Vegetation Science 2a - experiments using the Kuusk canopy reflectance model

In this practical, you will run a series of experiments using the Kuusk Canopy Reflectance model. The model uses prospect to simulate leaf-scale scattering, and embeds this in a model of single- and multipl-scattering in a turbid medium canopy. It also includes a semi-empirical method for accounting for clumping effects. The model therefore has all of the same parameters as for prospect, with the addition of canopy-scale parameters for a turbid medium (mainly: soil reflectance; Leaf Area Index (LAI); and Leaf Angle Distribution (an elliptical model)) as well as the clumping term.

First of all, you should read the man page for kuusk to familiarise yourself with the model parameters.

Experiment 1: Sensitivity

The first experiment is a sensitivity analysis, similar to that run for prospect last week. As a start on this, a shell ksensitivity is provided. If you don't already have the file defaults.dat, you will need to download that as well to run the shell.

If you run this shell, it will output datasets and associated graphs on the sensitivity of spectral reflectance at a given viewing/illumination geometry for sensitivity at a particular 'location' in parameter space. The data (& graphs) output include information on the sensivity of single-scattered radiation and multiply-scattered radiation.

As you run the shell, note down the regions of high and low sensitivity to the various parameters (1: LAI; 2: soil brightness; 3: Clumping; 4: leaf eccentricity; 5: Leaf N; 6: Leaf Dry Matter; 7: proportion of Senescence; 8 Chlorophyll; 9: Leaf water) and how they are manifested (is the impact on 1st-order scattering or multiple scattering or both?). Try to explain the sensitivities you observe, using what you know of how terms affect the 1st order scattering of this model.

To test whether these effects are consistent accross the range os parameter space, you should vary the 'base' parameters used in the sensivity analysis. You can do this by changing the lines of code looping over the parameters (such as foreach LAI).

You should also investigate how the sensitivities change with variations in viewing or illumination angles. You can do this by changing the values assigned to the variables vza (View Zenith Angle); sza (Solar Zenith Angle); and saa (Solar Azimuth Angle). The View Azimuth Angle is set to 0^o. All angles are in degrees.

Experiment 2: Vegetation Indices

In the next experiment, you should investigate using vegetation indices to define relationships with biophysical parameters. The shell kratios should form the basis of your experiments. By default, it calculates NDVI (NIR 800 nm; red 650 nm) as a function of LAI for fixed values of other model parameters.

You can change the behaviour of the shell by modifying the parameters near the start of the file. Here, you can change the wavebands for which you calculate the vegetation index (b1, b2). You can also change: the number of samples to be used in developing the relationship (nSamples) and the number of random samples generated (nReplicates) [N.B. this is 1 by default: you will need to increase it (e.g. 25) if you randomise any variables]; which parameter you want to form a relationship with (relationParam); any parameters you want to set to fixed values (fix gives the parameter index and fixValue the value the parameter will be fixed to). You can also change the viewing and illumination parameters as above. Parameters that are not 'fixed' are randomised over $nReplicates (e.g. 25) instances. You can also adjust the parameter 'L', which changes the NDVI calculation performed here into a SAVI relationship (see below).

By default, you will see that most of the parameters have been fixed, so that you are only seeing a VI as a function of LAI here, showing a 'clean' relationship between the VI and this parameter. The shell displays two graphs: one showing the relationship between the VI and the parameter of interest; the other giving a scatter plot of reflectance in the two bands chosen. Use the scatter plot to explain the variation in the VI relationship. If the VI relationship saturates, why is this? Could you get around it by chosing a different wavelength?

For each test that you run, you should attempt to fit a parameterised empirical model to the relationship you see. The 'goodness of fit' of this relationship will give you information on the uncertainty that might arise from using the relationship. To see how to fit a model, follow this link.

Using your knowledge of the sensitivity of reflectance at the wavelengths chosen to the other parameters, start to introduce the other parameters into the variation and examine their impact on uncertainty in the relationship. You might, for instance, introduce soil brightness variations (remove the terms refering to this in fix and fixValue) - what impact does that have? (Hint: examining the scatterplot should tell you most about this: think about how NDVI isolines lie in this space). One way of overcoming soil reflectance variations is to introduce a 'soil-adjusted VI' such as SAVI:

SAVI = (1+L)(NIR-red) / (NIR+red+L)

So, L=0 is the same as NDVI. A value of L = 0.5 is typically used. What effect does the parameter L have on the VI isolines? Does it improve things here? Could you give a better value of L for this case? (Hint: you don't have to re-run the whole shell to re-calculate a VI: columns 3 & 4 of the output file are band 1 & band 2 reflectance).

You will also notice that the parameter VI is set to "NDVI" in the shell. If you change this to "RATIO", then a band ratio is calculated:

RVI = (NIR-L)/red

Initially setting L = 0 (a standard band ratio) see if you can get a more stable relationship between the VI and LAI than that obtained using NDVI. Does changing the value of L have any impact? [Hint can you guess a suitable value of L in this case from the scatterplot?]

As you introduce variation due to other model parameters into the relationship, ask yourself which parameters introduce the most variation and why might that be so? [consider sensitivity].

By the time you have re-introduced variation to all model parameters, the relationship can become rather imprecise. Can you come up with any stategies to improve this situation?

Experiment 3: Red Edge

If you have time, you can explore tracking the red edge position of canopy reflectance with the shell krededge. The shell is very similar to those used above. Define a set of sensible experiments to explore whether red edge tracking is any more reliable than using vegetation indices.

4. Write Up

Follow the format suggested for last week's write up.

5. Follow up reading

Price, J., (1990), On the information Content of Soil Reflectance Spectra, Rem. Sens. Env., 33:113-121.

Nilson, T., and Kuusk, A., (1989), A reflectance model for the homogeneous plant canopy and its inversion, Rem. Sens. Env., 27:157-167.

Jaquemoud, S Kuusk, A., (1995), A Markov-chain Model Of Canopy Reflectance, Agricultural And Forest Meteorology, 76(3-4), 221-236

Kuusk, A., (1995), A Fast, Invertible Canopy Reflectance Model, Rem. Sens. Env. , 51(3), 342-350

Kuusk, A., (1994), A Multispectral Canopy Reflectance Model, Rem. Sens. Env. ,50(2), 75-82

Fourty, T, Baret, F, Jacquemoud, S, Schmuck, G, Verdebout, J, (1996), Leaf Optical-properties With Explicit Description Of Its Biochemical-composition - Direct And Inverse Problems, Remote Sensing Of Environment, Vol.57, No.3, P.185

Jacquemoud, S, Ustin, Sl, Verdebout, J, Schmuck, G, Andreoli, G, Hosgood, B, ((1996), Estimating Leaf Biochemistry Using The Prospect Leaf Optical Properties Model, Remote Sensing Of Environment, 1996, Vol.56, No.3, Pp.194-202

Jacquemoud, S, Baret, F, Andrieu, B, Danson, Fm, Jaggard, K, (1995), Extraction Of Vegetation Biophysical Parameters By Inversion Of The Prospect Plus Sail Models On Sugar-beet Canopy Reflectance Data - Application To TM And AVIRIS Sensors, Remote Sensing Of Environment, 1995, Vol.52, No.3, Pp.163-172

Baret, F, Vanderbilt, Vc, Steven, Md, Jacquemoud, S, (1994), Use Of Spectral Analogy To Evaluate Canopy Reflectance Sensitivity To Leaf Optical-properties, Remote Sensing Of Environment, 1994, Vol.48, No.2, Pp.253-260