1 Introduction

Turbulence is estimated to cost the aviation industry around US$200 million annually in the USA alone (Eichenbaum, 2003). These costs arise partly from additional airframe fatigue, requiring maintenance and subsequent loss of productivity, as well as occasional airframe damage. Additionally, passengers and crew suffer injuries, some requiring costly hospital treatment. Some aircraft turbulence occurs in well-defined locations, such as over mountain ranges or within the vicinity of convective storms, and is largely avoidable. However, clear-air turbulence (CAT) is difficult to observe in advance of an aircraft’s track using remote sensing methods. Furthermore, it is still challenging for aviation meteorologists to forecast CAT, partly because current Numerical Weather Prediction (NWP) models have grid sizes that are many times larger than the turbulent eddies that affect aircraft. Hence, operational forecasters use empirical turbulence diagnostics (e.g., Brown, 1973; Dutton, 1980; Ellrod & Knapp, 1992; Knox, 1997; Knox et al., 2008; McCann et al., 2012) calculated from the temperature and wind fields of NWP output. In recent years, these diagnostics have been combined into multi-diagnostic forecasts (Sharman et al., 2006).

Williams and Joshi (2013) applied 21 CAT diagnostics to the 200 hPa pressure surface (corresponding to a flight level of approximately 39,000 ft) of a climate model using a doubled-CO₂ scenario. They found that the future occurrence of moderate-or-greater (MOG) CAT increased substantially during winter in the North Atlantic. MOG CAT is defined by the Federal Aviation Administration (FAA, 2006) as the point at which unsecured objects begin to move, and at which people find it difficult to move around inside the cabin. Williams (2017) expanded the analysis to examine turbulence increases at different severity levels (light, moderate, and severe) and found an increase in the frequency of diagnosed CAT for nearly all threshold–diagnostic pairs. Storer et al. (2017) analyzed a CMIP5 simulation using the RCP8.5 scenario in 2050–2080 and compared it with a pre-industrial control simulation, covering the whole globe and each season at different flight levels. Within the jet stream regions of both hemispheres, the RCP8.5 scenario relative to the pre-industrial control showed around a 300% increase in CAT.

S. H. Lee et al. (2019) examined three reanalysis datasets over 1979–2017 and found evidence of a 15% increase in vertical wind shear strength at 250 hPa over the North Atlantic (30–70°N, 10–80°W). As is well known, when the ratio of thermal stability to vertical wind shear (Richardson number Ri) is less than some critical value, typically 0.25, Kelvin–Helmholtz instabilities can form and ultimately result in CAT. Therefore, stronger vertical wind shear is expected to increase the amount of turbulence. However, studies examining whether the amount of CAT measured by aircraft has increased due to recent warming trends are limited by the availability of suitable data. The record of automated, quantitative eddy dissipation rate (EDR) turbulence measurements is too short. Pilot reports (PIREPs) have a longer record, but are not quantitative, and the geographical distribution of CAT based on PIREPs is limited in spatial and temporal extent (Wolff & Sharman, 2008). Furthermore, long-term improvements in operational CAT forecast skill should be acting to reduce the probability of encountering turbulence, even if the amount of turbulence in the atmosphere is increasing.

Outside aviation, CAT is also of interest as a mechanism allowing the mixing of air between the troposphere and stratosphere. Jaeger and Sprenger (2007; hereafter JS07) used ERA40 reanalysis data (Uppala et al., 2005) to compute a winter and summer northern hemisphere CAT climatology (1958–2001) near the dynamic tropopause, using four CAT diagnostics: Richardson number, negative squared Brunt–Väisäla frequency, negative potential vorticity (Gidel & Shapiro, 1979), and Ellrod’s turbulence index (Ellrod & Knapp, 1992). An increase in all four of these indices over the north Atlantic, European, and US regions was found. However, for aviation purposes, aircraft fly along constant flight levels as opposed to the dynamic tropopause. Furthermore, the first 22 years of JS07’s climatology uses reanalysis data from before the start of meteorological satellite era in 1979, leading to data quality concerns. Marlton et al. (2021) and Simmons et al. (2020) showed that the commissioning and decommissioning of meteorological satellites can introduce biases. J. H. Lee et al. (2023) have recently updated JS07’s work (see Section 4 for a discussion).

Renalysis packages now contain four decades of data entirely in the satellite era, during which the world has continued to warm. Therefore, the present study aims to analyze CAT trends during 1979–2020 in the ERA5 reanalysis data set, which has more advanced model physics and higher vertical and horizontal resolution than ERA40. The 21 diagnostics used in Williams and Joshi (2013) and Williams (2017) will be computed, as opposed to the four in JS07, to yield an improved quantification of inter-diagnostic uncertainties. These 21 diagnostics have previously been validated using aircraft measurements of CAT and have generally been found to be skillful (e.g., Sharman et al., 2006). To make the results more applicable to global aviation, the diagnostics will be calculated on the 197 hPa pressure level, corresponding approximately to a flight level of 39,000 ft (FL390), rather than the tropopause, and for the entire globe as opposed to just the northern hemisphere considered by JS07 and J. H. Lee et al. (2023).

References