NDVI, EVI, and monitoring photosynthesis from space
2026-02-26
You should know
That plants interact with light in different ways at different wavelengths, and that ratios can help compare signals measured on different scales.
You will learn
How vegetation indices like NDVI and EVI are built, what they are measuring, and how satellites use reflected light to estimate greenness.
Why this matters
This is one of the clearest examples of computational geography connecting physics, biology, and Earth observation into one practical tool.
If this gets hard, focus on…
The essential idea is that healthy vegetation reflects near-infrared strongly and absorbs red light, so comparing those bands tells us something useful.
In the summer of 2012, a drought so severe that it was described as a 500-year event gripped the central United States. Corn yields across the Midwest fell by a third. The damage was visible from space — not as browning that a photograph would show, but as a measurable collapse in the near-infrared reflectance of the crop canopy relative to red reflectance. MODIS satellites, orbiting at 705 km altitude, had been tracking the drought’s progression across millions of hectares of cropland in near-real time, using a quantity called NDVI. The number that went into the emergency response briefings in Washington was computed from band arithmetic that takes about five keystrokes to type.
The spectral signature of healthy vegetation is one of the most distinctive in all of remote sensing: leaves absorb red light (chlorophyll uses it for photosynthesis) and reflect near-infrared light strongly (the cellular structure of leaves is nearly transparent to NIR). The ratio of the difference to the sum of these two reflectances — the Normalised Difference Vegetation Index — is near zero for bare soil and water, and approaches 1.0 for dense healthy canopy. It correlates reasonably well with leaf area index, photosynthesis rate, and green biomass. This model derives NDVI and its more sophisticated successor EVI from the underlying physics of leaf optics, explains why normalisation matters, and shows what the time series of a vegetation index reveals about ecosystem seasonality and stress.
How do satellites measure plant health and productivity from space?
From 700 km overhead, satellites observe Earth in multiple wavelengths (colors). Healthy vegetation has a distinctive spectral signature: - Red light (620–700 nm): Strongly absorbed by chlorophyll → low reflectance (~5–10%) - Near-infrared (NIR, 780–900 nm): Strongly reflected by leaf structure → high reflectance (~40–50%)
This contrast creates vegetation indices—mathematical combinations of spectral bands that quantify “greenness” and correlate with: - Leaf area index (LAI) - Photosynthesis rate (GPP from Model 20) - Biomass - Crop yield
The mathematical question: How do we combine red and NIR reflectance to create a robust vegetation index?
Reflectance (\rho) is the fraction of incident light reflected by a surface:
\rho_{\lambda} = \frac{E_{\text{reflected}}(\lambda)}{E_{\text{incident}}(\lambda)}
Where \lambda is wavelength.
Typical vegetation reflectance: - Blue (450–500 nm): Low (~5%, absorbed by chlorophyll) - Green (500–580 nm): Moderate (~10%, why leaves look green) - Red (620–700 nm): Very low (~5%, strong chlorophyll absorption) - NIR (780–900 nm): High (~40–50%, internal leaf structure scattering) - SWIR (1550–1750 nm): Low (~10–20%, water absorption)
Leaf internal structure: - Spongy mesophyll: Air-cell interfaces scatter light - Minimal absorption: No chlorophyll in NIR - Result: Multiple scattering → high reflectance
Senescent leaves (dying, autumn colors): - Chlorophyll breaks down - Red reflectance increases (~20–30%) - NIR decreases (~30–40%) - Red-NIR contrast weakens → lower vegetation index
Bare soil has: - Similar red and NIR (~15–25% both) - Low red-NIR contrast - Low vegetation index (as expected)
Partial cover: Mixture of vegetation and soil → intermediate index.
The most widely used vegetation index:
\text{NDVI} = \frac{\rho_{\text{NIR}} - \rho_{\text{red}}}{\rho_{\text{NIR}} + \rho_{\text{red}}}
Properties: - Range: −1 to +1 - Dense vegetation: NDVI ≈ 0.7–0.9 (high NIR, low red) - Sparse vegetation: NDVI ≈ 0.2–0.5 - Bare soil: NDVI ≈ 0.05–0.2 - Water: NDVI ≈ −0.1 to 0 (NIR absorbed by water) - Clouds/snow: NDVI ≈ 0 to 0.3 (both red and NIR high and similar)
Why normalize? - Reduces effects of illumination angle - Reduces atmospheric scattering - Makes values comparable across scenes
EVI reduces sensitivity to soil and atmosphere:
\text{EVI} = G \frac{\rho_{\text{NIR}} - \rho_{\text{red}}}{\rho_{\text{NIR}} + C_1 \rho_{\text{red}} - C_2 \rho_{\text{blue}} + L}
Where: - G = 2.5 (gain factor) - C_1 = 6, C_2 = 7.5 (coefficients for atmospheric correction) - L = 1 (soil adjustment factor)
Advantages over NDVI: - Less saturated at high LAI - Better atmospheric correction - Improved sensitivity in dense canopies
MODIS EVI uses these exact coefficients.
The simple ratio predates NDVI:
\text{SR} = \frac{\rho_{\text{NIR}}}{\rho_{\text{red}}}
Properties: - Range: 0 to ~30 - Dense vegetation: SR ≈ 8–15 - Bare soil: SR ≈ 1–2
Relationship to NDVI:
\text{NDVI} = \frac{\text{SR} - 1}{\text{SR} + 1}
SR has larger dynamic range but is more sensitive to noise.
Empirical relationship:
\text{LAI} \approx a \times \text{NDVI}^b
Or approximately linear for moderate LAI:
\text{LAI} \approx 6 \times \text{NDVI}
Saturation: At high LAI (> 5), NDVI saturates (approaches 0.9 asymptotically). EVI remains more responsive.
fPAR (fraction of Photosynthetically Active Radiation absorbed):
\text{fPAR} \approx 1.24 \times \text{NDVI} - 0.168
(For NDVI between 0.15 and 0.9)
GPP estimation:
\text{GPP} \approx \varepsilon \times \text{fPAR} \times \text{PAR}
Where: - \varepsilon = light use efficiency (~1–2 g C/MJ PAR) - PAR = photosynthetically active radiation (from solar radiation measurements)
This is the basis for MODIS GPP product.
Problem: A Landsat scene has the following reflectance values for a pixel: - Red: \rho_{\text{red}} = 0.08 - NIR: \rho_{\text{NIR}} = 0.42 - Blue: \rho_{\text{blue}} = 0.06
Calculate:
(a) NDVI
(b) Simple Ratio (SR)
(c) EVI
(d) Estimated LAI
(a) NDVI
\text{NDVI} = \frac{\rho_{\text{NIR}} - \rho_{\text{red}}}{\rho_{\text{NIR}} + \rho_{\text{red}}} = \frac{0.42 - 0.08}{0.42 + 0.08}
= \frac{0.34}{0.50} = 0.68
(b) Simple Ratio
\text{SR} = \frac{\rho_{\text{NIR}}}{\rho_{\text{red}}} = \frac{0.42}{0.08} = 5.25
Check relationship:
\text{NDVI} = \frac{SR - 1}{SR + 1} = \frac{5.25 - 1}{5.25 + 1} = \frac{4.25}{6.25} = 0.68 ✓
(c) EVI
\text{EVI} = 2.5 \frac{0.42 - 0.08}{0.42 + 6(0.08) - 7.5(0.06) + 1}
= 2.5 \frac{0.34}{0.42 + 0.48 - 0.45 + 1}
= 2.5 \frac{0.34}{1.45} = 2.5 \times 0.234 = 0.59
(d) Estimated LAI
\text{LAI} \approx 6 \times \text{NDVI} = 6 \times 0.68 = 4.08
Interpretation: NDVI = 0.68 indicates healthy, moderately dense vegetation (corn mid-season, temperate forest canopy). LAI ≈ 4 is typical for mature crops.
Below is an interactive vegetation index calculator with spectral reflectance curves.
<label>
Land cover type:
<select id="landcover-type">
<option value="dense-veg">Dense Vegetation</option>
<option value="moderate-veg" selected>Moderate Vegetation</option>
<option value="sparse-veg">Sparse Vegetation</option>
<option value="bare-soil">Bare Soil</option>
<option value="water">Water</option>
<option value="snow">Snow</option>
</select>
</label>
<label>
Red reflectance:
<input type="range" id="red-slider" min="0" max="0.5" step="0.01" value="0.08">
<span id="red-value">0.08</span>
</label>
<label>
NIR reflectance:
<input type="range" id="nir-slider" min="0" max="0.6" step="0.01" value="0.42">
<span id="nir-value">0.42</span>
</label>
<label>
Blue reflectance:
<input type="range" id="blue-slider" min="0" max="0.4" step="0.01" value="0.06">
<span id="blue-value">0.06</span>
</label><p><strong>NDVI:</strong> <span id="ndvi-result"></span></p>
<p><strong>EVI:</strong> <span id="evi-result"></span></p>
<p><strong>Simple Ratio:</strong> <span id="sr-result"></span></p>
<p><strong>Est. LAI:</strong> <span id="lai-result"></span></p>
<p><strong>Classification:</strong> <span id="class-result"></span></p>Try this: - Dense vegetation: High NIR peak (~850 nm), low red trough → high NDVI - Bare soil: Similar red and NIR → low NDVI (~0.1–0.2) - Water: Very low NIR absorption → negative NDVI - Snow: High reflectance across all bands → NDVI near zero - Notice: The “red edge” (sharp increase 700–750 nm) is characteristic of vegetation
Key insight: The red-NIR contrast uniquely identifies photosynthetically active vegetation.
NDVI time series tracks growing season: - Spring: NDVI rises (green-up, leaf emergence) - Summer: NDVI peaks (maximum LAI) - Autumn: NDVI declines (senescence, leaf fall) - Winter: NDVI low (dormancy, snow cover)
Example: Temperate deciduous forest: - January: NDVI ≈ 0.2 (bare branches) - July: NDVI ≈ 0.8 (full canopy)
Water stress reduces: - Leaf area (wilting, leaf drop) - Chlorophyll content - NIR reflectance (leaf structure degrades)
Result: NDVI declines during drought.
Agricultural monitoring: Compare current NDVI to historical average → detect crop stress.
NDVI maps reveal: - Tropical rainforests: NDVI > 0.8 year-round - Savannas: Seasonal variation (0.3–0.7) - Deserts: NDVI < 0.2 - Tundra: Brief summer peak (0.3–0.5) - Croplands: Strong seasonal cycle
MODIS NDVI (500 m resolution, 16-day) is the standard global product.
Aerosols and water vapor scatter blue/red more than NIR: - Increases apparent NIR - Decreases apparent red - Inflates NDVI
Mitigation: - Atmospheric correction (6S model, dark object subtraction) - EVI includes blue band for correction - Use imagery from clear days
In sparse vegetation, soil dominates signal: - Bright soil → high reflectance in all bands - Dark soil → low reflectance
Soil-Adjusted Vegetation Index (SAVI):
\text{SAVI} = \frac{(1 + L)(\rho_{\text{NIR}} - \rho_{\text{red}})}{\rho_{\text{NIR}} + \rho_{\text{red}} + L}
Where L = 0.5 for moderate cover (adjust 0–1 based on density).
NDVI saturates when LAI > 5: - Forest canopies (LAI = 6–8) all have NDVI ≈ 0.85–0.90 - Cannot distinguish between mature forest and very dense forest
Solution: Use EVI (less saturation) or NIRv (NIR × NDVI).
NDVI ∝ LAI (leaf area), not total biomass.
A grassland with LAI = 4 has similar NDVI to a forest with LAI = 4, but the forest has 100× more biomass (wood).
For biomass: Use SAR (Synthetic Aperture Radar) or LiDAR.
Normalized Difference Water Index (NDWI):
\text{NDWI} = \frac{\rho_{\text{NIR}} - \rho_{\text{SWIR}}}{\rho_{\text{NIR}} + \rho_{\text{SWIR}}}
Sensitive to water content in vegetation (drought stress).
Chlorophyll Indices: - Use red edge (705–750 nm) for chlorophyll content - More sensitive to plant health than NDVI
Photochemical Reflectance Index (PRI):
\text{PRI} = \frac{\rho_{531} - \rho_{570}}{\rho_{531} + \rho_{570}}
Tracks xanthophyll cycle → photosynthetic light use efficiency.
Problem: Reflectance values change with: - Illumination angle (sun elevation) - Atmospheric conditions - Sensor calibration
Solution: Normalize by forming ratios.
Example: Instead of \rho_{\text{NIR}} - \rho_{\text{red}}, use:
\text{NDVI} = \frac{\rho_{\text{NIR}} - \rho_{\text{red}}}{\rho_{\text{NIR}} + \rho_{\text{red}}}
Effect: - Range: Always −1 to +1 - Insensitive to uniform brightness changes - Comparable across scenes
Symmetric indices:
f(a, b) = -f(b, a)
Example: NDVI(b, a) = -NDVI(a, b)
Bounded:
Output constrained to known range (e.g., −1 to 1)
Monotonic:
Increases with target variable (e.g., NDVI increases with LAI)