Progress in the Understanding and
Improvement of the Community Land
Model at the University of Arizona
Xubin Zeng, Mark Decker,
Koichi Sakaguchi, Cindy Wang
Department of Atmospheric Sciences
University of Arizona
Contents and Conclusions
1. Soil moisture (SM) Richards equation
Comment: Numerical solution cannot maintain the steady state solution of the differential equation
Solution: Revised form of the Richards equation (Zeng and Decker 2008)
2. SM variability and water table depth (WTD)
Comment: CLM 3.5 has unrealistic vertical distribution of SM variability and its SM and WTD
incorrectly depend on grid structure
Solution: New and simple bottom condition (Decker and Zeng 2008)
3. Surface resistance (rs) and ground evaporation
Comment: CLM3.5’s rs improves simulations, but its formulation is inappropriate
Solution: Dead-leaf resistance and under-canopy turbulent stability (Sakaguchi and Zeng 08)
4. Soil ice fraction
Comment: Based on Noah, CLM3.5’s formulation is too sensitive to ‘B’ parameter
Possible Alternative: a new formulation (Decker and Zeng 2006)
5. Convergence of canopy roughness length (Zo)
Comment: Zo does not change for LAI from 0 to 7
Solution: A new formulation for this convergence (Zeng and Wang 2007)
6. Snow burial fraction
Comment: CLM3.5 does not distinguish snow over short veg. versus snow under trees
Solution: A new formulation (Wang and Zeng 2008)
1. Soil moisture (SM) Richards equation
Solution: revised form of the Richards equation
In the atmosphere: Vertical velocity equation:
dw 1 ∂p
=
−g
dt ρ ∂z
+ other terms
hydrostatic approximation:
1 ∂P
−g =0
ρ ∂z
In the soil: soil moisture-based Richards
equation:
∂θ ∂ ⎡ ∂ (ψ + z ) ⎤
=
K
−S
∂t ∂z ⎢⎣
∂z ⎥⎦
with a steady-state solution:
ψ (θ ) + z = ψ sat + z w
Deficiency: Numerical solution in CLM3.5 and other land
models cannot maintain this steady state solution of the
differential equation even for zero flux (top and bottom)
boundary conditions
Why was this not recognized in the past? Because free-drainage bottom
boundary condition is dominant.
Solution:
∂θ ∂ ⎡ ∂ (ψ + z ) ⎤
=
K
−S
∂t ∂z ⎢⎣
∂z ⎥⎦
ψ E ( z ) + z = ψ sat + z w
along with new bottom condition:
Compute θ(N+1) based on θE(z)
qs = -1,
1 mm/day
2. SM variability and water table depth (WTD)
Deficiency #1: CLM 3.5 has unrealistic vertical distribution
of SM variability
Our WTD computation:
−B
⎡θ E ( z ) ⎤
ψ sat ⎢
⎥ + z = ψ sat + z w
θ
⎣ sat ⎦
with mass conservation constraint:
the sum of soil moisture deficit from
all layers equals the integral of
θE(z) deficit.
Deficiency #2: CLM 3.5’s soil moisture
and WTD incorrectly depend on grid
structure
•WTD model domain dependent
Unsaturated
Saturated
•Physically Unrealistic: Soil Moisture
variability peaks in the 8th layer!
3. Surface resistance (rs) and ground evaporation
Comment: CLM3.5’s rs improves simulations, but its
formulation is inappropriate
Monthly average ground evaporation
Harvard forest (temperate) with BDT
Canada (boreal) with NET
Amazon KM83 with BET
AZ (desert) with C4 grass
CLM3.5 rs formulation: rsoil = (1 – fsno) exp(8.206 – 4.255 s1)
Two coefficients were obtained by best-fitting to observed data from
Konza Prairie and nearby pasture areas (Sellers et al., 1992)
Deficiency of the above rs formulation:
•
•
Over bare soil, rs is higher than ra,
independent of litter layer thickness
suggesting Eg is essentially independent
of ra, inconsistent with our understandings
Solution: Dead leaf resistance and turbulent
stability under canopy
Plant litter resistance
rlitter
(
1
=
1 − exp(− Leff
dl
0.004u*
)
no Rsoil
ctr(Rsoil)
ctr(Rsoil)+
Cs
Rlitter
Rlitter + Cs
Harvard forest
0.26
0.09
0.07
0.12
0.10
BOREAS SSA-Old Jack
0.27
0.21
0.17
0.19
0.15
Amazon KM83
0.10
0.09
0.07
0.08
0.06
Kendall
0.55
0.45
0.45
0.45
0.45
Leff
dl = Ldl [1 − min ( f snow,dl ,1)]
Turbulent stability under canopy
Cs = Cs ,bareW + Cs ,dense (1 − W )
C s ,dense =
RiB ' =
0.004
1 + 10 ⋅ min( RiB ' ,0.25)
gh(Ts − Tg )
Ts u*2
4. Soil Ice Fraction:
θ ice
θ total
Comments:
•Highly Sensitive to the B parameter
•Non-iterative Noah Formulation
•Semi-empirical formulation
New: Simple semi-empirical
formulation based on in-situ
observations
The new formulation increases ice fraction over high latitudes
5. Convergence of canopy roughness length (Zo)
Comment: Zo is independent of LAI
Solution: A new formulation for convergence
de = V d + (1 - V) dg
V = {1 - exp(-min(Lt,Lcr)]}/[1-exp(-Lcr)]
ln(Zoc,g) = V ln(Zoc) + (1 – V) ln(Zog)
with
bare soil dg = 0
Lcr = 2 (insensitive), and
Zog = ground (soil or snow) Zo
Cabauw daily
data in Jan
LH
SH
DJF
LH
JJA
LH
DJF
SH
JJA
SH
Using new formulations from (1)-(5)
New: 6m Range
Control: 2m Range
Global Simulation Results
Total Runoff
Control New
SH
0.91
NH
0.86
Global
0.87
Amazon
2.73
Siberia
0.60
0.98
0.83
0.88
3.05
0.61
Runoff Ration (srf/sub) Latent Heat
Control New
Control New
0.22
0.42
1.82
0.22
0.44
1.24
0.22
0.44
1.44
0.23
0.36
3.40
0.20
0.48
0.51
1.89
1.26
1.48
3.40
0.51
Transpiration / LH
Control New
0.41
0.40
0.39
0.40
0.40
0.40
0.47
0.46
0.54
0.55
•Surface Energy Fluxes very similar
•Increased Surface Runoff, Decreased
Subsurface Runoff
•Increase Ratio of Srf to Subsrf Runoff
to 0.44 from 0.22
•Increased Heterogeneity of WTD
•Control Run Has 5 m WTD over the
Sahara
•Increased WTD seasonal variability
6. Snow burial fraction
Comment: CLM does not distinguish snow over
short vegetation from snow under trees
Solution: A new formulation
In CLM vertical snow burial fraction
Fv,sno = (Zsno – Zbot)/(Ztop – Zbot)
Lt = Lt (1 – fv,sno)
Our new formulation for short
vegetation:
Fv,sno = min(Zsno,Zc)/Zc
with Zc = 0.02 m (insensitive)
DJF Average
Contents and Conclusions
1. Soil moisture (SM) Richards equation
Comment: Numerical solution cannot maintain the steady state solution of the differential equation
Solution: Revised form of the Richards equation (Zeng and Decker 2008)
2. SM variability and water table depth (WTD)
Comment: CLM 3.5 has unrealistic vertical distribution of SM variability and its SM and WTD
incorrectly depend on grid structure
Solution: New and simple bottom condition (Decker and Zeng 2008)
3. Surface resistance (rs) and ground evaporation
Comment: CLM3.5’s rs improves simulations, but its formulation is inappropriate
Solution: Dead-leaf resistance and under-canopy turbulent stability (Sakaguchi and Zeng 08)
4. Soil ice fraction
Comment: Based on Noah, CLM3.5’s formulation is too sensitive to ‘B’ parameter
Possible Alternative: a new formulation (Decker and Zeng 2006)
5. Convergence of canopy roughness length (Zo)
Comment: Zo does not change for LAI from 0 to 7
Solution: A new formulation for this convergence (Zeng and Wang 2007)
6. Snow burial fraction
Comment: CLM3.5 does not distinguish snow over short veg. versus snow under trees
Solution: A new formulation (Wang and Zeng 2008)