Transcript MOLOCH

Soil scheme of MOLOCH
T1 , q1
fraction of model box
covered by snow fSNOW
fraction of vegetation fVEG
first atmospheric level
q SKIN
TSKIN
air specific humidity
above the interface
soil skin temperature
z1 , T1G , q1G
z2 , T2G , q2G
z3 , T3G , q3G
Climatological layer
z4 , T4G , q4G
Soil and vegetation properties
•fVEG
•L.A.I.
•ZROOT
•qWILT, qREF
•qMIN, qMAX
•WKW
•G
•b
•GCG
•
•
Fraction of vegetation (seasonal function)
Leaf Area Index (seasonal function)
Root depth (m)
Evapotranspiration range (m3/m3)
Minimum and maximum water in soil (m3/m3)
Coefficient of water diffusivity in soil (kg/m2/s)
Hydric potential (m) at saturation
Exponent of hydric potential
Dry soil thermal capacity per unit volume (J/m3/oK)
Emissivity (function of water content and vegetation)
Albedo (function of water content and vegetation)
Physical and numerical constants used in the scheme
CP , CW , CI , W , 0 , LWI , LVW , t
K SNOW  .5
Thermal conductivity of snow in Watt/m/oK
Prognostic fields
T1G ,
T2G ,
T3G ,
q1G ,
q2G ,
q3G ,
H SNOW , WVEG
mass of water (kg/m2)
deposited over vegetation
Snow height (m of equivalent water)
Diagnostic fields
f SNOW , qSKIN , TSKIN ,  S C D

 H , q , VIS
, IR
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.)
E EVTR 
L.A.I .
180


 2051 VIS
1  0.19 ln 

57



VIS





qSAT  qSAT ( TSKIN )
*
fVEG
 fVEG ,

1  f SNOW .
fWETL 
C kW 
WVEG
MAX
WVEG
z*k
Z ROOT
,
Saturation of surface air at time t
f SNOW  1  fVEG
f SNOW  1  fVEG
MAX
WVEG
 0.02 L.A.I .

1,
 q G  q G
k
WILT
 G
G
q

q
 REF
WILT

0,
fraction of model box covered by
vegetation and free of snow
fraction of wet leaf
G
q kG  q REF
G
G
qWILT
 q kG  q REF
G
q kG  qWILT
k

z k ,
z j  Z ROOT



j 1
z*k  
k 1
k
Z
z j ,  z j  Z ROOT
 ROOT  
j 1
j 1

efficiency of root pumping
weighted by the layer depth
Definition of qSKIN at current time t
Air specific humidity over wet leaves
qLEAF  q1  maxqSAT  q1 , 0 EEVTR
 CWj
j
Air specific humidity over bare soil and pools (ZG is the surface wetness)
 q1 1  Z G 
q SOIL  q SAT Z G
ZG 

1

 S C D F1 q MAX  min(q MAX , q1G )
1
S  A
18.0
F2 
 .5,
b
F2
179.4


, F1  max .01,
 14.85 ,
b


1.75
T
 S  A  2.3 105  SKIN 
T0 

qSKIN 
coefficient of molecular
diffusivity of vapor into air


*
*
 fWETL qSAT  ( 1  fWETL )qLEAF   1  f SNOW  fVEG
f SNOW qSAT  fVEG
qSOIL
Atmospheric vertical diffusion
q1
Updated specific humidity at first atmospheric level
S CD
Updated drag coefficient of humidity and temperature (over land only)
 q  S CD qSKIN  q1 
Turbulent flux of specific humidity (kg/m2/s) positive upward


1  ( RV
/ Rd  1 ) qSKIN 
 S C D VSKIN  1V
H 
 P0

 PS



Rd
CP
Turbulent flux of heat (Watt/m2) positive upward
CP
Humidity flux disaggregation using the updated value of q1
Flux over snow in kg/m2/s
 SNOW  min( S C D f SNOW qSAT  q1  ,
W H SNOW / t )
Flux over the fraction of wet leaf
*
 qSAT  q1   min(  S C D fVEG
fWETL qSAT  q1  , WVEG / t
  
WETL 
*

qSAT  q1 
 S C D fVEG
 qSAT  q1  
Evapotranspiration from the fraction of dry leaf and from the k-th soil layer (kg/m2/s)
 q SAT
 EVTRK 
 q SAT
W

C
*
k
 q1    S C D fVEG 1  fWETL  q LEAF  q1 
C Wj
 

 q1  
j

0

Humidity flux over the fraction of bare soil and pools (it conserves water exactly).
 SOIL   q
  SNOW
 WETL
   EVTR k
k






) 


Residual precipitation and WVEG update
Precipitation intercepted by leaves (it can be negative)
MAX
*
PINTC  min((WVEG
 WVEG ) / t  WETL , PRAIN fVEG
)
WVEG update
WVEG  WVEG  t PINTC  t WETL
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)
PRES  PRAIN  PINTC
TSKIN : soil temperature at the upper interface from flux balance
Surface heat exchange coefficient 1
 2
H SNOW
z1 
G

K G  f SNOW ( K SNOW  K G ) ,
1  min
G CG  W CW q1  W C I

2 t 
z1
 z1
Numerical limitation
K G  0.5  1400e
 6 log10 
,
L  LVW  f SNOW LW
I ,

q MAX
  G 
 min(q G , q
1
MAX



) 
b
thermal diffusivity of ground
 H  1( TSKIN  T1G ) (heat flux from the ground)

 H ( TSKIN )  L q ( TSKIN )  VIS
 IR ( TSKIN )   H ( TSKIN )  R
dqSKIN
dT  q   S C D
,
dTSKIN
dT  H  C P  S C D ,
d T IR  4 0TSKIN 3
n1
n1

n1
n1
 H ( TSKIN
)  Lq ( TSKIN
)  VIS
 IR ( TSKIN
)   H ( TSKIN
)0
Newton step
R  ( dT  H  LdT q  dT IR  1 )TSKIN  0



Snow height update
H SNOW  H SNOW
t

( PSNOW   SNOW )
W
TSNOW  TSKIN  ( 1   )T1G ,
1-Fall-Sublimation
  1 / 2 (melting parameter)


C
max(
T

273
.
15
,
0
)
I
SNOW

H SNOW  H SNOW min1,
W


LI


PMELT  W H SNOW / t
(Kg/m2/s)
2-Melting
H SNOW  H SNOW  H SNOW
f SNOW  min1, H SNOW / H REF 
3-Snow fraction update
Water flux and content update of the first soil layer (m3/m3)
1   PRES  PMELT   SOIL  k 1  EVTR k
q1G ( t  t )  q1G ( t ) 
z1

W KW b
2  
G 
q
q MAX
 MAX
G
q2
q1G1 / 2
 k  2  EVTR k ,
q1G ( t  t )  qMIN




b2
Kg/m2/s
t
 1   2 
W z1
min(q MAX , q1G
q1G1 / 2
)  q2G
.5( z1  z 2 )
 W KW


q
 MAX
q1G1 / 2




2b  3
z1q2G  z 2 min(q MAX , q1G )

z1  z 2

z1W G

q1 ( t )  qMIN
  1 
  2
t
G

q1 ( t  t )  qMIN


Flux correction
Water flux and content update of the second soil layer (m3/m3)
2
q2G ( t
 t ) 
q2G ( t
t
  2   3 
)
W z 2
 q2G1 / 2 
W KW b

3  
G 
q

q MAX
 MAX 
 k 3  EVTRk ,
q2G ( t
 t )
 qMIN
 qMAX
b2
q2G1 / 2
q2G
 q3G
.5 ( z 2  z3 )
 W KW
 q2G1 / 2 


q

 MAX 
2b  3
z 2 q3G  z3 q2G

z 2  z3


z 2W  qMIN
G

 q2 ( t ) 
 3   2 

t  q MAX

 
qMIN
G

q2 ( t  t ) 

q MAX

Flux
correction
Internal heat exchange coefficients
K G  0.5  1400e
 6 log10 
,
 q MAX
  G  G
q
 11 / 2




b

H SNOW
z1 
2
G

 2  min
KG ,
 G CG  W CW q1  W C I

2t 
z1
 z1  z 2
K G  0.5  1400e
 6 log10 

2
 3  min
KG ,
 z 2  z3
,

 q MAX
  G  G
q
 21 / 2
G
C


C
q
G G
W W 2







b
 2z t 
2

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).
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

G CG z1

 W CW q1G z1  W C I H SNOW T1G   PMELT LWI t
 PRES tCW ( T1  T1G )  PSNOW tCI ( T1  T1G )
 1( TSKIN  T1G )t   2 ( T2G  T1G )t
  2 tCW ( T1G1 / 2  T1G )  PMELT CW ( 273.15  T1G )t



  (  SOIL    EVTRk )CW   SNOW C I  ( TSKIN  T1G )t
k


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 temperature TSKIN

T2G tendency

G
G
C

z


C
q

z

T
G G
2
W W 2
2
2 
  2 ( T1G  T2G )t   3 ( T3G  T2G )t
  2 tCW ( T1G1 / 2  T2G )   3 tCW ( T2G1 / 2  T2G )
Final temperature update
TkG  TkG  TkG ,
k  1, 2, 3
Runoff



t
1

Orography

R  min1,


1800


q1G ( t  t )  qMAX


q1G  q1G  R q1G  qMAX
