Wind kinetic energy climatology and effective resolution for the ERA5 reanalysis

Vol.:(0123456789) 1 3 Climate Dynamics (2022) 59:737–752 https://doi.org/10.1007/s00382-022-06154-y Wind kinetic energy climatology andeffective resolution fortheERA5 reanalysis P.Bolgiani1 · C.Calvo‑Sancho2 · J.Díaz‑Fernández1 · L.Quitián‑Hernández1 · M.Sastre1 · D.Santos‑Muñoz3 · J.I.Farrán2 · J.J.González‑Alemán1,4 · F.Valero1,5 · M.L.Martín2,5 Received: 2 September 2021 / Accepted: 12 January 2022 / Published online: 29 January 2022 © The Author(s) 2022 Abstract ERA5 represents the state of the art for atmospheric reanalyses and is widely used in meteorological and climatological research. In this work, this dataset is evaluated using the wind kinetic energy spectrum. Seasonal climatologies are generated for 30° latitudinal bands in the Northern Hemisphere (periodic domain) and over the North Atlantic area (limited-area domain). The spectra are also assessed to determine the effective resolution of the reanalysis. The results present notable differences between the latitudinal domains, indicating that ERA5 is properly capturing the synoptic conditions. The seasonal variability is adequate too, being winter the most energetic, and summer the least energetic season. The limited area domain results introduce a larger energy density and range. Despite the good results for the synoptic scales, the reanalysis’ spectra are not able to properly reproduce the dissipation rates at mesoscale. This is a source of uncertainties which needs to be taken into account when using the dataset. Finally, a cyclone tropical transition is presented as a case study. The spectrum generated shows a clear difference in energy density at every wavelength, as expected for a highly-energetic status of the atmosphere. Keywords Energy spectrum· Effective resolution· Climatology· ERA5 1 State oftheart At the present time, most of the meteorological predictions and forecasting products are based on numerical weather prediction (NWP) models. For this reason, NWP is both a major tool and principal research field for meteorology and climatology, as well as for other earth physics sciences. As a consequence, the assessment and validation of models, their evolutions and applications constitute a permanent topic of study and discussion. One of the most important variables to consider in the configuration of a model for a NWP experiment is resolution. Spatial and temporal resolutions play a major role in the model’s outcome (Adlerman and Droegemeier 2002; Bryan etal. 2003) but also in the computation power required to perform the task, so they need to be carefully considered before the simulation is run to be adequate to the subject of study. Moreover, thanks to the enhancement of computational resources, the constant increase of spatio-temporal resolution in NWP models has reached a challenging point for their own improvement, as nowadays limited-area mesoscalar model resolutions are verging on the microscale (Prósper etal. 2019; Siewert and Kroszczynski 2020). This represents an intrinsic problem, as it is obvious that mesoscale (400–4km) models are not originally designed for microscale (below 4km) simulation. Thus, we face the need for new adequate parametrizations and computations for those physical processes taking place in the microscale, which had been previously disregarded (Gramelsberger 2010; Hong etal. 2004; Muñoz-Esparza etal. 2017; Sun etal. 2013). These limits of the models render necessary to know the productive limit of the resolutions used before undertaking simulation (Bolgiani etal. 2020). This effective resolution is usually considered as the * C. Calvo-Sancho [email protected] 1 Department ofEarth Physics andAstrophysics, Faculty ofPhysics, Universidad Complutense de Madrid, Madrid, Spain 2 Department ofApplied Mathematics, Faculty ofComputer Engineering, Universidad de Valladolid, Segovia, Spain 3 Danmarks Meteorologiske Institut, Copenhagen, Denmark 4 Agencia Estatal de Meteorología (AEMET), Madrid, Spain 5 Interdisciplinary Mathematics Institute, Universidad Complutense de Madrid, Madrid, Spain 738 P.Bolgiani et al. 1 3 physical distance at which the model’s behaviour is reliable when considering a particular variable. Skamarock (2004) studied a simple method of effective resolution evaluation for NWP models. The author proposes the kinetic energy dissipation curve, or kinetic energy spectrum diagram, as an indicator for effective resolution. For this diagram, the model kinetic energy dissipation is computed from the spectral decomposition of the simulated wind speed field. At a certain point, NWP models stop computing the energy in the model and proceed to filter it through diffusion so as to comply with a proper turbulent kinetic energy closure (Knievel etal. 2006; Skamarock etal. 2008). The departure of the simulated kinetic energy curve from the observed curve indicates the effective resolution, which is usually around seven times the model’s grid size (7Δx). It has to be remarked that the computation beyond the effective resolution is not wrong in terms of physics, but a considerable uncertainty is introduced in the simulation. We can assert that the simulation below the effective resolution is not completely adequate, but that does not render it useless. For example, Skamarock (2004) defends that a finer orographic resolution or land surface processes can improve the PBL simulation, as far as the errors in energy dissipation are acknowledged. Knowing the limits and uncertainties of the tools we use is one of the motivations for the present study. It must be noted that, the kinetic energy spectra are often derived from the wind speed. However, others atmospheric variables have also been explored. Nastrom and Gage (1985) and Cho etal. (1999) use observational data of potential temperature as well as wind components to compute the energy spectra. They conclude the horizontal wind and potential temperature have a very similar behaviour and do not depart greatly from the curve expected. Furthermore, Cho etal. (1999) compute the energy spectra with other atmospheric and air quality variables (e.g., specific humidity, CO2, O3, CH4). The spectra behaviour of these variables follows again the curve produced by the wind speed. According to the observations by Nastrom and Gage (1985), the kinetic energy associated with planetary and large‐scale processes follows a theoretical dissipation curve proportional to k−3 (Kolmogorov 1941) while the mesoscale atmospheric energy dissipates proportionally to k−5/3. These upper troposphere observations show the theoretical curves falling to the microscale limit, which is considered to be at around 4km. In this context, Lindborg (1999, Eq.71) uses these observations to demonstrate an equation describing the energy dissipation. Notice that the domain selected can promote differences in the observed spectrum curve due to several issues, e.g. the synoptic conditions, the geographical region of study or even the local topography (Ricard etal. 2013; Skamarock 2004). The distance of sampling will also mark the lower limit of the curve (2Δx as per Nyquist 1928) and the longitude of the observation segment will define the upper limit of it (as it effectively filters the maximum wavelength). These conditions to the curve are also present in NWP simulations due to grid and domain sizes, and limitedarea models will introduce additional modifications to the curve (Skamarock 2004). Several researchers have been able to adequately reproduce the observations in global and limited area NWP simulations (Abdalla etal. 2013; Koshyk and Hamilton 2001; Ricard etal. 2013; Skamarock 2004; Takahashi etal. 2006), proving the effective resolution of the respective models used. Hamilton etal. (2008) remarks that some General Circulation Models (GCM) present rather different performances at the transition from k−3 to k−5/3. In particular, Palmer (2001) reports that the Integrated Forecasting System [IFS; ECMWF (2016)] shows a kinetic energy spectrum that steepens rather than shallows in the mesoscale, being outperformed by other GCMs which can simulate more realistic spectra (Koshyk and Hamilton 2001; Takahashi etal. 2006). However, later results by Abdalla etal. (2013) prove that the updated versions of the IFS have corrected this issue, producing a realistic spectrum deep into mesoscale. This disagreement is a direct example of effective resolution. Palmer (2001) uses the GCM with approximately 60km grid resolution, which yields an effective resolution of ≈420km, just verging out of the mesoscale, while Abdalla etal. (2013) use a version of the model at ≈16km, with an effective resolution (≈109km) able to capture the aforementioned transition. This is in line with previous results from Takahashi etal. (2006) which already show how the resolution affects the ability to capture the spectrum. Also, this shows the limitations of GCMs for the study of fine scale phenomena and the current value of limited-area high-resolution NWP models at the present state of the art. GCMs are not only used for operational forecasts and as boundary conditions for high-resolution NWP, but are also the basis for reanalyses, which have become a major research tool due to the proven enhancement by observations assimilation (Al-Yahyai etal. 2010; Bengtsson etal. 2017; Dee etal. 2011; Done etal. 2004; Hersbach etal. 2020; Uppala etal. 2005). Thus, knowing the energy spectra and effective resolution expected for global models and reanalyses is of paramount necessity to understand the limitations and uncertainties of these tools. Among the different atmospheric reanalyses available, the ERA5 dataset is currently considered a major reference. It represents a considerable improvement over previous versions (Hersbach etal. 2020) and is not only used as initial and boundary conditions for limited-area models but also frequently considered as an observational database (Aboobacker etal. 2021; Gil Ruiz etal. 2021; Molina etal. 2021; Olauson 2018; Rodríguez and Bech 2021; Taszarek etal. 2020; Zhang etal. 2021). In line with this, the principal objective of this paper is to provide seasonal climatological curves for the wind energy 739Wind kinetic energy climatology andeffective resolution fortheERA5 reanalysis 1 3 spectrum over the northern hemisphere and the North Atlantic area from the ERA5 data. This aims to procure basal curves for further studies where no observational data is available, and additionally to be used as a reference for highresolution simulations. Another discussion related to the mesoscale energy spectrum treats the origin of the additional energy which brings the curve slope from k−3 up to k−5/3 (Hamilton etal. 2008; Takahashi etal. 2006). Some results suggest that non-linear downscale energy cascades force the mesoscalar spectrum to a higher energy state (Lindborg 2007; Lindborg and Cho 2001; Tulloch and Smith 2006; VanZandt 1982). In line with this, Arimitsu and Arimitsu (2005) conclude that the synoptic part of the curve is a result of the global structure of turbulence, which is then followed by an inertial range controlled by the dissipative structure in turbulence, both sections governing the flow of turbulence. Other works support the idea of the mesoscale being energized by an upscale nonlinear motion transfer from microscale, produced mainly by moist convective processes and latent heat (Gage and Nastrom 1986; Lilly 1983; Vallis etal. 1997). This would be in line with the classical results by Van der Hoven (1957), which present a peak of energy at microscale most probably due to the turbulence derived from short-term high wind speeds. Idealized simulations by Hamilton etal. (2008) show a partial forcing from both mechanisms affecting the mesoscalar spectra. This suggests that major convective and latent heat processes should alter the energy curves in NWP simulations. Thus, a secondary objective of this article is to compare the climatological spectra with those produced for a case study, namely, a subtropical cyclone transitioning to a tropical cyclone in the North Atlantic area, where convective processes are prevalent in the evolution of the phenomenon. This work is organized as follows: Sect.2 presents the data used and methodology followed for producing the results, shown and discussed in Sect.3, along with the case study; Sect.4 yields the conclusions of this study. 2 Data andmethodology The ERA5 climate reanalysis (Hersbach etal. 2020) is the most updated dataset and constitutes the fifth-generation reanalysis created by the European Centre for Medium-Range Weather Forecasts (ECMWF). This atmospheric reanalysis represents the next step with respect to the previous ERA-40 (Uppala etal. 2005) and ERA-Interim (Dee etal. 2011) databases, improving the time coverage and spatial resolution. ERA5 is freely available through the EU-funded Copernicus Climate Change Service (CDS Copernicus 2020). The set is based on the IFS (Cy41r2) and holds quality-controlled uniform data from 1979 to present, with preliminary data available from 1950 to 1978. Also, work is in progress to provide the reanalysis in almost real-time conditions; at the date of writing of this paper, the product is available up to five days prior to the current. The resolution of the ERA5 is a big enhancement from the previous reanalysis. The horizontal grid resolution is 0.25° (approximately 27.8km in latitude), re-grided from the 31km resolution of the model. The vertical resolution includes 37 pressure levels, from 1000hPa up to 1hPa, interpolated from the 137 sigmapressure hybrid levels provided by the IFS. The temporal resolution is of hourly outputs. Observations from both satellites and surface-based instruments are assimilated into the global estimate, enhancing the quality of the product. A complete description of the ERA5 dataset characteristics can be found in Hersbach etal. (2020). In the present study, the two components of the horizontal wind field (u, v) are used from the 1979–2020 dataset at 00:00, 06:00, 12:00 and 18:00 Universal Time Coordinated (UTC). The geographical domains selected are three latitudinal bands, covering the whole longitude of the northern hemisphere (periodic domains): from 00° to 30° N, from 30° to 60° N and from 60° to 90° N. These are then limited in longitude to cover exclusively the North Atlantic area (nonperiodic or limited-area domains): from 080° to 010° W for the tropical area, from 070° to 000° E for the mid-latitudes and from 070° to 020° E for the polar area (Fig.1). The kinetic energy spectra are computed following the procedure of Skamarock (2004) and Abdalla etal. (2013). The process can be outlined as follows: Fig. 1 Domain of study (white area) for the kinetic energy spectra over the North Atlantic Ocean. Built as the sum of three latitudinal bands 740 P.Bolgiani et al. 1 3 • Wind speed field is derived using u and v components. • Anomalies are computed by removing the average wind speed. • In the case of limited-area domains, anomalies are also detrended, rendering the non-periodic data to periodic data for the spectral decomposition. • Energy spectral decomposition (through Fourier Analysis) is accomplished longitudinal‐wise using single vertical levels. • The obtained energy spectra are averaged over latitude, yielding a single result for each time step. • Plots are redimensioned into wave number and energy density for easier understanding (from frequency and variance), using the ERA5 latitudinal resolution. • The energy spectra for each time step are then plotted together with the corresponding total average. The Lindborg (1999) energy dissipation curve is added for reference. In preliminary results several levels and monthly curves were evaluated (not shown). The spectra for different isobaric surfaces perform as expected, in line with Skamarock (2004), showing more energy at synoptic scales for higher levels and shallower curves for lower levels. The curves for each month do not show important differences as to be presented individually. Therefore, seasonal climatologies are produced at 500hPa, as these are considered the most representative ones for this study. Also, it is worth mentioning that, as we are evaluating the energy on single levels using a large domain, the potential energy differences can be overlooked, and the contribution of the kinetic energy can be nearly considered as the whole energy of the system. Finally, it has to be noted that the same methodology was applied to the ERA5 monthly averages for wind speed. The average curves produced by these (not shown) are very similar to those produced by the aforementioned 6-h data. Thus, it was decided to shown results of only the later dataset in attention to the high temporal resolution provided. 2.1 Case study For the case study a highly active atmospheric system, a tropical storm formed by a tropical transition process (Davis and Bosart 2004), was selected due to the prominent convective activity and strong winds involved in the process. Among the multiple events available, storm Delta is to be evaluated (Beven 2005). This storm severely hit the Canary Islands archipelago in November 2005. Delta caused several casualties and many injuries, power outages, flooding and landslides. The system began to develop south-west of the Azores Islands on 19 NOV 2005 and gained subtropical cyclone characteristics on 22 NOV. By 23 NOV 2005 at 12:00 UTC the system underwent a tropical transition and continued intensifying until 27 NOV. The storm moved north-west and degraded to extratropical category with a warm-core just before hitting the Canary Islands on 28 NOV 2005 (Sánchez-Laulhé and Martin 2006). Storm Delta was detected by GPS measurements in the isle of La Palma and in the isle of Gran Canaria, showing an increase of rainfall and intensity of wind several hours prior to the effects of Delta on the ground (Seco etal. 2009). It is interesting to note, that during a tropical transition the cold-core cyclone is progressively losing its asymmetrical nature and is acquiring characteristics typical of warm-core symmetrical tropical cyclones. These transitions are of particular interest in terms of kinetic and thermodynamic atmospheric energy, expecting notable differences against the climatology in the energy spectra generated. The data retrieved from the ERA5 dataset has a spatial domain (Fig.2) restricted to ± 11° from the approximate centre of the system at the moment of transition, 27° N 041° W. The time window considered is ± 36h also centred at the Fig. 2 Domain of case study (white area) of tropical storm Delta 741Wind kinetic energy climatology andeffective resolution fortheERA5 reanalysis 1 3 approximate moment of transition, 12:00 UTC 23NOV2005. The energy spectra are obtained using the aforementioned procedure. Also the sea level pressure, 500hPa geopotential height, and surface and 500hPa wind speed and direction fields are plotted for assessment of the situation. 3 Results anddiscussion The results for the North Hemisphere latitudinal bands are shown in Fig.3, while the results for the North Atlantic are presented in Fig.4. A seasonal comparison is shown in Fig.5 and a latitudinal comparison in Fig.6. These figures are analysed several times in the paper, as the results for the effective resolution and the climatologies are evaluated in separate subsections. The results for the case study are then shown in Fig.8. For the sake of simplicity, in the discussion the seasons are named: DJF for December, January and February; MAM for March, April and May; JJA for June, July and August; SON for September, October and November. Also, the latitudinal band from 00° to 30° N is named Tropical, the band from 30° to 60° N is named Middle and the band from 60° to 90° N is named Polar. Before initiating the discussion, it must be noted that the numerical differences between the average curves are computed and the Mann–Whitney U test (Mann and Whitney 1947) is used to check the statistical significance of these differences. This is a non-parametric test of null hypothesis, for populations with equal distribution, which are compared to check the independence of both groups. The p-value used is 0.01. Every test resulted statistically significant except for the Polar MAM and SON curves for the periodic domain which are not different enough (p = 0.10). Also, a short discussion on the behaviour of the spectra with altitude is worth considering. As mentioned in the methodology section, the results here presented are for 500hPa wind speeds (Figs.3 and 4), but preliminary results were also produced for 1000hPa and 250hPa wind speeds (not shown). When the 250hPa spectra are compared with the 500hPa results, different energy densities are only patent at synoptic scales. The upper troposphere spectra present higher densities at synoptic wavenumbers which, in turn, drive the dissipation above 10–5rad m−1 to a steeper rate. Nevertheless, the energy in the mesoscalar range does not vary much. When the 1000hPa spectra are compared with the 500hPa results, evident differences can be seen in both spatial ranges. The near-surface spectra show lower energy densities at synoptic scales, but there are higher energy densities at the larger mesoscalar wavenumbers (around 8.10–5rad m−1), generating shallower dissipation rates along the major part of the curves. The results for 250hPa are in accordance with those by Nastrom and Gage (1985) and Lindborg (1999), who work with observations taken between 9 and 14km of altitude, and also with those by Skamarock (2004) and Hamilton etal. (2008), who also show the increment of energy densities at higher altitudes. The curves at 1000hPa are coincident with the conclusions derived by Van der Hoven (1957), who finds a secondary peak at microscale for near-surface wind spectra. However, it is known that upper troposphere spectra can be influenced by synoptic and planetary-scale waves, injecting energy in the system (Skamarock 2004). Also, ERA5 declares some reported issues with near-surface winds, i.e., a systematic jump in the boundary layer wind at the transition point for data assimilation, which can reflect on climatologies, and extremely large wind speeds (up to 300m s−1) near orographic features (Hersbach etal. 2020). As a consequence, we proceed only with the analysis for 500hPa results. 3.1 Effective resolution In this subsection, only the slope and shape of the curves will be assessed, disregarding the position or shape comparison with the theoretical dissipation curve. All of the periodic domain climatological spectra (Fig.3) seem very similar in terms of resolution. The curves present an initial shallow slope for the shortest wavenumbers, below 10–6rad m−1, coherent with the computation of the spectra in longitude and in line with those generated by Nastrom and Gage (1985), Takahashi etal. (2006) and Hamilton etal. (2008) for zonal winds. This does not match the results by Abdalla etal. (2013) for the satellite observations and the IFS, which present a decaying curve. However, as per the aforementioned authors, the decay seems to be associated with meridional winds. It is worth noting that most of the literature only evaluates the spectra down to 10–6rad m−1, so the curves beyond that point are mostly unknown. The climatological curves steepen when entering the synoptic scales, presenting an adequate energy dissipation close to k−3 between 10–6 and 10–5rad m−1 wavenumbers. When mesoscale is reached, at about 10–5rad m−1, the curves do not show the expected shallower dissipation either. As aforementioned, this was already addressed by Palmer (2001) and Hamilton etal. (2008), reaching the conclusion that GCMs do not properly represent the energy spectrum for mesoscalar winds, however it is only a matter of grid resolution. Abdalla etal. (2013) can reproduce the change in regime due to the use of ≈16km grid resolution (IFS version T1279). Nevertheless, ERA5 is based in a version of the IFS (T639) running at ≈31km grid size (Hersbach etal. 2020; not to be confused with the ERA5 final delivery 0.25° grid size), with an effective resolution of ≈260km, or ≈8Δx as per Abdalla etal. (2013). Thus, the reanalysis should in theory have the ability to reproduce the transition to k−5/3. However, it is not seen in the spectra. On the contrary, the energy curves slightly steepen around 4.10–5rad m−1, induced by 742 P.Bolgiani et al. 1 3 Fig. 3 Seasonal wind kinetic energy spectrum climatology for ERA5 North Hemisphere latitudinal bands. Data used in three bands: tropical (00°N–30°N), Middle (30°N–60°N) and Polar (30°N–90°N). Grey lines are individual spectra, black lines are averages, dashed lines correspond to the dissipation rate as per Lindborg (1999) 743Wind kinetic energy climatology andeffective resolution fortheERA5 reanalysis 1 3 Fig. 4 Seasonal wind kinetic energy spectrum climatology for ERA5 in the North Atlantic domains described in Fig.1. Grey lines are individual spectra, black lines are averages, dashed lines correspond to the dissipation rate as per Lindborg (1999) 744 P.Bolgiani et al. 1 3 the damping of energy by the model and the divergence from the computed rate of dissipation. The curves end a little beyond 10–4rad m−1, or ≈50km, as expected per 2Δx. The previous results present a remarkable aspect of the effective resolution of the ERA5. As the spectra do not present a transition to k−5/3, the reanalysis’ effective resolution cannot be determined by the divergence to a steeper slope from the mesoscale curve. As a consequence, the limit has to be set on the point where the simulated curve diverges from the observation, as proposed by Skamarock (2004). That point is clearly seen at lower wavenumbers than expected for most spectra, approximately at 1300km for the Tropical curves, at around 600km for the Middle band and approximately at 1200km for the Polar spectra (Fig.5). The results for the North Atlantic limited-area domains (Fig.4) present spectra not reaching the 10,000km wavelengths, as higher wavelengths are effectively filtered by the size of the domain. The curves are similar to those of the periodic domains in the global and synoptic scales, but present interesting differences at higher wavenumbers (Fig.5). The divergence to steeper slopes is more pronounced for these results. The rates of dissipation are also higher, mostly for the Middle and Polar bands. Without a careful assessment, the effective resolution for the limited-area seems to be closer to the mesoscale, but that is due to the larger spread of results in these domains. When the average curve is considered, the effective resolution may be defined approximately at 1100km for the Tropical spectra, around 500km for the Middle curves and approximately at 1000km for the Polar area. The poor results of the ERA5 in terms of effective resolution may be an interesting topic of research, albeit beyond the scope of this paper. Clearly, the grid and resolution changes from the IFS output to the ERA5 configuration take a toll on the effective resolution. Also, the assimilation of observations and the homogenization of data may affect the final effective resolution (Neyestani etal. 2021). Regardless of the source of it, the effective resolution marks the performance limits of the reanalysis and shows the necessity of using high-resolution NWP models for any research of mesoscalar phenomena (Bauer etal. 2015; Mass etal. 2002; Neyestani etal. 2021). It also presents the energetic uncertainties fed to those models when the dataset is used as initial and boundary conditions. In fact, the effective resolution of initial and boundary conditions should be considered when selecting the domain of study for a limited-area Fig. 5 Seasonal comparison of wind kinetic energy spectrum climatology for ERA5. Blue lines are DJF, black lines are MAM, red lines are JJA, green lines are SON, dashed lines correspond to the dissipation rate as per Lindborg (1999) 745Wind kinetic energy climatology andeffective resolution fortheERA5 reanalysis 1 3 Fig. 6 Latitudinal comparison of wind kinetic energy spectrum climatology for ERA5. Green lines are 00°N–30°N, red lines are 30°N–60°N, blue lines are 60°N–90°N, dashed lines correspond to the dissipation rate as per Lindborg (1999) 752 P.Bolgiani et al. 1 3 Quitián-Hernández L, González-Alemán JJ, Santos-Muñoz D, Fernández-González S, Valero F, Martín ML (2020) Subtropical cyclone formation via warm seclusion development: the importance of surface fluxes. J Geophys Res Atmos. https:// doi. org/ 10. 1029/ 2019J D0315 26 Quitián-Hernández L, Bolgiani P, Santos-Muñoz D, Sastre M, DíazFernández J, González-Alemán JJ, Farrán JI, Lopez L, Valero F, Martín ML (2021) Analysis of the October 2014 subtropical cyclone using the WRF and the HARMONIE-AROME numerical models: assessment against observations. Atmos Res. https:// doi. org/ 10. 1016/j. atmos res. 2021. 105697 Ricard D, Lac C, Riette S, Legrand R, Mary A (2013) Kinetic energy spectra characteristics of two convection-permitting limitedarea models AROME and meso-NH. Q J R Meteorol Soc 139(674):1327–1341. https:// doi. org/ 10. 1002/ qj. 2025 Robertson FR, Roberts JB, Bosilovich MG, Bentamy A, Clayson CA, Fennig K, Schröder M, Tomita H, Compo GP, Gutenstein M, Hersbach H, Kobayashi C, Ricciardulli L, Sardeshmukh P, Slivinski LC (2020) Uncertainties in ocean latent heat flux variations over recent decades in satellite-based estimates and reduced observation reanalyses. J Clim. https:// doi. org/ 10. 1175/ JCLI-D190954.1 Rodríguez O, Bech J (2021) Tornadic environments in the Iberian Peninsula and the Balearic Islands based on ERA5 reanalysis. Int J Climatol. https:// doi. org/ 10. 1002/ joc. 6825 Sanchez-Laulhe JM, Martin F (2006) Analysis of the extratropical transition of the tropical cyclone Delta. 5a Asamblea HispanoPortuguesa de Geodesia y Geofisica, 4 pp. ISBN: 84-8320-373-1 Santos-Muñoz D, Martín ML, Luna MY, Morata A (2006) Diagnosis and numerical simulations of a heavy rain event in the Western Mediterranean Basin. Adv Geosci. https:// doi. org/ 10. 5194/ adgeo-71052006 Seco A, González PJ, Ramírez F etal (2009) GPS monitoring of the tropical storm delta along the canary islands track, November 28–29, 2005. Pure Appl Geophys 166:1519–1531 Siewert J, Kroszczynski K (2020) GIS data as a valuable source of information for increasing resolution of the WRF model for warsaw. Remote Sens. https:// doi. org/ 10. 3390/ rs121 11881 Skamarock WC (2004) Evaluating mesoscale NWP models using kinetic energy spectra. Mon Weather Rev 132(12):3019–3032. https:// doi. org/ 10. 1175/ MWR28 30.1 Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker DM, Duda MG, Huang X-Y, Wang W, Powers JG (2008) A description of the advanced research WRF version 3. In Technical Report. https:// doi. org/ 10. 5065/ D6DZ0 69T Stefanova L, Krishnamurti TN (2011) Kinetic energy exchanges between the time scales of ENSO and the Pacific decadal oscillation. Meteorol Atmos Phys. https:// doi. org/ 10. 1007/ s007030110162-8 Sun Z, Franklin C, Zhou X, Ma Y, Zhu H, Barras V, Roff G, Okely P, Rikus L, Hu B, Bi D, Dix M, Marsland S, Yan H, Hanna N, Golebiewski M, Sullivan A, Rashid H, Uotila P, Puri K (2013) Improvements in atmospheric physical parameterizations for the Australian Community Climate and Earth-System Simulator (ACCESS). In CAWCR Technical Report No. 061. Takahashi YO, Hamilton K, Ohfuchi W (2006) Explicit global simulation of the mesoscale spectrum of atmospheric motions. Geophys Res Lett. https:// doi. org/ 10. 1029/ 2006G L0264 29 Taszarek M, Kendzierski S, Pilguj N (2020) Hazardous weather affecting European airports: climatological estimates of situations with limited visibility, thunderstorm, low-level wind shear and snowfall from ERA5. Weather Clim Extr 28:100243. https:// doi. org/ 10. 1016/j. wace. 2020. 100243 Tripoli GJ, Medaglia CM, Dietrich S, Mugnai A, Panegrossi G, Pinori S, Smith EA (2005) The 9–10 November 2001 Algerian flood: a numerical study. Bull Am Meteorol Soc. https:// doi. org/ 10. 1175/ BAMS86-91229 Tulloch R, Smith KS (2006) A theory for the atmospheric energy spectrum: depth-limited temperature anomalies at the tropopause. Proc Natl Acad Sci USA. https:// doi. org/ 10. 1073/ pnas. 06054 94103 Uppala SM, Kållberg PW, Simmons AJ, Andrae U, da Costa Bechtold V, Fiorino M, Gibson JK, Haseler J, Hernandez A, Kelly GA, Li X, Onogi K, Saarinen S, Sokka N, Allan RP, Andersson E, Arpe K, Balmaseda MA, Beljaars ACM, Woollen J (2005) The ERA-40 re-analysis. Q J R Meteorol Soc. https:// doi. org/ 10. 1256/ qj. 04. 176 Valero F, Luna MY, Martín ML, Morata A, González-Rouco F (2004) Coupled modes of large-scale climatic variables and regional precipitation in the western Mediterranean in autumn. Clim Dyn. https:// doi. org/ 10. 1007/ s003820030382-9 Vallis GK, Shutts GJ, Gray MEB (1997) Balanced mesoscale motion and stratified turbulence forced by convection. Q J R Meteorol Soc. https:// doi. org/ 10. 1256/ smsqj. 54208 Van der Hoven I (1957) Power spectrum of horizontal wind speed in the frequency range from 00007 to 900 cycles per hour. J Meteorol 14(2):160–164. https:// doi. org/ 10. 1175/ 15200469(1957) 014% 3c0160: PSOHWS% 3e2.0. CO;2 VanZandt TE (1982) A universal spectrum of buoyancy waves in the atmosphere. Geophys Res Lett. https:// doi. org/ 10. 1029/ GL009 i005p 00575 Zhang W, Villarini G, Scoccimarro E, Napolitano F (2021) Examining the precipitation associated with medicanes in the highresolution ERA-5 reanalysis data. Int J Clim. https:// doi. org/ 10. 1002/ joc. 6669 Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.