1. 1)Consideration of fractional cloud coverage Ferrier microphysics scheme is designed for use in high- resolution mesoscale model and do not consider partial cloud explicitly. 2)Representation of increase/decrease of cloud water due to moistening/drying by other processes When a physical or dynamical process other than cloud microphysics increases water vapor in a grid box, water vapor is not converted to cloud water in the process until the grid box is saturated. Ferrier microphysics scheme does not generate cloud water when super-saturation does not exist. Implementation of Ferrier microphysics scheme to GFS

2. Each grid box is divided into three parts. Ferrier microphysics scheme is applied separately to the cloudy and clear with precipitation portion of the grid. Cloud cover is obtained from total water mixing ratio and distribution width in grid from the previous time step assuming uniform PDF. Maximum-random cloud overlap is assumed in calculation of area and precipitation rate. Consideration of partial cloud Ferrier microphysics Ferrier microphysics (evaporation) CloudyClear with precipitation Clear w/o precipitation

3. total water q t PDF P(q t ) cloud part width  saturation mixing ratio q s grid mean value q t Uniform PDF

4. To represent increase of cloud water due to moistening by other processes, a part of the increased water vapor is considered as super- saturated water vapor in the cloudy portion assuming uniform PDF. Super-saturated water vapor is converted to cloud water through the Ferrier microphysics calculation. q vcld = q* + q supersaturate, q venv = (q v – C q vcld )/(1– C)  is diagnosed after Ferrier microphysics for the next time step. Cloudy portion is considered to be sub-saturated in a similar way when other processes dry grid box. Increase of cloud water total water x q*q* x cloud cover super-saturated water vapor q*q* t-1t-1 tt Schematic distribution of total water in a partially cloudy grid assuming uniform PDF. Distribution width  from the previous time step is used. 22 increased water vapor

5. Estimation of cloud cover considering super- saturation/sub-saturation by other processes using  from the previous time step Division of grid into three parts (cloud, clear with precipitation, clear without precipitation) Calculation of water properties in each parts (q v, q l, q i,…) Ferrier microphysics (cloudy, clear w/ precip. portion) Grid averaging and calculation of  for the next time step Flow chart of box Ferrier scheme

6. Cloud condensate forecast 48 hour forecast of zonal mean cloud water + cloud ice by GFS. Initial time of forecast is 00 UTC 12 June 2009. Box Ferrier Zhao

7. Backup Slides

8. FEATURE Zhao & Carr (1997) [Modified version in GFS] Ferrier et al. (2002) [In Eta, WRF option] Prognostic variables Water vapor, cloud condensate (water or ice) Water vapor, total condensate (cloud water, rain, cloud ice, snow/graupel/sleet) Condensation algorithm Sundqvist et al. (1989) Asai (1965) [used in high res models] Precip fluxes and storage Top-down integration of precip, no storage, & instantaneous fallout. Precip partitioned between storage in grid box & fall out through bottom of box Precip type Rain, freezing rain, snow Rain, freezing rain, snow/graupel/sleet (variable rime density for precip ice) Mixed-phase conditions No coexistence of supercooled cloud water & ice, simple melting eqn. Mixed-phase at >-10C, includes riming, more sophisticated melting/freezing Comparing grid-scale microphysics schemes Ferrier (2005)

9. Grid is divided to three part (cloudy, clear with precipitation from upper level, clear without precipitation from upper level). Area and precipitation rates are calculated from those at upper level. Cloud cover is given by Sundqvist et al. (1989) formulation. Maximum overlap is assumed for adjacent level cloud and random overlap is assumed for detached level cloud in the precipitation rate calculation. Ferrier microphysics is executed for cloudy portion and clear w/ precipitation portion separately. Cloud overlap L+1 L Ferrier scheme CVR(L) < CVR(L+1) CVR(L) > CVR(L+1) L+1 L Ferrier scheme (evap) averaging

10. To represent increase of cloud water due to moistening by other processes, a part of the increased water vapor is considered as super- saturated water vapor in the cloudy portion assuming uniform PDF. Super-saturated water vapor is converted to cloud water through the Ferrier microphysics calculation. q vcld = q* + q supersaturate, q venv = (q v – C q vcld )/(1– C)  is diagnosed after Ferrier microphysics for the next time step. Cloudy portion is considered to be sub-saturated in a similar way when other processes dry grid box. Modification of cloud water cloud cover Schematic distribution of total water in a partially cloudy grid assuming uniform PDF. Distribution width  from the previous time step is used. Moistening caseDrying case x sub-saturated water vapor q*q* t t-1 x super-saturated water vapor q*q* t-1 t 22 total water

11. Cloud water and water vapor is assumed to be in equilibrium in each time step after Ferrier microphysics calculation. Total water in a grid is distributed following uniform PDF centered at grid mean value q T. Distribution width  is determined from q v, q l and q* after Ferrier microphysics calculation and used in the next time step. total water PDF cloud part width  saturation mixing ratio q* grid mean value q T Uniform PDF

12. Cloud condensate forecast Box Ferrier ECMWF Zhao