Radiative Transfer Modeling with PROSAIL¶

Fabian Fassnacht

Radiative transfer modeling with PROSAIL¶

Overview¶

In this tutorial we will get to know the PROSAIL radiative transfer model for vegetation surfaces. This model is available in R and we will learn how to conduct some forward simulations with it. Radiative transfer models like PROSAIL summarize the current knowledge about the interaction between the electromagnetic radiation in the wavelengths from 400 to 2500 nm and vegetation. They are an interesting tool for scientific studies, but also for understanding better how certain plant traits influence the reflective properties of vegetation.

In today’s theoretical part you already learned a bit more about PROSAIL and in case you are interested in an even more detailed explanation of its functionalities, I have uploaded a comprehensive Review-paper on PROSAIL (Jacquemoud et al. 2009) to ILIAS. This review was written by the main developers of the model.

Learning objectives¶

The learning objectives of this Tutorial include:

running PROSAIL in forward mode
understanding how the plant traits implemented in PROSAIL influence the reflective properties of vegetation
understanding NDVI much better

Datasets used in this Tutorial¶

We do not use any external datasets in this tutorial.

Step 1: Running PROSAIL in forward mode¶

To run PROSAIL in forward mode, we will first have to download and install a package called “hsdar”. We can accomplish this by running:

library(hsdar)

If the package hsdar is not yet installed on your system, run the following command:

install.packages("hsdar")

We can then have a closer look at the help page of the main function of the hsdar package which is called “PROSAIL”.

?PROSAIL

If you read through the function-call you will see that it is actually quite straightforward to simulate a spectrum using the PROSAIL function. You basically only have to define values for all of the plant traits and additionally for the sun-sensor geometry and run the function. In case you do not specify all traits, default values will be used for the remaining undefined traits.

Now we are already ready to run a first PROSAIL simulation. For this, we have to define the vegetation traits within the PROSAIL function:

# simulate simple vegetation spectrum
veg_spectrum = spectra(PROSAIL(LAI=7, Cab = 40, Car=10, Cw = 0.1, Cm = 0.005, N=2, TypeLidf = 2, lidfa = 55))

As you an see, we call the PROSAIL function, nested in another function called spectra. This function directly extracts the resulting spectrum from the speclib-object that is created by the PROSAIL function. These speclib-objects contain a lot more detailed information about the function call etc. and it would also be possible to directly plot these objects. However, using the spectra-function will give us some advantages for some of the other plots that will follow below and we hence already introduce this approach here. To plot the spectrum, we run the following code:

plot(400:2500, veg_spectrum[1,], type="l", ylab="reflectance", xlab="wavelength [nm]", ylim=c(0,0.5), xlim=c(400,2500))
grid()

One important thing to consider is, that the variable veg_spectrum is only containing the reflectance values (plotted on the y-axis) while the corresponding wavelengths are not available anymore after applying the spectra function. We hence have to know in this case, that PROSAIL simulates the reflectance of the vegetation layer with the defined traits for the wavelengths between 400 and 2500 nm (at steps of 1 nm). We can then plot the reflectance values in the veg_spectrum variable over the wavelengths by providing a sequence (400:2500) as x-values in the plot.

You can now play around a bit with this simple way of calling PROSAIL and check how the spectrum changes if you change one or more of the vegetation traits during the call of the PROSAIL-function.

Step 2: Examining the influence of individual traits on the PROSAIL signal¶

The hsdar package provides a nice tools to simulate several spectra at the same time. To make use of this tool, we have to define a dataframe in which value ranges for all of the to be varied plant traits are stored. In the example below, we will only vary a single parameter and leave the remaining parameters at their default value.

For this, we first create a dataframe called parameter in which we add one column named “LAI” and in which we store 10 different values for the LAI parameter:

# simulate and plot multiple vegetation spectra
#define parameter space
parameter <- data.frame(LAI = seq(1,5, length.out=10))
parameter

        LAI
1  1.000000
2  1.444444
3  1.888889
4  2.333333
5  2.777778
6  3.222222
7  3.666667
8  4.111111
9  4.555556
10 5.000000

It is of course als possible to vary more than one parameter at the same time. To see how this works, please have a look at the help of the “PROSAIL” function. In our case we will now call the PROSAIL function again and make use of the additional parameter “parameterList” which we will set to the just created dataframe named “parameter”:

veg_spectra = spectra(PROSAIL(parameterList = parameter))

This will results in a total of 10 spectra. We will then plot all of these spectra, one after the other, using a for-loop:

# plot spectrum
plot(400:2500, ylab="reflectance", xlab="wavelength [nm]", ylim=c(0,0.5), xlim=c(400,2500))
for(i in 1:nrow(veg_spectra)){
  lines(400:2500, veg_spectra[i,])
}
grid()

This plot, hence shows how the spectra of vegetation change if the LAI of the vegetation changes. You can play around some more with this code to vary other plant traits and maybe to adjust the colors of the plot to understand which LAI value produces which curve.

Please use this part of code also to work on exercises 1 and 2 of today’s theoretical lecture. Remember that meaningful value ranges for all plant traits considered in PROSAIL are given in the powerpoint slides of today’s theoretical lecture.

Step 3: Simulating NDVI values with PROSAIL¶

In this last step of this short practical on radiative transfer models, we will first simulate a spectrum and then calculate the NDVI from the spectrum. Then, once we learned how to do this, your task is to work on exercise 3 of today’s theoretical lecture and try to find out some plant trait combinations that will produce NDVI values of 0.40, 0.60 and 0.80. Please also check whether you can find more than one trait combination that leads to these NDVI values and think about what this means in terms of using NDVI as a general and reliable vegetation proxy.

First, we calculate a spectrum:

# simulate and calculate NDVI
veg_spectrum_1 = spectra(PROSAIL(LAI=5, Cab = 25, Car=10, Cw = 0.05, Cm = 0.005, N=2, TypeLidf = 2, lidfa = 55))[1,]

To visualize the locations of the two bands from which NDVI is calculated, we define the wavelength of the NIR (900nm) and RED (650nm) band. In both cases we substract 399, as the spectra simulated by PROSAIL start at a wavelength of 400 nm and to hence later select the correct bands, we will have to substract 399:

nir_band = 900-399
red_band = 650-399

Next, we plot the spectrum and add the positions of the NDVI bands to the plot. For the plots, we actually add the 399 again - I hope it is clear to everyone why:

plot(400:2500, veg_spectrum_1, type="l", ylab="reflectance", xlab="wavelength [nm]", ylim=c(0,0.5), xlim=c(400,2500), lwd=2)
grid()
abline(v=nir_band+399, lty=2, col="darkred", lwd=2)
abline(v=red_band+399, lty=2, col="red", lwd=2)

We can now easily also calculate the NDVI by running the following code:

ndvi_1 = (veg_spectrum_1[nir_band] - veg_spectrum_1[red_band]) / (veg_spectrum_1[nir_band] + veg_spectrum_1[red_band])

To check the NDVI value of the simulated spectrum we run:

round(ndvi_1,2)

[1] 0.87

Now try to apply what you have just learned about the effects of the traits considered in PROSAIL on the simulated vegetation spectra to adjust the spectra in a way that they reach the following three NDVI values: 0.20; 0.40; and 0.80. In the next class we will compare the parameter values that each of you found to reach these NDVI values and discuss whether they are matching and what this means.

With this we are already at the end of today’s short excursion into the world of radiative transfer models. I hope that all of you see the benefits of using such models for better understanding how certain plants traits affect the reflectance of electromagnetic radiation in different wavelengths. You can maybe imagine that these models can be a very powerful tool when combined with high quality and fine spectral resolution remote sensing data which allow for an inversion of the models as we discussed at the end of today’s theoretical lecture.