A simple way to remember the NDVI range is that normalization ratios of the form \( \frac{A - B}{A + B} \) always constrain values between -1 and +1 when \( A \) and \( B \) are non-negative.
Step 1: Understanding the Concept:
The Normalized Difference Vegetation Index (NDVI) is a widely used remote sensing index that quantifies the health and density of vegetation.
It takes advantage of the unique spectral reflectance properties of green leaves, which absorb red light for photosynthesis and reflect near-infrared (NIR) light off their internal cell structure. Key Formula or Approach:
The mathematical equation used to calculate NDVI is:
\[
NDVI = \frac{NIR - Red}{NIR + Red}
\]
where:
\( NIR \) is the reflectance in the near-infrared band.
\( Red \) is the reflectance in the red visible band. Step 2: Detailed Explanation:
Let us analyze the range of this ratio mathematically:
Because spectral reflectance values are normalized between \( 0 \) and \( 1 \) (or \( 0\% \) and \( 100\% \)), the values of \( NIR \) and \( Red \) are always positive.
If a target absorbs all NIR light (\( NIR = 0 \)) and reflects all red light (\( Red > 0 \)), the formula becomes:
\[
NDVI = \frac{0 - Red}{0 + Red} = -1
\]
If a target reflects all NIR light (\( NIR > 0 \)) and absorbs all red light (\( Red = 0 \)), the formula becomes:
\[
NDVI = \frac{NIR - 0}{NIR + 0} = +1
\]
Therefore, the mathematical limits of the normalized ratio constrain the theoretical range of NDVI between \( -1 \) and \( +1 \).
Water, snow, and clouds generally have higher red reflectance than NIR, resulting in negative NDVI values.
Bare soil and rocks have low positive values close to \( 0 \).
Healthy, dense green vegetation yields high positive values ranging from \( 0.6 \) to \( 0.9 \). Step 2: Final Answer:
The theoretical range of the Normalized Difference Vegetation Index (NDVI) is -1 to +1.
