The simulations are evaluated using the CLIMATE-GRID (CG) dataset , a Belgian 5 km gridded observational dataset based on interpolated station data and developed at the Royal Meteorological Institute of Belgium. The dataset spans the period from 1961 until the present day. It includes daily average temperature and daily total precipitation, which are provided as areal averages over each pixel of the 5 km grid.

For sub-daily observations of precipitation, we employ station measurements from five measurement networks: VMM in Flanders, DGH in Wallonia, IBGE in Brussels, and the HYDRO and AWS networks covering all of Belgium. The VMM and DGH networks are managed by the Vlaamse Milieumaatschappij and the Direction de la Gestion Hydrologique of SPW Mobilité et Infrastructures, respectively. The IBGE network, established by the Ministry of the Brussels-Capital Region, has been managed by Brussels Environment since 2007 . The AWS and HYDRO networks are operated by the Royal Meteorological Institute of Belgium . The station locations are shown in Fig. b, while details about each network are provided in Table . Precipitation data from all networks are aggregated to an hourly resolution to align with the temporal resolution of the simulation output.

The ALARO-1 simulations are evaluated by calculating the mean bias for near-surface air temperature (simply called temperature from here on) and accumulated precipitation depth on annual, seasonal, and monthly timescales. For an exact mathematical formulation, we refer to Appendix .

To assess whether the biases are statistically distinguishable from zero, we apply a non-parametric bootstrap at each grid point. For a given field, the 31 years (1992–2022) are resampled with replacement 103 times. The climatological bias (simulation minus observations) is then recomputed for each resample. Next, the 95 % confidence interval is taken as the 2.5th–97.5th percentiles of the resulting distribution. A grid point is deemed significant where this interval excludes zero. Each simulation and the CLIMATE-GRID observations are anchored to the same historical years: the simulations are all originally driven by ERA5 reanalysis over the identical 1992–2022 period. Therefore, the resampling is paired: the same resampled set of years is used for the simulated and observed fields within each iteration. The same paired-bootstrap procedure is applied to the domain-averaged monthly biases, where the bias is first averaged over all grid points before the confidence interval is computed. A month is deemed significant where this interval excludes zero.

To ensure a consistent comparison, all data are regridded to a common latitude-longitude grid with a spacing of 0.07° longitude by 0.045° latitude, which closely aligns with the 5 km resolution of the CG dataset. For precipitation, a conservative remapping is applied to all simulations to preserve the spatially averaged precipitation depth . For temperature, the same conservative procedure is used to reproject ALARO-4km. For ALARO-12km and ALARO-25km, another regridding method is employed for temperature. Since low-resolution data are interpolated to a higher resolution, a conservative regridding method would effectively function as a nearest-neighbour approach in such cases. Therefore, a bilinear interpolation procedure is used instead, as it is more suitable for the smooth nature of temperature fields.

Simulations at convection-permitting scales generally add value through the improved representation of convection and, consequently, of precipitation in general . Therefore, this evaluation study also focuses on the statistics of extreme precipitation over Belgium. Extreme precipitation events are here defined as the annual maximum (AM) value for a given duration at a specific location or grid point. An advantage of this definition is its simplicity: there is no need to determine an arbitrary threshold. AM values are selected for durations of 1, 2, 3, 6, 12, 24, 48, and 72 h using a rolling-window approach over the hourly precipitation data.

The statistics of these AM values are calculated by fitting a generalised extreme value (GEV) distribution, as defined in Eqs. ()–() . A GEV distribution is defined by three parameters: the shape ξ, location μ, and scale σ. These parameters are fitted for each duration separately with the L-moments method as defined by . Consequently, these parameters are used to calculate the return level zd(T), i.e. the d-hourly precipitation intensity expected to be exceeded once every T years, where d is the duration and T the return period. For a mathematical description, we refer to Appendix .

Next, we apply the regional frequency analysis framework (RFA), as introduced by . The idea behind this framework is to aggregate precipitation data from different locations that share the (presumably) identical underlying distribution. A single fitting procedure is then performed for an entire region instead of fitting a separate distribution in each point, allowing for a more robust fit. Note that the precipitation data are aggregated and not averaged over a region. Recent literature, such as the work by  and , further supports the use of RFA for improving precipitation extreme estimations.

We subdivide Belgium into three distinct regions based on elevation: Low-Belgium (0–50 m), Middle-Belgium (50–200 m) and High-Belgium (> 200 m), as shown in Fig. b. Elevation is used as a discriminatory parameter since it correlates strongly with the annual precipitation totals, which themselves are closely linked to precipitation extremes . This subdivision strikes a balance between reducing uncertainties and maintaining relatively homogeneous climatic conditions within each region, as suggested by .

Intensity-Duration-Frequency (IDF) statistics jointly characterise the intensity of extreme precipitation as a function of both duration and return period, and are a standard tool for hydrological design and flood-risk assessment . The return levels for each region are subsequently presented per return period as a function of the duration to construct these IDF statistics. In order to gauge the return-level uncertainty, we derive the 95 % confidence interval using 104 bootstraps, obtained by resampling yearly data. For each simulation, the observational return levels are compared with their simulated counterparts by calculating the relative error. The error uncertainty is acquired with a pairwise calculation of the error between all observational and simulated bootstrap samples, respectively. This calculation results in a distribution of 108 samples for the relative error.

Figure  shows that ALARO-1 at all three resolutions exhibits a cold temperature bias with respect to the Belgian CLIMATE-GRID observations. This bias is most pronounced in the eastern, more elevated region. Near the coast, all simulations exhibit a small warm bias. The cold bias is statistically significant across almost the entire domain in ALARO-25km, whereas for ALARO-12km and ALARO-4km large parts of the interior are not significantly different from zero (hatched in Fig. ), consistent with their much smaller domain-mean biases of -0.25 and -0.32°C. Furthermore, the spatial bias patterns for ALARO-12km and ALARO-4km are very similar. Certain urban areas can be discerned in these simulations presenting themselves as areas with a warm bias.

While the bias difference between ALARO-12km and ALARO-4km is small, a large difference is present between ALARO-25km and ALARO-12km. As outlined in Table , apart from the resolution difference, the primary distinction between these two simulations is the inclusion of SURFEX into ALARO-12km. The dedicated ALARO-12km-noSFX experiment (Sect. ) shows that the inclusion of SURFEX, rather than the resolution increase, is the dominant driver of this difference, raising the annual-mean temperature by nearly 1 °C. Overall, ALARO-12km provides the best representation of mean annual temperature.

Considering the annual cycle of the biases, a more complex picture emerges. The spatially averaged biases per month are plotted in Fig. , while spatial bias patterns are shown per season in Fig. . In each season, ALARO-12km and ALARO-4km perform similarly, except during summer, when both simulations feature a warm bias which is larger in ALARO-12km, particularly in July and August when the bias exceeds 1 °C. This warm bias partially compensates for the cold bias in other seasons on an annual basis. Consequently, ALARO-12km exhibits a smaller annual cold bias than ALARO-4km, despite ALARO-4km performing better in more seasons. Additionally, both ALARO-12km and ALARO-4km strongly underestimate the temperature in spring, which also corresponds to the largest seasonal cold bias for ALARO-25km. The largest negative bias, which is around -1.5 °C, is attained in May. The domain-averaged monthly biases of ALARO-25km are significant year-round except in September, whereas for ALARO-12km and ALARO-4km significance is confined to the seasonal extremes: the spring cold bias (March–May/June), the summer warm bias (August), and a November cold bias (Fig. a).

During the seasons with warming sea surface temperatures (SST), spring and summer, there is a cold bias near the coast, while the opposite is true for autumn and winter (see Fig. ). This may be attributed to the monthly replacement of SST, creating a lag effect. In addition, coastal grid points partly consist of sea: the diagnosed 2 m temperature is the tile-weighted average over the land and sea fractions, so the (lagged) sea surface temperature is directly reflected in the near-surface temperature of these mixed cells.

In terms of significance (Fig. ), the cold bias of ALARO-25km is significant across the whole domain in every season. For ALARO-12km and ALARO-4km the bias is largely insignificant, except in spring, where the cold bias is significant domain-wide. In summer, ALARO-12km exhibits a significant warm bias over much of the domain, whereas in ALARO-4km this warm bias is weaker and largely insignificant, consistent with its cooler summer near-surface temperature.

ALARO-1, at all three resolutions, features a wet bias both annually (Fig. ) and across all months (Fig. ) and seasons (Fig. ), except for summer (July and August) in ALARO-12km and ALARO-4km, which coincides with a warm bias in these simulations. Similarly to temperature, the bias in annual precipitation is smallest for ALARO-12km. ALARO-4km is slightly wetter, while ALARO-25km features a bias nearly twice as high as ALARO-12km. The wet bias is significant over essentially the whole domain for all three simulations (Fig. ).

However, once more, ALARO-4km performs best when evaluating the seasons separately. ALARO-12km shows a smaller bias only during springtime. Similarly to temperature, the precipitation bias in spring is substantially larger (in absolute values) compared to the other seasons. Regarding significance (Fig. ), the wet bias is significant across essentially the whole domain for all three simulations in autumn, winter, and spring. Summer is the exception: ALARO-25km retains a significant wet bias only in the south of the domain, whereas ALARO-12km and ALARO-4km show a significant dry bias in the north. Consistent with its smaller domain-mean dry bias, ALARO-4km shows a significant dry bias over a smaller northern area than ALARO-12km, with the central domain no longer significantly biased.

Figure  shows the diurnal cycle of precipitation in Uccle, Belgium. The diurnal cycle is first analysed across all hours (Fig. a). All simulations overestimate precipitation for all hours. Apart from the systematic bias, ALARO-4km neatly reproduces the diurnal precipitation variation. The observed afternoon peak around 16:00 UTC, for instance, is also present in ALARO-4km albeit with a higher intensity. ALARO-12km displays a smaller and slightly delayed peak, while ALARO-25km lacks a clear peak, maintaining roughly uniform precipitation amounts throughout the day. During wet hours (i.e. hours with a precipitation rate > 0.1 mm h⁻¹), on the other hand, there is a dry bias for all models (Fig. b). ALARO-4km again aligns most closely with observations, followed by ALARO-12km and ALARO-25km. The afternoon peak at 16:00 UTC remains visible for the observations but is less pronounced and slightly delayed for ALARO-4km. The delay is even larger for ALARO-12km and ALARO-25km, with progressively smaller peaks as resolution decreases. In summer (Fig. c), average precipitation values and peak amplitudes are considerably higher, although the simulated peaks occur slightly later and are less intense at lower resolutions. In winter (Fig. d), no clear peak is observed, and the average precipitation intensity is approximately half of the summer values.

Overall, these results indicate that although the simulations reproduce the timing of the diurnal cycle reasonably well, they overestimate precipitation frequency – raining too often with too little intensity – especially at coarser resolutions. To quantify this, we decompose the mean hourly precipitation P¯ into the frequency and intensity contributions from wet hours, defined as hours with a precipitation rate > 0.1 mm h⁻¹ (Table ). All simulations overestimate the wet-hour frequency n¯wet (11.8 % observed) while underestimating the wet-hour intensity P¯wet (0.791 mm h⁻¹ observed), most severely at 25 km (17.2 % and 0.692 mm h⁻¹). Increasing resolution reduces the frequency bias and raises the wet-hour intensity, shifting the simulations from frequent-weak towards less-frequent, more-intense precipitation. This confirms that the mean wet bias arises from a too-high precipitation frequency combined with too-weak wet-hour intensities, rather than from excessive intensity.

The calculated IDF statistics are presented in Fig.  for each topographic region. The difference in observational return levels between the regions is apparent for both sub-daily durations (<6 h) and durations extending beyond one day (≥24 h). In the former case, the values for Middle- and High-Belgium are similar to one another, but those for Low-Belgium are smaller, while in the latter case, the difference between Middle- and Low-Belgium disappears and the return levels over High-Belgium exceed those over the other two regions.

The observational return levels decrease approximately linearly with precipitation duration on a log-log scale (Fig. ), corresponding to the power-law scaling of extreme precipitation. The simulated return levels follow the same linear behaviour for durations of 6 h and longer, but deviate at short durations (<6 h), where they curve downward, away from the observations. To quantify this behaviour, a linear regression of the log-transformed return levels against the log-transformed duration was performed for each dataset, region, and return period. The resulting slopes and coefficients of determination (R2, the fraction of variance in the return levels explained by the linear fit) are shown in Fig. ; the fitted lines themselves are not overlaid on Fig. . The slope is steepest for the observations, followed by the simulations in order of decreasing resolution (ALARO-4km, ALARO-12km, ALARO-25km). The linear fit is also best for the observations (R2 closest to 1), again followed by ALARO-4km, ALARO-12km, and ALARO-25km, reflecting the increasing downward curvature at short durations as resolution decreases. Comparing return periods, longer return periods yield a steeper (more negative) slope but a lower R2.

Despite its strong wet bias for average precipitation, ALARO-25km underestimates the sub-daily (<6 h) return levels for all regions and return periods, as shown in Fig. . For the (multi-)daily (≥24 h) durations, the performance depends on the return period. The least extreme events, i.e. those with the shortest return period, are overestimated, while the events with the longest return period generally tend to be underestimated, although the uncertainty is large. Conversely, ALARO-12km provides smaller return levels than ALARO-25km for sub-daily (<6 h) durations, except for hourly events in Low- and Middle-Belgium (Fig. a, d). Hence, the sub-daily extreme precipitation intensities are also underestimated by this simulation. For (multi-)daily (≥24 h) durations, this intensity decrease with higher resolution is also present, especially in High-Belgium (Fig. g–i). Finally, for ALARO-4km the hourly return levels are substantially closer to the observational values for a 2-year return period and markedly closer for longer return periods. Generally, the ALARO-4km extremes increase in intensity compared to the ALARO-12km simulation, leading to improvements for some durations and regions, but not universally.

Figure  presents the diurnal and seasonal cycles of the frequency of annual-maximum hourly precipitation intensities over Belgium. In the diurnal cycle, the observations clearly show a primary peak in the afternoon. ALARO-4km captures both the timing and magnitude of this peak with high accuracy. ALARO-12km also reproduces a peak, but it occurs slightly later (i.e. 1–2 h) and with a higher frequency than observed. For ALARO-25km, the peak occurs even later (around 22:00 UTC) and has a lower frequency compared to the observations.

Figure  shows the annual-mean difference between ALARO-12km and ALARO-12km-noSFX, which isolates the effect of the SURFEX land-surface scheme, as all other components are identical between the two simulations. Both differences are significant across the entire domain (Fig. a, b). The temperature difference is roughly constant across the domain, except for some urban areas (e.g., Brussels) where the warming is stronger. On the other hand, the precipitation difference exhibits a clear north-south gradient, with the southern part of Belgium experiencing a stronger reduction in precipitation than the northern part. Moreover, the diurnal cycle of precipitation over Belgium (Fig. c) isolates how SURFEX acts on the sub-daily distribution. Both configurations share the same single afternoon peak at 16:00–17:00 UTC. Introducing SURFEX leaves the timing and shape of the cycle essentially unchanged except for a reduction in amplitude, damping the afternoon peak more strongly than the overnight minimum. Therefore, the resolution-dependent shift in peak timing seen in Fig.  is not a consequence of the land-surface scheme.

To identify the mechanism, we examine the surface energy balance (Fig. ), showing the seasonal diurnal cycle of the latent (a–d) and sensible (e–h) heat fluxes. The simulations separate by land-surface scheme rather than resolution: ALARO-12km-noSFX closely tracks ALARO-25km, while the SURFEX simulations (ALARO-12km and ALARO-4km) cluster together. Introducing SURFEX reduces the latent heat flux and increases the sensible heat flux, in both cases most strongly in summer, and slightly advances the diurnal peak of each. The net surface radiation is essentially identical across all simulations (Fig. ), so the available energy at the surface is unchanged. The sum of the latent and sensible heat fluxes is correspondingly near-identical in daily-mean magnitude, but its diurnal cycle is advanced in the SURFEX simulation. This phase shift, together with the shift toward sensible heating, points to a reduced surface thermal inertia, consistent with drier soil responding more rapidly to daytime forcing. This is consistent with the flux differences being driven by the surface state, as the net surface radiation, which sets the total available energy, is essentially unchanged.

As a whole, it is shown that the introduction of SURFEX reduces the latent heat flux and increases the sensible heat flux, especially in summer. This can be partly attributed to the inclusion of urban elements, which contain no moisture and therefore reduce the latent heat flux. However, the effect is also present in non-urban areas, indicating that the difference is not solely due to urbanisation. Although the differing soil discretisations of the two schemes preclude a direct quantitative comparison of soil moisture, the reduced latent heat flux, drier summers, and associated warming are all consistent with reduced soil moisture in the SURFEX configuration. This shift in the partitioning of the surface fluxes is consistent with the observed warming of near-surface air temperature and the reduced precipitation.

A clear distinction in climatology can be drawn between ALARO-25km on the one hand, and ALARO-12km and ALARO-4km on the other hand, both for near-surface air temperature and accumulated precipitation. The cold bias from ALARO-25km of -1.14 °C over Belgium is significantly improved by about 1 °C in the two simulations with the highest resolutions, as shown in Fig. . Furthermore, these simulations both exhibit a reduced wet bias in comparison with ALARO-25km. The difference between ALARO-12km and ALARO-4km is mostly small when compared to ALARO-25km. Aside from the difference in resolution, ALARO-12km employs the land-surface model SURFEX, while ALARO-25km still uses the built-in module ISBA. The dedicated ALARO-12km-noSFX experiment (Sect. ), which holds resolution fixed, shows that this difference in land-surface scheme, rather than the resolution increase, is responsible for the clear distinction between these two sets of simulations.

In  30-year simulations over Europe were performed with ALARO-0, a previous version of the ALARO model, and the built-in land surface scheme ISBA. These simulations were performed at resolutions of 0.44° (∼50 km) and 0.11° (∼12 km) and contained an area-averaged yearly bias in near-surface air temperature of a little less than -1 °C over the Middle-European sub-region (which covers Belgium, the Netherlands, most of Germany, and parts of neighbouring countries). This result is very similar to the yearly bias of ALARO-25km in this work. The seasonal temperature biases of  over Middle-Europe are also in line with the results of ALARO-25km.

Furthermore, in , simulations with ALARO-0 for a 10-year period were carried out in three different configurations, one of which consisted of continuous simulations as performed in this work. It should be noted that, contrary to those of , these simulations were performed with the SURFEX model, albeit a previous version, SURFEXv5. Over Middle-Europe, an average yearly temperature bias of -1.6 °C was found, while for winter and summer a bias of -1.3 °C was presented. This is comparable to the results of  and of ALARO-25km, even though the latter simulations did not use SURFEX.

Lastly, 4 km ALARO-0 simulations without SURFEX were performed in the context of the CORDEX.be I project . In the final report  a cold bias of 1.3 °C in the average yearly temperature over Belgium was presented. This value is in line with the results from , , and ALARO-25km, but contrasts with the temperature bias of the here-presented ALARO-12km and ALARO-4km, even though these CORDEX.be I simulations were run at 4 km. This is consistent with our ALARO-12km-noSFX experiment (Sect. ), which directly demonstrates that the use of SURFEX, and not the resolution increase, is responsible for the improved temperature bias, through a shift in the partitioning of the surface heat fluxes.

Evaluation against the CG dataset reveals that all ALARO-1 simulations exhibit a consistent annual wet bias over Belgium, with this bias most pronounced in ALARO-25km. Seasonal analyses confirm a wet bias across all seasons, except for a dry bias in summer in both ALARO-12km and ALARO-4km. Differences between ALARO-12km and ALARO-4km remain insubstantial across seasons. The ALARO-12km-noSFX experiment (Sect. ) confirms that the inclusion of SURFEX, rather than the change in spatial resolution, exerts the dominant influence on average precipitation.

Our results for precipitation (Fig. ) are now compared to previous continuous simulations from  (resolutions of 50 and 12.5 km). The annual precipitation bias of ALARO-25km (33.7 %) is markedly larger than the annual bias of approximately 20 % over Middle-Europe (ME) reported by  (for both their 50 and 12.5 km simulations), whereas ALARO-12km (15.3%) and ALARO-4km (17.0 %) are somewhat smaller. On the other hand, the annual precipitation bias over ME in  (at 20 km resolution) was 15 %, which agrees almost perfectly with the results from ALARO-12km and ALARO-4km. For summer and winter precipitation, the biases of  and  are similar to each other and resemble closely those of ALARO-25km. Conversely, the winter, and particularly the summer precipitation totals are much drier in ALARO-12km and ALARO-4km compared to ALARO-25km. The large wet bias in spring, reported in  is also present (and slightly increased) in the simulations in this work. Finally, the large bias in autumn was absent in the simulations of , where the bias was between 0 % and 10 %.

Previous 4 km simulations showed results similar to ALARO-4km. Compared to the HRES-simulations from CORDEX.be I, the bias in winter precipitation was of comparable magnitude . Biases from  were slightly smaller for summer precipitation than for ALARO-4km: their 4 km simulation showed a bias of only 3 %. Notably, those simulations employed daily restarts, which could have a significant impact–especially in summer, when soil moisture feedbacks tend to play a more important role. There was a difference of roughly 10 percentage points between their 10 km and 4 km simulations in summer precipitation bias, which is also present between ALARO-12km and ALARO-4km but with an opposite sign. Both cases can be interpreted as an improvement in the representation of (convective) precipitation when increasing the resolution.

In , the multi-scale behaviour of ALARO-0 was investigated by means of the diurnal cycle of precipitation in summer and winter. An identical distinction between all hours and wet hours is made in this work, as shown in Fig. . It was shown in  that in summer the timing and amplitude of the diurnal peak were improved for simulations with ALARO-0 at 10 and 4 km compared to a 40 km simulation, when considering all hours. However, the timing of the afternoon peak as reproduced by the model was still too early. A similar behaviour is evident in this work, although ALARO-4km captures the timing better (later) than in . For winter precipitation, the 4 km simulation from  exhibited a weak peak in the early afternoon, which is absent in the observations. Our ALARO-4km simulation reproduces this constant diurnal pattern better than those in . Since winter precipitation over Belgium is predominantly stratiform, the spurious afternoon peak in their ALARO-0 simulation points to convective triggering when little is expected; its near-absence in ALARO-1 suggests less spurious wintertime triggering, though isolating the responsible change is left for future research.

When considering only wet hours (i.e. hours with a precipitation rate >0.1 mm h⁻¹), the observations show no diurnal variation (regardless of some noise) in winter (Fig. d). All simulations in this paper reproduce this pattern, with the mean precipitation increasing towards the observed value as the resolution increases. For wet hours in summer (Fig. c), all simulations contain an afternoon/evening peak, with increasing amplitude for higher resolutions, similar to the study of . The timing of the peak does not significantly differ between ALARO-25km and ALARO-12km, and is slightly earlier for ALARO-4km. However, for all simulations, the summer wet-hour peak occurs later than the observed peak, in contrast with the well-captured peak timing reported by  for ALARO-0. This contrast reflects the change from ALARO-0 to ALARO-1 and cannot be attributed to the scale-aware 3MT scheme, which is common to both versions, nor to the land-surface scheme, which the ALARO-12km-noSFX experiment shows does not affect the peak timing (Sect. , Fig. c). A further candidate is the difference in experimental setup: the ALARO-0 simulations of were reinitialised daily, whereas ours run continuously. Such daily restarts can plausibly influence the phase of the simulated diurnal cycle. However, we cannot isolate the responsible factor from the available output. Overall, for both all-hour (Fig. a) and wet-hour (Fig. b) precipitation, the diurnal cycles in ALARO-4km are comparable to those in the work of .

In our analysis of the mean diurnal precipitation cycle, notable differences emerge when comparing simulations at varying resolutions with observational data, as shown in Fig. . Specifically, while the “all-hour” precipitation cycle overestimates precipitation relative to observations, the “wet-hour” cycle underestimates it, which Table  attributes to an overestimated wet-hour frequency combined with an underestimated wet-hour intensity. This is most pronounced in ALARO-25km and minimised in ALARO-4km, showing that the coarser resolution overestimates precipitation amounts through an overly high precipitation frequency, i.e. a substantial drizzle contribution.

This drizzle bias is a well-known deficiency of regional climate models . It arises largely because parameterised convection triggers on weak instability and releases it gradually, producing precipitation that is too frequent and too light. The improvement with resolution reflects the sharper humidity and updraught fields at higher resolution, which reduce the widespread simultaneous triggering dominating the coarser runs. The residual bias in ALARO-4km is consistent with 3MT still parameterising part of the convective spectrum in the grey zone.

Furthermore, both the timing and amplitude of the diurnal precipitation peak are best represented at high resolution, as well established for CPMs . Most RCMs exhibit a premature diurnal peak, primarily due to the limited memory of atmospheric instabilities; this behaviour is notably absent here, and at lower resolutions the ALARO peak even occurs later than at higher resolutions. The ALARO-12km-noSFX experiment (Sect. , Fig. c) shows that introducing SURFEX reduces the amplitude of the diurnal cycle but leaves the timing of the peak unchanged, so the resolution-dependent shift in peak timing is not driven by the land-surface scheme. Its origin lies instead in the convection scheme. Conventional mass-flux schemes that close on CAPE remove instability almost as soon as it is generated by surface heating, so that simulated precipitation peaks around local noon, in phase with the surface fluxes, rather than in the late afternoon as observed . In contrast, 3MT employs a prognostic closure that retains memory of the updraught mesh fraction and updraught velocity between time steps, with the mesh fraction evolving through the moisture budget. Instability is therefore released gradually over several time steps rather than instantaneously, shifting the peak away from noon; none of our configurations peaks near midday. At coarser resolutions this gradual release appears to be too gradual, delaying the convective peak, and the timing sharpens as explicit convection progressively takes over at higher resolutions. A full attribution of the responsible mechanism would require dedicated sensitivity experiments and is left to future work.

IDF statistics are presented in Fig.  for durations of 1 to 72 h across three distinct topographic regions in Belgium. The regional differences in return levels, with smaller sub-daily (<6 h) values in Low-Belgium and higher (multi-)daily (≥24 h) values in High-Belgium, are consistent with the findings of . In each case, the return levels scale linearly with duration on a log-log scale, for both observations and simulations. This corresponds to a power-law relationship on a linear scale and reflects the underlying scale invariance and multifractal characteristics of extreme precipitation. These phenomena can be effectively captured using simple scaling techniques, which in turn result in a power-law relationship . However, for short precipitation durations (1–3 h), simulated return levels deviate from this linear trend, curving downward, whereas observational return levels do not exhibit this pattern. This discrepancy arises entirely from model error, as precipitation values from both observations and simulations were first aggregated to an hourly resolution before extracting the annual maxima. As shown in Fig. b, the smaller R2-values indicate a less optimal fit for larger spatial scales. The higher (less negative) linear coefficients at these scales may also reflect this underestimation at short durations. However, previous studies have also shown that annual-maximum precipitation at larger spatial scales has a higher linear coefficient with respect to duration than at smaller scales . Next, these linear coefficients can be compared to those from a simple-scaling model by . In that work, station-specific values in the range of -0.75 and -0.64 were found for 16 stations over Belgium. The observational coefficients depicted in Fig. a correspond to this range, although they are slightly more negative.

At durations of 1 to 3 h, lower-resolution simulations increasingly underestimate return levels compared to observational values, highlighting the added value of the convection-permitting ALARO-4km simulation. A similar result was found by , who also constructed IDF statistics for ALARO-0 simulations at different resolutions. In that study, the 4 and 10 km ALARO-0 simulations accurately captured sub-daily intensities, with a slight underestimation, while ALARO-40km significantly underestimated sub-daily precipitation amounts. For longer durations (>24 h), ALARO-25km tends to overestimate the return levels, particularly for short return periods (Fig. a–c). reported a similar finding, as all ALARO-0 simulations (4, 10, and 40 km) overestimated the 2-year return level for daily precipitation. Additionally, while  observed increasing overestimation for longer return periods in the 4 km ALARO-0 simulation, this effect is notably absent – and even reversed – in ALARO-4km.

The scale-aware design of the 3MT scheme provides a smooth transition between parameterised and resolved convection, which would lead one to expect a gradual change of the extreme-precipitation statistics with resolution, as found in previous studies . In contrast, the return levels presented in this study display a more abrupt, step-wise change when transitioning from 12 to 4 km resolution. This behaviour is more similar to that observed in other models without a scale-aware convective scheme, where the step-wise shift is typically attributed to the deactivation of the deep convective parameterisation at high resolutions. For 3MT, however, no such deactivation occurs, and the apparent abruptness may be partly an artefact of comparison: the 25 to 12 km change is small, so the 12 to 4 km change stands out as step-wise by contrast. We propose two contributing effects. First, the difference between ALARO-25km and ALARO-12km conflates resolution with the land-surface scheme: the drying effect of SURFEX (Sect. ) reduces precipitation and may partly offset the resolution-driven increase in extreme intensity at 12 km, suppressing the apparent 25 to 12 km change. Second, the step from 12 to 4 km crosses the grey zone of convection (∼4–10 km) , where 3MT transitions from a parameterised towards a resolved representation of deep convection. This transition is expected to affect the extreme-precipitation statistics most strongly. Isolating the contributions of these two effects is left to future work.

The diurnal cycle of hourly AM precipitation frequencies is well captured by ALARO-4km (see Fig. a). Both the frequency peak amplitude and timing are in agreement between ALARO-4km and the observational data. The peak occurs later in ALARO-12km and is further delayed in ALARO-25km, while the peak amplitude increases in ALARO-12km but decreases in ALARO-25km. This peak delay is also present in 0.11° EURO-CORDEX simulations . It should be noted that the relatively large diurnal variation in extreme precipitation frequency of ALARO-25km is quite remarkable, as most models exhibit almost no diurnal variation at similar resolutions . The diurnal cycle of extremes from previous ALARO-0 simulations at 12 and 4 km was shown in . However, they did not find a large difference in the diurnal cycle between both resolutions, in contrast to the simulations of this work. As with the peak-timing differences discussed above, this stronger resolution sensitivity of ALARO-1 relative to ALARO-0 most plausibly reflects the broader physics update between the two versions rather than the scale-aware convection scheme common to both, and is left to future work.

Similarly to the diurnal cycle, the seasonal cycle of hourly extreme-precipitation frequency is well captured by our three simulations, as shown in Fig. b. The frequency peak in summer due to the convective nature of hourly extreme precipitation is apparent. This result corresponds to previous simulations from , who also did not find a difference in the seasonal cycle between 12 and 4 km ALARO-0 simulations. In contrast,  reported the slight outperformance of a 12 km RCM simulation compared to a 4 km convection-permitting WRF simulation in capturing the seasonal cycle of hourly AM occurrences over North America.