1. Introduction
Despite recent advancements in the real-time detection of high ice water content (HIWC, defined herein as IWC ≥ 1.0 g m−3) conditions in convective anvil clouds, the overall frequency of this aviation hazard remains unquantified (Haggerty et al. 2019a). Under HIWC conditions, high concentrations of small ice crystals are ingested into jet engines and accrete onto heated parts until large chunks of ice are shed, damaging and/or stalling the engine in so-called engine events (Lawson et al. 1998; Mason et al. 2006; Bravin and Strapp 2019). Although the engine ice accretion process has been reproduced in wind tunnels, the absence of data on the engine performance in HIWC has hindered HIWC research (Haggerty et al. 2019a). Recent HIWC field campaigns have facilitated the development of real-time HIWC diagnostic systems, but no climatology of HIWC conditions currently exists. Such a climatology would be advantageous for strategic planning and hazard mitigation by identifying regions where flights are most likely to encounter HIWC. To fill this niche, we develop a global analysis of HIWC frequency and a regional analysis of HIWC conditions over the contiguous United States (CONUS).
Details on the precise meteorological conditions required for HIWC engine icing are lacking, although common observations from engine events include low reflectivity (almost always < 30 dBZ, and often < 20 dBZ) on the pilots’ X-band radars, moderate to heavy surface precipitation, and light to moderate turbulence (Grzych and Mason 2010). A flight campaign out of Darwin, Australia, in 2014 provided particle size distributions (PSDs) in HIWC conditions with similarly low X-band radar reflectivity (Dezitter et al. 2013). The PSDs derived from various cloud imaging probes in conditions with IWC of at least 1.5 g m−3 typically had median mass diameters (MMDs) of 250–500 μm, although MMDs up to 2 mm were observed in one tropical storm (Leroy et al. 2017). Images of the ice particles, which were largely columns and capped columns, suggested growth by vapor deposition. It is well established that large quantities of these vapor-grown ice crystals can cause engine events, but it is unclear whether HIWC in the form of hail, graupel, or snow aggregates also poses a threat.
In addition to its relationship with hail, the relationship between lightning and HIWC is uncertain, despite HIWC typically being considered a convective phenomenon. Eyewitness reports from engine events often include heavy rain below the aircraft, but rarely hail or lightning (Grzych and Mason 2010). HIWC has been observed in the vicinity of hail and lightning during research flights targeting deep convection, however (Ratvasky et al. 2019). By comparing patterns in HIWC occurrence to those of hail, lightning, and precipitation, we can further explore these relationships while providing guidance to the aviation community on the unique threat posed by HIWC.
To provide global statistics on the occurrence of HIWC, we use IWC retrievals from the Cloud Profile Radar (CPR) and the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) on the CloudSat and Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellites, respectively, from 2007 to 2017. While CloudSat and CALIPSO (CC) IWC retrievals provide global sampling, the satellites are nadir pointing and polar orbiting, so they do not sample a large area at once and only resample the same location every 16 days. As a result, CC data alone cannot be used to derive statistics on HIWC storm areal extent, development, duration, or motion.
To provide convective storm-scale statistics over the CONUS, we turn to an HIWC diagnostic tool called the Algorithm for Prediction of HIWC Areas (ALPHA). ALPHA uses data from geostationary satellites to provide output every 30 min on a 4.5 km grid over the CONUS (Haggerty et al. 2020). The CONUS analysis presented uses ALPHA output during 8 summers (May–August from 2012 to 2019) to produce statistics on the frequency, size, duration, motion, and timing of HIWC. The summer months are isolated for the CONUS analysis because the global CC analysis in section 3a suggests the CONUS experiences the most HIWC during this time. ALPHA was validated against in situ IWC measurements from an isokinetic probe during four HIWC-focused field campaigns (Davison et al. 2010, 2016; Strapp et al. 2016). These field campaigns consist of two international campaigns in Darwin, Australia (2014), and Cayenne, French Guiana (2015), and two domestic field campaigns based out of Fort Lauderdale, Florida, in 2015 and 2018 (Dezitter et al. 2013; Harrah et al. 2016; Ratvasky et al. 2019). These field campaigns have provided the first research-quality database documenting HIWC conditions in convective clouds, but the subsequent validation of ALPHA has several caveats (Haggerty et al. 2020).
Most of the observational data used in ALPHA validation were collected in tropical and subtropical oceanic convection, so ALPHA’s ability to detect HIWC in extratropical and continental convection is uncertain (Haggerty et al. 2020; Dezitter et al. 2013; Harrah et al. 2016; Ratvasky et al. 2019). It is also difficult to gauge ALPHA’s performance from field campaign data because the in situ data from the HIWC campaigns contain a higher proportion of HIWC conditions than naturally occurs in the atmosphere as a whole. As a result, probability of detection statistics derived from the field campaign data are biased due to the conditional sampling of the atmosphere. To better quantify ALPHA’s performance and provide consistency between our global and CONUS analyses, we validate ALPHA using CC IWC retrievals over the CONUS during May–August from 2012 to 2017.
We describe data and methods in section 2, including the validation of ALPHA using CC IWC retrievals. Section 3 presents global HIWC frequency statistics from 11 years of CC IWC retrievals (2007–17) and a storm-scale analysis over the CONUS using ALPHA for 8 summers (May–August from 2012 to 2019). We discuss the results in section 4, emphasizing the uncertainties associated with the CC analysis and the contrasts between patterns in hail, lightning, and HIWC. We conclude with implications and a summary in section 5.
2. Data and methods
a. CloudSat and CALIPSO IWC retrievals
The Protat et al. (2016) method is used where the lidar is fully attenuated because it was developed and verified specifically for HIWC applications. In areas with 532-nm lidar signals, we use the IWC from the 2C-ICE product because it benefits from both radar reflectivity and lidar backscatter to better constrain IWC. The 2C-ICE IWC estimates are derived by adjusting a priori IWC values from the European Centre for Medium-Range Weather Forecasts (ECMWF) model using radar and lidar signals (Deng et al. 2010, 2015). Lidar signals are sensitive to the second moment of the size distribution, while radar reflectivity is sensitive to the sixth moment. The smaller, more numerous particles in the size distribution therefore influence the lidar signal more than the radar signal. By using both radar and lidar data, the 2C-ICE product can better constrain the size distribution of ice particles and therefore produce a more accurate estimate of IWC than the Protat et al. (2016) relationship. Unfortunately, lidar signals attenuate rapidly below cloud top so most (96.3%) of the HIWC inferred from CC profiles was inferred using the Protat et al. (2016) method.
The Protat method has estimated error and bias of 30% and −20% when compared with in situ IWC for retrieved IWC ≥ 1 g m−3 (Protat et al. 2016). After combining the Protat method with the 2C-ICE product, we discard areas with ECMWF model temperatures above 0°C to reduce errors associated with mixed/liquid phase and because no engine events have been recorded in above-freezing temperatures (Grzych and Mason 2010). Both the CloudSat radar reflectivity used in the Protat method and the 2C-ICE IWC retrievals used are from January 2007 through December 2017 and are publicly available. These data also include the ECMWF model temperature output and flags indicating where the lidar signals are fully attenuated.
CC statistics are shown for the column-maximum IWC and the layer-maximum IWC between flight level 270 (FL270; 27 000 ft or 8.230 km) and FL420 (42 000 ft or 12.801 km). The column maxima exclude the lowest 1500 m above the ground to eliminate potential ground clutter contaminations of the radar signal. For the layer maxima, FL270 and FL420 are used because they encompass the most common cruising altitudes for commercial aircraft and the altitudes of 147 of the 168 (85.1%) Boeing engine events with altitude data (Bravin and Strapp 2019). The layer-maximum results should be considered a lower limit and the column-maximum an upper limit on HIWC frequency. Justification for this interpretation and a discussion of the implications is found in section 4a.
The column- and layer-maximum IWC values (including values of zero IWC) are averaged over 30 km horizontally (27 profiles spaced 1.1 km apart), a length scale based on a 2-min transect time for a commercial jet moving at 250 m s−1. No studies have quantified the exposure time needed for engine events, but 2 min is sufficient to cause similar HIWC icing of air data systems (Haggerty et al. 2019b). In total, 37 015 CC granules, resulting in about 53 million 30-km composites are used for the global HIWC analysis.
For visualization purposes, the 30-km mean IWC retrievals are put onto a 1.5° by 2.0° (latitude by longitude) grid between −84°S and −84°N to produce near-global HIWC frequency statistics. We define HIWC frequency as the percent of 30-km composites (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. The rate is smoothed by computing the mean frequency over 3 by 3 grid boxes to eliminate artifacts (e.g., diagonal stripes) introduced by nonuniform sampling from the CC orbits. When describing the average HIWC frequency over a region, the frequencies from the 1.5° by 2.0° grid are weighted by the area of the grid cell. Computing averages in this manner accounts for the higher density of profiles at high latitudes.
b. ALPHA
CC IWC retrievals provide critical data for our global analysis of HIWC frequency, but they cannot provide statistics on the size, duration, or movement of HIWC conditions. The CC satellites are in a sun-synchronous near-polar orbit, so they cannot continuously observe the same system. The instruments are also nadir pointing (i.e., do not scan across the orbital path), and therefore sample only a narrow 1.4 km swath. In contrast to CC, ALPHA is a regional product but provides gridded and frequent data over the CONUS, southern Canada, northern Mexico, and surrounding oceans.
To provide a higher resolution analysis of HIWC over the CONUS, we ran ALPHA for eight summers (1 May–31 August from 2012 to 2019). The HIWC team at the National Center for Atmospheric Research developed ALPHA using an iterative machine-learning technique and IWC measurements from four field campaigns (Haggerty et al. 2020). ALPHA blends information from geostationary satellites, NWP models, and ground-based radar into a three-dimensional field called HIWC Potential, which ranges from 0 to 1, with higher values indicating a higher likelihood of HIWC conditions (Haggerty et al. 2020).
To save computation time, we isolated the satellite component of ALPHA and produced a simplified, two-dimensional, 1-input version of HIWC Potential. ALPHA already offered a three-dimensional, two-input version with only satellite and NWP because radar data are not globally available. Further omission of the model input has a negligible impact on the results because the model primarily acts to mask areas above cloud and below the 0°C isotherm in the two-input version of ALPHA (Haggerty et al. 2020). The HIWC Potential used in this study is effectively a two-dimensional column-maximum of the full two-input HIWC Potential.
The satellite data used in ALPHA come from the Satellite Cloud and Radiation Property Retrieval System (SatCORPS) operating at NASA Langley (Minnis et al. 2008) utilizing methods described by Trepte et al. (2019) and Minnis et al. (2021) that have been adapted for application to geostationary satellite data. Both the SatCORPS data and HIWC Potential are on a roughly 4.5 km grid with a 30-min temporal cadence. The SatCORPS data are derived from GOES-13, GOES-15, GOES-16, or GOES-17 observations depending on the time and portion of the domain. ALPHA has never been applied to older generations of GOES satellites so the first summer when both GOES-13 and GOES-15 were operational (2012) was chosen as the beginning of the study period. The east and west GOES satellites are blended down the center of the CONUS where the two satellites are equidistant from the surface. This discontinuity produces artifacts in some figures.
To provide storm-scale statistics on HIWC over the CONUS, we have to define storm boundaries. When referring to these boundaries in a single ALPHA output time, we use the term “feature”; “storms” are then series of features tracked through time, as described in a following section. To define features, HIWC Potential is smoothed using the mean of a 5 by 5 pixel moving window. Smoothing in this manner reduces the number of features identified, especially where multiple areas of high HIWC Potential are separated by a few pixels of lower potential. Features are then areas of at least 0.27 smoothed HIWC Potential over a contiguous area of at least 706 km2. The HIWC Potential threshold of 0.27 is based on the probability of detection characteristics of ALPHA in comparison with layer-maximum IWC retrievals from CC (described in the following section). The 706-km2 threshold is based on a 2-min transit time for a circular feature with a diameter of 30 km, the same distance used for CC averaging.
Quantifying the diurnal cycle in HIWC derived from ALPHA requires additional processing to handle satellite terminator effects. ALPHA uses different algorithms during night and satellite terminator hours than during the daytime, which creates artifacts in the diurnal cycle (Haggerty et al. 2020). To eliminate these, output during day and night are used to interpolate values through the terminator hours using cubic splines, and then smoothed.
1) ALPHA validation
To determine the HIWC Potential threshold most consistent with the global CC analysis, the 30-km CC layer-maximum IWC values are matched to the mean HIWC Potential of a 7 by 7-pixel neighborhood (31.5 km by 31.5 km) surrounding the midpoint of the profile’s 30-km footprint. This is done for all six summers when both the ALPHA and CC datasets were available (May–August from 2012 to 2017) and includes 325 823 30-km CC IWC retrievals.
Performance of ALPHA relative to CC is evaluated using a receiver operating characteristic (ROC) curve (Fig. 1). This curve is generated by varying the HIWC Potential threshold used to define an HIWC diagnosis and plotting the resulting probability of detection (POD) against probability of false detection (POFD). POD is the proportion of HIWC CC retrievals that were correctly warned at the given HIWC Potential threshold. The definition of POFD is slightly more complex and follows methods from Haggerty et al. (2020) and Yost et al. (2018). POFD is the number of false positives divided by the number of false positives plus correct negatives. False positives are CC IWC values below 1.0 g m−3 that have an HIWC Potential at or above the threshold of interest and correct negatives are CC IWC values between 0.1 and 1.0 g m−3 where HIWC Potential is below the threshold of interest. The lower threshold of 0.1 g m−3 is used to isolate the skill of the algorithm in distinguishing between moderate IWC (0.1–1.0 g m−3) and HIWC.
ROC curve showing POD vs POFD as the HIWC Potential threshold used to define a positive diagnosis is varied from 0 (top-right corner) to 1 (bottom-left corner). Data are from 2012 to 2017, for May–August, over the CONUS. The area under the curve is 0.70, and the open circle marks the performance of the HIWC feature definition used in this study (HIWC Potential and area thresholds of 0.27 and 706 km2, respectively).
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
ROC curve showing POD vs POFD as the HIWC Potential threshold used to define a positive diagnosis is varied from 0 (top-right corner) to 1 (bottom-left corner). Data are from 2012 to 2017, for May–August, over the CONUS. The area under the curve is 0.70, and the open circle marks the performance of the HIWC feature definition used in this study (HIWC Potential and area thresholds of 0.27 and 706 km2, respectively).
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
ROC curve showing POD vs POFD as the HIWC Potential threshold used to define a positive diagnosis is varied from 0 (top-right corner) to 1 (bottom-left corner). Data are from 2012 to 2017, for May–August, over the CONUS. The area under the curve is 0.70, and the open circle marks the performance of the HIWC feature definition used in this study (HIWC Potential and area thresholds of 0.27 and 706 km2, respectively).
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
On an ROC plot, a perfect algorithm would reach the upper-left corner and have an area under the curve (AUC) of 1.0. The actual ROC curve for ALPHA in comparison with layer-maximum CC IWC retrievals has an AUC of 0.70 and is closest to the upper left at an HIWC Potential threshold of 0.27, so this threshold was used to define HIWC features. The POD and POFD for HIWC features are 62.3% and 31.2%, respectively.
2) TITAN
To track the movement of HIWC storms, we used the Thunderstorm Identification, Tracking, Analysis, and Nowcasting tool (TITAN; Dixon and Weiner 1993). Within TITAN, HIWC features are approximated by an ellipse surrounding the feature’s centroid, which is weighted by HIWC Potential. Features in consecutive 30-min outputs are matched favoring the following: 1) slower storm propagation (a maximum speed of 100 km h−1 is also enforced) and 2) matches that maintain similar size, shape, and HIWC Potential. A cost function combines these assumptions to produce the most probable pairings. We use the term “storm” to refer to the sequence of features matched through time using TITAN. Output from TITAN includes storm area, centroid location, age, remaining duration, and propagation speed and direction based on movement of the storm’s centroid.
Defining storms is important for meteorological analysis, but the aviation community may also be interested in HIWC conditions over a fixed point, such as an airport. To capture these conditions, we define an HIWC “event.” Such an event begins when an HIWC feature is first observed over the point of interest and ends when there is no longer a feature there. The duration of an HIWC event is thus the amount of time a geographic point is continuously under an HIWC feature. Because ALPHA provides output every 30 min, it is possible that multiple HIWC storms pass over a location during a single event (i.e., one moves off but another moves over within the 0.5-h gap between output).
3. Results
a. Spatial and seasonal occurrence of HIWC
Here we examine global HIWC frequency, defined as the proportion of CC column- or layer-maximum IWC retrievals exceeding 1.0 g m−3 from 2007 to 2017. Since all CC observations are from either 0130 or 1330 local time, HIWC frequency is not necessarily representative of diurnally averaged values. The CC IWC retrievals also have a bias of about −20% relative to in situ IWC for retrieved IWC values of at least 1 g m−3 (Protat et al. 2016). Assuming a uniform −20% bias across all geographic regions and altitudes, a retrieved IWC value of 0.8 g m−3 would on average correspond to a true IWC value of 1.0 g m−3. Using a 0.8 g m−3 retrieved IWC threshold increases both column and layer-maximum HIWC frequency by about 50% (not shown). While this 50% increase provides one estimate of the errors associated with the reported CC HIWC frequency, the assumption of uniformity is a poor one. A detailed discussion of the uncertainties and errors in CC HIWC frequency is found in section 4a.
Figure 2 shows the annual HIWC frequency over the globe using column-maximum IWC (top), layer-maximum IWC (middle), and the locations of 174 engine events from the Boeing database (bottom; Bravin and Strapp 2019). The global area-averaged column-maximum HIWC frequency is 1.03%. Of the 174 approximate engine event locations, 147 have column-maximum frequency of at least 1% and 58 have column-maximum frequency of at least 2%. Layer-maximum HIWC frequency is much lower than column-maximum HIWC frequency, with a global mean of 0.21%. Only 13 and 0 events have layer-maximum frequency of at least 1% and 2%, respectively; 132 and 80 events have at least 0.25% and 0.5%, respectively.
(top) Global HIWC frequency from 30-km column-maximum CC IWC retrievals from 2007 through 2017. HIWC frequency is defined as the percent of 30-km column- or layer-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes indicate 11 regions discussed in the text. (middle) As in the top panel, but using layer-maximum CC IWC retrievals. (bottom) Locations of 174 HIWC engine events from the Boeing database (from Bravin and Strapp 2019).
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
(top) Global HIWC frequency from 30-km column-maximum CC IWC retrievals from 2007 through 2017. HIWC frequency is defined as the percent of 30-km column- or layer-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes indicate 11 regions discussed in the text. (middle) As in the top panel, but using layer-maximum CC IWC retrievals. (bottom) Locations of 174 HIWC engine events from the Boeing database (from Bravin and Strapp 2019).
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
(top) Global HIWC frequency from 30-km column-maximum CC IWC retrievals from 2007 through 2017. HIWC frequency is defined as the percent of 30-km column- or layer-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes indicate 11 regions discussed in the text. (middle) As in the top panel, but using layer-maximum CC IWC retrievals. (bottom) Locations of 174 HIWC engine events from the Boeing database (from Bravin and Strapp 2019).
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
HIWC frequency in deserts, polar regions, and the eastern portions of subtropical ocean basins is below 0.5%, but column-maximum values between 3% and 4% and layer maximum values between 1% and 2% are found in many parts of the intertropical convergence zone (ITCZ), South America, and the Maritime Continent (Fig. 2). Column-maximum HIWC frequency is slightly (4%) higher in the tropics (30°S–30°N) than extratropics, but layer-maximum HIWC frequency is over 4 times higher in the tropics than extratropics (Table 1; Fig. 2). Column-maximum HIWC frequency is higher over oceans than land, especially in the extratropics, but layer-maximum HIWC frequency is higher over land (Table 1). The disparities between column- and layer-maximum results are primarily due to the exclusion of low altitudes (below FL270) in the layer maxima, rather than high (above FL420) altitudes (not shown). The maximum frequencies for column- and layer-maximum IWC are 4.41% and 1.88%, respectively, and occur in the eastern Pacific off the coasts of Panama and Colombia (Fig. 2).
HIWC frequency (percent of all 30-km CC IWC retrievals with at least 1.0 g m−3) by latitude and surface type. Tropics are defined as 30°S–30°N. Values outside and inside the parentheses are for column- and layer-maximum IWC values, respectively. Averages are computed from the 1.5° × 2.0° latitude–longitude gridded frequencies, weighted by the area of each grid cell. Computing averages in this manner accounts for the higher density of CC profiles at high latitudes.
To quantify seasonal HIWC frequency, we define 11 regions and compute the mean HIWC frequency for December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON). Seasonal column-maximum and layer-maximum HIWC frequency are shown in Figs. 3 and 4, respectively, with the 11 regions outlined and numbered in black. Region numbers increase west to east and north to south, and the seasonal mean frequencies for each region are listed in Table 2.
Seasonal HIWC frequency from 30-km column-maximum CC IWC retrievals. HIWC frequency is defined as the percent of 30-km column-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes define the 11 regions used to produce the statistics shown in Table 2.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Seasonal HIWC frequency from 30-km column-maximum CC IWC retrievals. HIWC frequency is defined as the percent of 30-km column-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes define the 11 regions used to produce the statistics shown in Table 2.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Seasonal HIWC frequency from 30-km column-maximum CC IWC retrievals. HIWC frequency is defined as the percent of 30-km column-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes define the 11 regions used to produce the statistics shown in Table 2.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Seasonal HIWC frequency from 30-km layer-maximum CC IWC retrievals. HIWC frequency is defined as the percent of 30-km layer-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes define the 11 regions used to produce the statistics shown in Table 2.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Seasonal HIWC frequency from 30-km layer-maximum CC IWC retrievals. HIWC frequency is defined as the percent of 30-km layer-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes define the 11 regions used to produce the statistics shown in Table 2.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Seasonal HIWC frequency from 30-km layer-maximum CC IWC retrievals. HIWC frequency is defined as the percent of 30-km layer-maximum IWC retrievals (including clear-air profiles) that exceed 1.0 g m−3 within a grid box. Black-outlined boxes define the 11 regions used to produce the statistics shown in Table 2.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
HIWC frequency (percent of all 30-km CC IWC retrievals with at least 1.0 g m−3) for various regions (numbered in Figs. 3 and 4) and seasons. Seasonal maxima are indicated in boldface type. Values outside and inside the parentheses are for column and layer maximum IWC values, respectively. Averages are computed from the 1.5° × 2.0° latitude–longitude gridded frequencies, weighted by the area of each grid cell. Computing averages in this manner accounts for the higher density of CC profiles at high latitudes.
The location and seasonality of HIWC in the equatorial eastern Pacific (region 5) and Atlantic and Africa (region 7) is consistent with deep ITCZ convection. Column-maximum HIWC frequencies range from 0.86% in DFJ to 2.41% in JJA for region 5 and from 0.65% to 1.44% for region 7 (Table 2). Layer maximum HIWC frequencies range from 0.26% in DFJ to 0.94% in JJA for region 5 and from 0.26% to 0.62% for region 7 (Table 2). Smaller portions of region 5 have even larger seasonal amplitudes with column-maximum frequencies ranging from below 1% to over 6% and layer maximum frequencies ranging from below 0.5% to over 3%. This is the highest seasonal layer-maximum HIWC frequency found globally, but column-maximum frequency is even higher along the coast of Myanmar.
In a smaller area along the western coast of Myanmar, column-maximum and layer-maximum HIWC frequency reaches 8.39% and 2.55%, respectively, in JJA, coincident with the local monsoon season (Figs. 3 and 4; Roy and Kaur 2000). The encompassing region 4 experiences the highest seasonal amplitude of all regions with column-maximum (layer maximum) frequencies ranging from 0.36% (0.06%) in DJF to 3.09% (1.17%) in JJA—a seasonal amplitude of 2.73% (1.11%). This contrasts with the Maritime Continent (region 9), which borders region 4 to the south. Seasonality in region 9 is low, with amplitudes of 0.29% and 0.10% for column-maximum and layer-maximum frequencies, respectively. Despite having low seasonal amplitude, region 9 has the highest annual HIWC frequency for all regions at 2.45% and 0.88% for column-maximum and layer-maximum retrievals, respectively.
South America (region 6) has the second highest annual HIWC frequency at 1.70% and 0.70% for column-maximum and layer-maximum frequencies, respectively. The region also experiences relatively high seasonal minima in JJA at 1.05% and 0.39% due to high frequencies in northern South America. This northern portion experiences JJA column-maximum (layer maximum) frequencies between 2% and 5% (1% and 2.5%) while most of the continent experiences JJA frequencies below 1% (0.5%). The high JJA frequency in the northern portion of South America is consistent with region 5 to the west, which experiences an annual maximum in JJA.
Seasonality in southern Africa (region 8) and Australia (region 10) is similar to South America, with maxima and minima in DJF and JJA, respectively. Mean DJF column-maximum (layer maximum) frequencies for regions 8 and 10 are 1.93% (0.81%) and 1.73% (0.59%), respectively, but smaller areas of both regions exceed 4% (2%). In JJA, HIWC can be found below FL270, but almost no HIWC occurs between FL270 and FL420: JJA layer-maximum frequencies for regions 8 and 10 are 0.02% and 0.01%, respectively. Farther south, the Southern Ocean (region 11) has virtually no HIWC between FL270 and FL420 in JJA (0.00%).
The high and midlatitude oceanic regions 1 (northern Pacific) and 11 (Southern Ocean) both have negligible HIWC above FL270: layer-maximum frequencies for regions 1 and 11 range from 0.01% to 0.03% and from 0.00% to 0.02%, respectively. This is a stark contrast to column-maximum frequencies that range from 0.99% in JJA to 1.98% in DJF for region 1 and 0.98% in DJF to 1.30% in JJA for region 11. Similar order-of-magnitude differences between column- and layer-maximum results are seen in region 3.
Layer-maximum HIWC frequencies over Europe and Asia (region 3) range from 0.00% in DJF to 0.15% in JJA, though JJA values exceed 1% along the border with region 4 and range from 0.25 to 0.5% in eastern Europe. Column-maximum frequencies are about an order of magnitude higher, with means of 0.37% and 1.22% in DJF and JJA, respectively. Despite similar latitudes, HIWC between FL270 and FL420 is more common over the CONUS than Europe and Asia.
The Midwest of the United States is the only area poleward of 35° latitude where layer-maximum HIWC frequency exceeds 0.5% annually and 1% seasonally. The uniquely high layer-maximum HIWC frequency given the latitude of the central CONUS motivates the summer ALPHA analysis presented in the following section.
b. Characteristics of HIWC over the CONUS
To characterize HIWC over the CONUS we use 1) monthly HIWC activity, 2) the size of HIWC features, 3) the duration of HIWC events, and 4) the direction and speed of storm propagation. HIWC activity is defined as the amount of time (in hours) a location is occupied by an HIWC feature (at least 0.27 HIWC Potential and 706 km2) and is normalized to a 30-day month. To measure feature size, we compute the mean area of all features before transforming that area into an area-equivalent diameter. For HIWC event durations, we consider the 90th percentile instead of the mean of all events. Recall “event” here refers to the time a fixed geographic point is continuously under an HIWC feature. We consider the 90th percentile for event durations because most events are short in duration (less than 2 h, not shown) regardless of geographic location. The 90th percentile of the duration better distinguishes areas capable of producing long-lasting HIWC conditions, even though most events are much shorter. Four major regions, outlined in Fig. 5, are identified by considering the monthly activity, mean size, and 90th percentile of event duration.
Mean HIWC activity over central North America for May–August, based on ALPHA output from 2012 to 2019. Thick black-outlined boxes indicate the four regions examined in the text.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Mean HIWC activity over central North America for May–August, based on ALPHA output from 2012 to 2019. Thick black-outlined boxes indicate the four regions examined in the text.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Mean HIWC activity over central North America for May–August, based on ALPHA output from 2012 to 2019. Thick black-outlined boxes indicate the four regions examined in the text.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Regional characteristics
The western coast of Mexico has low activity (<5 h) in May throughout the region and an average of only 0.6 h. Activity is higher in July and August, with averages of 22 and 24 h, respectively. Portions of western Mexico have over 60 h in July and/or August (Fig. 5). Diurnally, there is a rapid increase in HIWC activity from less than 0.25 h per 30 days at 1000 LST (1700 UTC) to almost 1 h at 1800 LST (0100 UTC; Fig. 6). This means that on average between May and August, a point in this region has an HIWC feature at 1000 LST less than once every four months but has a feature at 1800 LST almost once a month. HIWC events in this region can exceed 4 h, and features have a mean diameter of 175 km (Fig. 7). Storms generally propagate toward the west-northwest at 20–40 km h−1 (Fig. 8, top left).
Diurnal cycle in HIWC activity for each of the four North American regions. Because of artifacts in ALPHA during solar terminator, statistics during night and day are interpolated using cubic splines and smoothed to estimate the 24-h cycle.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Diurnal cycle in HIWC activity for each of the four North American regions. Because of artifacts in ALPHA during solar terminator, statistics during night and day are interpolated using cubic splines and smoothed to estimate the 24-h cycle.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Diurnal cycle in HIWC activity for each of the four North American regions. Because of artifacts in ALPHA during solar terminator, statistics during night and day are interpolated using cubic splines and smoothed to estimate the 24-h cycle.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
(top) Mean area-equivalent diameter and (bottom) the 90th percentile of the duration of HIWC events for all months May–August 2012–19. If there were fewer than 10 total events on record, no duration percentile is plotted, leaving white areas in the Pacific Ocean and along the West Coast. Black-outlined boxes indicate four regions examined in the text.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
(top) Mean area-equivalent diameter and (bottom) the 90th percentile of the duration of HIWC events for all months May–August 2012–19. If there were fewer than 10 total events on record, no duration percentile is plotted, leaving white areas in the Pacific Ocean and along the West Coast. Black-outlined boxes indicate four regions examined in the text.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
(top) Mean area-equivalent diameter and (bottom) the 90th percentile of the duration of HIWC events for all months May–August 2012–19. If there were fewer than 10 total events on record, no duration percentile is plotted, leaving white areas in the Pacific Ocean and along the West Coast. Black-outlined boxes indicate four regions examined in the text.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Radial histograms showing the direction toward which storms propagate in four regions of North America. Radial circles are every 2% up to 18% and represent the percent of total storms in the region.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Radial histograms showing the direction toward which storms propagate in four regions of North America. Radial circles are every 2% up to 18% and represent the percent of total storms in the region.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
Radial histograms showing the direction toward which storms propagate in four regions of North America. Radial circles are every 2% up to 18% and represent the percent of total storms in the region.
Citation: Journal of Applied Meteorology and Climatology 60, 2; 10.1175/JAMC-D-20-0163.1
In the Great Plains, HIWC activity is highest in June with an average of 25 h, though the average in May is nearly as high at 24 h (Fig. 5). Activity in May is highest in the southern portion of the region with a maximum between 40 and 42.5 h in parts of Oklahoma (Fig. 5, top left). In June, the HIWC moves northward and has a maximum between 37.5 and 40 h around the border between Nebraska and Iowa (Fig. 5, top right). Diurnally, HIWC activity peaks between 1.25 and 1.5 h per month around midnight (0600 UTC) and reaches minimum around noon (1800 UTC) with 0.25–0.5 h (Fig. 6). Features are large relative to other areas; the mean diameter for the whole region is 265 km, but portions of Nebraska, Kansas, Oklahoma, Missouri, and Iowa have mean diameters over 400 km (Fig. 7, top). Events can last over 4 h, especially in the southern portion of the region (Fig. 7, bottom). Storms in the Great Plains generally move eastward from the Rocky Mountains into the Midwest at about 50 km h−1 (Fig. 8, top right).
The northern coast of the Gulf of Mexico and western Atlantic are both characterized by moderately low activity in May with an average of 8 h in both regions. Mean activity increases to 16 and 13 h in August for the northern Gulf of Mexico and western Atlantic, respectively. Some areas experience over 20 h in June, July, and/or August, notably the west coast of Florida (Fig. 5). Activity in the western Atlantic peaks between 0400 and 0500 LST (0900 to 1000 UTC) at nearly 0.75 h and reaches a minimum between 1800 and 2000 LST (2300 and 0100 UTC) slightly above 0.25 (Fig. 6). The northern Gulf of Mexico experiences an afternoon maximum slightly above 0.5 h around 1500 LST (2100 UTC) and a minimum of about 0.25 at midnight (0600 UTC; Fig. 6).
Features in the western Atlantic are smaller and events are shorter than in the other regions considered—the mean diameter is 146 km and events rarely exceed 4 h (Fig. 7). Storms in the western Atlantic move toward the east-northeast at about 50 km h−1 (Fig. 8, bottom left). In the northern Gulf of Mexico, features have a mean diameter of 178 km and event duration increases from east to west across the region (Fig. 7). Storms move slowly (<40 km h−1) and in no particular direction (Fig. 8, bottom right).
4. Discussion
a. Sources of uncertainty
There are two fundamental sources of uncertainty in the CC analysis: 1) limitations of the radar and lidar IWC retrievals and 2) uncertainties about which meteorological and microphysical situations cause HIWC engine events. Most (96.3%) CC HIWC is inferred using only radar reflectivity because the lidar signal is quickly attenuated below the cloud top in HIWC-bearing clouds. The −20% bias of these retrievals could cause a 50% increase in HIWC frequency if this bias is uniform throughout the atmosphere. This assumption of uniformity is a poor one, however, because the errors depend on the particle size distribution. Radar reflectivity is proportional to the diameter of particles to the sixth power (assuming Rayleigh scattering), so clouds with large particles have higher reflectivities than clouds with smaller, more numerous particles despite the same IWC. The Protat et al. (2016) method will therefore overestimate the IWC in clouds with large particles such as hail, graupel, and aggregates and underestimate the IWC in clouds with smaller vapor-grown ice crystals. The difference between hydrometeor species is also where uncertain engine sensitivity arises.
Vapor-grown ice crystals can cause engine events, but it is unclear whether larger forms of ice can also (e.g., Lawson et al. 1998; Mason et al. 2006). Larger hydrometeors are more likely to appear on a pilot’s radar and are thus typically avoided by aircraft. The lack of observed engine events in such conditions could be due to pilots simply avoiding such conditions.
Uncertainties in the CC results combine such that the column-maximum and layer-maximum HIWC frequencies are upper and lower bounds on of the true threat of HIWC to engines, respectively. Hail, graupel, and aggregates are typically found at lower altitudes than the vapor-grown crystals known to cause engine events (e.g., Takahashi and Keenan 2004; Ilotoviz and Khain 2016). The column-maximum IWC retrievals are thus more likely to include these hydrometeors that may not pose an actual threat to aircraft engines. Even if these hydrometeors are a threat, they are typically larger than vapor-grown crystals, which could lead to overestimation of IWC despite overall −20% bias of the retrieval method. The smaller vapor-grown particles, which are better isolated by the layer-maximum results, are more likely to cause an underestimation of IWC, especially given the overall −20% bias. The layer-maximum also excludes altitudes where engine events have been documented: 23 (13.7%) and 2 (1.2%) of 168 engine events occurred at altitudes below FL270 and above FL420, respectively. The true frequency of the HIWC threat likely lies between the column-maximum and layer-maximum results.
b. Comparison with engine events
Along with HIWC frequency, air traffic density is an important factor in the locations of HIWC engine events. Unfortunately, the comparison between engine events, air traffic density, and CC HIWC frequency presented herein is highly qualitative since 1) the time periods for each dataset differ, 2) all CC IWC observations are from 0130 and 1330 local time, and 3) the HIWC engine events are reported by Boeing and do not include events on non-Boeing aircraft or the full breadth of engine types.
The Boeing company is based in the United States while their main competitor, Airbus, is based in Europe. Therefore, the distribution of Boeing aircraft across the globe is not proportional to air traffic statistics. According to delivery reports from Boeing and Airbus between 2006 and 2020, 56.8%, 37.0%, 43.7%, 44.5%, and 43.3% of deliveries to the Americas, Europe, Asia and the Pacific, the Middle East, and Africa, respectively, were Boeing aircraft (Boeing 2020; Airbus 2020). These statistics only represent sales and do not account for third party manufacturers but are an estimate of the bias in the engine event locations in Fig. 2 due to the Boeing-only dataset.
Most engine event location have high HIWC frequency and/or air traffic density (Fig. 2). Southern and eastern Asia have numerous engine events; 77 of the 174 approximate event locations fall between 0° and 40°N and 60° and 150°E. The annual column-maximum (layer maximum) HIWC frequency in this box is 1.63% (0.51%), or 158% (243%) of the global average. Air traffic here is also high: of the 13 countries with over 100 million passengers in 2019, 6 are at least partially within the box [International Air Transport Association (IATA) World Air Transport Statistics 2019; https://www.iata.org/WATS/]. The eastern CONUS is also high in engine events, HIWC frequency, and air traffic (Fig. 2). Between 20° and 50°N and 100° and 70°W, there are 26 engine events and a mean column-maximum (layer maximum) HIWC frequency of 1.40% (0.35%), or 136% (167%) of the global average. In 2019, the United States had 796 million air passengers, the most of any country (IATA World Air Transport Statistics 2019; https://www.iata.org/WATS/). South America, defined as region 6 in Figs. 3 and 4, also had 28 engine events, an average column-maximum (layer maximum) HIWC frequency of 1.70% (0.70%), and about 217 million passengers in 2019 (IATA World Air Transport Statistics 2019; https://www.iata.org/WATS/). More events in South America than the eastern CONUS despite lower air traffic could be due to the higher HIWC frequency. Boeing also dominates the market in the Americas, creating a bias for more events compared to other regions with similar air traffic and HIWC frequency.
Europe and Australia have five and eight engine events, respectively, despite HIWC frequencies below the global average. This could be due to high air traffic; six countries in Europe had over 100 million passengers in 2019, and Australia had 97 million. Another eight events lie along transoceanic routes between North America and Europe (two events), South America and Europe (three), and Australia and the Americas (three). There are only five engine events over Africa despite areas of high HIWC frequency (2%–3% in central Africa), likely because of relatively low air traffic.
The aviation community would likely benefit from more quantitative relationships between engine events, HIWC frequency, and air traffic. We are unable to provide more quantitative relationships given the limited data on the time and precise locations of engine events and the need for more detailed air traffic data.
c. Regional storm characteristics over the CONUS
Over the CONUS, HIWC features are largest (over 300 km in diameter) in the Great Plains (Fig. 5). One might expect the northern Gulf of Mexico and western Atlantic regions to have large features since hurricanes produce HIWC, but hurricanes and tropical storms are relatively rare in comparison with smaller diurnal convection (Ratvasky et al. 2019). Peak hurricane season (September) was also not included in our CONUS analysis; we expect HIWC features in the Atlantic and Gulf of Mexico are larger in autumn than summer (Landsea 1993). Tropical storm activity could also explain why more of the northern Atlantic has column-maximum (layer maximum) HIWC frequencies above 0.5% (0.25%) in SON than in JJA (Fig. 3).
In the Great Plains there is a north–south gradient in event duration. North of 41°N, the 90th percentile of events ranges from 3.5 to 4.5 h, but in the south, they reach up to 5 h. This is likely due to slower storms; storms north of 41°N move at mean (median) speed of 38.8 km h−1 (38.5 km h−1) but south of 41°N they move at 34.3 km h−1 (33.1 km h−1, not shown) according to TITAN. This difference in means is statistically significant (P < 0.001) and could explain the difference in event durations since slower storms spend more time over a fixed point.
d. Mechanisms of HIWC formation
HIWC was observed in the vicinity of hail and lightning during HIWC field campaigns, but most pilots have reported no hail or lightning during postevent interviews (Ratvasky et al. 2019; Grzych and Mason 2010). This discrepancy may be explained by the fact that the field campaigns intentionally sampled areas near convective cores, while most pilots will avoid hail, lightning, and convective cores using the pilot radar, instead traversing anvils where only HIWC is found. It may also be possible that HIWC exists in convection too weak for hail and lightning, and that HIWC even exists in nonconvective clouds. Patterns in layer-maximum HIWC frequency are consistent with HIWC as a convective phenomenon. HIWC that only exists below FL270 may be the result of shallow convection capped by low midlatitude and/or winter tropopause heights but may also have nonconvective origins.
1) Convective
Spatial patterns in layer-maximum HIWC frequency are generally consistent with areas of frequent deep convection since high HIWC frequency is found along the ITZC and over warm, moist continents. These spatial patterns still contrast with those reported in hail and lightning climatologies, however. Hail and lightning are about an order of magnitude more common over land than ocean, but HIWC layer-maximum frequency is only 30% more common over land. Sixteen years (1998–2013) of Lightning Imaging Sensor (LIS) data found open-ocean lightning flash rates range from 0 to 2 flashes per kilometer squared per year, while land rates often exceeded 10 flashes per kilometer squared per year (Cecil et al. 2015). Meanwhile, eight years (2003–10) of microwave satellite imagery suggest that storms likely to produce severe hail (2.5 cm or greater) rarely exceed 1 storm per 500 km2 per year over the open ocean but often exceed 10 storms per 500 km2 per year over land (Cecil and Blankenship 2012).
Lower rates of hail and lightning over the oceans are likely the result of oceanic updrafts being about 10 m s−1 weaker than in continental convection (Jorgensen and LeMone 1989; Kelley et al. 2010). Hailstones fall quickly and require vigorous updrafts to grow to severe sizes, so severe hail is less common in the weaker oceanic convection (Knight and Knight 2001). The relationship between lightning and updraft strength is less certain, but Williams and Stanfill (2002) found the weaker oceanic updrafts to be the most likely cause for lower oceanic lightning rates. That HIWC layer-maximum frequency is almost as high over oceans as land suggests that HIWC formation is less dependent on updraft strength than hail or lightning are. Future research relating HIWC to nearby convective cores may provide further insight into the mechanisms behind convective HIWC formation.
2) Nonconvective
Patterns in column-maximum HIWC are very similar to those in global precipitation patterns. An analysis of 23 years (1979–2002) of precipitation estimates from microwave and infrared satellite data shows maximum precipitation (~8 mm day−1) along the ITCZ (Adler et al. 2003). Precipitation is also high (4–7 mm day−1) in extratropical areas with column-maximum HIWC frequency of at least 2% annually but is low (under 2 mm day−1) in areas with column-maximum frequencies below 1% (Adler et al. 2003).
The prevalence of extratropical and especially winter column-maximum HIWC suggests it is not exclusively formed through convection. The mechanism behind the low level HIWC that appears in column maxima but not layer maxima is unclear, but possibilities include atmospheric rivers and polar jets. Atmospheric rivers would explain the similar patterns in extratropical HIWC and precipitation, and polar jets could explain the increase in column-maximum HIWC in winter over extratropical oceans. However, as noted in section 4a, it is unclear to what extent column-maximum HIWC is representative of the vapor-grown crystals known to cause engine events. More research is needed to better understand the mechanism(s) leading to HIWC conditions and engine events.
5. Conclusions
Eleven years (2007–17) of CC IWC retrievals provide global statistics on the frequency of HIWC using column-maximum IWC and layer-maximum IWC between FL270 and FL420. The layer-maximum IWC retrievals also validate ALPHA over the CONUS, which provides the higher spatial and temporal resolution (4.5 km and 30 min) needed to derive storm-scale statistics for the CONUS in summer (May–August 2012–19). Uncertainties in the radar IWC retrievals and which meteorological and microphysical environments cause engine events suggest the column-maximum and layer-maximum HIWC frequencies produced are over- and underestimates of the true threat of HIWC engine events, respectively. That all CC IWC retrievals are from 0130 or 1330 local time also means the CC HIWC frequencies are not necessarily representative of diurnally averaged values. Despite these limitations, main results of this study include the following:
Patterns in layer-maximum HIWC frequency can be explained by convection in the ITCZ and over warm, moist landmasses. The global average layer-maximum HIWC frequency is 0.21%, although seasonal rates exceed 2% in some areas (Table 2, Fig. 4).
Contrasts between layer-maximum HIWC frequency and climatologies of hail and lightning suggest that HIWC formation does not require updrafts as vigorous as those needed for hail and lightning.
In addition to areas with convection, column-maximum HIWC frequency is high (≥ 2%) in extratropical oceans, especially during the winter because of HIWC below FL270 (Table 2, Fig. 3). HIWC here may be the result of shallow convection, polar jets and/or atmospheric rivers, although it is also possible the IWC found in these areas is overestimated and/or composed of different types of ice than cause actual engine events.
Some engine events have occurred in areas of little air traffic and low HIWC frequency, but the majority of engine events are found in areas of elevated air traffic, HIWC frequency, or both, such as the eastern CONUS, South America, and southern and eastern Asia.
The largest HIWC features over the CONUS are found in the Great Plains with diameters exceeding 300 km (Fig. 7). HIWC activity in this area is highest in June (25 h per 30 days; Fig. 5).
Acknowledgments
The authors thank the CloudSat Data Processing Center at Colorado State University for providing the 2C-ICE and radar reflectivity retrievals and the NASA Langley SATCORPS team for providing the satellite products used in ALPHA. We also thank Rodney Potts, Cathy Kessinger, Katja Friedrich, and two anonymous reviewers for helpful comments and discussion that enhanced this analysis. The National Center for Atmospheric Research is sponsored by the National Science Foundation. A portion of this research is in response to requirements and funding by the Federal Aviation Administration (FAA). The views expressed are those of the authors and do not necessarily represent the official policy or position of the FAA. The authors declare no conflicts of interest.
Data availability statement
CloudSat and CALIPSO datasets were obtained from the CloudSat Data Processing Center, which are accessible online (http://www.cloudsat.cira.colostate.edu). For access to other datasets (e.g., ALPHA output), please contact the authors.
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