LIBERTY
Leaf Incorporating Biochemistry Exhibiting Reflectance and Transmittance Yields


Introduction

LIBERTY is a general purpose radiative tranfer model for predicting the reflectance and transmittance spectra of a leaf, or stack of leaves in the visible and near infrared wavelengths (400 - 2500 nm). By treating a leaf as an aggregation of cells, with multiple radiation scattering between cells, output spectra is a function of three structural parameters and the combined absorption coefficients of leaf biochemicals. It is simple to use with the user being prompted for input values and the model output is written to an external file for use with graphing and spreadsheet packages as well as for coupling with vegetation canopy or ecosystem models. The code is in C and has been incorporated into the 5-Scale model.

LIBERTY for Windows can use external data files instead of the defaults. This allows the user to easily provide new absorption coefficients:
 

PIGMENT.DAT 
Absorption coefficient of in-vivo chlorophylls and carotenoids

ALBINO.DAT 
Absorption coefficient of dried albino leaf due to lignin (visible wavelengths)

WATER.DAT 
Water absorption coefficient

LIGCELL.DAT 
Combined absorption coefficient of lignin and cellulose

PROTEIN.DAT 
Protein absorption coefficient
 
Model inputs

 
Variable
Description
Typical values 
(and range)
Cell Diameter
Average leaf cell diameter (m-6)
40 (20 - 100)
Intercellular air space
Determinant for the amount of  radiative flux passing between cells 
0.045 (0.01 - 0.1)
Leaf thickness
Arbitrary value to determine single leaf reflectance and transmittance from infinite reflectance criteria
1.6 (1 - 10)
Baseline absorption
Wavelength independent absorption to compensate for changes in absolute reflectance
Fresh: 0.0006
Dry: 0.0004
Albino absorption
Absorption in the visible region due to lignin
2 (0 - 4)
Chlorophyll content
Chlorophyll (pigment) content (mg.m-2)
200 (0 - 600)
Water content
Water content (g.m-2)
100 (0 - 500)
Lignin and Cellulose content
Combined lignin and cellulose content (g.m-2)
40 (10 - 80)
Nitrogen content
Nitrogen content (g.m-2)
1 (0.3 - 2.0)
Model Output

LIBERTY produces a space delimited text file, example as below:
W R refl trans
400 0.029629 0.029592 0.035535
405 0.030031 0.029991 0.036120
 ...
2500 0.517565 0.414745 0.394991
The first column is the wavelength, second column is the predicted spectra for infinite reflectance as demonstrated by stacked leaves, and the third and fourth column is the predicted single leaf reflectance and transmittance spectra, respectively.

Notes

LIBERTY has been developed specifically for conifer needles so you will find the facility to estimate single leaf reflectance and transmittance spectra from stacked needles particularly useful. However, the program is equally valid for any leaf species with a minor caveat; The in-vivo absorption coefficients used were determined from empirical work on various pine species so you may need to re-calibrate variable values for other vegetation types.