Supplementary material to: ‘A multi-level
canopy radiative transfer scheme for
ORCHIDEE (SVN r2566), based on a
domain-averaged structure factor’
November 14, 2016
(McGrath M.J., Ryder J., Pinty B., Otto J., Naudts K., Valade A.,
Chen Y., Weedon J. and Luyssaert S.)
S1
List of Figures
S1
S2
S3
S4
S5
Two level fluxes of transmission (TRAN), total albedo (ALB),
top of the canopy (CAN ALB) and absorption by the soil
(SOIL ABS) as a function of the one level results for broad
wide range of input parameters (see table 2). Different fluxes
are represented by different colours. This figure corresponds
to the REAL dataset (Table 2 in the main text defines the
range of input values of each dataset). The equivalent plot for
the ALL dataset is Figure 4 in the main text. . . . . . . . . .
Signed differences for various canopy fluxes of transmission
(TRAN), total albedo (ALB), top of the canopy (CAN ALB)
and absorption by the soil (SOIL ABS), between the two level
results and the one level results (φ2 − φ1 ) as a function of the
one level results for a broad range of input parameters. This
figure corresponds to the REAL dataset (Table 2 in the main
text defines the range of input values of each dataset). The
equivalent plot for the ALL dataset is Figure 3 in the main text.
Signed difference for various canopy fluxes of transmission
(TRAN), total albedo (ALB), top of the canopy (CAN ALB)
and absorption by the soil (SOIL ABS), between the two level
results and the single level results (φ2 − φ1 ) as a function of
the fraction of LAI in the top level for a broad range of input parameters. This figure corresponds to the REAL dataset
(Table 2 in the main text defines the range of input values
of each dataset). The equivalent plot for the ALL dataset is
Figure 4 in the main text. . . . . . . . . . . . . . . . . . . . .
Marginal values of each of the independent input variables
against the fraction of points for which the absolute difference
single
multi
-αcollim
), is less than 0.01 (red), 0.02 (green) and
of (αcollim
0.03 (orange) for the 10 level multi-layer model, and below
0.01 (blue) for the 2 level multilevel model. . . . . . . . . . . .
Marginal values for each of the independent input variables
against nsteps , the total number of iterations required to arrive
at a solution, for the ALL dataset, for 2 level model (blue)
and the 10 level model (red). . . . . . . . . . . . . . . . . . . .
S2
S4
S5
S6
S7
S8
S6
S7
Marginal values of each of the independent input variables
against the fraction of points for which the absolute difference
single
multi
of (αcollim
-αcollim
), is less than 0.01 for the REAL value dataset
(blue), and the ALL value dataset (red). . . . . . . . . . . . . S9
Marginal values for each of the independent input variables
against nsteps , the total number of iterations required to arrive
at a solution for the REAL value dataset (blue), and the ALL
value dataset (red). . . . . . . . . . . . . . . . . . . . . . . . . S10
S3
Figure S1: Two level fluxes of transmission (TRAN), total albedo (ALB),
top of the canopy (CAN ALB) and absorption by the soil (SOIL ABS) as
a function of the one level results for broad wide range of input parameters
(see table 2). Different fluxes are represented by different colours. This figure
corresponds to the REAL dataset (Table 2 in the main text defines the range
of input values of each dataset). The equivalent plot for the ALL dataset is
Figure 4 in the main text.
S4
Figure S2: Signed differences for various canopy fluxes of transmission
(TRAN), total albedo (ALB), top of the canopy (CAN ALB) and absorption
by the soil (SOIL ABS), between the two level results and the one level results (φ2 − φ1 ) as a function of the one level results for a broad range of input
parameters. This figure corresponds to the REAL dataset (Table 2 in the
main text defines the range of input values of each dataset). The equivalent
plot for the ALL dataset is Figure 3 in the main text.
S5
Figure S3: Signed difference for various canopy fluxes of transmission
(TRAN), total albedo (ALB), top of the canopy (CAN ALB) and absorption
by the soil (SOIL ABS), between the two level results and the single level
results (φ2 − φ1 ) as a function of the fraction of LAI in the top level for
a broad range of input parameters. This figure corresponds to the REAL
dataset (Table 2 in the main text defines the range of input values of each
dataset). The equivalent plot for the ALL dataset is Figure 4 in the main
text.
S6
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frac. of (αmulti − αsingle) > specified limit
2 levels (< 0.01)
10 levels (< 0.01)
10 levels (< 0.02)
10 levels (< 0.03)
c)
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b)
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fLAI(LAI frac. in top half of canopy)
Figure S4: Marginal values of each of the independent input variables against
single
multi
the fraction of points for which the absolute difference of (αcollim
-αcollim
), is
less than 0.01 (red), 0.02 (green) and 0.03 (orange) for the 10 level multi-layer
model, and below 0.01 (blue) for the 2 level multilevel model.
S7
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number of iterations (nsteps)
2 levels
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b)
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a)
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SZA (Solar Zenith Angle) (°)
0.0
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0.4
0.6
0.8
1.0
fLAI(LAI frac. in top half of canopy)
Figure S5: Marginal values for each of the independent input variables
against nsteps , the total number of iterations required to arrive at a solution, for the ALL dataset, for 2 level model (blue) and the 10 level model
(red).
S8
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frac. of (αtwo − αsingle) > 0.01
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wl (single scattering albedo)
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REAL value set
ALL value set
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fLAI(LAI frac. in top half of canopy)
Figure S6: Marginal values of each of the independent input variables against
single
multi
the fraction of points for which the absolute difference of (αcollim
-αcollim
), is
less than 0.01 for the REAL value dataset (blue), and the ALL value dataset
(red).
S9
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REAL value set
ALL value set
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0.0
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fLAI(LAI frac. in top half of canopy)
Figure S7: Marginal values for each of the independent input variables
against nsteps , the total number of iterations required to arrive at a solution for the REAL value dataset (blue), and the ALL value dataset (red).
S10
List of Tables
1
Table of the contribution from each input variable to the desingle
multi
viance in the value of (αcollim
- αcollim
), the difference of the
collimated albedo for the multi-level and for the single level
model, and of the contribution of each input variable to the
deviance in the value of nsteps , the total number of iterations
required to reach a result in the multi-level model. Same data
is displayed in Figures 5 and 6, in the main text . . . . . . . . S12
S11
Table 1: Table of the contribution from each input variable to the deviance
single
multi
- αcollim
), the difference of the collimated albedo for
in the value of (αcollim
the multi-level and for the single level model, and of the contribution of each
input variable to the deviance in the value of nsteps , the total number of
iterations required to reach a result in the multi-level model. Same data is
displayed in Figures 5 and 6, in the main text
2 levels
10 levels
single
single
multi
multi
) nsteps
(αcollim -αcollim ) nsteps (αcollim -αcollim
LAIef f
3.18e-2
2.43e-2
7.45e-4
5.59e-3
wl
2.87e-1
5.92e-1
4.43e-1
5.31e-1
Rbgd
3.07e-2
3.72e-2
1.31e-1
8.55e-2
dl
6.45e-3
1.96e-2
3.06e-3
3.09e-3
SZA
3.33e-2
5.44e-2
1.05e-3
7.62e-4
fLAI,tot
1.37e-1
1.80e-2
3.42e-2
4.04e-2
(LAIef f , wl )
3.31e-2
4.23e-2
6.22e-2
7.61e-2
(LAIef f , Rbgd )
1.24e-2
1.03e-2
3.35e-3
1.45e-3
(LAIef f , dl )
2.80e-4
9.75e-4
5.17e-6
3.43e-6
(LAIef f , SZA)
3.05e-3
6.26e-3
5.89e-5
1.18e-5
(LAIef f , fLAI,tot )
3.94e-2
4.97e-3
6.95e-4
4.02e-4
(wl , Rbgd )
3.04e-2
3.97e-2
1.92e-1
1.35e-1
(wl , dl )
4.24e-3
1.11e-2
3.16e-3
4.69e-3
(wl , SZA)
2.25e-2
2.38e-5
2.38e-5
2.95e-5
(wl , fLAI,tot )
1.22e-1
1.10e-2
1.88e-2
2.33e-2
(Rbgd , dl )
2.18e-3
3.80e-3
1.35e-3
7.27e-4
(Rbgd , SZA)
3.63e-5
5.88e-5
1.00e-4
4.62e-5
(Rbgd , fLAI,tot )
1.03e-2
1.31e-4
1.12e-2
1.70e-2
(dl , SZA)
2.27e-4
7.75e-4
5.06e-6
2.32e-6
(dl , fLAI,tot )
2.81e-3
6.63e-4
1.06e-4
1.62e-4
(SZA, fLAI,tot )
1.07e-2
5.01e-4
9.36e-5
5.98e-5
S12