Reveal the hidden meaning of an index

Question

I am an GIS coordinator currently working with satellite data which we use to present ecological maps. The satellite images which we get given are usually some sort of index which has various meanings to the trained individual for example the "Vegetation Condition Index" or the "Normalized Difference Vegesation Index".

Healthy vegetation (chlorophyll) reflects more near-infrared (NIR) and green light compared to other wavelengths. But it absorbs more red and blue light.

The indices themselves are relatively simply formulas, but my question is - What mathematical characteristic is created by this algebraic formula which makes it useful?

e.g. NDVI = (NIR — VIS)/(NIR + VIS)

there are 2 variables NIR (near infrared and VIS = visible red). For arguments sakes, we will let NIR = 50 and VIS = 75. So -25/100 = -25. What does this tell me?

other indices include:https://www.indexdatabase.de/db/i.php

ps. my choice of tag was random - I have no ideas even if this question is viable

Answer 1

Call $\text{NIR + VIS}$ the $\text{TOTAL}$ amount of light (at least - the total amount of light we are interested in for this measurement). Then we can write the index as $$\text{NDVI } = \ \frac{\text{NIR }-\text{ VIS}}{\text{TOTAL}} = \frac{\text{NIR}}{\text{TOTAL}}-\frac{\text{VIS}}{\text{TOTAL}}$$

Now $\text{rNIR }=\ \frac{\text{NIR}}{\text{TOTAL}}$ is the ratio (if multiplied by 100, the percentage) of the total light coming in which is in the NIR range, while $\text{rVIS }=\ \frac{\text{VIS}}{\text{TOTAL}}$ is the ratio of light coming in which is in the VIS range.

These are relative measures. If the total amount of light shining on the area changes (say because the sun is now shining at a different angle than it was a few hours ago), then both $\text{NIR}$ and $\text{VIS}$ will change, but $\text{rNIR}$ and $\text{rVIS}$ should not (or at least, not nearly as much - there is a lot going on in the real world that isn't captured in this simple model).

This makes the relative measures more useful than an absolute measure, since you cannot control how much total light is shining on the area.

Note that because $\text{NIR}$ and $\text {VIS}$ are both positive values, and each can be no higher than $\text{TOTAL}$, we must have $0 \le \text{ rNIR } \le 1$ and $0 \le \text{ rVIS } \le 1$. So $\text{NDVI } = \text{ rNIR } - \text{ rVIS}$ takes on values between $-1$ and $1$. A value of $-1$ indicates all the light is in the VIS range, while a value of $1$ indicates all the light is in the NIR range. When $\text{NDVI } = 0$, half the light is in each range.

Whoever set up this index preferred to have a negative value when visible light was greater the near infrared, and positive when near infrared was greater than visible light. But this was a personal choice. $\text{rNIR}$ by itself gives the same information content. It just ranges from $0$ to $1$ instead of from $-1$ to $1$.

The key things that make this index useful are:

• It varies over a fixed range ($-1$ to $1$).
• It is independent (mostly) of the total illumination of the area.
• It increases in value when NIR light increases faster than VIS light.

This allows you to compare the index values for different regions obtained under different lighting conditions, and still have some hope that the comparison means something.