
\section{Nucleation}
\labelappendixsection{nuc}

\subsection{MAM4 Intermediate Nucleation Rate coefficients}
\labelappendixsubsection{nuc:coeff_nucrate}

\begin{align}
a(T,x^*) &= 0.14309 + 2.21956 T - 0.0273911 T^2 \nonumber \\
             &+ 0.0000722811 T^3 + \frac{5.91822}{x^*} \,, \\
b(T,x^*) &= 0.117489 + 0.462532 T - 0.0118059 T^2 \nonumber \\
             &+ 0.0000404196 T^3 + \frac{15.7963}{x^*} \,, \\
c(T,x^*) &= -0.215554 - 0.0810269 T + 0.00143581T^2 \nonumber \\
             &- 4.7758 \cdot 10^{-6} T^3 - \frac{2.91297}{x^*} \,, \\
d(T,x^*) &= -3.58856 + 0.049508 T - 0.00021382 T^2 \nonumber \\
             &+ 3.10801 \cdot 10^{-7} T^3 - \frac{0.0293333}{x^*} \,, \\
e(T,x^*) &= 1.14598 - 0.600796 T + 0.00864245 T^2 \nonumber \\
             &- 0.0000228947 T^3 - \frac{8.44985}{x^*} \,, \\
f(T,x^*) &= 2.15855 + 0.0808121 T - 0.000407382 T^2 \nonumber \\
             &- 4.01957 \cdot 10^{-7} T^3 + \frac{0.721326}{x^*} \,, \\
g(T,x^*) &= 1.6241 - 0.0160106 T + 0.0000377124 T^2 \nonumber \\
             &+ 3.21794 \cdot 10^{-8} T^3 - \frac{0.0113255}{x^*} \,, \\
h(T,x^*) &= 9.71682 - 0.115048 T + 0.000157098 T^2 \nonumber \\
             &+ 4.00914 \cdot 10^{-7} T^3 + \frac{0.71186}{x^*} \,, \\
i(T,x^*) &= -1.05611 + 0.00903378 T - 0.0000198417 T^2 \nonumber \\
            &+ 2.46048 \cdot 10^{-8} T^3 - \frac{0.0579087}{x^*} \,, \\
j(T,x^*) &= -0.148712 + 0.00283508 T - 9.24619 \cdot 10^{-6} T^2 \nonumber \\
            &+ 5.00427 \cdot 10^{-9} T^3 - \frac{0.0127081}{x^*} \,.
\end{align}

\subsection{MAM4 Total Molecule Number in Critical Clusters}
\labelappendixsubsection{nuc:coeff_ntot}

\begin{align}
A(T,x^*) &= -0.00295413 - 0.0976834 T + 0.00102485 T^2 \nonumber \\
             &- 2.18646 \cdot 10^{-6} T^3 - \frac{0.101717}{x^*} \\
B(T,x^*) &= -0.00205064 - 0.00758504 T + 0.000192654 T^2 \nonumber \\
              &- 6.7043 \cdot 10^{-7} T^3 - \frac{0.255774}{x^*} \\
C(T,x^*) &= 0.00322308 + 0.000852637 T - 0.0000154757 T^2 \nonumber \\
              &+ 5.66661 \cdot 10^{-8} T^3 + \frac{0.0338444}{x^*} \\
D(T,x^*) &= 0.0474323 - 0.000625104 T + 2.65066 \cdot 10^{-6} T^2 \nonumber \\
              &- 3.67471 \cdot 10^{-9} T^3 - \frac{0.000267251}{x^*} \\
E(T,x^*) &= -0.0125211 + 0.00580655 T - 0.000101674 T^2 \nonumber \\
             &+ 2.88195 \cdot 10^{-7} T^3 + \frac{0.0942243}{x^*} \\
F(T,x^*) &= -0.038546 - 0.000672316 T + 2.60288 \cdot 10^{-6} T^2 \nonumber \\
              &+ 1.19416 \cdot 10^{-8} T^3 - \frac{0.00851515}{x^*} \\
G(T,x^*) &= -0.0183749 + 0.000172072 T - 3.71766 \cdot 10^{-7} T^2 \nonumber \\
              &- 5.14875 \cdot 10^{-10} T^3 + \frac{0.00026866}{x^*} \\
H(T,x^*) &= -0.0619974 + 0.000906958 T - 9.11728 \cdot 10^{-7} T^2 \nonumber \\
              &- 5.36796 \cdot 10^{-9} T^3 - \frac{0.00774234}{x^*} \\
I(T,x^*) &= 0.0121827 - 0.00010665 T + 2.5346 \cdot 10^{-7} T^2 \nonumber \\
             &- 3.63519 \cdot 10^{-10} T^3 + \frac{0.000610065}{x^*} \\
J(T,x^*) &= 0.000320184 - 0.0000174762 T + 6.06504 \cdot 10^{-8} T^2 \nonumber \\
             &- 1.42177 \cdot 10^{-11} T^3 + \frac{0.000135751}{x^*}
\end{align}

