foursail {ccrtm} R Documentation

## Optimized R implementation of foursail (4SAIL)

### Description

The foursail (or 4SAIL) radiative transfer model is commonly used to simulate bidirectional reflectance distribution functions within vegetation canopies. Foursail (4SAIL) refers to "Scattering by Arbitrary Inclined Leaves" in a 4-stream model. The four-streams represents the scattering and absorption of upward, downward and two directional radiative fluxes with four linear differential equations in a 1-D canopy. The model was initially developed by Verhoef (1984), who extended work by Suits (1971) 4-steam model.

### Usage

```foursail(rho, tau, bgr, param)
```

### Arguments

 `rho` input leaf reflectance from 400-2500nm (can be measured or modeled) `tau` input leaf transmittance from 400-2500nm (can be measured or modeled) `bgr` background reflectance. Usual input is soil reflectance spectra from 400-2500nm (can be measured or modeled) `param` A named vector of SAIL parameter values (note: program ignores case):  = Leaf angle distribution function parameter a (LIDFa)  = Leaf angle distribution function parameter b (LIDFb)  = Leaf angle distribution function type (see ?lidfFun)  = Leaf area index (LAI)  = Hot spot effect parameter (hspot)  = Solar zenith angle (tts)  = Observer zenith angle (tto)  = Sun-sensor azimuth angle (psi)

### Value

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

•  = bi-hemispherical reflectance (rddt). White-sky albedo: the reflectance of the canopy under diffuse illumination. The BRDF integrated over all viewing and illumination directions.

•  = hemispherical directional reflectance (rsdt). Black-sky albedo: reflectance of a surface under direct light without a diffuse component. It is the integral of the BRDF over all viewing directions.

•  = directional hemispherical reflectance (rdot). Diffuse reflectance in the vieweing direction.

•  = bi-directional reflectance (rsot). The ratio of reflected radiance in the viewing direction to the incoming radiant flux in the solar direction.

•  = Canopy transmission of diffuse light through the canopy (taud).

•  = transmission of direct light through the canopy (taus).

### References

Suits, G.H., 1971. The calculation of the directional reflectance of a vegetative canopy. Remote Sens. Environ. 2, 117-125.

Verhoef, W. (1984). Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model. Remote Sens. Environ. 16, 125-141.

### Examples

```## lower-level implementation example
## see ?fRTM for the typical mode of simulation
## e.g. fRTM(rho~prospectd+foursail)

## 1) get parameters
params<-getDefaults(rho~prospectd+foursail)
## getDefaults("foursail") will also work
bestpars<-params\$foursail\$best
## ensure the vector is named
names(bestpars) <- rownames(params\$foursail)

## 2) get leaf reflectance and transmission
rt<-fRTM(rho+tau~prospectd)

## 3) get soil reflectance to model background reflectance
data(soil)

## a linear mixture soil model
bgRef<- bestpars["psoil"]*soil[,"drySoil"] + (1-bestpars["psoil"])*soil[,"wetSoil"]

## 4) run 4SAIL
foursail(rt[,"rho"],rt[,"tau"],bgRef,bestpars)

```

[Package ccrtm version 0.1.6 Index]