On 16 September 2017 Italy was under the influence of a cyclone that developed to the lee of the Alps. The storm crossed Italy from NW to SE leaving light precipitation over most of the peninsula with moderate rainfall over central Italy. Figure 1 shows the precipitation recorded by the Italian rain gauge network on 16 September 2017. Light precipitation (<5 mm d-1) is reported by 1018 rain gauges out of the 1666 stations measuring precipitation (≥0.2 mm d-1) on this day. A total of 14 stations over central Italy recorded more than 50 mm d-1. The maximum precipitation was 90 mm d-1 in Città di Castello (Umbria region, Fig. 1). Because the meteorological radar closest to the maximum precipitation is over Mount Serrano (Fig. 1), hereafter this event will be referred to as Serrano.

The synoptic conditions during the event are shown in Fig. 2. At 500 hPa (Fig. 2a), a trough, elongated in the SW–NE direction, extends over western Europe and air masses are advected from SW towards the western Alps. The interaction between the airflow and the Alps generates a low pressure to the lee of the Alps over northern Italy.

The analysis at the surface (Fig. 2b) shows the meteorological front represented by the equivalent potential temperature gradient between air masses advected over the Mediterranean Sea from the NW and air masses advected from the south over the Tyrrhenian Sea. The advection of warm unstable air masses towards central Italy is notable.

Infrared satellite images (Fig. 3), from 00:00 UTC on 16 September to 00:00 UTC on 17 September, show that the cold front structure moved slowly from NW to SE. Interestingly, at 00:00 UTC on 16 September, the well-defined cloud system over central Italy (red circle of Fig. 3a) that caused most of the daily precipitation observed between 43.50 and 45.0∘ N is apparent.

The well-defined cloud system over central Italy is also shown in the radar constant-altitude plan position indicator (CAPPI) at 3 km above sea level at 02:00 UTC on 16 September (Fig. 4). This CAPPI is formed by interpolating all the available data from the federated Italian radar network coordinated by the Department of Civil Protection (22 radars; see Sect. 3.3 for their positions) and it is also referred to as the national radar composite (hereafter also mosaic). Several convective cells exceeding 35 dBz can be noted over central-northern Italy. Importantly, the cloud system over central Italy shown by the satellite infrared channel at 00:00 UTC (Fig. 3a) and that of the radar at 02:00 UTC have similar positions, showing that the cloud system was active for several hours over central Italy.

Figure 5 shows the lightning recorded by LINET (lightning detection network; Betz et al., 2009) on 16 September 2017. More than 105 000 flashes were recorded; most of them occurred in the afternoon and evening, but a secondary maximum occurred in the night, from 00:00 to 06:00 UTC. In this phase, more than 3000 flashes were observed over central Italy.

On 9 and 10 September 2017, Italy was hit by a severe storm characterized by intense and widespread rainfall over the country. Figure 6a shows the precipitation on 9 September recorded by the Italian rain gauge network. Rainfall was intense over the Alps, where the maximum daily precipitation was observed (193 mm d-1), and over Liguria, with precipitation of the order of 30–50 mm d-1. One station over Tuscany reported 90 mm d-1, showing that intense precipitation had already started over the region. The storm on 9 September was intense: 20 rain gauges reported more than 100 mm d-1 and 70 rain gauges more than 60 mm d-1. In most cases, this precipitation occurred within a few hours.

The following day (see Fig. 6b) had higher rainfall. Precipitation occurred mainly over central Italy, especially over Lazio, and over northern Italy, in particular over the northeast. In Tuscany, the two stations close to the sea, in the Livorno area, recorded about 150 mm d-1 mostly falling between 00:00 and 06:00 UTC.

Synoptic conditions leading to this storm are shown in Fig. 7. At 500 hPa (Fig. 7a) a trough extended from northern Europe towards the Mediterranean. The interaction between the air masses and western Alps generated a low-pressure system to the lee of the Alps, which crossed the whole peninsula from NW to SE. It is noted that the divergent flow over central and northern Italy favoured upward motions.

At the surface, Fig. 7b, the equivalent temperature gradient over the western Mediterranean is caused by the contrast between pre-existing air masses over the sea and air masses advected from France towards the Mediterranean. The pressure field at the surface advects air masses from the south over the Tyrrhenian Sea. These warm and humid air masses feed the cyclone during its development.

From a synoptic point of view, the Livorno and Serrano cases were similar and represented two cyclones developing to the lee of the Alps (Buzzi and Tibaldi, 1978). However, the Livorno case was more intense than Serrano.

The notable intensity of the Livorno case is confirmed by the lightning observations (Fig. 8). During the evening of 9 September (after 18:00 UTC) about 38 000 flashes were recorded by LINET. On 10 September about 290 000 flashes were recorded over Italy, following the movement of the storm from NW to SE. Therefore, more than 300 000 flashes were recorded from 18:00 UTC on 9 September to 00:00 UTC on 11 September, which is more than 3 times those recorded for Serrano.

Thermal infrared satellite images (channel, 10.8 µm; Fig. 9) show the extension of the cloud coverage every 12 h. It is very evident that the cloud system was associated with a cold front over Europe. More specifically, the satellite image at 00:00 UTC shows the cloud system over the Livorno area (red circle in Fig. 9b), before the most intense precipitation period over Tuscany (00:00–06:00 UTC), while Fig. 9c shows the cloud system over central Italy (orange circle), at the end of the period of intense precipitation over Lazio (06:00–12:00 UTC).

We conclude the synoptic analysis of the case study with two CAPPIs at 3 km observed by the radar network of the Department of Civil Protection. The CAPPI in Fig. 10a, at 00:00 UTC on 10 September, shows the cloud system over Tuscany with reflectivity factors up to 40 dBz. Other clouds caused rainfall over northern Italy. The CAPPI of Fig. 10a is the last one assimilated by the 00:00–03:00 UTC VSF on 10 September described in detail in Sect. 4.2.1.

Figure 10b shows the CAPPI of the national radar mosaic at 3 km above the sea level and at 06:00 UTC. The cloud system is moving towards central Italy with reflectivity factors up to 45 dBz. Other cloud systems are apparent over northern Italy. Figure 10a–b represent the movement of the storm towards the SE well and Fig. 10b shows the last CAPPI assimilated by the 06:00–09:00 UTC VSF shown in Sect. 4.2.2.

The RAMS@ISAC is used as a NWP driver in this work. The model is based on the RAMS 6.0 model (Cotton et al., 2003) with the addition of four main features, as well as a number of minor improvements. First, it implements additional single-moment microphysical schemes, whose performance is shown in Federico (2016): among them, the WSM6 (Hong and Lim, 2006) is used in this paper. Second, it predicts the occurrence of lightning following the diagnostic method of Dahl et al. (2011), with the implementation discussed in Federico et al. (2014). Third, the model assimilates lightning through nudging (Fierro et al., 2012, 2015; Federico et al., 2017a). Fourth, the model implements a 3D-Var data assimilation system (Federico, 2013, hereafter also RAMS-3DVar), whose extension to the radar reflectivity factor is presented in this paper (Sect. 3.3).

The list of the physical parameterization schemes used in the simulations of RAMS@ISAC is shown in Table 1.

Considering the domains and the configuration of the grids (Fig. 11 and Table 2), two different set-ups are used for Serrano and Livorno. For the first case, we use the domains D1 and D2, while for Livorno we also use the domain D3. The first domain covers a large part of Europe and extends over North Africa. Grid horizontal resolution is 10 km (R10). The second domain covers all of Italy and part of Europe and the grid has 4 km horizontal resolution (R4). The third domain covers the Tuscany region, has 4/3 km horizontal resolution (R1), and it is used for Livorno to represent the precipitation field over Tuscany with higher spatial detail. The fine structures of the precipitation field are smeared out over Tuscany using only domains D1 and D2. The operational implementation of the RAMS@ISAC model uses the domains D1 and D2 and no refinements for specific areas of Italy are used because this would require a computing power which is not currently available. Also, grid refinements over Italy would require careful testing of the model performance and data assimilation system, which are out of the scope of this paper.

All domains share the same vertical grid, which covers the troposphere and the lower stratosphere. Vertical levels are more packed close to the ground. Among the 36 levels used in this paper 10 are below 1 km, 14 below 2 km, and 17 below 3 km. The first vertical level is at 50 m above the surface in the terrain following coordinates used by RAMS@ISAC; level 21 is at 5122 m. Above 6 km the model levels are about 1000 m apart, while the maximum allowed distance between two levels is 1200 m. The complete list of the vertical levels is shown in the Supplement of this paper (Table S2 in the Supplement).

The vertical grid is the same as the operational setting of RAMS@ISAC and is a compromise between vertical resolution and computing time. The number of vertical levels will be increased to 42, starting from September 2019, to better resolve the phenomena in this direction (planetary boundary layer processes, vertical motions, interaction between air masses and orography, etc.). Nevertheless the current setting was successfully applied to the forecast of several heavy precipitation events over Italy. A sensitivity test, using 42 vertical levels for the Livorno case, shows similar results to those reported in Sect. 4. Details on this simulation can be found in the Supplement of this paper.

The nesting between the first and second domains is one-way, while the nesting between the second and the third domains is two-way.

VSF was implemented as shown in Fig. 12. First a run with the R10 configuration was performed using the 0.25∘ horizontal resolution Global Forecast System (GFS) analysis–forecast cycle issued at 12:00 UTC as initial and boundary conditions. The R10 run, which started at 12:00 UTC on 16 September for Serrano and at 12:00 UTC on 9 September for Livorno, lasted 36 h and does not assimilate either radar reflectivity factor or lightning. The R10 run was not updated after the acquisition of new data by the analysis system and this is a limitation of the results shown in this paper. However, a sensitivity test for the Livorno case study showed that this limitation does not have a significant impact on the results presented in the next section. Details on this experiment can be found in the Supplement of this paper.

Starting from 12:00 UTC, 10 VSFs were performed using R4 for Serrano and both R4 and R1 for Livorno. The VSF lasted 9 h and used R10 simulation as initial and boundary conditions (one-way nesting). The 9 h forecast was divided into two parts: the first 6 h are the assimilation stage when RAMS@ISAC simulation was adjusted by data assimilation, whereas the last 3 h are the forecast stage, without data assimilation. During the assimilation stage, flashes are assimilated by nudging (Sect. 3.2), while radar reflectivity factor is assimilated every hour by RAMS-3DVar (Sect. 3.3).

It is noted that data assimilation is performed over the domain D2 (R4) only, and the innovations are transferred to the domain D3 (R1) for the Livorno case by the two-way nesting. The domain D3 is used for the Livorno case to refine the resolution of the precipitation field over Tuscany and to show the spatial and temporal precision of the precipitation forecast over Tuscany using data assimilation. However, its usage is exceptional because, as stated above, Italy is a complex orographic country and grid refinements for specific areas are used only after the occurrence of the event. For this reason, the domain D3 is usually not used in RAMS@ISAC and no statistics about the background error are available for this grid.

Because lightning and radar reflectivity factors are cloud-scale observations, their assimilation at higher horizontal resolution by 3D-Var is foreseeable in future works.

The verification of the VSF for precipitation was done by visual comparison of the model output with the rain gauge network of the Department of Civil Protection, which has more than 3000 rain gauges all over Italy.

In addition we considered the FBIAS (frequency bias; range [0, +∞)), where 1 is the perfect score, i.e. when no misses and false alarms occur), POD (probability of detection; range [0, 1], where 1 is the perfect score and 0 the worst value), ETS (equitable threat score; range [-1/3, 1], where 1 is the perfect score and 0 is a useless forecast), and TS (threat score; range [0, 1], where 1 is the perfect score and 0 the worst value). Scores were computed from 2×2 dichotomous contingency tables (Wilks, 2006) for different rainfall thresholds and for different neighbourhood radii. Moreover, performance diagrams (Roebber, 2009) were used to summarize the scores.

Lightning data are provided by LINET (lightning detection network; Betz et al., 2009; nowcast, 2019), which has more than 500 sensors worldwide with the greatest density over Europe (more than 200 sensors). The network has a good coverage over central Europe, and western Mediterranean (from 10∘ W to 35∘ E and from 30 to 60∘ N). The area of good coverage includes the region considered in this paper.

LINET exploits the VLF and LF (very low frequency and low frequency) electromagnetic bands and provides measurements of both intra-cloud (IC) and cloud-to-ground (CG) discharges. IC strokes are detected as long as lightning occurs within 120 km of the nearest sensor thanks to optimized hardware and advanced techniques of data processing (TOA-3D; Betz et al., 2004). According to Betz et al. (2009), LINET has a location accuracy of 125 m for an average distance of 200 km among the sensors verified by strikes into towers of known positions.

The good performance of the LINET network and its ability to detect IC strokes is shown in Lagouvardos et al. (2009) for a storm in southern Germany, while the good performance over Italy, including both CG and IC strokes, is discussed in Petracca et al. (2014).

The lightning data assimilation scheme is that of Fierro et al. (2012, 2014, 2015) and uses the total lightning, i.e. intra-cloud plus cloud-to-ground flashes.

The method starts by computing the water vapour mixing ratio qv: 1qv=Aqs+Bqstanh⁡(CX)(1-tanh⁡(Dqgα)), where coefficients are set to A=0.86, B=0.15, C=0.30, D=0.25, and α=2.2, qs is the saturation mixing ratio at the model atmospheric temperature, and qg is the graupel mixing ratio (g kg-1). X is the number of total flashes (IC+CG) falling in a grid box of domain D2 (R4) in the past 5 min. The mixing ratio qv of Eq. (1) is computed only for grid points where flashes are recorded. More specifically, for each grid point we consider the number of flashes falling in a grid box centred at the grid point in the last 5 min. The mixing ratio of Eq. (1) is compared with that predicted by the model. If the mixing ratio of Eq. (1) is larger than the simulated one, the latter is nudged towards the value of Eq. (1), otherwise the modelled mixing ratio is left unchanged. This method can only add water vapour to the forecast.

The check and eventual substitution of the water vapour is performed every 5 min and it is made within the mixed phase layer zone (0 and -25 ∘C), wherein electrification processes caused by the collision of ice and graupel are the most active (Takahashi, 1978; Emersic and Sounders, 2010; Fierro et al., 2015).

The scheme of Fierro et al. (2012, 2015) was adapted to RAMS@ISAC in Federico et al. (2017a). In particular, the coefficient C of Eq. (1) was rescaled from that of Fierro et al. (2012) considering the different spatio-temporal resolution of gridded lightning data; then the coefficient C was tuned (increased) by sensitivity tests considering two case studies of HyMeX-SOP1 (15 and 27 October 2012; HyMeX stands for the Hydrological cycle in the Mediterranean Experiment – First Special Observing Period occurring between 6 September and 6 November 2012; Ducrocq et al., 2014). The C constant was adapted subjectively as a compromise of increasing the hits and minimizing false alarms. POD and ETS scores were considered metrics for this purpose. Then, Eq. (1) was applied to 20 case studies of HyMeX-SOP1 giving a statistically significant (90 %, or 95 % depending on the rainfall threshold) improvement of the RAMS@ISAC precipitation VSF (3 h).

Nevertheless, a definitive statistic on the performance of rainfall VSF to nudging formulation in RAMS@ISAC is missing and further studies are needed in this direction. Also, the optimal choice of the coefficients A,B,C,D, and α is case dependent.

Fierro et al. (2012) applied the method using Earth Networks Total Lightning Network (ENTLN), which has a detection efficiency (DE) greater than 50 % for IC over Oklahoma, where the ENTLN data were used. The emphasis on IC flashes in the set-up of Fierro et al. (2012) is given because observational and model studies have provided evidence that IC flashes correlate better than CG flashes with various measures of intensifying convection (updraft strength, volume, graupel mass flux, etc.; MacGorman et al. 1989, 2005, 2011; Carey and Rutledge, 1998; Wiens et al., 2005; Kuhlman et al. 2006; Fierro et al., 2006; Deierling and Petersen, 2008). For these reasons methods using both IC and CG flashes perform better than those using CG only, CG flashes being correlated with the descent of reflectivity cores and the onset of the demise of the storm's updraft core (MacGorman and Nielsen, 1991).

The analysis of the case studies shows that IC strokes are about 30 % of the total number of strokes reported by LINET. Also, the fraction of IC strokes to the total strokes depends on the position. For example, for the Serrano case, the fraction of IC strokes detected by LINET over the area hit by the largest precipitation is more than 50 % while over the Adriatic Sea it decreases to 10 %.

It is also noted that the detection efficiency (DE) for IC strokes cannot be reliably compared between LINET and ENTLN because the area is different and the technical details about IC detection remain unclear (type of signals, VLF–LF or very high frequency (VHF), discrimination IC or CG).

For all the above reasons the application of the Fierro method to RAMS@ISAC is not straightforward and it is appropriate to study the dependence of the rainfall VSF on the nudging formulation. This subject is studied in the Supplement of this paper (Supplement Sect. S3) and the results show that the choice of the coefficient of Eq. (1) used in this paper is reasonable.

It is finally noted that despite the limitations noted above, the lightning data assimilation, with the setting of this paper, had a significant and positive impact on RAMS@ISAC rainfall VSF (Federico et al., 2017a, b).

The method assimilates CAPPI of radar reflectivity factor operationally provided by the Italian Department of Civil Protection (DPC). Radar data are provided over a regular Cartesian grid with 1 km horizontal resolution and for three vertical levels (2, 3, 5 km above the sea level). The CAPPIs at 2, 3, and 5 km can be considered under-sampled vertical profiles. CAPPIs are composed starting from the 22 radars of the Italian Radar Network (Fig. 13), 19 operating at the C band (i.e. 5.6 GHz) and 3 at the X band (i.e. 9.37 GHz). The data quality control and CAPPI composition is performed by DPC. Data quality processing chain aims at identifying most of the uncertainty sources as clutter, partial beam blocking, and beam broadening. The radar observations are processed according to nine steps detailed in Vulpiani et al. (2014), Petracca et al. (2018), and references therein.

Radial velocity is not assimilated into RAMS@ISAC because it is not operationally processed, and the scan strategy being optimized for quantitative precipitation estimation (QPE) purposes. Furthermore, the implementation of a radial velocity data assimilation scheme is under development in RAMS-3DVar and it is not currently available for testing. For these reasons, we did not consider the assimilation of this parameter.

Before entering data assimilation, the Cartesian grid is downscaled to 5 km by 5 km in order to reduce the numerical cost of the data assimilation and the effect of correlated observation errors (Rohn et al., 2001). Thus, the radar grid (Fig. 4, for example) is a Cartesian grid with 5 km grid spacing and three vertical levels.

It is important to note that pure sampling of the data could result in implementation of errors (for example reflectivity given by insects or birds) or extremes. Creating super-observations would reduce this problem, the main drawback being missing very localized phenomena. While the aim of this paper is to present the update of the data assimilation system of RAMS@ISAC and its application to two challenging cases, the problem of using super-observations will be considered in future studies because it impacts the results.

The methodology to assimilate radar reflectivity factor is that of Caumont et al. (2010), named 1D+3D-Var, which is a two-step process: first, using a Bayesian approach inspired by GPROF (Goddard profiling algorithm; Olson et al., 1996; Kummerow et al., 2001), 1-D pseudo-profiles of model variables are computed, and second those pseudo-profiles are assimilated by 3D-Var. Both steps are discussed below.

The first step computes a pseudo-profile of relative humidity, weighting the model profiles of relative humidity around the radar profile (Bayesian approach). The pseudo-profile is computed by 2zop=∑iRHiWi∑jWj, where RHi is the RAMS@ISAC vertical profile of relative humidity at a grid point inside a square of 50×50 km2 centred at the radar vertical profile, Wi is the weight of each profile, and zop is the relative humidity pseudo-profile. The weights are determined by the agreement between the simulated and observed reflectivity factors: 3Wi=exp⁡-12zo-hz(xi)TRz-1zo-hz(xi), where hz is the forward observation operator, transforming the background column xi into the observed reflectivity factor. The radar forward observation operator is taken from the RIP (Read/Interpolate/Plot) software (https://dtcenter.org/wrf-nmm/users/OnLineTutorial/NMM/RIP/index.php, last access: 3 March 2019) and is given in the Supplement of this paper (Sect. S8). It assumes a Marshall–Palmer hydrometeor size distribution and Rayleigh scattering, and depends on the mixing ratios of rain, graupel, and snow.

The matrix Rz in Eq. (3) is diagonal and its value is nσ2, where σ is 1 dBz and n is the number of available observations in the vertical profile (from 1 to 3). In this way, we give more weight to vertical profiles containing more data.

The error of radar data is assumed to be small (1 dBz) for two reasons: (a) reflectivity data are carefully checked by the Civil Protection Department; (b) the performance of the control simulation, not assimilating any data, is rather poor for the case studies. This setting, however, could not be optimal for cases when the control forecast performs better. A sensitivity test using σ=5 dBz for the Livorno case showed small differences compared to σ=1 dBz. The results of this sensitivity test are detailed in the Supplement of this paper (Sect. S4).

It is important to point out that the 50 km length scale of the above step does not represent the horizontal correlation length scale of the background error, which determines the horizontal spread of the innovations in the 3D-Var data assimilation (the latter length scale is between 14 and 25 km depending on the level). The 50 km length scale is used to set a square for computing the pseudo-profile of relative humidity (Eq. 2). This profile is given by a weighted average whose weights are determined by the agreement between the simulated and observed reflectivity factors. The larger the agreement the larger the weight. This distance is appropriate because the spatial error of meteorological models in simulating meteorological features, for example fronts, can be of this order. The control simulation of the two events considered in this paper confirms this choice.

The method is not able to force convection when the model has no rain, snow, or graupel in a square around (50×50 km2) a radar profile with a reflectivity factor greater than zero. In this case, the pseudo-profile of relative humidity is assumed saturated above the lifting condensation level and with no data below (Caumont et al., 2010).

It is also noted that the method is able to reduce spurious convection when the reflectivity factor is simulated but not observed because the pseudo-profile of relative humidity gives more weight to the drier relative humidity profiles simulated by RAMS@ISAC inside the 50×50 km2 square centred at the radar profile. Of course, the ability to reduce spurious convection depends on the availability of dry model profiles around the specific radar profile (see the example below). Finally, if the observed profile is dry and the profile simulated by RAMS@ISAC is dry too, the pseudo-profile is not computed.

In summary, pseudo-profiles are computed for each profile of the radar grid whenever reflectivity is observed or simulated.

The pseudo-profiles computed with the procedure introduced above are then used as observations in the RAMS-3DVar data assimilation (Federico, 2013), minimizing the cost function: 4J(x)=12(x-xb)TB-1(x-xb)+12(zop-h(x))TR-1(zop-h(x)), where x is the state vector giving the analysis when J is minimized, xb is the background, B and R are the background and observation error matrices, zop is the pseudo-vertical-profile computed by Eq. (2), and h is the forward observation operator transforming the state vector (RAMS@ISAC water vapour mixing ratio) into observations. The cost function in RAMS-3DVar is implemented in incremental form (Courtier et al., 1994) and its minimization is performed by the conjugate-gradient method (Press et al., 1992). No multi-scale approach is used.

The background error matrix is divided into three components along the three spatial directions (x,y,z). The Bx and By matrices account for the spatial correlation of the background error. The correlations are Gaussian with length scales between 14 and 25 km, depending on the vertical level. These distances are computed using the National Meteorological Center (NMC) method (Barker et al., 2012) applied to the HyMeX-SOP1 period. It is again stressed that the spread of the innovations along the horizontal spatial directions in the 3D-Var analysis is determined by the length scales of Bx and By matrices.

The Bz matrix contains the error for the water vapour mixing ratio, which is the control variable used in RAMS-3DVar. This error is about 2 g kg-1 at the surface and decreases with height. In particular, it is larger than 0.5 g kg-1 below 4 km, and less than 0.2 g kg-1 above 5 km. The vertical decorrelation of the background error depends on the level and can be roughly estimated to be 500–2000 m. The observation error matrix R in Eq. (4) is diagonal and observation errors are uncorrelated. This choice is partially justified due to the sampling of radar reflectivity factor observation by choosing one point every five grid points in both horizontal directions of the radar Cartesian grid. However, correlation observation errors have a significant impact on the final analysis, as shown for example in Stewart et al. (2013), and different choices of the matrix R will be considered in future studies.

The value of the elements on the diagonal of R depends on the vertical level and is one-fourth of the diagonal element of the Bz matrix at the corresponding height. With these settings, larger weights are given to the observations than to the background, and analyses strongly adjust the background towards observations. Bz matrix is computed using the NMC method (Parrish and Derber, 1992; Barker et al., 2004) applied to HyMeX-SOP1; this choice is motivated by the fact that HyMeX-SOP1 contains several heavy precipitation events over Italy and the background error matrix is representative of the convective environment of the cases considered in this paper. In particular, 10 out of 20 declared IOPs (intense observing periods) of HyMeX-SOP1 occurred in Italy (Ferretti et al., 2014). In contrast, the period of September 2017, especially before the events selected in this study, was characterized by fair and stable weather conditions over Italy and the background error matrix for September 2017 is less representative of the convective environment that characterizes the events of this paper.

Because it is the first time that we show the assimilation of radar reflectivity factor in RAMS@ISAC, it is useful to discuss an example of analysis. We select the analysis of the Livorno case study at 06:00 UTC. The observed CAPPI at 3 km above sea level is shown in Fig. 10b. The corresponding CAPPI simulated by the background is shown in Fig. 14a. In general, the comparison between simulated and observed reflectivity factor highlights the difficulty of the model to represent convection properly. In particular, the model is able to represent the convection over northern Italy but it has poor performance over Sardinia, south of Sicily, and over central Italy. The difference between the analysis and background relative humidity after and before the analysis is shown in Fig. 14b (absolute values less than 1 % are suppressed in the figure for clarity). Both positive (convection enhancing) and negative (convection suppressing) adjustments are found. Over central Italy, Sardinia, and south of Sicily relative humidity is increased because the model does not simulate the observed reflectivity (Fig. 10b). The occurrence of this condition added most of the water vapour to the RAMS@ISAC simulations for the case studies of this paper. Over northern Italy the model is partially dried for two different reasons: in the northwest of Italy because RAMS@ISAC simulates unobserved reflectivity, in the north and northeast of Italy because the model simulates larger values of reflectivity factor compared to the observations. The RAMS-3DVar reduces the relative humidity field north from Corsica island, where the RAMS@ISAC predicted unobserved reflectivity, while RAMS-3DVar did not suppress the unobserved convection west of Sardinia because the pseudo-profiles computed over this area were not appreciably drier than the background.

Cross correlations among different variables of the data assimilation system are neglected in this study and the application of RAMS-3DVar affects the water vapour mixing ratio only. Cross correlations among different variables can improve the performance of the data assimilation system, and an example of their impact in RAMS-3DVar is shown in Federico (2013). Nevertheless, the impact of cross correlations among different variables in the precipitation VSF will be explored in future works.

Since lightning data assimilation also adjusts the water vapour mixing ratio, it follows that the data assimilation presented in this study adjusts only this parameter.

Despite the fact that both radar reflectivity factor and lightning adjust the water vapour mixing ratio, different impacts on the VSF can be expected a priori because radar reflectivity factor and lightning are different types of observations and because they are used in different ways in the data assimilation system.

In particular, lightning is recorded when deep convection develops, while radar reflectivity factor is observed also for light stratiform rain. Flashes of ground-based networks, such as LINET, are available over the open sea, even if with a reduced detection efficiency, while radar reflectivity factor is confined to the range of coastal radars in the network. Lightning has a seasonal dependence over Italy, with the maximum in summer and autumn, while radar reflectivity factor is available in all seasons.

Also, differences in data assimilation of lightning and radar reflectivity factor play a role. In addition to the methods used to assimilate observations, lightning saturates the layer from 0 ∘C to -25 ∘C where and when it is detected, while radar reflectivity factor can be assimilated by pseudo-profiles or by saturation above the lifting condensation level where observed reflectivity is greater than zero.

Therefore, despite both observations adjusting the same model prognostic variable, which is a drawback of the methodology presented in this paper, the impacts of lightning and radar reflectivity factor is expected to be different as will be evident from the results of this paper.

There are, however, advantages using the methodology of this paper. In addition to being simple, it does not rely on approximate relationship between radar reflectivity factor and hydrometeor mixing ratio, leaving to the model the task of evolving the water vapour added and subtracted. Also, the impact of the data assimilation on model results is substantial (Fabry and Sun, 2010; Caumont et al., 2010), as also shown by the results of this paper.

Lightning and radar data assimilation may produce sharp gradients in the vertical direction caused by the addition of water vapour to specific layers. In the case of lightning, the water vapour is added by nudging to reduce sharp gradients. However, radar data assimilation, which accounts for the largest mass of water added to RAMS@ISAC (see Sect. S2), directly adjusts the water vapour into the model. Our experience with RAMS@ISAC, however, shows that results are reliable and the sudden addition of water vapour does not cause shocks to the model simulation, despite the notable gradients of specific humidity.

It is finally noted that the data assimilation increases or decreases the water vapour in the model depending on the cases. The eventual increase or decrease in the forecasted rainfall depends on the physical and dynamical processes occurring in the meteorological model, without any specific tuning.

In this period, an intense and localized storm hit central Italy, while light precipitation occurred over northern Italy (Fig. 15a). Considering the storm over central Italy, 10 rain gauges observed more than 30 mm every 3 h, six more than 40 mm every 3 h, three more than 50 mm every 3 h, and one more than 60 mm every 3 h, the maximum observed value being 63 mm every 3 h.

The CTRL forecast, Fig. 15b, misses the rainfall over central Italy and considerably underestimates the precipitation area over northern Italy, giving unsatisfactory results.

The assimilation of the radar reflectivity factor improves the forecast, as shown in Fig. 15c. In particular, RAD forecast shows localized precipitation (30–35 mm every 3 h) close to the area were the most abundant precipitation was observed. Maximum precipitation is underestimated. Also, the RAD forecast better represents the precipitation over northern Italy compared to CTRL.

The rainfall forecast of LIGHT, Fig. 15d, shows some improvements compared to CTRL because the precipitation over central Italy has a maximum of 25–30 mm every 3 h, close to the area where the maximum precipitation was observed. LIGHT; however, it has a worse performance compared to RAD because it underestimates the precipitation area over northern Italy. LIGHT underestimates the maximum precipitation in central Italy.

The RADLI forecast, Fig. 15e, has the best performance. The precipitation over central Italy is well represented because the maximum rainfall (40–45 mm every 3 h) is in reasonable agreement with observations, and also because the area of intense precipitation (>25 mm every 3 h) is elongated in the SW–NE direction in agreement with rain gauge observations. The precipitation over northern Italy is well represented by RADLI.

A performance diagram for 1 mm every 3 h and 30 mm every 3 h and for 4 and 25 km neighbourhood radii is shown in Fig. 15f. Different radii are considered to account for the well-known double penalty error (Mass et al., 2002; Mittermaier et al., 2013) caused by displacement errors of the detailed precipitation forecast in convection-allowing grids. RADLI has the best performance thanks to the synergistic contribution of lightning and radar reflectivity factor data assimilation.

The Livorno case study lasted for several hours starting at 18:00 UTC on 9 September 2017 and ending more than a day later. The most intense phase in Livorno and its surroundings was observed during the night between 9 and 10 September. In the following, we will show two representative VSFs (3 h), including the most intense phase in Livorno.