The impact of horizontal resolution on the representation of atmospheric circulation types in Western Europe using the MPI‐ESM model

In this study, the added value in using the sea level pressure field from the coupled higher‐resolution version of the Max Planck Institute Earth System Model (MPI‐ESM‐HR), compared to the lower‐resolution version (MPI‐ESM‐LR) for circulation typing, within the regional context of Western Europe was examined. The results show that the MPI‐ESM‐HR and the MPI‐ESM‐LR simulations can produce the classified circulation types (CTs) and their long‐term statistical characteristics as obtained from the ERA5 reanalysis. Overall, there are improvements in the composite maps, probability of occurrence and annual cycle of the simulated CTs in the MPI‐ESM‐HR compared to the MPI‐ESM‐LR. The model bias in simulating the structure of anticyclonic circulations over the Western European landmass was reduced by 14% under MPI‐ESM‐HR. Furthermore, under the shared socio‐economic pathways (SSP2‐4.5 and SSP5‐8.5) future emission scenarios, the historical CTs in the region of assessment were classified, suggesting that in Western Europe, the same historical CTs are present under future climate change scenarios. However, the frequency distribution and geographical structure of some of the CTs in Western Europe are projected to change by the MPI‐ESM model, especially under the higher future emission scenario.


| INTRODUCTION
The Max-Plank Institute Earth System Model (MPI-ESM) uses the MPI-ESM1.2version as a baseline for the Coupled Model Intercomparison Project Phase 6 (CMIP6).The MPI-ESM1.2 climate simulations include a coupled higher horizontal resolution version (MPI-ESM-HR), henceforth referred to as MPIH, and a lower horizontal resolution version (MPI-ESM-LR), henceforth referred to as MPIL.A study by Müller et al. (2018) evaluated the MPIH relative to the MPIL; the authors reported that as a result of the increase in the model horizontal resolution in MPIH, biases in atmospheric processes such as upperlevel zonal wind, atmospheric jet stream position in the northern extratropics, sea surface temperature and blocking frequency over the European region were modestly reduced.According to Müller et al. (2018), MPIH showed a slightly reduced bias in sea level pressure (SLP) over the North Atlantic and a consistently reduced bias over the North Pacific and southern Atlantic compared to MPIL, indicating an improved representation of atmospheric circulations.The study also revealed that the global SLP error decreased in MPIH relative to MPIL.
The impacts of increasing the horizontal resolution of coupled climate models have been widely studied (Polyakov et al., 2009;Shaffrey et al., 2009;Zappa et al., 2013).According to Scaife et al. (2014), the simulation of storm tracks and atmospheric blocking was improved in higher-resolution models.A study by Dawson and Palmer (2015) found that the simulation of weather regimes was improved over the North Atlantic in higher-resolution coupled models.Additionally, Berckmans et al. (2013) reported that by increasing atmospheric resolution, the simulated frequency of European blocking frequency was improved.de Souza et al. (2017) reported that increasing the resolution in the HadGEM1 model enhanced the representation of the simulated circulation patterns over South America and the adjacent oceans.Over the Tropics, Boyle and Klein (2010) found that the simulated diurnally forced circulations over the Maritime continent improved with increasing model horizontal resolution, resulting in better representation of the land-sea breeze.According to Hack et al. (2006) a more realistic representation of large-scale dynamical circulation was attained in the higher horizontal resolution version of the Community Atmosphere Model version 3 simulations.Over the Southern Hemisphere, Roeckner et al. (1992) found that increasing model horizontal resolution can generally lead to improved simulated timemean circulation.Also, using the Chinese Academy of Sciences Flexible Global Ocean-Atmosphere-Land System climate model, Li et al. (2021) investigated the effect of horizontal resolution on the simulation of tropical cyclones and found that the characteristics of simulated tropical cyclones such as the wind-pressure relationship improved in the simulation using the high-resolution model.Thus, the atmospheric circulation biases in GCMs can be reduced by increasing the resolution of the models.The model improvements in higher-resolution models can be regionally dependent and can also depend on the variable analysed (Jungclaus et al., 2013).
Using the MPI-ESM simulations, this study examines the representation of circulation patterns in the MPIH and MPIL within the regional context of Western Europe.Müller et al. (2018) compared SLP from MPIH and MPIL and found some improvements under MPIH, such as the improved representation of the Aleutian low and reduced SLP bias in the southern Atlantic.However, the authors noted that both MPIH and MPIL models exhibited similar patterns of bias in SLP, characterized by alternating bands of bias over the North Atlantic and Eurasian continent.The main goal of this study is to evaluate the differences in the representation of structure and annual cycle of circulation types (CTs) for Western Europe using SLP fields from MPIH and MPIL.To the author's knowledge and for Western Europe, no study has addressed if there are differences in the structure and annual cycle of CTs arising from the choice of climate models with different horizontal resolutions.Further, the persistence of the historical CTs in Western Europe under future climate change will be examined.Improvements in climate modelling that capture the intricate interplay of the climate system and its interactions are expected to lead to significant advances in climate projections and

| DATA AND METHODOLOGY
SLP fields are obtained from the higher-resolution (100 km) and lower-resolution (200 km) versions of the MPI-ESM1.2GCM (using the "r1i1p1f1" realization) that is featured in the CMIP6 (Eyring et al., 2016).The model configurations of the MPI-ESM1.2GCM are explained in detail by Mauritsen et al. (2019) and Müller et al. (2018).For the future emission scenarios, simulated SLP datasets are obtained under the shared socioeconomic pathways (SSP) SSP2-4.5 and SSP5-8.5, from 2040 to 2100.The reference CTs utilized for evaluating the simulated CTs were classified using ERA5 reanalysis SLP data (Hersbach et al., 2020), which has an original resolution of 0.25 longitude and latitude.All data sets for the historical climate (i.e., both ERA5 reanalysis and MPI-ESM simulations) are obtained at daily temporal resolution from 1979 to 2014.ERA5 SLP data is originally obtained at hourly resolution, hence daily averages were computed.Before the analysis, to enable comparison between the datasets, the data sets from the GCMs (in a nonregular grid) and ERA5 are interpolated to a common regular 1.0 longitude and latitude using bilinear interpolation (Müller et al., 2018).Thus, the reference CTs are the interpolated ERA5 fields (e.g., Müller et al., 2018).The spatial extent used for the circulation typing is 20 W to 19 E, and 25 N to 60 N. Since moisture transport and atmospheric circulation in the North Atlantic and the Mediterranean impact rainfall formation in Western Europe (Davis et al., 1997;Skliris et al., 2018), the selected region captures part of the Mediterranean, the North Atlantic Ocean, the Baltic Sea and the North Sea.The classification of the CTs is applied independently to the daily SLP fields from ERA5, MPIH and MPIL.
The classification method used in this work is the same as applied in Ibebuchi (2022), within the regional context of Western Europe-i.e., the fuzzy obliquely rotated T-mode (the columns/variables are the time series and the rows/observations are the grid points) principal component analysis (PCA)-hence the reference CTs obtained from ERA5 are similar.The SLP dataset is standardized, for the individual days, before the analysis to give equal weight to all days; the similarity matrix relating the raw SLP field between the time series in the analysis period is the correlation matrix.The standardized T-mode data matrix is diagonalized using singular value decomposition (Paige & Saunders, 1981).Hence the eigenvalues, eigenvectors, and PC scores are obtained.The eigenvectors are time series while the PC scores are the corresponding spatial patterns.The eigenvectors are multiplied by the square root of their corresponding eigenvalues to obtain the PC loadings.The PC loadings are correlations between the PC scores and the standardized SLP field.Oblique rotation, with the Promax algorithm, is applied to the (retained) PCs.The aim of rotating the PC loadings is generally to enhance their physical interpretability (Ibebuchi & Richman, 2023).This is achieved by maximizing the number of near zero loadings.As noted in Ibebuchi and Richman (2023) only those rotated PC loadings that match the correlation vectors they are indexed to in the good range (i.e., with a congruence match; see Equation (A4) in Appendix B of at least 0.92) should be retained.So, the loadings were rotated iteratively keeping 2, 3… components.In each case, all the rotated loadings are respectively matched to the correlation vectors they are indexed to, i.e., the correlation vector that indexes the largest loading magnitude for the PC (Ibebuchi & Richman, 2023).The optimal number of components to keep is the solution where the maximum number of retained components all match the correlation vectors, they are indexed to with a congruence match of at least 0.92 (Dyer & Mercer, 2013;Ibebuchi, 2022;Ibebuchi & Richman, 2023;Richman, 1986).Since the reference CTs in Western Europe that are analysed in this study are the similar as those obtained in Ibebuchi (2022), 4 optimal PCs are also retained in this study, and the details for retaining 4 PCs are further provided in the aforementioned study.The oblique rotation utilized at a power of 2 relaxes orthogonality constraint.As a result of the oblique rotation, the Annual cycle of the classified circulation types in Figure 2 from ERA5 and the MPI-ESM simulations.Relative frequency is calculated as the ratio of the number of days assigned to a given month to the total number of days assigned to the CT scores are intercorrelated, and the number of near-zero loadings is maximized; hence a unique number of days with similar spatial patterns can be grouped under a given retained component.This fits the goal of circulation typing which is to cluster days with a similar spatial pattern.
Loadings that are near zero contribute weakly to the PC scores (Compagnucci & Richman, 2008;Ibebuchi & Richman, 2023) and can be discarded using the ±0.2 threshold (Ibebuchi & Richman, 2023;Richman & Gong, 1999) resulting in two asymmetric CTs from the same PC mode. Figure A1 shows the flowchart followed in classifying the CTs using the rotated T-mode PCA.The characteristics of the CTs evaluated from the MPIH and MPIL models are (i) the shape of the composite SLP patterns; (ii) eigenvalues; (iii) annual cycle; and (iv) probability of occurrence, calculated as the ratio of the number of days assigned to a CT to the total number of days in the analysis period.A visual inspection of the composite maps, which are created by calculating the average SLP field (i.e., from the raw SLP data, not the anomaly field) of all the days when a given CT occurred, is also used to investigate the match obtained from the statistical metrics such as Pearson correlations and congruence matches of the z-score standardized maps.By standardizing the composite maps and using the congruence coefficient, the differences between the composite maps become more apparent, making it more robust to identify and compare the patterns.Also, the classification of the CTs is fuzzy implying that a day can be assigned to more than one CTs which implies the CTs that occurred on the day in question (Ibebuchi & Richman, 2023).

| Comparisons between the simulated and reference circulation types
Figure 1 shows the explained variance from the first 11 PCs.The variance explained by the respective PCs from the MPI-ESM simulations is close to their counterparts from ERA5.The first retained PC that explains most of the variability (38%) contains the most dominant atmospheric circulation mode (Table 1).Thus PC1 (i.e., CT1+/CT1−) yields the most frequent CT, i.e., CT1+ from Table 1, which is designated as the dominant state of the atmosphere.Therefore, PC1 needs to be well represented in the MPI-ESM simulations.From Figure 1, the explained variance of the first retained component from MPIH is closer to ERA5 (bias in explained variance is 0:9 j j%) compared to MPIL (bias in explained variance is 2:3 j j%).Also from Table 1, there are notable disparities in the probability of occurrence of the CTs derived from the MPI-ESM simulations.While the bias in the representation of the probability of occurrence of the CTs is dependent on the CT of interest, on average the MPIH outperforms the MPIL model.
Figure 2 shows the standardized SLP composite maps of the classified CTs.The pattern of the reference CTs from ERA5 was captured in the simulated CTs.Table 2 shows the congruence coefficient between the simulated SLP composite anomaly maps from MPIH and MPIL and their counterparts from ERA5.Except for CT3+ and CT4-+, the congruence matches between the simulated CTs and ERA5 CTs are overall greater than 0.9.CT3+ is associated with a ridge stretching from the North Atlantic towards the Baltic Sea and covering vast regions of Western Europe (Figure 2).From Table 2, the spatial pattern of CT3+ is among the least captured by the MPI-ESM simulations.Similarly, CT4+ reflects enhanced anticyclonic activity over large parts of Western European landmass.The spatial pattern of CT4+ is the least captured by the climate models (Table 2).This can be because from Figure 2, unlike in ERA5 where the anticyclonic system dominates over northwestern Europe, in the climate  models, the blocking anticyclone extends towards the Mediterranean and the subtropical landmass.Further, the spatial variation of SLP under each CT is improved in MPIH compared to MPIL-the average improvement in the congruence matches between the simulated and assimilated patterns is 5%.Under CT3+ and CT4+ which are the least represented CTs, up to 14% improvements were recorded in the spatial variation of SLP in the higher-resolution version compared to the lower-resolution version of the MPI-ESM model (Table 2).Figure 3 also shows that the MPI-ESM simulations capture the overall structure in the annual cycle of the CTs, though the biases appear to be seasonally dependent on the CT-the models generally tend to underestimate the frequency in the cool season and overestimate the frequency in the warm season.Based on the mean absolute error (Table 3), overall, the annual cycle of the CTs is again improved under MPIH compared to MPIL, except under CT3−.

| Stationarity of the classified patterns under future climate change
The stationarity of large-scale circulation patterns is a long-debated topic (IPCC, 2007); hence it is addressed in this section using the MPIH model, by investigating the CTs in Western Europe under the future climate change scenarios.The reference CTs used to investigate the CTs classified under future emission scenarios, are the simulated CTs from MPIH under the historical run.Figure 4 shows that the eigenvalues of the respective PCs as classified from the historical experiment and under future climate change were barely altered.The slight alteration in the eigenvalues of the matched patterns is more pronounced in the higher warming scenario (SSP5-8.5),especially under PC1, suggesting changes in the mean state of the atmospheric circulation (i.e., CT1+).By applying the classification technique to the simulated SLP data under the future climate change scenarios, Figure 5 shows that the historical CTs in Western Europe are present under future climate change scenarios; therefore, it is possible to assess future changes in the statistical characteristics of the same historical CTs.From Table 4, except for CT3− under the higher warming scenario, the congruence matches between the CTs from the historical analysis and their counterparts under future climate change scenarios are greater than or equal to 0.9.On average, the changes in the spatial pattern of SLP in the CTs are higher under the SSP5-8.5 scenario.Figure 6 also indicates that the structure of the annual cycle of CTs is not notably altered by climate change, even though at a monthly scale the magnitude in the frequency of occurrence of CTs in Western Europe is projected to be altered especially under the SSP5-8.5 scenario.For example, in the SSP5-8.5 scenario, during boreal summer, the frequency of occurrence of CT3+ (CT3−) is projected to decrease (increase) implying an increase in the frequency of occurrence of a cyclonic circulation over the Baltic Sea.Also, using the MPIL model gives similar results as obtained from the MPIH model but with different magnitudes of projected changes (not shown).
The reliability of climate models used for understanding the climate systems and for climate projections is precluded by several source of uncertainties, which ultimately result to systematic biases in the climate model output (Richter, 2015;Wang et al., 2014).Although climate models have greatly improved over the years, some physical processes still occur at spatial scales that are not resolved by the current horizontal resolution of these models (Gentry & Gary, 2010;Petch et al., 2002).Such unresolved processes can have a significant impact on the accuracy of climate projections, particularly in regions with complex terrain or where small-scale atmospheric phenomena play a crucial role (e.g., Rotach & Zardi, 2007).The accurate representation of small-scale atmospheric processes is essential for improving the accuracy of climate models and understanding the complex interactions between small and large-scale atmospheric processes (Kuang et al., 2005;Schenk & Vinuesa, 2019).This implies that unresolved small-scale processes might lead to errors in the simulation of largescale atmospheric patterns.Under MPIH Müller et al. (2018) noted that stratocumulus parametrization was activated and processes such as cloud cover scheme were improved, which led to several improvements in the bias structure of MPIH relative to MPIL.Nonetheless, as reported by Jungclaus et al. (2013), improvements in higher-resolution models can depend both on the region of assessment and the variable of interest.This is because different regions of the world can exhibit different climatic characteristics and physical processes that may be sensitive to changes in model resolution.In the same respect, variables that are strongly influenced by local processes may benefit more from higher-resolution models.In this study, focusing on Western Europe, and using SLP for circulation typing, it was found that there is relative improvement in the long-term statistical characteristics of the CTs under MPIH.Therefore, by using MPI-ESM model, it is shown that the bias in large-scale circulations and their longterms statistics were reduced by increasing the model resolution.This can be linked to improved parametrization of smaller scale processes leading to improved atmospheric dynamics, which enhances the representation of the simulated SLP (Müller et al., 2018) and to improved sea surface temperature in the higher-resolution version of the climate model (Milinski et al., 2016).The bias in simulating anticyclonic circulations over Western Europe as reported by Ibebuchi (2022) was reduced by 14% under MPIH.The improvements in the CTs classified from the MPIH SLP data is consistent with the finding of Müller et al. (2018) that the global SLP error decreased under MPIH relative to MPIL.The conclusions of this study on the relatively better representativeness of the CTs created from MPIH remained unchanged when different realizations of the MPI-ESM model, other than r1i1p1f1, were used (not shown).Hence higher-resolution climate models may improve the representation of circulation patterns by the models; reduce circulation biases when the GCMs are downscaled dynamically, and therefore, improve the credibility of future climate projections.
Using the MPIH, which is more representative of the actual climate system, the historical CTs in Western Europe are present under future climate change scenarios (Figures 5 and 6), regardless of the time within the future emission scenarios that the analysis is focused on.Whether the presence of the historical CTs under future climate projections represents stability of CTs over time or an inability of GCMs to simulate potential changes in synoptic-scale circulation remains debatable (Hewitson & Crane, 2002).Anyway, there were some relative changes in the frequency distribution, spatial pattern, and magnitude of SLP in the CTs under future climate change, which can be linked to changes over time, in the geographical features associated with the CTs (Lorenz, 1967).Schär et al. (1996) applied higher-resolution regional climate models with surrogate climate change scenarios (i.e., artificially generated climate scenarios used for studying the impacts of climate change), and showed that for parts of Europe (e.g., the Alps) increased warming does not alter synoptic conditions.Haberlandt et al. (2015) reported that under climate change, changes in some of the characteristics of the synoptic circulations are expected.For other regions, studies have also investigated changes in synoptic circulations under future climate change and reached similar conclusions as presented herein (e.g., Faranda et al., 2020).
Finally, it has been demonstrated in this work that increasing the model resolution can improve the CTs classified with SLP.As this study is focused on the MPI-ESM model, on SLP and for Western Europe, it is necessary to investigate the validity of the results for other regions using other suites of climate models and climate data that explain atmospheric circulation.If the same conclusions are reached, then the results herein can be generalized.

| CONCLUSIONS
This study examined the added value in using the SLP field from the higher-resolution version of the MPI-ESM1.2climate simulation, compared to the lowerresolution version, for circulation typing within the regional context of Western Europe.It was found that the CTs and their characteristics as obtained from ERA5 reanalysis were reproduced from both MPI-ESM1.2simulations with modest bias.On average, the spatial variation of SLP, annual cycle, and probability of occurrence of the CTs were relatively improved in the higherresolution version of the MPI-ESM1.2simulation.
Under future climate change, it was found that the simulated historical CTs were present under future climate change scenarios; nevertheless, the long-term characteristics of the CTs in Western Europe can be altered, especially under the higher warming scenario.
The wider implication of this study is that using climate models with higher horizontal resolution can result in a more realistic representation of CTs in the region of assessment and therefore enhance the applicability of the climate model in projecting future changes in the CTs and their long-term characteristics.

F
I G U R E 1 Percentage of variance explained by the first 11 components from the ERA5 and their counterparts from the MPI-ESM simulations in the historical analysis.The analysis period is from 1979 to 2014 [Colour figure can be viewed at wileyonlinelibrary.com]

4
Percentage of variance explained by the first 11 components for the historical, SSP5-8.5, and SSP2-4.5 MPIH simulations.The analysis period for the circulation typing is 2040 to 2100 [Colour figure can be viewed at wileyonlinelibrary.com]F I G U R E 5 Classified circulation types from historical analysis, SSP5-8.5 and SSP2-4.5 MPI-ESM-HR simulations for the 2040-2100 period.The composite maps were z-score standardized [Colour figure can be viewed at wileyonlinelibrary.com]

F
Congruence matches between the composite anomaly maps of the simulated historical CTs and their counterparts from the climate change scenarios, exemplified by the MPIH I G U R E 6 Annual cycle of the CTs in Figure5