RTMs

Radiative transfer models for soil, leaf and canopy.

Soil

BSM(soilpar, spec, emp)

Spectral parameters

Leaf

fluspect_B_CX()

function [leafopt] = fluspect(spectral,leafbio,optipar) calculates reflectance and transmittance spectra of a leaf using FLUSPECT, plus four excitation-fluorescence matrices

Authors: Wout Verhoef, Christiaan van der Tol (c.vandertol@utwente.nl), Joris Timmermans, Nastassia Vilfan Date: 2007-2020 Update from PROSPECT to FLUSPECT: January 2011 (CvdT)

Nov 2012 (CvdT) Output EF-matrices separately for PSI and PSII

31 Jan 2013 (WV) Adapt to SCOPE v_1.40, using structures for I/O 30 May 2013 (WV) Repair bug in s for non-conservative scattering 24 Nov 2013 (WV) Simplified doubling routine 25 Nov 2013 (WV) Restored piece of code that takes final refl and

tran outputs as a basis for the doubling routine

03 Dec 2013 (WV) Major upgrade. Border interfaces are removed before

the fluorescence calculation and later added again

23 Dec 2013 (WV) Correct a problem with N = 1 when calculating k

and s; a test on a = Inf was included

01 Apr 2014 (WV) Add carotenoid concentration (Cca and Kca) 19 Jan 2015 (WV) First beta version for simulation of PRI effect 20 Jan 2021 (CvdT) Include PROSPECT-PRO coefficients

usage: [leafopt] = fluspect_b(spectral,leafbio,optipar)

inputs: Cab = leafbio.Cab; Cca = leafbio.Cca; V2Z = leafbio.V2Z; % Violaxanthin - Zeaxanthin transition status

[0-1]

Cw = leafbio.Cw; Cdm = leafbio.Cdm; Cs = leafbio.Cs; N = leafbio.N; fqe = leafbio.fqe;

nr = optipar.nr; Kdm = optipar.Kdm; Kab = optipar.Kab; Kca = optipar.Kca; KcaV = optipar.KcaV; KcaZ = optipar.KcaZ; Kw = optipar.Kw; Ks = optipar.Ks; Kp = optipar.Kp; Kcbc = optipar.Kcbc; phi = optipar.phi; outputs: refl reflectance tran transmittance Mb backward scattering fluorescence matrix, I for PSI and II for PSII Mf forward scattering fluorescence matrix, I for PSI and II for PSII

fluspect_B_CX_PSI_PSII_combined()

Canopy

RTMf(constants, spectral, rad, soil, leafopt, canopy, gap, angles, etau, etah)

function ‘RTMf’ calculates the spectrum of fluorescent radiance in the observer’s direction and also the TOC spectral hemispherical upward Fs flux

Authors: Wout Verhoef and Christiaan van der Tol (c.vandertol@utwente.nl.nl) Date: 12 Dec 2007 Update: 26 Aug 2008 CvdT small correction to matrices

07 Nov 2008 CvdT changed layout

Update: 19 Mar 2009 CvdT major corrections: lines 95-96,

101-107, and 119-120.

Update: 7 Apr 2009 WV & CvdT major correction: lines 89-90, azimuth

dependence was not there in previous verions (implicit assumption of azimuth(solar-viewing) = 0). This has been corrected

Update: May-June 2012 WV & CvdT Add calculation of hemispherical Fs

fluxes

Update: Jan-Feb 2013 WV Inputs and outputs via structures for

SCOPE Version 1.40

Update: Aug-Oct 2016 PY Re-write the calculation of emitted SIF

of each layer. It doesnt use loop at all. with the function bsxfun, the calculation is much faster

Update: Oct 2017-Feb 2018 PY Re-write the RTM of fluorescence Update: Jan 2020 CvdT Modified to include ‘lite’ option,

mSCOPE representation

Update: 25 Jun 2020 PY Po, Ps, Pso. fix the problem we have with the oblique angles above 80 degrees

RTMo(spectral, atmo, soil, leafopt, canopy, angles, constants, meteo, options)

calculates the spectra of hemisperical and directional observed visible

and thermal radiation (fluxes E and radiances L), as well as the single and bi-directional gap probabilities

the function does not require any non-standard Matlab functions. No changes to the code have to be made to operate the function for a particular canopy. All necessary parameters and variables are input or global and need to be specified elsewhere.

Authors: Wout Verhoef (w.verhoef@utwente.nl)

Christiaan van der Tol (c.vandertol@utwente.nl) Joris Timmermans ()

updates: 10 Sep 2007 (CvdT) - calculation of Rn

5 Nov 2007 - included observation direction

12 Nov 2007 - included abs. PAR spectrum output

• improved calculation efficiency

13 Nov 2007 - written readme lines 11 Feb 2008 (WV&JT) - changed Volscat

(JT) - small change in calculation Po,Ps,Pso

• introduced parameter ‘lazitab’

• changed nomenclature

• Appendix IV: cosine rule

04 Aug 2008 (JT) - Corrections for Hotspot effect in the probabilities 05 Nov 2008 (CvdT) - Changed layout 04 Jan 2011 (JT & CvdT) - Included Pso function (Appendix IV)

• removed the analytical function (for checking)

02 Oct 2012 (CvdT) - included incident PAR in output

Jan/Feb 2013 (WV) - Major revision towards SCOPE version 1.40:

• Parameters passed using structures

• Improved interface with MODTRAN atmospheric data

• Now also calculates 4-stream reflectances rso, rdo, rsd and rdd analytically

Apri 2013 (CvT) - improvements in variable names

and descriptions

Dec 2019 CvdT mSCOPE representation, lite option

Table of contents of the function

0. Preparations

0.1 parameters 0.2 initialisations

1. Geometric quantities

1.1 general geometric quantities 1.2 geometric factors associated with extinction and scattering 1.3 geometric factors to be used later with rho and tau 1.4 solar irradiance factor for all leaf orientations 1.5 probabilities Ps, Po, Pso

2. Calculation of upward and downward fluxes

3. Outgoing fluxes, hemispherical and in viewing direction, spectrum

4. Net fluxes, spectral and total, and incoming fluxes A1 functions J1 and J2 (introduced for stable solutions) A2 function volscat A3 function e2phot A4 function Pso

references:

{1} Verhoef (1998), ‘Theory of radiative transfer models applied in

optical remote sensing of vegetation canopies’. PhD Thesis Univ. Wageninegn

{2} Verhoef, W., Jia, L., Xiao, Q. and Su, Z. (2007) Unified optical -

thermal four - stream radiative transfer theory for homogeneous vegetation canopies. IEEE Transactions on geoscience and remote sensing, 45,6.

{3} Verhoef (1985), ‘Earth Observation Modeling based on Layer Scattering

Matrices’, Remote sensing of Environment, 17:167-175

Usage: function [rad,gap,profiles] = RTMo(spectral,atmo,soil,leafopt,canopy,angles,meteo,rad,options)

The input and output are structures. These structures are further specified in a readme file.

Input:

spectral information about wavelengths and resolutions atmo MODTRAN atmospheric parameters soil soil properties leafopt leaf optical properties canopy canopy properties (such as LAI and height) angles viewing and observation angles meteo has the meteorological variables. Is only used to correct

the total irradiance if a specific value is provided instead of the usual Modtran output.

rad initialization of the structure of the output ‘rad’ options simulation options. Here, the option

‘calc_vert_profiles’ is used, a boolean that tells whether or not to output data of 60 layers separately.

Output:

gap probabilities of direct light penetration and viewing rad a large number of radiative fluxes: spectrally distributed

and integrated, and canopy radiative transfer coefficients.

profiles vertical profiles of radiation variables such as absorbed

PAR.

RTMt_planck(spectral, rad, soil, leafopt, canopy, gap, Tcu, Tch, Tsu, Tsh)

function ‘RTMt_sb’ calculates total outgoing radiation in hemispherical direction and total absorbed radiation per leaf and soil component. Radiation is integrated over the whole thermal spectrum with Stefan-Boltzman’s equation. This function is a simplified version of ‘RTMt_planck’, and is less time consuming since it does not do the calculation for each wavelength separately.

Authors: Wout Verhoef and Christiaan van der Tol (c.vandertol@utwente.nl) date: 5 Nov 2007 update: 13 Nov 2007

16 Nov 2007 CvdT improved calculation of net radiation 27 Mar 2008 JT added directional calculation of radiation 24 Apr 2008 JT Introduced dx as thickness of layer (see parameters) 31 Oct 2008 JT introduced optional directional calculation 31 Oct 2008 JT changed initialisation of F1 and F2 -> zeros 07 Nov 2008 CvdT changed layout 16 Mar 2009 CvdT removed Tbright calculation

Feb 2013 WV introduces structures for version 1.40

04 Dec 2019 CvdT adapted for SCOPE-lite 17 Mar 2020 CvdT mSCOPE representation

Table of contents of the function

0 preparations

0.0 globals 0.1 initialisations 0.2 parameters 0.3 geometric factors of Observer 0.4 geometric factors associated with extinction and scattering 0.5 geometric factors to be used later with rho and tau 0.6 fo for all leaf angle/azumith classes

1 calculation of upward and downward fluxes 2 total net fluxes Appendix A. Stefan-Boltzmann

usage: [rad] = RTMt_sb(constants,rad,soil,leafbio,canopy,gap,Tcu,Tch,Tsu,Tsh,obsdir,spectral)

Most input and output are structures. These structures are further specified in a readme file. The temperatures Tcu, Tch, Tsu and Tsh are variables.

Input:

constants physical constants rad a large number of radiative fluxes: spectrally distributed

and integrated, and canopy radiative transfer coefficients

soil soil properties leafopt leaf optical properties canopy canopy properties (such as LAI and height) gap probabilities of direct light penetration and viewing Tcu Temperature of sunlit leaves (oC), [13x36x60] Tch Temperature of shaded leaves (oC), [13x36x60] Tsu Temperature of sunlit soil (oC), [1] Tsh Temperature of shaded soil (oC), [1]

Output:

rad a large number of radiative fluxes: spectrally distributed

and integrated, and canopy radiative transfer coefficients. Here, thermal fluxes are added

RTMz(constants, spectral, rad, soil, leafopt, canopy, gap, angles, Knu, Knh)

function ‘RTMz’ calculates the small modification of TOC outgoing radiance due to the conversion of Violaxanthin into Zeaxanthin in leaves

Author: Christiaan van der Tol (c.vandertol@utwente.nl) Date: 08 Dec 2016

17 Mar 2020 CvdT added cluming, mSCOPE representation 25 Jun 2020 PY Po, Ps, Pso. fix the problem we have with the oblique angles above 80 degrees

RTMt_sb(constants, rad, soil, leafbio, canopy, gap, Tcu, Tch, Tsu, Tsh, obsdir, spectral)

function ‘RTMt_sb’ calculates total outgoing radiation in hemispherical direction and total absorbed radiation per leaf and soil component. Radiation is integrated over the whole thermal spectrum with Stefan-Boltzman’s equation. This function is a simplified version of ‘RTMt_planck’, and is less time consuming since it does not do the calculation for each wavelength separately.

Authors: Wout Verhoef and Christiaan van der Tol (c.vandertol@utwente.nl) date: 5 Nov 2007 update: 13 Nov 2007

16 Nov 2007 CvdT improved calculation of net radiation 27 Mar 2008 JT added directional calculation of radiation 24 Apr 2008 JT Introduced dx as thickness of layer (see parameters) 31 Oct 2008 JT introduced optional directional calculation 31 Oct 2008 JT changed initialisation of F1 and F2 -> zeros 07 Nov 2008 CvdT changed layout 16 Mar 2009 CvdT removed Tbright calculation

Feb 2013 WV introduces structures for version 1.40

04 Dec 2019 CvdT adapted for SCOPE-lite 17 Mar 2020 CvdT mSCOPE representation

Table of contents of the function

0 preparations

0.0 globals 0.1 initialisations 0.2 parameters 0.3 geometric factors of Observer 0.4 geometric factors associated with extinction and scattering 0.5 geometric factors to be used later with rho and tau 0.6 fo for all leaf angle/azumith classes

1 calculation of upward and downward fluxes 2 total net fluxes Appendix A. Stefan-Boltzmann

usage: [rad] = RTMt_sb(constants,rad,soil,leafbio,canopy,gap,Tcu,Tch,Tsu,Tsh,obsdir,spectral)

Most input and output are structures. These structures are further specified in a readme file. The temperatures Tcu, Tch, Tsu and Tsh are variables.

Input:

constants physical constants rad a large number of radiative fluxes: spectrally distributed

and integrated, and canopy radiative transfer coefficients

soil soil properties leafopt leaf optical properties canopy canopy properties (such as LAI and height) gap probabilities of direct light penetration and viewing Tcu Temperature of sunlit leaves (oC), [13x36x60] Tch Temperature of shaded leaves (oC), [13x36x60] Tsu Temperature of sunlit soil (oC), [1] Tsh Temperature of shaded soil (oC), [1]

Output:

rad a large number of radiative fluxes: spectrally distributed

and integrated, and canopy radiative transfer coefficients. Here, thermal fluxes are added