Convection in future winter storms over Northern Europe

Precipitation within extratropical cyclones is very likely to increase towards the end of the century in a business-as-usual scenario. We investigate hourly precipitation changes in end-of-century winter storms with the first km-scale model ensemble covering northwest Europe and the Baltic region. This is an ensemble that explicitly represents convection (convection permitting models (CPMs)). Models agree that future winter storms will bring 10%–50% more precipitation, with the same level of light precipitation but more moderate and heavy precipitation, together with less frequent frozen precipitation. The warm sector precipitation rates will get closer (up to similar) to those in present-day autumn storms, along with higher convective available potential energy and convective inhibition, suggesting more convection embedded in storms. To the first order, mean hourly precipitation changes in winter storms are driven by temperature increase (with little relative humidity changes) and storm dynamical intensity (more uncertain), both captured by regional climate models (RCMs). The CPMs agree with this, and in addition, most CPMs show more increase in intense precipitation in the warm sector of storms compared to their parent RCM.


Introduction
Climate change is likely to bring milder and wetter winters to Northern Europe (Doblas-Reyes et al 2021). Given the current vulnerability of northern European societies to extensive winter flooding (Muchan et al 2015), we need to better understand how the nature of winter precipitation will change. Precipitation is expected to intensify in a warming climate, in the first order due to increased water holding capacity of the atmosphere (Fischer and Knutti 2016). In regions and seasons not limited in atmospheric moisture supply, this will translate into an increase in mean precipitation, like in Northern Europe in winter (Poujol et al 2021). Global climate models project more precipitation per storm (Hawcroft et al 2018 but dynamical changes in storm tracks, storm numbers and storm intensity are less certain (Zappa et al 2013, Fereday et al 2018. The most robust dynamical changes over Europe in winter are an eastward extension of North Atlantic jet stream, which means an increase in storm numbers over the UK and Baltic regions (Harvey et al 2020, Albern et al 2021 and an increase in dynamically extreme storms (Priestley and Catto 2021).
With the growing availability of ensembles of km-scale models at climate scales (Ban et al 2021, Pichelli et al 2021, we can examine finer-scale hourly precipitation processes in future winter (FW) storms. Indeed, case studies show that many precipitation processes in mid-latitude cyclones are improved at km-scale modelling: shallow convection in the cold sector/dry intrusion overlaying a warmer surface (Grossman and Betts 1990), slantwise convection releasing conditional symmetric instability associated within fronts (Lean and Clark 2003, Glinton et al 2017, Chen et al 2021, better representation of frontal structures, dry intrusion overrunning the warm sector (Browning 1997), embedded convection in warm conveyor belt and cold fronts (Neiman et al 1993, Rasp et al 2016, Oertel et al 2019. In this study, we investigate how the nature of hourly precipitation and its rate may change in FW storms in a business-as-usual RCP8.5 end-ofcentury scenario. A change in the nature of precipitation within storms will have strong local impacts through its modulation of surface runoff and will also affect storm predictability through modification of the upper-level potential vorticity field by convection (Oertel et al 2020).
After showing that the sub-sampling of models that we use is representative of the uncertainty range of a larger ensemble, we show how precipitation rates change in different sectors of the storms. We then investigate reasons behind the diversity of storm precipitation projections between models and finally examine changes in convective properties in the model with the highest level of warming.

Data
We use five pairs of convection permitting models (CPMs) at 2-3 km resolution, double nested in 12 km regional climate models (convection-parameterised) (RCMs) and general circulation models (GCMs) (table 1). The model evaluation papers are listed in table 1. CPMs were shown to better represent hourly precipitation characteristics. KNMI and HCLIMcom use the same CPM (but different RCM and GCM), while CNRM also uses a similar CPM. ETHZ uses a pseudo-global warming (PGW) approach: the present-day RCM is driven by ERA-interim reanalysis and the future RCM by ERA-interim plus a 3D Max Planck Institut-Earth System Model-Low Resolution (MPI-ESM-LR)-derived thermodynamical climate change signal which includes slow circulation changes (Brogli et al 2019, Hentgen et al 2019. By design, the number of extratropical cyclones entering the domain is the same between the present and future ETHZ runs. MOHC does not use an intermediate nest since it is driven by a 25 km GCM. We use the 25 km GCM as reference (and call it RCM for simplicity in the figures). KNMI downscales different members of their GCM ensemble for the presentday and future time slices to be able to get a reasonably unbiased response with respect to the ensemble mean response in a number of parameters (De Vries, personal communication).
We compare a ten-year historic time-period with a ten-year end-of-century time period. ETHZ and MOHC simulations do not share the exact same dates as they were run before a common protocol was agreed in the European Climate Prediction project (EUCP). Both the GCM and time period difference mean that ETHZ has the smallest warming signal and MOHC the strongest (see section 3.1). The future scenario is RCP8.5. Figure 1 shows the diversity of CPM domains covering Northern Europe. The reason for this choice was to keep the computing costs reasonable while covering most of Europe within the EUCP project. CPM data is regridded to the RCM grid for a fair comparison, except in section 3.4, where the CPM is analysed on its native grid.

Tracking algorithm
We track the storms using a widely used feature tracking package called TempestExtremes Ullrich 2017, Ullrich et al 2021). Candidates are identified as local minima in the sea level pressure (SLP). Candidates with SLP increasing by 150 Pa over a 5 • radius around them are selected (closed contour criteria). Individual candidates are then stitched together into tracks based on further criteria (e.g. minimum lifetime, maximum distance between each point, minimum total distance). The same parameters were used for all RCMs (supplementary material).

Selection of tracks
Tracks are selected within subregions centred on the CPM domain (boxes in figure 1). The regions are slightly different between CPMs, but always remain within the region of mean precipitation increase in all CPMs. We show that the processes at play are consistent between models and regions. Sensitivity tests to the exact region definition showed little impact on the results (not shown). The driving model is masked to match the CPM domain for a fair comparison.
Once the track is identified in the RCM, we find the associated minimum SLP in the CPM within a 3 • radius, commonly used in inter-tracking comparisons (Neu et al 2013). For all models, the CPM SLP minima stays within 2 • of the RCM one for at least 75% of the storm frames. The CNRM CPM is closest to its parent RCM and MOHC CPM is furthest away, potentially because of the large domain and GCM/CPM configuration differences .

Storm size and within-storm variables
Once the storm is selected, SLP, precipitation and wet bulb potential temperature (WBPT) are used within a 10 • radius of the SLP minima, which is large enough to encompass some of the trailing front and shallow convection within the dry intrusion (Pfahl and Sprenger 2016). We also removed all the data points within the Mediterranean region to focus on Central and Northern Europe (up to 63 N), where models agree on the sign of precipitation change. We used WBPT at 850 hPa (θ w ) to separate storm sectors as it incorporates both temperature and humidity fields. θ w is preferred over θ as its inclusion of temperature and humidity, which change in the same direction across fronts, allows a better separation of storm sectors (Hewson 1937). It is also a good indicator of frozen precipitation when it is below 273 K (Knox et al 2017). θ w at 850 hPa is directly output by the MOHC and CNRM models. For the other models, we calculated it using temperature and specific or relative humidity (RH). Following Knox et al (2017), we developed a simple but accurate formula for the 850 hPa θ w (supplementary material and figure S1).

Storm intensity
We define the storm intensity as the difference between the SLP minimum at the storm centre and the average SLP on a 2 • radius around it to avoid variations in the climatological mean, following Pfahl and Sprenger (2016). Figure 2 illustrates a few storm samples. We regrid the CPMs onto the RCM grid via conservative remapping, which means a 12 km grid for most models except MOHC, for which the GCM has a 25 km resolution. Following the simplest way of defining frontal zones provided in Thomas and Schultz (2019), we use the moderate baroclinic zone definition of Sanders (1999) to define fronts as zones where the norm of θ w gradients is larger than 4 K/110 km on the 25 km MOHC grid. This value is too low for the 12 km RCM grids (too many non-frontal gradients included) so we use 5 K/110 km for them. Sensitivity analysis on the thresholds used to define the fronts do not change the main results as long as the threshold is not too low, which would select small scale frontal structures outside the main ones. We then take the median of θ w values in this zone to separate a cold sector and a warm sector. As illustrated in figure 2, precipitation in the warm sector is associated with the warm conveyor belt ascent, the cold front and part of the warm front. In this definition of the cold sector, precipitation is mostly coming from shallow convection in the dry intrusion and precipitation ahead of the warm front, in the cloud head. Finally, we also define a central sector (within a 2 • radius of the storm centre), where convection is also likely to happen. These definitions are computationally simple and require few variables to provide a first order understanding of which parts of the storms contribute most to precipitation increase. Figure 1 shows mean precipitation increases by 15%-40% over Northern Europe at the end of the century. MOHC model shows the largest changes, and the CPM amplifies the change by a further 10%-20%. In contrast, the other CPMs have mean changes closer to their parent RCM. Figure S2 shows that this ensemble is representative of the range of precipitation changes in traditional convection-parameterised ensembles over the largest box shown in figure 1.   Figure S3 further highlights that mean precipitation increase comes from the top half of the precipitation intensity distribution. Models agree on this and there is little land sea contrast in this change. However, the magnitude is different between models, from a 30% increase in the top half of the distribution in most models to a doubling in MOHC models. The further increase in the MOHC CPM also comes from the top half of the distribution. With the same model on a smaller domain,  showed that about half of the larger increase in precipitation was linked with better ability for shower advection over land in the CPM compared to the RCM. We further investigate this from the perspective of precipitation within storms to understand where the remaining differences come from, as well as whether similar amplification happens in other models. From figure S3, ETHZ CPM is very close to its RCM and CNRM, KNMI and HCLIMcom CPM models have a shifted distribution towards higher intensities, which translates into larger changes in the tail of the distribution.

Precipitation increases dominated by the warm sector
Interestingly, the increases in the top half of the distribution seen in the precipitation climatology (figure S3) are also found for in-storm precipitation (figure 3). This emphasizes that the dominant mechanism for increased precipitation in winter is more precipitation per storm, consistent with . For the MOHC models, the larger increases in the CPM (plain line) compared to the RCM (dashed line) shown in the climatology (figure S3) are also found inside storms (figure 3), indicating that the processes generating RCM/CPM differences happen within storms.
By breaking down the precipitation distribution by sectors (defined in section 2.2.5), we show that about two thirds of precipitation comes from the warm sector of storms in present-day winter storms, and most of the intense precipitation happens there. Intense precipitation also happens within the storm centre, but it is a smaller contributor. Frontal zones as defined here are a small contributor, mostly because of their small area.
Looking at future changes, models agree that the warm sector is the main contributor to future changes for the top half of the precipitation distribution. In all models, the increased precipitation contribution from the cold sector peaks at lower precipitation rates (1.5-2 mm h −1 ) compared to the warm sector. Compared to other models, the MOHC models show a larger contribution to precipitation change from the cold sector, likely linked to increases in the size of the cold sector of storms in these models, as discussed later in section 3.4.
There is also moderate agreement among models that the largest difference between CPMs and RCMs in terms of future changes in precipitation is found for the heaviest precipitation in the warm sector of storms. CNRM, KNMI, MOHC and HCLI-Mcom CPMs all show significant larger increases in the warm sector for rates above 4 mm h −1 . Indeed, at these high rates, the dashed red line representing the RCM is often below the red-shaded range of CPM changes in figure 3. Except in the MOHC model, these larger CPM increases at high rates have a small impact on mean increase.
Larger increases in precipitation in the MOHC CPM compared to the RCM come equally from the cold and warm sectors. The larger increase in cold sector precipitation in the CPM is consistent with the findings of Kendon et al (2020), who diagnosed shallow convection and showed it propagates into land in the CPM, and not the RCM. They quantified that this explained 60% of the larger increase in the CPM over land. Figure 3 shows that the rest of the CPM rainfall increase comes from the warm sector. We will explore this in section 3.4.

Thermodynamical changes dominate the precipitation increase
We now investigate the sources of the spread in projections of mean hourly precipitation per storm between RCMs and the difference in projected changes for moderate to heavy precipitation in CPMs compared to RCMs. Because the warm sector is a dominant contributor to mean precipitation and precipitation changes, we use median θ w in the warm sector to scale the spatial mean and 99th percentile of hourly precipitation in storms in figures 4 and S4.
The relationship between median θ w in the warm sector and hourly mean precipitation is robust, with Pearson correlation coefficient (R) above 0.5 for most models in present-day winter and FW (figure 4). Note that this relationship is less robust if using the whole storm median θ w , consistent with the warm sector being the largest contributor to in-storm total precipitation and changes (figure 3). These high correlations and the fact that the present-day and future slopes are similar suggest that the firstorder driver of increased precipitation per storm is the increase in temperature in the warm sector. The slope ranges between 8% K −1 and 14.2% K −1 in present-day winters and 9.7%-13.6% K −1 in FWs, depending on models and regions. This is above the Clausius-Clapeyron 6%-7% rate (thin black lines in figure 4). This is potentially explained by the fact that storm precipitation also depends on storm dynamical intensity (R between 0.2 and 0.4 (not shown)), in line with Pfahl and Sprenger (2016), and storm intensity is lower at lower θ w in the warm sector (R between 0.1 and 0.2). To illustrate mean precipitation dependency on dynamical intensity, we added dots to highlight the strongest storms (minimum SLP depression <−5 hPa) in intensification phase (decreasing minimum SLP trend, Catto and Raveh-Rubin (2019)). They are all above the fitted line, confirming that for a given θ w range, intense storms reach larger precipitation rates.
The models with an increasing proportion of these dynamically strong storms in the future (MOHC, HCLIMcom and CNRM, table 2) tend to have a steeper mean precipitation increase per degree of θ w in the future (although other factors may play a role in the similar present and future trends in MOHC). In the KNMI model, storms become less dynamically intense (table 2 and figure S5(a)), and the slope is less steep in the future. This illustrates model disagreement in how mean storm dynamical intensity will change , and consequently how it will modulate thermodynamical precipitation increase. Figure 4 also shows the fitted line for present-day autumn (PDA) storms in grey, to explore the hypothesis that the relationship between precipitation and . Joint density of mean hourly precipitation per storm and warm sector wet bulb potential temperature (median) in present storms (blue) and future (red). Individual variable density shown at the top (WBPT) and right (mean precipitation). Each panel shows a different model pair. Plain line shows best fit for the CPM, dotted line for the RCM. Grey line is for present-day autumn storms (underlying density not shown). Slope in % K −1 and Pearson correlation coefficient are given in insets. Dots represent intense storms; crosses are storms with low relative humidity in their warm sector. Thin grey lines represent Clausius-Clapeyron (CC) 7% K −1 scaling and thin red lines show 2×CC scaling. θ w in FW storms may be similar to PDA storms. However, the correlation coefficient and slope for PDA storms are much lower for all models. Their intensity is not the main explanation (table 2), although figure S6(a) suggests the median PDA storm is less intense. The largest differences between PDA and FW storms is the median RH in the warm sector which is 2%-6% higher in FW storms than in PDA storms ( figure S6(b)). To highlight this, we added crosses for storms with RH below 84% in figure 4. Most of these crosses are below the fitted line in present-day winter and FW: for a given θ w , storms with lower RH have less precipitation. The proportion of storms with low RH changes from 0% to 15.5% in present winter and FW to 4%-20% in PDA (table 2). PDA storms are therefore limited by lower RH at higher temperature. In contrast, RH in the warm sector of winter storms remains, in future, significantly higher than in PDA storm ( figure S6(b)). This explains why FW storms could become as or more rainy than PDA storms while remaining 1 to 2 K cooler (figures S6(c) and (d)). Figure S4 shows that the 99th percentile of precipitation in PDA storms (ranging from 1 to 9 mm h −1 ) does reach a similar slope and correlation coefficient as FW storms, suggesting that lower RH in PDA is reducing mean precipitation by reducing lower precipitation rates.
We now investigate the difference in projected changes for moderate to heavy precipitation in CPMs compared to RCMs (for all CPMs apart from ETHZ, figure 3). Figure S4 shows that the slopes between the 99th percentile of precipitation and median θ w is similar between CPMs and RCMs (when R > 0.4), but CPM values are shifted higher. This shift is especially large in PDA storms and FW storms, suggesting that fine-scale processes at larger θ w values contribute to heavier precipitation in CPMs. . Frequency (right axis) of low precipitation rates (0.1-1 mm h −1 ) scaled by 1/15, moderate rates (1-5 mm h −1 ) scaled by 1/10, intense rates (5-10 mm h −1 ) and heavy rates (>10 mm h −1 ), CAPE (>250 J kg) and CIN (<−100 J kg −1 ) scaled by 1/10, total column water (TCW >20 mm) scaled by 1/30, binned by θw values and normalised by the number of points in all storms on the native grid of the MOHC CPM. Grey vertical line is median θw, black vertical line is the freezing point.
The MOHC models shows a peculiar behaviour in two ways: the CPM shows more intense 99th values only in the future and the cold sector contributes significantly to future changes (figure 3). We will investigate these in the next section.

Understanding MOHC larger increases in storm precipitation
In figure 5, individual grid-points in storms are pooled and binned by θ w values. Intense precipitation (>5 mm h −1 ) in storms occurs at θ w above 280 K and is accompanied by moderate convective available potential energy (CAPE) (>250 J kg −1 ). In present-day winter storms, these are infrequent, but they become much more frequent in FW storms. When comparing FW storms with PDA storms, the range of θ w spanned by all storms is the same: 272-292 K. The proportion of grid-points with intense precipitation is similar between FW storms and PDA storms. The frequency of moderate CAPE, convective inhibition (CIN) and high total column water increase in FW storms, favouring more intense convection (Rasmussen et al 2017) in the warm sector of storms. Nevertheless, it remains lower than PDA storms. As shown in figure S5(b) and discussed above, RH in the warm sector remains high in FW storms, higher than PDA storms (figure S6b). Because CIN is closely related to low-level RH (Chen et al 2020), higher winter RH may explain why CIN values are not as large as PDA storms. Subsequently, CAPE may be released before it can build up to higher values.
In other models, figure S7 shows that θ w change is less large than in the MOHC model: FW storms in those models are only half-way between presentday winter and autumn ones, and intense precipitation increases in the warm sector are significant but less large than in the MOHC model.
Regarding the larger increase in cold sector precipitation in MOHC models compared to other models, figure 5 shows a skewed θ w distribution towards lower temperatures compared to the present-day distribution. Figure S5(e) confirms that the cold sector size increases in the future in the MOHC model. A possible explanation is the change in storm types in this model, with more frequent occurrences of Shapiro-Keyser storms (Manning et al 2022). The CPM-RCM difference in rain frequency over land due to the lack of shower advection over land in the RCM shown by Kendon et al (2020), already known in present-day weather situations, is enhanced in the future because of the cold-sector size increase in the MOHC model. This process, which can be detected in a differential change in wet-hour frequency between land and sea, with further increases in the CPM over land, is only at play in the MOHC model ( figure S8).
Finally, we note that the frequency of conditions for frozen precipitation (θ w < 273 K) decreases by at least two thirds in all models (figures 5 and S7).

Conclusions and discussion
We investigated the changes in hourly precipitation in FW storms (extratropical cyclones) in a multi-model regional ensemble at km-scale resolution together with its driving 12-25 km ensemble. The main difference between the two sets of models is that km-scale models allow an explicit representation of convective precipitation (CPMs).
We showed that our small ensemble of five model pairs give a representative sample of end-of-century FW precipitation projections for Northern Europe as provided by more traditional models (CMIP5, CMIP6, CORDEX) in a strong warming scenario (RCP8.5). Changes in storm numbers depend on the global driving model and on inter-decadal variability, and therefore are not investigated here: we examine hourly precipitation within 10 • of low-pressure centres.
Our main results are that mean precipitation will increase in FW storms, due to increased moderate and intense precipitation. This increase mostly comes from the warm sector of storms. Differences between models are linked with differences in their warming levels in the warm sector of storms and differences in changes in dynamical strength of storms. The latter is less certain, with little model agreement , also potentially because dynamical strength is more prone to inter-decadal variability. Our small ensemble design is too limited to address this.
Because WBPT ranges in FW storms may reach similar values to PDA ones, we compare both sets of storms. Hourly mean precipitation in FW storms reaches larger values than PDA storms because FW storms have higher RH in their warm sector, and more light precipitation. Intense (>5 mm h −1 ) and heavy (>10 mm h −1 ) precipitation within winter storms increase in frequency, and get closer to (or even up to for one model) PDA storms. The frequency of favourable conditions for frozen precipitation also gets closer to PDA storms, with a decrease by at least two thirds in frequency.
The warm sector increase in precipitation is likely linked with more convection, as shown by CAPE and CIN increases in the MOHC model, which is coherent with other CPMs also showing a greater increase in intense precipitation rates (>4 mm h −1 ) than RCMs in this sector. A particular feature of the MOHC CPM is a larger increase in precipitation in the cold sector, likely linked with a deficiency in the RCM to advect showers over land . This may be because this model shows the largest increase in cold sector size in future storms or it may be a particular feature of the convection scheme used in the MOHC RCM.
This study shows that the magnitude of the larger increase in mean precipitation in the MOHC CPM is not found in other RCM/CPM pairs. We therefore recommend consideration of multi-model ensembles when possible. We showed that CPMs are useful tools to better understand changes in intense rain rates and fine-scale processes in winter storms. Nevertheless, levels of warming within the warm sector of storms and dynamical strength of storms, well captured by RCMS, are the largest factors explaining mean hourly precipitation changes in storms.