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Satellites record light in bands; healthy leaves reflect near infrared and absorb red, and NDVI turns that contrast into an index of greenness.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to explain what spectral bands record, compute NDVI, and use it to compare places and dates.
You know a raster is a grid of cells, each with one value, and you can measure ground area from cell counts. This lesson shows where many rasters come from: satellites that record light in several bands, and the indexes that turn those bands into information.
| Term | What it means |
|---|---|
| Remote sensing | Gathering information about the Earth from a distance, usually by satellite or aircraft. |
| Band | One range of wavelengths a sensor records, stored as its own raster. |
| Reflectance | The fraction of incoming light a surface reflects, from 0 to 1. |
| Near infrared | Light just beyond red, invisible to the eye, strongly reflected by healthy leaves. |
| NDVI | The normalized difference vegetation index: near infrared less red, over their sum. |
| Spectral signature | The pattern of reflectance across bands that identifies a surface. |
A satellite sensor records reflected light in separate bands, each a raster of reflectance values.
Another way: picture
Picture a row of flashlights shining red, green and invisible near infrared light at a leaf. The leaf swallows most of the red to power photosynthesis, but bounces near infrared back like a mirror. A sensor that measures both sees the gap between them, and the wider the gap, the healthier the leaf.
Another way: steps
The eye sees blue, green and red. Sensors also record near infrared, shortwave infrared and thermal infrared. A "true color" image combines the visible bands; a "false color" image puts near infrared in the red channel, so vegetation glows red.
Most of what satellites reveal about plants, water and heat lies in the bands the eye cannot see.
| Surface | Red | Near infrared | NDVI |
|---|---|---|---|
| Dense forest | 0.05 | 0.50 | 0.82 |
| Crops in season | 0.08 | 0.40 | 0.67 |
| Bare soil | 0.25 | 0.30 | 0.09 |
| Lake | 0.05 | 0.02 | −0.43 |
The values are typical, not fixed; the pattern across bands is what identifies each surface.
The plain difference, near infrared less red, changes with how bright the scene is: a hazy day lowers both bands and shrinks the difference. Dividing by the sum cancels much of that, so NDVI can be compared across dates and places.
Normalizing also keeps the index between minus one and one, whatever the brightness.
The Landsat program, run by NASA and the U.S. Geological Survey, launched its first satellite in 1972 and has imaged the Earth ever since. Landsat 8, launched in 2013, and Landsat 9, launched in 2021, record bands at thirty meters and pass over each place about every sixteen days each.
Since 2008 the whole archive has been free, and it holds the longest continuous satellite record of the Earth's land.
A single NDVI value says how green a place is; a series says how it is changing. Cropland rises through spring, peaks in summer and falls at harvest. Forest stays high all year if evergreen.
A sharp drop outside the usual cycle signals trouble: drought, fire, storm damage or clearing. Agencies compare each season with the long-term average to spot it.
After a wildfire, near infrared falls as leaves are lost and shortwave infrared rises as the ground dries and chars. Indexes built from those bands map burn severity.
Federal Burned Area Emergency Response teams use such maps within days of a fire to decide where to seed slopes, protect water supplies and warn of debris flows.
Thermal infrared records heat the ground emits, not sunlight it reflects. It shows urban heat islands, where pavement and roofs run hotter than parks, and cooling water leaving power plants.
Cities from Phoenix to New York use thermal maps to decide where to plant trees and add cool roofs.
Checking an answer. NDVI must lie between minus one and one. It is positive when near infrared exceeds red, as over plants, and negative over water.
Subtracting red from near infrared is allowed because the gap between them measures how much active leaf is present. Dividing by the sum is allowed because it scales the gap by overall brightness, so the index compares fairly.
Comparing dates is allowed when both images are corrected for the atmosphere and sun angle, which agencies do before release.
Land cover maps, like the National Land Cover Database from the layers lesson, are made by sorting pixels by their spectral signatures. Software learns what forest, cropland, water and pavement look like across the bands, then labels every pixel.
Analysts check the result against places visited on the ground or seen in finer images, and report its accuracy.
NDVI is one member of a family. Any two bands that a surface treats differently can be combined as a normalized difference, $(A - B) / (A + B)$, which always lies between minus one and one.
The normalized difference water index uses green and near infrared light to pick out open water, which reflects some green but almost no near infrared. The normalized burn ratio uses near infrared and shortwave infrared to map fire scars, since burning lowers the first and raises the second. Snow, built-up land and crop moisture each have indexes of their own.
The arithmetic is always the same; the skill is choosing bands whose contrast matches the question, and checking the index against the ground. An index that looks convincing on a map can still mislead where soil, shadow or haze changes the bands.
The most common slip is stopping at the difference without dividing by the sum. Another is swapping the bands, which flips the sign.
A third is reading NDVI as a percent of land covered by plants; it is an index of greenness, not a share. A fourth is treating a satellite image as a photograph, when its most useful information is invisible.
Every band is a raster, and indexes are computed cell by cell, like any raster overlay. The next lesson asks what those rasters cannot show: the limits set by pixel size, revisit time, clouds and the need to check on the ground.
Every week of the growing season, analysts at the U.S. Department of Agriculture and at private firms compare vegetation indexes from satellites with the long-term average for each county. In the drought of 2012, maps of the Corn Belt turned from green to brown across July as NDVI fell well below normal.
Those maps fed into crop forecasts, futures markets and relief decisions long before harvest totals were counted. Farmers now buy the same kind of data field by field, and some tractors vary fertilizer and water by the NDVI of each part of a field.
The index shows where crops are struggling, not why. Drought, pests, disease and poor drainage can all lower it, so someone still has to walk the field.
After large wildfires on federal land, Burned Area Emergency Response teams arrive within days. They use satellite images from before and after the fire, comparing near infrared, which falls as leaves are lost, with shortwave infrared, which rises as the ground is exposed and dried.
The result is a map of burn severity, pixel by pixel. Slopes that burned severely above towns or reservoirs are at risk of floods and debris flows in the next storms, so crews seed them, place barriers and warn residents.
Because Landsat's archive reaches back to the 1970s, researchers also use these indexes to show how the size and severity of western fires have changed over the decades.
It is natural to think of a satellite image as a picture from very high up, showing what an astronaut would see. But sensors record bands the eye cannot see, and those bands carry most of the information about plants, water and heat.
NDVI uses one of them, near infrared, to measure greenness, and its value only makes sense as a normalized difference: near infrared less red, over their sum.
A pixel reflects $0.5$ near infrared and $0.1$ red. Subtract.
$0.5 - 0.1 = 0.4$
The contrast.
Add the two bands.
$0.5 + 0.1 = 0.6$
The sum.
Divide the difference by the sum.
$0.4 \div 0.6 \approx 0.67$
The index.
Read the index.
$\text{healthy vegetation}$
Well above zero.
A lake reflects $0.02$ near infrared and $0.05$ red. Subtract.
$0.02 - 0.05 = -0.03$
Negative.
Add the two bands.
$0.07$
The sum.
Divide the difference by the sum.
$-0.03 \div 0.07 \approx -0.43$
Below zero.
Say why it is negative.
$\text{water absorbs near infrared}$
Less than red.
Compare with soil.
$\text{about } 0.09$
Near zero.
Before a fire, a pixel reflects $0.45$ near infrared and $0.05$ red. Find the NDVI.
$0.4 \div 0.5 = 0.8$
Dense forest.
After, it reflects $0.3$ near infrared and $0.2$ red. Find the NDVI.
$0.1 \div 0.5 = 0.2$
Sparse.
Subtract after from before.
$0.8 - 0.2 = 0.6$
The drop.
Name the plain-difference slip.
$0.4 - 0.1 = 0.3$
Not normalized.
Say what the drop shows.
$\text{severe burn}$
Leaves lost.
Say who would use it.
$\text{emergency response teams}$
To plan repairs.
Subtract and add.
$0.4 \text{ and } 0.8$
Difference and sum.
Divide the difference by the sum.
$0.5$
The index.
Read the index.
A satellite pixel reflects $0.5$ of near infrared light and $0.1$ of red light. What is its NDVI, to two decimals?
Complete the worked solution: a pixel reflects $0.4$ near infrared and $0.1$ red. Find the difference, the sum and the NDVI.
Find the difference.
$\text{near infrared} - \text{red} =$ d
The contrast.
Find the sum.
$\text{near infrared} + \text{red} =$ s
To normalize.
Find the index.
$\text{difference} \div \text{sum} =$ k
NDVI.
Read the index.
$\text{vegetation, fairly healthy}$
Well above zero.
Match each band to what it reveals best.
| bright over healthy vegetation | dark over vegetation, as chlorophyll absorbs it | the temperature of the surface | the water in soil and leaves, and burn scars | |
|---|---|---|---|---|
| near infrared | ||||
| red | ||||
| thermal infrared | ||||
| shortwave infrared |
Fill in the NDVI, to two decimals, for dense forest (near infrared $0.5$, red $0.05$), bare soil (near infrared $0.3$, red $0.25$) and a lake (near infrared $0.02$, red $0.05$).
| NDVI | |
|---|---|
| dense forest NDVI | |
| bare soil NDVI | |
| lake NDVI |
A pixel's red reflectance is $0.15$. Write its NDVI as a function of its near infrared reflectance $x$.
Answer:
Before a wildfire, a forest pixel reflected $0.4$ near infrared and $0.1$ red. After it, the pixel reflected $0.3$ near infrared and $0.2$ red. By how much did its NDVI fall?
Answer:
A farmer checks a Landsat image of their fields, which has 30 m pixels. Suppose $800$ pixels have an NDVI low enough to flag the crop as stressed. About how many acres is that? An acre is about $4047$ square meters.
Answer: acres
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A pixel's red reflectance is $0.1$. Write its NDVI as a function of its near infrared reflectance $x$.
Answer:
You can reason with spectral bands. Explain why NDVI divides by the sum of the two bands instead of using their difference alone.
24. Your turn: a pixel reflects $0.6$ near infrared and $0.2$ red. What is its NDVI?, step 3
$\text{moderate vegetation}$
Between soil and forest.