This study employs the hourly precipitation fields from MERIDA HRES , a reanalysis developed for the Italian domain, resolving explicit convection to better represent localised and intense precipitation events. MERIDA HRES, developed by Ricerca sul Sistema Energetico (RSE), employs the Weather Research and Forecasting (WRF) model to dynamically downscale over Italy the global ERA5 reanalysis to a higher-resolution horizontal grid of approximately 4 km and 56 vertical levels, with increased vertical resolution in the lower atmosphere (levels located at 10, 35, 70, 100, 130, 180, 250, 325, 415, and 500 m). It is driven by large-scale initial and boundary conditions from ERA5 and applies a spectral nudging technique to constrain synoptic-scale features while filtering out smaller-scale perturbations that could introduce spurious signals. Additionally, SYNOP surface air temperature observations are assimilated through an observational nudging technique , further enhancing the representation of regional atmospheric characteristics. The dataset spans the period from 1986 to 2022, but is constantly updated with about a two-year lag. The analyses for this work are calculated over the domain 5.84 to 18.96° E and 35.37 to 48.25° N, centred on the Italian peninsula, for the period 1986–2022, enclosing the full period of availability for MERIDA HRES at the time of writing.

The specific choice of MERIDA HRES reanalysis is supported by previous validation studies. In particular, its precipitation fields have been assessed from climatological to daily and hourly timescales, also comparing with other convection-permitting reanalyses for the same area, highlighting both its strengths and limitations. The effective horizontal spatial resolution of MERIDA HRES has been evaluated in previous works using a wavelet spectral decomposition approach (see , Fig. 2), which demonstrated its ability to represent convective precipitation, although it may not fully resolve the smallest structures. Moreover, MERIDA HRES shows good agreement with both gridded and station-based observations, and demonstrates overall temporal stability when compared with homogenised observational datasets . These qualities make it an appropriate product for hourly precipitation trend analyses. Other convection-permitting models available for Italy, such as MOLOCH and SPHERA , have been found to generally produce larger deviations from observed precipitation trends than MERIDA HRES , while results from VHR-REA_IT indicate a slightly weaker agreement with daily-scale observations . These aspects may limit the applicability of other products in this study.

Nevertheless, these studies also indicate that MERIDA HRES occasionally overestimates rainfall amounts during summer in specific regions, including the Po Valley–Adriatic interface, parts of the Calabrian mountains, southern Apulia, and the southern portions of the main islands, with local deviations from observations reaching 10–30 mm. However, since these regions are generally dry during summer, the relative error can be substantial, up to locally doubling the observed rainfall amounts in July and August . Moreover, the trend in the annual differences between MERIDA HRES and homogenised observations precipitation totals is on average 4 % per decade, meaning that this fraction of annual precipitation increase might be attributable to a deviation from observations rather than a true climate signal . This mismatch is not uniform across the territory (see the supplementary material of ). The knowledge of these specific inhomogeneities of MERIDA HRES will be taken into account when discussing the results of this work (Sect. ).

The first step involves identifying coherent Hourly Precipitation Spatial Structure (HPSSs) in each MERIDA HRES hourly field. To account for seasonal and regional differences, thresholds are calculated for each grid point of the reanalysis and separately for each season by taking the median (i.e., 50th percentile) of precipitation values exceeding 1 mm. After that, a spatial smoothing filter with a 20 km radius is applied to reduce noise and improve spatial consistency across neighbouring grid cells (Fig. ).

Precipitation values below 1 mmh-1 are excluded to distinguish meaningful precipitation from background noise. Indeed, below 1 mmh-1 the spatial variability is very high, whereas it significantly decreases above it, indicating that precipitation becomes more spatially coherent and representative of broader areas . During the first stages of this work, a fixed 1 mm threshold was applied to detect HPSS. Nevertheless, the choice of a uniform threshold across the entire domain and for all seasons did not adequately account for the spatial and seasonal variability of precipitation regimes, leading to the merging of multiple distinct convective cells into a single, large cluster that did not reflect the localised nature of HPSSs. This mismatch between the actual physical scale of convective systems and the scale of the detected clusters motivated the choice of a percentile-based threshold. In determining the most suitable smoothing radius, several values were tested. Radii larger than 20 km excessively smoothed areas with higher thresholds, reducing the ability to resolve regions of intense precipitation. Conversely, smaller radii retained too much noise, limiting the effectiveness of the thresholds in isolating coherent precipitation structures. Moreover, 20 km approximately corresponds to the boundary between the meso-β and meso-γ atmospheric scales , below which convective phenomena typically occur.

Contiguous grid points exceeding the thresholds (Fig. ) are treated as an individual cluster. To reduce noise, clusters composed of fewer than five grid points are excluded: approximately 95 % of them exhibit intensities below 10 mmh-1, and therefore have a negligible impact on the focus of this study on extreme precipitation. Each retained cluster is identified as an HPSS. More specifically, in this work HPSSs are spatially continuous hourly precipitation structures, identifying detectable and relevant precipitation with reference to a given area and season. Figure  shows an example of the procedure used to identify HPSSs, applied to the hourly precipitation field of 20 October 2011 at 13:00:00 UTC. On that day, intense precipitation affected Rome and the surrounding areas, causing several floods throughout the city and widespread power outages .

Each identified HPSS is characterized by a set of features describing its date and time of occurrence, position, and total and maximum precipitation intensity, as summarized in Table . The maximum linear spatial extent of a HPSS is defined as the major axis of its minimum enclosing ellipse – i.e., the smallest ellipse that fully contains all grid points belonging to the structure . The choice of characterizing the shape of an HPSS by its maximum linear extent is motivated by the fact that atmospheric spatial scales are generally defined in linear terms . Moreover, deriving this feature from the minimum enclosing ellipse allows for a consistent characterization of precipitation structure having very different shapes. Additional features are included in the complete database available only, while only features used in this study are reported here.

The HPSS detection methodology described above produced the HOPSS-X dataset, which can be analysed through the set of features associated with each HPSS. First, the seasonal distributions of mean precipitation intensity (tot_tp/area), peak precipitation intensity (tp_max), and maximum linear spatial extent (max_extent) of all HPPS are examined. Then, spatial patterns of hourly precipitation are investigated. To account for location uncertainty inherent in reanalysis data and avoid misleading point-scale analyses, statistics are not evaluated at individual grid points but within a 0.5° moving window (≈156 grid points) with 0.1° increments in both latitude and longitude. In each of these windows, the Number of occurrences (N) of HPSSs whose centre of mass (cdm_lat,cdm_lon) fell inside the window is counted. Because the sliding distance (0.1°) is smaller than the window size (0.5°), a single HPSS is counted in multiple adjacent windows, ensuring smooth spatial transitions. Then, some features are averaged among all the HPSSs falling in a window. Specifically, the Average Mean Intensity (MeanInt), Average Peak Intensity (PeakInt), and Average Maximum Linear Spatial Extent (SpatExtent) are obtained by averaging tot_tp/area, tp_max and max_extent respectively, as detailed in Table .

To help disentangle the respective contributions of the hourly spatial density of HPSSs and their frequency of occurrence, alternative metrics to N – such as the frequency of wet hours (i.e., the percentage of hours with at least one structure detected in the window) – were also evaluated (Fig. S1 in the Supplement). These analyses produced very similar results, and N is preferred as the indicator of HPSS occurrence due to its easier interpretability.

Both MeanInt and PeakInt are expressed in millimetres per hour (mmh-1), but they reflect different aspects of precipitation intensity. MeanInt represents the average intensity across all grid points of all HPSSs within a given window, while PeakInt refers to the mean of the maximum intensities recorded at a single point for each HPSS. SpatExtent indicates the average maximum linear extent of the HPSSs within the same window. Finally, these values are cumulated (for N) or averaged (for MeanInt, PeakInt, SpatExtent) over time to obtain characteristic values for each location. Statistics on the full dataset, including climatologies of these indicators, are presented in Sect. .

After characterising the properties of the HPSSs, the Hourly Precipitation Extremes (HPEs) are selected from the full dataset. The selection criterion is based on the annual maxima of hourly precipitation (RX1hour), calculated for each grid point and each year. The resulting time series of 37 RX1hour values are then averaged throughout the period 1986–2022 to derive a threshold value for each cell of the grid, representing the average RX1hour at that location. Higher threshold values were found to excessively restrict the statistical sample of extremes, whereas lower values, although expanding the subset of identified structures, would have blurred the distinction between HPEs, as defined by Extreme Value Theory , and more moderate high-quantile HPSSs, thereby reducing the interpretability of the results.

This approach is similar to the methodology used by , who introduced the Extreme Rain Multiplier to classify extreme daily precipitation events. employ ERA5 and consider daily precipitation accumulations to compute the mean of the annual daily maxima (RX1day). The daily accumulation is the most appropriate timescale considering the coarse spatial scale of ERA5 . In contrast, this study uses a regional convection-permitting reanalysis, which provides a more accurate representation of hourly precipitation and associated extremes. Therefore, it is possible to define a threshold based on hourly maxima (RX1hour). As the last step, the same Gaussian filter as specified in Sect.  is applied to smooth the average RX1hour field and reduce local-scale noise (Fig. ).

Finally, a HPSS is identified as HPE if its maximum precipitation value (tp_max) exceeds the average RX1hour value in the position where it occurred (lat_max,lon_max). The selected HPEs can be interpreted as extreme precipitation events within a fixed-area (Eulerian) framework, which is more suitable for this study since no tracking of individual events is performed, unlike in a Lagrangian approach that follows storm structures over time . In support of this interpretation, in Sect.  the local persistence of HPEs is investigated, showing that HPSSs exceeding the extreme threshold are typically short-lived, rarely persisting for more than one hour, thus aligning with the common use of “extreme event” terminology.

Extreme statistics are calculated within the subset of HPSSs classified as HPEs with the same methodology described in Sect. . Subsequently, the trends of the yearly series of N, MeanInt, PeakInt and SpatExtent are computed (results shown in Sect. ). The similarity between N and wet-hour frequency (see Fig. S1) also applies to HPEs and their respective trends (figures not shown). Within each moving window, the trend analysis is performed using the Theil–Sen slope estimator , suitable for non-parametric data. The statistical significance of the trends is evaluated using the Mann–Kendall test . To control for the multiple testing problem across the spatial domain, the False Discovery Rate (FDR) correction is applied . Since the FDR procedure tends to be conservative in the presence of spatial correlation, approximately correct global results can be obtained by setting the FDR threshold to twice the desired global significance level . Therefore, results are considered statistically significant if the FDR-corrected p-value is below 0.1, corresponding to a global significance level of 0.05. The results of the trend analysis are presented in the Results Sect. .

Before focusing on extremes, the overall patterns of HPSSs across the dataset are first examined, providing a broader climatological context to facilitate the interpretation of the subsequent results on extreme precipitation. The dataset consists of approximately 160 000 precipitation HPSSs per year over the period 1986–2022. The interannual variability, calculated as the relative standard deviation of the annual number of HPSSs, is around 10 %. At the seasonal level, the highest number of HPSSs is generally recorded in autumn (SON), accounting for 29 % of the total, while summer (JJA) shows the lowest share, with 21 %. Winter (DJF) and spring (MAM) contribute similarly, representing 26 % and 24 % of the total number of HPSSs, respectively. The fraction of hours showing no identified HPSSs across the entire domain varies seasonally, with approximately 11 % for winter, 12 % for spring, 9 % for summer, and 7 % for autumn. The number of HPSSs detected per hour follows the distribution of Fig. .

The maximum number of HPSSs recorded in a single hour is 136, observed at 14:00 UTC on 11 June 1992, as a result of a widespread low-pressure area associated with large quasi-stationary cyclone influencing the whole Italian peninsula. Intensity and spatial scale distributions exhibit markedly skewed shapes, with a sharp peak at low values followed by an approximately exponential decay as their magnitude increases (Fig. ).

During summer and autumn, HPSSs tend to exhibit higher median values and heavier tails for both mean precipitation intensity (tot_tp/area, Fig. a) and peak precipitation intensity (tp_max, Fig. b). The maximum linear spatial extent (max_extent, Fig. c) distributions show less pronounced seasonal variation, with only summer displaying HPSSs with a slightly smaller extent. A small percentage of HPSSs fall outside the range of the distributions plotted in Fig. : 0.22 % of HPSSs exhibit a mean precipitation intensity greater than 15 mmh-1, 0.96 % have a peak precipitation intensity above 40 mmh-1, and 2.98 % show a maximum linear extent larger than 100 km. According to definitions of atmospheric scales in the scientific literature , phenomena with lifetimes ranging from about one hour to one day – such as isolated thunderstorms or groups of storms – typically occur within the lower portion of the mesoscale, with spatial extents from approximately 2 km up to 200 km. The results of HPSSs distribution analysis confirm that, at the hourly timescale, they generally fall within the meso-γ scale (2–20 km), with only occasional instances exhibiting larger spatial extents. This result is consistent with the fact that precipitation structures are extracted from a 4 km convection-permitting reanalysis precipitation field, which is capable of representing convection even if it may not fully resolve it at the smaller scales. This finding is particularly relevant for applications that require knowledge of the typical spatial scales of hourly precipitation, such as spatial analysis of precipitation fields . In general, structures with smaller spatial extents tend to correspond to higher intensities (see Fig. S2 in the Supplement). Overall, the majority of HPSSs concentrate on low values of intensity and small spatial extents. This underscores the need to isolate the most extreme HPSSs to better understand their specific characteristics.

HPSSs are analysed using the methodology described in Sect. 2.3, resulting in seasonal maps of N (Fig. ), SpatExtent (Fig. ), MeanInt (Fig. ) and PeakInt (not shown, see Supplement). Higher values in a given area indicate a greater number of HPSSs with their centre of mass located within that region (for N), or larger values of MeanInt, PeakInt and SpatExtent for those same HPSSs. HPSSs may extend beyond the boundaries of the window in which they are counted, since the averaging considers only the HPSSs whose centre of mass lies within the window. However, most of the recorded HPSSs are well delimited in a small space (Fig. c). It is also important to emphasise that these means are computed from distributions that are strongly right-skewed, as shown in Fig. . Consequently, the values presented in the maps should be interpreted with some caution. While they may not fully capture the absolute characteristics of typical HPSS intensity and spatial extent, they are informative when used to explore spatial and seasonal patterns and their relative differences.

The spatial distribution of N (Fig. ) shows that, in summer, most of the HPSSs occur in the Prealpine regions, with secondary hotspots along parts of the Apennines, and almost no HPSSs over the sea. In autumn and winter, the areas with high N shift toward coastal and offshore areas, particularly along the Tyrrhenian and Ligurian seas. During spring, the Prealps and Apennines are again prominent, although the occurrences are generally lower than in summer. The Po Valley and Prealpine region exhibit very low N during the winter season. These seasonal patterns reflect the typical climatology of convective precipitation in Italy, which tends to be more frequent during the warmer months and over mountainous regions and coastal areas .

The seasonal maps of SpatExtent (Fig. ) reveal that during summer HPSSs have generally smaller extents, with typical average SpatExtent ranging between 10 and 20 km, especially along coastal areas and in southern Italy, and from 20 to 30 km in the other Italian areas. This is consistent with the convective nature of summer precipitation. Spring shows slightly larger SpatExtent, but still below 30 km over the Prealps and in southern regions, where autumn also displays similar values, despite showing larger ones over plain areas in the north and central Italy. In contrast, winter is characterised by generally larger HPSSs, especially over the Po Plain, where average SpatExtent commonly reach 50 km, exceeding values registered over the Alps and Apennines. This broader extent reflects the influence of large-scale synoptic systems typical of wintertime precipitations over Italy. Overall, these patterns highlight a seasonal modulation in SpatExtent, reflecting the shift from localised convective activity in summer to more widespread, synoptic-driven precipitation in autumn and winter.

The spatial distribution of MeanInt (Fig. ) highlights summer as the season with the highest average intensities, often exceeding 5 mmh-1 with maxima of more than 7 mmh-1 in some areas along the Adriatic coast, such as Calabria, the Tyrrenian sea, southeastern parts of the islands and southern Apulia. In winter, intensities generally range between 2 and 3 mmh-1 over most of the peninsula, dropping below 2 mmh-1 along the Alpine arc and exceeding this value only slightly in some southern areas and along the Tyrrhenian coast. During spring, values between 3 and 4 mmh-1 are widespread throughout Italy, except for isolated spots over 4 mmh-1 in similar areas to those observed in summer. In autumn, slightly higher intensities, ranging from 4 to 5 mmh-1, cover most of the country, while lower values persist mostly in the Prealpine and Alpine regions. Intensities above 5 mmh-1 are found mainly along the coastal areas and over the surrounding seas.

The seasonal patterns of PeakInt (Fig. S3 in the Supplement) closely resemble those for MeanInt, although PeakInt are generally higher. PeakInt increases from winter values ranging between 2 and 7 mmh-1 to well over 15 mmh-1 during summer, with spring and autumn showing intermediate values. Notably, in autumn, PeakInt exceeding 10 mmh-1 are mostly confined to coastal areas and the surrounding seas. In summer, PeakInt surpasses 17 mmh-1 in the same regions characterised by high summer MeanInt (Fig. ).

Since it is not straightforward to determine the extent to which the seasonal differences in those maps are influenced by the use of seasonally varying thresholds for HPSS selection, a set of corresponding figures derived from the dataset built using a fixed 1 mm threshold is provided in the Supplement (Figs. S4–S7). These figures display very similar spatial patterns, albeit with generally lower intensity values. This suggests that the observed seasonal differences primarily reflect the signal of the model rather than artefacts introduced by the clustering method. Overall, these results are consistent with the established climatology of the region . However, while MeanInt and PeakInt seasonal maps appropriately reflect higher values during the autumn and summer seasons, they also show some regions with unrealistically high precipitation. This overestimation of summer precipitation has been previously documented through comparisons with observational precipitation fields in earlier studies . This issue will be examined in greater detail in the Discussion Sect. .

A subset of the dataset HOPSS-X is obtained (according to Sect. ) to gain insight into the HPEs patterns and tendencies. This resulted in approximately 4.8 % HPSSs selected as HPEs, corresponding to an average of around 7800 HPEs per year across the whole domain, with a notable interannual variability of about 30 %. Most HPEs are selected from summer (11 % of all summer HPSSs) and autumn (7 %), while only a marginal fraction is identified in spring (1.5 %) and winter (0.5 %). This seasonal breakdown results from the combined effect of higher thresholds applied for HPSS identification during summer (Fig. ), which selected relatively intense HPSSs even within the full dataset for that season, and the use of a fixed threshold (average RX1hour) for HPE selection throughout the year. The greater number of HPEs in summer and autumn is also consistent with the expectation that hourly precipitation more effectively captures extremes and their associated impacts at smaller spatial scales, such as convective storms and other meso-γ scale phenomena, particularly prevalent during the warmer seasons. Consequently, Sect.  and focus exclusively on summer and autumn precipitation extremes.

A comparison between the distributions of intensity and spatial scale within the HPEs subset (Fig. ) and those from the full dataset (Fig. ) confirms that the applied filter effectively excludes a substantial number of HPSSs from the lower tails of the distributions. This effect is quite obvious for the peak intensity, which is explicitly used as the filtering parameter. However, it also significantly influences the distribution of mean intensity, suggesting that, on average, HPEs are not only more intense locally but also tend to have higher mean values. Moreover, the spatial extent distributions are shifted towards larger values. Summarising, the applied filtering leads to the exclusion of a large fraction of small and weak HPSSs, not meaningful for the HPEs analysis.

The climatological seasonal maps of N within the HPEs subset (Fig. ) highlights clear seasonal differences between summer and autumn.

In summer, HPEs occur predominantly over mountainous areas, particularly the Alps and some spots along the Apennines, and Calabria, reaching 20 to 30 HPEs per 0.5° grid window per year. In contrast, coastal and marine regions display a significantly lower N, often fewer than 3 per window per year. In autumn, N is substantially less compared to summer. However, a clear spatial shift emerges: mountain areas experience fewer to none HPEs, while coastal and marine zones see some, with over 7 occurrences per window per year observed along many stretches of coastline. The seasonal redistribution is likely driven by the persistence of warm sea surface conditions beneath a cooler atmosphere, creating conditions favourable to convection and sustaining intense precipitation activity into autumn. .

Marked differences between summer and autumn also emerge in terms of SpatExtent (Fig. ). In summer, HPEs rarely exceed 50 km in size, except in limited areas such as Friuli (North-East) and South Switzerland, and remain well below 20 km across much of southern Italy and the islands. Conversely, in autumn, significantly larger HPEs (exceeding 100 km in spatial extent) are frequently observed. Spatial extents remain small mainly in the south, along the Adriatic coast, and over the islands. This suggests that HPEs are typically small, convective systems during summer across most of the Italian territory, and during autumn along the southern coastlines. In contrast, in northern Italy and neighbouring regions, autumn HPEs are more frequently associated with larger-scale systems.

The climatological maps for the MeanInt and the PeakInt of HPEs are provided in the Supplement (Figs. S8 and S9). Overall, their spatial patterns closely resemble those observed for the full dataset, though with generally higher values, due to the filtering, which also reduces the seasonal differences. Specifically, the MeanInt range from approximately 5 to 15 mmh-1, increasing from the Alpine regions to southern Italy for both seasons, while the PeakInt range from 20 up to 50 mmh-1, with the lowest values again found over the Alps and the highest values concentrated in the same hotspots highlighted before, such as the southern Apulia.

Finally, given the context provided by the previous results, a trend analysis within the subset of HPEs is conducted, following the methodology outlined in Sect. . Significant trends in the number of HPEs occurrences (N) during summer and autumn are detected (Fig. ). Trends are expressed as percentages relative to the seasonal and local mean values of N (i.e., normalised by the values shown in Fig. ). For example, a 10 % trend in Fig.  means a decadal increase of 10 % in N, indicating that, on average in that area, approximately 30 % more HPEs occur at the end of the study period compared to its beginning. Overall, a general increase in HPEs occurrences is detected across the peninsula, even though only some regions exhibit statistically significant trends.

In summer, a significant increase of approximately 20 % to 30 % per decade is detected across several Alpine and Prealpine regions, and in some parts of Calabria. In autumn, significant trends are primarily concentrated over the southern Apennines, and various coastal and sea areas, such as Ligurian eastern coast, the eastern coast of Sardinia, the southern Adriatic Sea, and the Ionian Sea. Individual series of some selected areas (specifically, inside colored 0.5 degree boxes of Fig. ) are extracted to visualise the HPEs annual occurrences along with the detected trends (Fig. ). In summer, trends ranging from 10 % to 40 %, depending on the region, correspond to an increase of 2 to 6 HPEs per decade. In autumn, comparable percentage changes are associated with a smaller increase of 1 to 2 HPEs per decade. In both seasons, some regions also display positive trends that are not statistically significant (e.g., boxes 4 and 8 in Figs.  and ), likely due to high interannual variability that dominates the signal.

Trends are also computed for the SpatExtent, MeanInt, and PeakInt of HPEs (see Figs. S10–S12 in the Supplement, respectively). Overall, only weak trends (below 10 % per decade) are observed, primarily over land points in summer and over some marine areas in autumn, showing spatial heterogeneity in the sign of the signal with a slight tendency toward increasing intensities and decreasing spatial scales. However, none of these trends is statistically significant at any location. This suggests that the detected increase in N is potentially driven by an underlying intensification of extreme precipitation that, while not statistically significant in MeanInt or PeakInt, results in more frequent exceedances. Owing to its lower noise sensitivity, the metric N allows these changes to emerge more clearly and to reach statistical significance.

Trend estimates could be biased by potential double-counting of temporally persistent HPEs, as the analysis is conducted at hourly resolution. To address this, an additional analysis quantifies HPEs persistence, defined as the number of consecutive hours during which an HPSS exceeds the local average RX1hour threshold within the same window.

Results (Fig. ) show that persistence exceeds one hour only marginally in most regions, with average persistence values above 1.5 h limited to a few localised areas expecially during autumn, such as the Ligurian Gulf, where persistent mesoscale convective systems are more common , and in parts of eastern Sardinia and southeastern Sicily, where prolonged convective activity can occur . These findings support the overall temporal isolation of most HPEs and suggest that the impact of double-counting on trend estimates remains limited.