2. Running PROSPECT in inverse mode: iterative optimization

Jean-Baptiste Féret, Florian de Boissieu

2020-09-23

1 Running prospect in inverse mode: generalities

PROSPECT can be inverted using iterative optimization, by calling the function Invert_PROSPECT. This iterative optimization is based on the function fmincon included in the package pracma.

By default, the merit function used for the inversion minimizes the RMSE between the simulated and the measured leaf optical properties. However, users can define their own merit function with associated criterion to minimize by defining their own merit function and adding it as input variable, such as MeritFunction = MyOwnMeritFunction.

The results of inversion will also depend on the prospect version, i.e. on the parameters included in the prospect model. The following table shows the correspondance between prospect versions and prospect parameters. Each parameter can be considered as parameter to estimate or a fix value in the model, depending on the apriori knowledge.

Version 5 5B D DB PRO PROB
CHL
CAR
ANT
BROWN
EWT
LMA
PROT
CBC
N

1.1 Input variables

The function Invert_PROSPECT requires either reflectance, or transmittance, or both. User can define which input variables of PROSPECT should be estimated during inversion, and which ones should be set to a given value (0 or user’s choice). The list of input variables for inversion is :

1.2 Output variables

Invert_PROSPECT returns a list containing estimated values of PROSPECT input parameters

1.3 Run PROSPECT-D inversion over the full spectral domain

All parameters are estimated, except alpha and BROWN which are set to their default value.

1.4 Run PROSPECT-D inversion over the VNIR domain

All parameters are estimated, except alpha and BROWN which are set to their default value. The same optical properties as previous example are used.

1.5 Run PROSPECT-D inversion over the VNIR domain with LMA and EWT value set

Only pigments and N are estimated. The same optical properties as previous example are used.

1.6 Run PROSPECT-D inversion over the SWIR domain between 1700 nm and 2400 nm

EWT, LMA and N are estimated. The same optical properties as previous example are used.

2 Invert PROSPECT-D using the optimal configuration for the estimation of leaf constituents

The function Invert_PROSPECT_OPT automatically sets the optimal spectral domains during inversion for all constituents to be estimated.

Optimal spectral domains and configuration are defined in Féret et al. (2019), Féret et al. (2020), and Spafford et al. (2020, submitted).

N does not need to be part of Parms2Estimate, as it is automatically estimated when needed.

# define set of parameters to be estimated
Parms2Estimate  = c('CHL','CAR','ANT','EWT','LMA')
# define initial values for the inversion (should not impact final results)
InitValues <- data.frame(CHL=40, CAR=8, ANT=0.1, BROWN=0, EWT=0.01, LMA=0.01, N=1.5)
# call Invert_PROSPECT_OPT in order to automaticall get optimal estimation of leaf parameters following latest published results
ParmEst <- Invert_PROSPECT_OPT(SpecPROSPECT=SpecPROSPECT, lambda=LRT_D$wvl, Refl = LRT_D$Reflectance,Tran = LRT_D$Transmittance,
                               PROSPECT_version = 'D',Parms2Estimate = Parms2Estimate,
                               InitValues = InitValues)

2.0.1 run PROSPECT-PRO inversion

Such definition of optimal spectral domains can also be set manually. For example, here is how to estimate proteins from leaf optical properties using the optimal spectral domain defined in Féret et al. (2019).

Please note that N needs to be added to Parms2Estimate, if user want it to be estimated during the inversion, otherwise it will be set to its default value.