SURFEX is an externalized surface modelling system that parameterizes all components of the surface . It uses a tiling approach to represent subgrid surface heterogeneity, with the surface split into four tiles: continental natural surfaces, sea, inland water and urban areas. The SURFEX tiling approach assumes that the interaction of each surface tile with the overlying atmosphere is completely independent of the other tiles present in the grid box. Continental natural surfaces are further divided into subtiles or patches, accounting for different vegetation characteristics within a grid box. The number of patches can be chosen between 1 and 12, but for simplicity it is typically set to 2 in HCLIM38, representing open land and forest.

The NWP setup of HARMONIE–AROME uses simplified surface processes like the force-restore approach in the soil and the composite snow scheme by . Such simplified physics are appropriate for short timescales in combination with surface data assimilation, but for climate timescales more sophisticated surface physics are required that can represent e.g. long soil memory and proper snow characteristics. The default SURFEX version in HCLIM38 was 7.2 . However, the state of the more sophisticated surface physics options in v7.2 was not considered to be adequate for HCLIM purposes. Therefore, a stepwise upgrade of SURFEX was performed. First, v7.2 was replaced by v7.3, and then the land-surface physics scheme in v7.3 (ISBA) was replaced by the corresponding scheme from v8.1. The list of SURFEX parameterizations and the related references used in HCLIM38 is given in Table . These include e.g. the ISBA multi-layer soil diffusion option (ISBA-DIF) with soil organic carbon taken into account and a 12-layer explicit snow scheme (ISBA-ES). For a proper simulation of temperature in deep and large lakes the inland water (rivers and lakes including any ice cover) is simulated by FLake. In HCLIM38, FLake uses the lake depth obtained from the Global Lake Data Base (GLDB; ) and is initialized from a climatology of lake profiles which vary over time and space. HCLIM38 implements the same SICE model as in the NWP setup to simulate the sea ice temperature. The difference in HCLIM38 is that the sea surface temperature and sea ice concentration are updated together with the lateral boundaries to capture their long-term variation. The urban tile is parameterized by the Town Energy Balance model (TEB; ), which is used only at convection-permitting resolutions.

The land cover and soil properties are obtained from the ECOCLIMAP version 2.2 database at 1 km resolution and the Food and Agriculture Organization database , respectively. SURFEX is fully coupled to the atmospheric model, receiving atmospheric forcing over each patch and tile and returning grid-averaged values (heat and momentum fluxes, etc.).

ALADIN is the default choice in HCLIM38 for simulations with grid spacing close to or larger than 10 km. It is the limited-area version of the global model ARPEGE, from which it inherits all dynamics and physics options. The version of ALADIN available in HCLIM38 corresponds to the one used in NWP, with the dynamics and physics options listed in Table  and described in . The difference in HCLIM38 is only in the surface parameterizations, which are more suitable for climate simulations as described above. HCLIM38-ALADIN is predominantly used as a hydrostatic model with a convection parameterization, so it is not envisaged for use at grid spacings much smaller than 10 km. Therefore, there is a gap, usually termed “the grey zone” for convection, between the grid spacing of 10 km and the convection-permitting scales with grid spacing smaller than 4 km. HCLIM38 simulations with grid spacing within the grey zone should be avoided if possible.

ALARO has been designed to also operate in the convection grey zone (Fig. ; ). Unlike traditional moist convection parameterizations, the Modular Multiscale Microphysics and Transport scheme (3MT; ) addresses the fact that the size of convective cells becomes significant compared to the model grid spacing as the resolution increases. This allows for great flexibility in applying the model, which is highly desirable in climate applications. Therefore, ALARO was the default choice in HCLIM36 . However, the coupling of ALARO with SURFEX as used in HCLIM38 resulted in evaporation from oceans that is too weak in low latitudes, causing considerable underestimation of atmospheric moisture content and consequently a lack of precipitation in long climate simulations. Similar issues have not been observed at high latitudes , implying that ALARO can be used there. However, it is not the default option in HCLIM38 because the modelling system should be applicable at all latitudes. The detailed ALARO description in refers to a newer version called ALARO1. HCLIM38 uses an older version, ALARO0, with some updates from a development version of ALARO1 and as such does not correspond to any canonical model configuration. Specifically, in HCLIM38-ALARO the radiation scheme ACRANEB from ALARO0 was replaced by an early version of ACRANEB2 used in ALARO1. Since it is based on ALARO0, HCLIM38-ALARO still uses the pseudo-prognostic turbulent kinetic energy (pTKE) turbulence scheme , which has been replaced by TOUCANS in ALARO1. At the same time, HCLIM38-ALARO is coupled to SURFEX, making this configuration different from the NWP model configuration. The full list of used parameterizations and references is given in Table .

HCLIM38-AROME is a nonhydrostatic CPRCM based on the HARMONIE–AROME NWP model configuration (Table ), but with different surface model options that are more suitable for climate applications as described above. It is the recommended option in HCLIM38 for simulations at convection-permitting scales. AROME is the main focus of HCLIM development due to the recognized need of the participating institutes for a CPRCM. As such, it is becoming the backbone of convection-permitting regional climate projections for a number of European countries.

There is no deep convection parameterization in AROME, so it can only be used at convection-permitting resolutions, which are generally considered grid spacings smaller than 4 km. This implies that for downscaling low-resolution GCMs, it is currently not possible to use the same model configuration at intermediate scales of O(10 km) and convection-permitting scales of O(1 km). As described above, the intermediate scales in the current setup are typically simulated by HCLIM38-ALADIN. This is the preferred option because the two model configurations share the same surface model. In this case the soil state in HCLIM38-AROME is initialized in a consistent way, the only difference being the resolution change. This could help decrease the soil spin-up time, which is typically 1 year, provided that the precipitation climatology is similar between the two model configurations. However, HCLIM38-AROME can also be used with other climate models at the lateral boundaries.

HCLIM38-AROME uses a shallow convection parameterization based on the eddy diffusivity mass-flux framework (EDMFm; ). The default choice for the turbulence parameterization is the scheme called HARMONIE with RACMO Turbulence (HARATU; ), even though the CBR scheme with the diagnostic mixing length from is available as well. HARATU and CBR mostly differ in the formulation of length scales and values of constants . A one-moment microphysics scheme, ICE3 , is used, with additional modifications for cold conditions called OCND2 . The cloud fraction is determined using a statistical scheme . Similarly to ALADIN, the radiation scheme is a simplified version of the scheme used at the ECMWF, described in . The six-spectral-band shortwave radiation (SW6) is based on . A rapid radiative transfer model (RRTM) with 16 spectral bands is used for longwave radiation . Monthly aerosol climatologies are provided by .

Here, HCLIM38 is compared to other state-of-the-art RCMs over Europe . HCLIM38-ALADIN has been run with a couple of domain configurations similar to the EURO-CORDEX domain with a horizontal grid spacing of 12 km (EURO-CORDEX uses 0.11∘ resolution; ). The boundary conditions were taken from the ERA-Interim reanalysis . Differences in daily mean near-surface air temperature (T2m) and precipitation between nine RCMs (including HCLIM38-ALADIN) and E-OBS version 17 gridded observations were calculated for the Prediction of Regional scenarios and Uncertainties for Defining European Climate change risks and Effects (PRUDENCE) regions in Europe based on a common 10-year period (1999–2008). RCMs were interpolated to the E-OBS 0.25∘ regular grid prior to comparison. Figure shows the results for the winter (DJF) and summer (JJA) seasons for the Scandinavia and Mediterranean regions. The results for these two regions, which are representative for most PRUDENCE regions, show that HCLIM38-ALADIN is generally colder and wetter than E-OBS. However, it can be seen that most of the other RCMs are also wetter than E-OBS and that HCLIM38-ALADIN is generally in close agreement with E-OBS in winter (Fig. S1). Larger differences are mostly seen in connection with mountainous regions. This is also the case for temperature in winter. For example, the negative temperature bias in winter over Scandinavia is mostly associated with 2–4 ∘C lower values over the Scandinavian mountains. At lower altitudes the temperature is much better represented by the model (Fig. S1). Still, the cold bias in HCLIM38-ALADIN is present throughout most seasons and is spatially widespread over Europe. The reason for this systematic bias is not yet known and needs to be further investigated. Finally, we note that for the two versions of ALADIN, HCLIM38-ALADIN consistently shows lower temperatures than CNRM-ALADIN53 for large parts of Europe, apart from western and southern Europe. The precipitation differences compared to E-OBS, however, are generally smaller in HCLIM38-ALADIN. We conclude that the performance of HCLIM38-ALADIN over Europe, in terms of multi-year means of T2m and precipitation, is generally within the range of the performance of other RCMs used within EURO-CORDEX.

Due to its complex topography and the exposure of the western coast to large amounts of moisture transported over the North Atlantic, Norway is a challenging area for which to provide accurate climate model simulations and constitutes an ideal testing environment. To evaluate the performance of the HCLIM38-AROME model in this region at convection-permitting scales, it was run at 2.5 km for an area covering Norway, parts of Finland, Sweden and Russia for the time period 2004–2016 , downscaling the ERA-Interim reanalysis. An intermediate HCLIM38-ALARO simulation at 24 km resolution was used to avoid an excessively large jump across the boundaries (results not analysed here).

For the evaluation over Norway, we use the gridded observation dataset seNorge v2.1 for precipitation and temperature ; seNorge provides daily precipitation and temperature back to 1957 at a grid resolution of 1 km. The dataset has a special focus on providing meteorological input for snow and hydrological simulations at the regional or national level. Thus, it not only covers the Norwegian mainland but also neighbouring areas in Finland, Sweden and Russia to include regions impacting the Norwegian water balance. The station data are retrieved from MET Norway's climate database and the European Climate Assessment and Dataset (ECA&D, ). More details on the spatial interpolation schemes and the dataset in general are given in .

Note that gridded observation datasets in remote regions of Norway should be considered with caution. For certain regions of Norway it may be difficult to judge the quality of the seNorge data due to the inhomogeneous station distribution. While terrain height can reach 2000 m or more, most stations are located below 1000 m. There is also a difference in the station density between the southern and northern parts, with a higher density in the south of Norway . For precipitation, have shown that seNorge2 gives values that are too low in very data-sparse areas. For temperature, an evaluation in has shown that the interpolation actually yields unbiased estimates, with the exception of a warm bias for very low temperatures, and that the grid point estimates show a precision of 0.8 to 2.4 ∘C.

Generally, HCLIM38-AROME shows an underestimation of precipitation at the south-western coast and over the Lofoten islands, while precipitation in the mountains is overestimated (Fig. ). The largest differences appear in autumn and winter (not shown). Values for precipitation that are too high can also be seen for spring and summer over central–southern Norway. Similar differences have been shown by for the Nordic operational NWP setup of HARMONIE–AROME and by comparing the HCLIM38-AROME precipitation data to observed precipitation.

However, despite the biases found in simulated precipitation, the HCLIM38-AROME data have been successfully used by together with in situ observations to obtain improved monthly precipitation climatologies over Norway. The high-resolution model data are used to provide a spatial reference field for an improved interpolation of the in situ observations where there are no measurements. The result is not a purely bias-corrected RCM dataset, nor are the in situ observations corrected. The approach is used to overcome the uneven station network over Norway, and it was shown that the simulated precipitation could be used to improve the climatologies significantly, especially over the most remote regions. For instance, for the wettest area in Norway around Ålfotbreen, the combined data result in a mean annual precipitation of over 5700 mm. Measurements of snow accumulation during the winter half-year together with estimates of drainage from river basins (performed by the Norwegian Water Resources and Energy Directorate) indicate mean annual precipitation amounts over 5500 mm in the area . The purely observation-based estimates are almost 2000 mm lower.

The combined dataset shows systematically higher precipitation values than seNorge for the observation-sparse mountainous regions. As the seNorge dataset is likely to underestimate precipitation in these areas we expect this to be an improvement. However, whether this is true still needs to be verified e.g. by the use of hydrological simulations .

Annual mean temperature in HCLIM38-AROME is generally lower than in seNorge, but the differences are small (Fig. ). Averaged over the whole area, HCLIM38-AROME is about 1 ∘C colder than seNorge. The differences range from about -7 to 4 ∘C, but for most of the area, the temperature differences are below ±2 ∘C and larger biases are restricted to the mountains. All seasons show similar patterns to the annual biases with the largest differences in the mountains, but the general increase in the bias with altitude is most pronounced in winter (not shown).

Better resolving summertime precipitation is arguably the most important reason for running CPRCMs and a primary variable for which we anticipate added value compared to coarser-resolution RCM models. In this section we discuss statistics of summer precipitation in two 10-year ERA-Interim forced climate simulations for the period 2000–2009, carried out with HCLIM38-AROME at convection-permitting scales. The focus will be on the summer half-year (April–September). The first CPRCM experiment (E1) conducted by KNMI receives lateral boundary conditions from the RCM RACMO2 . In the second experiment (E2) conducted by SMHI, the host model is HCLIM38-ALADIN. Both host models are forced by ERA-Interim. For both E1 and E2 the domain covers the pan-Alpine region as defined in the CORDEX FPS on convection , but the E1 domain extends substantially further to the north-west, covering a large part of the North Sea. Output is compared to two types of observations: radar data (for the Netherlands) and rain gauges (for a part of Germany).

For the evaluation of the CPRCMs to rain radar over the Netherlands, we can only use output from E1 since the E2 domain does not cover the Netherlands. The radar data are an hourly gridded product (2.4 km horizontal resolution) that has been calibrated against automatic and manual rain gauges . Data from both the CPRCM (HCLIM38-AROME, 2.5 km) and the RCM (RACMO2, 0.11∘) are put on the radar grid using nearest-neighbour interpolation. Two statistics are studied. First, we look at hourly spatial precipitation maxima found within the Netherlands. We call this the hourly FLDMAX statistic. The analysis focuses on model performance at the grid scale, and here we expect to find added value. Note that in this formulation the FLDMAX does not account for the spatial extent of the precipitation, nor does it account for the possible existence of several convective clusters at the same hour. Secondly, we study the hourly FLDMEAN statistic (i.e. the hourly area-average precipitation). If a CPRCM outperforms its host model for the latter statistic, this is an example of upscale added value: the higher horizontal resolution also pays off at larger spatial scale. This is not guaranteed, especially not in winter, when precipitation is often caused by large-scale weather systems. Confidence intervals (95 %) are estimated using bootstrapping. The bootstrapping technique consists of constructing a large number of “synthetic” time series by resampling days from the original time series (sampling with replacement) and computing the target statistic for each of the resamples. This gives an empirical distribution for the target statistic, from which the confidence interval can be estimated. The resulting estimate is overconfident as it ignores time correlations.

We expect the largest benefits of using a high-resolution model at the finest scales, which cannot be reached by the non-CPRCM. This is confirmed for the Netherlands in Fig. a, which shows for each hour an estimate of the average and the 90th and 99th percentile of the FLDMAX precipitation; 3-hourly sliding windows are used to improve statistical robustness, and confidence bands were determined using bootstrap resampling on hourly basis. HCLIM38-AROME simulates the diurnal cycle very well. Although the diurnal cycle of HCLIM38-AROME is about an hour delayed with respect to the radar observations, it is much improved compared to RACMO2, which hardly shows signs of a diurnal cycle. Results for the winter half-year are qualitatively similar, but the amplitude of the daily cycle is much less pronounced (not shown). For the FLDMEAN statistic, the amplitude in the diurnal cycle is dampened, and RACMO2 and HCLIM38-AROME are generally more similar (not shown). Figure b and c show the precipitation distributions as exceedance plots. The exceedance plots are computed by simple ordering of the FLDMAX or FLDMEAN data and inferring the empirical probability of a given value based on its order position. Not only at the grid scale (FLDMAX), but also at the largest spatial scale available (FLDMEAN, the Netherlands), HCLIM38-AROME generally outperforms RACMO2, especially for the larger precipitation amounts. It could be argued that a non-CPRCM cannot be expected to reproduce the radar-observed precipitation statistics because of its coarser resolution. For this reason, we have recomputed the statistics shown in Fig.  using the data that were re-gridded to the 12 km RCM grid prior to computation. This upscaling to 12 km was done using simple conservative interpolation. Figure S3 shows that the differences between CPRCMs and RCMs remain qualitatively the same after upscaling to the RCM grid. Therefore, even at these spatial scales there is clear added value of the CPRCM.

For the evaluation of the CPRCMs over Germany, we compare E1 and E2 to hourly rain gauge data. As a proxy for the rain gauge location we use the nearest model grid point. In addition, we consider only stations that have an altitude lower than 500 m (see Fig. S4 for the rain gauges involved). Similarly to the evaluation done over the Netherlands, we use the FLDMAX and FLDMEAN approach in which the appropriate statistical operator is applied over the hourly data.

The differences between CPRCMs and RCMs for FLDMAX for Germany are similar to the results for the Netherlands presented above, with the CPRCM agreeing better with observations (Fig. ). Note how similar the HCLIM38-AROME simulations are, despite the rather different characteristics of their host model. Although the diurnal cycle is better represented by the CPRCMs, the modelled late afternoon peaks are too high. It appears that the overestimation of the peak is related to the elevation: if we constrain to the subset spanned by gauges at lower elevation, the CPRCMs agree better with the observations (not shown). The overestimation of intense precipitation (10–40 mm h-1) is consistent with the analysis of the UKMO and ETH-COSMO models in for Germany. Similar to the results over the Netherlands, the differences between CPRCMs and RCMs are smaller for the FLDMEAN statistic (not shown).

The Mediterranean region is characterized by a complex morphology due to the presence of many sharp orographic features: high mountain ridges surround the Mediterranean Sea on almost every side, the presence of distinct basins and gulfs, and islands and peninsulas of various sizes. These characteristics have important consequences on both sea and atmospheric circulations because they introduce large spatial variability and the presence of many subregional and mesoscale features e.g.. Moreover, the Mediterranean region is considered to be a hotspot for climate change e.g.. It is frequently exposed to recurring droughts and torrential rainfall events, both of which are projected to become more frequent and/or intense as a result of future climate change. Therefore, it is an area where climate models have to be tested. In this study we focus on eastern Spain in summer (JJA) when precipitation events are scarce and mainly convective e.g.. Our aim is to study the performance of HCLIM38 in representing convective precipitation in dry zones at high temporal and spatial resolution.

We compare results from two HCLIM38 simulations, one at high resolution with the AROME configuration and another at lower resolution with the ALADIN configuration, against hourly precipitation records. These are the experiments performed.

AROME: 10 years (1990–1999), 2.5 km resolution, Iberian Peninsula

Both simulations were forced directly with ERA-Interim data at the boundaries. The simulations are compared with a dense set of around 500 automatic and manual rain gauges recording hourly precipitation that are distributed over eastern Spain (Fig. S5). These observations are extracted from the National Weather Data Bank of AEMET Chapter 9 and have been used in other studies of intense precipitation events e.g..

The selected period for observations is 2008–2018 because hourly data from automatic stations started to be available in 2008. This period has 7 years of overlap with the HCLIM38-ALADIN simulation, but it does not overlap the HCLIM38-AROME simulation. We assume that the precipitation characteristics have not substantially changed in the last 30 years and that in two nearby 10-year periods the mean statistics calculated from hourly precipitation are comparable. The assumption that rainfall characteristics are not dependent on the period analysed, when periods are not far from each other, will be verified below and has been shown in other studies e.g..

Two aspects of summer (JJA) precipitation are studied: the timing of the maximum hourly precipitation within a day and the hourly intensity. At hourly scales we expect the convection-permitting nonhydrostatic physics (AROME) to better reproduce the precipitation characteristics compared to the hydrostatic physics (ALADIN). For the timing and intensity we calculate for each rain gauge the 10-year mean of the hour of maximum precipitation in a day and the corresponding hourly intensity, respectively. The same is calculated for the two models after interpolating the modelled precipitation to the nearest-neighbour observation. The 10-year observation mean is subtracted from the 10-year model means to get the difference in every point. These differences for every location are pooled together, and PDFs of the timing differences and hourly intensity differences are obtained for AROME and ALADIN. Gaussian distributions are fitted to the PDFs with the same mean and variance for a clearer comparison.

Several hourly thresholds have been tested (0, 5, 10, 15 and 20 mm h-1), filtering out hourly precipitation below each threshold. Finally, we use the threshold of 5 mm h-1 to remove periods with weak precipitation while keeping a sufficient number of events for robust statistics. The number of points fulfilling this condition is near 500 for AROME and around 400 for ALADIN.

The histograms of the differences of the hour of maximum precipitation and intensity between models and observations are shown in Fig. . The distributions of differences for both timing and intensity are centred at zero for HCLIM38-AROME, while they are shifted to negative values for HCLIM38-ALADIN. This indicates that the ALADIN physics underestimate both the timing and intensity of maximum hourly precipitation, while the convection-permitting physics AROME are able to reproduce both realistically. In the case of timing the PDF of HCLIM38-AROME is narrower, while HCLIM38-ALADIN shows a wider spread in the hour of maximum precipitation. For the intensity both models have similar spread.

Even though HCLIM38-ALADIN has 7 years of overlap with observations and HCLIM38-AROME has none, HCLIM38-AROME is closer to the observations. Therefore, it seems that the decadal variability in the distribution is sufficiently small to allow for a comparison between observations and simulations of different (but close) periods in this case.

In conclusion, the convection-permitting model HCLIM38-AROME shows a clear improvement in the representation of key characteristics of precipitation as exemplified by timing and hourly intensity compared to the hydrostatic model HCLIM38-ALADIN. While HCLIM38-ALADIN underestimates the mean values of both variables, HCLIM38-AROME shows very small biases for the threshold used (>5 mm h-1). In accordance with previous CPRCM studies e.g., the main reason for this improvement is that AROME explicitly resolves deep convection , while HCLIM38-ALADIN parameterizes it.

Since HCLIM38 has not previously been applied over the African continent, the ALADIN pan-African simulation at 50 km was compared to the CORDEX-Africa (http://www.csag.uct.ac.za/cordex-africa, last access: 18 March 2020) RCM ensemble at about the same resolution . Figure  shows an example with the differences in mean July–September near-surface temperature and precipitation over the West Africa–Sahel region between the RCMs and the Climate Research Unit Time-Series (CRU, v. 4.01; ). HCLIM38-ALADIN is somewhat dry and cold, but the performance is well within the range of that of the CORDEX-Africa ensemble. On an annual timescale HCLIM38-ALADIN biases are mainly between -2 and 1.5 ∘C for temperature and -1.5 and 1.5 mm d-1 for precipitation (Fig. S6), which is also within the range of the CORDEX-Africa ensemble.

In order to define an optimal configuration for convection-permitting HCLIM38-AROME simulations in Africa, a number of sensitivity experiments were performed for 2005–2006 over a wider Lake Victoria region within the ELVIC CORDEX FPS. The experiments include the downscaling of ERA-Interim by HCLIM38-ALADIN at 25 km (pan-Africa and eastern Africa) and 12 km (eastern Africa) resolution. In a subsequent step HCLIM38-AROME downscaled all three HCLIM38-ALADIN simulations over the Lake Victoria Basin at 2.5 km. In the HCLIM38-ALADIN simulations precipitation over land is triggered early during the diurnal cycle compared to the Tropical Rainfall Measuring Mission (TRMM-3B42, v. 7; ) (Fig. ). This too early peak is a common problem in the majority of the CORDEX-Africa RCMs . In contrast to HCLIM38-ALADIN, the time of maximum precipitation intensity during the diurnal cycle over land is very well simulated by HCLIM38-AROME at 2.5 km. This is in accordance with the HCLIM38-AROME results shown above for different European regions and with previous results using other CPRCMs , which strongly implies that the improvement is a result of the difference in model physics, i.e. the absence of convection parameterization, rather than only increased resolution.