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Spectral Indices

Spectral indices combine reflectance values from multiple spectral bands to highlight specific physical surface properties, such as vegetation health, open water, soil characteristics, or urban footprints.

1. The Physics of Spectral Refectance

Different earth features interact uniquely with electromagnetic radiation:

  SPECTRAL SIGNATURE COMPARISON
  Reflectance %
   100 |
       |                           --. (Vegetation - NIR peak)
    50 |                 _..------'
       |       .--------'             `--. (Bare Soil - Gradual rise)
       |      /
     0 +-----+---------+---------+---------+
            Blue     Green      Red       NIR

  • Vegetation: Strongly absorbs Red light (chlorophyll absorption) and strongly reflects Near-Infrared (NIR) energy (spongy mesophyll cell structure).

  • Water: Absorbs almost all NIR and Shortwave Infrared (SWIR) energy, showing moderate reflectance only in the Blue and Green bands.

  • Built-up / Urban: Shows a gradual increase in reflectance from visible to SWIR bands, often peaking in the SWIR range.

2. Core Environmental Indices

By calculation ratios of these bands, we can minimize topographic shadow effects and atmospheric variations.

Normalized Difference Vegetation Index (NDVI)

NDVI is the standard index for monitoring vegetation density, health, and phenology.

\[\text{NDVI} = \frac{\text{NIR} - \text{Red}}{\text{NIR} + \text{Red}}\]

  • Physical Meaning: Values range from \(-1.0\) to \(+1.0\).

    • \([-1.0 \text{ to } 0.0]\): Water bodies, snow, and clouds.

    • \([0.0 \text{ to } 0.15]\): Bare soil, sand, and rocks.

    • \([0.15 \text{ to } 0.4]\): Sparse vegetation, grasslands, and crops in early growth stages.

    • \([0.4 \text{ to } 1.0]\): Dense canopy forests and healthy active crops.

Soil Adjusted Vegetation Index (SAVI)

SAVI introduces a soil brightness correction factor (\(L\)) to reduce background soil noise in regions with sparse vegetation.

\[\text{SAVI} = \frac{(\text{NIR} - \text{Red}) \times (1 + L)}{\text{NIR} + \text{Red} + L}\]

  • Parameter \(L\): Ranges from \(0.0\) (very dense vegetation) to \(1.0\) (barren soil).

    The standard value of \(L = 0.5\) is applied in most agricultural settings.

Normalized Difference Water Index (NDWI)

NDWI is used to delineate open surface water features and monitor flood extent.

\[\text{NDWI}_{\text{McFeeters}} = \frac{\text{Green} - \text{NIR}}{\text{Green} + \text{NIR}}\]
  • Water Contrast: Since water absorbs NIR and reflects Green, water bodies yield positive values, while soil and vegetation yield negative values.

Normalized Difference Built-up Index (NDBI)

NDBI is designed to map urban footprints, buildings, and concrete structures.

\[\text{NDBI} = \frac{\text{SWIR} - \text{NIR}}{\text{SWIR} + \text{NIR}}\]
  • Urban Contrast: Concrete and asphalt reflect SWIR more strongly than NIR, yielding positive values for built-up surfaces.

3. Step-by-Step Exercise: Computing NDVI and NDWI in QGIS

  1. Import Band Rasters:

    Load band_4_red.tif and band_8_nir.tif (from a Sentinel-2 scene) into QGIS.

  2. Open Raster Calculator:

    Go to Raster > Raster Calculator....

  3. Write NDVI Expression:

    Enter the formula using the layer names in your panel:

    ("band_8_nir@1" - "band_4_red@1") / ("band_8_nir@1" + "band_4_red@1")

    Note: Ensure the output layer name is specified as ndvi_output.tif and the output format is GeoTIFF.

  4. Review the Output:

    Click OK.

    Double-click ndvi_output.tif in the Layers Panel.

    Go to Symbology and set Render Type to Singleband pseudocolor.

    Select a green color ramp (e.g., YlGn - Yellow to Green) to visualize the vegetation distribution.

  5. Compute NDWI:

    Load band_3_green.tif.

    Re-open the Raster Calculator and run:

    ("band_3_green@1" - "band_8_nir@1") / ("band_3_green@1" + "band_8_nir@1")

    Save as ndwi_output.tif.

    Style the output with a blue ramp.

    Apply a threshold filter to keep only values \(> 0\) to cleanly isolate the water bodies.