1. A Brief Introduction to ET Estimate in the Community Land Model
The Community Land Model version 4.0 (CLM) [Lawrence et al., 2011; Oleson
et al., 2010] is the land-surface model portion of Community Earth System Model
version 1.0.3. CLM 4.0 examines biogeochemical and biogeophysical processes
through which terrestrial ecosystems affect and are affected by climate across a
variant of spatial and temporal scales. A detailed description of the model is given by
Oleson et al.[2010]. Here we show an index of ET estimation as follows.
In the case of a vegetated surface, the water vapor flux is calculated from an
iteration which stopped after one of the following two conditions is met: (1) two or
more steps have finished if the maximum vegetation temperature change is less than
0.01 K and the change in latent heat flux from vegetation is lower than 0.1 mm H2O
s-1 in two convergences inter, or (2) forty iterations have been carried out (Section
5.3.2 in Oleson et al.[2010]). The canopy water vapor flux is controlled by the water
stored on the canopy (Wcan, Section 7.1) at each time step, aerodynamic (ra, Section
5.1), leaf boundary layer (rb, Section 5.3.1) and stomatal (rs, Section 8.1) resistances,
and then updated from the change in vegetation temperature (Tveg, Section 5.3). The
saturation specific humidity at the vegetation temperature ( qTsatveg ) or the actual specific
humidity at the ground surface (qgrnd) is derived from the saturation vapor pressure
(Section 5.5) as a function of vegetation temperature (Tveg, Section 5.3) or ground
temperature (Tgrnd, i.e., the temperature of the top sown/soil layer, Section 6.1).
Moreover, the soil water factor (βsoi, Section 5.2) in the calculation of the water vapor
flux from ground is an empirical function of the soil water content (Section 7.4).
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2. Supporting Information for ET Estimate in the Dynamic Land Model
The
Dynamic
Land
Model
(DLM)
is
an
update
version
of
the
remote-sensing-based ecosystem-atmosphere simulation scheme (EASS) released by
Chen et al. [2007]. DLM is a half-hourly time-step model with sunlit-shaded leaf
stratification strategy and multiple soil layers that provide a framework for different
plant functional types to exchange resources (radiation, heat flux, water and carbon).
At the leaf level, water vapor flux is calculated from an iteration which terminated
after the leaf temperature change is less than 0.02 K, or after the number of cycles is
greater than twenty-two. The transpiration estimated on the basis of the
Penman-Montith equation is controlled by the radiation absorbed by canopy (Eqs. (S8)
and (S10)), aerodynamic (Eq. (S1)) and stomatal (rs, Eq. (S25)) resistances. The
evaporation of precipitation intercepted by the sunlit or shaded leaf is calculated by
changing rs to 0. The evaporation from the ground is estimated by replacing the rs
with the ground surface resistance (rgrnd) as a function of the soil moisture (Eq. (S30)),
and by replacing the radiation absorbed by canopy with that absorbed by ground (Eqs.
(S9) and (S11)).
Here, we give the derivations needed to obtain equations for calculating the
evaporation and transpiration. In this notation, the subscripts sun and sha denote sunlit
and shaded leaves, reactively, the subscripts can and grnd denotes canopy and ground,
respectively, the superscript dir is incident direct beam radiation above canopy,
including visible (vis) and near-infrared (nir) waveband, and dif is diffuse radiation.
2
2.1 Aerodynamic Resistance and Leaf Boundary Layer Resistance
The aerodynamic resistance above the canopy (ra, in s m-1) is affected by
observational height of wind (hwind, in m), zero plane displacement height (d, in m),
roughness length (z0, in m), friction velocity ( u* , in m s-1) and the von Karman
constant (0.41). The terms d and z0 depend on height of the canopy (ztop, in m),
defined by d  0.8 ztop . ra is within the range of 2 to 100 s m-1. It is given by :
ra 
ln  hwind  d  z0   0.5  hwind  d   L
k  u*
(S1)
with
u* 
uk
ln  ztop  d  z0 
L
and
(S2)
u gH
 2.0
atm  C p  Tair  u*3
(S3)
where u is the observed wind speed above canopy (in m s-1), g is the gravitational
constant (9.806 m s-2), H is the sensible heat flux above the canopy (in W m-2), and
was initialized with 0 W m-2. This value is updated after recalculation of H for the
sunlit and shaded leaves.
The aerodynamic resistance of the ground surface ( ragrnd , in s m-1) is :
ragrnd 
 exp    exp   ztop   ra .
  kh 
ztop
(S4)
The leaf boundary layer resistance (rb, in s m-1) is :
rb  0.5  0.1   Nu
(S5)
with
  18.9  0.07 Tair  273.15  106 and
(S6)
3
Nu  Re 0.5
(S7)
where Nu and Re are the Nusselt and Reynold’s number, respectively.
2.2 Radiation Flux
Sunlit and shaded leaf irradiances are important variables for computing sunlit
and shaded leaf photosynthesis rates and net radiation of layers. The total solar
irradiance above the plant canopy is first partitioned into direct and diffuse irradiance
( S dir  and S dif  , in W m-2). The direct beam (Sdir, in W s-1) and diffuse (Sdif, in W
s-1) radiation are both absorbed by canopy and ground with effects from albedos
(α),with the fractional area of sun-flecks on a horizontal plane below the leaf area LAI:
dir
Scan
 S dir   1  0.5  vis   nir   exp  0.5   LAI  
(S8)
dir
vis
nir
S grnd
 S dir   1  0.5  grnd
  grnd
  exp  0.5   LAI  
(S9)
dif
Scan
 S dif   1  0.5  vis   nir   exp  0.5   LAI q  
0.21 S dir   1.1  0.1LAI   exp    
dif
vis
nir
S grnd
 S dif   1  0.5  grnd
  grnd
  exp  0.5   LAI q  .
(S10)
(S11)
Active radiation absorbed by sunlit and shaded leaves ( Ssun and Ssha ) are both
affected by shortwave and longwave radiation absorbed by canopy (Scan and Lcan),
which are used in leaf temperature estimation:
dir
Scan
Lcan

LAI sun LAI  SAI
(S12)
dif
Scan
Lcan


.
LAI sha LAI  SAI
(S13)
S sun 
S sha
The absorbed photosynthetically active radiation (PAR) averaged for the sunlit
and shaded leaf are:
sun   R dir  R dif  1   can 
(S14)
4
sha  Rdif 1  can 
(S15)
with
R dir 
R
dif
0.5  S dir 
(S16)



S dif   1  exp  0.5    LAI  SAI  q 

.
LAI  SAI
 0.07 S dir   1.1  0.1  LAI  SAI    exp    
(S17)
2.3 Photosynthesis and Stomatal Resistance
Photosynthesis in C3 plants is based on the Farquhar model [Collatz et al., 1991].
The photosynthesis (A, in μ mol CO2 m-2 s-1) of sunlit and shaded leaf are all
determined from A  min  wc ,w j ,we   Rd .
The Rubisco limited rate of carboxylation (wc, in μ mol CO2 m-2 s-1) is:
wc 
Vcmax   ci  * 
ci  K c
(S18)
with
Vcmax  Vcmax 25 f Tleaf  f  N  t f  DYL 
* 
(S19)
0.5  CCO2
f T 
2904.12  e leaf
(S20)
o 

K c  kc 1  i 
 ko 
(S21)
where Vcmax is the maximum rate of arbonxylaiton , Γ* is CO2 compensation point (in
Pa), ci is the internal leaf CO2 partial pressure (in Pa), Kc is the Michaelis-Menten
constant for CO2.
The light-limited rate of carboxylation (wj, in μ mol CO2 m-2 s-1) is dependent on
PAR absorbed by the sunlit or shaded leaf (Eq. (S17) or (S18)) and light-saturated rate
5
of electron transport (Jmax):
wj 
 c  * 
J max  PPFD
 i
PPFD  2.1J max ci  2  *
(S22)
with
PPFD  4.55q25
J max  J max 25 f Tleaf
(S23)

(S24)
where PPFD is the photosynthetic photon flux density, q25 is the quantum efficiency at
25˚C. The export limited rate of carboxylation (we, in μ mol CO2 m-2 s-1) is
we  0.5Vc max .
The sunlit and shaded leaf stomatal resistance (rs, in μ mol m-2 s-1) are all
calculated from the Ball-Woodrow-Berry model:
1
A es
m
 gs0
rs
cs ei
(S25)
in which photosynthetic rate (A, in μ mol CO2 m-2 s-1) is adjusted for environmental
variables, including the vapor pressure at the leaf surface (es, in Pa), the saturation
vapor pressure (ei, in Pa) inside the leaf at the vegetation temperature and the CO2
partial pressure at the leaf surface(cs, in Pa), gs0 and m are the minimum (residual)
conductance (in μ mol-1 m2 s) and the slope of the photosynthesis-conductance
relationship, respectively.
2.4 Leaf Temperature
n
Sunlit or shaded leaf temperature ( Tleaf
, in K) is updated on the base of the leaf
n 1
temperate from previous time step ( Tleaf
) and its change ( Tleaf ):
n
n 1
Tleaf
 Tleaf
 Tleaf
(S26)
6
Tleaf 
sat
S   eair
 eair   p *   atm  c p
 Gh    p   
*
atm
(S27)
 cp
where S is total solar radiation absorbed by sunlit or shaded leaves drive from Eq.
sat
(S15) or (S16), eair
and eair are the saturated and the actual air water vapor
pressure (in Pa), respectively, atm is the density of moist air ( in kg m-3), cp is the
specific heat of air at a constant pressure (in J kg-1 k-1), Gh is the heat conductance
for leaf (in m s-1),  is the slope of the saturated vapor pressure-temperature curve (in
k Pa K-1), p * is the heat conductance factor for water on leaf (W m-2 K-1). Using the
two-leaf up-scaling approach, the vegetation temperature at the time n is given by:
n
n
Tveg  Tleaf
, sun LAI sun  Tleaf , sha LAI sha .
(S28)
2.5 Soil/Snow Temperatures and Soil Moisture
We adopted same formulas as that in CLM4.0 yield soil/snow temperature, and
soil moisture (Sections 6.1 and 7.4 in Oleson et al.[2010]). The second law of heat
conduction in one dimensional form is solved numerically to calculate the soil and
snow temperate for a fifteen-layer soil column with up to five overlying layers of
snow with the boundary condition of the heat flux into the snow/soil surface from the
overlying atmosphere:
c
Ts   Ts 
 

t z  z 
(S29)
where c is the volumetric soil heat capacity (in J m-3 K-1), t is time (in s), λ is thermal
conductivity (in W m-1 K-1), Tsoil z is the spatial gradient of soil or snow
temperature (in K m-1), z is in the vertical direction (in m) and is positive downward.
The top soil/snow layer is taken as the ground surface.
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The soil moisture distribution is derived from a modified Richards equation
[Lawrence et al., 2011; Zeng and Decker, 2009]:
       E   
 k 
  Q
t z  
z
 
(S30)
where θ is the volumetric soil water content (in mm3 of water mm-3 of soil), k is the
hydraulic conductivity (in mm s-1 ), ψ is the soil matric potential, ψE is the equilibrium
soil matric potential (in mm), and Q is a soil moisture sink term representing soil
water losses due to transpiration (in mm of water mm-1 of soil s-1).
References
Chen, B., J. M. Chen, and W. Ju (2007), Remote sensing-based ecosystem–atmosphere simulation
scheme (EASS) -- model formulation and test with multiple-year data, Ecological Modelling,
209(2-4), 277-300.
Collatz, G. J., J. T. Ball, C. Grivet, and J. A. Berry (1991), Physiological and environmental
regulation of stomatal coductance, photsynthesis and transpiration: a model that includes a
laminar boudary layer, Agricultural and Forest Meteorology, 51, 109-136.
Lawrence, D. M., et al. (2011), Parameterization improvements and functional and structural
advances in version 4 of the Community Land Model, Journal of Advances in Modeling
Earth Systems-Discussion, 3, M03001, 03027 pp., doi:03010.01029/02011MS000045.
Oleson, K. W., et al. (2010), Technical Description of version 4.0 of the Community Land Model
(CLM), National Center for Atmospheric Research, Boulder, Colorado.
Zeng, X., and M. Decker (2009), Improving the numerical solution of soil moisture - based
Richards equation for land models with a deep or shallow water table, Journal of
Hydrometeorology, 10(1), 308-319.
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