Hurricane Lidia originated from a tropical wave on 3 October 2023 (Pasch, 2024a). Between 3 and 5 October, it remained a disorganized system, marked by significant uncertainty in both track and intensity forecasts (Fig. S1 in the Supplement). From 5 to 7 October, Lidia generally tracked westward under the influence of a mid-level ridge but remained poorly organized. By 8 October, the subtropical jet stream was positioned between 20 and 30° N, aligned with Lidia's latitude (Figs. A1 and 2 in Appendix A). At this stage, a mid-to-upper-level trough approaching the Baja California Peninsula began to influence Lidia's motion, steering the system northward and subsequently eastward.

At approximately 18:00 UTC on 9 October, Lidia entered a phase of intensification (Pasch, 2024a). This intensification was accompanied by a northeastward turn induced by an approaching trough from the northwest, although considerable spread in forecast trajectories persisted at this time (Fig. 1a). On 10 October, Lidia underwent RI, with maximum sustained winds increasing by 82 km h⁻¹ over an 18 h period, ultimately reaching a peak intensity of nearly 220 km h⁻¹. This placed Lidia at Category 4 on the Saffir–Simpson Hurricane Wind Scale.

Figure 1a shows the trajectories of Hurricane Lidia's ensemble members from the ECMWF, initialized at 00:00 UTC on 8 October. The trajectories of the most intense members are positioned further north relative to those of the lower-intensity members, relative to the NHC best track. This suggests that the trough's proximity influenced event predictability, increasing uncertainty in both track and intensity forecasts (Figs. A1 and 2). This pattern aligns with findings from Callaghan (2020) and Sato et al. (2020) in the Atlantic basin, indicating the contribution of synoptic environment to the low predictability of both trajectory and intensity of the cyclone, as here evidenced by the large spread in Fig. 1a, b. Furthermore, based on the temporal evolution of Lidia's MSLP and wind speed (Fig. 1b), seven members in the P80-ensemble group, along with the ensemble mean, successfully simulate Lidia's rapid intensification, exceeding the RI threshold.

As is well known and formulated in the Emanuel model (Emanuel, 1986) and used in Chen et al. (2021), the oceanic and atmospheric variables such as Ts, T0 and saturation parameters (Eq. 1), determine the PI that the TC could acquire. Both ensembles display similar PI distributions around Hurricane Lidia (Fig. 2a, b). However, somewhat unexpectedly the P20-ensemble shows a higher PI value (∼ 250 km h⁻¹) compared to the P80-ensemble (∼ 240 km h⁻¹), although the differences are not statistically significant (not shown).

Based on the PI time series (Fig. 2c), this diagnostic variable alone does not appear to support Lidia's RI. Therefore, this suggests that thermodynamic factors are necessary but not sufficient to trigger RI. This finding is consistent with recent studies (e.g., Gilford, 2021; Shi and Chen, 2021) which suggest that while PI provides an upper bound, the actual intensification process is modulated by environmental dynamics, including ventilation and vertical motion induced by synoptic-scale features such as upper-level troughs. These results highlight the potential value of ensemble forecasts for anticipating RI events under favorable environmental and synoptic conditions. In the following sections, we examine the temporal evolution and structural characteristics of the large-scale dynamical forcing, including the trough interaction, to support this interpretation.

Similarity, the spatial SST differences between the P80- and P20-ensembles (Fig. 3a–f) reinforce the conclusion that thermodynamic conditions alone do not explain the contrasting intensification outcomes. While some localized differences exceeding ±5° appear at specific time steps, these do not persist or align consistently with the RI period. The warm anomalies observed in the P20-ensemble are mainly displaced to the north and northeast of Lidia's core. This spatial misalignment suggests that, despite slightly warmer SSTs, the coupling between oceanic energy supply and inner-core dynamics was likely suboptimal.

Statistical significance markers confirm that most SST anomalies are not spatially coherent enough to produce systematic differences in PI. This is consistent with the similar PI fields seen in both ensembles (Fig. 2a, b) and the absence of a clear thermodynamic advantage during the intensification period. Therefore, these SST patterns likely played a secondary role compared to the dynamically driven processes, such as enhanced vorticity advection and upper-level divergence.

This supports the notion that SSTs, in this case, provided a necessary but not sufficient condition for RI. The findings from Bister and Emanuel (2002), Fischer (2018), and Fischer et al. (2019) reinforces this view by emphasizing that, without favorable upper-level forcing and adequate storm structure, warm SSTs alone are insufficient to trigger RI, even when PI values appear theoretically consistent.

Since SST fail to explain the differences observed among the ensemble members in Lidia's intensification, we examine the mid- and upper-level dynamic environment. Figure 4 shows the eastward progression of a trough in both ensemble groups. The trough is notably broader in the P80-ensemble, particularly from time step +55 h. At 250 and 300 hPa (Fig. 4a, b), the isohypses in the P80-ensemble exhibit substantial deformation toward Lidia. The trough deepens further at 500 hPa (Fig. 4c), extending southward to approximately 20° N. This southward intrusion brings the trough into closer proximity with the tropical cyclone, especially in the RI ensemble members, where a more pronounced elongation is observed. This configuration likely favored a moist and unstable environment ahead of the cyclone, while simultaneously enhancing vorticity advection and synoptic-scale ascent.

Such a configuration is consistent with previous findings on optimal trough–tropical cyclone interactions (e.g., Hanley et al., 2001; Fischer et al., 2019), which suggest that intensification is favored when the trough approaches from the northwest at an appropriate distance. Although Fischer et al. (2019) noted that narrower upper-tropospheric troughs may be more conducive to RI, the enhanced interaction observed here may result from the deeper and more equatorward positioning of the broader trough in the RI group (particularly at +45 and +55 h in Fig. 4c). Additionally, although our analysis focused primarily on dynamical variables, we acknowledge that mid-level tropospheric humidity, particularly the intrusion of dry air, may also have influenced the timing or suppression of RI in some ensemble members, as highlighted in recent work by Fischer et al. (2023). A more detailed analysis of the humidity and ventilation effects is presented in later sections.

The EFC is computed to diagnose the trough-TC interaction in Hurricane Lidia. The results indicate that P80-ensemble exhibits significantly higher EFC values compared to the P20-ensemble group. These differences begin to emerge around +40 h and become significant between +50 h and +80 h just before and during Lidia RI period (Fig. 5), suggesting that enhanced EFC may have contributed to the onset and maintenance of RI in the P80 members. P80-ensemble is closely aligns with ERA5 reanalysis (exceeding 10 m s⁻¹ d⁻¹ during RI period). These elevated EFC values are consistent with the findings of DeMaria et al. (1993) for the North Atlantic basin, where EFC values greater than 10 m s⁻¹ d⁻¹ serve as an indicator of a trough-TC interaction. Therefore, the obtained EFC values highlight a strong interaction between Lidia and the trough, suggesting that dynamic forcing, estimated using a QG diagnostic framework, specifically the Trenberth formulation enhances vertical motion and may contribute to upper-level divergence, potentially triggering RI. This behavior in the Pacific is analogous to the quasi-stationary effect of the tropical upper tropospheric trough (TUTT) in the Caribbean, previously analyzed by Sanders (1983). However, unlike the Caribbean TUTT, which tends to be more persistent and conducive to cyclogenesis, the trough interacting with Hurricane Lidia in the Pacific was transient and engaged with an already mature TC. While we do not explore track changes in detail here, prior analyses suggested that this synoptic feature may have also influenced Lidia's trajectory in earlier initializations. Nonetheless, our focus remains on the intensification phase. These types of interactions are particularly relevant for hazard assessment, as they can increase the risk for densely populated areas in Mexico during late summer, when TCs are most frequent in the eastern Pacific basin (López-Reyes and Meulenert Peña, 2021).

To assess the dynamical processes supporting Lidia's intensification, EPS outputs during the RI period are compared with ERA5 fields. Although quasi-geostrophic diagnostics are typically applied in extratropical contexts, this approach is particularly relevant in the northeastern Pacific, where the presence of the subtropical jet during the boreal autumn increases the likelihood of TC-subtropical jet stream (Hanley et al., 2001). These interactions can play a key role in TC intensification and recurvature, especially in a region where high-resolution forecasts remain limited.

In Fig. 6a and b, the ∇⋅Vag > 0 values, associated with the trough and jet streak, are located to the northeast of Lidia. This configuration strongly favors enhanced upper-level divergence over Lidia and acts as a mechanism that drives upward motions. The quasi-geostrophic ∇⋅Vag is notably higher in P80 than in P20-ensemble (Fig. 6a–c); P80-ensemble closely matches ERA5 across nearly all regions surrounding Lidia (Fig. 6d), suggesting a stronger forcing induced by the interaction with the trough and jet streak.

Figure 6e reveals distinct differences in the evolution of ageostrophic divergence between the two ensemble groups. The P80-ensemble shows consistently higher values of ageostrophic divergence, particularly between +50 and +75 h, coinciding with Lidia's RI period. In contrast, the P20-ensemble exhibits lower and declining values during this period, indicating weaker dynamical forcing. ERA5 closely follows the P80-ensemble pattern, supporting the physical credibility of the ensemble signal. These results highlight the role of upper-level divergence and jet-induced ascent in supporting RI in the P80-ensemble.

According to the quasi-geostrophic theory, regions with positive (negative) vorticity advection are associated with upward (downward) vertical motions (Bluestein, 1992). In Fig. 7a and b, V⋅∇(ξ+f) is associated with a trough configuration, depicting predominant positive (negative) values in front (behind) of the trough axis. In the same way, V⋅∇(ξ+f) shows stronger and statistically significant positive values near Lidia's position in P80 compared to P20-ensemble (Fig. 7c); in addition, a branch with positive vorticity advection values around Lidia is only identified in P80-ensemble, and similar to ERA5 (Fig. 7d). The above is consistent with the greater proximity of the trough to Lidia in P80-ensemble, highlighting a more intense cyclonic vorticity advection over Lidia (also at earlier time steps; not shown). However, we acknowledge that part of this signal also reflects the contribution from the TC circulation itself. Nonetheless, at the synoptic scale, coherent differences associated with the trough's position and structure are clearly discernible between ensemble groups. Therefore, the trough-TC interaction is more robust in P80 than in P20 as indicated earlier with the EFC metric. This finding shows that a mid- and upper-levels trough can facilitate the development of a moist layer (Wu et al., 2015), contributing to Lidia intensification.

Figure 7e confirms the stronger vorticity forcing in the P80-ensemble throughout Lidia's intensification period. From time step +40 h onward, the P80 group exhibits consistently higher values of vorticity advection, peaking near the RI window (+55 to +70 h), while the P20 group remains consistently weaker, with little variability. The ERA5 line again follows the P80 trajectory, supporting the robustness of the dynamical signal. The statistically significant differences suggest that enhanced cyclonic vorticity advection, likely associated with the trough's mid- and upper-levels deformation, played a crucial role in promoting upward motion and intensification in the P80-ensemble.

The Q field in the P80-ensemble (Fig. 8a) shows a more intense upward forcing in the right region of the trough and extending to the divergence zone at the right entrance of the jet streak in comparison to P20 Q values (Fig. 8b). We selected the 500 hPa level because this level exhibited stronger trough elongation and clearer interaction with the TC. This contrast becomes even more evident when considering only RI members within P80-ensemble (Figs. 9 and A3) are selected and reinforces the idea of the influence of the trough in Lidia's RI. Based on Eq. (1), negative values of the forcing term Q correspond to regions of upward vertical motion induced by vorticity advection via the thermal wind (Dostalek, 2012). The areas surrounding Lidia are strongly influenced by the dynamical forcing induced by the trough and the jet streak in the P80-ensemble (Figs. 8c and A3). It is worth noting that the QG ascent patterns near the TC center may partially reflect contributions from the TC's own circulation. This implies that some contamination from the TC's inner-core vorticity cannot be completely ruled out. To assess this, we performed an additional localized filtering applied exclusively to the TC circulation, which effectively removes most of the mesoscale contribution of the vortex. As shown in Fig. A3, the resulting Trenberth forcing field reveals a clearer synoptic-scale signal associated with the trough and the jet-streak interaction, supporting that the large-scale forcing dominates despite minor contamination near the TC center.

This result is further supported by the ERA5 reanalysis data (Fig. 8d), which reveals a Q pattern similar to that observed in the P80-ensemble, but with greater intensity (note that ERA5 is only a member, not a composite group). In the absence of substantial thermodynamic differences (Figs. 2 and 3), these results highlight the dominant role of dynamic interaction between the trough, the jet streak, and the cyclone during RI. However, we acknowledge that tropospheric moisture, particularly the intrusion of mid-level dry air, may also have influenced the timing or suppression of RI in some members, as suggested by Fischer et al. (2023). These findings are particularly relevant for operational forecasting, also demonstrating the capability of the ECMWF EPS to simulate Lidia's RI, even under complex extratropical interactions influences.

The temporal evolution of the Trenberth forcing (Fig. 8e) reveals a clear and consistent signal in the P80-ensemble, with significantly more negative values, indicative of stronger synoptic-scale upward motion. This enhanced forcing begins slightly before the onset of Lidia's RI (which starts around +55 h), with statistically significant differences emerging at approximately +50 h, and peaks between +50 and +70 h. This temporal analysis supports a causal interpretation, suggesting that the synoptic-scale dynamical forcing likely contributed to initiating the RI process, rather than being a consequence of it. In contrast, the P20-ensemble shows much weaker and less coherent values throughout, indicating and absence of favorable dynamical support for RI.

In P80-ensemble, the trough is broader at Lidia's latitude, we found a difference of ≈ 300 km between the continuous and dashed contours and positioned closer to Lidia (around 500 km; Fig. 3a, b), in agreement with previous studies showing that favorable trough–TC interactions occur when the trough lies to the northwest at an optimal distance (Hanley et al., 2001). Significant differences are observed in both the amplitude and distance relative to Lidia (Fig. 2c). A similar pattern has been noted in some Atlantic basin cases (Hanley et al., 2001; Fischer et al., 2019; Sato et al., 2020), where effective trough–TC interactions are facilitated by a favorable distance, typically between 500 and 1000 km. However, Fischer et al. (2019) found that northwestward-approaching troughs were associated with the lowest rates of RI among the configurations they examined, with stronger intensification occurring when a cutoff low was located to the southwest of the TC. While Lidia's interaction does not fully match this optimal configuration, the proximity and orientation of the trough in the RI group (Fig. 3a) still suggest a dynamically favorable setup, compared to the less aligned structure seen in the non-RI group (Fig. 3b). Although the TC itself may contribute to modifying the trough structure in the P80-ensemble, it is noteworthy that a broader and deeper trough is already evident from the early forecast hours (see Fig. 4), suggesting a pre-existing synoptic configuration conducive to stronger TC–trough interaction.

These findings further support the hypothesis that dynamical forcing triggered Lidia's RI. In the P80-ensemble the trough is broader (∼ 300 km) and closer to Lidia (∼ 500 km; Fig. 10a, b). Evident differences are observed in both the amplitude and distance relative to Lidia (Fig. 10c). A similar configuration has been noted in some Atlantic basin cases (Hanley et al., 2001; Fischer et al., 2019; Sato et al., 2020), where effective trough–TC interactions require a favorable distance. This configuration is associated with different behavior of Virr at upper-levels (Fig. 10d–f), where the proximity of the trough's divergence zone enhances evacuation mass in the P80-ensemble (Fig. 10d) with significant Virr differences reaching ∼ 4 m s⁻¹ to the west-northwest of Lidia. Consequently, the superposition of both divergence zones amplifies the upper-level anticyclonic circulation, consistent with increasing EFC values in P80-ensemble toward Lidia (Fig. 5) strengthens upward motion and enabling RI.

On the other hand, the VWS remains moderate around Lidia's center in both ensemble groups, with values between 10 and 15 m s⁻¹ during RI period (Fig. 10g, h). Slightly higher VWS values are observed to the south of Lidia. To the west and near of Lidia center, VWS values are higher in P80-ensemble (around ∼ 5 m s⁻¹; Fig. 10i), though still within favorable ranges for intensification (Sharma and Varma, 2022). In contrast, regions beyond 2° radial distance in P80-ensemble show significantly lower VWS values, consistent with the position and shape of the jet stream. In P20-ensemble, a stronger jet stream is present north of Lidia, resulting in a more significant increase in VWS compared to P80-ensemble. Thus, the position and intensity of the jet streak relative to Lidia's position could potentially limit its intensification in P20-ensemble.

The results suggest that the upward motions induced by dynamical mechanisms associated with Lidia's interaction with a trough are consistent with the greater RH in P80, particularly near the center of Lidia and in the southern region where the trough appears to enhance its influence (Fig. 10j–l). This region coincides with the trough-cyclone interaction, where vertical motions are strongly driven by dynamical forcing. Additional checks performed for forecast hours prior and during to RI already showed discernible differences in RH between both ensembles, with higher mid-tropospheric humidity in P80-ensemble compared to the weak-intensifying members. The analyzed atmospheric patterns, including the dynamical forcing associated with the trough and jet streak, suggest that higher RH in P80 may be linked to increased condensation rates during air ascents around the center of Hurricane Lidia, leading to core warming (Emanuel, 1986; Zhang et al., 2013; Zhang and Emanuel, 2016). A moister mid-tropospheric environment can also suppress the intrusion of dry air, reduce ventilation and allow convection to remain deeper and more symmetric (Tang and Emanuel, 2010, 2012; Riemer et al., 2010; Ge et al., 2013). The enhanced latent heat release in such a moist environment strengthens the warm core and facilitates a greater and improved divergence in height, which facilitates the evacuation of mass from the core of the TC and favors a sustained ascent. This supports a more efficient upper-level outflow, effectively mitigating the detrimental influence of environmental VWS (Rios-Berrios and Torn, 2017; Qiu et al., 2020).

Specifically, the reduction in VWS observed in the P80-ensemble reflects a weakening of the environmental vertical wind gradient over the storm core. This occurs as the interaction with the upper-level trough enhances mass divergence aloft, weakening the upper-level winds immediately above the cyclone. Simultaneously, stronger and more vertically aligned convection, sustained by the higher mid-tropospheric humidity, reinforces the upper-level outflow and reorganizes the wind field around the vortex, effectively reducing the shear acting on the inner core (Riemer and Montgomery, 2011; Ge et al., 2013; Tang and Emanuel, 2012; Ryglicki et al., 2019). This process illustrates how the moist environment can offset the detrimental influence of environmental shear by reducing ventilation and enabling greater vertical mass flux within the TC core (Alland et al., 2021a), rather than by promoting a more efficient coupling between the outflow and the ambient flow (Figs. 10g–l and 11c, d). Therefore, the observed reduction in shear is better understood as a localized, dynamically and thermodynamically mediated adjustment rather than a broad environmental change. Together, higher RH, reduced ventilation, and enhanced synoptic-scale forcing acted synergistically to precondition the vortex and create an optimal environment for rapid intensification in the P80-ensemble.

While the mean RH differences between the P80- and P20-ensembles were modest in magnitude, Figure 10l reveals statistically significant anomalies of approximately 10 % near the storm center and along its southern flank. These regions of enhanced mid-tropospheric moisture likely played an active role in sustaining deep convection and facilitating the vertical alignment of the vortex, consistent with the stronger and more organized convective structure observed in the P80-ensemble. This behavior is in agreement with previous studies (e.g., Alland et al., 2021b; Tang and Emanuel, 2010), which demonstrated that higher mid-level humidity reduces ventilation and supports the maintenance of deep, symmetric convection even under moderate vertical wind shear.

Similarly, Hamaguchi and Takayabu (2021) described how upper-level dynamical forcing can induce synoptic-scale ascent that moistens the mid–upper troposphere prior to convective amplification in tropical disturbances. A comparable sequence is evident in the P80-ensemble, where enhanced negative Trenberth forcing and upper-level divergence preceded a significant increase in mid-level relative humidity during the rapid intensification period (Fig. 11c, d). This correspondence reinforces the interpretation that upper-level dynamical ascent and mid-tropospheric moistening acted together to precondition the environment for RI in the P80-ensemble.

Instead, the P80-ensemble is characterized by early and sustained dynamic forcing, particularly the strong negative Trenberth forcing observed before the RI onset, which likely initiated upward motion and enhanced upper-level mass divergence near the storm core. This synoptic-scale ascent, coupled with the release of latent heat, contributed to a favorable adjustment of the potential vorticity structure in the upper troposphere, reinforcing the outflow and aiding in the vertical alignment of the vortex. Consequently, the observed reduction in VWS in P80-ensemble can be interpreted as a combined result of both dynamic and thermodynamic processes acting in phase, rather than as a purely dynamical outcome. This reduction is related to higher Trenberth forcing, supporting a causal sequence in which synoptic-scale forcing preconditions, such as strong convection and vortex alignment, subsequently amplify this favorable state, accelerating the intensification process (Chen and Gopalakrishnan, 2015; Komaromi and Doyle, 2018; Stevenson et al., 2014). Figure 11 confirms this evolution: stronger divergence and PV anomalies emerge after the initial forcing, aligning with the onset of RI. The combined evidence supports the conclusion that in the case of Hurricane Lidia, RI was dynamically triggered by the interaction with the upper-level trough and jet stream, while thermodynamic factors such as PI, SST, and RH acted in concert with the dynamical forcing, serving as supportive components that enhanced the overall efficiency of the intensification process.

To better connect the individual diagnostics discussed in this study, Fig. 12 presents a conceptual schematic summarizing the key mechanisms acting before, at the onset, and during Lidia's RI. The illustration integrates the main results: (i) the approach and deformation of the upper-level trough, (ii) the strengthening of synoptic-scale ascent diagnosed through negative Trenberth forcing, (iii) the increase in upper-level divergence and cyclonic vorticity advection, (iv) the moistening of the mid-troposphere, and (v) the subsequent reduction of VWS and enhancement of the upper-level outflow. This schematic encapsulates how the combination of dynamic forcing and favorable thermodynamic conditions preconditioned and then accelerated the intensification process in the P80-ensemble in this case of study.