foursail2 {ccrtm}R Documentation

R implementation of the foursail2 model with 2 canopy layers.


The foursail2 model is a two layer implementation of the foursail model described in Verhoef and Bach (2007). Layers are assumed identical in particle inclination and hotspot, but may differ in the relative density and types of particles (see foursail2b for a layer specific inclination angle). In comparison to foursail, the background (soil), can now be non-Lambertain, having it own 4-stream BDRF (not implemented here but may be input by the user). There are two types of particles, generalized to primary and secondary (originally termed "green" and "brown" particles). The realtive abundance of the secondary particle in the top canopy is regulated by the dissociation paramerter.The model 4SAIL2 combines with prospect, libery or procosine for the reflectance and transmittance of the particles, and with the the foursail or Hapke elements for the background reflectance. If run alone, these require direct inputs which could be measured leaf reflectance.


foursail2(rhoA, tauA, rhoB = NULL, tauB = NULL, bgr, rsobgr = NULL,
  rdobgr = NULL, rsdbgr = NULL, rddbgr = NULL, param)



primary particle reflectance from 400-2500nm (can be measured or modeled)


primary particle transmittance from 400-2500nm (can be measured or modeled)


secondary particle reflectance from 400-2500nm (can be measured or modeled)


secondary particle reflectance from 400-2500nm (can be measured or modeled)


background reflectance. Usual input is soil reflectance spectra from 400-2500nm (can be measured or modeled)


: background bidirectional reflectance (rso)


: background directional hemispherical reflectance (rdo)


: background hemispherical directional reflectance (rsd)


: background bi-hemispherical diffuse reflectance (rdd)


A named vector of 4SAIL2 parameter values (note: program ignores case):

  • [1] = Leaf angle distribution function parameter a (LIDFa)

  • [2] = Leaf angle distribution function parameter b (LIDFb)

  • [3] = Leaf angle distribution function type (TypeLidf, see ?lidfFun)

  • [4] = Total Leaf Area Index (LAI), including primary and secondary particles (brown and green leafs).

  • [5] = fraction secondary particles ("brown leaf fraction", fb)

  • [6] = Canopy dissociation factor for secondary particles ("diss")

  • [7] = Hot spot effect parameter (hspot). Often defined as the ratio of mean leaf width and canopy height.

  • [7] = vertical crown coverage fraction (Cv), models clumping in combination with parameter zeta.

  • [7] = tree shape factor (zeta), defined as the ratio of crown diameter and height.

  • [6] = Solar zenith angle (tts)

  • [7] = Observer zenith angle (tto)

  • [8] = Sun-sensor azimuth angle (psi)


spectra matrixwith 4 reflectance factors and canopy transmission for wavelengths 400 to 2500nm:


Verhoef, W., Bach, H. (2007). Coupled soil-leaf-canopy and atmosphere radiative transfer modeling to simulate hyperspectral multi-angular surface reflectance and TOA radiance data. Remote Sens. Environ. 109, 166-182.


## see ?foursail for lower-level implementations

[Package ccrtm version 0.1.6 Index]