Europe’s Invisible Flight-Level Turbulence Rises and Pulses With a Solar Rhythm

Clear-air turbulence is the hazard pilots cannot see. It lurks in cloudless skies near the tropopause, where powerful wind shear tears at aircraft without any radar signature or visual warning, and it has long been treated as a fixed feature of the upper atmosphere. A new study published in the journal Climate Dynamics now suggests that over Europe and North Africa, the large-scale atmospheric conditions that breed this invisible menace have been shifting for decades, and that part of that shifting follows a surprisingly regular rhythm of about 2.45 years that appears to echo short-period cycles in solar activity.

The research, led by Gabriel Pascual, Júlia Soliva, Jordi Mazon and David Pino of the Universitat Politècnica de Catalunya in Barcelona, takes an unusual but well-established approach. Rather than tracking individual turbulence events, which last seconds or minutes and cannot be resolved in monthly data, the team analyzed 75 years of monthly ERA5 reanalysis data from 1950 to 2025 to map the slow evolution of the synoptic-scale environments in which clear-air turbulence forms. The method acts like a temporal low-pass filter: it strips away the stochastic noise of individual encounters and reveals the steady, low-frequency variability of the background flow, much as climate scientists use monthly averages of convective available potential energy and wind shear to chart where severe thunderstorms are likely rather than where any single storm struck.

The study domain stretches from 75 degrees north to 20 degrees north and from 35 degrees west to 50 degrees east, covering the Euro-Mediterranean flight corridor. The researchers extracted data at two pressure levels, 200 and 225 hectopascals, which correspond to standard cruise altitudes for long-haul commercial aviation and coincide with the mid-latitude jet stream core and the oscillating boundary of the tropopause, where vertical wind shear and static stability gradients are most pronounced. From the 21 turbulence diagnostics proposed in earlier literature, seven indices were selected for their consistency across previous studies: Horizontal Divergence, the Richardson Number, the Brown Index, the North Carolina State University Index NCSU1, the two Ellrod Indices, and Potential Vorticity.

Each index captures a different facet of turbulence physics. The Richardson Number expresses the dimensionless ratio of buoyancy to shear generation and is the classical measure of whether a flow is dynamically stable; values below the critical threshold indicate that small disturbances can grow into full turbulence. The Ellrod Indices combine vertical wind shear with horizontal deformation, the kinematic precursors identified by Ellrod and Knapp in 1992, and the second variant, which adds a horizontal convergence term, has been verified against pilot reports with a probability of detection between 70 and 84 percent. The NCSU1 index integrates localized rotation, vertical shear and buoyancy-related instability to identify the flow’s capacity to amplify minor perturbations, particularly near jet streams and mountain waves, while Potential Vorticity serves as a tracer for the tropopause itself.

Before searching for trends, the team first tested how the indices relate to one another when computed from time-averaged fields, using the Spearman rank correlation because the data are not normally distributed. The Ellrod Index 1 emerged as the most robust proxy for general turbulence trends, correlating strongly, above 0.70, with EI2, NCSU1 and the Brown Index, all of which share a dependence on vertical wind shear or the deformation tensor. In contrast, Horizontal Divergence and the Richardson Number showed negligible correlation with the deformation-based suite, and Potential Vorticity displayed a consistent moderate negative correlation, reflecting the inverse relationship between PV-defined stability and turbulent kinetic energy. All correlations were statistically significant at the 0.05 level, with their strength varying between the two pressure levels.

The trend analysis then focused on three non-redundant indices: HDG, the negative Richardson Number and NCSU1. The results were strikingly index-dependent. Horizontal Divergence showed no statistically significant long-term trend at either level, with regression p-values of 0.532 at 200 hectopascals and 0.358 at 225 hectopascals, far above the significance threshold. The negative Richardson Number, by contrast, declined significantly over the 75 years, with a p-value of 2.88 times ten to the minus four, indicating a systematic shift toward reduced static stability and enhanced macroscopic vertical wind shear at cruise altitudes. NCSU1 showed a statistically significant positive trend, with a p-value of precisely 0.05, suggesting a long-term expansion of atmospheric configurations prone to generating clear-air turbulence, though the authors caution that this result sits right at the conventional significance threshold and is accompanied by considerable interannual variance.

The seasonal breakdown added further nuance. Winter emerged as the most turbulent season, with Richardson Number values closest to zero, indicating the strongest mechanical turbulence, and with NCSU1 values in some cases twice as large as the annual averages. Summer and autumn were the most quiescent, and their temporal evolutions resembled each other more than they resembled winter or spring. The seasonal trends also diverged in direction: for the negative Richardson Number, every season except spring showed a descending trend consistent with a year-round shift toward a more unstable upper-tropospheric background flow, while spring alone bucked the pattern with a positive trend and very high interannual variability. For Horizontal Divergence, winters actually became more stable over the period, potentially because rising vertical temperature gradients affect lapse rates.

The most eye-catching finding came from frequency-domain analysis. Applying the Fast Fourier Transform to the annually averaged series, the team found a dominant periodicity of 2.45 years in the Horizontal Divergence and Potential Vorticity indices, with related short-period peaks of about 2.8 years appearing in NCSU1 and EI2. Crucially, no index showed a periodicity corresponding to the familiar 11-year solar cycle. Instead, the 2.45-year signal aligns with historical findings by Clough in 1928, who showed that once the 11-year cycle is removed, variations in solar activity with a most common period of roughly 2.4 years become visible, a periodicity he argued was not accidental because purely stochastic variations would more likely cluster around 1.6 years. When the researchers compared the years in which the 2.45-year periodicity was most prominent with the onset years of the 11-year solar cycles from 1950 to 2025, none coincided, further suggesting the shorter-period solar cycles rather than the primary cycle are at play.

The physical mechanism, the authors propose, runs through the stratosphere. Quasi-biennial oscillations of solar activity have been documented in sunspot records using methods such as Empirical Mode Decomposition and Singular Spectrum Analysis, and the interaction between solar maxima and the easterly phase of the Quasi-Biennial Oscillation is known to precondition the polar vortex for sudden stratospheric warmings. When these warmings occur, the polar vortex breaks down dramatically and disrupts the jet stream, the primary driver of enhanced turbulence over Europe. Recent work by Vokhmyanin and colleagues achieved an 86 percent success rate in predicting winter stratospheric warming occurrences as early as the preceding August by modeling the interplay between solar and geomagnetic activity and the QBO, underscoring that the 2.45-year turbulence cycle is not a random fluctuation but is consistent with solar-driven oscillations modulating the large-scale stratospheric dynamics that dictate upper-tropospheric conditions. The authors are careful to note that a definitive causal link cannot yet be established and that the hypothesis requires further validation with longer time series or higher-resolution solar proxy data.

The study also carries practical weight for aviation. Previous research has shown that a doubling of carbon dioxide concentrations could raise the frequency of moderate-to-severe North Atlantic turbulence by 40 to 170 percent, that severe turbulence exposure there grew by 55 percent between 1979 and 2020, and that anthropogenic warming strengthens vertical wind shear at 250 hectopascals by 27 percent while reducing stratification and the Richardson number by 47 percent. Yet this new analysis shows that over continental Europe the picture is less uniform than over the open ocean: orographic forcing and higher surface roughness disrupt the coherence of vertical wind shear, making regional trends strongly dependent on which diagnostic is used. Distinguishing these macroscopic climate precursors from microscale turbulence events, the authors argue, is essential for aviation safety risk assessments in a changing climate, and the finding that part of Europe’s turbulence-prone environment pulses on a quasi-biennial solar rhythm adds an unexpected, and potentially predictable, dimension to the forecast.

Subject of Research: Long-term climatology of clear-air turbulence-favorable atmospheric conditions over Europe and their modulation by quasi-biennial solar cycles

Article Title: Climatology of large-scale atmospheric conditions favorable to clear-air turbulence over Europe (1950–2025): the role of quasi-biennial solar modulation

Article References: Pascual, G., Soliva, J., Mazon, J., & Pino, D. (2026). Climatology of large-scale atmospheric conditions favorable to clear-air turbulence over Europe (1950–2025): the role of quasi-biennial solar modulation. Climate Dynamics, 64(11), Article 459. https://doi.org/10.1007/s00382-026-08418-3

Image Credits: AI Generated

DOI: 10.1007/s00382-026-08418-3

Keywords: clear-air turbulence, aviation safety, ERA5 reanalysis, Richardson number, Ellrod index, potential vorticity, jet stream, quasi-biennial oscillation, solar activity, stratospheric dynamics, climate change, Europe