Soil scheme of MOLOCH

1. Soil scheme of MOLOCH first atmospheric level fraction of vegetation fVEG fraction of model box covered by snow fSNOW air specific humidity above the interface soil skin temperature Climatological layer

2. Soil and vegetation properties • fVEGFraction of vegetation (seasonal function) • L.A.I. Leaf Area Index (seasonal function) • ZROOT Root depth (m) • qWILT, qREF Evapotranspiration range (m3/m3) • qMIN, qMAX Minimum and maximum water in soil (m3/m3) • WKW Coefficient of water diffusivity in soil (kg/m2/s) • G Hydric potential (m) at saturation • b Exponent of hydric potential • GCG Dry soil thermal capacity per unit volume (J/m3/oK) •  Emissivity (function of water content and vegetation) •  Albedo (function of water content and vegetation)

3. Physical and numerical constants used in the scheme Thermal conductivity of snow in Watt/m/oK Prognostic fields mass of water (kg/m2) deposited over vegetation Snow height (m of equivalent water) Diagnostic fields Drag coefficient Turbulent fluxes of heat and specific humidity (positive upward) and radiation fluxes (positive downward) Efficiency of evapotranspiration (depending on temperature, insolation, and L.A.I.)

4. Saturation of surface air at time t fraction of model box covered by vegetation and free of snow fraction of wet leaf efficiency of root pumping weighted by the layer depth

5. Definition of qSKIN at current time t Air specific humidity over wet leaves Air specific humidity over bare soil and pools (ZG is the surface wetness) coefficient of molecular diffusivity of vapor into air

6. Atmospheric vertical diffusion Updated specific humidity at first atmospheric level Updated drag coefficient of humidity and temperature (over land only) Turbulent flux of specific humidity (kg/m2/s) positive upward Turbulent flux of heat (Watt/m2) positive upward

7. Humidity flux disaggregation using the updated value of q1 Flux over snow in kg/m2/s Flux over the fraction of wet leaf Evapotranspiration from the fraction of dry leaf and from the k-th soil layer (kg/m2/s) Humidity flux over the fraction of bare soil and pools (it conserves water exactly).

8. Residual precipitation and WVEG update Precipitation intercepted by leaves (it can be negative) WVEG update Computation of residual precipitation at the ground - When the intercepted precipitation is negative, the (negative) specific humidity flux increases the residual precipitation (in parole povere, rugiada che cade a terra)

9. TSKIN : soil temperature at the upper interface from flux balance Surface heat exchange coefficient 1 Numerical limitation thermal diffusivity of ground (heat flux from the ground) Newton step

10. Snow height update 1-Fall-Sublimation (melting parameter) 2-Melting (Kg/m2/s) 3-Snow fraction update

11. Water flux and content update of the first soil layer (m3/m3) Kg/m2/s Flux correction

12. Water flux and content update of the second soil layer (m3/m3) Flux correction

13. Internal heat exchange coefficients If both 1 and 2 are equal to their upper bounds, T1G at new time step becomes the arithmetic average between TSKIN and T2G (due to diffusive terms alone).

14. T1G tendency: irreversible mixing and heat diffusion heating due to heat exchange with snow at air temp. T1 heating due to mixing with rain at air temp. T1 Cooling due to melting snow heat capacity at new time level heating due to mixing with water diffused from below (including root pumping) diffusion of heat heating due to mixing with melted snow at freezing temp. cooling (heating) due to the increase (decrease) of evaporating water/ice to temperatureTSKIN

15. T2G tendency Final temperature update Runoff