Assessment of simulations of a polar low with the Canadian Regional Climate Model

the other simulations is negative from 1600 UTC on (not shown). Overall, the RMSE of 24d12h and 24d18h increases from 1100 UTC on, and the latter has smaller RMSE than the rest of the simulations most of the time (Fig 11B). The time series of the Spearman correlation coefficient varies widely between simulations, with correlation coefficients ranging from -0.19 to 0.85, and even the same simulation shows a wide range of correlation coefficients (not shown). The aggregate ME of ERA5 (1.9 m s-1) is almost twice as that of the simulations that have captured the PL, but its RMSE (3.9 m s-1) is lower and its correlation coefficient is higher (0.81) (Table 7). However, the difference in the RMSE and the correlation coefficient between ERA5 and 24d18h is very small. Like the simulations that have captured the PL, the ME of Fig 11. Time series of the (a) RMSE-VWD of the simulated and ERA5 10-m wind, and RMSE of the simulated and ERA5 (b) wind gusts and (c) 1-h accumulated precipitation. The datasets used as reference to compute the RMSE-WVD and RMSE are the observations at surface stations. https://doi.org/10.1371/journal.pone.0292250.g011 PLOS ONE Assessment of simulations of a polar low with the canadian regional climate model PLOS ONE | https://doi.org/10.1371/journal.pone.0292250 October 5, 2023 19 / 28

ERA5 remains positive most of the time (not shown). The time series of the RMSE of ERA5 follows closely that of 24d18h (Fig 11B). The correlation coefficient of ERA5 shows less vari- ability than that of the simulations, remaining between 0.58 and 0.84 (not shown). 3.3.7 1-h accumulated precipitation. The aggregate statistics indicate that 24d18h has the most skill at representing precipitation (Table 8). The ME of the simulations is positive, with 23d12h and 24d18h having the lowest mean bias (0.1 mm). The latter also has the lowest RMSE (1.3 mm) and the highest correlation coefficient (0.53), indicating modest correlation with the observations. The other simulations have virtually no correlation with the observations, except for 24d12h, which shows weak correlation with them. During most of the time, the ME of all the simulations ranges from -1 to 1 mm (not shown). The highest values of RMSE are found at 16:00 and 17:00 UTC, just after the observed SLP minimum is attained (Fig 11C). There is a large spread of the correlation coefficients of the simulations (not shown). In contrast with the simulations, ERA5 has a negative ME (-0.1 mm) (Table 8). The RMSE of ERA5 (1.2 mm) is lower than that of all the simulations, although it is only slightly lower than that of 24d18h. ERA5 shows modest correlation with the observations (0.62). Most of the time, ERA5 shows a somewhat smaller RMSE compared to the simulations (Fig 11C), and its correlation coefficients are higher than those of most of the simulations (not shown). The

ERA5 1-h accumulated precipitation never exceeds 2.5 mm, which is likely due to its relatively low resolution. In contrast, the maximum simulated precipitation is 9.5 mm, corresponding to 24d12h, and the maximum observed precipitation is 20.6 mm. This agrees with the finding of Hu and Franzke [50] that ERA5 underestimates the daily precipitation extremes observed by weather stations in Germany. Table 7. Aggregate statistics computed to verify the simulated and ERA5 wind gusts against the observations from surface stations. ME [m s-1] RMSE [m s-1] r 23d00h -0.8 6.2 0.51 23d06h -1 7.5 0.37 23d12h 0.1 6.3 0.38 23d18h -1.2 6.1 0.53 24d00h -0.1 5.1 0.65 24d06h 0 5.4 0.52 24d12h 1 4.9 0.74 24d18h 1 4 0.8 ERA5 1.9 3.9 0.81 https://doi.org/10.1371/journal.pone.0292250.t007 Table 8. Aggregate statistics computed to verify the simulated and ERA5 1-h accumulated precipitation against the observations from surface stations. ME [mm] RMSE [mm] r 23d00h 0.2 1.6 0.22 23d06h 0.3 1.8 0.22 23d12h 0.1 1.6 0.35 23d18h 0.2 1.5 0.34 24d00h 0.5 1.8 0.19 24d06h 0.5 1.8 0.23 24d12h 0.2 1.6 0.42 24d18h 0.1 1.3 0.53 ERA5 -0.1 1.2 0.62 https://doi.org/10.1371/journal.pone.0292250.t008 PLOS ONE Assessment of simulations of a polar low with the canadian regional climate model PLOS ONE | https://doi.org/10.1371/journal.pone.0292250 October 5, 2023 20 / 28

3.4 Final discussion To understand why only 24d12h and 24d18h correctly capture the development of the PL, it is necessary to analyse the simulated atmospheric fields from a few hours before its formation until its genesis time. It is assumed that, during this period, the synoptic conditions are favour- able for PL formation in 24d12h and 24d18h, but not in the other simulations. Fig 12 shows the SLP, the geopotential height at 500 hPa and the 1000-500 hPa thickness on 25 March at 0000 UTC. There is a 500-hPa through with a northeast-southwest orientation in all simulations. Although its shape is slightly different in the simulations, the through is in the Fig 12. Simulated and ERA5 fields showing the PL on 25 March 2019 at 0000 UTC. The colourmap represents the 1000-500 hPa thickness (dam), the black isobars represent the SLP (hPa, contours every 2 hPa) and the red dashed lines represent the geopotential height at 500 hPa (dam, contours every 2 dam). The black outlining represents the coastline, and the white dashed line represents the sea ice edge, which is defined as the 0.15 contour of the sea ice concentration. ERA5 fields have been interpolated to the grid of the simulation using bicubic interpolation for the SLP, 1000-500 hPa thickness, and geopotential height, and bilinear interpolation for the sea ice concentration. The sea ice edge in ERA5 corresponds to the 25 March 2019 at 1200 UTC. The dataset used to plot the geographic contours has been obtained from the GSHHG [33] under a CC BY license, with permission from Dr. Paul Wessel.

https://doi.org/10.1371/journal.pone.0292250.g012 PLOS ONE Assessment of simulations of a polar low with the canadian regional climate model PLOS ONE | https://doi.org/10.1371/journal.pone.0292250 October 5, 2023 21 / 28

same region and shows the same depth. The incipient PL in 24d12h and 24d18h with a well defined SLP minimum is located on the right side of this mid-tropospheric through, whereas in the other simulations only a weak (low-level) through within the SLP field in this area is observed. The 1000-500 hPa thickness field shows that the cold air tongue associated with the MCAO has a northwest-southeast orientation in all simulations. Since the atmospheric conditions aloft are similar in all simulations during the genesis time of the PL, they cannot explain why it has only been correctly captured by 24d12h and 24d18h (with respect to both observations and reanalysis data). Therefore, the difference between the simulations must be in the lower atmosphere. Fig 13 shows the geopotential height, tempera- ture and horizontal wind at 900 hPa on 24 March at 1900 UTC in the region where the low- level through preceding the genesis of the PL started to form (i.e. 5 hours before the PL shown in Fig 12). All simulations show a strong northwest-southeast temperature gradient to the west of Jan Mayen, close to the sea ice edge. In contrast with the other simulations, the northerly cold air advection and winds in 24d12h and 24d18h are more intense and more widely extended; therefore, the cold airmass moves further south in these two simulations. At the same time, on the east side of this cold air, a warm front pushes northward in these two simula- tions, with a more widely defined and stronger warm air advection in this area than the other

simulations. These results indicate that, in the presence of a baroclinic environment, only the low-level atmospheric conditions with a well defined cold/warm air temperature advection present in 24d12h and 24d18h lead to baroclinic instability, which is involved in the genesis of the PL. It is also clear in Fig 13 that the low-level pressure deepens or vorticity (wind rotation) starts to develop in these two simulations, i.e. small scale features corresponding to the PL development phase. Since 24d12h and 24d18h are the latest initialised simulations, their atmospheric fields dur- ing the hours preceding the PL formation are more similar to those of ERA5, the driving data, compared to those of the other simulations. Thus, the fact that the other simulations except for 23d12h do not represent the PL is due to forecast error growth and missing small-scale features during the initial stage of the PL formation. Nevertheless, the question remains about why 23d12h represents a PL at a later moment in time. In 23d12h, a strong low-level baroclinic zone forms a few hours before the PL forms in this simulation (Fig 14), and the PL shows baro- clinic development. This PL makes landfall shortly after being formed, thus dissipating before it can reach a larger size. Fig 14 reveals also clearly that stronger winds over both cold (west) and warm (east) near the developed PL induce small scale conditions (i.e., temperature advec- tions) favourable to strengthen low-level baroclinity and cyclogenesis in the latest initialised simulations, not present in the other simulations.

In conclusion, on the 24–25 March, the simulated environmental conditions are favourable for PL development, with a low-level baroclinic environment and an upper-level through, but the different evolution of the low-level circulation and small-scale features explains why a few simulations capture the PL whereas the others do not. 4. Conclusion Compared to low-resolution models, convection-permitting models provide a better represen- tation of physical processes [20]. Therefore, they are a powerful tool to study mesoscale phe- nomena, including PLs. This study has focused on a PL that made landfall in Norway in 2019, and the aim was to analyse the impact of the initial conditions on the simulation of the PL, and to analyse the skill of the CRCM6/GEM4 at reproducing it. The main limitations of this study is that the available conventional observations mostly cover the mature and dissipation stages of the PL, and that they are irregularly distributed in space. PLOS ONE Assessment of simulations of a polar low with the canadian regional climate model PLOS ONE | https://doi.org/10.1371/journal.pone.0292250 October 5, 2023 22 / 28

Fig 13. Simulated and ERA5 fields on 24 March 2019 at 1900 UTC over the region around Jan Mayen. The colourmap represents the temperature at 900 hPa (˚C), the black isolines represent the geopotential height at 900 hPa (dam, contours every 1 dam), and the arrows represent the horizontal wind at 900 hPa. The white dashed line represents the sea ice edge, which is defined as the 0.15 contour of the sea ice concentration. ERA5 fields have been interpolated to the grid of the simulation using bicubic interpolation for the temperature and geopotential height, and bilinear interpolation for the horizontal wind and sea ice concentration. The sea ice edge in ERA5 corresponds to the 24 March 2019 at 1200 UTC. The dataset used to plot the geographic contours has been obtained from the GSHHG [33] under a CC BY license, with permission from Dr. Paul Wessel. https://doi.org/10.1371/journal.pone.0292250.g013 PLOS ONE Assessment of simulations of a polar low with the canadian regional climate model PLOS ONE | https://doi.org/10.1371/journal.pone.0292250 October 5, 2023 23 / 28

One of the main findings of this study is that the ability of the CRCM6/GEM4 to capture the PL strongly depends on the initial conditions. In effect, only 23d12h and the latest initia- lised simulations 24d12h and 24d18h capture the development of the PL. The latter two repre- sent well the lifetime, track and size of the observed PL. In contrast, the PL represented in 23d12h is much smaller than the observed PL, and its lifetime is less than half the lifetime of the observed PL. Further, the verification of the simulations against conventional observations Fig 14. Same as Fig 13, but for 25 March 2019 at 0900 UTC and over the region to the west of the Norwegian coast. https://doi.org/10.1371/journal.pone.0292250.g014 PLOS ONE Assessment of simulations of a polar low with the canadian regional climate model PLOS ONE | https://doi.org/10.1371/journal.pone.0292250 October 5, 2023 24 / 28

has shown that 24d18h has more skill than 24d12h at reproducing most of the near-surface variables analysed. These results indicate that the initialisation time has an important impact on whether the model captures or not this PL, and on how well it is represented. The two latest initialized simulations show northerly cold air advection and winds that are more intense than in the other simulations, leading to baroclinic instability and, subsequently, to the genesis of the PL. Nevertheless, since the environmental conditions– strong low-level temperature gradi- ent and an upper-level through –on the 24 and 25 March are favourable for PL development, a PL can form at a later time if the low-level conditions are favourable for baroclinic instability to grow, which is what happens in 23d12h. In view of these results, it is suggested that future studies should investigate the potential to improve PL forecasts by using spectral nudging to maintain the low-level atmospheric fields and small scale features close to the driving data. Sensitivity tests should be conducted with different spectral nudging parameters and nudging horizontal wind, temperature, or both. Another key finding is that the processes involved in the development of the PL need to be improved in the model in order to decrease the mean bias of the simulations that have cap- tured it. Although all the statistics clearly show the better performance of 24d12h and 24d18h at reproducing SLP compared to the other simulations, it is notable that, for the other vari-

ables, these two simulations show similar or higher aggregate absolute mean bias. In particular, the parameterization of the surface heat fluxes in the CRCM6/GEM4 needs to be improved. In effect, the fact that 24d12h and 24d18h represent a PL deeper than the observed one, and show higher temperature mean bias compared to the other simulations and ERA5, seems to indicate that the ocean surface fluxes may be too strong. Finally, the results have shown that ERA5 has more skill than the simulations, including those that have captured the PL, at reproducing the observed PL during its mature and dissi- pation stages. Table 9 shows the added value of the CRCM6/GEM4 compared to ERA5 when considering the best simulation (24d18h). For all the near-surface variables analysed here, the model does not provide added value in terms of accuracy (based on the RMSE val- ues shown in Tables 2–8). It is surprising that the CRMC6/GEM4, a high-resolution model, does not provide added value compared to ERA5, the coarser reanalysis that drives it. There are two main reasons that could explain the fact that ERA5 has better skill than CRMC6/ GEM4. First, conventional observations are assimilated into ERA5. Second, the verification of high-resolution simulations using standard statistics has some limitations. For instance, when verifying the simulation of a PL using dropsonde observations, Stoll et al. [17] found that a fuzzy verification method showed that the regional model AROME-Arctic had higher skill at capturing extreme values at small scales than the global model ECMWF HRES,

whereas standard verification statistics were similar for both models. Finally, note that for this work we used GEM4, but a new version with improved physics parameterizations, GEM5, was recently released [51]. Therefore, an interesting course of research would be to analyse if this new version of GEM provides added value compared to ERA5 and to the cur- rent CRCM6/GEM4 simulations. Table 9. Added value of the CRCM6/GEM4 (simulation 24d18h) compared to ERA5 for the following variables: Sea level pressure (SLP), 2-m temperature (T2m), 2-m dew point temperature (Td,2m), 10-m wind (V10m), wind gusts (WG) and 1-h accumulated precipitation (PR). The added value has been computed using the aggregate RMSE (RMSE-WVD for the 10-m wind), based on values presented in Tables 2–8. The added value computation is based on the study of Di Luca et al. [52; Equa- tion 1)]. SLP T2m Td,2m RH V10m WG PR -0.8 hPa -0.9˚C -0.9˚C -2% -1.2 m s-1 -0.1 m s-1 -0.3 mm https://doi.org/10.1371/journal.pone.0292250.t009 PLOS ONE Assessment of simulations of a polar low with the canadian regional climate model PLOS ONE | https://doi.org/10.1371/journal.pone.0292250 October 5, 2023 25 / 28

Acknowledgments Computations were made on the supercomputer Beluga, managed by Calcul Que´bec and the Digital Research Alliance of Canada. The authors are deeply indebted to Katja Winger for her essential support in the use of the CRCM6/GEM4, as well as for downloading and preparing available ERA5 reanalyses. The authors would also like to thank Franc¸ois Roberge for his valu- able help in the use of the r.diag toolkit and the CRCM6/GEM4. Author Contributions Conceptualization: Marta Moreno-Iba´ñez, Rene´ Laprise. Formal analysis: Marta Moreno-Iba´ñez, Rene´ Laprise, Philippe Gachon. Funding acquisition: Rene´ Laprise. Investigation: Marta Moreno-Iba´ñez. Methodology: Marta Moreno-Iba´ñez, Rene´ Laprise. Project administration: Rene´ Laprise. Resources: Rene´ Laprise. Software: Marta Moreno-Iba´ñez. Supervision: Rene´ Laprise, Philippe Gachon. Validation: Rene´ Laprise, Philippe Gachon. Visualization: Marta Moreno-Iba´ñez. Writing – original draft: Marta Moreno-Iba´ñez. Writing – review & editing: Marta Moreno-Iba´ñez, Rene´ Laprise, Philippe Gachon. References 1. Walsh JE, Ballinger TJ, Euskirchen ES, Hanna E, Mård J, Overland JE, et al. Extreme weather and cli- mate events in northern areas: A review. Earth-Science Reviews. 2020; 209: 103324. https://doi.org/ 10.1016/j.earscirev.2020.103324 2. Turner J, Rasmussen EA, Carleton AM. Introduction. In: Rasmussen EA, Turner J, editors. Polar Lows: Mesoscale Weather Systems in the Polar Regions. Cambridge: Cambridge University Press; 2003. p. 1–51.

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