bRTM: Backward implementation (inversion) of coupled Radiative...

In MarcoDVisser/ccrtm: Coupled Chain Radiative Transfer Models

Backward implementation (inversion) of coupled Radiative Transfer Models.

Description

Backward implementation (inversion) of coupled Radiative Transfer Models.

Usage

bRTM(fm = rho ~ prospect5, data = NULL)

Arguments

fm	A formula specifying which rtm to run (see details).
data	(measured) reflectance spectra. Expected are reflectance values between 0 and 1 for wavelength between 400 and 2400 at 1 nm steps. The range 400 to 2400 is based on the largest common range in most leaf spectral datasets - and hence is a range that can be generated by most spectrometers.

Details

Formula: In general the form of the formula specifies the both the model and the data supplied (transmittance or reflectance), however, currently only reflectance data is expected (transmission not included yet).

Models: At current the following radiative transfer models are implemented for backward / inversion mode

Example of a formula	Model
rho ~ prospect5	prospect5
rho ~ prospectd	prospectd

Inversion is rapid, and based on emulation of prospect models by a multivariate neural net (MANN) and a partial least squares regression (PLSR) model. The two methods are selected as the performance of NN or PLSR differ for each inverted parameter - with one method outperforming the other depending on the parameter. The predictions are then combined using a linear Bayesian mixing model that weights the NN and PLSR prediction for each parameter - and includes an estimate of model inversion uncertainty.

Model inversion uncertainty estimates the 95% credible intervals under which the parameter will fall compared to a perfect inversion. Model inversion uncertainty arises due to parameter identifiability issues, and does not reflect the uncertainty in the data. Uncertainty in the data should be estimated with replicate measurements and standard statistical methods (not implemented).

Questions and requests can be made on the ccrtm github page.

Value

a list of inverted parameters and their 95% CI

Examples

## get reflectance for a single leaf on simulated spectra

## make a parameter list
parameters<-list(prospectd=c(N=3,Cab=40,Car=15,Cw=0.01,Cm=0.025,Canth=26,Cbrown=4))

## simulate spectra at the inversion requirements 
ref <- fRTM(rho~prospectd,pars=parameters,wl=400:2400)

## reorder with replicates measurements over rows, and make into matrix
refdata<-t(as.matrix(ref))

fit<-bRTM(rho~prospectd,data=refdata)
summary(fit)

## compare fit with simulation on log-scale so all parameter are visible
plot(parameters$prospectd,fit$mu,xlab="expected",ylab="inverted",pch=16,log="xy")

## add uncertainty
segments(parameters$prospectd,fit$lower.ci,
parameters$prospectd,fit$upper.ci,lwd=2)

## 1 to 1 line
abline(0,1)

## Inversion for multiple leaf spectra

## using lower-level vectorized prospect function
set.seed(1234)
## we simulate all spectra at once
nsim<-300 ## number of leaves

## random leaf parameters
parmat<-cbind(N=runif(nsim,1,6),
Cab=runif(nsim,5,80),
Car=runif(nsim,1,40),
Cw=runif(nsim,0.001,.02),
Cm=runif(nsim,0.002,0.03)+0.01,
Canth=runif(nsim,0,6),
Cbrown=runif(nsim,0,4)
)

## simulate with the lower level prospect for rapid simulation
## of many leaves
ref<-ccrtm:::.prospectdv(parmat)[[1]][,1:2001] ## subset to 400:2400 wl

## invert the simulations
fit<-bRTM(rho~prospectd,data=ref)
summary(fit)

## check inversion performace for LMA
plot(parmat[,"Cm"],fit$mu[,"Cm"],xlab="expected",ylab="inverted",pch=16)

## add uncertainty
segments(parmat[,"Cm"],fit$lower.ci[,"Cm"],
         parmat[,"Cm"],fit$upper.ci[,"Cm"],lwd=2)
abline(0,1)

## replace the simulated ref with measured reflectance over wavelengths 400:2400
## to invert for spectrometer data

MarcoDVisser/ccrtm documentation built on Feb. 19, 2025, 1:15 p.m.