We perform our analysis over the North Atlantic using the European Centre for Medium Range Weather Forecasting (ECMWF) ERA5 reanalysis for the period from 1979 to 2022 at a spatial resolution of 0.5° × 0.5° for DJF (December, January, February) (Hersbach et al., 2020). Following Yu et al. (2025), we calculate 12-h forecast errors using the analyses and respective 12-h forecasts. Specifically, the forecast data utilised here serve as the background fields (first-guess trajectories) for the ERA5 4D-Var data assimilation. We select the short-range forecasts initialised at 06:00 and 18:00 UTC because they provide the background for the subsequent 09:00–21:00 and 21:00–09:00 UTC assimilation windows, respectively, ensuring close consistency between the forecasts and analyses. Such close consistency is desirable, as the differences between these internally coupled forecasts and analyses can serve as a robust indicator of the model's physical realism (Rodwell and Palmer, 2007). Note that conditioning the verification on analysis-defined cases can introduce a selection bias. This selection bias is minimised by choosing a 12-h lead time, though we acknowledge that the challenge to disentangle the signal from this bias.

We use mean sea level pressure (MSLP), temperature at 850 hPa, wind at 925 hPa, total column water vapour (TCWV), total column liquid water (TCLW), total column ice water (TCIW), water vapour flux (WVF), and potential vorticity (PV) as well as geopotential height at 300 hPa. In addition, to evaluate the low-level circulation and frontal dynamics, we compute tangential and radial wind components at 925 hPa relative to the cyclone centre, as well as kinematic frontogenesis at 850 hPa (e.g., Miller, 1948) 1DFkinDt=-1/2|∇pθ|∂u∂x+∂v∂y︸-1|∇pθ|12∂u∂x-∂v∂y∂θ∂x2-∂θ∂y2+∂v∂x+∂u∂y∂θ∂x∂θ∂y︸, where θ is potential temperature, and (u,v) are the horizontal wind components.

ETCs are detected and tracked using the algorithm based on Murray and Simmonds (1991a, b), as implemented and refined by Spensberger and Marcheggiani (2024) and Marcheggiani et al. (2025) (algorithm is publicly available as part of dynlib, Spensberger, 2024). We identify cyclones as local maxima in the Laplacian of the analysis MSLP field and track them over time using a nearest-neighbour approach combined with the most probable propagation direction. In addition, we apply several criteria to filter out non-developing and spurious systems: tracks must have a minimum lifetime of 24 h and travel a minimum distance of 500 km during their lifetime over the North Atlantic region (30–68° N, 80° W–12° E). All tracked cyclone centres are required to be identified as a closed system at least once within their lifetime, in line with Murray and Simmonds (1991a, b). Specifically, the cyclone centre must be enclosed by at least one closed isobar, ensuring the feature develops into a distinct low-pressure system rather than an open trough. After applying these criteria, a total of 2667 cyclone positions are retained. Our subsequent composite analysis focuses on the timestep of maximum intensification, defined as the most rapid decrease in central sea level pressure. Given that our analysis is based on 06:00 or 18:00 UTC, we chose the analysis time closest to the timestep of maximum intensification. Other timesteps, such as genesis or maximum intensity, feature similar but weaker patterns (see Fig. S1 in the Supplement).

To classify ETCs into strong and weak diabatic categories, we use the diabatic temperature tendencies derived from the ERA5 short-term forecasts. Following Tsopouridis et al. (2021b) and Weijenborg and Spengler (2020), these tendencies are accumulated over a ±3-h around the respective timesteps. Specifically, we take the diabatic temperature tendency due to physical parameterisations (originally on model levels and interpolated to pressure levels) and subtract the radiative diabatic tendencies. Following Papritz and Spengler (2015), radiation is excluded because it acts as a slow background cooling.

We vertically integrate the diabatic heating over the 700–300 hPa layer and then average it within a 750 km radius around the cyclone centre at the time of maximum intensification (similar to Tsopouridis et al., 2021a). By focusing on the free troposphere, the direct diabatic influence of the lower tropopause/boundary layer (typically below 700 hPa) is excluded.

Cyclones with the heating above the 70th percentile are classified as strong heating (red shading in Fig. 1a), while cyclones below the 30th percentile are classified as weak heating (blue shading in Fig. 1a). Note that maximum intensification of strong heating cyclones predominantly occurs at lower latitudes, often located around the SST front regions along the Gulf Stream, whereas weak heating cyclones occur more frequently at higher latitudes (Fig. 1b). Although our classification method is for the free troposphere (700–300 hPa), this distinct latitudinal distribution demonstrates the indirect role of the lower troposphere/boundary layer. More surface sensible and latent heat fluxes over higher SST provide favourable conditions for the strong heating cyclones. To ensure that the presented bias patterns are related to diabatic heating rather than latitudinal differences, we also analysed cyclones restricted to a latitudinal band between 45–55° N. As the results are qualitatively the same (not shown), we perform our analysis on all cyclones in the Atlantic.

We analyse cyclone forecast biases at maximum intensification using cyclone-relative composites for the two heating categories. Following Catto et al. (2010), cyclone-relative composites were calculated by averaging over all cyclones. During this procedure, all fields are rotated to align the propagation direction of each cyclone along the x axis. As individual cyclones move in diverse directions, this rotation is essential to prevent misalignment of features, such as warm and cold fronts, that would then be smoothed out during the averaging process.

The thus derived composites illustrate why we chose to include one additional step in the analysis method (Fig. 2). Cyclone-centred error composites for both weak and strong heating show a systematic underestimation of intensity, with forecasted MSLP contours (blue contours) having a smaller radius compared to the analysis (black contours, Fig. 2a, b). For weak heating, this intensity underestimation is also clearly depicted by the positive MSLP bias (shading, Fig. 2b) and the corresponding negative bias in the 925 hPa wind around the cyclone centre (Fig. 2d).

For strong heating, however, the MSLP bias features a pronounced dipole pattern (Fig. 2a), attributable to a southwestward displacement of the forecasted cyclone, implying a too slow propagation of the cyclone in the forecast. This positional bias is supported by the strong dipole pattern observed in the 925 hPa wind field near the centre (Fig. 2c). This bias is consistent with intense diabatic heating accelerating cyclones (Stoelinga, 1996; Coronel et al., 2015). The combined bias in both intensity and propagation is also congruent with the ECMWF model generally forecasting too shallow and too slow cyclones in the Northern Hemisphere winter (Froude et al., 2007). While the forecast bias for weak heating is predominantly associated with an underestimation of intensity, a slight southwestward displacement is also evident.

To focus on cyclone-centre-relative errors, we remove the aforementioned positional bias by redefining the respective cyclone centres in both analysis and forecast as the location of the nearest minimum in MSLP compared to the originally detected cyclone centre in the analysis. Analogous to the tracking, the MSLP field is spatially filtered using spectral triangular truncation (T84). This filtering procedure effectively filters out small-scale noise. We require that the identified MSLP minima in both the analysis and forecast must be within a 250 km radius of the originally detected centre in the analysis. Any cyclone record failing this criterion is discarded.

The “strong” and “weak” heating groups, defined as the top and bottom 30 % of the diabatic heating distribution, initially comprise 801 and 799 cyclones, respectively. After this filtering and re-centring, a total of 774 and 627 analysis-forecast pairs are retained for the strong and weak heating group, respectively. A smaller proportion of strong heating cyclones is filtered out, which physically reflects that their kinematic centres and MSLP minima are more consistently co-located. We use the recentred data for analysis and forecast to compile our cyclone-centred composite analysis. Given that both analysis and forecast are now centred on the position of minimum MSLP, the positional bias in the composites has been removed (compare Figs. 2 and 3).

Cyclone-centred MSLP biases reveal an underestimation of cyclone intensity, with structural differences for the two groups (Fig. 3a, b). In the strong heating group, a broad area of positive bias is evident (Fig. 3a, shading), indicating that the forecasted cyclones are generally too weak. This intensity underestimation is also visible in the forecasted MSLP contours (blue), which exhibit a smaller radius compared to the analysis (black). Furthermore, the spatial location of the maximum underestimation in the strong heating group is in the upper right-hand quadrant of the composite centre. In contrast, for the weak heating group, the intensity underestimation is mainly around the cyclone centre (Fig. 3b).

Notably, a comparison with the non-centred results (Fig. 2a, b) reveals that the recentred composites (Fig. 3a, b) exhibit a smaller domain-averaged bias but a larger domain-averaged RMSE. This counter-intuitive increase is most likely due to the elimination of error compensation, where the position bias originally masked the systemic intensity underestimation. Specifically, in the non-recentred composite (Fig. 2a, b), the southwestward displacement partially overlaps with the regions of intensity underestimation, leading to a cancellation of biases over the left-hand quadrants of the composite. Once recentred (Fig. 3a, b), this spatial offset is removed, revealing a more consistent and domain-wide intensity bias. While recentring reduces the large error magnitudes near the cyclone centre, broadly distributed errors lead to a higher domain-averaged RMSE.

The weak heating group displays an underestimation of 925 hPa wind around the cyclone centre (Fig. 3d), which is consistent with the underestimated depression in MSLP (Fig. 3b). The strong heating group exhibits a wind speed underestimation in the warm sector (Fig. 3c). However, an overestimation manifests in the cold sector region, associated with Cold Conveyor Belts (CCBs), dry intrusions (DIs), and sting jets (SJs) (Schultz, 2001; Browning, 1997, 2004). One potential explanation for this overestimation is that the stronger forecasted winds may actually be closer to reality. The incremental 4D-Var assimilation system in ERA5 computes analysis increments at a reduced spatial resolution (Hersbach et al., 2020; ECMWF, 2016). Hence, highly localised sharp wind gradients are often smoothed out. This is consistent with previous findings that marine CCB jets are underestimated in ERA5 (Gentile and Gray, 2023). Despite these spatial variations, both heating groups demonstrate a domain-averaged underestimation of 925 hPa wind speed, which generally aligns with previous feature-based analyses (Yu et al., 2025).

For the strong heating group, the total column water vapour (TCWV) composite reveals a distinct negative bias, indicative of a moisture deficit in the forecast (Fig. 4a). This underestimation is most pronounced in the warm sector, especially along the boundaries of high TCWV filament (about 4 %). A comparison of the composite contours shows that the water vapour in the forecast (blue) is narrower compared to the analysis (black). In addition, a pronounced negative bias of the water vapour flux (WVF) is evident in both the along and across components relative to cyclone propagation on the warm side of the cyclone (Fig. 4e, f). The TCWV deficit is thus consistent with insufficient moisture transport in the warm sector, most likely coinciding with warm conveyor belts (WCBs).

To quantify the linkage with WCBs, we employ moisture transport axes (MTAs, Spensberger et al., 2025) and create a mask around them with a 200-km distance threshold around the identified axis (see Yu et al., 2025). The MTA algorithm extracts well-defined maxima in the water vapour transport (Spensberger et al., 2025), effectively capturing coherent moisture filaments, which are variously known as atmospheric rivers, warm moist intrusions, and WCBs. For the strong heating group, the MTA frequency in the warm sector reaches over 70 %, whereas it remains below 10 % for the weak heating group (Fig. S2). Hence, for strong heating cyclones, there is a strong link between the aforementioned biases and biases in WCBs.

The high-value core of total column ice water (TCIW) is located at the upper right-hand quadrant of the composite cyclone, with its trailing region at the bottom right-hand quadrant. There is a negligible bias within the maximum of TCIW, with negative/positive biases at the leading/trailing edge of the TCIW maximum (Fig. 4b). The TCIW plume in the forecast (blue contours) is more elongated than in the analysis (black contours). This more elongated structure of the forecasted TCIW is the main cause of the positive bias in the trailing region, indicating that the ice water is less cyclonically wrapped up in the forecast. This weaker wrap-up is consistent with the insufficient moisture transport and underestimated wind (Fig. 3c, d).

In contrast to the underestimation for vapour, the total column liquid water (TCLW) shows a notable positive bias (approximately 10 % overestimation) within the upper two quadrants of the composite close to the cyclone centre, commonly referred to as the cloud head region. (Fig. 4c). Given that the strong heating group is fundamentally characterised by free tropospheric diabatic heating and the associated intense moisture filaments (MTAs), this bias points toward error sources from both microphysics and dynamics.

The positive TCLW bias is concentrated within the strong ascent region (Fig. 4c). Given the corresponding negative biases in TCWV, this positive bias strongly suggests an under-representation of precipitation efficiency within the microphysical scheme, where liquid droplets remain suspended instead of precipitating out. Furthermore, as liquid water is not directly constrained by data assimilation (DA) (Geer et al., 2017), the model must rely on indirect corrections via adjustments to thermodynamic and kinematic observations, which may feature systematic deviations, potentially yielding the positive liquid water bias.

Given that vertical velocity in the analysis is diagnosed and not directly observed, we employ the kinematic frontogenesis of potential temperature (θ) as a proxy, as it quantifies the dynamic forcing that drives a secondary vertical motion (Sawyer, 1956; Eliassen, 1962). Pronounced frontogenesis at 850 hPa is evident in the upper left- and right-hand quadrants of the cyclone centre (Fig. 4d). The frontogenesis positioned closer to the cyclone centre is associated with a positive bias in frontogenesis near the centre (∼17 %). As Martínez-Alvarado et al. (2014b) showed that latent heating strongly influences cyclone frontal structure, this bias reflects a feedback between dynamic and diabatic processes. In accordance with thermal wind balance, the resulting enhanced temperature gradient corresponds to a stronger vertical shear of the geostrophic wind, consistent with the wind speed overestimation (Fig. 3c). The intensified frontogenesis is also associated with a secondary circulation that produces enhanced vertical motion on the warm side of the front (not shown). This ascent can enhance condensation, resulting in an overestimation of liquid water along the warm front (Fig. 4c).

Compared with the strong heating group, the weak heating group exhibits a much weaker bias of TCWV, mainly around the centre (approximately 1 %) as well as on the left side of the high TCWV filament (Fig. 5a). Accordingly, moisture transport also shows only very weak biases near the centre (Fig. 5e, f). The biases are smaller and exhibit a more symmetric distribution of positive and negative bias compared with the strong heating group (compare Figs. 4e, f and 5e, f). Unlike the strong heating group, where pronounced warm sector biases are associated with a high frequency of intense moisture transport, the weak heating group exhibits a very low MTA frequency (Fig. S2b). Correspondingly, the moisture biases in this group remain small and symmetric. Furthermore, because weak heating cyclones primarily occur at higher latitudes (Fig. 1b), the colder background environment limits the moisture supply, resulting in weaker biases.

Both TCIW and TCLW composites also display notably smaller negative biases in the respective high-value regions (∼1 %, Fig. 5b, c). The smaller biases for both liquid and frozen water for the weak heating group is likely also related to the lower moisture availability at higher latitudes, also resulting in the reduced diabatic heating.

Consistent with the biases above, the bias in kinematic frontogenesis is also much smaller compared to the strong heating group (Fig. 5d). This primarily reflects the weaker baroclinicity and frontogenetic intensity of these higher-latitude cyclones.

For cyclones with strong heating, tangential winds at 925 hPa are underestimated in the warm sector, indicating a weaker cyclonic circulation in forecasts (Fig. 6a). This is consistent with the underestimated wind at 925 hPa (Fig. 3c) as well as the underestimated moisture transport (Fig. 4e, f). In contrast, tangential winds are overestimated near the cyclone centre, consistent with the wind bias around the CCB, DI, and SJ (Fig. 3c). The latter overestimation of cyclonic wind is also associated with the overestimation of frontogenesis (Fig. 4d). An accurate representation of these winds is particularly important, as the CCB region is most frequently associated with compound wind-wave hazards (Gentile and Gray, 2023), with SJs often contributing to extreme wind gusts (Clark and Gray, 2018).

Radial wind also features a domain-averaged positive bias, indicating an underestimation of inflow in the forecast (Fig. 6c), which is consistent with the previously reported wind direction bias for cyclones (Yu et al., 2025). Notably, a pronounced negative bias is observed in the radial wind within the upper right-hand quadrant of the composite cyclone near the centre. This negative bias indicates an overestimation of inflow (convergence), which aligns with the overestimated vertical motion related to the frontogenesis bias (Fig. 4d).

The low-level tangential wind composite for cyclones with weak heating exhibits a clear underestimation near the cyclone centre (Fig. 6b). This indicates a weaker cyclonic circulation in the forecast, consistent with cyclones in this group being forecasted too weak (Fig. 3b). Correspondingly, the radial wind component generally displays a small domain-averaged positive bias (Fig. 6d). The clearest positive bias is located in the warm sector. This reflects a weaker inflow and insufficient convergence within the warm sector, which is essential for cyclonic development and warm frontal ascent.

These cyclonic circulation biases are associated with the thermal structure through altered temperature advection. The temperature bias for the strong heating group shows a pronounced cold bias in the upper right-hand quadrant. This is consistent with the underestimated cyclonic flow and water vapour transport in the warm sector, thus featuring reduced warm air advection (Figs. 3c, 4e,f, and 6a). Additionally, the lower-left quadrant also exhibits a notable cold bias. This cold bias is linked to the upper level potential vorticity (PV) biases discussed in the following section.

For the weak heating group, the temperature bias at 850 hPa manifests as a cold bias in the warm sector (lower-right quadrant) and a warm bias in the cold sector (upper-left quadrant, Fig. 6f). This pattern is consistent with the underestimation of cyclone intensity.

The upper-level PV field for the strong heating group displays a distinct trough-ridge pattern, with a pronounced positive bias around the ridge (Fig. 7a). This underestimation of the upper-level ridge in the presence of strong diabatic heating is consistent with previous studies (Martínez-Alvarado et al., 2016; Grams et al., 2018; Oertel et al., 2020). Furthermore, although the trough axis generally exhibits an underestimation (negative bias), there is an elongated positive PV bias along the trough axis, indicating an overestimation of PV in the forecast. The positive PV bias co-locates with the cold bias in the lower-left quadrant (Fig. 6e). This overestimation of upper level PV is likely associated with enhanced descending along dry intrusions (DI), which can result in larger cold and dry air advection within the cold sector (Catto and Raveh-Rubin, 2019).

Consistent with the upper level PV bias, the bias in geopotential height at 300 hPa for cyclones with strong heating features an underestimation of the ridge (Fig. 7c). Note, however, that the trough is not underestimated in terms of geopotential. The biases in both the upper-level PV and geopotential dynamically reflect the misrepresentations of diabatic heating, which is specifically tied to the deficits in WCBs. This aligns with previous studies showing that an underestimation in WCB intensity results in a weaker negative PV anomaly and thus a weaker upper-level ridge (Martínez-Alvarado et al., 2016; Grams et al., 2018; Harvey et al., 2020; Oertel et al., 2020). As demonstrated by Coronel et al. (2015), diabatic amplification of the downstream ridge alters the upper-level steering flow, typically deflecting the cyclone track poleward. Therefore, the underdevelopment of the downstream upper-level ridge can be related to the southward displacement bias for the strong heating group.

The PV composite for the weak heating group shows a maximum in PV above the cyclone centre, with contours extending upstream (Fig. 7b). The bias generally features an underestimation of upper-tropospheric PV, consistent with a weaker cyclone in terms of MSLP (Fig. 3b). In contrast to the strong heating group, the geopotential height field in the weak heating group generally shows a spatially uniform positive bias (Fig. 7d), consistent with the PV trough being underestimated, as well as the underestimation of cyclone intensity (Fig. 3b).