Diffuse Light Interception

This subroutine calculates the interception factors for diffuse radiation for a canopy layer. It returns approximations for diffuse reflectance and transmittance factors and an approximation for diffuse radiation sources from interception of direct beam.

These calculations are done to get individual reflectance and transmittance factors for layers when these layers are relatively thick (DF > 0.1). Without these calculations, thicker layers cause errors in radiation penetration calculations (it is assumed that the probability of mutual shading within a layer is small). With this calculation thick layers (DF >= 1) can be used with negligible errors and the radiation calculations require much less computer time.

RETURNS:

  RLAYR(K)     	  Reflectance factor for diffuse radiation of a 
               	  layer. Subscripted by K for wavelength band.
               		
  TLAYR(K)     	  Transmittance factors for diffuse radiation of a 
               	  layer. Subscripted by K for wavelength band.

  SOURDN(K,IHR)   Source term for downward diffuse radiation for 
               	  the wavelength band K and IHR for one layer.
               		
  SOURUP(K,IHR)   Source term for upward diffuse radiation for
               	  the wavelength band K and IHR for one layer.

View definitions of variables used in this subroutine:

• in sequence encountered in subroutine
• in alphabetical order

Calculate EXPDIF

• Integrate Equation 4 over increments in zenith angle, WZ.
• Documentation says 90 intervals should be used for best accuracy. Currently only 9 are used (???)

Calculate TLAYR and RLAYR

To improve accuracy, we split the canopy layer into 10 sublayers and calculate the up and downward diffuse fluxes within sublayers following the strategy outlined by Norman (1979). Reflectances and transmittances are calculated based on the relative strength of these fluxes between layers.

• The non-interception factor for each sublayer is DIFSUB = EXPDIF**0.1 [70]

• The diffuse transmittance (TSUBL) and reflectance (RSUBL) for a sublayer are calculated from DIFSUB [75]

• Because leaf distribution is not purely horizontal (???), we must iteratively hone in on the upward and downward fluxes:
  1. From bottom to top, calculate the ratio of upward to downward flux for each sublayer (ADUM(J)) assuming there is no direct beam flux (i.e., D(K,LAYSP1) = 1).
     • We can do this because ADUM depends only on the ADUM from the layer below and TSUBL and RSUBL (which we have approximated) (see Eq 5).
     • ADUM(0) (the lower edge of the layer) is set to 0 for this first approximation. (???)
  2. From top to bottom,
     • calculate D from ADUM (Eq. 5)
     • calculate U = ADUM*D

• RLAYR(K) = U(K,11), TLAYR(K) = D(K,1)

Calculate SOURUP and SOURDN

Note that above (in bullet 1.) we assumed there was no direct beam flux into the layers when calculating RLAYR and TLAYR. However, a certain amount of direct beam flux will be converted into diffuse emission at each layer. We now consider this additional source of diffuse emission.

These sources for upward and downward diffuse radiation can be formulated as a layer property, in terms of the fraction of intercepted direct beam incident to that layer. However, since the amount of intercepted direct beam radiation depends on the solar zenith angle, the following calculations are carried out for each IHR and the variables derived in this routine are subscripted by K (for the wavelength band) and IHR. The calculations are only carried out for IHR's for which the solar zenith angle is less than 89.4 degrees and/or the contribution of direct beam radiation is greater than 1%.

Again we divide the layer into 10 sublayers for greater accuracy.

• Calculate DIRSUB - the fraction of direct beam radiation penetrating through a sublayer is calculated. [128]

• A first estimate for the direct radiation that is scattered downward into sublayer 10, SDNSUB(K,LAYSP1), and the direct radiation scattered upward out of sublayer 10, SUPSUB(K,LAYSP1), is obtained using the leaf transmittance and reflectance properties.

• Then, going from the top sublayer to the bottom, the fractions of scattered radiation passing each sublayer are compounded for the upward and the downward direction using DIRSUB as the non-interception factor.

• To approximate the total relative diffuse radiation fluxes in both directions, D and U from previous calculations are zeroed and recalculated:
  • DOWN is the total downward flux for each sublayer and is now calculated from the sublayer transmittance and reflectance factors plus the contribution of downward scattered radiation originating in direct beam radiation.
  • UP is the total upward flux for each sublayer and is calculated from sublayer reflectance and transmittance plus the contribution of upward scattered radiation originating in direct beam.
  • For all layers U is set to UP and D set to DOWN and the calculation is reiterated using the previously determined diffuse radiation reflectance and transmittance properties of the sublayer.
  • The convergence criterion is satisfied when for each layer, the difference between the pairs is less than 0.0001.

• Diffuse radiation fluxes out of the layer in the upward direction, SOURUP(K,IHR),is set to U of the topmost sublayer. Similarly, SOURDN(K,IHR), the diffuse radiation flux in the downward direction is set to D of the lowest sublayer.

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