable to storm detection and characterization. An
example of this can be seen in Figure1 where the left panel shows the tropopause temperature obtained
from GEOS-5, which exhibits extensive high frequency spatial variability.
In order to obtain a reliable and stable reference temperature threshold, the following spatial filtering is
applied to the tropopause temperature, Ttp. Within a circle of 500 km diameter around the current pixel
(which is allowed to be clipped at the boundary of the user-selected domain), the area mean
Ttp
and stand-
ard deviation
Ttp
of the tropopause temperature are calculated and the filtered temperature is obtained as:
T TT
tpfiltered tp tp
06.
(1)
This filtering produces a much smoother tropopause temperature field, which is designed to be biased
slightly colder than the original tropopause in areas of strong spatial gradients. Such biasing accounts for
situations where the updraft region of a storm may be rooted on the colder side of a gradient, but the anvil
extends into the warm side. A discontinuity in the anvil and OT detection would occur here if the sharp
tropopause gradient were preserved, so the right-side term of this equation extends cold temperatures to the
warm side of a tropopause gradient. An example of a filtered tropopause analysis is shown in the right panel
of Figure1, which is much more amenable to IR-based convective storm detection and analysis.
IR temperature normalization by the tropopause is accomplished through a parameter referred to as the
“BT-score.” It is obtained from the filtered tropopause temperature as follows:
p tpfiltered
score 60 340,BT BTTD BTTD BT T
(2)
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Figure 1. An example of the original (left) and filtered (right) GEOS-5 tropopause temperature over the Southwest
U.S., Mexico, and Eastern Pacific Ocean.
Journal of Geophysical Research: Atmospheres
where BTTD is BT minus Tropopause temperature difference, BTp is the brightness temperature of the cur-
rent pixel, and the scale (340) and the offset (60) are designed to fit the resulting BT-score to the range of a
2-byte integer. Thus, extremely strong OT events of 20K colder than the tropopause would yield a BT-score
of 27,200. This BT-score parameter is similar to S-score used by Bedka and Khlopenkov(2016), which relied
on a difference of the local temperature from a regional mean temperature and a difference from a reference
IR temperature of 255K. The new BT-score, however, presents an improvement over the S-score in that it
allows all subsequent analysis to be independent of absolute temperature thresholds by instead making
it relative to the local tropopause temperature. Figure2 (left panel) shows a GOES-16 10.3μm BT scene
with numerous OT-producing and severe storms across the U.S. southern Great Plains. The corresponding
BT-score image is shown in the right panel of Figure2. The rectangular frame highlights a strong supercell
storm that will be used to demonstrate subsequent stages of the detection process.
3.2. IR Anvil Mask
As shown in Figure2, anvil clouds appear as a spatially continuous area of cold pixels. By quantifying the
“coldness” and spatial continuity it is possible to derive an anvil mask. The anvil mask is a 1-byte rating that
indicates a confidence in anvil detection, with values over 10 roughly corresponding to human perception
of anvil cloud extent while values over 100 indicate a very high level of confidence. This anvil rating is
crucial for successful OT detection as it is used during several processing phases described below. The new
anvil mask algorithm has been improved significantly over the version from Bedka and Khlopenkov(2016),
which was based on 16-vertex polygons constructed around each OT candidate. That method required a
distinct OT to be present for an anvil to be detected. Also, it was not always possible to capture curved anvil
boundaries using simple polygon shapes. In this new method, calculation of the anvil rating/mask can be
roughly described in the following three steps: Histogram analysis, expansion to encompass the anvil spatial
extent, and final refinements.
Here and further in the description of the algorithm, we present several key algorithm parameters, which
may appear arbitrary/empirical but, in fact, have been derived after years of extensive tests on large volumes
of real satellite data and have been found to work best in various convection scenarios. Some specific values
are helpful in improving the computational performance, which is especially critical in large volume data
processing. The current version of the algorithm can process a typical GOES-16 full disk scene in 15–30s
when executed on a typical 3GHz CPU in a single thread mode.
KHLOPENKOV ET AL.
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Figure 2. GOES-16 10.3μm brightness temperature on May 5, 2019 at 23:00 UTC across the U.S. Southern Plains (left)
and the corresponding image of BT-score (right). A scale of brightness temperature (BT) minus tropopause difference
(BTTD) is also provided for reference.
Journal of Geophysical Research: Atmospheres
The input BT-score image is processed in subsets taken by a circular
22km diameter window at every other pixel and every other line. The
local distribution of BT-score within each subset is analyzed by construct-
ing a histogram H having N= 32 bins, covering the BT-score range of
8,500–24,884. A value of 8,500 corresponds to clouds at a level of 35 K
warmer than the tropopause, which is an extremely low tropopause-rel-
ative bound for anvil clouds. The upper limit of 24,884 indicates a level
13K colder than the tropopause, which only occurs in updraft regions or
adjacent anvil outflow. Pixels colder than this threshold are accumulated
in the last bin.
As noted previously, BTs within anvils are, in most cases, cold and spatial-
ly uniform, which would yield a sharply peaked histogram of BT-score.
Thus, the anvil rating should be made proportional to the peak's height
(Hi, which is the number of counts in the i-th bin) and to that bin's index
i, because a higher bin corresponds to a colder region. After extensive
testing, Equation3 is found to be able to describe the dependence of anvil
rating, ranvil, on index i reasonably well:
anvil 28
Hi
r C Hi N i
(3)
Here, CH is a normalization coefficient and the term in parentheses flattens the dependence out at high
values of i in order to simulate the natural saturation of confidence (similar to any probability in general)
in anvil detection when the anvil BT is extremely low. Figure3 shows ranvil for the outlined region in the
middle of Figure2 (right). Here, CH is equal 0.35/D2 where D is the diameter of the histogram window in
pixels. This normalizes the result by the total number of pixels in the histogram to account for varying sat-
ellite pixel size.
One can immediately see in Figure3 that the obtained anvil rating field is very non-uniform and consists of
large spots of higher rating separated by smaller, low rating areas. The main anvil area has the rating rang-
ing from about 50 to 200 units. The lower rating is produced not only outside the main anvil but also very
close to the primary OT area in the lower left part of the anvil (see Figure4 (left) for a BT-score image cor-
responding to the same region). The OT and nearby vicinity exhibit a highly non-uniform BT field, which
translates into a broad histogram and a smaller dominant peak resulting in a lower anvil rating calculated
from Equation3. This becomes a problem for all subsequent OT detection steps because the OT area itself
may happen to be excluded from or penalized in further processing due to the low anvil rating.
KHLOPENKOV ET AL.
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Figure 3. Initial anvil rating based on the dominant peak on the
brightness temperature (BT)-score histogram calculated for GOES-16
case of May 5, 2019 23:00 UTC. The image boundaries correspond to the
rectangular region in Figure2 right panel.
Figure 4. A subset of the BT-score image (left) with white circles showing four locations where histogram's peaks are analyzed. BT-score histogram (right)
calculated at four selected location: Around the main Overshooting cloud tops (OT) (locations A and B), at the anvil's upper extent (location C), and at the
anvil's boundary (location D). Brightness temperature (BT) minus tropopause temperature difference scale is provided at the top axis for reference.
Journal of Geophysical Research: Atmospheres
To highlight this problem, examples of the obtained histogram are analyzed at four selected locations shown
with white circles in Figure4 (left). The circle diameters represent the actual size of the window where the
histogram is probed. Although in the middle of the anvil the histogram's peak reaches well over 30 counts,
it falls below 25 in selected anvil locations A, B, and C as demonstrated by Figure4 (right). Location A in-
cludes many extremely cold pixels from the OT core that are counted in the last bin of the histogram making
it the highest peak in this case (black curve). The histogram also reveals two minor peaks at around 17,000
and 19,500 highlighted by the arrows in the figure. On the other hand, location B (which is just 8km east-
ward from A) produces a completely different picture. The peak in the last bin disappears and the other two
peaks become merged into a single peak at 18,500 (red curve). Location C, though located in a seemingly
uniform anvil region far from the OT area, still develops two distinct peaks of the same height (green curve).
Lastly, location D at the edge of the anvil produces a broad histogram distribution that is shifted much more
towards lower BT-scores. The latter logically yields a low anvil rating because of the smaller peak and the
low i-index. The first three locations, however, can produce a completely volatile result because the height
and position of the peak irregularly fluctuate.
The problem of high volatility in the anvil rating can be solved by combining the contributions from several
peaks:
anvil 28
Hi
i
r C Hi N i
(4)
Here the summation is carried out over the three highest histogram bins and the bins are allowed to be
adjacent. This allows a single large peak to be counted together with its neighboring bins, and if the peak
splits into two or more separated bins (as is the case with location C above), the total contribution remains
comparable, which should help the overall stability of the resulting rating across the entire anvil region.
This is confirmed by Figure5 (left) which depicts the preliminary anvil rating obtained from Equation4.
The normalization coefficient CH used here is smaller, 0.22/D2, to compensate for the summation of several
bins. The primary difference from Figure3 is that the anvil rating field is now much more homogeneous
within most of the anvil area, except for the main OT and downwind from the OT where warm tempera-
tures are present due to an above anvil cirrus plume. The white contour in this figure shows the extent of
the main anvil using a BT-score threshold of 16,000, or 13K warmer than the tropopause. One can see that
the uniform orange region nearly reaches the anvil boundary outlined in white. There is, however, an ap-
parent margin along the contour where the anvil rating drops significantly even though the BT-score level
is high. This is due to how the histogram is derived: When the circular window reaches the anvil boundary,
the number of cold pixels within the window declines, thereby reducing the contribution to the major cold
peaks. This reduction is further corrected by additional processing steps that involve a spatial expansion and
refinement of the anvil rating, as described in AppendixA2.
The outcome of this refinement is the final anvil rating shown in Figure5 (right), which demonstrates a
very much improved depiction of the anvil extent and a more uniform anvil rating field. The OT vicinity is
now covered by a higher anvil rating and the transition of the rating from a high level to background is now
smooth at the anvil boundaries. This is important for cases when OT centers are situated at the boundary,
due to strong advection of anvil away from the OT. Validation of the IR anvil mask is described by Scarino
etal.(2020) where it was demonstrated to have accuracy comparable to several other anvil identification
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Figure 5. Preliminary anvil rating (left) obtained as a summed contribution from three highest peaks in BT-score
histogram. The white contour selects the main anvil cloud at BT-score level of 16,000. Final anvil rating (right) after
spatial expansion and refinement.
Journal of Geophysical Research: Atmospheres
approaches. Scarino etal. (2020) noted that while true anvil clouds are
identified well with this method, other spatially coherent areas of cold
cloud with temperatures near to or colder than the tropopause could
also be identified. For example, non-convective cold cloud shields along
fronts within mid-latitude cyclones could be mis-identified as anvil, so
Scarino etal.(2020) propose use of environmental parameters such as
Convective Available Potential Energy (CAPE) to filter out false anvil de-
tection where deep convection is extremely unlikely. For the purpose of
OT detection, anvil cloud identification simply provides a search region
for identification of OT candidates. Additional algorithm logic would
mitigate false OT detection in such frontal cloud patterns.
3.3. Identification of Initial OT Candidates
OTs appear as localized cold spots with diameters typically less than
15km embedded within a surrounding anvil cloud (Bedka etal., 2010).
Therefore, the starting phase for OT detection involves a search to identi-
fy cold spots followed by a series of distance tests. This is to ensure that detected OT candidates have appro-
priate spacing and thus two pixels from the same OT are not classified as two distinct OT areas. The required
spacing gradually reduces for candidates with higher BT-score. This allows colder OT cores, more likely
to truly be OTs, to form a denser distribution, thus increasing their chances to pass all the detection tests.
Unlike the method used by Bedka and Khlopenkov(2016), the current algorithm identifying local maxima
in a pixel image is an original one, developed specifically for OT candidate selection. It is also quite general,
so it can be used for any other image data, such as visible reflectance, temperature, and others. The process
begins with analyzing 3 × 3 pixel subsets of the BT-score image in order to identify pixels surrounded by all
lower scored nearest neighbor pixels, which guarantees that the pixel is a true local maximum. As a result,
the initial local maxima are spaced apart by at least two pixels. Then, for each identified maximum, its 11
× 11 pixel proximity is checked for the presence of an even higher maximum. If a better candidate is found
in this proximity, then the current candidate is discarded. A “better candidate” refers to a higher nearby
maximum that was not yet discarded. Thus, this process continues recursively and thins out the initial list
of candidates leaving the most prominent local maxima in the BT-score field. This proximity check uses an
effective distance Deff, and if the geometrical pixel distance between the two candidates is less than Deff, then
the weaker one is discarded. Deff is based on the minimal desired distance L (its default value is 4km), which
is corrected with two factors:
eff
17000 min ,
1 10 1 170
AB AB
DL Z Z
AB
(5)
where A and B are the two BT-scores of the candidates in the pair, Z(x) equals x for positive arguments or
zero otherwise (i.e., the ramp function), and the other constants here are derived from empirical testing.
The first term in the outer brackets increases the effective distance if the candidates' BT-scores are too
different, meaning that a weaker candidate can survive only if the stronger one is further away than the
default distance L. The second term increases the effective distance if either of the candidates is too weak,
which allows for a more dense population of colder candidates and aids detection of smaller OTs inside a
large cluster of cold pixels. The result of this optimization is demonstrated in Figure6, where the discarded
candidates are shown with black squares.
3.4. Calculation of OT Probability
Ideal OT areas appear “cold” based on their tropopause-relative IR temperature and comparisons with the
surrounding anvil, and are located within broad and cold, spatially uniform anvils. Such a conventional
description can be quantified by means of an IR OT rating, which has previously been obtained as the sum
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Figure 6. White squares denote the refined list of brightness temperature
(BT) minima after optimization, overlaid on the BT-score image. Discarded
candidates are shown with black squares and the arrows point to a few less
noticeable spots.
Journal of Geophysical Research: Atmospheres
of several terms corresponding to characteristics of an analyzed OT such
as its BT, shape, and area measured along the rays cast from OT candidate
pixels (Bedka & Khlopenkov,2016).
The currently presented approach is a result of significant revision of the
algorithm by Bedka and Khlopenkov(2016), improved mathematical jus-
tification, extensive testing with data from several GEO and low Earth
orbit imagers, and rigorous analysis and verification. The core of the al-
gorithm is a combination of four different factors each designed to de-
pict the following metrics: (a) a tropopause factor, TropopauseF, showing
how cold the OT candidate is relative to the tropopause temperature; (b)
a prominence factor, ProminenceF, showing how cold the OT candidate
is relative to the anvil mean temperature; (c) an anvil area factor, AreaF,
showing how large the anvil area is in the OT vicinity; and (d) an anvil
rating factor, AnvilF, showing the uniformity of the anvil around the OT.
Each of these factors is scored from a range of 0–1, with larger values
indicating higher confidence in an OT detection. Aggregation of all of the
factors together helps the overall robustness of the detection scheme and ensures that a high OT probability
corresponds to a true OT with strong convection. Contributions from these four factors have to be combined
in such a way to properly account for the role of each contributor. For example, although the TropopauseF
is the most significant factor among the four, it alone cannot define the resulting OT probability because an
OT candidate pixel may be very cold relative to the tropopause but can, in fact, be just a small perturbation
in a broad uniformly cold anvil cloud (Cooney etal.,2021). Therefore, the IR OT probability OTprob is con-
structed as follows:
0.6 1/ 1
100OTprob TropopauseF
(6)
where 100 is a scale factor that scales the resulting OT probability into the range of 50–100 for the strongest
OT detections. λ is a function proportional to the remaining three factors (more details are provided below)
and ranges from 0 to 1. The main factor TropopauseF here is raised to the power of 1/λ−1, which makes
the result close to zero when
0
and close to 1 when
1
. The power of 0.6 is needed here to control
the growth rate of OTprob with the four factors and was found to achieve the best agreement in validation
(described in the next section). Overall, this formula makes the OTprob grow with the TropopauseF while
the growth rate is suppressed, if the other factors are insignificant, or inflated when λ is high (Figure7).
When all of the factors comprising λ are high (e.g., λ>0.7) the resulting OTprob reaches 70 and higher even
at low level of 0.3 of TropopauseF. For a low λ of 0.2, the same OTprob
requires a high TropopauseF of 0.9. On the other hand, embedded cold
spots in broken cirrus can achieve anomalously high temperature differ-
ences between an OT candidate and the surrounding warmer semi-trans-
parent cloud, though this scenario is uncommon because broken cirrus is
rarely identified as anvil. Thus, it is important to reduce the influence of
ProminenceF at warmer temperatures, and therefore a low TropopauseF
in Equation6 causes OTprob to remain small for virtually any λ, as λ nev-
er reaches 1.0 in reality.
The three factors comprising λ are derived from an anvil region in the OT
candidate vicinity, so we first need to describe how that area is evaluated.
The goal here is to calculate the anvil mean parameters averaged over a
set of pixels that represent the most homogeneous area around a candi-
date. In the first step, two histograms of brightness temperature are com-
puted within circles of radius, RH, of 16 and 24 km around a candidate
(see Figure8), which allows for adequate capturing of both small- and
large-scale anvils. A small area around the candidate is excluded here,
which is taken as 3 × 3 pixels in the center (for 2km or finer spatial res-
olution) or just the central pixel with its four immediate neighbors (for
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Figure 7. Infrared (IR) Overshooting cloud tops (OT) probability (shown
in numbered contours) as a function of the tropopause factor and other
factors combined in λ.
Figure 8. A concept drawing showing two circular areas where the
histograms are probed and the sampling pattern of the nearby anvil to
derive anvil mean parameters: Temperature, rating, and effective area.
Journal of Geophysical Research: Atmospheres
coarser resolution). The histograms have 40 bins covering the tempera-
ture range from BTp (the central pixel's BT) to BTp+25K. Within each
histogram, the two highest bins are selected, and their peak positions are
calculated as:
1
1
peak 1
1
i
n
ni
i
n
ni
nH
X
H
(7)
where i is the index of the selected bin. This is converted to the corre-
sponding temperature BTpeak, which gives us four temperature values
from the two histograms.
In the second step, 32 rays are cast off from the center with their initial
offset from the center varying in the pattern depicted by Figure8. The
offset pattern is needed to reduce spatial oversampling around the center
and to achieve a reasonably uniform sampling coverage in the OT candi-
date vicinity. These offsets can be obtained by taking each ray's ordinal
number in binary form (e.g., 0000, 0001, 0010, 0011, 0100, etc.,) and using the number of trailing zero bits
z (4, 0, 1, 0, 2, respectively) to scale down the number 8 (the pattern period) by means of the bitwise ‘shift-
right' operation as 8 >> z (to get 0, 8, 4, 8, 2, respectively).
Samples of the BT and the anvil rating are acquired along each ray (by using the Lanczos interpolation)
as long as local BT stays within the range of allowed temperatures defined as BTpeak ±1.3K, a threshold
based on empirical testing. The processing of each ray stops when the distance from the center exceeds the
current radius, RH, or more than one out-of-range samples are encountered, which effectively means that
the anvil boundary has been reached. As a result, the mean temperature WinAvgBT and the mean anvil
rating WinAvgAnvil are computed by averaging all of the samples acquired along the rays. The number of
used samples is divided by the maximum possible number of pixels along all rays for the current radius,
and this ratio defines an effective anvil area AnvilArea. As a last step, the four cases of WinAvgBT, WinA-
vgAnvil, and AnvilArea obtained for the two major peaks of the two histograms are weighted-averaged
with the weights equal to their corresponding effective anvil areas. For the strongest OT region embedded
in the anvil cloud shown in Figure6, the derived anvil extents satisfying the BTpeak ±1.3K condition are
shown in Figure9. Accordingly, the following anvil mean parameters are found: WinAvgBT=209.55K,
WinAvgAnvil=127.6, and AnvilArea=0.2377, with the OT's lowest BT of 196.76K, and the tropopause
temperature of 208.24K.
Our extensive tests have found that the described two-peak approach is imperative in situations when the
OT vicinity is comprised of complex non-uniform cloud structures, especially in cases when multiple OTs
are clustered together. Having the histograms sampled over differently sized areas and blending the results
from two histogram peaks ensures a smooth change in the resulting anvil metrics when the histogram's
maximum transitions from one peak to another due to a natural time evolution of a convective area. This
ultimately helps the overall temporal stability of the OT probability, in particular when dealing with 30-s to
1-min Mesoscale Domain Sector observations from the GOES-16/17 imager.
Once the anvil mean parameters are retrieved it is possible to describe how the factors comprising the OT
probability are constructed. The TropopauseF quantifies the effect of OT temperature on the resulting OT
probability, as a colder OT implies a higher detection confidence. This confidence flattens out at extremely
low temperatures as any probability derivation in general saturates when approaching 100%. Therefore, the
TropopauseF is calculated as follows:
3
2
1 / 0.91 4.3 /
p tp
TropopauseF Z Z BT T SensOTtemp
(8)
where SensOTtemp is a “Sensitivity to OT temperature” parameter, typically 0.65±0.10. Figure10a shows
the TropopauseF curves calculated for a tropopause temperature of 200K for different values of SensOT-
temp. The shape of the curve is based on empirical analyses of tropopause-relative BT characteristics of OTs
by the authors, supported by NEXRAD-based OT analyses described below. The formula is built around the
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Figure 9. Extents of the anvil cloud (dark transparent shading) derived
for the strongest OT, overlaid on the brightness temperature (BT) score
image for GOES-16 case of May 5, 2019 23:00 UTC.
Journal of Geophysical Research: Atmospheres
ratio of the OT brightness temperature, BTp, to the tropopause temperature, Ttp, and thus works relative to
the changing tropopause temperature and eliminates fixed temperature thresholds used in previous OT de-
tection algorithms (e.g., Bedka etal.,2010 and references therein). The square power in Equation8 controls
how the curves approach the saturation level of 1.0, while the third power is responsible for a smoother
decay towards zero. One can see from Figure10, TropopauseF decreases slower with higher values of Sen-
sOTtemp, implying that a higher sensitivity makes the TropopauseF larger for the same ratio of BTp to Ttp.
The ProminenceF describes the effect of OT prominence (in terms of temperature) relative to surrounding
anvil, and so it is based on the ratio of WinAvgBT to the BTp and is calculated as follows:
2
2
p
1 1 / 1.02 0.02 40ProminenceF Z Z WinAvgBT BT SensOTprom SensOTprom
(9)
where SensOTprom is a “Sensitivity to OT prominence” parameter, typically 0.80±0.10. Figure10b shows
three sample curves (solid lines) of the ProminenceF obtained for different values of SensOTprom at a fixed
BTp of 200K. The ratio of WinAvgBT to BTp is effectively scaled by SensOTprom to enhance the steepness
of the curve and, similar to the TropopauseF factor, a higher sensitivity SensOTprom yields a larger Prom-
inenceF. The formula also includes a small offset of 0.02⋅SensOTprom, which shifts the curve to the right
with lower SensOTprom and delays the rise of the ProminenceF until the difference from the anvil mean
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Figure 10. Dependences of (a) the tropopause factor on the OT temperature calculated for the tropopause temperature of 200K (b) the prominence factor on
the anvil mean temperature calculated at the fixed OT BT of 200K (c) the area factor on the effective anvil area, and (d) the anvil factor on the mean anvil rating.
Sensitivities associated with optimal GOES-13 and -16 detection of human-identified OT regions are depicted by dashed curves.
Journal of Geophysical Research: Atmospheres
temperature becomes sufficient. This prevents false detection of minor dips in the temperature field of
non-perfectly uniform anvils.
The profiles of the two sensitivity curves above are supported by cumulative frequency diagrams (CFD)
derived using a large database of GridRad 20dBZ echo tops (59,248 samples) above the level of tropopause
altitude minus 2km (see Cooney etal.,2021) and reported severe weather events from the NOAA National
Weather Service Storm Prediction Center database (3,967 samples). This database of high-altitude echo
tops was compiled at 5-min intervals over 15days in the year 2017 across the U.S. when both GOES-16 and
GOES-13 (Hillger & Schmit,2007) were observing the same storms in periods of widespread intense con-
vection. Figure11 shows the cumulative frequency as a function of tropopause-relative IR BT (see BTTD in
Equation2) and IR minus anvil BT difference (i.e., prominence). The bulk of the distribution ranges from
+10 to −15K for BTTD and from −1 to −14K for prominence. These frequency distributions suggest that
the corresponding TropopauseF and ProminenceF curves should stay inside these limits, because virtually
no OTs are actually observed outside these ranges. Extending the sensitivity curves beyond these limits is
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Figure 11. Cumulative frequency diagrams of the coldest GOES-16 (top) and GOES-13 (bottom) infrared (IR) minus anvil brightness temperature (BT)
difference (i.e., prominence) and tropopause-relative IR BT values within 10km of GridRad radar echoes at varying tropopause-relative heights, 20dBZ echo
top 2km below tropopause and 1km below tropopause, and 10dBZ top at or above the tropopause defined by MERRA-2. Distributions of the same GOES IR
parameters within 2.5min (GOES-16) or 7.5min (GOES-13) and ∼30km of severe weather reports are also shown. The database is dominated by wind and
1–2 inch (2.5–5cm) hail events, but includes 189 tornado and 173 2+ inch diameter hail events. The sensitivity curves found to be optimal based on analysis of
GOES data within human-identified OT regions are also shown.
GOES-16
0
20
40
60
80
100
Cumulative Fraction (%) or Sensitivity
GOES-16
10 5 0 -5 -10 -15
-20
Min TMERRA2 within 10 km of OTN Columns (K)
GOES-13
0-1-2-3-4-5-6-7-8-9 -10 -11-12 -13 -14-15
Min IR-Anvil BTD within 10 km of OTN Columns (K)
GOES-13
0
20
40
60
80
100
Cumulative Fraction (%) or Sensitivity
Tornado
Wind
Hail < 2 in
Hail 2 in
10 dBZ > 0 km
20 dBZ > -1 km
20 dBZ > -2 km
OTProm Sensitivity
Tornado
Wind
Hail < 2 in
Hail 2 in
10 dBZ > 0 km
20 dBZ > -1 km
20 dBZ > -2 km
OTTemp Sensitivity
Tornado
Wind
Hail < 2 in
Hail 2 in
10 dBZ > 0 km
20 dBZ > -1 km
20 dBZ > -2 km
OTProm Sensitivity
Tornado
Wind
Hail < 2 in
Hail 2 in
10 dBZ > 0 km
20 dBZ > -1 km
20 dBZ > -2 km
OTTemp Sensitivity
10 50
-5 -10 -15
-20
Min TMERRA2 within 10 km of OTN Columns (K)
0-1-2-3-4-5-6-7-8-9 -10 -11-12 -13 -14-15
Min IR-Anvil BTD within 10 km of OTN Columns (K)
Journal of Geophysical Research: Atmospheres
not desired, as this will make them less steep and will also reduce the
operating range of TropopauseF and ProminenceF factors. As seen from
Figure11, coarser resolution of GOES-13 reduces the CFD ranges, which
suggests that the steepness of the sensitivity curves need to be increased
by adjusting their corresponding sensitivities. The effect of coarser sen-
sor's resolution on the OT detection efficiency is discussed in Section5.
The third factor contributing to the OT probability is the area factor, Are-
aF. Experience with analysis of OT-producing storms has revealed that
storms with larger anvils are more likely to generate OTs than storms
with little to no anvil area. Thus, AreaF is designed to lower the OT prob-
ability when an OT candidate has insufficient anvil area nearby:
2
11AreaF Z SensAnvilArea AnvilArea
(10)
where the SensAnvilArea is a configurable parameter (typical value is
1.0±0.2) that controls the influence of the area factor on the OT proba-
bility, as shown in Figure10c.
The last component of the OT probability is the anvil factor, AnvilF,
which is designed to assign higher OT probability to OTs located in ar-
eas with a higher anvil rating, which in turn describes mostly the anvil's
uniformity and coldness in a tropopause-relative sense of its BT field (see
Equation4). It is more likely that a pixel is truly an OT if it is embedded
within a region of uniformly cold anvil cloud, in contrast to a cold spot
surrounded by broken cold pixels that are not as likely to comprise a true
anvil cloud. Thus, it is made proportional to the mean anvil rating WinAvgAnvil obtained by sampling with
the ray casting above:
0.3/
/ 200
SensAnvilFlatness
AnvilF WinAvgAnvil
(11)
Here the SensAnvilFlatness is a configurable parameter (typical value is 0.8±0.2) that, being in the power
of the exponent, controls the steepness of the curve and thereby the sensitivity to the anvil rating as shown
in Figure10d.
These three factors–the prominence, area, and anvil–describe an OT's prominence relative to a wide, uni-
form anvil cloud. If any of these conditions are not met, then the OT candidate is not likely to correspond to
a true OT and thus should be assigned a lower detection probability. After extensive tests and comparisons
of various formulations, we decided to combine all three factors symmetrically in one λ-function as follows:
ProminenceF AreaF AnvilF
(12)
Using all three factors in one product requires all of them to be high concurrently in order to produce a
significant level of λ. The square root here corrects for too-low levels of the three-component product and
helps to balance the distribution of contour lines in Figure7.
Thus far, an OT candidate represents a single pixel corresponding to a local maximum of BT-score, however,
an overshooting updraft core typically extends beyond one IR pixel. The process for expanding the updraft
core to encompass all pixels within a given OT is described in AppendixA3. Once an OT's extent is defined,
its pixels are filled with the derived IR OT probability making up a region that spatially matches the input
reprojected BT. This is demonstrated in Figure12 where the resulting OT probability is overlaid on a gray-
scale BT image. The OT probability is presented in color scale from 0 to 100 percent. One can see that all
strong OT cores (see Figure2) are covered with regions of OT probability reaching 80% and higher.
In summary, we have provided a detailed technical background on a new OT detection method, that offers
several significant improvements relative to the previous Bedka and Khlopenkov(2016) method:
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Figure 12. Final product of OT probability after the spatial expansion
of OT cores (colored pixels) overlaid on a grayscale image of GOES-16
10.3μm brightness temperature on May 5, 2019 at 23:00 UTC.
Journal of Geophysical Research: Atmospheres
(1) IR BT is now normalized to the tropopause, whereas the previous version used an areal mean BT as a
reference.
(2) IR anvil mask is now a completely new product and presents a per-pixel anvil rating, whereas the pre-
vious version used polygons to identify anvil cloud only in the near vicinity to an OT candidate that
excluded the outer periphery of cold anvil regions.
(3) Identification of OT candidates has been fully redesigned.
(4) OT probability is derived using a completely new approach based on combination of four factors that
better captures the spatial characteristics of the OT candidate and anvil region.
(5) The current algorithm is using a more sophisticated method for estimating anvil mean parameters
around an OT candidate.
(6) OT spatial extent is defined more accurately.
(7) Key sensitivities are derived from an extensive statistical analysis based on manual OT identification
(see Section4 below).
(8) The current algorithm automatically adjusts the sensitivities according to the spatial resolution of the
input BT image in order to achieve, on average, the same OT probability independent of the satellite
(see Section5 below)
4. Optimization of OT Probability
During development and improvement of the OT detection algorithm, expert feedback from scientists has
been constantly utilized to fine-tune the key parameters and thresholds used in the equations above. This
way, the human perception can serve as the first direct validation of the correct performance of our algo-
rithm provided that this analysis is rigorously formulated and quantified. Detection performance relative
to OT detections from precipitation radars such as NEXRAD, a quantitative estimate for OT locations, is
demonstrated by Cooney etal.(2021). The current algorithm is designed to assign high confidence to fea-
tures that are clearly OTs to human analysts, and thus can only detect features that are distinct in the
imagery. Therefore, a pixel mask of OT locations was produced by a human analyst based primarily on the
VIS image but supported by IR data from the same case as Figure12. The higher resolution VIS image is
particularly helpful for manual identification of OT locations and was used as an independent verification
since the OT detection scheme described above is based solely on IR-based data.
Three classes are included in the human identified mask, that is no-OT, weak OT, and strong OT. Compared
to a binary (yes/no) mask, the weak OT class is helpful in that it provides more flexibility in the statistical
comparison between a continuous variable (the OT probability from 0 to 100) and a discrete human OT
identification. The exact pixel locations of OT cores in the human identified mask were bound to the local
BT minima in the IR image, so as to exclude any misdetections due to spatial mismatch and to focus only
on the accuracy of detection probability. In total, the human mask shown in Figure13 contains 40 strong
OT locations and 39 weak OT ones. We should note that this analysis excludes pixel pairs where the human
mask shows no-OT and the OT detection probability is below 0.5%, which are the majority of pixels in the
image and correspond to “true negative” detections.
With these considerations, the human mask is matched against the algorithm-generated OT detection prob-
ability with the following major goals (a) find the optimal set of algorithm's parameters (i.e., sensitivities
SensOTtemp, SensOTprom, SensAnvilArea, and SensAnvilFlatness): That yields the best agreement with the
human identified mask; and (b) assess the statistical accuracy of OT detection, that is achieving the highest
probability of detection (POD) while keeping the false alarm ratio (FAR) low.
As a measure of agreement between the OT probability and the human mask, the Spearman correlation
is appropriate, because it is designed to analyze the statistical dependence between continuous and rank
(i.e., discrete) variables. Therefore, the Spearman correlation coefficient, ρ, can be used to optimize the
four sensitivities so as to achieve the highest correlation with the human mask. This can be implemented
by means of the Powell's conjugate direction method (Powell,1964), which iteratively converges to a local
minimum of a function (this can be, for example, 1−ρ) in multidimensional space while varying the input
sensitivities. Due to the high dimensionality of our problem, the iterative routine may be trapped around
a local minimum if the initial guess values happen to be far from the actual absolute minimum. To avoid
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Journal of Geophysical Research: Atmospheres
that, the correlation was first computed over the following pre-selected ranges of the four sensitivities:
SensOTtemp=0.65±0.10, SensOTprom=0.80±0.10, SensAnvilArea=1.00±0.10, and SensAnvilFlat-
ness=0.90±0.10. The 0.10 variance in the analysis of SensOTtemp and SensOTprom allows the sensitivities
to encompass the dynamic range of GOES-13 and GOES-16 tropopause-relative BT and anvil prominence
shown in Figure11. Each of the sensitivities is varied by a 0.05 step, which translates into a total of 5×5×5
× 5=625 calculations of the correlation. Among those, the two best sets of sensitivities are selected and
then used as the initial guess values in the Powell's minimization. Thus, the iterative routine is executed
twice and the highest correlation among the two results is selected, yielding the optimal set of the four
sensitivities. This approach significantly improves the overall stability of the convergence and helps the
iterative routine to converge to the true absolute minimum. As a result of this optimization, the correlation
ρ of 0.7914 is achieved with the following sensitivities: SensOTtemp=0.6313, SensOTprom=0.8275, Sen-
sAnvilArea=0.9020, and SensAnvilFlatness=0.7502.
Once the key sensitivities are defined, the OT detection algorithm is ready to be applied to any IR satellite
image with 2–4km spacing per pixel at nadir, which includes nearly all current and historical geostationary
imagers from recent decades. In order to validate the sensitivities derived from this single case, we have
selected three additional cases of GOES-16 data from May 18, 2017 at 22:47 UTC (see Figure14) August
13, 2017 23:02 UTC, and April 29, 2017 23:00 UTC for analysis. Figure14 image and the other two cases
(not shown) provide a wide variety of convective regions with varying intensity extending across a broad
geographic domain. If the OT detection algorithm is capable of detecting OTs correctly from these cases,
then this builds confidence that it will operate reliably afterwards. To demonstrate the qualitative agree-
ment between OT probability and human OT identifications, two zoomed in areas of the mask are shown in
Figure15, which correspond to the red frames in Figure14. The large anvil cloud in the left frame exhibits
much lower temperature down to 190K, while the convective cells in the right frame are mostly warmer
with OT cores at 205–210K. The colder anvil area in Figure15-upper left is identified to have a higher
density of OT locations compared to the convective cells in Figure15-upper right. The human mask for this
case is also using three classes for OT identification: no-OT, weak OT (cyan color), and strong OT (magenta
color). For all of the three cases in total, 452 strong OT and 985 weak OT locations are identified, which
presents a much larger statistical sample than the case shown in Figure13.
The OT probability data obtained from the three additional cases are added to those from the initial
May 5, 2019 case and their corresponding human masks are also combined into one statistical sample for
subsequent optimization of the algorithm's sensitivities. Table1 presents an example of how the correlation
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Figure 13. Human identified mask overlaid on a GOES-16 infrared (IR) brightness temperature (BT) image (left) and
VIS image (right) on May 5, 2019 at 23:00 UTC. The most confident OT locations are shown with magenta (“strong OT”
class) and less confident overshooting cloud tops (OTs) are colored in cyan (“weak OT” class).
Journal of Geophysical Research: Atmospheres
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Figure 15. Two subset images of the human identified mask of OT locations (using the same color scheme as in
Figure13) overlaid on BT image (grayscale) for GOES-16 case on May 18, 2017 at 22:47 UTC (Upper panels). The same
BT images overlaid with the overshooting cloud tops (OT) probability (colored spots) computed using the optimized set
of sensitivities (Lower panels).
Figure 14. GOES-16 0.65μm visible reflectance image on May 18, 2017 22:47 UTC. The two frames in red show the
regions where the human overshooting cloud tops (OT) mask will be zoomed in for closer viewing.
Journal of Geophysical Research: Atmospheres
coefficient, ρ, changes while varying the input sensitivities. To simpli-
fy the presentation, the “Sensitivity to Anvil Area” and “Sensitivity to
Anvil Flatness” are fixed here at 1.00 and 0.95, respectively. The best
correlation ρ of 0.8920 is observed at SensOTtemp=0.65 and SensOT-
prom=0.80. These values are then used as the initial guess values for
the iterative minimization, which finally yields ρ of 0.8941 with Sen-
sOTtemp=0.6252, SensOTprom=0.8052, SensAnvilArea=1.0284, and
SensAnvilFlatness=0.9676. The following mean and standard deviation
values of OT probability have been achieved: 8.97 ± 10.04 for no-OT
class, 38.93± 14.81 for weak OT class, and 77.90± 10.04 for strong OT
class. The obtained sensitivities are similar to those derived for the May
5, 2019 case alone, except with slightly higher SensAnvilArea and Sen-
sAnvilFlatness. This can be explained by a higher variability in sizes and
homogeneity of anvil clouds in the three additional cases due to a much
larger sample, which causes the optimization to adjust to the higher sen-
sitivities SensAnvilArea and SensAnvilFlatness. The corresponding OT probability computed by using the
optimized set of sensitivities is shown in the bottom panels of Figure15.
Sensitivity curves associated with these parameters are shown in Figure11 (orange lines). They align very
well with the distribution for echo tops above the height 2km beneath the tropopause. As echo tops in-
crease in height, GOES tropopause-relative BT and to a lesser extent, prominence, indicate a more intense
storm. Severe storms, especially those that produce tornadoes and 2+ inch (5+ cm) diameter hail, are colder
and have greater prominence compared with non-severe storms that dominate the NEXRAD OT database.
The sensitivity curves would allow most severe storms to be detected, except ∼5%–10% of the severe storm
population where BTTD>10K.
5. Impact of Image Resolution on OT Detection
For effective climate analyses, detection algorithms must be able to operate consistently across transitions
in satellites, such as from the GOES-8 to −15 era to GOES-16/17, where imager spatial sampling, image
navigation, and sensor noise characteristics improve throughout this 25+ year data record. Higher res-
olution, better-quality imagery causes OTs to appear more prominently, which would bias a time series
if such image improvements are not accounted for in detection algorithm formulation. Figure16 shows
an example of how the appearance of cloud tops differs between imagery from different satellite sensors.
The tropopause height, derived from MERRA-2 where convection is present, ranges from 12–13km. Thus,
reflectivity exceeding 20 dBZ derived from the NEXRAD GridRad data set at an altitude of 12km provides
a good proxy for OTs (Figure16a). The Suomi-NPP Visible Infrared Imaging Radiometer Suite (VIIRS)
collected 11.45μm channel IR BT imagery of these OT-producing storms with 375m pixel spacing at nadir
(Figure16b). This imagery depicts a very complex BT pattern throughout the anvil cloud regions. NEX-
RAD OT regions overlaid upon the VIIRS image (cyan contours) are usually co-located with distinct IR
BT minima, but the coldest BTs associated with the OTs vary considerably and many cold areas (magenta)
occur outside the NEXRAD OTs. GOES-16 ABI viewed these storms within 1min of the VIIRS image at a
resolution of ∼2.5–3km/pixel and shows much warmer cloud tops in the 10.3μm data (Figure16c). Differ-
ences in OT region BTs exceed 10K in nearly all instances which is mostly attributed to a factor of seven or
greater difference in pixel size. The GOES-13 Imager viewed these storms ∼3min after the ABI and VIIRS
with 5–6km pixel size (Figure16d). Though this image looks quite similar to the ABI image, close inspec-
tion of OT regions reveals BT differences exceeding 2K for nearly all OTs. This example is consistent with
differences across a large OT database described in this paper and further reinforces that no single IR BT
threshold will provide consistent OT detection accuracy, even across a relatively small region, thus detection
algorithms should be flexible to account for variations in image detail and quality.
Assuming the derived sensitivities are the optimal parameters for reliable OT detection, it is important to
verify the algorithm's performance when applied to IR BT observed by older satellites, such as GOES-13
with a coarser pixel resolution of 4km/pixel at nadir. The three additional GOES-16 scenes listed above
were observed very close in time by GOES-13 (time difference ∼2min). Thus, the spatial mismatch between
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Sens. anvil area=1.00 Sensitivity to peak prominence
Sens. anvil flatness=0.95 0.70 0.75 0.80 0.85 0.90
Sensitivity to OT
Temperature
0.55 0.7812 0.8342 0.8693 0.8824 0.8728
0.60 0.8301 0.8720 0.8912 0.8876 0.8627
0.65 0.8581 0.8874 0.8920 0.8749 0.8385
0.70 0.8702 0.8873 0.8803 0.8527 0.8079
0.75 0.8727 0.8785 0.8617 0.8257 0.7756
Table 1
Dependence of the Correlation Coefficient ρ on a Range of “Sensitivity to
OT Temperature” and “Sensitivity to Peak Prominence” for a Combined
Statistical Sample From GOES-16 Cases
Journal of Geophysical Research: Atmospheres
the cloud features is minimal in this case, which allows us to focus on the
influence of the imager's spatial resolution on the derived OT probability.
Figure17 provides a zoomed view of IR BT images recorded by the two
different imagers for one of the three scenes used to validate both GOES-
13 and -16. The image from GOES-13 is naturally less sharp and does not
resolve many of the compact convective cells (indicated by white arrows
in the Figure), which are more evident in the GOES-16 ABI data. This not
only reduces the OT prominence relative to anvil, but also causes some
local BT minima (used as initial OT candidates) to disappear complete-
ly. As a result, the OT probability product from GOES-13 can be biased
lower, and this needs to be compensated by adjusting the algorithm's pa-
rameters in order to arrive at another set of sensitivities optimized for a
coarser resolution input.
To ensure as equivalent as possible operation with GOES-13 imagery, it
is important to use a human identified OT mask from the same scene (as
shown in Figure14) with the same number of weak OT and strong OT
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Figure 16. (a) NEXRAD GridRad reflectivity exceeding 20 dBZ at 12km altitude, compiled using data collected from
19:50-19:55 UTC on 18 May 2017 over western Oklahoma and northern Texas. (b) Suomi-NPP VIIRS 11.45μm infrared
(IR) brightness temperature (BT) at 19:52 UTC. The image was shifted to account for parallax and align with the GOES-
16 and GOES-13 data. (c) Parallax-corrected GOES-16 10.3μm IR BT at 19:52 UTC. (d) Parallax-corrected GOES-13
10.7μm IR BT at ∼19:56 UTC. Cyan contours on the VIIRS, GOES-16, and GOES-13 images correspond to the radar
echoes in the upper-left panel.
Figure 17. Comparison of BT images from GOES-16 on May 18, 2017
at 22:47 UTC at 2km/pixel (left panel) and GOES-13 on May 18, 2017 at
22:45 UTC at 4km/pixel (right panel) over the same area in Oklahoma
corresponding to the middle of the left frame of Figure14.
Journal of Geophysical Research: Atmospheres
locations. To achieve that, the OT locations in the GOES-16 human OT mask are first displaced according
to motion vectors computed from correlation matching between IR images from GOES-16 and GOES-13,
and then bound to the nearest local minima in GOES-13 BT. As a result of this process, 86 locations hap-
pened to have no matching local minimum due to the lower sharpness of the GOES-13 image. Among
other locations, 36 are found to have zero OT probability, which can be corrected by increasing the sensitiv-
ities, and so the human mask was assigned to the weak OT class at such locations. This refined mask was
finally used in the iterative minimization, which resulted in the correlation ρ of 0.7518 with the following
optimal sensitivities: SensOTtemp=0.7135, SensOTprom=0.8881, SensAnvilArea=1.1558, and SensAn-
vilFlatness=0.8829. Sensitivity curves from these parameters are depicted by the red dashed curves in
Figure10. The following mean and standard deviation values of OT probability have been achieved in this
case: 11.83±13.79 for no-OT class, 39.66±20.05 for weak OT class, and 68.70±23.83 for strong OT class.
As expected, all of these GOES-13 sensitivities are higher than those derived for GOES-16, except for the
lower SensAnvilFlatness. This is because the effect of the anvil rating controlled by SensAnvilFlatness is
quite stable and uniform across most anvils (see the uniform field in Figure5 right panel), and thus vari-
ation of SensAnvilFlatness merely scales up or down the overall OT probability. Therefore, the increase in
the first three sensitivities (caused by the reduced sharpness of GOES-13 imagery) is automatically com-
pensated by the optimization routine with the lower level of SensAnvilFlatness. These adjusted sensitivities
should help to offset resolution-induced bias, but some weak OTs will still be difficult to detect with coarser
imagery like that from GOES-13. Cooney etal.(2021) quantifies the accuracy and consistency of OT detec-
tions relative to NEXRAD GridRad, but an initial estimate of accuracy can also be gained from analysis of
human-identified OTs.
6. Statistical Analysis
The OT probability product provides a flexible rating that estimates the confidence in a detection from 0 to
100. This flexibility, however, does not answer what threshold best separates positive detections from nega-
tive. For the purpose of a dichotomous (yes/no) forecasting, the OT probability has to be converted to either
positive (OT is detected) or negative (no detection) events using a certain probability threshold (PT). On the
other side, the human OT mask can also be reduced to a two-class variable by one of two ways, by treating
only the strong OT class as true OTs and the rest as no OTs (conservative mask) or using both weak OT and
strong OT classes (liberal mask). Thus, there are four possible combinations of forecasts (OT detection) and
observations (the human mask): True positive (TP), false positive (FP), true negative (TN), and false nega-
tive (FN). Probability of detection (POD), defined as POD=TP/(TP+FN), and the false alarm ratio (FAR),
defined as FAR =FP/(TP+FP), are the well-known statistical metrics used to assess the quality of a forecast
product. Their main advantage is that they are not based on the TN events, which have no practical use with
OT detection given that the vast majority of the imagery has clear sky or low cloud, which is always correctly
identified as TN by our algorithm.
Dependence of POD on FAR is analyzed in the form of receiver operating characteristic (ROC) curves
shown in Figure18, where the red curves use the conservative OT masks and the blue curves use the liberal
masks. The numerical labels next to the data points show the probability threshold (PT) associated with a
given POD and FAR. For GOES-16 (left panel) and a PT of 50%, 95% of the strong OTs were detected, but
24% of the GOES detections were not co-located with a strong OT. Using the liberal mask, 51% of OTs were
detected for PT of 50. The reduction is caused by the fact that subtle textured areas in the anvil may have
very minimal prominence in IR imagery and are harder to detect. But the false detection rate decreases to
4% when weak OTs are included because a substantial fraction of the GOES detections happen to be co-lo-
cated with weak OTs. Area under the ROC curve (AUC) are both near 0.94. The greatest POD minus FAR
difference for conservative (liberal) is from a PT of 61 (23) with POD of 0.9067 (0.9504) and FAR of 0.0933
(0.1716).
For GOES-13 and a PT of 50, the POD (0.80) is lower than for GOES-16 (0.95) with the conservative mask
because OTs especially evident in visible imagery are not always especially cold or prominent in coarser
resolution GOES-13 data. The 15% reduction in detection rate is consistent with the GOES-16 versus -13
results from Cooney etal. (2021) based on NEXRAD OT regions. For the liberal mask, GOES-13 POD is
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Journal of Geophysical Research: Atmospheres
nearly equal to GOES-16, but false alarm rate increased by 10%. This is likely caused by the fact that higher
sensitivities required for optimal detection (Figure10) allow warmer and less prominent cold spots to be
detected. Our experience indicates that anvils routinely have random spatial temperature variations of 3K
or more, so trying to detect weak OT feature that too has a 3K prominence increases likelihood of false de-
tection. AUC is 0.765 (0.803) for the liberal (conservative) mask. The greatest difference in POD minus FAR
for conservative (liberal) is from a PT of 68 (32), very similar to GOES-16, with POD of 0.6267 (0.7686) and
FAR of 0.2101 (0.2791). Despite differences in POD and FAR between the two satellites, Cooney etal.(2021)
shows that the GridRad echo top distribution is nearly the same between GOES-13 and GOES-16 for the
same PT, which gives us confidence that the optimal sensitivity values found in this paper provide as con-
sistent as possible detection capability between the two satellites.
ROC curves for the Bedka and Khlopenkov(2016) method are also shown in Figure18 (magenta and cyan).
It is clear that detection performance is significantly poorer than the method described in this paper, and
relative to the results derived from MODIS cases shown in Bedka and Khlopenkov(2016). We attribute
a reduced POD to how OT candidates were filtered in the previous method, where metrics of anvil area,
spatial uniformity, and OT shape were previously used to include/exclude an OT candidate from further
processing, which prohibited detection of some human-identified OTs here. We attribute increased FAR,
which most often occurred in random temperature variations in cold non-OT anvil cloud, to less precise
derivation of anvil cloud properties. Overall performance is worse for these cases than the MODIS-based
results because of (a) reduced GOES spatial resolution and OTs being less prominent and (b) differences in
validation criteria where MODIS detections were formerly considered a hit if they were up to 10km away
from a human-identified OT which was reduced to 5km for this study. In addition, continued experience
working with NWP and reanalysis-derived convective equilibrium level temperature, used in the Bedka and
Khlopenkov method, has indicated that this field, even after spatial smoothing, can be quite noisy and in
disagreement with IR BT observations, especially over relatively data poor regions where deep convection
is frequent such as Africa, South America, South Asia, and ocean in general. The approach described in this
paper relies on only tropopause temperature, which is much more spatially coherent than equilibrium level,
after some smoothing is applied.
One might assume that OT detection performance metrics for GOES-13 would be the same as those from
GOES-8 to −12 imager, considering that the pixel sizes and imager optics for these satellites are essential-
ly identical. Figure19 shows that GOES-12 imagery of Tropical Storm Alberto in June 2006 suffers from
increased intra-scanline noise and “striping” compared with GOES-13 imagery of Hurricane Matthew in
2016. During the GOES-13 Science Test in 2006, Hillger and Schmit(2007) found that “the GOES-13 Imager
striping is less than that on GOES-12, possibly due to the longer black-body look.” A longer black-body look
would improve imager calibration and reduce striping. Some evidence of striping can be seen in GOES-13
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Figure 18. Receiver operating characteristic (ROC) curves showing probability of detection (POD) versus false alarm ratio (FAR) low FAR accumulated using
data from four GOES-16 images (left) and three GOES-13 images (right) for the current detection method (red and blue lines, see legend) and the Bedka and
Khlopenkov(2016) method (magenta and cyan lines). GOES-13 images were collected within two minutes of the corresponding GOES-16 images.
Journal of Geophysical Research: Atmospheres
data as well, but the intra-line BT variations were only 0.5–1.0K, compared with 1.0–3.0K from GOES-12.
GOES-12 striping is substantial enough to trigger OT candidate detection, and the 1–3K magnitude is an
appreciable fraction of the dynamic range of the GOES-13 anvil prominence that ranges from about −1 to
−14K (Figure11). Therefore, it is critical to remove these stripes before generation of GOES climate data
records of OT detections. Methods for de-striping have been developed at NASA LaRC and will be described
in a future paper.
In general, a satellite imager can be affected by sensor thermal noise, spectral band crosstalk, inaccurate
black body measurements, and other factors. For the IRW band of the Advanced Himawari Imager (AHI)
instrument, sensor noise is reported to be about 0.45K for a 200K target (Ai etal.,2017). This estimation
of the brightness temperature bias can be used to analyze our algorithm's uncertainty as a function of the
input BT error. We selected three OT probability ranges, 25, 50, and 75, and used a simulated convection
region, similar to the one shown in Figure4, to estimate a variation in the OT probability, as calculated by
Equation6, in response to an artificial increase in the input BT by 0.5K. As a result of this simulation, OT
probability is decreased from 25.0 to 22.3, from 50.0 to 47.1, and from 75.0 to 73.0, respectively, which is
considered to be relatively negligible.
7. Summary
This paper provides extensive theoretical background of an updated method for automated detection of
overshooting cloud tops using a combination of spatial IR BT patterns that have been quantified in a variety
of ways and NWP tropopause temperature. IR temperatures are converted to a tropopause-relative temper-
ature, which serves as a stable reference that modulates how cold a convective cloud should become within
a given region. Anvil clouds are identified using histogram analysis to generate an anvil rating that is used
in subsequent phases of processing. Cold spots embedded within anvils serve as OT candidate regions. OT
candidates are then assigned an OT probability and the spatial extent of OT cores is found.
The OT probability can be interpreted as a metric of storm intensity and an estimate of confidence in a
detection for a particular pixel. It is produced using an original mathematical composition of four fac-
tors: Tropopause-normalized temperature, prominence relative to the surrounding anvil, surrounding anvil
area, and spatial uniformity of anvil temperature, which are calculated from empirically derived sensitivity
curves. Such a design that aggregates the four factors together, coupled with analysis of surrounding anvil
properties, provides for a higher reliability and accuracy of the OT probability product, and also helps its
temporal stability when dealing with 30-s to 1-min Mesoscale Domain Sector observations from the GOES-
16/17 imager or other high-temporal resolution GEO imagers. The shape of the sensitivity curves is support-
ed by independent analysis of a large sample of matched IR and NEXRAD-observed OT regions. An optimal
sensitivity for each factor was determined by maximizing correlation between the OT probability and a set
of human-identified OT regions. Coarser spatial resolution of GOES-13 data cause OTs to be less prominent
compared to GOES-16, necessitating different sensitivities for each satellite. The statistical accuracy of OT
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Figure 19. (a) GOES-12 10.7μm IR brightness temperature image of Tropical Storm Alberto on June 12, 2006 at 11:02
UTC. (b) GOES-13 10.7μm IR brightness temperature image of Hurricane Matthew on October 1, 2016 at 04:45 UTC.
Journal of Geophysical Research: Atmospheres
detection was also assessed by analyzing the probability of detection (POD) and false alarm ratio (FAR),
which revealed notable improvements over the Bedka and Khlopenkov(2016) method.
Though deep learning pattern recognition methods have shown promise for OT detection (e.g., Cintineo
etal.,2020; Kim etal.,2017), the approach described here, developed through years of experience and
empirical testing, identifies and quantifies OT features at the individual satellite pixel scale similar to how
a human analyst would perform such identification. Cintineo etal.(2020) seeks to identify the “probability
of intense convection” within a 64× 64km region using a combination of GOES-R series visible (when
available), IR, and geostationary lightning mapping imagery. While their method can perform quite well,
their detections encompass a spatial scale larger than typical OT regions and their scheme requires at least
two of the imagery inputs above and cannot yet operate on IR imagery alone. Bedka and Khlopenkov(2016)
demonstrated that filtering of IR-based detections using visible wavelength texture detection can further
improve accuracy. Nevertheless, well-performing techniques based on IR imagery alone like the one de-
scribed in this paper are extremely valuable for defining the climatology of intense convection at high tem-
poral frequency throughout the diurnal cycle and studying their climate impacts.
Though our method seeks to identify features evident to a human in the imagery, there is no guarantee that
precipitation echo tops that reach altitudes near to the tropopause will generate detectable BT perturba-
tions. Cooney etal.(2021) quantifies the detectability of echo tops near to and above the tropopause, based
on NEXRAD processing methods described in Cooney etal.(2018). In addition, consistency in detections
between the GOES-13 Imager and GOES-16 ABI data is also quantified. Such consistency is critical to estab-
lish when one seeks to develop climate data records from the modern-era, 25+ year duration GOES satellite
data record beginning with GOES-8 and continuing to the present with GOES-16 and -17, assuming sensor
noise and calibration described above can be sufficiently addressed.
Appendix A1: Image Reprojection and Boundary Data Processing
Each of the input images is remapped to the output projection by means of a so-called inverse mapping.
First, the valid data boundary in the input image (satellite perspective) is constructed as a polygon defined
by a set of vertices (typically 500), which are then remapped to the output projection. Then for each output
location within the remapped boundary, its latitude and longitude are sought in the input latitude/longi-
tude images. This is implemented by means of the concurrent gradient search (Khlopenkov & Trishchen-
ko, 2008). This search yields a fractional position in terms of the input image coordinates, which is then
used to interpolate the adjacent input values by means of a 6 × 6 pixel resampling function. At the image
boundaries, the missing contents of the 6 × 6 pixel window is padded by replicating the edge pixel values.
Here and further in these algorithms, image resampling operations are implemented as Lanczos filtering
(Duchon1979) extended to the 2D case with the parameter a= 3. This interpolation method is based on
the sinc filter, which is known to be an optimal reconstruction filter for band-limited signals, e.g., digital
imagery. The interpolated value is finally stored at the current location in the output image. This inverse
mapping process has two main advantages: (a) it ensures that all output pixels are filled with valid data, and
(b) the interpolation is performed in the input pixel/line space where samples are aligned in a regular grid,
which allows for straightforward resampling even with higher order polynomials. Similar to the described
reprojection from the satellite perspective to a geographic map, the algorithm also provides the capability
to remap storm detection and characterization products back to the original satellite perspective, which can
be useful for some applications.
As the algorithms below use various window-based filters, it is important to ensure that those operate cor-
rectly on pixels close to the boundary of valid data that may not necessarily be rectangular. This is achieved
by first creating a per-pixel mask of valid data in the reprojected image. Then the valid data are extrapolat-
ed spatially by about 36km beyond the boundary, which is implemented by replacing the out-of-boundary
fill values with a window mean calculated from the nearby valid pixels. The window mean is obtained
as a weighted average with the weights defined by a radial basis Gaussian function having σ= 3.2km.
The fraction of valid pixels within the averaging window can be adjusted from 10% to 50%. Using a larger
fraction results in higher output quality but requires more processing passes before the requested length
of extrapolation is achieved. Smaller fractions allow for fewer passes but may result in noticeable striping
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in the extrapolated areas. Once the spatial extents of the valid input data are expanded, all the subsequent
processing is carried out using fixed-size spatial filters as if the image contained no fill values. This may
produce false detections and other artifacts near the new (expanded) edges of the valid data, but those
would occur in the extrapolated areas only and do not impact the valid pixels. At the end of processing, all
the output images are screened out by the valid pixel mask obtained above (before the extrapolation) and
so any near-boundary artifacts are replaced by fill values.
Appendix A2: Spatial Expansion of the Anvil Mask
The anvil mask obtained from Equation4 has to be expanded in order to ensure that it includes all pixels
inside the circular window that have a high enough BT-score. First, a minimum threshold MinAnvilScore
is introduced as:
8500 512 0.5 32
peak anvil
MinAnvilScore X r
(A1)
where Xpeak is the effective horizontal coordinate of the peak in the histogram:
peak
i
i
i
i
iH
XH
(A2)
Here, the index i again denotes the summation over the three highest histogram bins. The 32 ranvil term
subtracted in EquationA2 makes the MinAnvilScore somewhat smaller than the peak-equivalent BT-score
in order to include pixels with BT-score lower than the effective peak's position. This allowance is made
proportional to the anvil rating, which helps to include the anvil boundary pixels adjacent to very cold OT
cores when the peak may be shifted to higher bins.
Once the MinAnvilScore is calculated, the anvil rating mask can be expanded by raising the anvil rating for
pixels inside the circular window. Specifically, for pixels with BT-score higher than MinAnvilScore their
anvil rating is increased to reach that of the current pixel. This effectively fills out all lower rated pixels
around the current one. In addition, the anvil mask has to be refined in order to absorb some pixels (such
as inside curved cloud edges) surrounded by many neighbors with high anvil rating. To achieve this, for any
pixel inside the circular window having BT-score of at least 2/3 of the MinAnvilScore threshold, a dedicated
counter associated with that pixel is incremented to indicate a high rating neighbor nearby. The amount
of the increment equals the spatial resolution (km/pixel) squared, which corrects for lower pixel count at
coarser resolution. In this way, the neighbor counters are incremented while the whole image undergoes
the anvil mask expansion. On the second pass, if a pixel's ranvil is still under 115 but that pixel's neighbor
counter exceeds 130 (or 80 but its BTscore is over 11,000) then a sum of anvil ratings SAR is calculated over
pixels having BTscore>10,000 within a circle of 14km diameter around the current pixel. The current pix-
el's anvil rating is then set to SAR/(N+1) where N is the number of pixels in the sum, which helps to slightly
reduce the calculated average when N is low. The obtained image of the anvil rating is finally filtered by a
Gaussian blur with σ=2 pixels in order to smooth out minor pixel-size artifacts caused by integer counting,
resulting in the final anvil mask.
Appendix A3: Spatial Expansion of OT Cores
To derive the spatial extent of OT cores, a temperature threshold BTmax is introduced that defines the highest
level of BT for a nearby pixel to be included into the OT:
max p p 0.1BT BT Z WinAvgBT BT SensOTsize TropopauseF
(A3)
Here, SensOTsize is a configurable parameter controlling the sensitivity of OT size expansion with the typ-
ical range of 0.7–1.0. This sensitivity is additionally factored by the λ function, which reduces the OT ex-
pansion for candidates with weak prominence or those located inside uneven anvil areas. Without this
correction, the OT may expand to an unreasonably wide region in a very cold cloud (high TropopauseF)
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but weak spatial gradient (low ProminenceF). On the other hand, uneven areas are also often encountered
within large clusters of very cold OTs, and then the second correction using the tropopause factor is added
to help to capture smaller but still cold OTs when a more significant OT is located nearby.
With the BTmax threshold defined, the pixels surrounding the initial OT candidate are tested to have the BT
below that threshold. Pixels that pass the test are added to the OT extents by flagging them with the same OT
identification number, which is unique for each OT in each scene. This test is carried out along 16 rays cast
off from the OT candidate pixels similarly to the process shown in Figure8 but within an 8km radius from
the center. As a result, this routine ensures that the included pixels form a contiguous OT shape.
Data Availability Statement
The IR OT detection data and locations of the human-identified OT signatures are available through NASA
Langley Research Center at https://science-data.larc.nasa.gov/LaRC-SD-Publications/2021-04-26-001-
KMB/. NEXRAD GridRad data for data analyzed to create Figure11 are available at: https://science-data.
larc.nasa.gov/LaRC-SD-Publications/2021-04-29-001-KMB/. Level 1b radiances from NOAA's GOES-R se-
ries satellite used in this study are available through cloud infrastructures such as Amazon Web Service:
https://registry.opendata.aws/noaa-goes/ or Google Cloud Platform: https://console.cloud.google.com/
launcher/details/noaa-public/goes-16 and https://console.cloud.google.com/launcher/details/noaa-pub-
lic/goes-17 or through NOAA's online subsetter: https://www.ncei.noaa.gov/access/search/data-search/
goesr-abi-level-1b-radiances. Level 1b radiances from NOAA's GOES-M and GOES-N series satellites are
available through: https://www.avl.class.noaa.gov/saa/products/search?sub_id=0&datatype_family=G-
VAR_IMG. Level 1b radiances from NASA's Suomi NPP VIIRS satellite are available through: https://lad-
sweb.modaps.eosdis.nasa.gov/search/order/1/VNP02IMG--5110. Tropopause data are available through
NASA GMAO: https://doi.org/10.5067/3Z173KIE2TPD. Severe storm reports are available through NOAA's
Storm Prediction Center: https://www.spc.noaa.gov/climo/reports/. See also data references below: Bow-
man and Homeyer, (2017), Global Modeling and Assimilation Office GMAO (2015), GOES-R (2017),
NOAA(1994), VIIRS(2016).
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Acknowledgments
This work was supported by the NASA
Applied Sciences Disasters program
project award 18-DISASTER18-0008
and work within the NASA Earth
Venture Suborbital DCOTSS mission.
The authors thank Benjamin Scarino
and Douglas Spangenberg for their
valuable feedback and numerous
contributions to this algorithm devel-
opment effort. The authors also thank
the Data Center within the University
of Wisconsin-Madison Space Science
and Engineering Center for providing
the GOES data used in this study and
for continued development of the
McIDAS-X software package.
Journal of Geophysical Research: Atmospheres
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