In this work, we use the WRF model V4.1 with 400 grid points in both the west-east and south-north directions, and 55 vertical levels extending from the surface to 50 hPa . The model horizontal grid resolution is 4 km, and the domain covers the Central Mediterranean basin. The center of the domain is located at (15° E, 40° N) (see Fig. ). The physical parameterisation used in the model include the Thompson microphysics scheme , the Mellor–Yamada–Janjic turbulent kinetic energy boundary layer scheme , the Dudhia scheme for shortwave radiative transfer , and the Rapid Radiative Transfer Model (RRTM) for longwave radiation . Convection is assumed explicitly resolved and no cumulus parameterization is activated. The setting of the WRF model outlined above is the result of a compromise between the quality of the results and the computational resources. , in a comparative study using different settings of the WRF model for the simulation of the Medicane Ianos, showed that a setting similar to that used in this paper gave the best result. In addition, the results of this model setting is well in line with the results of , who used several NWP models, including WRF, to simulate the evolution of Ianos.

The different members of the WRF ensemble are generated taking initial and boundary conditions (IC/BC) from the European Centre for Medium-range Weather Forecast – Ensemble Prediction System (ECMWF-EPS) of the Integrated Forecasting System (IFS) run issued at 12:00 UTC on 15 or 16 September 2020, depending on the numerical experiment considered. The ECMWF-EPS consists of one unperturbed (control) member and 50 perturbed members, resulting in a total of 51 WRF runs nested within the ECMWF-EPS initial and boundary conditions. As a result of this setting the WRF ensemble has 51 members and each member of the WRF ensemble is numerated following the ECMWF-EPS member that initialized WRF. The spatial horizontal grid resolution of the ECMWF-EPS for the Medicane Ianos is about 18 km.

In the following we refer to the numerical experiment starting at 12:00 UTC on 16 September 2020, initialized from ECMWF-EPS analysis/forecast cycle issued at the same time (see Fig.  for a schematic of the simulations discussed in this paper). Other experiments, starting at different times are discussed in Sect. .

Two different data assimilation experiments are considered: a 3-hourly cycle and a 24-hourly cycle. In the 3-hourly cycle, referred to as WIV_3h, WIVERN winds along the LoS are assimilated every 3 h for 48 h. Although WIVERN would have sampled Ianos less frequently, this 3 h experiment is used to assess the effectiveness of WIVERN wind data assimilation under idealized conditions, assuming the satellite operates in a constellation formation. In addition, the WIV_3h experiment will be used to show some characteristics of the data assimilation. Hereafter, “WIVERN winds DA” refers to the assimilation of WIVERN in-cloud winds measured along the line of sight.

In the 24-hourly cycle, referred to as WIV_24h, a single assimilation of WIVERN winds is performed at 12:00 UTC on 17 September, when Ianos was already fully developed. Finally, a control ensemble, CTRL, starting at 12:00 UTC on 16 September 2020 and running for 2 d, is included as reference. This ensemble is run without any data assimilation (no other data are assimilated in the experiments considered in this paper, except WIVERN winds), using only different initial and boundary conditions derived from the ECMWF-EPS.

For data assimilation, we use the 3DVar developed by , based on the work of (see also for recent developments of the 3DVar software). For both WIV_3h and WIV_24h the background error covariance matrix is computed from the CTRL ensemble members at 12:00 UTC on 17 September 2020 by: 1B=XXT2X=1Nens-11/2xb1-xb‾,xb2-xb‾,…,xbNens-xb‾, where Nens is the number of ensemble members and xb‾ is the ensemble average. Further details about the background error matrix and its implementation in the 3DVar are given in Appendix A. For a complete reference, the reader is referred to and . The date of the 12:00 UTC on 17 September was used to compute the background covariance error matrix for two main reasons: (a) the WRF forecast is far enough from the initialization time and the model has developed its own dynamic and thermodynamics characteristics; (b) the spread of the ensemble is similar to that of at the same time, and the results of this paper can be representative of more general conditions, using an ensemble of different models.

To evaluate the impact of WIVERN Doppler data assimilation on the WRF forecast, we adopted the following steps:

First, we generated an ensemble of the WRF model nested in the ECMWF-EPS of the IFS, starting at 12:00 UTC on 16 September 2020 (CTRL ensemble).

Figure  shows the 51 trajectories of the CTRL ensemble. Each trajectory is defined by tracking the position of minimum sea-level pressure around the area of the Medicane. The model output is saved every 1 h and two consecutive sea-level pressure minima are connected by a segment. The color bar corresponds to the colors of the segments and indicates the pressure at the initial point of each segment. The dots, plotted every 3 h for clarity, correspond to the position of the cyclone at different times (there are three segments between two dots). As expected, the trajectories are initially close to each other, but diverge with time, due to the amplification of small differences in the initial conditions by the evolving atmospheric flow. This is confirmed by the spread of the ensemble, which steadily increases from 23.2 km at 00:00 UTC on 17 September to 60.4 km at 06:00 UTC on 18 September. The red line in Fig.  shows the best a posteriori estimated trajectory. According to this trajectory, Medicane Ianos made landfall between the islands of Zakynthos and Kefalonia . As stated in Sect.  the minimum surface pressure of the best estimated trajectory remains too high compared to observations. This discrepancy is because the reference trajectory is derived from the ERA5 reanalyses, whose horizontal resolution (30 km) smears out the minimum pressure at the center of the storm. This is confirmed by the fact that the ECMWF-IFS operational analysis, having a higher horizontal resolution (9 km), is about 10 hPa lower than the ERA5 reanalysis. Therefore, we only considered the trajectory, i.e. the position of the surface minimum pressure, and not the sea level pressure values, when comparing the WRF ensemble trajectories of the Medicane Ianos with the reference trajectory.

As shown in Fig. , most simulated trajectories are displaced to the south of the best a posteriori estimated trajectory. This result is in agreement with that of , showing that the forecast of the Ianos trajectory of several meteorological models, including WRF, is to the south of the best estimated trajectory.

The representative member of the WRF ensemble was selected by minimizing the average distance between the members and the best estimated trajectory. This average distance is calculated as: 3dbe,m(t)=rbe(t)-rm(t),4D‾=∑t=1T∑m=1Mdbe,m(t)TM, where rm and rbe are the position vectors of the minimum sea-level pressure of the mth ensemble member and the best estimated trajectory, respectively, at time t. The distance of the whole ensemble from the best estimated trajectory (D‾) is given by averaging dbe,m over all ensemble members M and forecast times T. The trajectory error was computed over the period from 15:00 UTC on 16 September 2020 to 06:00 UTC on 18 September 2020, based on the hourly WRF output. This time range was chosen considering two requirements: (a) the simulation starts at 12:00 UTC on 16 September, and the minimum pressure at this initial time is determined by the ECMWF-EPS initialisation rather than by the WRF evolution; (b) after 06:00 UTC on 18 September, many ensemble members made their landfall. To simplify the analysis, we consider the trajectory of the Ianos evolution over the Ionian Sea.

The distances between each member of the CTRL ensemble and best estimated trajectory from were computed. The smallest distance, 30.0 km, is achieved by member 42, while the largest, 101.2 km, is achieved by member 11. The trajectory of member 42 is shown in black in Fig. . It is apparent that this member follows well the best estimated trajectory of Ianos. According to the result of Fig. , member 42 is chosen as the representative member and is used to generate pseudo-observations of the Medicane Ianos, as if it would have been observed by WIVERN. From now on, the member 42 represents our truth, i.e. the simulation to reproduce after applying WIVERN winds DA to other ensemble members.

WIVERN has a conically scanning geometry with the antenna pointing at 41° off nadir. The antenna does 12 rpm and the winds along the LoS are a combination of the zonal, meridional and vertical wind components. The winds along the LoS are given by: 5fU,V,W=Usin⁡θcos⁡ϕ+Vsin⁡θsin⁡ϕ+Wcos⁡θ, where θ is the angle between the WIVERN antenna and the vertical direction (41°), ϕ is the azimuth, and U, V, W are the zonal, meridional and vertical wind components. Assimilation is done in stratiform areas where W is negligible. Stratiform areas are simply identified by the presence of a radar echo above a minimum threshold (-15 dBz), as the attenuation of the radar signal in deep convective areas prevents the return of the echo from these areas (see below). In addition, for the setting of the WIVERN simulator used in this paper, we are considering observations averaged over a volumes of 5 by 5 km² in the horizontal and 500 m thickness in the vertical direction and it is not common to have W velocities comparable to U and V velocities on these large volumes. Finally, there could be occurrences where/when we assimilated the WIVERN winds in volumes where W is not negligible compared to U and V, nevertheless we assumed W negligible. For stratiform areas, the WIVERN winds along the LoS are given by: 6f(U,V)=Usin⁡θcos⁡ϕ+Vsin⁡θsin⁡ϕ.

Pseudo-observations generated applying the WIVERN simulator to the representative member 42 scene at 12:00 UTC on 17 September 2020 are shown in Fig.  for three different vertical levels. Figure  displays also the position of the Ianos minimum sea level pressure, which is well inside the WIVERN swath, showing that the storm is well sampled. The value of the pseudo-observation is the component of the wind in the direction where the antenna is pointing. As shown by Eq. (), the wind component along the LoS are dependent on the azimuth and on the angle between the radar antenna and the vertical direction (41°) and they do not have a straightforward physical interpretation.

As shown in Fig. , Ianos is well sampled by WIVERN at 12:00 UTC on 17 September. However, WIV_3h simulation uses WIVERN pseudo-observations from 15:00 UTC on 16 September to 09:00 UTC on 18 September every 3 h. Figure b shows that the Ianos center is well inside the WIVERN swath for most of the times, so we can infer that the storm is well sampled. However, as Ianos approaches the land, its center is closer to the WIVERN swath edge and the sampling of Ianos becomes suboptimal.

The observation error σLoS2, decreases with increasing signal to noise ratio, as discussed in . For WIVERN winds along the LoS, the observation error is given by: 7σLOS2=1NvNyq22(πβ)21+1SNR2-β2, SNR=10Z-Zmin⁡10;β=e-12π2σv2vNyq2;vNyq=λ4THV, where λ = 3 mm is the radar wavelength, THV = 20 µs is the separation between the two polarized pulses H and V, N = 40 is the number of pulse pairs, σv = 4 m s⁻¹ is the Doppler spectral width, vNyq is the Nyquist velocity, and Zmin⁡ = -15 dBZ. With these settings, WIVERN pseudo-observations are generated at 5 km horizontal resolution. The σLOS2 does not take into account errors like non uniform beam filling, wind shear, and mispointing errors . These errors are expected to be lower than 1 m s⁻¹ . However, to account for these errors the corrected observation error σcLOS2 is: 8σcLOS2=σLOS2+c12 with c1 = 1 m s⁻¹. In summary, the error associated to each pseudo-observation is given by Eq. () and is a function of the signal-to-noise ratio, which is a function of the reflectivity. The observation error covariance matrix is diagonal, i.e. that observation errors are assumed uncorrelated. However, observation errors are correlated and their correlation decreases with the distance among the observations . In this paper, pseudo-observations are generated at 5 km horizontal resolution, nevertheless they are thinned to 10 km distance to partially account for assuming a diagonal observation error covariance matrix.

In WIVERN simulator the winds along the LoS are generated starting from the WRF wind components of the member 42 and applying Eq. (). The noise is added to the observation through Eq. (), which depends on the signal-to-noise ratio. To have wind pseudo-observations along the LoS, a minimum reflectivity of -15 dBZ must be observed. The reflectivity is computed from the distribution of the WRF hydrometeors simulated by member 42. It follows that pseudo-observations are not generated if clouds are optically too thin or, as the simulator accounts for the radar signal attenuation, if the radar beam is attenuated, as in deep convective areas. Figure a, shows the number of pseudo-observations available at different vertical levels at 12:00 UTC on 17 September, which is particularly important as it is the time when WIVERN winds are assimilated in WRF for WIV_24h experiment. The largest number of observation is at 7 km height and decreases at higher levels due to the reduced optical thickness of clouds, and at lower levels due to radar signal attenuation.

Figure b shows the wind observation error averaged for each vertical level (black curve), the model wind speed error (blue curve) and the radio-sounding wind errors used in the WRF data assimilation (red line) as functions of altitude. The latter was derived from the file SPD.txt available in the WRFDA tool (see https://www2.mmm.ucar.edu/wrf/users/wrfda/, last access: 12 January 2026). The comparison between the WIVERN LoS error and the radio-sounding error shows the good performance of WIVERN observations, whose error is lower than radio-sounding above 4.5 km.

The model wind speed error is given by the square root of squared error for the zonal and meridional wind components. These errors are given, for each level, by the diagonal elements of the vertical component of the background error matrix (Bz, see Appendix B of for details). The model wind speed error is larger than the observation error; this suggests a large impact of WIVERN data assimilation for the Ianos case study. To study the sensitivity of the results to the assumed observation error, Sect.  presents an experiment in which the observation error is inflated to match the model wind speed error.

Finally, no data thinning is applied in the vertical direction and pseudo-observations are assimilated starting from 1 km above the sea (the largest part of the pseudo-observations assimilated) and 2 km above the land, to account for ground clutter.

After generating pseudo-observations, we performed a run of the whole ensemble assimilating WIVERN pseudo-observations every 3 h. Before showing the results of assimilating WIVERN winds on the WRF forecast, it is important to assess how WIVERN observations are being assimilated. For this purpose, we consider observation diagnostics in the form of mean innovation (e.g., bias), root-mean-square innovation (RMSI) and the total number of data assimilated for each assimilation cycle . Innovation and RMSI are calculated by taking the difference between prior and posterior fields H(x) and comparing against observations y: 9INNOV=yn-H(xn) and: 10RMSI=∑i=1NINNOVi/N, where N represents the number of pseudo-observations assimilated.

These statistics are reported in Fig. . The RMSI slowly increases from the start of the simulation until the end. This reflects the increase of the spread of the ensemble. Close to the end of the forecast, there is an increase of the RMSI as a consequence of the increased spread of the trajectories approaching the landfall. The RMSI is reduced by 15 % through WIVERN DA at the start of the forecast; this percentage decreases as the forecast progresses (down to 5 %) then it increases again close to the end of the forecast, when Ianos approaches the landfall (15 %–20 %). The bias remains small before and after DA, showing that WIVERN pseudo-observations are unbiased. Moreover, WIVERN DA tend to reduce this small bias. The number of pseudo-observations assimilated are about 50 % of the total number of pseudo-observations available; this is expected because a data thinning of 10 km is applied at each level and pseudo-observations are generated at 5 km horizontal resolution.

The result of assimilating WIVERN winds every 3 h is shown in Fig. . The assimilation of WIVERN winds every 3 h impacts the Ianos trajectory in two ways: first, all the trajectories are now focused along the trajectory of the representative member 42, which is shown in black and without dots for clarity; second, the landfall occurs in the northern part of the Peloponnese with many member crossing the Zakynthos island or passing through the gap between the Kefalonia and Zakynthos islands. The D‾ from the member 42 is 14.9 km, to be compared with 62.5 km of the CTRL ensemble (Table ).

Importantly, the En3DVar used in this paper neglects cross correlation among variables and only zonal and meridional wind components are adjusted by the DA. Nevertheless, the other atmospheric variables are adjusted by the model physics. For example, the cyclostrophic flow is important for Medicanes and, once velocities are adjusted by DA, the pressure field is adapted to the adjusted winds . These changes propagates to other variables through the model physics and, in general, the simulation has a different evolution. This point is demonstrated, for example, for the minimum sea level pressure in Fig. , with the spread of the minimum sea level pressure substantially reduced by the WIVERN winds DA. It is also noted the increase of the minimum sea level pressure of WIV_3h ensemble forecast (Fig. b) compared to the CTRL ensemble forecast (Fig. ) as many members of the CTRL ensemble were predicting a pressure lower than the member 42.

It is important to note that the current setup of WIV_3h has a very short spin-up time (3 h). Since the WRF model is run on a single, relatively small domain at convection-permitting resolution, the atmospheric fields initialized from the coarser ensemble forecast could produce imbalances in the WRF forecast, lowering its quality. While a longer spin-up time will be adopted in future studies, we did a sensitivity experiment to evaluate the impact of the short spin-up time for the WIV_3h experiment. We chose randomly 20 members of the ensemble and we assimilated the WIVERN winds starting from 00:00 UTC on 17 September allowing for a 12 h spin-up time. Results for the 20 members (not shown) are similar to those of Fig. , in the sense that the trajectories of the ensemble strictly follow the trajectory of member 42 after 12 h from the first DA time, i.e. 12:00 UTC on 17 September. So, for the specific case study and settings of this paper, the short spin-up time used by WIV_3h does not impact the quality of the results.

Hereafter we focus on the WIV_24h numerical experiment. In this experiment, data assimilation is done at 12:00 UTC on 17 September for each member of the ensemble, then follows a 24 h forecast. The motivations for choosing the 12:00 UTC on 17 September are: (a) the storm is well formed, so we can generate a good pseudo-scene; (b) the landfall is far enough (18 h before the landfall) and the forecast is of practical importance. WIV_24h represents a realistic scenario in which WIVERN sample Ianos one-time in the period of the simulations considered in this paper. Indeed, considering the 1.5 d revisiting time at the equator of WIVERN and the fact that Ianos lasted few days, the Ianos Medicane would have been sampled at least once. We chose the 12:00 UTC on 17 September for the reasons stated above; in this scenario, the Ianos Medicane would have been sampled two times (Fig. b) in the time window considered in this work, but the second time would have been too close to the landfall for the forecasting purposes of this paper.

The trajectories of WIV_24h ensemble are shown in Fig. . The comparison of Fig.  and Fig.  shows the positive impact of WIVERN DA on the forecast of the Ianos trajectories. In particular, the CTRL forecast, Fig.  shows several trajectories going towards the southern part of the Peloponnese; these trajectories are shifted northward in the experiments with WIVERN DA, even if the WIV_24h trajectories still tend to go to the south of the member 42 trajectory.

In Fig. , the violet arrow indicates the time of analysis. It is interesting to note that the trajectories converge after the analysis, as the different ensemble members tend towards the representative member 42. These results are summarized in Table , for the period 12:00 UTC on 17 September to 06:00 UTC on 18 September, showing the D‾ of the ensemble from the member 42 for the CTRL, WIV_3h and WIV_24h ensembles. The table also includes the skill of the WIV_3h and WIV_24h ensembles compared to CTRL. The skill score, I(%), is given by: 11I(%)=100D‾CTRL-D‾exp⁡D‾CTRL, where D‾ is given by Eq. () and exp can be 3 or 24 h.

It is interesting to examine the trajectory error as a function of the ensemble member (i.e. Eq.  without averaging over members) and as a function of time (i.e. Eq.  without averaging over time). These statistics are shown in Fig. . Considering the error as a function of ensemble member, Fig. a, there are a few points to note. First, the WIV_3h ensemble performs better than CTRL across all members. This shows that assimilating WIVERN every 3 h gives a strong constraint on storm evolution for all the members. Assimilating WIVERN only once (WIV_24h) still has a positive impact on the simulation of the Medicane Ianos' trajectory, with the error reduced for almost all members. Sometimes, the error is substantially reduced, as for the member 11 (and many others), sometimes the improvement of the trajectory forecast is small, as for member 47, and few times there is a negative impact of assimilating WIVERN winds, as for member 35.

Overall, the analysis of Fig. a, leads to three main conclusions: (a) assimilation of WIVERN winds along the LoS improves the forecast of the Ianos trajectory; (b) the magnitude of the improvement varies depending on the ensemble member; and (c) the negative impact of WIVERN DA is limited to few cases and less than 10 km, while the positive impact is often larger than 15–20 km. In addition, while the improvement of WIVERN DA is dependent on the member, this dependence is greatly reduced if WIVERN is assimilated every 3 h, showing the ability of WIVERN to substantially change the storm evolution, when frequently assimilated.

Figure b shows the trajectory error as a function of forecasting time from 15:00 UTC on 16 September to 06:00 UTC on 18 September. The error of the CTRL ensemble increases with the forecast time, as expected. The WIV_24h forecast differs from the CTRL forecast after the analysis (12:00 UTC on 17 September). The improvement given by WIVERN winds DA is large and lasts until the end of the period considered, showing a long-lasting effect of WIVERN DA. This point will be further investigated in Sect. .

To study the impact of WIVERN DA on the WRF forecast in more detail, we focus on the member 10, one of the members showing a substantial impact of WIVERN DA. Figure  shows the impact of 3DVar on meridional wind component. The background (panel a) represents the strong winds associated with the Medicane Ianos, with meridional wind speeds in the lower troposphere reaching up to about 40 m s⁻¹, and a cyclonic circulation around the storm center (bipolar structure). After assimilation (panel b), the winds are still very intense and the cyclonic circulation well represented as in the background; however, the whole circulation has shifted several tens of kilometers to the east (refer to the longitude 17.5° E).

The difference between the two fields has a “tripolar” pattern (panel c). From west to east, the meridional wind difference is positive to the west of 17.5° E, negative between 17.5 and 19° E, and then positive again towards the east. This pattern corresponds to the net eastward shift of the storm center, and to a small reinforcement of the meridional wind component.

The vertical cross-section of the meridional wind difference (analysis minus background) is shown in Fig. d). It highlights a main tripolar pattern close to the storm center (around 18.0° N), with negative values reaching up to -34 m s⁻¹ at about 2500 m a.s.l. This tripolar pattern reaches 8.5 km height and is a consequence of the eastward shift of the storm center in the analysis. Interestingly, despite a decrease of the number of pseudo-observations in the lower troposphere (Fig. a) caused by the attenuation of the radar signal, the number of pseudo-observations is enough to produce a substantial change of the circulation in the lower troposphere. Above 8.5 km, the difference between the analysis and background becomes more complex with several localized positive and negative differences. This pattern is determined by observations at these levels and by the vertical structure of the background error matrix.

The impact of WIVERN winds DA is long lasting; Fig.  shows the 18 h forecast of the sea level pressure and surface winds starting from the analysis of Fig. . The impact of WIVERN DA on the evolution of this member is high. First, the position of the storm is much improved by WIVERN DA; while the member 42 (panel a) has just crossed the Zakynthos island, the storm center of member 10 without WIVERN DA is in the open sea (about 100 km to the SW of Zakynthos). The storm center of the member 10 after DA is close (about 10 km) to Zakynthos. Importantly, the minimum sea level pressure is also adjusted by WIVERN DA; it is about 983 hPa for member 42 and for member 10 after DA, while it is lower than 975 hPa for member 10 without data assimilation. Similarly, the maximum wind speed at the surface of member 10 with WIVERN DA (28.1 m s⁻¹) is much closer to the representative member 42 (31 m s⁻¹) compared to the member 10 without WIVERN DA (39.8 m s⁻¹). In summary, Fig.  shows that the assimilation of WIVERN winds changes the evolution of the storm not only for the trajectory but also for the physical characteristics, providing a representation of the Medicane Ianos closer to member 42. It is important to note that, as we assimilated WIVERN winds pseudo-observations derived from member 42, this member becomes our truth and being closer to it is equivalent to have an improvement of the forecast.

In this section we discuss the impact of assimilating the WIVERN winds along the LoS on the prediction of the precipitation in Kefalonia. As stated before, member 42 represents our truth and comparison is done against its output, and no real observations are considered in this section. Figure  shows the precipitation accumulated from 12:00 UTC on 17 September to 12:00 UTC on 18 September for the CTRL ensemble (average), the representative member 42, and the WIV_24h ensemble (average). The precipitation accumulated by the member 42 clearly mirrors the trajectory followed by the cyclone with accumulated rainfall larger than 300 mm d⁻¹ in a swath oriented from SW to NE, ending over the Kefalonia island.

The CTRL ensemble shows a precipitation pattern which is oriented in the NW-SE direction, differently from the pattern of the member 42. The field of CTRL is smoothed compared to the representative member, but this feature is caused by the average operator. The precipitation on the island of Kefalonia is largely underestimated compared to member 42 because the rainfall is 150 mm d⁻¹ for CTRL compared to more than 300 mm d⁻¹ for the member 42.

The rainfall accumulated by the ensemble WIV_24h is in better agreement with the representative member 42 compared to CTRL because the intense precipitation swath is oriented in the SW-NE direction and the rainfall predicted over Kefalonia is greater than 300 mm d⁻¹. This is confirmed by the RMSE, calculated with respect to member 42 and averaged over the area defined by the longitudes 17.5–22.5° E and by the latitudes 36.0–39.0° N (red rectangle of Fig. ), which decreases from 51.0 mm of CTRL to 40.5 mm of WIV_24h. Although the RMSE is improved by WIVERN DA, the average precipitation over the red rectangle of Fig.  is slightly worsened. The average rainfall of the member 42, of the CTRL ensemble and of the WIV_24h ensemble are, respectively, 59.3, 63.6, and 64.1 mm. This result, i.e. a notable improvement of the RMSE and a similar bias, confirms that the improvement of the RMSE is determined by a better representation of the location and intensity of the rainfall in the most intense part of the storm (i.e. north of the trajectory of the representative member 42).

In this section we consider the results of two sensitivity tests: in the first test we inflated the observation error, in the second test we changed the background error covariance matrix. For the first experiment the observation error is assumed to be equal to the model wind speed error and dependent only on height. The observation error is shown in Fig. b (curve E2) and roughly corresponds to inflating the WIVERN error by a factor of 1.5–2; we will refer to this experiment as E2.

In the second sensitivity experiment, we changed the background error covariance matrix, which was computed applying the NMC (National Meteorological Center; ) method to the period 1–30 September 2020. Specifically, the background error matrix was computed from the difference of two WRF forecasts, with lead times of 12 and 24 h, verifying at the same time, both 12:00 and 00:00 UTC, for the whole period. The WRF forecasts use the operational analysis/forecast cycle issued by the ECMWF at 00:00 and 12:00 UTC on each day of September as initial and boundary conditions. In this configuration the background error matrix is representative of the meteorological conditions of the month of September 2020, while in the approach used for the WIV_24h experiment, Eq. (), the background error matrix is representative of the error of the day. This sensitivity experiment will be referred to as NMC.

Results of both experiments are represented by the distribution of the trajectory errors of the ensemble members, i.e. D‾ without averaging over members, shown in Fig. . The largest error correspond to the CTRL experiment, followed by NMC, E2, and WIV_24h experiments.

The assimilation of WIVERN winds has, in general, a positive impact on the prediction of the Medicane Ianos trajectory as the experiment with doubled observation error has a performance much closer to WIV_24h than to CTRL. Specifically, the average error of the experiment E2 is very similar to that of WIV_24h ensemble (both about 34.4 km), however the median error is larger (35.4 km) for E2 compared to WIV_24h (32.7 km). Similarly, the spread of the ensemble error is larger for E2 (14.5 km) compared to WIV_24h (13.3 km). Statistics for the trajectories error distributions are summarized in Table .

To better understand the low sensitivity of this case study to the observation error, Fig.  shows the bias and RMSE of CTRL as a function of the vertical level. The first guess error (RMSE) is larger than the observation error and also of the model wind speed error (Fig. b), and inflating the observation error has a relatively small impact on the WIVERN winds DA performance. However, it is important to point out that winds around Medicanes are very intense, and a wrong positioning of the storm results in high first-guess errors for the winds; in general it is expected that the role of the WIVERN observation error is larger than that reported for the Ianos case study.

Changing the background error matrix for this specific case has a notable impact on the trajectory forecast (Fig. ). This is expected in some measure, as the physical characteristics of the Medicane are rather different from those of the circulation of the period, and choosing a climatological and static background error matrix is suboptimal compared to choosing a background error matrix aware of the specific error of the day. Specifically, the trajectory error averaged over the whole ensemble for the NMC experiment is 44.7 km (35.4 km for WIV_24h), the median is 42.7 km (32.7 km for WIV_24h) and the spread of the ensemble is 16.9 km (13.3 km for WIV_24h). All these statistics show the sensitivity of the WIVERN DA impact to the choice of the background error matrix (Table ).

In this section we consider the result of two experiments in which the ensemble is initialized one day before compared to that of previous sections, i.e. at 12:00 UTC on 15 September, and two analysis/forecasts are considered: (a) assimilation at 12:00 UTC on 16 September and forecast from 12:00 UTC on 16 September to 00:00 UTC on 18 October (36 h forecast, Fig. ), experiment WIV_24h16; and (b) assimilation at 00:00 UTC on 16 September and forecast from 00:00 UTC on 16 September to 00:00 UTC on 18 October (48 h forecast, Fig. ), experiment WIV_12h. The technique, the WRF and the data assimilation settings are those discussed in previous sections, with the following differences: (a) when generating pseudo-observations, the track of the WIVERN satellite (Fig. b) was shifted by 2° to the west to center the storm position; (b) the model output was saved every 3 h and there are two traits between two dots; (c) the background error matrix was computed at 12:00 UTC on 16 September 2020, i.e. 24 h after the ensemble initial time. We also consider the result of the CTRL forecast, starting at 12:00 UTC on 15 September 2020 (Fig. ).

Figure a shows the result of the CTRL forecast. The best forecast, whose trajectory is in best agreement with the a posteriori estimated trajectory of Ianos , is that of the member 32 whose track is depicted in black. Looking to the results of Fig. a there are two main points to highlight: (a) the spread of the trajectory is much larger than that of Fig. ; (b) many trajectories go south of Greece and towards the Aegean Sea and, for there trajectories, the surface pressure remains greater than 1000 hPa. These two points show the lower predictability of the Medicane Ianos on 15 September compared to 16 September; more specifically, from Fig. a it is not clear if the storm would have deepened, and the spread of the trajectories remains wide to take precise actions.

Both uncertainties are solved by the assimilation of WIVERN pseudo-observations in the WIV_24h16 forecast (Fig. b). The trajectories of this ensemble are all going towards the western Peloponnese and the storm is deepening. The trajectories of the WIV_12h forecast are shown in Fig. c; all trajectories, with just one exception, approach the western and southern Peloponnese; again most of these trajectories show a clear deepening of the cyclone improving the forecast of the CTRL ensemble.

All in all the results of this section show that WIVERN would have been able to constrain the forecast of the Medicane Ianos also for the ensemble issued on 15 September 2020, giving a clear suggestion, with more than a day of advance, that the Medicane would have made its landfall in western/southern Peloponnese and that the storm would have deepened. It is also noticed that the forecast of the Medicane Ianos can be refined by the WIVERN wind observations DA as the Medicane is approaching the landfall; this is clearly shown by the comparison of the ensemble forecasts of Figs. , , and b, c.