1. MOLOCH : ‘MOdello LOCale’ on ‘H’ coordinates. Model description ISTITUTO DI SCIENZE DELL'ATMOSFERA E DEL CLIMA, ISAC-CNR Piero Malguzzi:

2. Objectives Develop a tool for very high resolution-short range operational weather forecast; Resolve explicitly atmospheric convection (without parameterisation); Develop a tool for research purposes (cloud model, flows over complex orography) Model dynamics non hydrostatic, fully compressible Arakawa C grid; terrain-following coordinate time split, implicit for vertically propagating sound waves, FB for horizontally propagating waves advection: FBAS (Malguzzi & Tartaglione, 1999); also Weighted Average Flux WAF (Toro 1989; Hubbard & Nikiforakis, 2001) nested in BOLAM runs Model physics radiation, vertical diffusion, surface turbulent fluxes, soil water and energy balance provisionally similar to BOLAM new cloud microphysics (partly based on Drofa, 2003) no dry and moist convection Piero Malguzzi:

3. The vertical scale H is given by the density scale height Terrain following vertical coordinate smoothly relaxing to horizontal surfaces above the orography h(x,y): H-Coordinate Piero Malguzzi:

4. q CW q CI qVqV Piero Malguzzi: The non hydrostatic model MOLOCH: parameterisation of microphysical processes

5. Accretion of freezing rain by snow Accretion of rain by melting snow Accretion of cloud water by rain Accretion of cloud ice by snow “Riming” Accretion of cloud ice by freezing rain Accretion of cloud water by melting snow q PW q PI Piero Malguzzi:

6. Microphysical hypothesis Cloud particles Precipitating particles Liquid and solid cloud particles: gamma-distribution (Levi distribution) for the number of particles per unit volume and unit radius D:  and are determined from the condition: Liquid and solid precipitation: Marshall-Palmer distribution N 0 =10 6 -10 7 (m -4-  ) and  =6 for cloud drops N 0 = 10 7 -10 8 (m -4-  ) and  =3 for cloud crystal N 0 = 8·10 6 (m -4 ) for precipitating drops N 0 function of crystal shape for precipitating ice and where a=  /6·  W, b=3 for cloud and precipitating water; a=100, b=2.5 for cloud ice; a and b function of crystal shape (temperature) for precipitating ice. The result is: where m is the mass of a particle of diameter D: Piero Malguzzi:

7. where is the rate of change of the mass of a single particle Condensation-sublimation where F is the ventilation coefficient, equal to 0.8 for cloud particles. For precipitating particles the following expression is implemented: where  dif is the dynamical molecular viscosity of air: U, the terminal velocity of the particle; and Sc, the Shmidt number (= 0.6). The suffix k can be W or I, indicating liquid water or ice, respectively. L W V and L I V are the condensation and sublimation latent heat; , the coefficient of molecular diffusion of vapour into air; K a, the thermal conductivity of air; and q V, the specific humidity. The rate of change of the specific concentration q due to a particular microphysical process is given by: Piero Malguzzi:

8. Melting and freezing where L I W is the latent heat due to ice melting. Accretion of cloud particles by rain/snow/graupel In this process it is assumed that all cloud particles have the same probability to be collected by a precipitating particle where D and u are diameter and terminal velocity of accreting particles (solid or liquid precipitation), q k is specific mass of the accreted particles (cloud water or cloud ice), E is the accretion coefficient (0.6 for the interaction rain–cloud water: 0.1 for the interaction snow/graupel–cloud ice; 1.0 for the interaction rain-cloud ice and snow/graupel-cloud water[riming]). Accretion of rain by iced precipitating particles where U is the precipitation terminal velocity and E=1. The rate of change of the specific concentration of precipitating ice is the given by: Accretion of cloud water by melting snow Accretion of rain by meltig snow Piero Malguzzi:

9. Autoconversion of precipitation The parameterisation of this process is based on the following formulas: for rain for snow/graupel  is the autoconversion coefficient, in the range from 1 to 3 10 -3 s -1 q th is the threshold value of cloud specific mass: q cw th =5 · 10 -4 kg/kg, q ci th =10 -3 kg/kg. Piero Malguzzi:

10. The terminal velocity of one precipitating particle is: where n=0.8 and k=842 m 1-n s -1 for rain n and k function of the crystal shape for snow/graupel Average terminal velocity: Fall of precipitating species The fall is computed with the backward upstream scheme (unconditionally stable and dispersive). Piero Malguzzi:

11. Conservation of entropy during microphysical processes partial pressure of water vapor Saturation formulas (Pressman) with respect to water and ice Specific heat at constant pressure Piero Malguzzi: