1. Introduction
“Please fasten your seat belts.” It is hour 3 of your 15-h flight, the flight attendants have just completed the dinner service, and the announcement has not indicated how long the anticipated turbulence will last. Or maybe, it’s a short flight, and you were really hoping to catch a nap. Regardless, this is not something people are eager to hear in the middle of a flight, and for the airline industry, turbulence poses a significant hazard. Severe turbulence can lead to passenger and flight attendant injuries, and turbulence avoidance costs airlines tens of millions of dollars each year (Kauffmann and Sousa-Poza 2001; Sharman et al. 2006). According to a 2021 National Transportation Safety Board (NTSB) review of 111 turbulence-related accidents between 2009 and 2018, 57.7% (64) of cases were in the immediate proximity of convection (NTSB 2021).
The importance of meteorology in aviation has been understood almost since its inception (Bulletin of the American Meteorological Society 1919). A desire for a detailed understanding of thunderstorms and their potential as an aviation hazard began in earnest during World War II, and the first major proposed project to study thunderstorms, The Thunderstorm Project, took place in the summers of 1946 and 1947 (Byers and Braham 1949), relying almost entirely on flights for in-cloud observations.1 This resulted in the first analyses of storm-induced turbulence. A National Advisory Committee for Aeronautics (NACA; the predecessor to NASA) technical note by Tolefson (1947) concludes, “The results indicate that some regions of thunderstorms may present no great hazard to flight, while exceptionally severe conditions of atmospheric turbulence may occur in other regions, or even in the same region, at about the same time.” In another note, Press and Binckley (1948) provide the first estimates of turbulence frequency inside versus outside of ground-based radar echoes and recommend that pilots avoid regions of radar echo to reduce turbulence. They are also the first to suggest that an “intermediate zone” exists outside the radar echo and is a “less turbulent region than the radar echo, but more turbulent than the surrounding area.” Our understanding of turbulence in and near storms has increased substantially in the last 76 years, but the challenges underlined by these statements remain one of the cornerstones of our work.
During the late 1950s and early 1960s, a group of researchers known as the National Severe Storms Project developed a series of experiments in which aircraft flew through thunderstorms to measure turbulence; examples include the Tornado Research Airplane Project (1958–59) and project “Rough Rider” (1965).2 As a result of this work, the first “Advisory Circular” on Severe Weather Avoidance was issued by the U.S. Federal Aviation Administration (FAA) in 1964, advising all pilots that “Recent research has proven beyond any doubt that all thunderstorms are potentially dangerous and should be avoided if possible or penetrated only when the pilot has no other choice.” Citing the urgent nature of the problem and the time needed for data analysis and publication, in 1968, the FAA provided a detailed update based on preliminary findings from National Severe Storms Laboratory (NSSL) flights through springtime thunderstorms in Oklahoma between 1964 and 1967 (AC 00-24; FAA 1968). Relevant excerpts from this document and current guidelines can be found in the sidebar: the 1968 FAA Advisory Circular and guidelines today. In 1969, Burnham and Lee published “Thunderstorm Turbulence and its Relationship to Weather Radar Echoes,” based on a 6-week 1965 Oklahoma springtime period (Fig. 1), finding mild turbulence 5 mi from the boundary and 20 mi from the center of WSR-57 (thunderstorm) echoes.
“Sketch showing how distance from a storm core is defined” from Burnham and Lee (1969).
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
The 1968 FAA Advisory Circular and guidelines today
The U.S. FAA releases Advisory Circulars (ACs) as a means to communicate nonregulatory material. They can be found online, and hundreds can be active at a given time. This sidebar provides relevant excerpts from the 1968 AC titled Thunderstorms [Fig. SB1, AC 00-24; FAA (1968)] and text in the most recent FAA Aviation Information Manual (FAA 2023) and Aviation Weather Handbook (FAA 2022).
Selections of text from (a) 1968 FAA Advisory Circular entitled “Thunderstorms” (FAA 1968). Turbulence in relation to (b) altitude and intensity, (c) distance from storm core, (d) distance from storm edge, and (e) turbulence above storm tops.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
Each image included in Fig. SB1 has information related to aspects of the storm–turbulence relationships considered in this study. Of these, that in Fig. SB1d is of particular interest. Compare this to the statement and formal guideline below from the 2023 FAA Aviation Information Manual and the 2022 FAA Aviation Weather Handbook.
“Severe turbulence can be expected up to 20 mi from severe thunderstorms.7 This distance decreases to about 10 mi in less severe storms” (FAA 2023).
“GUIDELINE 14: Do avoid by at least 20 mi any thunderstorm identified as severe or giving an intense radar echo. This is especially true under the anvil of a large cumulonimbus” (FAA 2023, 2022).
The 1968 AC was updated in 1978, 1983, and 2013 with additional definitions and timely information about technology such as Doppler radar. Sometime after the Lane et al. (2012) study, the guideline in Fig. SB1e that they reference was removed and does not appear in the current guidance (FAA 2022, 2023). In December 2022, all remaining ACs pertaining to weather were canceled and consolidated into the Aviation Weather Handbook (FAA 2022). However, the specific guidance for avoidance distance in the horizontal has remained virtually unchanged.
The current guidance regarding turbulence intensity with altitude states, “While there is some evidence that maximum turbulence exists at the middle level of a thunderstorm, recent studies show little variation of turbulence intensity with altitude” (FAA 2023). This guidance closely resembles text in the Aviation Information Manual from 2000 (FAA 2000) and Fig. SB1a. Recent research investigating turbulence intensity with altitude suggests that in-storm turbulence varies significantly with altitude (Lane and Sharman 2014). How CIT intensity varies with altitude at a distance from storms has yet to be fully quantified.
Separate from the “Thunderstorm Avoidance Guidance” in the Thunderstorm section, CIT is now defined in part of a larger section on turbulence by the FAA (2022), and some additional distance information is provided:
“Outside the cloud, shear turbulence has been encountered several thousand feet above and up to 20 mi laterally from a severe storm. Additionally, CAT may be encountered 20 or more miles from the anvil cloud edge. These kinds of turbulence are sometimes referred to as Convectively Induced Turbulence (CIT).”
However, 20 mi is still used, and while the distance from the anvil cloud edge is mentioned in one instance, it is somewhat unclear how the distance from a severe storm is defined.
Finally, in 1968, storm altitude was primarily addressed to contextualize results. By the early 2000s, the guideline [17 in the most recent Aeronautical Information Manual (AIM)] was established:
GUIDELINE 17: Do regard as extremely hazardous any thunderstorm with tops 35 000 ft or higher whether the top is visually sighted or determined by radar (FAA 2023) was included. There is no clear connection between this guideline and existing research.
Thanks in large part to advances in numerical modeling, we now know that convection-induced turbulence (CIT) is often associated with gravity waves generated by the convection. Within clouds, updrafts and downdrafts can lead to large gradients in static stability and wind shear, while cloud edges are known to support Kelvin–Helmholtz billows. Anvil and trailing stratiform regions can be particularly turbulent, where the development of a mesoscale downdraft can lead to strong vertical shear, while precipitation phase changes can lead to large gradients in stability. There is also evidence that upper-level convective outflow can induce turbulence through local modifications of stability and shear which leads to Kelvin–Helmholtz instabilities at significant distances from the parent thunderstorms. For the interested reader, detailed reviews of CIT processes can be found in Lane et al. (2012), Sharman and Lane (2016), and Sharman and Trier (2019). Recently, some of these concepts have been used to develop new methods for identifying breaking gravity waves near storms in model forecasts (Kim et al. 2019, 2021). Additional information about numerical forecasts of turbulence can be found in Sharman et al. (2006), Kim et al. (2011, 2015), and Sharman and Lane (2016).
There have also been significant advances in turbulence observations. The details of automated turbulence report development and comparison with pilot reports can be found in Sharman et al. (2014) and Sharman and Lane (2016), but key points are briefly summarized here. For a long time, the primary source of turbulence intensity information was from verbal pilot reports (PIREPS). While these are still made and useful for communicating the effects of turbulence on an aircraft and passengers, they are voluntary, highly subjective, typically have displacement errors in space and time (Schwartz 1996), and are limited to five basic categories: “smooth,” “light,” “moderate,” “severe,” and “extreme.” Since the late 1990s and early 2000s, an increasing number of U.S. and international commercial air carriers have begun automated recording of in situ estimates of turbulence (Cornman et al. 1995, 2004; Cornman 2016). Specifically, they record the cube root of eddy dissipation rate (EDR; ϵ1/3 m2/3 s−1), an aircraft-independent metric which can be derived from vertical wind speed or acceleration. The automated reports include the mean and peak intensity EDR over the previous minute and a fractional time of the peak within the minute in tenths providing a spatiotemporal accuracy of up to ∼2.5 km and 6 s for an aircraft traveling around 250 m s−1.
There are some differences in EDR thresholds used for light, moderate, and severe in past studies, though the impacts are likely superficial. In many disciplines, percentiles are used to evaluate the extreme nature of an event. With this in mind, we computed the 99.5th, 99.9th, and 99.99th percentiles of quality-controlled in situ EDR reports from commercial aircraft between 2009 and 2017 to be 0.16, 0.22, and 0.34 m2/3 s−1, respectively. These correspond exceptionally well with light, moderate, and severe thresholds used in recent studies (Sharman and Pearson 2017; Sharman and Trier 2019; Trier et al. 2022)3 and are what we use to define light or greater (LoG), moderate or greater (MoG), and severe or greater (SoG) subsets (and consequently their background frequencies). The remaining events are referred to as nonevents (NEs).
In 2012, a BAMS article by Lane et al. on Recent Advances in the Understanding of Near-Cloud Turbulence included a figure based on 2 years of warm season months (7 million EDR reports) that suggested the risk of MoG turbulence exceeded the background risk at horizontal and vertical distances well beyond FAA guidelines at the time. The analysis of risk above echo tops supported previous findings by Lane and Sharman (2008, 2006) that the avoidance guideline at the time defining safe flight over echo tops was inconsistent with our understanding of underlying dynamics and that the distances recommended were insufficient, creating the potential for severe turbulence encounters above cloud tops. Since then, this guideline has been removed entirely.
The complexity of multiscale interactions, incomplete understanding of storm and turbulence dynamics, and computational and observation limitations are all obstacles to improving avoidance methods. However, a comparison of the most current (FAA 2023) guidance around thunderstorms and the 1968 Advisory Circular4 (AC 00-24; FAA 1968) suggests that comprehensive analysis of near-storm turbulence observations has significant potential value to the aviation community.
A decade after the Lane et al. (2012) review, the available turbulence data have grown considerably. We now have 9 years (2009–17) of archived commercial turbulence reports (roughly 200 million) and coincident radar data that we can use to revisit and expand upon their analysis. We will focus on two key questions in this article: 1) Where does storm-induced turbulence occur? 2) What environmental factors influence the spatial distribution? Each is addressed in the following sections in turn alongside current and historical guidance and followed by key takeaways from this work that could aid in future guideline revision.
2. Where does storm-induced turbulence occur?
a. Turbulence risk in the horizontal.
Horizontal distances are computed between EDR reports and the closest 10-dBZ reflectivity boundary at aircraft altitude (distance “A” in Figs. 2a,c). This boundary represents a horizontal slice through a larger storm object (Figs. 2a,b,d), so an aircraft some distance from the 10-dBZ boundary may still be located above radar echoes (see the appendix A for more detail). Pilots may not always have access to the most recent composite reflectivity images and often rely on the onboard radar that may only show returns at a single level or range of depths near the flight level. Note also that the 10-dBZ boundary is more realistically treated as a fuzzy boundary, where the visible cloud boundary likely extends at least a few kilometers beyond. Because we limit EDR reports to those reaching 8 km and above, by default all storms in Fig. 3a reach at least 8 km. This method for storm identification is different from Lane et al. (2012), who use vertically integrated liquid (VIL) above 3.5 kg m−2 and echo tops above 4.6 km. A VIL of 3.5 kg m−2 is more likely to correspond to storm cores and has been previously identified as indicative of severe hail (e.g., Amburn and Wolf 1997). However, by using an integrated quantity, Lane et al. (2012) may include distances away from storms which do not reach 8 km. Risk is reduced significantly for aircraft flying at a distance from any radar-identified echo tops; a more detailed discussion of this can be found in appendix B.
(a),(b) Schematic depiction and (c),(d) example using real data of near-storm distance metrics (A, B, C, and D) applied in analyses. (a) The letter A represents the distance between an aircraft and the 10-dBZ radar reflectivity boundary (teal line) at the flight level. The letter B represents the vertical distance between an aircraft and the ETH at the same location. (b) The letters “C” and “D” represent the horizontal and vertical displacements of an aircraft from the maximum (or peak) echo top (blue plus sign) within a convective region (light blue contour), respectively. (c) Distance A using one of the real EDR reports (dots; with colors representing severity) within a 15-min window of a radar scan, ETHs (shading), and a 10-dBZ boundary at 12 km (teal outline). (d) Distance C using EDR reports as in (c) and peak echo tops as in (b). Convective regions are outlined in blue. The orange line in (a), (b), and (d) denotes the edge of regions with valid echo tops; this is unlikely to represent the true cloud boundary (see appendix A for more detail).
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
(a) Relative risk of turbulence as a function of horizontal distance from 10-dBZ object boundaries at flight level. The value −5 represents distance within 5 km inside the echo boundary, and all other distances (<−5) inside are combined into one bin (−10). Distance along the x axis corresponds to A in Fig. 2a. (b) Relative risk of turbulence as a function of distance above or below ETHs, where negative distances indicate aircraft altitudes below echo top at aircraft location. The value −1 represents flights within 1 km below echo top, and all other distances below echo top (<−1) are combined into one bin (−2). Distance along the y axis corresponds to B in Fig. 2a. The dashed line represents the current federal guidelines (20 mi or ∼32 km). Numbers in the upper-right-hand corner are the percentage of points in each category that occur in “clear” regions (where no echo tops are identified).
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
Not surprisingly, the risk of turbulence increases as an aircraft nears a storm, and the risk is highest inside regions of reflectivity (Fig. 3). Despite differences in our definitions, like Lane et al. (2012), we find the risk of turbulence of any severity (including MoG) is twice the background risk as far away as 70 km (43 mi) from the 10-dBZ boundary (Fig. 3). Note that risk is relative to the background risk of the same severity, and risks cannot be compared across categories (e.g., it cannot be said that the risk of SoG is larger than the risk of LoG at the 10 dBZ boundary). Instead, the risk of SoG is nearly 30 times greater at a 10-dBZ boundary (nearly 50 times greater inside the boundary) than at 100 km, and LoG is 12 times greater than the background risk of LoG turbulence at the 10-dBZ boundary and still greater than the background risk at 100 km away.
b. Turbulence risk in the vertical.
Above echo tops (distance “B” in Fig. 2a), the risk of turbulence (of any severity) effectively remains above the background risk at all separation distances. Risk is highest within 1 km of echo tops, where SoG turbulence is nearly 50 times more likely, but turbulence of any severity is still twice as likely at 7 km above radar echoes.6 The estimated risk magnitude in Fig. 3b for MoG turbulence is lower than that in Lane et al. (2012) at distances they include, but this could reflect differences in echo-top height calculation methods [not provided in Lane et al. (2012)] and that their method of storm identification captured more intense regions, while we use all echo tops within a storm object.
The numbers in the upper right of Fig. 3b display the percentage of reports in each category which correspond to a “no echo top” pixel. They show that the majority of reports in all categories actually occur outside (and not above) identified storms; this may be expected, since commercial aircraft will typically try to avoid thunderstorms. However, the percentage of SoG, MoG, and LoG reports that occur in storm regions is significantly higher than that of nonevents. In fact, the risk of SoG turbulence is around 45 times higher for aircraft at locations designated as convective and 10 times higher at locations designated as stratiform via Steiner et al. (1995) (Fig. 4). MoG and LoG follow the same pattern.
Relative risk of turbulence for locations with no cloud, stratiform, and convective pixels at the horizontal location of the report. Convective classifications are performed via Steiner et al. (1995).
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
Neither Fig. 3b nor Fig. 4 takes into consideration the echo-top height (ETH) at the location of the aircraft. Figure 5a shows that while there is an increased risk flying through reflectivity associated with echo tops at any height, this risk increases dramatically with height; MoG increases from 5 times the background at 6 km to over 30 times the background at 12 km. The relative risk of MoG and LoG appears to decrease slightly for echo tops above 13 km, but it remains high, and it should be interpreted cautiously.
Relative risk of turbulence as a function of the ETH at the aircraft location. Aircraft reports may be anywhere in the column with an echo top (e.g., above, at, or below ETH altitude).
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
c. Spatial distribution of risk near convective echo tops.
The risk of turbulence at horizontal and vertical separation distances from storms is important but may not capture all scenarios. Measures using integrated or maximum radar fields combine the risk for all altitudes at a given separation distance. What is the risk for an aircraft above echo tops for some horizontal distance from them? Another way to visualize turbulence risk is to examine the location relative to local maxima in convective echo-top height (demonstrated in Figs. 2b,d). The local maximum in convective echo-top height is designed to mimic the tallest local cloud tops which are often visually identifiable and conceptually intuitive.
Figure 6 adds information about risk at a location that is displaced both vertically and horizontally from echo tops. Figures 6b and 6c indicate that the risks of LoG or MoG are larger than their background risks nearly everywhere within 100 km of peak convective echo tops. Data are insufficient to define the risk of SoG at some locations, but the risk is enhanced at least 50 km laterally at altitudes above echo tops and increases toward echo-top peaks. For example, at an altitude more than 5 km above peak echo tops and a horizontal distance of 20 km (12.5 mi), the risk of MoG turbulence is double the background risk. At or above the peak echo-top altitude, the vertical extent of the region where risk is twice that of the background decreases around 1 km for every ∼12-km horizontal separation distance. Even though distances are measured from echo-top peaks inside convective regions of storms, the majority of reports in Fig. 6 occur outside regions of 10-dBZ echoes. The exception to this is below the echo tops and at close proximity [the region bounded by (0, 0), (20, −4), and (0, −4)].
Spatial distribution of risk relative to convective echo-top peak locations (shading) for (a) SoG, (b) MoG, (c) LoG, and (d) NE EDR reports (shading). Distances in the horizontal Δx and vertical Δz correspond to C and D, respectively, in Fig. 2b. Areas where the relative risk is at least two are dotted. Dashed gray lines represent angles of 1°, 2.5°, 5°, and 10° from the echo top. Locations which are unfilled had either fewer than 15 total observations or 5 observations at that severity level.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
The 1968 AC reported moderate-to-severe turbulence 1/5 as often at horizontal distances of 20 mi (32 km) (for cores of ∼>40 dBZ) as in the cores and up to 10 mi (16 km) from the center of a less severe storm (∼30–40 dBZ) (Fig. SB1c). We have no direct comparison for this, as thankfully, unlike the research flights the 1968 AC is based on, commercial aircraft generally avoid flying through storm cores. This said, without discriminating by storm intensity, we find that at 20 mi, MoG is about 1/10 as frequent as near-peak echo tops. There, the risk of MoG turbulence is nearly 5 times the background risk at altitudes 2 km above the peak echo-top height and still more than double the background risk at 4 km above the tallest echoes.
Currently, the primary guideline which references the vertical (and applies to cruising altitudes) recommends caution around thunderstorms taller than 35 000 ft (10.7 km; see sidebar). The analysis shown in Fig. 6 considers all peak echo tops together, but understanding how turbulence risk changes with nearby echo-top heights is potentially useful. For simplicity in interpretation, if we consider the risk as a function of the height of the nearest peak convective echo top, we find that for peaks above 8–9 km, the risk of turbulence exceeds the background risk, and for peaks above 10 km, the risk of SoG doubles (not shown).
d. The role of storm intensity.
While the guideline pertaining to distance from storms only lists a single lateral avoidance distance, additional text in the Aviation Information Manual makes a distinction between expected distances of severe turbulence from more or less severe storms, 20 and 10 mi, respectively (FAA 2023).
From Fig. 7, it is clear that storms with the highest reflectivity (Q4) are most likely to lead to turbulence. In fact, the top 25% of storms account for more than 75% of the risk within ∼50 km of a 10-dBZ boundary for each category, but the percent contribution decreases with horizontal distance (not shown). Storms with reflectivity greater than 40.5 dBZ (the top 50%) account for almost all of the risk outside reflectivity regions. Repeating this analysis using echo-top height gives the same qualitative results, with slight differences in specific magnitudes.
Risk sensitivity to storm intensity where quantiles [(b) legend] are determined by 99th-percentile reflectivity within the closest storm. Quantiles are divided by the thresholds of 35.9, 40.5, and 44.9 dBZ, respectively, where Q4 exceeds 44.9 dBZ. In each of the three left panels, the risk is a function of horizontal distance from the nearest 10-dBZ edge at flight altitude for (a) SoG, (c) MoG, and (e) LoG, and in the three right panels, the risk is a function of vertical distance from ETH for (b) SoG, (d) MoG, and (f) LoG. Risk is scaled such that if each quantile had an equal probability of occurring everywhere, the risk would be 1, so the total risk in each bin of Fig. 3 is 1/4 times the sum of the risks from all quantiles.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
3. What environmental factors influence the spatial distribution?
a. Wind and shear.
While no current formal FAA guidelines exist regarding the impact of upper-level winds on potential turbulence mitigation needs, early advice from the 1968 AC suggests that there is a slight preference for turbulence on the downstream side of storms. Anecdotally, we also understand that this kind of information may still be considered by some airline companies in their own internal guidelines. More recently, studies have discussed wake-like features downwind of overshooting convective cores (Wang et al. 2010; Trier and Sharman 2018). Others have suggested that dynamically, the shear direction may be more crucial (e.g., Lane and Sharman 2008), as convective gravity waves that propagate away from a storm can amplify and break when they approach a critical level, and that upshear-propagating waves are less likely to encounter a critical level (Sharman and Trier 2019).
We use ERA5 (Hersbach et al. 2020) hourly pressure-level winds to explore the role of wind speed and direction in the spatial distribution of turbulence near storms. Specifically, winds are interpolated to flight altitude and averaged over a region of 100-km radius around the 10-dBZ boundary location closest to each EDR report. The 100-km radius is chosen to approximate the background winds in that region, and an example can be found in Fig. 8a.
(a) Example of EDR report locations near a region of ETHs (grayscale) and 10-dBZ echo boundary at an altitude of 12 km (teal outline) as in Fig. 2c that now includes wind speed in a 100-km radius around the closest edge point (color shading), winds at 12 km (black barbs), and 8–12-km bulk wind difference (blue barbs). The wind direction at the closest edge to the report is given by the thick blue arrow. The gray dashed line represents the ray between the closest edge and the report. (b) Example of rotation of (a) onto coordinate system where wind direction becomes the right side of the page (wind vectors generally point east at upper levels over the United States).
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
Figure 9a demonstrates that the horizontal extent of turbulence risk increases exponentially with wind speed, providing different curves for each risk threshold. For example, when wind speeds are 20 m s−1, MoG is 5 times more likely up to nearly 30 km from storms, and at 40 m s−1, this increases to over 100 km. At speeds above 30 m s−1 (58 kt), MoG turbulence is twice the background risk at distances beyond 200 km from storms. However, 30 m s−1 is also indicative of the presence of a collocated jet stream, which is also long known as a source of turbulence (Bannon 1952), even in the absence of storms (Chambers 1955).
Relative risk (shading; color scale at right) of (a),(d) horizontal distance from the closest 10-dBZ object at flight altitude and magnitude; (b),(e) relative relationship between the aircraft, the nearest 10-dBZ boundary, and direction; and (c),(f) magnitude and direction relative to wind/BWD vector, for MoG EDR reports. Wind at aircraft altitude is assessed in (a)–(c), and 8–12-km BWD is assessed in (d)–(f). Areas where the relative risk is at least two are dotted. Locations which are unfilled had either fewer than 15 total observations or 5 observations at that severity level.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
To explore the role of wind direction, the report location relative to the closest storm edge is plotted on a rotated coordinate system where the wind/bulk wind distance (BWD) vector points to the right of the page (Fig. 8). MoG exists in every direction with 25–50 km of a storm, but higher risk of turbulence of any severity extends nearly twice as far downstream and is enhanced in the quadrant to the left of the wind vector (∼−45° Fig. 9b).
When speed and direction are considered together, the region where the risk of MoG turbulence is larger than the background risk extends predominately in the region between −90° and +45° from the mean wind, but the risk increases for larger magnitudes in the downstream direction. The highest risk of MoG turbulence lies between −45° and 0°, when wind speeds are larger than 50 m s−1 (Fig. 9c).
The horizontal extent of turbulence risk also increases exponentially with the magnitude of 8–12-km bulk wind difference (Fig. 9d). A BWD of 10 m s−1 increases the risk of MoG turbulence by 5 times at horizontal distances over 20 km from the nearest 10-dBZ boundary, and this distance increases to 80 km for BWD of 20 m s−1. The spatial distribution of turbulence with respect to the BWD vector also resembles the distribution around the wind vector (Fig. 9e), and while turbulence risk exceeds the background over a larger range of angles, it is predominately downstream and to the left of the BWD vector at magnitudes less than 20 m s−1.
One potential explanation for the enhanced risk in the quadrant “left” of the wind and shear vector is provided by the results of Trier and Sharman (2009). Often, summertime MCSs occur to the south of the environmental upper-level jet, and they found that anticyclonic MCS outflow can enhance the jet in the downstream region. If this is the case, the finding is region specific and likely only applicable in the Northern Hemisphere extratropics. However, the present study considers all seasons and convective organizations in the continental United States, so additional work is needed to more thoroughly investigate this finding.
Earlier studies and versions of FAA guidelines had included risk above cloud tops as a function of wind speed. While these guidelines have since been deleted, understanding this risk is still important. Figure 10 demonstrates the risk of turbulence above echo tops as a function of wind and BWD direction and magnitude. Critically, the risk of LoG, MoG, and SoG turbulence at effectively all altitudes, magnitudes, and directions within regions of sufficient data exceeds the background risk and by 2× nearly everywhere (LoG and SoG not shown). As speed increases, the vertical extent of enhanced turbulence risk increases. An aircraft is 5 times more likely to experience MoG turbulence at 2 km above echo tops once wind speeds reach 10 m s−1. When winds reach 25 m s−1, the risk region expands to 4 km above echo tops (Fig. 10e). Risk above echo tops shows little dependence on wind direction (Fig. 10b).
Relative risk (shaded; color scale at right) as a function of vertical distance from ETH and (a) wind speed, (b) wind direction, (c) BWD magnitude, and (d) BWD direction. Areas where the relative risk is at least two are dotted. Locations which are unfilled had either fewer than 15 total observations. Bin widths are 5 m s−1 for magnitudes and 10° for direction.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
Even when BWD values are less than 5 m s−1, the risk of MoG turbulence is 10 times the background risk for aircraft less than 2 km above echo tops. Like with wind speed, higher BWD magnitudes have larger risks over deeper layers above echo tops, but little dependence on direction (Fig. 10).
b. Tropopause.
At the tropopause, the increase in stability and presence of shear are capable of creating a duct that can support the propagation of gravity waves away from their source, while the upper-level outflow from convection can lead to decreases in static stability and increases in shear that can reduce the gradient Richardson numbers and support turbulence. This has been shown in observations and simulations of individual cases (see Lane et al. 2012; Sharman and Lane 2016; Sharman and Trier 2019; Zovko-Rajak et al. 2019; Trier et al. 2022, and citations therein). It is therefore useful to consider turbulence risk at a horizontal distance from echo-top peaks as a function of the echo-top peak altitude and aircraft altitude relative to tropopause height [tropopause via Tinney et al. (2022); see appendix 3d for details] (Fig. 11).
Relative risk (shaded; color scale at right) as a function of horizontal distance from echo-top peak and (a) the vertical distance between echo-top peak and tropopause height and (b) the vertical distance between aircraft altitude and tropopause height. Areas where the relative risk is at least two are dotted. Locations which are unfilled had fewer than 15 total observations.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
Figure 11 demonstrates that at large distances, the highest risk exists for aircraft flying within 3 km below the tropopause and for echo tops above the tropopause. More generally, as echo tops approach the tropopause, the risk increases over larger distances. However, once echo tops reach an altitude 4 km below the tropopause, the risk becomes double the background risk within 100 km of echo-top peaks. At small lateral distances, higher risks extend over all tropopause-relative aircraft and echo-top depths. These are more likely to coincide with regions of cloud.
4. Summary and recommendations
Extensive recent archived data provide an opportunity to more robustly quantify the spatial extent of turbulence around thunderstorms. Our study reinforces the initial analysis shown in Lane et al. (2012) but benefits from more data that allow us to be stricter in our analysis methods. We also provide additional detail around turbulence intensity, storm intensity, and environmental characteristics that help potential users make more informed decisions about risk.
In summary, enhanced turbulence risk essentially always exists above storms and is significant above convection. Enhanced turbulence risk can also extend large horizontal distances from radar-derived convective echo tops, even when the aircraft is above the height of the tallest nearby echo. Enhanced turbulence risk is most likely to extend over the largest horizontal distances for aircraft flying near the tropopause (and up to 3 km below), near storms whose echo tops approach the tropopause and/or storms with (90th percentile) radar reflectivity larger than ∼40 dBZ, and in environments with stronger background wind speeds and/or vertical wind shear. These findings apply to aircraft flying above 8 km.
Although there is still work to do to more thoroughly explore the occurrence of turbulence around thunderstorms, there are aspects of our analysis that could be used to further refine turbulence avoidance guidelines in the future. To fully benefit from our quantification of the enhanced turbulence risk, such guidelines would, however, require a value judgment on how much enhanced turbulence risk is appropriate for a commercial airliner and its passengers and how this should vary with turbulence intensity. While we are not suggesting specific amendment language, key elements of refined guidelines would be consistent with the spirit of the original early guidelines and recognize that
While distances from a storm (and storms themselves) are not straightforward to define objectively, different clearly defined radar-based metrics can be used to determine near-storm turbulence risk that can be refined based on the data available to decision-makers and their needs.
Turbulence risk decreases exponentially as the horizontal distance between the aircraft and reflectivity echoes increases, but enhanced turbulence risk (as defined in this work) extends over horizontal distances well beyond 32 km. A MoG turbulence encounter is still twice as likely at a location 70 km (43 mi) away from a flight-level reflectivity echo (10 dBZ).
Enhanced turbulence risk still extends over large horizontal distances even if the aircraft is at an altitude above the tallest nearby echo top.
The risk of turbulence above and around echo tops increases with the height of echo tops, especially for those that reach the tropopause.
The risk of turbulence is enhanced downstream and downshear of storms.
Over the United States, the risk of turbulence is enhanced in the quadrant to the left of the wind direction and wind shear vectors, though this is likely only true in the Northern Hemisphere extratropics.
The risk of turbulence around storms is enhanced significantly when storms have larger radar reflectivities or if the wind speeds and/or vertical wind shear is stronger in the upper troposphere.
We hope the results are useful and begin a conversation about the future of turbulence avoidance guidance. At the same time, we recognize that the complexities identified above make it difficult to develop turbulence guidelines that are simple, adequate, and appropriate for both general and commercial aviation applications.
This work represents a starting point, a big-picture analysis based on turbulence–storm relationships at cruising levels for all seasons and storms within our 9-yr dataset of turbulence encounters over the United States. One particular challenge we did not address, which is part of the current guidance, is how risk changes when there are multiple storms in a region. There are also other potential environmental factors beyond the basic wind and tropopause measures described in this work that may influence where turbulence occurs near storms. Finally, there is still much room for progress in understanding the sensitivity of the relationships we analyzed to details like time of year, or storm and environmental characteristics, which are the basis of our ongoing and future work.
Because balloons were tracked visually using theodolites at the time, tracking them in the cloud was not possible.
In 1964, this group merged with the Weather Radar Laboratory in Norman, Oklahoma, becoming the NSSL.
The 0.3 m2/3 s−1 used by Lane et al. (2012) falls between our MoG and SoG thresholds of 0.22 and 0.34.
AC 00-24 was canceled in December 2022 (recently enough that the work discussed here was already well underway!), but much of the information in it was merged with other weather-related advisories into the Aviation Weather Handbook (FAA 2022).
Reports use pressure altitude; see the appendix A for additional information.
The lowest echo tops considered were 4 km.
While not immediately relevant to our study, it should also be acknowledged that the severe thunderstorm criteria listed in the most recent edition reference 3/4 in. hail. The National Weather Service now (since 2010) defines severe hail as 1 in.
Acknowledgments.
Thank you to the airline companies that contribute to NCAR Research Application Laboratory’s (RAL) archive of commercial EDR data. We are grateful for Greg Meymaris’s assistance with EDR data acquisition and advice on best-use practices. SH’s discussions with Ewan Short (conceptualization and object identification) and Nick Thorne (practical applications) during the course of this work improved our study. Thanks to three anonymous reviewers and the editor for their feedback on this manuscript. This research is supported by the Australian Research Council (DP200102516) and the Centre of Excellence for Climate Extremes (CE170100023). WD, RS, and ST would like to acknowledge in part support 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 National Center for Atmospheric Research is sponsored by the National Science Foundation under Cooperative Agreement 1852977. SH’s visit to RAL at NCAR funded in part by their Visiting Scientist Program greatly benefited the project. Computational resources were provided by the National Computing Infrastructure (Australia), and SH benefited from the support and tools developed by the CLEX CMS team. Finally, the Australia-based (at the time of writing) American-led author SH would like to thank her flights across the Pacific for lots of first-hand experience with in-flight turbulence.
Data availability statement.
The contents of the in situ EDR archive are proprietary to the air carriers and are covered by licensing agreements between the air carriers and NCAR, which state that the observations cannot be passed on to other entities and cannot be placed onto a publicly available server. We are permitted to use the data in scientific publications provided individual flights cannot be directly identified, as in this work. ECMWF ERA5 data were accessed via the Australian National Computing Infrastructure database. GridRad data are available at the NCAR Research Data Archive; see Bowman and Homeyer (2017).
APPENDIX A Method Details
a. Automated turbulence reports.
Automated turbulence estimates from commercial aircraft typically report the cubed root of energy dissipation rate (EDR), an aircraft-independent measure derived from the vertical wind speed and is proportional to the root-mean-square of vertical acceleration. For the in situ data used here, EDR is computed on board from spectra derived from the 8-Hz vertical wind speed data, using a 10-s window (80 samples) with a 5-s overlap. The EDR is proportional to the spectral level, with the mean and maximum (peak) of the 12 spectra recorded every minute; see Sharman et al. (2014) for details. EDR reports are binned at 0.02 EDR intervals and downlinked routinely at carrier-specified intervals and also immediately when the peak EDR exceeds 0.18 m2/3 s−1. In the latter instance, EDR reports for the 5 min before and after are also triggered. If the interval is more than 1 min and EDR is less than 0.18 m2/3 s−1, reports are backfilled as null. When peak EDR is reported, a decimal rounded to the nearest tenth marking the time of the peak within the minute is also recorded.
We use peak EDR reports from 2009 to 2017 with confidence of at least 0.9 and require that all points within the previous minute are good (Meymaris et al. 2019). We calculate a more precise location using the recorded time of the EDR peak, which improves the accuracy from 15 to 2.5 km for an aircraft traveling approximately 480 kt (∼250 m s−1). At these speeds, an aircraft can cover about 15 km in a minute and 900 km in an hour. To reduce potential spatial errors due to timing differences between reports and hourly radar data (see next section), the analysis only includes EDR reports within ±15 min of the hour. Sensitivity tests using a range of windows down to ±2 min suggest that results are robust; the smaller window had a slightly larger risk at closer distances. A choice of window was made to balance the competing challenges of inclusion of more data for statistical benefits and potential distance displacements. Reports with known positions or other errors were not included in the analysis. The vertical position of the aircraft is recorded in pressure altitude (ft) which is converted to kilometers and is rounded to the nearest kilometer for comparison with gridded radar data when necessary. The expected departure between pressure altitude and true altitude is less than the adjustment to the vertical spacing of the gridded reflectivity data.
Figure A1 shows a large increase in the number of observations seen between 2013 and 2015, which represents the introduction of an additional carrier to this dataset, and the decrease in 2016 is due to a change in onboard software and the temporary removal of the EDR reporting program on some aircraft (Fig. A1a), and the decrease in 2017 is due to the exclusion of aircraft with seemingly random position errors. The vast majority of all EDR reports are between 8- and 12-km altitudes, where most commercial aircraft spend the majority of their time. The focus of this study is on turbulence encountered at cruising altitudes, so reports are limited to those above 8 km (∼26 000 ft). The combined effects of the time window and cruising altitude selection reduce our dataset from 200 million to 38.3 million reports.
(left) Number of available EDR observations each year. (right) Number of observations by altitude.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
Analysis was also constrained to the portion of the U.S. landmass within the domain of the radar archive. A heat map of flight paths for the analysis period is shown in Fig. A2. Favored altitudes and flying routes are important to consider in analysis; this is accounted for by computing a frequency that is scaled by the background frequency within an intensity subset (see also main text.).
Heat map of all EDR report locations in the analysis.
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
To reduce the likelihood of classifying a report that may be due to mountain-wave turbulence (MWT) as CIT, a report was classified as likely MWT if it 1) occurred west of the 104 west (W) longitude line, 2) exceeded the EDR threshold for light turbulence, and 3) was 200 km or more from a 10-dBZ boundary at flight level. These reports are not removed before computing the background frequency of EDR exceeding a particular threshold [e.g., the denominator of Eq. (1)] but are removed before computing CIT frequencies (and consequently risk) in various scenarios [e.g., the numerator in Eq. (1)]. This does not, however, guarantee that every report used in our analysis is CIT.
b. Radar observations.
This study uses version 3.1 of the gridded NEXRAD WSR-88D radar (GridRad) archive, which includes hourly, three-dimensional merged reflectivity data over most of the United States on a 0.02° × 0.02° × 1 km Cartesian grid that extends to 24 km above sea level (Homeyer and Bowman 2017). All locations in the domain are observed by at least one radar, and most locations are observed by at least three (see Homeyer and Bowman 2021). Regions where vertical sampling may be reduced generally correspond with regions that were either excluded from our analysis (coastal waters) or where reports far from convection were treated as if they were from a cause other than convection (west of 104°W). Data were quality controlled prior to analysis following the recommendations of Homeyer and Bowman (2017). The period of analysis (2009–17) is limited by the availability of both EDR and radar data, and so many of the issues that impact the early 2000s (Homeyer and Bowman 2021) do not affect our analysis.
Echo-top heights were computed using the methods of Cooney et al. (2018), excluding the requirement of reflectivity greater than 20 dBZ at the location of an ERA-Interim reanalysis tropopause. Convective–stratiform classification was performed according to Steiner et al. (1995).
c. Calculation of spatial relationships.
To calculate useful spatial relationships between EDR reports and storms, we need to define 1) What is a storm? 2) For what part(s) of the storm do we want to know the relationship of EDR reports? Four key measurements are used to place each EDR report into a spatial context: 1) the horizontal distance from the report to the closest 10-dBZ echo at the same altitude as the report, 2) the horizontal distance from the report to the closest “storm” object (see appendix B), 3) the vertical distance between the report and ETH in the same column, and 4) the 3D distance between the report and peak convective ETH in the closest storm. While it would be helpful, it is not possible to determine the visible cloud edge or cloud top with the available data. Instead, we use relationships to 10-dBZ echoes and ETH calculations with the acknowledgment that the boundary is likely a fuzzy representation of the cloud boundary, which likely extends at least a few kilometers beyond. With this in mind, we have defined a storm as a region defined by a region of ETHs that spans at least four grid points (∼16 km2), where at least four grid points are also convective via Steiner et al. (1995). The storm edge is defined using the find_boundaries function of Python’s skimage module (van der Walt et al. 2014) to create sets of points that describe the 2D footprint of the outermost border. Within a storm, at each altitude, 10-dBZ objects are identified using a similar method, where the edges mark the region enclosing reflectivity ≥10 dBZ over at least four grid points at that altitude. The convective pixel requirement is not applied at individual altitudes. A point may be within the storm region, but still in an echo-free region at a particular altitude. An example of this could be a plane flying over a stratiform region of a larger complex. The distance between EDR reports and the edges of storm and 10-dBZ objects is calculated and assigned a negative value if the report lies inside the object and a positive value if the point lies outside the object. We use Python’s skimage peak_local_max (van der Walt et al. 2014) to identify local maxima in ETH within convective regions of identified storm objects. All horizontal distances are computed using the Haversine (great circle) formula.
d. Meteorological analysis.
We used hourly pressure-level data for temperature, geopotential height, and wind from ERA5 reanalysis over the study period (2009–17) to compute near-storm upper-level environment characteristics. ERA5 is the fifth major global reanalysis produced by the European Centre for Medium-Range Weather Forecasts (Hersbach et al. 2020) and has a horizontal resolution of 0.25° × 0.25° and 37 pressure levels.
The altitude of the tropopause at each grid point was calculated using the potential temperature gradient tropopause (PTGT) algorithm of Tinney et al. (2022). PTGT defines the first tropopause at the location where the potential temperature gradient dθ/dz increases to 10 K km−1 and remains above 10 K km−1 for at least 2 km. If above that the potential temperature gradient decreases to below 10 K km−1, a second tropopause can be defined using the same method as with the first and a threshold of 15 K km−1, but this was not used here. We made one small adjustment, requiring that the potential temperature gradient remain above the threshold for two grid points rather than 2 km. In the range of expected tropopause altitudes over the United States, the vertical distance between grid points is generally between 1 and 1.5 km.
To find the relevant mean background wind vectors, zonal and meridional winds were interpolated to a regular altitude grid with 1-km vertical spacing. Mean wind vectors were averaged over a 100-km region surrounding the closest 10-dBZ boundary to the EDR report. Bulk wind difference, a typical proxy for vertical wind shear, was computed over the 8–12-km layer and then averaged over the same region as above.
APPENDIX B Horizontal Distance from Storm (Composite 10 dBZ) Boundary
We include this appendix to share how horizontal distance results demonstrated in Fig. 3a change if instead of the 10-dBZ boundary at aircraft altitude, a storm boundary is defined over a contiguous region of ETH as in Fig. 2d (the orange border; see appendix A for a detailed definition). This definition of a storm will be more conservative than the method used in the main text and than that used in Lane et al. (2012) and significantly extends coverage of storm regions such that few reports outside of the storm boundary correspond to radar echoes in any layer.
In short, the risk of turbulence is much lower if locations with identified echo tops (e.g., regions with reflectivity of 10 dBZ or larger over a 3 km depth) are avoided (Fig. B1). However, double the risk of MoG turbulence still exists out to 15–20 km (9–12 mi), and the risk of MoG turbulence exceeds the background to near 60 km. The risk of SoG drops off significantly in the first ∼10 km, suggesting SoG events are most likely in the immediate vicinity of storms, when the storm is defined as the entire composite region of ETHs.
As in Fig. 3a, but for the relative risk of turbulence as a function of horizontal distance from composite 10-dBZ object boundaries. The value −5 represents distance within 5 km inside the echo region, and all other distances inside are combined into one bin (<−5).
Citation: Bulletin of the American Meteorological Society 106, 1; 10.1175/BAMS-D-23-0142.1
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