Soil scheme of MOLOCH

GG q,T,z 111

GG q,T,z 222

GG q,T,z 333

GG q,T,z 444

11 q,T

SKINT

fraction of model box covered by snow fSNOW

SKINqfraction of vegetation fVEG

Climatological layer

air specific humidity above the interface

soil skin temperature

first atmospheric level

Soil and vegetation properties

•fVEG Fraction 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 potentialGCG Dry soil thermal capacity per unit volume (J/m3/oK) Emissivity (function of water content and vegetation) Albedo (function of water content and vegetation)

t,L,L,,,C,C,C VW

WIWIWP 0

Efficiency of evapotranspiration (depending on temperature, insolation, and L.A.I.)

Physical and numerical constants used in the scheme

VEGSNOWGGGGGG W,H,q,q,q,T,T,T 321321

Prognostic fields

VIS

VISEVTR ln.

.I.A.LE

57

20511901

180

DSSKINSKINSNOW C,T,q,f Diagnostic fields

Drag coefficient

mass of water (kg/m2) deposited over vegetation

Snow height (m of equivalent water)

Thermal conductivity of snow in Watt/m/oK

5.KSNOW

IRVISqH ,,, Turbulent fluxes of heat and specific humidity (positive

upward) and radiation fluxes (positive downward)

.I.A.L.W,W

Wf MAX

VEGMAXVEG

VEGWETL 020 fraction of wet leaf

k

jROOTj

k

jjROOT

k

jROOTjk

*k

GWILT

Gk

GREF

Gk

GWILT

GREF

Gk

GWILT

GREF

GWILT

Gk

ROOT

*kW

k

Zz,zZ

Zz,z

z

qq

qqq

qq

,qq

qq,

Z

zC

1

1

1

1

0

1

efficiency of root pumping weighted by the layer depth

)T(qq SKINSATSAT Saturation of surface air at time t

VEGSNOWSNOW

VEGSNOWVEG*VEG ff.f

ff,ff

11

1 fraction of model box covered by vegetation and free of snow

SOIL

*VEGSNOWLEAFWETLSATWETL

*VEGSATSNOW

SKIN

qffq)f(qffqf

q

11

Definition of qSKIN at current time t

Air specific humidity over wet leaves

j

WjEVTRSATLEAF CE,qqmaxqq 011

751

0

52

1

11

1

10325018

85144179

01

1

1

1

2

.SKIN

AS

AS

FGMAXMAXDS

G

GGSATSOIL

TT.,.

b

.F

,.b

.,.maxF,

)q,qmin(qFCZ

ZqZqq

Air specific humidity over bare soil and pools (ZG is the surface wetness)

coefficient of molecular diffusivity of vapor into air

Atmospheric vertical diffusion

1qqC SKINDSq

Turbulent flux of specific humidity (kg/m2/s) positive upward

Updated specific humidity at first atmospheric level

DSC

q

1

P

SKINdV

CR

S

VVSKINDS

H C

q)R/R(P

P

C

P

d

110

1

Turbulent flux of heat (Watt/m2) positive upward

Updated drag coefficient of humidity and temperature (over land only)

Humidity flux disaggregation using the updated value of q1

)t/H,qqfCmin( SNOWWSATSNOWDSSNOW 1

1

1

1

1

qqfC

)t/W,qqffCmin(

qq

qq

SAT*

VEGDS

VEGSATWETL*

VEGDS

SAT

SATWETL

0

1 1

1

1

j

Wj

Wk

LEAFWETL*

VEGDS

SAT

SATEVTR

C

CqqffC

qq

qqK

k

kEVTRWETLSNOWqSOIL

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).

Precipitation intercepted by leaves (it can be negative)

)fP,t/)WWmin((P *VEGRAINWETLVEG

MAXVEGINTC

WETLINTCVEGVEG tPtWW

WVEG update

INTCRAINRES PPP

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)

Residual precipitation and WVEG update

TSKIN : soil temperature at the upper interface from flux balance

01111 )T()T()T(L)T( nSKINH

nSKINIRVIS

nSKINq

nSKINH

01 SKINIRTqTHT T)dLdd(R

b

MAXGMAX

Glog

G

SNOWIW

GWWGGGSNOWSNOWG

)q,qmin(

q,e.K

z

HCqCC

t

z,)KK(fK

zmin

1

6

11

1

11

10140050

2

2

30

11

4 SKINIRTDSPHTSKIN

SKINDSqT

SKINHSKINIRVISSKINqSKINH

GSKINH

WISNOW

VW

Td,CCd,dT

dqCd

R)T()T()T(L)T(

)TT(,LfLL

(heat flux from the ground)

Surface heat exchange coefficient 1

thermal diffusivity of ground

Numerical limitation

Newton step

Snow height update

)P(t

HH SNOWSNOWW

SNOWSNOW

SNOWSNOWSNOW

SNOWWMELT

WI

SNOWISNOWSNOW

GSKINSNOW

HHH

t/HP

L

),.Tmax(C,minHH

/,T)(TT

0152731

211 1

1-Fall-Sublimation

2-Melting

(Kg/m2/s)

(melting parameter)

REFSNOWSNOW H/H,minf 1 3-Snow fraction update

Water flux and content update of the first soil layer (m3/m3)

211

11

z

t)t(q)tt(q

W

GG

11 k EVTRSOILMELTRES kPP

MING

MINGW

MING

q)tt(q

q)t(qt

zq)tt(q

1

11

121

Gq2

Kg/m2/s

1z

21

12212112

32

211

21

21

2

2112 5

zz

)q,qmin(zqzq,

q

qK

)zz(.

q)q,qmin(

q

q

q

bK

GMAX

GG

/k EVTR

b

MAX

G/

WW

GGMAX

b

MAX

G/

GMAX

WW

k

Flux correction

322

22

z

t)t(q)tt(q

W

GG

2

MAX

MING

G

MAX

MINW

MAX

MING

q

q)tt(q

)t(qq

q

t

z

q

q)tt(q

2

22

23

2

32

23322123

32

212

32

32

2

2123 5

zz

qzqzq,

q

qK

)zz(.

qq

q

q

q

bK

GGG

/k EVTR

b

MAX

G/

WW

GGb

MAX

G/

GMAX

WW

k

Water flux and content update of the second soil layer (m3/m3)

Flux correction

t

zqCC,K

zzmin

q

q,e.K

z

HCqCC

t

z,K

zzmin

q

q,e.K

GWWGGG

b

G/

MAXG

logG

SNOWIW

GWWGGG

b

G/

MAXG

logG

2

2

140050

2

2

140050

22

323

212

6

11

1

212

211

6

10

10

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).

t)TT(CC)(

t)T.(CP)TT(tC

t)TT(t)TT(

)TT(tCP)TT(tCP

tLPTHCzqCzC

GSKINISNOWW

kEVTRSOIL

GWMELT

GG/W

GGGSKIN

GISNOW

GWRES

WIMELT

GSNOWIW

GWWGG

k

1

112112

12211

1111

1111

15273

Cooling due to melting snowheating due to mixing with rain at air temp. T1

heating due to mixing with water diffused from below (including root pumping)

heating due to heat exchange with snow at air temp. T1

cooling (heating) due to the increase (decrease) of evaporating water/ice to temperature TSKIN

heating due to mixing with melted snow at freezing temp.diffusion of heat

T1G tendency: irreversible mixing and heat diffusion

heat capacity at new time level

)TT(tC)TT(tC

t)TT(t)TT(

TzqCzC

GG/W

GG/W

GGGG

GGWWGG

2212322112

233212

2222

T2G tendency

321 ,,k,TTT Gk

Gk

Gk

Final temperature update

Runoff

MAXGGG

MAXG qqRqqq)tt(q

Orographyt,minR

1111

1800

11