In order to isolate the effect of each physics scheme from the total configuration, we have calculated the mean differences between simulations that only differ in one type of physical parameterization (PBL, MIC or CUM), while the rest of the setup is identical. For example, to explore how different the results between the two PBL schemes can be, we created composites of the differences between runs with IDs 1 - 4, 2 - 5, 3 - 6, 7 - 10, 8 - 11, and 9 - 12 (see Table 1). Similar differences were calculated for the CUM and MIC parameterizations. Relevant sensitivity plots of these differences can indicate how sensitive each of the tested surface variables is to the parameterization of the selected physical processes in the WRF model and for the MENA region.

As mentioned above, in this WRF physics inter-comparison we focus on three surface variables, being most relevant for impact studies. Analysis for monthly PR, TX and TN was performed. In order to objectively explore the performance of each simulation, we used a range of statistical metrics after calculating the monthly values of the model output and the gridded observational data. For precipitation observations we averaged the three available datasets on a monthly basis. A short description of each metric is presented in the following.

・ The Pearson’s correlation coefficient (COR), a measure of linear correlation between the observations (OBS) and simulations (SIM)

where n is the number of the sample, COV is covariance and σ is the standard deviation.

・ The Mean Absolute Error (MAE), used to describe the average model performance error. This metric has some advantages over the widely used Root Mean Square Error [43] . In this study, the authors suggest that RMSE tends to become increasingly larger than MAE (but not necessarily in a monotonic fashion) as the distribution of error magnitudes becomes more variable. This makes MAE a more natural measure of average error magnitude.

・ The Modified Index of Agreement (MIA), as a standardized measure of the degree of the model prediction error. This index varies between 0 and 1. It was introduced by Willmott [44] and refined by Legates and McCabe [45]

・ The error in the standard deviation (STDE) of the two samples (monthly OBS and SIM) to explore if the modeled variability realistically represents the that of the observations.

The statistical metrics described in the previous paragraph were applied to the monthly time-series of the gridded observational data and each of the 12 CLWRF simulations. Every grid point of the MENA domain was independently analyzed. For each grid point the 12 runs were ranked according to their metrics performance for all of the three variables (TX, TN and PR). All variables and scores were equally weighted in the ranking. Finally, the total number of grid points where each run was ranked first was recorded. The runs with the highest number of first-ranking grid points are considered as the best performing ones.

Because of the large areal extent of the MENA-CORDEX domain, the selection might be biased from the performance over grid points not necessarily relevant for studies over the traditional MENA definition territories³, especially near the tropics. To avoid this, we repeated the analysis including only grid points over sub- domains of special interest, which are defined in Figure 3 (left panel). These sub-regions include the most densely populated areas and the sources of the most important rivers of the region. These are the core-MENA (MNA) region, the Atlas Mountains (AM), the northeast Mediterranean coast of Africa (MED), the east Sahara territories (ES), the Ethiopian Highlands (EH), Egypt (EG), Saudi Arabia (SA), Iran (IR), the Balkans (BAL), the Anatolian Peninsula (ANA), the sources of Tigris and Euphrates rivers region (TE) and the Levantine (LEV). Some of the above mentioned regions overlap. Since the CRU dataset does not cover water bodies, the analysis was restricted to land grid points. A similar type of analysis between the ECA&D station data and the closest model grid points was performed.

The average TX of the CRU data for the study period is presented in the left panel of Figure 4 as a reference while the mean annual TX biases between the 12 ensemble members and the CRU data are depicted in Figure 5. It is clear from the bias maps that the model performs better for the runs where the WSM6 microphysics scheme is used (IDs 1, 2, 3, 4, 5 and 6). On the contrary, the majority of the simulations using the GCE scheme (IDs 7, 8, 9, 10, 11 and 12) tend to strongly underestimate TX especially over the African part of the domain. These large TX departures from CRU observations reach up to 10˚C. This coincides with the increased cloudiness produced by the latter scheme over the locations of the strongest TX overestimation (c.f. Figure 5 and Figure 6). These positive cloud biases generated for the GCE-driven runs (Figure 6) limit the incoming solar radiation and thus induce large negative temperature biases.

The more realistically produced TX for the WSM6 microphysics scheme over the core-MENA subdomain is also clear in the time-series comparison of Figure 7 (left panel). In general, the seasonal cycle of TX is captured

well by most of the simulations; however, the model performance is relatively better for the transition seasons between winter and summer (i.e., the monsoon).

A consistent overestimation of TX for all simulations over the southern Arabian Peninsula is also evident for the forcing ERA-Interim data in the same region and strong temperature biases are found when they are compared with CRU [46] .

We find that the choice between the two selected PBL schemes is not critical for TX as the mean differences between all simulations are small (not shown). Similarly, the cumulus parameterization selection appears to be of minor influence on TX compared to the MIC selection. For most of the domain the differences between the three tested CUM schemes as derived from the sensitivity plots (not shown) are less than 1˚C.

The CRU reference of TN averaged for the December 1988-November 1990 period is presented in Figure 4 (right panel). TN biases (Figure 8) are in general larger and more extensive than TX biases. Consistent with the latter though, the model performs better for runs with the WSM6 microphysics scheme (IDs 1, 2, 3, 4, 5, and 6). The mean difference between the two schemes is also presented in Figure 9 (right panel). Large deviations, up to more than 8˚C are found. In general, the WSM6 yields higher TN and is closer to observations (Figures 8(a)-(f)). TN differences related to the PBL parameterizations are smaller (Figure 9―left panel), however, the YSU scheme is, over most of the MENA, relatively warmer (1˚C - 3˚C) than the MYJ scheme. This feature is more prominent over the desert areas of the domain. Similarly with TX, TN appears to be relatively insensitive to the selection of CUM parameterization (not shown). The monthly TN time-series averaged for the core- MENA domain are presented in Figure 7 (right panel). Simulations with the WSM6 microphysics scheme (blue and green lines) consistently perform better over the study period and capture well the inter-annual variability of the observations within the 2-year study period. In agreement with the TX time-series, this is more evident during the transitional seasons and mainly during spring.

Annual mean absolute PR biases are depicted in Figure 10. The annual observations for this figure (OBS) were produced by the averaging the three available gridded datasets (CRU, GPCC and University of Delaware) for the study period. Biases from each individual dataset were also checked but since the patterns were found to be very similar they are not presented. In all cases the dry North African and Middle East part of the domain is realistically simulated. However, since this region is ultra-arid, we explored in more depth the relationship between the simulations and OBS data by calculating the relative PR biases expressed in percentages (Figure 11). The reference OBS annual precipitation for the two years of simulations and for each of the three datasets is presented in Figure 12. There are obvious similarities in the precipitation patterns of the three datasets for these two years of comparison. Yet local differences exist. For example the Ethiopian Highlands are found to be relatively wetter in the GPCC dataset while the Sahara desert is found relatively drier in the University of Delaware observations. More information regarding the differences of the selected gridded precipitation datasets and over the northernmost part of the MENA-CORDEX domain can be found in Tanarhte et al. [40] . A consistent overestimation of precipitation (up to a factor of two relative to CRU) over the Sahara desert is evident in all simulations. Nevertheless, these high percentages should be viewed from the perspective that the observed amounts of precipitation are very low (0 - 10 mm/year). Noteworthy, absolute PR biases (of the order of 1000 mm/year or more) are found in large parts of the domain and especially in low latitudes. In the tropics, the WSM6 microphysics scheme (used in runs with IDs 1, 2, 3, 4, 5 and 6) is generally much wetter than GCE (runs with IDs 7, 8,

9, 10, 11 and 12). This is shown in the relevant sensitivity map (Figure 13―top left panel). From the PR biases of Figure 10 it is not clear which of the two microphysics options is closer to the observations as runs under WSM6 are generally wetter and runs under GCE are drier than OBS. Nevertheless, the scores of the statistical metrics for the core-MENA sub domain (Table 3) are generally better for the former scheme. The PR monthly time-series of Figure 14 corroborate the closer agreement between WSM6-driven runs (green and blue lines) and CRU observations (black line). From this plot it is evident that for this sub-domain, simulations with IDs 1, 2, 3, 4, 5, and 6 capture reasonably well the seasonal cycle of precipitation and the timing of the wettest months of the period of study.

The PR sensitivity to the CUM parameterization is depicted in the top right and bottom panels of Figure 13. As expected, the southernmost part of the MENA domain, where deep convection is prevailing, shows the larg-

est sensitivity to the selection of the CUM parameterization. In general, the KF scheme is relatively wetter comparing to the BMJ and GD schemes (Figure 13―bottom panels). The mean PR difference of the two latter schemes (Figure 13―top right panel) is limited to localized regions in the tropics and is less in terms of PR amounts. The annual mean PR differences between the two tested PBL schemes are of less importance and found only over the tropics. Locally, the YSU scheme appears to be wetter (300 - 900 mm/year) compared to MYJ (not shown).

The four statistical metrics described in the methods section were applied to all grid points of the domain. Results averaged over the core-MENA subdomain are presented in Table 3. Regarding TX and TN, the correlation

and index of agreement scores are clearly higher for the WSM6 microphysics cluster of simulations (IDs 1, 2, 3, 4, 5, 6). This is also evident from the time-series of Figure 7. Similarly, for these runs, the mean absolute biases and the difference in standard deviation are lower. For the calculations of the PR statistics the monthly averages of the three available datasets where used. Independent dataset statistical analysis was also performed, but since the values where very similar only the ones for the averaged OBS are presented in Table 3. As expected, PR scores are generally lower than the ones for temperature and there is no apparent advantage between any of the 12 simulations. However, slightly better statistics are found for the WSM6-driven runs. Moreover, as seen in Figure 14, enhanced precipitation months are simulated reasonably well in runs with the WSM6 scheme (green and blue lines). In contrast, GCE driven simulations miss the rainy season in the core MENA region (red and grey lines). These relatively wetter periods in this subdomain mainly occur during summer, related to the West- African monsoon.

To objectively select the best performing simulation we have ranked their skill and counted the number of grid points where each of the 12 runs performed best. We consider the simulation with the higher number of ranking-first grid points as the best performer. These results are presented in percentages in the three panels of Figure 15. There is a clear distinction between the runs under the WSM6 microphysics scheme over the simulations using GCE, with the former performing generally better. This is in agreement with the discussion of the biases presented in the previous sections. The simulation with run ID #1 appears to be the one that ranks first in most of the MENA-CORDEX domain. This percentage is almost 40% when considering every land grid point of the domain (Figure 15―left panel), while this number is reduced to around 22% for grid points over the sub-re- gions of special interest (Figure 12―middle panel). The selected physics for this run were the YSU planetary boundary layer, the KF cumulus and WSM6 microphysics schemes. The second best-performing simulation is the one with ID #3. This run was ranked first in about 10% of the total and around 15% of the sub-region grid points. The configuration differs from the ID #1 only in the CUM parameterization where the BM scheme is used instead of KF.

Similarly to the analysis presented in the previous paragraph, a comparison between simulations and ECA&D stations was performed. More information regarding the location of the 12 stations and their data availability over the simulation period is presented in Figure 3 (right panel) and Table 2. The closest model land grid point to the station coordinates is considered to be the most representative. The mean monthly distribution of TX for the two years of simulations is illustrated in Figure 16. In addition to the ECA&D station data, TX of the closest

CRU grid point is also presented for comparison. Overall there is a good representation of TX for most of the simulations. A TX underestimation over some stations can be explained by the relatively unrealistic surface topography resolved in this model resolution (≈50 km). For example, for the Algeria, Palmyra, Kerman, Eilat and Van stations the model elevation is much higher than in reality (Table 2). A vertical lapse rate temperature correction could improve the statistics by a more realistic TX representation over these stations. Besides the resolution-related elevation errors the station location and the nearest grid points in the model may lead to discrepancies. Nevertheless, here we perform a comparison between model configurations, and the absolute (dis) agreement is not our foremost objective. In agreement with the gridded data comparison, the simulations that are driven by the WSM6 microphysics scheme (IDs 1, 2, 3, 4, 5 and 6) are consistently closer to the ECA & D station data. As expected, remarkable differences are found even between the station and gridded observational data as a result of the relatively coarse resolution of the latter and the interpolation methods applied for their construction. For most of the cases though, the modeled TX is closer to the gridded CRU data, which are of similar horizontal resolution.

The seasonal cycle of TN is generally captured well by the model and for most of the ECA & D stations (Figure 17). Exception is the Gabes station where the peak TN occurs 3 months earlier than observations. A general underestimation of TN, more pronounced during the summer season, is evident in most stations. In agreement

with TX, the WSM6-driven simulations (blue and green lines) are in most of the cases performing better.

Time-consistent PR data for the period of comparison were more difficult to be obtained. Unfortunately, only at nine of the twelve stations PR was recorded adequately (or data were available). The comparison between these stations and the 12 different physics setups of CLWRF are presented in Figure 18. The monthly average of the three observational datasets (OBS) is additionally presented in Figure 18. As expected, and in agreement with the relevant bias maps and the calculated statistical metrics, the model skill to reproduce PR is worse compared to temperature. In some cases, such as Gabes, Van, Kerman and Algiers stations, the annual cycle of PR is realistically reproduced, however the amounts of PR are overestimated. In all aforementioned stations the model elevation is higher than in reality and this can induce relatively larger water amounts related to orographic precipitation triggering. From Figure 18 it is not evident which physics configuration represents PR most realistically.

The ranking procedure discussed in the previous paragraph was also applied for the 12 ECA & D stations. The statistical metrics between the 12 simulations and one relatively well performing (Seville) and one poor-per- forming model location (Jerusalem) are indicatively presented in Table 4 and Table 5. For all stations, the number of metrics where the simulation ranks first was recorded and the results are presented in percentages in the right panel of Figure 15. Again, there is a clear advantage of using the WSM6 microphysics scheme (simulation IDs 1, 2, 3, 4, 5, and 6). The aforementioned simulations were ranked equally first in about 13% - 15% of the applied ranking tests. This is consistent with the results presented in the previous sections.