## 3 Methods
### WRF Physical Parameterization Schemes
#### 3.1.1 Planetary Boundary Layer Scheme  
For the PBL schemes, we selected three non-local and five local closure schemes. The non-local closure schemes are YonSei University (YSU) scheme [34], Asymmetrical Convective Model version 2 (ACM2) scheme [35], and Total Energy-Mass Flux (TEMF) scheme [36]. The local closure schemes are Mellor-Yamada-Janjic (MYJ) scheme [37], Quasi-Normal Scale Elimination (QNSE) scheme [38], Mellor-Yamada-Nakanishi-Nino level-2.5 (MYNN2) scheme [39], Bougeault-Lacarrere (BouLac) scheme [40], and University of Washington (UW) scheme [41]. Local schemes only consider vertical levels that are immediately adjacent in the model, whereas non-local schemes can consider deeper layers containing multiple levels when exhibiting the effect of vertical mixing through PBL. The YSU scheme [34] is a 1.0-order non-local scheme with an explicit entrainment layer and a parabolic K-profile in an unstable mixed layer. It is a modified version of the Medium Range Forecast (MRF) scheme from the legacy MM5 model. The YSU scheme determines PBL height where the bulk Richardson number (\(\mathrm{Ri_{b}}\)) exceeds a threshold value of 0 for the stable flow while it is 0.25 for the unstable flow. The MYJ scheme [37] is a 1.5-order prognostic turbulent kinetic energy (TKE) scheme with local vertical mixing and has been used in the operational Eta model. It determines the PBL height by the level where TKE decreases to a prescribed small value of 0.2 m\({}^{2}\) s\({}^{-2}\). The QNSE scheme [38] is a 1.5-order local closure scheme with a TKE prediction option to apply a new theory for stable boundary layers. It determines the PBL height as the height where the TKE profile decreases to a prescribed low value of 0.01 m\({}^{2}\) s\({}^{-2}\). The MYNN2 scheme [39] is a 1.5-order local closure scheme that predicts the sub-grid TKE terms. Like the QNSE scheme, MYNN2 is a local scheme based on the comparison with large eddy simulations. The PBL height is defined as the height where the TKE falls below a critical value of 1.0 \(\times\) 10\({}^{-6}\) m\({}^{2}\) s\({}^{-2}\). The ACM2 scheme [35] is a 1.0-order non-local closure scheme that describes non-local upward mixing and local downward mixing. It is a hybrid closure scheme that uses local closure for stable conditions and non-local closure for unstable conditions. The PBL height is determined as the height where the \(\mathrm{Ri_{b}}\) exceeds a threshold value of 0.25. \begin{table}
\begin{tabular}{c c c|c c|c c} \hline \hline  & **PBL Schemes** & & \multicolumn{2}{c|}{**Land Surface Schemes**} & \multicolumn{2}{c}{**Radiation Schemes**} \\ \hline
**Option** & **Scheme** & \multicolumn{2}{c|}{**Surface Layer Scheme**} & \multicolumn{2}{c|}{**Option**} & \multicolumn{2}{c}{**Scheme**} & \multicolumn{1}{c}{**Option**} & \multicolumn{1}{c}{**Shortwave**} \\ \hline
1 & YSU & MM5 similarity & 1 & TD & 1 & Dudhia \\
2 & MYJ & ETA similarity & 2 & Noah & 3 & CAM \\
4 & QNSE & QNSE & 3 & RUC & 4 & RRTMG \\
5 & MYNN2 & MYNN & 4 & Noah-MP & Option & Longwave \\
7 & ACM2 & MM5 similarity & & & 1 & RRTM \\
8 & BouLac & MM5 similarity & & & 3 & CAM \\
9 & UW & MM5 similarity & & & 4 & RRTMG \\
10 & TEMP & TEMF & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical parameterization schemes of the WRF model used for the optimization with the option numbers the same as in the WRF namelist. The non-local closure schemes are YSU, ACM2, and TEMF scheme. The local closure schemes are MYJ, QNSE, MYNN2, BouLac, and UW scheme. The BouLac scheme [40] is a 1.5-order local closure scheme with a TKE prediction formulation designed for use with the BEP (Building Environment Parameterization) multilayer urban canopy model [42]. It diagnoses the PBL height by a level where the prognostic TKE reaches a sufficiently low value of 0.005 m\({}^{2}\) s\({}^{-2}\). The UW scheme [41] is a 1.5-order local TKE closure scheme. It is from the Community Earth System Model [43].