# Appendix S1. A brief description of the model of solar radiation

```Appendix S1. A brief description of the model of solar radiation transmission through the canopy.
Solar radiation (S0) was separated into diffuse (Sd0) and direct beam components (Sb0) as described in
Leuning et al. (1995) [31]:
S d 0  f d  S0
(1)
Sb 0  (1  f d )  S 0
(2)
where fd is the fraction of diffuse radiation. S0 was observed, and fd was estimated using a segmented
function of atmospheric transmissivity (τa) [57]:
1


f d  1  2  a  0.3

0.2

 a  0.3
for 0.3   a  0.7
for
 a  0.7
for
(3)
where τa was estimated using;
 a  S0  Sc  sin  

(4)

Sc  1367 1  0.033cos 2  td  10  / 365
(5)
where td is Julian day; Sc is solar radiation; β is solar altitude (°) and sinβ can be calculated as:
sin   a  b  2 (th  12) / 24
(6)
where th is solar time, and the a and b parameters can be calculated using functions 7 to 11:
a  sin l  sin  s
(7)
b  cos l  cos  s
(8)
sin  s   sin(23.5 /180)  cos 2 (td  10) / 365
(9)
where λl is latitude and δs is solar declination.
The Q varied with canopy location; therefore, the Q of each canopy layer was calculated separately.
Qd 0  f d  Q0
Qb0  1  f d   Q0
(10)
(11)
where Qd0 and Qb0 represent the diffusion and direct radiation components of the observed Q0,
respectively, and 1 W∙m-2 (S0) =2 μmol∙m-2 s-1 (Q0) [31]. Shaded leaves receive diffuse radiation only, and
sunlit leaves receive diffuse and direct beam radiation. The Q absorbed by shaded (Qsh) and sunlit leaves
(Qsl) was calculated as:
Qsh ( )  Qld '( )  Qlbs ( )
(12)
Qsl ( )  Qlb ( )  Qsh ( )
(13)
In equation (12), ξ is cumulative leaf area index from the top canopy; Qld′ and Qlbs represent the incident
diffuse and scattered beam radiation, respectively, which are related to the extinction coefficient for
radiation and the leaf area index (LAI) [58-59]. In equation (13), Qlb represents absorbed beam radiation
[31]. Qld′ and Qlbs were calculated as:
Qld '( )  Qd 0  kd ' (1  cd )  exp(kd '  )
(14)
Qlbs ( )  Qb0 kb ' (1  cb )  exp(kb '  )  kb  (1   l )  exp(kb   )
(15)
where ρcb is the canopy reflection coefficient for direct radiation, which can be calculated with the
canopy reflection coefficient for horizontal leaves (ρh) using equation (16) [58]. ρcd is the canopy
reflection coefficient for diffusion radiation, with values of 0.057 and 0.389 for visible and near-infrared
light, respectively, when diffusion radiation is uniformly distributed in a canopy with spherical leaf angle
distribution [31, 59]. kd′ and kb′ represent the canopy extinction coefficient of diffusion and direct beam
radiation, respectively, calculated using kb and kd in equations (17)-(18):
cb  1  exp  2  h  kb  1  kb  
(16)
kd '  kd  1   l 
(17)
kb '  kb  1   l 
(18)
1/2
1/2
In equation (16), ρh can be calculated as:
1  1   l 
1/2
h 
1  1   l 
1/2
(19)
In equations (17)-(18), kb and kd represent the extinction coefficients of direct beam and diffusion
radiation, respectively, in an ideal canopy where a leaf is viewed as a “black body”. σl is the scattering
coefficient (σl= 0.2 for visible light; σl= 0.8 for near-infrared radiation). Goudriaan and Van Laar (1994)
reported that kd is approximately 0.8 for spherical leaf angle distributions [59]. kb is a function of β as
follows:
kb  0.5 sin 
(20)
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