_The MAR model description comes from Section 2.1 from [Christoph Kittel's PhD thesis](https://orbi.uliege.be/handle/2268/258491), with some minor format changes. This is Section 2.1.3.1._
The model includes a cloud-microphysical scheme solving conservation equations for the concentration of five water species (cloud droplets $q_{w}$, ice crystal $q_{i}$, rain drops $q_{r}$, snow particles $q_{s}$, and specific humidity $q_{v}$ firstly described by Gallée (1995)[^1]) and the ice crystal number $n_{i}$ (Massager et al., 2004[^2]). MAR solves the following conservative equation for every horizontal pixel and vertical-$\sigma$ layer:
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where the three first terms represent the 3D advection by the wind following the $x, y$ and $\sigma$ directions, $F_{q \alpha}$ the turbulent flux divergence of the hydrometeor specie, and $P_{sed}$ a source term. $P_{sed}$ is an additional term that describes the sedimentation of precipitating hydrometeors (rain drops, snow particles, and ice crystals) depending on their specific falling velocities. The source term in the above equation represents the 21 microphysical processes detailed in Table 1 originally based on Kessler (1969)[^3] parameterisations in addition to the sedimentation towards the surface of the three precipitating hydrometeors. Since graupels are not (fully yet) included in the model, all accretion processes that should result in graupel following Lin et al. (1983)[^4] lead to snowflake formation assuming a Marshall-Palmer size distribution (Gallée, 1995)[^1].
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| Microphysical processes | References |
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**Table 1:** Microphysical processes represented in MAR and associated references as firstly described by Gallée (1995)[^1] and modified afterwards.
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Table 1 also lists the parameterisations that have been recently included in MAR since the original description by Gallée (1995)[^1]. In particular, the ice crystal nucleation used by Lin et al. (1983)[^4] (and based on Fletcher (1962)[^12] overestimates ice crystal concentration leading to the model underestimation of the downwelling solar radiation towards the surface, the convective available potential energy (CAPE), and rain (Massager et al., 2004[^2]). It has thus been replaced by Meyers et al. (1992)'s parameterization[^7] later improved by Prenni et al. (2007)[^8]. Ice crystal sedimentation is not neglected anymore by adding a prognostic equation for ice crystal number according to Levkov et al. (1992)[^6]. Furthermore, the conversion rate of cloud droplets to rain particles takes into account an adapted parameterisation from Sundqvist (1988) [^9]. It relies on two parameters: a critical cloud water mixing ratio ($q_{wo}$) enabling the rainfall formation and a characteristic time scale for auto-conversion processes ($C_{o}$). Note that a low fraction of cloud droplets can be converted to rain even if $q_{w}$ is lower than $q_{wo}$ (Delobbe and Gallée, 1998[^13]). In [MARv3.11](https://gitlab.uliege.be/especes/mar/stable/-/releases/v3.11.5), $q_{wo}$ and $C_{o}$ values are respectively fixed to $1 \cdot 10^{-3} (\text{kg kg}^{-1})$ and $1 \cdot 10^{-4}$. Finally, other subtle adjustments such as an increase in snowfall sedimentation velocity or cloud lifetime (Fettweis et al., 2017[^11], 2020[^14]) have been made to tune the model in order to more accurately reproduce clouds over the polar ice sheets.
