Combined Impact of Jet Stream and Turbulence on Long-term Trans-Oceanic Flight Routes over North Atlantic Ocean Using ERA5 Reanalysis

Combined Impact of Jet Stream and Turbulence on Long-term Trans-Oceanic Flight Routes over North Atlantic Ocean Using ERA5 Reanalysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Combined Impact of Jet Stream and Turbulence on Long-term Trans-Oceanic Flight Routes over North Atlantic Ocean Using ERA5 Reanalysis Joon Hee Kim, Jung-Hoon Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7910453/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract Transatlantic aviation operations routinely enhance flight efficiency by leveraging daily jet streams, but they face growing safety risk from clear-air turbulence (CAT). Previous studies have assessed the climatological impacts of winds and turbulence separately, yet a comprehensive assessment integrating their effects along dynamically optimized flight routes has remained absent, despite the close relation between jet and CAT. Here, using an integrated routing framework applied to 44 years of reanalysis data, we provide the first multi-decadal quantification of safety-efficiency trade-off. While changing wind patterns shortened the fastest round-trip routes by about two minutes, the additional time required to avoid CAT has grown so substantially that it negates and even reverses these efficiency gains for the safest routes. This rising cost is driven by a significant increase in CAT, which disproportionately affects eastbound flights. Our findings highlight the need for integrated approaches to assess aviation’s evolving risks in a changing climate. Earth and environmental sciences/Climate sciences Earth and environmental sciences/Ocean sciences Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 INTRODUCTION An aircraft in cruise phase is influenced by upper-level atmospheric conditions. To minimize flight time and fuel consumption, flight operators optimize routes daily, by leveraging favorable jet streams 1 – 3 while avoiding weather hazards such as turbulence and deep convection 4 – 8 . Beyond these day-by-day operations, recent studies have highlighted the link between aviation and atmospheric variability on longer time scales. For instance, major climate variabilities such as El Niño–Southern Oscillation (ENSO) or the North Atlantic Oscillation (NAO) are shown to significantly modulate flight times, optimal route locations, and turbulence exposure 9 – 11 . Given these close coupling, long-term climate change is expected to affect aviation operations by altering upper-level flow 12 . This impact has been actively studied in the North Atlantic, one of the world's busiest air corridors, with a focus on how changes in jet stream characteristics affect flight times 13 – 16 . These studies have quantified potential changes in flight times by directly computing optimal flight routes using climate model simulations, thereby isolating the impact of altered atmospheric states. Such routes are idealized but they reflect operational planning and thus provide a realistic baseline 17 , 18 . Although uncertainties in climate models remain 16 , projections suggest that strengthening of the westerly jet could increase roundtrip flight durations in the future 9 , 14 , 15 . While these time increases may appear modest, they can translate into substantial economic costs for the fuel-sensitive airline profits 9 , 19 . From an environmental perspective, longer flights imply higher emissions, which contribute to radiative forcing and further accelerate warming 20 , 21 . Understanding this two-way interaction is therefore important for both aviation and climate science. Yet despite these insights, much of the existing literature has focused narrowly on flight efficiency, often overlooking operational safety due to weather hazards closely related to jet systems. Aviation turbulence poses a direct threat to flight safety and is a leading cause of weather-related injuries in aviation operations 22 , 23 . Among various kinds of turbulence, clear-air turbulence (CAT) is of particular importance, which constitutes a substantial fraction with recent studies suggesting up to 70% 24,25 and is closely related to upper-level jet systems. To take advantage of tailwinds, optimal routes are often positioned close to strong jets (in contrast, placed away in the opposite direction) 13 , 15 , where CAT is climatologically frequent 26 – 29 and dynamically favored 30 – 33 . In practice, operators routinely adjust routes to avoid expected turbulence. This operational necessity becomes increasingly critical as many studies project a significant future increase in CAT 22 , 34 – 37 with some evidence suggesting this trend is already emerging 25 , 27 – 29 , 38 – 40 . As CAT becomes more prevalent, it will not only increase the direct threat to flight safety but also reduce operational efficiency by forcing less optimal routes to avoid turbulent areas 23 , 41 . Some of these inefficiencies may already be embedded in current operations: improved forecasting systems and heightened awareness of turbulence likely reduce observed turbulence encounters, masking the increasing trends suggested by previous studies 42 – 44 . However, these hidden costs have not been explicitly quantified in the context of growing turbulence. Moreover, most climatological assessments of CAT measure temporal changes over fixed locations, which do not explicitly account for the variability of daily flight routes optimized relative to jet and its associated CAT hotspots. Therefore, a more comprehensive assessment of aviation under a changing climate must consider not only changes in jet stream characteristics but also the operational implications of increasing turbulence. Herein, we use an integrated route optimization framework to assess the impact of 44 years of atmospheric changes on transatlantic aviation. Specifically, we first analyze the characteristics and long-term trends of wind-optimal routes (WORs), with a focus on directional asymmetry and turbulence exposure. We then quantify the cost of safety by generating turbulence-avoiding routes with varying avoidance strength and comparing them to WORs. Finally, tracking the trend in this cost reveals the evolving trade-off between flight efficiency and safety, offering new insights that are more realistic to the challenges facing aviation in a changing climate. RESULTS We used ERA5 reanalysis data from the ECMWF 45 , on a 0.25° grid and 3-hourly intervals to evaluate atmospheric conditions at cruising altitude (200 and 250 hPa). WOR, which minimize travel time by leveraging cruising-level winds, between New York (JFK) and London (LHR) were calculated for eastbound (EB) and westbound (WB) flights, with departures at 00, 06, 12, and 18 UTC, for each day between 1979 and 2022. Clear-air turbulence (CAT) was diagnosed using the TI3, which was designed to capture multiple sources of clear-air turbulence near jet stream 46 , 47 and showed good performance against observations 48 – 50 . The intensities of CAT were categorized using thresholds based on rarity in the probability distribution. For example, we assumed Moderate-Or-Greater intensity CAT (MOG-CAT) occurs within grid cells with TI3 values exceeding the 98th percentile 36 , 51 . Further methodological details are described in the Methods. Characteristics of optimal flights Figure 1 illustrates the characteristic spatial configuration of the jet stream, CAT, and WORs under daily weather conditions at cruising altitude (250 hPa). EB and WB WORs are shown alongside the great-circle route (GCR), which represents the shortest path between JFK and LHR; without wind, the WOR is reduced to GCR. In Fig. 1 a, the EB WOR (green) follows the core region of strong westerly to benefit from tailwinds, whereas the WB WOR (magenta) detours northward to minimize headwind. Because regions of intense CAT broadly coincide with areas of strong wind speed, the EB WOR passes through turbulent zones, while the WB WOR generally remains outside of them. A similar configuration is found in another representative case (Fig. 1 b). The linkage between upper-level wind fields and WOR is also apparent at seasonal and longer timescales. Figure 2 a presents the seasonal mean wind speed at 250 hPa and the climatological distribution of WORs over the 44-year period. In all seasons, EB WORs are generally concentrated along the axis of strong westerly flow, with some spread that reflects daily variation of weather patterns (Fig. 1 ). In contrast, WB WORs show a broader meridional distribution, with their highest density located north of the GCR to avoid headwinds near the jet core. The spread of WB WORs is largest in winter when the winds are the strongest. These spatial features are consistent with earlier studies on the influence of jet stream structure on optimal transatlantic routing 10 , 11 , 13 , 14 . In addition to the climatological features, Fig. 2 b shows the linear trends in seasonal WOR density and wind speed. In many regions, the trends in WOR density coincide with those in wind speed, especially where the wind trend is located either north or south of the GCR, rather than directly overlapping it. This alignment is particularly evident in spring, when wind speed trends exhibit a dipole pattern around the GCR. Similar patterns are found at 200 hPa (Fig. S1 ). Clear-air turbulence along optimal routes While upper-level winds play a central role in shaping optimal routes, CAT poses constraints on flight safety and efficiency. Figure 3 a shows the climatological distribution of MOG-CAT occurrence at 250 hPa, with the seasonal mean wind speed. MOG-CAT occurs most frequently on the cyclonic shear side of the jet, with maxima near its exit region 29 . A secondary peak is found near the southern tip of Greenland, likely associated with partially resolved mountain-wave activity 29 . Frequency peaks in winter and appears to be lowest in summer. However, summer values must be interpreted with caution as TI3 is not designed to capture convectively generated turbulence and shows the weakest skill against observations during that season 50 . The absolute change in MOG-CAT probability from 1979 to 2022 (estimated from linear trend, see Methods) are shown in Fig. 3 b, with trends in wind speed. The increasing trend in CAT frequency is most significant in spring, especially south of the GCR. Winter trends are generally positive but spatially limited, while summer and autumn show little change. Similar patterns appear at 200 hPa, but both the occurrence frequency and absolute changes are more pronounced than at 250 hPa (Fig. S2). Unlike the close correspondence between wind speed and WORs (Fig. 2 b), CAT trends exhibit poor spatial alignment with wind trends. This spatial mismatch is understandable: CAT typically occurs not within straight jet cores, but along curved segments associated with upper-level ridges and troughs 33 , 52 . As these features are transient 53 and tightly coupled to synoptic weather systems, they are often filtered out in temporal averaging. However, daily route optimization is shaped by such transient features. Therefore, the crucial next step is to characterize the CAT encounter risk along these dynamic routes rather than using a static grid-based analysis. To achieve this, we introduce the MOG-CAT Area Ratio (MCAR), a proxy for MOG-CAT encounter probabilities along the route's vicinity. To highlight the impact of dynamic routing, we compare the MCAR for WORs against two static references: The great-circle route (GCR) and the WOR Domain (see Methods and the Fig. S3 for details). Figure 4 a shows the 44-year average of MCAR as a heatmap, with route types in columns and seasons in rows. The result for the broad WOR domain provides a baseline of MOG-CAT frequency over the North Atlantic corridor. Its annual mean MCAR of 2.8% exceeds the 2% threshold used to define MOG-CAT, implying frequent turbulence over the North Atlantic due to strong climatological jet. When focusing area is confined to GCR vicinity, the MCAR increases to 3.7%, as the region more closely overlaps with the climatological jet axis. A clear directional asymmetry appears in dynamically optimized WORs. Compared to GCR, EB WORs consistently show higher MCAR values (annual average of 4.6%) while the WB WORs exhibit lower MCAR values (2.8%). In winter, the probability of encountering MOG-CAT near EB routes is nearly twice that of WB routes. This supports more strongly the interpretation of Fig. 1 : EB WORs fly closer to the turbulent jet stream for tailwinds, while WB WORs avoid it, leading to contrasting turbulence exposures. Interestingly, the MCAR for Roundtrip (RT) WORs (3.7%) is almost identical to that of GCR. This suggests that while daily EB and WB routes diverge tactically, these deviations occur almost symmetrically around the GCR. Consequently, their opposing turbulence exposures tend to cancel out over the long term, causing their average exposure to converge with that of the geographically direct path. Similar patterns appear at 200 hPa (Fig. S4), but directional contrasts are more pronounced: EB shows greater mean MCAR due to more frequent MOG-CAT occurrence at that level (Fig. S2). We next examine the long-term trends in MCAR, presented in Fig. 4 b (slope) and Fig. 4 c (relative change from 1979 to 2022). For static references, the WOR domain exhibits a statistically significant increasing trend in annual mean MCAR (+ 0.04%/decade). Seasonally, all seasons except summer exhibit significant increases, with the strongest trend in spring and a more modest but still significant trend in winter. These increasing trends are more pronounced over GCR vicinity. Notably, the dynamic WORs again exhibit directional asymmetry: EB WORs exhibit consistently stronger increases than the GCR, while WB WORs show weaker changes. This contrast peaks in spring, when MCAR for EB WORs increased by more than 40% over 44 years. This substantial increase is attributed to the spatial overlap between long-term trends in flight routes (Fig. 2 ) and CAT frequency (Fig. 3 ): The region of increasing CAT in spring located south of the GCR, which is precisely where EB WORs have become more concentrated whereas WB WORs are more dispersed. In summary, CAT encounter risk has increased significantly over the past four decades, with its magnitude strongly dependent on routing strategy. This leads to the important next question of how these changes in turbulence risk can be translated to flight efficiency. The turbulence-avoidance routes and extra flight times To answer above question, this section focuses on flight time. We investigate the degradation in flight efficiency by comparing the standard wind-optimal routes (WORs) with their turbulence-avoiding counterparts. We adopted a simplified avoidance strategy where aircraft were forced to completely avoid regions where diagnosed turbulence exceeds a certain threshold while minimizing flight time. Although idealized, this strict constraint approach helps clarify the cost of turbulence avoidance, providing estimates of reduced efficiency caused by horizontal deviation. The limitations of this approach and more realistic operational strategies are addressed in the Discussion. Figure S5 introduces the concept of turbulence-avoiding routes (TORs) using an example case from October 19, 2002, showing how they deviate from the WOR to avoid turbulent regions. Each TOR is indicated by a minimum CAT threshold (percentile-based, e.g., s97). The WOR (black line) is optimized solely to minimize flight time and therefore passes through turbulent areas. In contrast, TORs diverge from the WOR depending on the threshold, with stricter constraints (lower percentiles) resulting in longer flight times due to greater deviations (see legend). As a result, Fig. 5 illustrates how changing atmospheric conditions have affected both flight safety and efficiency. A representative TOR (blue line) avoiding MOG- CAT is compared to WOR (black line). In Fig. 5 a, the risk time—time spent in MOG-CAT region—along the WOR has increased significantly over the past 44 years. In contrast, TOR has maintained consistently low risk time (non-zero values are due to the exclusion of avoidance constraints near airports). As a result, the difference in turbulence exposure between two routes has steadily widened. However, maintaining safety comes at a cost. Shifting focus to flight time (Fig. 5 b), the WOR roundtrip flight time has slightly decreased over the same period, suggesting a modest gain in efficiency under changing jet stream conditions. In comparison, the flight time penalty for avoiding turbulence—defined as difference between TOR and WOR (red dashed line)—has increased steadily and significantly. This reveals that the price of maintaining safety has grown substantially over time. Furthermore, unlike WOR, the TOR no longer shows a statistically significant decrease in total flight time. To further investigate the safety-efficiency trade-off, we extend analysis to TORs with varying CAT intensities (s97 to s99.6; see Fig. S5). Figure 6 a presents the 44-year mean characteristics of these strategies, showing the relative difference in risk time and flight time compared to WOR. Stricter avoidance strategies (i.e., lower percentile thresholds) yield greater reductions in mean risk time (red bars) at the cost of a larger flight time penalty (blue bars). This penalty is directionally asymmetric as shown in lower panel; EB routes, which are more frequently exposed to turbulence, require a greater flight time sacrifice than WB routes. Figure 6 b reveals how this trade-off has evolved over the 44-year period. While WOR shows decrease in a net flight time due to favorable wind changes, this efficiency gain is progressively diminished as the avoidance constraint becomes stricter. For the most stringent strategy (s97), the gain disappears entirely, leading to a statistically significant increase in total flight time. This reversal demonstrates that the implicit cost of ensuring safety has grown so substantially that it can now outweigh the efficiency benefits gained from a changing climate. We finally assess how the implicit cost of safety from turbulence has grown over time. Figure 7 shows this cost across different avoidance strategies over the 44-year period, defined as the additional flight time required for turbulence avoidance compared to WOR baseline. Directionally, the flight time penalty is consistently higher for EB routes, both in its long-term average and its increase. In terms of avoidance strength, stricter strategies (lower thresholds) incur larger absolute increases in penalties. In contrast, the relative increase in the penalty is most pronounced for strategy avoiding only the most severe turbulence. This finding implies that more intense CAT has increased more rapidly, as consistent with prior research, and makes it difficult to ignore the growing cost of avoidance. 22 , 35 The increasing time penalty for maintaining flight safety against turbulence carries substantial operational and environmental consequences. For a representative case (s98, avoiding MOG-CAT), the additional flight time required to avoid turbulence has grown by approximately 150 seconds per crossing over the past four decades. The extrapolation to transatlantic traffic estimates that this change corresponds to an additional annual cost of $ 50 million in fuel and an extra 160 million kilograms of CO 2 emissions compared to 44 years ago, using standard assumption for transatlantic traffic (~ 300 daily crossings) and aircraft operations (1 ~ gallon/sec fuel burn, $ 3/gallon fuel cost, 9.6 kg CO 2 /gallon). This change may be even more pronounced for flights cruising near 200 hPa, where MOG-CAT occurrence is more frequent (Fig. S6). DISCUSSION Using four decades of reanalysis data, we found that the North Atlantic optimal route has shown a marked rise in route along-route CAT exposure and a concurrent growth in the time cost of maintaining safety. While wind conditions have generally become more favorable for shortening optimal roundtrip flight times, the additional time required to avoid turbulence has increased such that the safety cost can offset (and locally reverse) efficiency gains. The magnitude and trend of this cost depend sensitively on routing strategy. We further discuss the details and implications of results. The main results including pronounced directional asymmetries arise from interplay between the atmospheric structure and routing behavior. The high frequency of CAT near jet streams is supported by both theory and observation. Mechanisms include strong vertical wind shear favoring Kelvin–Helmholtz instability 31 , 46 , reduced inertial stability especially in south of the jet, and the emission of gravity waves via ageostrophic adjustment in jet exit regions 47 . Consistent with these processes, aircraft observations indicate that up to two-thirds of CAT events occur in jet vicinities 33 . Therefore, the position of flight route relative to jet stream strongly influences their CAT exposure. Crucially, routing decisions are made daily, and both the jet and associated CAT hotspots vary strongly in space and time. Because the jet-CAT system is not stationary, grid-based climatology could dilute these localized and transient features, obscuring the signals apparent along actual optimal routes. Previous climatological assessments typically measured CAT frequency or trends at fixed locations over daily mean basis, an approach directly applicable for fixed paths but not for variable transatlantic traffic. In practice, about half of crossings follow the North Atlantic Organized Track System (NAT-OTS), issued daily by Air traffic control and resembling WOR in construction. Our route-based result show that CAT encounter probability along EB WORs is more than GCR. Moreover, its increasing trend is also pronounced, especially in spring when region of increasing CAT and preferred routing overlaps. Thus, a more realistic assessment of CAT impact to aviation should account for the dynamic characteristics of operation. The increasing CAT could also affect flight time. Solely considering wind changes, results shows that the long-term decreasing trend in the annual mean roundtrip flight time along WORs over the 44-year period, although trend is not statistically significant when disaggregated by direction (EB and WB). It is also seen in seasonal average of spring and summer (Fig. S7). Notably, this trend is absent in GCRs, suggesting that the reduction in flight time is specific to dynamically optimized routes. We attribute this trend to long-term structural changes in the North Atlantic jet stream (Fig. S8). Relative to the climatological mean (contours), the jet has intensified near its core while weakening along its flanks, particularly in spring. Thus, EB WORs can leverage the strengthened jet core, while WB WORs are routed through weakened headwind regions along the jet edge. Together, these changes contribute to the overall reduction in roundtrip flight time. The decrease in roundtrip flight time identified in our reanalysis-based study aligns qualitatively with recent climate model projections. Cheung et al. (2022) 16 , using an ensemble of CMIP5 models combined with wind-optimal routing methodology, project a future reduction in transatlantic flight times regardless of direction. This contrasts with earlier studies based on single CMIP3 15 or and small ensemble of CMIP5 14 , which predicted an increase in westbound and roundtrip travel time. These discrepancies are likely attributed to ensemble sizes and experimental design. However, none of these assessments accounted for CAT. We show that when turbulence avoidance is imposed, increasing CAT could negate the efficiency gain from wind changes, which magnitude are strongly dependent on routing strategies. While projections of jet stream features remain uncertain 54 , the increase in CAT is consistently reported in both reanalysis and climate models 22 , 29 , 34 , 35 , 37 , 40 . Considering that stronger CAT increase faster, efficiency reduction induced by turbulence avoidance cannot be ignored. Previous studies speculated that more prevalent turbulence under climate change might erode flight efficiency, but none quantified this cost. By directly comparing optimal and turbulence-avoiding routes, we provide the first multidecadal quantification of growing cost of maintaining safety against increasing CAT. It is noted that all discussions here are based on the assumption that there is no significant improvement on turbulence canceling technology that stabilizes aircraft in turbulent air. These results are based on an idealized framework assuming fully optimal routes and should not be interpreted as exact realization of past operational changes. Our aim is to assess isolated atmospheric effects influencing aviation operations. In the transportation and aviation sectors, technological advances have enabled partial implementation of optimal routing, and case studies have analyzed associated efficiency benefits. Beyond that, we suggest that atmospheric variabilities on longer time scales are at play: as turbulence continues to increase, the safety–efficiency trade-off will intensify. The change in individual flights accumulated can translate into substantial economic and environmental loss, potentially feeding back to accelerate climate change itself. Therefore, understanding the evolving interaction between climate and aviation demands a multidimensional analytical framework, with joint consideration of meteorological dynamics, operational strategies, and systemic feedback. This study has several limitations mostly on aeronautical engineering in this study. Route optimization was restricted to horizontal dimensions assuming constant altitude and Mach number, although wind variation during flight was included. This simplification was motivated by various considerations. First, 3D optimization is computationally prohibitive in a climatological analysis. Second, these simplifications are consistent with our aim to isolate the atmospheric influence on flight efficiency, independent of aircraft type or engine performance. Fixed true airspeed together with constant altitude also allows fuel usage to scale linearly with flight time, simplifying cost interpretation and facilitating scenario comparisons. Moreover, aircraft flying on NAT-OTS normally maintain a constant altitude and airspeed, justifying our assumptions 13 . A more critical limitation lies in the treatment of turbulence avoidance. In practice, flights often slow down or maneuver vertically in response to unexpected turbulence 55 . Here, turbulence avoidance was modeled strictly in two dimensions, such that cost of avoidance was reduced to additional flight time. Unlike typical operations where flights deviate temporarily from the optimal route and then return, our framework assumed that aircraft could follow a newly optimized minimum-time path that simultaneously avoids turbulence, under the assumption of perfect knowledge at the planning stage. This idealized representation provides a transparent measure of the safety–efficiency trade-off but inevitably departs from operational reality. Future work should incorporate more realistic 3D avoidance strategies and the uncertainties of turbulence forecasting to bridge this gap. Methodologically, trend detection and turbulence diagnostics present further challenges. The identified trends based on seasonal-mean regression were consistent across alternative approaches. Similar results were obtained when seasonal medians or the non-parametric Mann–Kendall test were applied. The assumption of residual independence required for the linear regression significance test was also satisfied in most cases, supporting the statistical validity of the regression-based trends and temporal changes (relative and absolute) estimated from them. Diagnosing CAT with a single index is inherently imperfect, but the TI3 index was selected for its integrated formulation and superior performance in prior studies. Future research could build on this by employing multiple turbulence diagnostics in an ensemble framework to enable probabilistic assessments of changing turbulence risk. METHODS Data This study used the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis to analyze atmospheric conditions and compute optimal flight routes for the 44-year period from 1979 to 2022 45 . We utilized horizontal winds (u, v), temperature (T), and geopotential height (z) at a 0.25° horizontal resolution and 3-hourly intervals. The data were primarily analyzed on the 250 hPa and 200 hPa pressure levels, representing typical cruising altitudes, with neighboring levels used for vertical derivatives. Turbulence Diagnostics Since current resolution of reanalysis data (and operational NWP models) cannot directly resolve aviation-scale turbulence, we employed an empirical index to diagnose turbulence from large-scale flow disturbances. We adopted the TI3 index, which is well-validated for its high predictive skill for CAT near the jet stream as it considers multiple generation mechanisms 47 – 51 . To categorize turbulence intensity, a common methodology for climatological turbulence assessment is employed: we used threshold based on its rarity indicated by percentile value from its probability density function (PDF). The PDF is constructed over the Northern Hemisphere mid-latitudes (20°N–60°N) for the entire study period 29 , 40 . The primary threshold for Moderate-or-Greater CAT (MOG-CAT) was defined as the 98th percentile (top 2%) of the distribution 36 , 51 . Route Optimization Algorithms This study focuses on the North Atlantic flight corridor, one of the world's busiest aviation regions, accounting for a substantial portion of global air traffic and emissions 13 . Following the previous studies 2 , 10 , 13 – 15 , the New York (JFK) to London (LHR) route was selected as the representative of transatlantic flight. This choice is supported by the strong spatial agreement between the wind-optimal routes of JFK-LHR and the operational North Atlantic Organized Track System (NAT-OTS), where much of the daily traffic is concentrated. Wind-optimal routes between diverse airport pairs crossing the North Atlantic exhibit an organized spatial distribution 3 , indicating that the findings derived from the JFK–LHR case can be extended to broader regional traffic patterns. Optimal routes were calculated using A* path-finding algorithm, which identifies the least-cost path in a weighted node-network. In this framework, the connection weight between nodes was defined as the flight time, simulated by assuming the aircraft cruises at a constant altitude and Mach number. Our methodology follows the framework of Cheung (2018) 56 with several modifications for computational efficiency. We constructed the node network on a cubed-sphere grid, which avoids polar convergence and ensures homogeneous coverage, and computed the connection weights directly from ERA5 data using GPU parallelization. The grid resolution is about 1 degree, since there are about 91 × 91 nodes per one face. These weights were archived at 3-hour intervals for the entire study period (1979–2022). The A* algorithm then determined the optimal routes by referencing the pre-computed networks, accounting for the temporal progression of flights through the varying wind and turbulence fields. A nearest-matching approach was applied to select the appropriate 3-hourly weights for each path segment. The structure of node-network and neighboring scheme are presented in Fig. S9. Within this framework, two types of routes were generated: Wind-Optimal Route (WOR): This is the time-minimal path, computed using only the flight time as the cost function. It serves as the baseline route representing maximum flight efficiency. Turbulence-Avoiding Route (TOR): This is the safety-conscious path, designed to avoid regions where TI3 values exceed specified intensity thresholds (see Sec 2.1) while minimizing flight time. This was implemented as a hard-constraint approach, where a near-infinite cost penalty is assigned to any path segment encountering the specified turbulent region; however, such cost penalty was not applied within 500 km of the origin and destination to ensure the algorithm could always find the optimal solution. We tested multiple thresholds (e.g., 97th, 98th, 99.1th, and 99.6th percentiles) to assess the effect of different avoidance strengths. Trend Quantification To quantify long-term changes, a linear regression model was applied to the 44-year time series (1979–2022) for each variable (e.g., MCAR, flight time) on a seasonal and annual basis. This provides fitted values for the start (ŷ 1979 ) and end (ŷ 2022 ) of the period, representing the amount of change over research periods without interannual variability. From these fitted values, we calculated: Absolute Change: The difference between the fitted values (ŷ 2022 − ŷ 1979 ). Relative Change: The absolute change divided by the starting value ([(ŷ 2022 − ŷ 1979 ) / ŷ 1979 ] × 100%). Quantification of Turbulence Encounter Probabilities To quantify MOG-CAT occurrence in the vicinity of 6-hourly optimal routes, we introduced a proxy called the MOG-CAT Area Ratio (MCAR). For each route, a 'route vicinity' was defined as the set of 2°x2° grid cells that the route intersects. The MCAR was then calculated as the ratio of the MOG-CAT area within this vicinity to the total area of the vicinity. This area-based approach, rather than sampling only along a route line, enhances statistical stability by enlarging the sampling domain and are in construction area weighted. To ensure temporal consistency, each 6-hourly route was segmented into 3-hour intervals then the MOG-CAT field was matched to each segment's valid time. Fig. S3 illustrates the procedures for calculating MCAR for WOR. Note that the MCAR is calculated for every 6-hourly WOR. MCAR for two static references are additionally considered to highlight the impact of dynamic routing: (1) The great-circle route (GCR), for which the MCAR was calculated using the same route-vicinity method as the WOR. (2) the 'WOR Domain' defined as a fixed rectangular area that encompasses all WORs during the study period (36.5°-67.25°N, 0°-75.5°W). DATA AVAILABILITY The ERA5 reanalysis dataset is publicly accessible from the Copernicus Climate Change Service Climate Data Store (CDS, https://cds.climate.copernicus.eu , last access: 10 October 10, 2025; ref. 45). CODE AVAILABILITY The codes supporting the findings of this study are developed by the corresponding authors and available on reasonable request. Declarations FUNDING STATEMENTS This work is funded by the Korea Meteorological Administration Research and Development Program (Grant KMI2022-00310 and KMI2022-00410) and supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2025-24683550). ACKNOWLEDGMENTS The authors thank the Korea Meteorological Administration and the National Research Foundation of Korea for their continuous support. AUTHOR CONTRIBUTIONS Conceptualization: J.H.K., J.-H.K. Methodology: J.H.K., J.-H.K. Investigation and visualization: J.H.K. Supervision: J.-H.K. Writing–original draft: J. H.K. 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1","display":"","copyAsset":false,"role":"figure","size":241113,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExample of jet stream, clear-air turbulence and WOR over North Atlantic. \u003c/strong\u003e(a) The eastbound (green) and westbound (magenta) WOR between JFK and LHR, departing at 00 UTC on June 1, 1980. The routes account for evolving wind conditions throughout the flight, updated at 3-hour intervals. The red line denotes the great circle route between the two airports. Wind direction and speed at 00 UTC are represented by black arrows and purple shading, respectively. Regions where the turbulence index (TI3) exceeds a certain threshold are highlighted in color. (b) Same as (a), but for flights departing at 00 UTC on December 1, 1990.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/9069c61d4fe23532fddcb6f8.png"},{"id":97787344,"identity":"5eba24f5-3a4c-47ad-947f-c045c57e1e8d","added_by":"auto","created_at":"2025-12-09 11:04:24","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":715407,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSeasonal spatial distribution and long-term trends of WORs between JFK and LHR.\u003c/strong\u003e The spatial distribution of WOR grid-crossing frequency at 250 hPa over 44 years (1979–2022). Panel (a) shows the cumulative frequency, calculated as the total number of times WORs, departing daily at 00 UTC, passed through each 2° grid cell. Results are shown for each season (MAM, JJA, SON, DJF), with contours indicating the mean horizontal wind speed at 250 hPa. Panel (b) presents the changes from 1979 to 2022, inferred from the linear trend in WOR grid-crossing frequency at each grid cell. Statistically significant trends (p \u0026lt; 0.05) are stippled. Contours in (b) represent the linear trend of mean horizontal wind speed at 250 hPa (m s⁻¹ year⁻¹).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/49a7b657bff1465951bf87af.png"},{"id":97897719,"identity":"385a61ea-1bf3-403b-b8ad-d578be368c46","added_by":"auto","created_at":"2025-12-10 15:38:08","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":574674,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSpatial distribution and long-term trends of MOG-level CAT occurrence.\u003c/strong\u003e The spatial distribution of MOG-level CAT occurrence at 250 hPa over 44 years (1979–2022). Panel (a) shows the occurrence probability, calculated as the percentage of time steps in which the TI3 value at each 0.25° grid point (lat × lon) exceeded the threshold (top 2%). Results are shown for each season (MAM, JJA, SON, DJF), with contours indicating the mean horizontal wind speed at 250 hPa. Panel (b) presents the linear trend in occurrence probability, showing the change from 1979 to 2022. Statistically significant trends (p \u0026lt; 0.05) are stippled. Contours in (b) represent the linear trend of mean horizontal wind speed at 250 hPa (m s⁻¹ year⁻¹).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/d0296b056acac8de47334a09.png"},{"id":97787341,"identity":"4cb5fd74-549a-4d4f-b9f0-d299bd21eea3","added_by":"auto","created_at":"2025-12-09 11:04:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":93488,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eHeatmap of CAT encounter probability along different routes and its long-term trends.\u003c/strong\u003e The seasonal mean CAT encounter probability for different routes between JFK and LHR over 44 years (1979–2022). Panel (a) shows the seasonal mean CAT encounter probability, calculated as the proportion of the area affected by MOG-level CAT relative to the total area of each route or fixed region. The heatmap is structured as a 5×5 matrix, where rows correspond to different seasons (annual mean, MAM, JJA, SON, DJF) and columns represent different routes (EB, WB, roundtrip, GCR, and WOR domain. Colors indicate CAT encounter probability. Panel (b) shows the linear trend (slope) in CAT encounter probability, calculated from annual and seasonal mean values. Panel (c) presents the relative change in 2022 compared to 1979, estimated using the linear trend. Statistically significant trends (p \u0026lt; 0.05 and p \u0026lt; 0.01) are marked with an asterisk (*, **) in black text.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/96a68ae0cac8c506265d5ff9.png"},{"id":97787342,"identity":"c6339241-d5ed-4fdc-a9f2-ca1265a32f69","added_by":"auto","created_at":"2025-12-09 11:04:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":199640,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eRisk time and flight time of WOR and TOR with strict constraints.\u003c/strong\u003e The annual mean risk time and total flight time for WOR (black solid line) and TOR (blue solid line) from 1979 to 2022. TOR represents a turbulence-optimized route that avoids MOG-level CAT by applying a strict constraint. Panel (a) shows the annual mean risk time, defined as the total duration spent flying through regions of MOG-level CAT during a roundtrip flight. The red dashed line represents the difference between WOR and TOR. Panel (b) presents the same analysis as (a), but for total roundtrip flight time. Linear regression trends are shown for three routes. The legend includes the mean values, absolute change (A.C.) and relative change (R.C.) from 1979 to 2022 estimated from the linear trend, and the p-value of the regression.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/e9d5fe1b4d16990a8845e0de.png"},{"id":97896558,"identity":"33705fc6-2d13-4821-99e3-5e383d4a3ce4","added_by":"auto","created_at":"2025-12-10 15:36:45","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":130719,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCharacteristics of routes optimized with various thresholds.\u003c/strong\u003e (a) Top panel presents the 44-year (1979–2022) mean relative differences (%) in roundtrip flight time (blue) and risk time (red) between WOR and routes optimized with various strict constraints. The number behind ‘s’ refers the minimum strength of turbulence in percentiles acting as the constraint threshold for corresponding route. Note that s98 is same as TOR in Fig. 5. The bottom panel shows decomposition of EB and WB flight time. (b) shows the absolute changes from 1979 to 2022 estimated from linear regression.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/0dd63f5c7d164f4c7844c718.png"},{"id":97897684,"identity":"1d62709f-3e82-450f-9e01-e6552851d6f5","added_by":"auto","created_at":"2025-12-10 15:38:05","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":121355,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAnnual mean extra flight time required to avoid turbulence of varying intensities on transatlantic flight.\u003c/strong\u003e The x-axis denotes different turbulence avoidance strategies, where 's' followed by a number indicates the minimum percentile of turbulence intensity being avoided (e.g., s97 means avoiding turbulence stronger than the 97th percentile). Green, red, and blue bars represent Eastbound (EB), Westbound (WB), and Round Trip (RT) flights, respectively. For each strategy, light-shaded bars show estimated values for 1979, and dark-shaded bars show estimated values for 2022. These values are derived from a linear regression of 44 years of annual mean flight time differences. Annotations on the 2022 bars indicate the absolute change (AC, in seconds) and relative change (RC, in %) in extra flight time over the 44-year period from 1979 to 2022.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/cfd5e34214100952cb53159c.png"},{"id":98774491,"identity":"9d0871eb-cab1-41a9-9def-fc50ddf98f3f","added_by":"auto","created_at":"2025-12-22 11:42:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2615705,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/600d89a2-b8b6-482e-b341-472ef44f18c4.pdf"},{"id":97787368,"identity":"80068644-a8ca-4cb1-84fa-98d115726e83","added_by":"auto","created_at":"2025-12-09 11:04:26","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":38010489,"visible":true,"origin":"","legend":"","description":"","filename":"KimandKimWindTurbclimatenpj2025supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-7910453/v1/6400ef82c008a6bf2970f297.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Combined Impact of Jet Stream and Turbulence on Long-term Trans-Oceanic Flight Routes over North Atlantic Ocean Using ERA5 Reanalysis","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eAn aircraft in cruise phase is influenced by upper-level atmospheric conditions. To minimize flight time and fuel consumption, flight operators optimize routes daily, by leveraging favorable jet streams\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e while avoiding weather hazards such as turbulence and deep convection\u003csup\u003e\u003cspan additionalcitationids=\"CR5 CR6 CR7\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Beyond these day-by-day operations, recent studies have highlighted the link between aviation and atmospheric variability on longer time scales. For instance, major climate variabilities such as El Ni\u0026ntilde;o\u0026ndash;Southern Oscillation (ENSO) or the North Atlantic Oscillation (NAO) are shown to significantly modulate flight times, optimal route locations, and turbulence exposure\u003csup\u003e\u003cspan additionalcitationids=\"CR10\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eGiven these close coupling, long-term climate change is expected to affect aviation operations by altering upper-level flow\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. This impact has been actively studied in the North Atlantic, one of the world's busiest air corridors, with a focus on how changes in jet stream characteristics affect flight times\u003csup\u003e\u003cspan additionalcitationids=\"CR14 CR15\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. These studies have quantified potential changes in flight times by directly computing optimal flight routes using climate model simulations, thereby isolating the impact of altered atmospheric states. Such routes are idealized but they reflect operational planning and thus provide a realistic baseline\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Although uncertainties in climate models remain\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, projections suggest that strengthening of the westerly jet could increase roundtrip flight durations in the future\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. While these time increases may appear modest, they can translate into substantial economic costs for the fuel-sensitive airline profits\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. From an environmental perspective, longer flights imply higher emissions, which contribute to radiative forcing and further accelerate warming\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Understanding this two-way interaction is therefore important for both aviation and climate science. Yet despite these insights, much of the existing literature has focused narrowly on flight efficiency, often overlooking operational safety due to weather hazards closely related to jet systems.\u003c/p\u003e\u003cp\u003eAviation turbulence poses a direct threat to flight safety and is a leading cause of weather-related injuries in aviation operations\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Among various kinds of turbulence, clear-air turbulence (CAT) is of particular importance, which constitutes a substantial fraction with recent studies suggesting up to 70%\u003csup\u003e24,25\u003c/sup\u003e and is closely related to upper-level jet systems. To take advantage of tailwinds, optimal routes are often positioned close to strong jets (in contrast, placed away in the opposite direction)\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, where CAT is climatologically frequent\u003csup\u003e\u003cspan additionalcitationids=\"CR27 CR28\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e and dynamically favored\u003csup\u003e\u003cspan additionalcitationids=\"CR31 CR32\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. In practice, operators routinely adjust routes to avoid expected turbulence. This operational necessity becomes increasingly critical as many studies project a significant future increase in CAT\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan additionalcitationids=\"CR35 CR36\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e with some evidence suggesting this trend is already emerging\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan additionalcitationids=\"CR39\" citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eAs CAT becomes more prevalent, it will not only increase the direct threat to flight safety but also reduce operational efficiency by forcing less optimal routes to avoid turbulent areas\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Some of these inefficiencies may already be embedded in current operations: improved forecasting systems and heightened awareness of turbulence likely reduce observed turbulence encounters, masking the increasing trends suggested by previous studies\u003csup\u003e\u003cspan additionalcitationids=\"CR43\" citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. However, these hidden costs have not been explicitly quantified in the context of growing turbulence. Moreover, most climatological assessments of CAT measure temporal changes over fixed locations, which do not explicitly account for the variability of daily flight routes optimized relative to jet and its associated CAT hotspots. Therefore, a more comprehensive assessment of aviation under a changing climate must consider not only changes in jet stream characteristics but also the operational implications of increasing turbulence.\u003c/p\u003e\u003cp\u003eHerein, we use an integrated route optimization framework to assess the impact of 44 years of atmospheric changes on transatlantic aviation. Specifically, we first analyze the characteristics and long-term trends of wind-optimal routes (WORs), with a focus on directional asymmetry and turbulence exposure. We then quantify the cost of safety by generating turbulence-avoiding routes with varying avoidance strength and comparing them to WORs. Finally, tracking the trend in this cost reveals the evolving trade-off between flight efficiency and safety, offering new insights that are more realistic to the challenges facing aviation in a changing climate.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eWe used ERA5 reanalysis data from the ECMWF\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, on a 0.25\u0026deg; grid and 3-hourly intervals to evaluate atmospheric conditions at cruising altitude (200 and 250 hPa). WOR, which minimize travel time by leveraging cruising-level winds, between New York (JFK) and London (LHR) were calculated for eastbound (EB) and westbound (WB) flights, with departures at 00, 06, 12, and 18 UTC, for each day between 1979 and 2022.\u003c/p\u003e\u003cp\u003eClear-air turbulence (CAT) was diagnosed using the TI3, which was designed to capture multiple sources of clear-air turbulence near jet stream\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e,\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e and showed good performance against observations\u003csup\u003e\u003cspan additionalcitationids=\"CR49\" citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e. The intensities of CAT were categorized using thresholds based on rarity in the probability distribution. For example, we assumed Moderate-Or-Greater intensity CAT (MOG-CAT) occurs within grid cells with TI3 values exceeding the 98th percentile\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e. Further methodological details are described in the Methods.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eCharacteristics of optimal flights\u003c/h2\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates the characteristic spatial configuration of the jet stream, CAT, and WORs under daily weather conditions at cruising altitude (250 hPa). EB and WB WORs are shown alongside the great-circle route (GCR), which represents the shortest path between JFK and LHR; without wind, the WOR is reduced to GCR. In Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea, the EB WOR (green) follows the core region of strong westerly to benefit from tailwinds, whereas the WB WOR (magenta) detours northward to minimize headwind. Because regions of intense CAT broadly coincide with areas of strong wind speed, the EB WOR passes through turbulent zones, while the WB WOR generally remains outside of them. A similar configuration is found in another representative case (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe linkage between upper-level wind fields and WOR is also apparent at seasonal and longer timescales. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea presents the seasonal mean wind speed at 250 hPa and the climatological distribution of WORs over the 44-year period. In all seasons, EB WORs are generally concentrated along the axis of strong westerly flow, with some spread that reflects daily variation of weather patterns (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In contrast, WB WORs show a broader meridional distribution, with their highest density located north of the GCR to avoid headwinds near the jet core. The spread of WB WORs is largest in winter when the winds are the strongest. These spatial features are consistent with earlier studies on the influence of jet stream structure on optimal transatlantic routing\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. In addition to the climatological features, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb shows the linear trends in seasonal WOR density and wind speed. In many regions, the trends in WOR density coincide with those in wind speed, especially where the wind trend is located either north or south of the GCR, rather than directly overlapping it. This alignment is particularly evident in spring, when wind speed trends exhibit a dipole pattern around the GCR. Similar patterns are found at 200 hPa (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eClear-air turbulence along optimal routes\u003c/h3\u003e\n\u003cp\u003eWhile upper-level winds play a central role in shaping optimal routes, CAT poses constraints on flight safety and efficiency. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea shows the climatological distribution of MOG-CAT occurrence at 250 hPa, with the seasonal mean wind speed. MOG-CAT occurs most frequently on the cyclonic shear side of the jet, with maxima near its exit region\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. A secondary peak is found near the southern tip of Greenland, likely associated with partially resolved mountain-wave activity\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. Frequency peaks in winter and appears to be lowest in summer. However, summer values must be interpreted with caution as TI3 is not designed to capture convectively generated turbulence and shows the weakest skill against observations during that season\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe absolute change in MOG-CAT probability from 1979 to 2022 (estimated from linear trend, see Methods) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb, with trends in wind speed. The increasing trend in CAT frequency is most significant in spring, especially south of the GCR. Winter trends are generally positive but spatially limited, while summer and autumn show little change. Similar patterns appear at 200 hPa, but both the occurrence frequency and absolute changes are more pronounced than at 250 hPa (Fig. S2).\u003c/p\u003e\u003cp\u003eUnlike the close correspondence between wind speed and WORs (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), CAT trends exhibit poor spatial alignment with wind trends. This spatial mismatch is understandable: CAT typically occurs not within straight jet cores, but along curved segments associated with upper-level ridges and troughs\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. As these features are transient\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e and tightly coupled to synoptic weather systems, they are often filtered out in temporal averaging. However, daily route optimization is shaped by such transient features.\u003c/p\u003e\u003cp\u003eTherefore, the crucial next step is to characterize the CAT encounter risk along these dynamic routes rather than using a static grid-based analysis. To achieve this, we introduce the MOG-CAT Area Ratio (MCAR), a proxy for MOG-CAT encounter probabilities along the route's vicinity. To highlight the impact of dynamic routing, we compare the MCAR for WORs against two static references: The great-circle route (GCR) and the WOR Domain (see Methods and the Fig. S3 for details).\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea shows the 44-year average of MCAR as a heatmap, with route types in columns and seasons in rows. The result for the broad WOR domain provides a baseline of MOG-CAT frequency over the North Atlantic corridor. Its annual mean MCAR of 2.8% exceeds the 2% threshold used to define MOG-CAT, implying frequent turbulence over the North Atlantic due to strong climatological jet. When focusing area is confined to GCR vicinity, the MCAR increases to 3.7%, as the region more closely overlaps with the climatological jet axis. A clear directional asymmetry appears in dynamically optimized WORs. Compared to GCR, EB WORs consistently show higher MCAR values (annual average of 4.6%) while the WB WORs exhibit lower MCAR values (2.8%). In winter, the probability of encountering MOG-CAT near EB routes is nearly twice that of WB routes. This supports more strongly the interpretation of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e: EB WORs fly closer to the turbulent jet stream for tailwinds, while WB WORs avoid it, leading to contrasting turbulence exposures. Interestingly, the MCAR for Roundtrip (RT) WORs (3.7%) is almost identical to that of GCR. This suggests that while daily EB and WB routes diverge tactically, these deviations occur almost symmetrically around the GCR. Consequently, their opposing turbulence exposures tend to cancel out over the long term, causing their average exposure to converge with that of the geographically direct path. Similar patterns appear at 200 hPa (Fig. S4), but directional contrasts are more pronounced: EB shows greater mean MCAR due to more frequent MOG-CAT occurrence at that level (Fig. S2).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWe next examine the long-term trends in MCAR, presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb (slope) and Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec (relative change from 1979 to 2022). For static references, the WOR domain exhibits a statistically significant increasing trend in annual mean MCAR (+\u0026thinsp;0.04%/decade). Seasonally, all seasons except summer exhibit significant increases, with the strongest trend in spring and a more modest but still significant trend in winter. These increasing trends are more pronounced over GCR vicinity. Notably, the dynamic WORs again exhibit directional asymmetry: EB WORs exhibit consistently stronger increases than the GCR, while WB WORs show weaker changes. This contrast peaks in spring, when MCAR for EB WORs increased by more than 40% over 44 years. This substantial increase is attributed to the spatial overlap between long-term trends in flight routes (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and CAT frequency (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e): The region of increasing CAT in spring located south of the GCR, which is precisely where EB WORs have become more concentrated whereas WB WORs are more dispersed.\u003c/p\u003e\u003cp\u003eIn summary, CAT encounter risk has increased significantly over the past four decades, with its magnitude strongly dependent on routing strategy. This leads to the important next question of how these changes in turbulence risk can be translated to flight efficiency.\u003c/p\u003e\n\u003ch3\u003eThe turbulence-avoidance routes and extra flight times\u003c/h3\u003e\n\u003cp\u003eTo answer above question, this section focuses on flight time. We investigate the degradation in flight efficiency by comparing the standard wind-optimal routes (WORs) with their turbulence-avoiding counterparts. We adopted a simplified avoidance strategy where aircraft were forced to completely avoid regions where diagnosed turbulence exceeds a certain threshold while minimizing flight time. Although idealized, this strict constraint approach helps clarify the cost of turbulence avoidance, providing estimates of reduced efficiency caused by horizontal deviation. The limitations of this approach and more realistic operational strategies are addressed in the Discussion.\u003c/p\u003e\u003cp\u003eFigure S5 introduces the concept of turbulence-avoiding routes (TORs) using an example case from October 19, 2002, showing how they deviate from the WOR to avoid turbulent regions. Each TOR is indicated by a minimum CAT threshold (percentile-based, e.g., s97). The WOR (black line) is optimized solely to minimize flight time and therefore passes through turbulent areas. In contrast, TORs diverge from the WOR depending on the threshold, with stricter constraints (lower percentiles) resulting in longer flight times due to greater deviations (see legend).\u003c/p\u003e\u003cp\u003eAs a result, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates how changing atmospheric conditions have affected both flight safety and efficiency. A representative TOR (blue line) avoiding MOG- CAT is compared to WOR (black line). In Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea, the risk time\u0026mdash;time spent in MOG-CAT region\u0026mdash;along the WOR has increased significantly over the past 44 years. In contrast, TOR has maintained consistently low risk time (non-zero values are due to the exclusion of avoidance constraints near airports). As a result, the difference in turbulence exposure between two routes has steadily widened. However, maintaining safety comes at a cost. Shifting focus to flight time (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb), the WOR roundtrip flight time has slightly decreased over the same period, suggesting a modest gain in efficiency under changing jet stream conditions. In comparison, the flight time penalty for avoiding turbulence\u0026mdash;defined as difference between TOR and WOR (red dashed line)\u0026mdash;has increased steadily and significantly. This reveals that the price of maintaining safety has grown substantially over time. Furthermore, unlike WOR, the TOR no longer shows a statistically significant decrease in total flight time.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo further investigate the safety-efficiency trade-off, we extend analysis to TORs with varying CAT intensities (s97 to s99.6; see Fig. S5). Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea presents the 44-year mean characteristics of these strategies, showing the relative difference in risk time and flight time compared to WOR. Stricter avoidance strategies (i.e., lower percentile thresholds) yield greater reductions in mean risk time (red bars) at the cost of a larger flight time penalty (blue bars). This penalty is directionally asymmetric as shown in lower panel; EB routes, which are more frequently exposed to turbulence, require a greater flight time sacrifice than WB routes. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb reveals how this trade-off has evolved over the 44-year period. While WOR shows decrease in a net flight time due to favorable wind changes, this efficiency gain is progressively diminished as the avoidance constraint becomes stricter. For the most stringent strategy (s97), the gain disappears entirely, leading to a statistically significant increase in total flight time. This reversal demonstrates that the implicit cost of ensuring safety has grown so substantially that it can now outweigh the efficiency benefits gained from a changing climate.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eWe finally assess how the implicit cost of safety from turbulence has grown over time. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows this cost across different avoidance strategies over the 44-year period, defined as the additional flight time required for turbulence avoidance compared to WOR baseline. Directionally, the flight time penalty is consistently higher for EB routes, both in its long-term average and its increase. In terms of avoidance strength, stricter strategies (lower thresholds) incur larger absolute increases in penalties. In contrast, the relative increase in the penalty is most pronounced for strategy avoiding only the most severe turbulence. This finding implies that more intense CAT has increased more rapidly, as consistent with prior research, and makes it difficult to ignore the growing cost of avoidance.\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe increasing time penalty for maintaining flight safety against turbulence carries substantial operational and environmental consequences. For a representative case (s98, avoiding MOG-CAT), the additional flight time required to avoid turbulence has grown by approximately 150 seconds per crossing over the past four decades. The extrapolation to transatlantic traffic estimates that this change corresponds to an additional annual cost of \u003cspan\u003e$\u003c/span\u003e50\u0026nbsp;million in fuel and an extra 160\u0026nbsp;million kilograms of CO\u003csub\u003e2\u003c/sub\u003e emissions compared to 44 years ago, using standard assumption for transatlantic traffic (~\u0026thinsp;300 daily crossings) and aircraft operations (1\u0026thinsp;~\u0026thinsp;gallon/sec fuel burn, \u003cspan\u003e$\u003c/span\u003e3/gallon fuel cost, 9.6 kg CO\u003csub\u003e2\u003c/sub\u003e/gallon). This change may be even more pronounced for flights cruising near 200 hPa, where MOG-CAT occurrence is more frequent (Fig. S6).\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eUsing four decades of reanalysis data, we found that the North Atlantic optimal route has shown a marked rise in route along-route CAT exposure and a concurrent growth in the time cost of maintaining safety. While wind conditions have generally become more favorable for shortening optimal roundtrip flight times, the additional time required to avoid turbulence has increased such that the safety cost can offset (and locally reverse) efficiency gains. The magnitude and trend of this cost depend sensitively on routing strategy. We further discuss the details and implications of results.\u003c/p\u003e\u003cp\u003eThe main results including pronounced directional asymmetries arise from interplay between the atmospheric structure and routing behavior. The high frequency of CAT near jet streams is supported by both theory and observation. Mechanisms include strong vertical wind shear favoring Kelvin\u0026ndash;Helmholtz instability\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e,\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e, reduced inertial stability especially in south of the jet, and the emission of gravity waves via ageostrophic adjustment in jet exit regions\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. Consistent with these processes, aircraft observations indicate that up to two-thirds of CAT events occur in jet vicinities\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Therefore, the position of flight route relative to jet stream strongly influences their CAT exposure.\u003c/p\u003e\u003cp\u003eCrucially, routing decisions are made daily, and both the jet and associated CAT hotspots vary strongly in space and time. Because the jet-CAT system is not stationary, grid-based climatology could dilute these localized and transient features, obscuring the signals apparent along actual optimal routes. Previous climatological assessments typically measured CAT frequency or trends at fixed locations over daily mean basis, an approach directly applicable for fixed paths but not for variable transatlantic traffic. In practice, about half of crossings follow the North Atlantic Organized Track System (NAT-OTS), issued daily by Air traffic control and resembling WOR in construction. Our route-based result show that CAT encounter probability along EB WORs is more than GCR. Moreover, its increasing trend is also pronounced, especially in spring when region of increasing CAT and preferred routing overlaps. Thus, a more realistic assessment of CAT impact to aviation should account for the dynamic characteristics of operation.\u003c/p\u003e\u003cp\u003eThe increasing CAT could also affect flight time. Solely considering wind changes, results shows that the long-term decreasing trend in the annual mean roundtrip flight time along WORs over the 44-year period, although trend is not statistically significant when disaggregated by direction (EB and WB). It is also seen in seasonal average of spring and summer (Fig. S7). Notably, this trend is absent in GCRs, suggesting that the reduction in flight time is specific to dynamically optimized routes. We attribute this trend to long-term structural changes in the North Atlantic jet stream (Fig. S8). Relative to the climatological mean (contours), the jet has intensified near its core while weakening along its flanks, particularly in spring. Thus, EB WORs can leverage the strengthened jet core, while WB WORs are routed through weakened headwind regions along the jet edge. Together, these changes contribute to the overall reduction in roundtrip flight time.\u003c/p\u003e\u003cp\u003eThe decrease in roundtrip flight time identified in our reanalysis-based study aligns qualitatively with recent climate model projections. Cheung et al. (2022)\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, using an ensemble of CMIP5 models combined with wind-optimal routing methodology, project a future reduction in transatlantic flight times regardless of direction. This contrasts with earlier studies based on single CMIP3\u003csup\u003e15\u003c/sup\u003e or and small ensemble of CMIP5 \u003csup\u003e14\u003c/sup\u003e, which predicted an increase in westbound and roundtrip travel time. These discrepancies are likely attributed to ensemble sizes and experimental design.\u003c/p\u003e\u003cp\u003eHowever, none of these assessments accounted for CAT. We show that when turbulence avoidance is imposed, increasing CAT could negate the efficiency gain from wind changes, which magnitude are strongly dependent on routing strategies. While projections of jet stream features remain uncertain\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e, the increase in CAT is consistently reported in both reanalysis and climate models\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. Considering that stronger CAT increase faster, efficiency reduction induced by turbulence avoidance cannot be ignored. Previous studies speculated that more prevalent turbulence under climate change might erode flight efficiency, but none quantified this cost. By directly comparing optimal and turbulence-avoiding routes, we provide the first multidecadal quantification of growing cost of maintaining safety against increasing CAT. It is noted that all discussions here are based on the assumption that there is no significant improvement on turbulence canceling technology that stabilizes aircraft in turbulent air.\u003c/p\u003e\u003cp\u003eThese results are based on an idealized framework assuming fully optimal routes and should not be interpreted as exact realization of past operational changes. Our aim is to assess isolated atmospheric effects influencing aviation operations. In the transportation and aviation sectors, technological advances have enabled partial implementation of optimal routing, and case studies have analyzed associated efficiency benefits. Beyond that, we suggest that atmospheric variabilities on longer time scales are at play: as turbulence continues to increase, the safety\u0026ndash;efficiency trade-off will intensify. The change in individual flights accumulated can translate into substantial economic and environmental loss, potentially feeding back to accelerate climate change itself. Therefore, understanding the evolving interaction between climate and aviation demands a multidimensional analytical framework, with joint consideration of meteorological dynamics, operational strategies, and systemic feedback.\u003c/p\u003e\u003cp\u003eThis study has several limitations mostly on aeronautical engineering in this study. Route optimization was restricted to horizontal dimensions assuming constant altitude and Mach number, although wind variation during flight was included. This simplification was motivated by various considerations. First, 3D optimization is computationally prohibitive in a climatological analysis. Second, these simplifications are consistent with our aim to isolate the atmospheric influence on flight efficiency, independent of aircraft type or engine performance. Fixed true airspeed together with constant altitude also allows fuel usage to scale linearly with flight time, simplifying cost interpretation and facilitating scenario comparisons. Moreover, aircraft flying on NAT-OTS normally maintain a constant altitude and airspeed, justifying our assumptions\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eA more critical limitation lies in the treatment of turbulence avoidance. In practice, flights often slow down or maneuver vertically in response to unexpected turbulence\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. Here, turbulence avoidance was modeled strictly in two dimensions, such that cost of avoidance was reduced to additional flight time. Unlike typical operations where flights deviate temporarily from the optimal route and then return, our framework assumed that aircraft could follow a newly optimized minimum-time path that simultaneously avoids turbulence, under the assumption of perfect knowledge at the planning stage. This idealized representation provides a transparent measure of the safety\u0026ndash;efficiency trade-off but inevitably departs from operational reality. Future work should incorporate more realistic 3D avoidance strategies and the uncertainties of turbulence forecasting to bridge this gap.\u003c/p\u003e\u003cp\u003eMethodologically, trend detection and turbulence diagnostics present further challenges. The identified trends based on seasonal-mean regression were consistent across alternative approaches. Similar results were obtained when seasonal medians or the non-parametric Mann\u0026ndash;Kendall test were applied. The assumption of residual independence required for the linear regression significance test was also satisfied in most cases, supporting the statistical validity of the regression-based trends and temporal changes (relative and absolute) estimated from them. Diagnosing CAT with a single index is inherently imperfect, but the TI3 index was selected for its integrated formulation and superior performance in prior studies. Future research could build on this by employing multiple turbulence diagnostics in an ensemble framework to enable probabilistic assessments of changing turbulence risk.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eData\u003c/h2\u003e\u003cp\u003eThis study used the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis to analyze atmospheric conditions and compute optimal flight routes for the 44-year period from 1979 to 2022\u003csup\u003e45\u003c/sup\u003e. We utilized horizontal winds (u, v), temperature (T), and geopotential height (z) at a 0.25\u0026deg; horizontal resolution and 3-hourly intervals. The data were primarily analyzed on the 250 hPa and 200 hPa pressure levels, representing typical cruising altitudes, with neighboring levels used for vertical derivatives.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eTurbulence Diagnostics\u003c/h3\u003e\n\u003cp\u003eSince current resolution of reanalysis data (and operational NWP models) cannot directly resolve aviation-scale turbulence, we employed an empirical index to diagnose turbulence from large-scale flow disturbances. We adopted the TI3 index, which is well-validated for its high predictive skill for CAT near the jet stream as it considers multiple generation mechanisms\u003csup\u003e\u003cspan additionalcitationids=\"CR48 CR49 CR50\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e. To categorize turbulence intensity, a common methodology for climatological turbulence assessment is employed: we used threshold based on its rarity indicated by percentile value from its probability density function (PDF). The PDF is constructed over the Northern Hemisphere mid-latitudes (20\u0026deg;N\u0026ndash;60\u0026deg;N) for the entire study period\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. The primary threshold for Moderate-or-Greater CAT (MOG-CAT) was defined as the 98th percentile (top 2%) of the distribution\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003ch3\u003eRoute Optimization Algorithms\u003c/h3\u003e\n\u003cp\u003eThis study focuses on the North Atlantic flight corridor, one of the world's busiest aviation regions, accounting for a substantial portion of global air traffic and emissions\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Following the previous studies\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, the New York (JFK) to London (LHR) route was selected as the representative of transatlantic flight. This choice is supported by the strong spatial agreement between the wind-optimal routes of JFK-LHR and the operational North Atlantic Organized Track System (NAT-OTS), where much of the daily traffic is concentrated. Wind-optimal routes between diverse airport pairs crossing the North Atlantic exhibit an organized spatial distribution\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, indicating that the findings derived from the JFK\u0026ndash;LHR case can be extended to broader regional traffic patterns.\u003c/p\u003e\u003cp\u003eOptimal routes were calculated using A* path-finding algorithm, which identifies the least-cost path in a weighted node-network. In this framework, the connection weight between nodes was defined as the flight time, simulated by assuming the aircraft cruises at a constant altitude and Mach number. Our methodology follows the framework of Cheung (2018)\u003csup\u003e\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e with several modifications for computational efficiency. We constructed the node network on a cubed-sphere grid, which avoids polar convergence and ensures homogeneous coverage, and computed the connection weights directly from ERA5 data using GPU parallelization. The grid resolution is about 1 degree, since there are about 91 \u0026times; 91 nodes per one face. These weights were archived at 3-hour intervals for the entire study period (1979\u0026ndash;2022). The A* algorithm then determined the optimal routes by referencing the pre-computed networks, accounting for the temporal progression of flights through the varying wind and turbulence fields. A nearest-matching approach was applied to select the appropriate 3-hourly weights for each path segment. The structure of node-network and neighboring scheme are presented in Fig. S9.\u003c/p\u003e\u003cp\u003eWithin this framework, two types of routes were generated:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eWind-Optimal Route (WOR): This is the time-minimal path, computed using only the flight time as the cost function. It serves as the baseline route representing maximum flight efficiency.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eTurbulence-Avoiding Route (TOR): This is the safety-conscious path, designed to avoid regions where TI3 values exceed specified intensity thresholds (see Sec 2.1) while minimizing flight time. This was implemented as a hard-constraint approach, where a near-infinite cost penalty is assigned to any path segment encountering the specified turbulent region; however, such cost penalty was not applied within 500 km of the origin and destination to ensure the algorithm could always find the optimal solution. We tested multiple thresholds (e.g., 97th, 98th, 99.1th, and 99.6th percentiles) to assess the effect of different avoidance strengths.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eTrend Quantification\u003c/h2\u003e\u003cp\u003eTo quantify long-term changes, a linear regression model was applied to the 44-year time series (1979\u0026ndash;2022) for each variable (e.g., MCAR, flight time) on a seasonal and annual basis. This provides fitted values for the start (ŷ\u003csub\u003e1979\u003c/sub\u003e) and end (ŷ\u003csub\u003e2022\u003c/sub\u003e) of the period, representing the amount of change over research periods without interannual variability. From these fitted values, we calculated:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eAbsolute Change: The difference between the fitted values (ŷ\u003csub\u003e2022\u003c/sub\u003e \u0026minus; ŷ\u003csub\u003e1979\u003c/sub\u003e).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eRelative Change: The absolute change divided by the starting value ([(ŷ\u003csub\u003e2022\u003c/sub\u003e \u0026minus; ŷ\u003csub\u003e1979\u003c/sub\u003e) / ŷ\u003csub\u003e1979\u003c/sub\u003e] \u0026times; 100%).\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eQuantification of Turbulence Encounter Probabilities\u003c/h2\u003e\u003cp\u003eTo quantify MOG-CAT occurrence in the vicinity of 6-hourly optimal routes, we introduced a proxy called the MOG-CAT Area Ratio (MCAR). For each route, a 'route vicinity' was defined as the set of 2\u0026deg;x2\u0026deg; grid cells that the route intersects. The MCAR was then calculated as the ratio of the MOG-CAT area within this vicinity to the total area of the vicinity. This area-based approach, rather than sampling only along a route line, enhances statistical stability by enlarging the sampling domain and are in construction area weighted. To ensure temporal consistency, each 6-hourly route was segmented into 3-hour intervals then the MOG-CAT field was matched to each segment's valid time. Fig. S3 illustrates the procedures for calculating MCAR for WOR. Note that the MCAR is calculated for every 6-hourly WOR. MCAR for two static references are additionally considered to highlight the impact of dynamic routing: (1) The great-circle route (GCR), for which the MCAR was calculated using the same route-vicinity method as the WOR. (2) the 'WOR Domain' defined as a fixed rectangular area that encompasses all WORs during the study period (36.5\u0026deg;-67.25\u0026deg;N, 0\u0026deg;-75.5\u0026deg;W).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eDATA AVAILABILITY\u003c/h2\u003e\u003cp\u003eThe ERA5 reanalysis dataset is publicly accessible from the Copernicus Climate Change Service Climate Data Store (CDS, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cds.climate.copernicus.eu\u003c/span\u003e\u003cspan address=\"https://cds.climate.copernicus.eu\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, last access: 10 October 10, 2025; ref. 45).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eCODE AVAILABILITY\u003c/h2\u003e\u003cp\u003eThe codes supporting the findings of this study are developed by the corresponding authors and available on reasonable request.\u003c/p\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFUNDING STATEMENTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is funded by the Korea Meteorological Administration Research and Development Program (Grant KMI2022-00310 and KMI2022-00410)\u0026nbsp;and supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2025-24683550).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eACKNOWLEDGMENTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors thank the Korea Meteorological Administration and the National Research Foundation of Korea for their continuous support.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAUTHOR CONTRIBUTIONS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualization: J.H.K., J.-H.K. Methodology: J.H.K., J.-H.K. Investigation and visualization: J.H.K. Supervision: J.-H.K. Writing–original draft: J. H.K. Writing–review and editing: J.-H.K.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCOMPETING INTERESTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eInternational Civil Aviation Organization (ICAO). \u003cem\u003eNorth Atlantic Operations and Airspace Manual\u003c/em\u003e. https://www.icao.int/EURNAT/Pages/nat.aspx (2025).\u003c/li\u003e\n\u003cli\u003eWells, C. A., Williams, P. D., Nichols, N. K., Kalise, D. \u0026amp; Poll, I. Reducing transatlantic flight emissions by fuel-optimised routing. \u003cem\u003eEnviron. Res. Lett.\u003c/em\u003e \u003cstrong\u003e16\u003c/strong\u003e, 025002 (2021).\u003c/li\u003e\n\u003cli\u003eSridhar, B., Ng, H. K., Linke, F. \u0026amp; Chen, N. Y. 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Flight planning: node-based trajectory prediction and turbulence avoidance. \u003cem\u003eMeteorol. Appl.\u003c/em\u003e \u003cstrong\u003e25\u003c/strong\u003e, 78\u0026ndash;85 (2018).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7910453/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7910453/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTransatlantic aviation operations routinely enhance flight efficiency by leveraging daily jet streams, but they face growing safety risk from clear-air turbulence (CAT). Previous studies have assessed the climatological impacts of winds and turbulence separately, yet a comprehensive assessment integrating their effects along dynamically optimized flight routes has remained absent, despite the close relation between jet and CAT. Here, using an integrated routing framework applied to 44 years of reanalysis data, we provide the first multi-decadal quantification of safety-efficiency trade-off. While changing wind patterns shortened the fastest round-trip routes by about two minutes, the additional time required to avoid CAT has grown so substantially that it negates and even reverses these efficiency gains for the safest routes. This rising cost is driven by a significant increase in CAT, which disproportionately affects eastbound flights. Our findings highlight the need for integrated approaches to assess aviation\u0026rsquo;s evolving risks in a changing climate.\u003c/p\u003e","manuscriptTitle":"Combined Impact of Jet Stream and Turbulence on Long-term Trans-Oceanic Flight Routes over North Atlantic Ocean Using ERA5 Reanalysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-09 11:04:19","doi":"10.21203/rs.3.rs-7910453/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-25T08:21:10+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-24T17:26:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"313408024952750815895797794879017110420","date":"2026-02-11T16:15:33+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-17T00:12:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"267683387897264010041147827791664474512","date":"2026-01-12T14:17:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"284433662489634711525456779929732149337","date":"2025-12-10T13:41:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"297242101732381011430757975783933002927","date":"2025-12-07T10:06:13+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-05T10:01:40+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-02T04:49:02+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-28T13:34:08+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-24T13:05:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-10-24T13:02:07+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"577affab-002d-4f8c-8442-6a74ffd97199","owner":[],"postedDate":"December 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":59222870,"name":"Earth and environmental sciences/Climate sciences"},{"id":59222871,"name":"Earth and environmental sciences/Ocean sciences"}],"tags":[],"updatedAt":"2026-04-22T09:41:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-09 11:04:19","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7910453","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7910453","identity":"rs-7910453","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}