Inside NDVI: what the number measures, and where it stops

What a satellite actually records

An optical satellite does not photograph a field the way a phone camera does. Its instrument measures how much sunlight comes back from the ground in a set of narrow wavelength ranges called bands. After processing, each band becomes a reflectance value for every pixel. The United States Geological Survey describes its Landsat surface reflectance products as measuring the fraction of incoming solar radiation that is reflected from Earth's surface to the Landsat sensor. A reflectance of 0.05 in a band means roughly five per cent of the incoming light in that range came back; a reflectance of 0.45 means roughly forty-five per cent.

Reflectance is a ratio, so it has no units, and it is the raw material for every vegetation index. The word surface matters too. Light passes through the atmosphere twice, once on the way down and once on the way back up, and haze, smoke and thin cloud change what reaches the sensor. USGS notes that surface reflectance processing accounts for atmospheric effects such as aerosol scattering and thin clouds, which is what makes images from different dates comparable. An index calculated from data that has not been corrected this way is measuring the air as well as the field.

Why healthy leaves are dark in red and bright in near-infrared

NDVI rests on a contrast inside the leaf. NASA's Earth Observatory explains it in two sentences. The first: "The pigment in plant leaves, chlorophyll, strongly absorbs visible light (from 0.4 to 0.7 µm) for use in photosynthesis." The second: "The cell structure of the leaves, on the other hand, strongly reflects near-infrared light (from 0.7 to 1.1 µm)." Green leaves therefore send back little red light and a great deal of near-infrared light, which the human eye cannot see.

Bare soil behaves differently. Its reflectance tends to rise gradually across the same wavelengths, without the deep dip in the red and the steep climb into the near-infrared. The diagram below shows the two shapes schematically. It is drawn to show the pattern only, and no value should be read from it.

The steep climb between the red and the near-infrared has its own name. Horler, Dockray and Barber, writing in 1983, defined the red edge as "the sharp change in leaf reflectance between 680 and 750 nm". It comes back later in this guide, because some newer indices are built on it.

The formula and its range

NASA's Earth Observatory writes the index in words: near-infrared radiation minus visible radiation, divided by near-infrared radiation plus visible radiation. Its own notation is NDVI = (NIR − VIS)/(NIR + VIS). In practice, with modern sensors, the visible term is taken from the red band, and USGS and most software write the formula as NDVI = (NIR − Red)/(NIR + Red).

The subtraction in the numerator captures the contrast between the two bands. The sum in the denominator normalizes it, which is the N in the name: dividing by the total keeps the result on a fixed scale and partly cancels differences in overall brightness, such as a slightly hazier day or a different sun angle. Because both reflectances are positive, the result can never be smaller than minus one or larger than plus one. USGS states that NDVI values range from +1.0 to -1.0.

Values near the top of the scale arise only when red is a small fraction of near-infrared. Values near zero arise when the two bands are close to equal. NASA gives one anchor at the low end: "Very low values of NDVI (0.1 and below) correspond to barren areas of rock, sand, or snow." This guide deliberately gives no ranges for crops. A value depends on the sensor, the processing, the date, the field and the crop, and a single band of numbers would suggest a precision the index does not have.

A worked example

The two pixels below use hypothetical reflectance values, chosen only to make the arithmetic easy to follow. They are not measurements and not reference values for any crop or field. Pixel A stands for a dense, green canopy: near-infrared 0.45, red 0.05. The difference is 0.40, the sum is 0.50, and 0.40 divided by 0.50 gives 0.80. Pixel B stands for sparse cover with more soil showing: near-infrared 0.25, red 0.15. The difference is 0.10, the sum is 0.40, and the result is 0.25.

The same arithmetic shows the first limit. Take two more hypothetical pixels in which red stays at 0.03 while near-infrared rises from 0.50 to 0.60, a twenty per cent increase in the band that responds to more leaf material. NDVI moves from 0.47 divided by 0.53, about 0.887, to 0.57 divided by 0.63, about 0.905. A large change in one band has become a change of less than two hundredths in the index. When red is already near its floor, the ratio has little room left to move.

Where the number stops

Saturation is the best documented limit. Anatoly Gitelson's 2004 paper on the Wide Dynamic Range Vegetation Index reports that visible red reflectance "exhibits a nearly flat response once the leaf area index (LAI) exceeds 2", while near-infrared reflectance continues to respond to moderate-to-high vegetation density. That difference, the paper notes, is not reflected in NDVI, which shows a saturated pattern. NASA's Earth Observatory makes the same point at global scale when it says the Enhanced Vegetation Index "does not become saturated as easily as the NDVI" over rainforests and other areas with large amounts of chlorophyll. In a dense canopy, two areas that differ substantially in leaf area can return very similar NDVI values.

Soil background is the second limit, and it matters most where cover is sparse. When soil fills part of a pixel, its brightness changes the red and near-infrared values, so the same plants can produce different NDVI values over a dark, moist soil and a pale, dry one. Alfredo Huete's 1988 Soil-Adjusted Vegetation Index adds a constant to the denominator to shift the calculation; his abstract reports that the transformation "nearly eliminated soil-induced variations in vegetation indices" in the canopies he tested. USGS describes SAVI as correcting NDVI for the influence of soil brightness where vegetative cover is low, and gives L = 0.5 as the default.

The atmosphere is the third. Aerosols scatter light, especially at shorter wavelengths, and thin cloud or smoke can lower the contrast between red and near-infrared without anything changing on the ground. The Enhanced Vegetation Index, developed for NASA's MODIS instruments, uses the blue band as well as red and near-infrared. USGS describes EVI as similar to NDVI but correcting for some atmospheric conditions and canopy background noise, and as more sensitive in areas with dense vegetation. Huete and colleagues reported in 2002 that NDVI asymptotically saturates in high biomass regions such as the Amazon while EVI remained sensitive to canopy variations.

None of these alternatives makes NDVI obsolete. Each was designed to reduce one specific weakness, and each carries its own assumptions, such as the constants in SAVI and EVI. The table compares four of them.

What red-edge bands add

A red-edge band samples the steep part of the leaf reflectance curve, between the deep red absorption and the near-infrared plateau. Because reflectance there is neither at its floor nor at its ceiling, it can keep changing in canopies where the red band has stopped responding. Indices built on it replace or supplement the red band. The Normalized Difference Red Edge index, or NDRE, keeps the NDVI form but puts a red-edge band where the red band was; Barnes and colleagues described it in 2000 using reflectance near 720 and 790 nanometres.

Sentinel-2, the European Copernicus mission, carries red-edge bands. The European Space Agency's mission description lists six 20 metre bands, including "4 narrow Bands in the VNIR vegetation red edge spectral domain", centred near 704, 740, 783 and 865 nanometres; the last of these is usually treated as a narrow near-infrared band rather than red edge. These bands are coarser than Sentinel-2's 10 metre red and near-infrared bands, so a red-edge index trades some spatial detail for its different spectral view. A red-edge index is a different measurement, with its own limits and its own sensitivity to soil, atmosphere and viewing geometry, rather than a corrected version of NDVI.

Why NDVI cannot name a cause

Everything above points to one conclusion. NDVI summarizes how much red and near-infrared light came back from a pixel on one date. A lower value in one part of a field says the contrast between those two bands is smaller there. It does not say why. Less leaf area, a more open canopy, more visible soil, a different variety, standing water, a later seeding date, residue, haze over that part of the image or a mixed pixel along a boundary can all reduce the contrast, and several of them can do so at once. The index has no channel for any of these explanations.

This is why a satellite index is best read as a pointer to where someone should look, not as an answer. A difference that persists across several clear dates, follows no field boundary and has been checked on the ground is worth far more than a single low pixel. When reading an NDVI map, it helps to ask a few plain questions before drawing any conclusion.

• Which sensor and which date produced each value being compared, and was the image atmospherically corrected?
• Was the area clear of cloud, cloud shadow and haze on that date?
• Does the same pattern appear on more than one clear date?
• Does the difference follow a boundary, such as a headland, an old fence line or a change in soil?
• Is the canopy dense enough that NDVI may be near saturation, or sparse enough that soil fills much of each pixel?
• Has someone looked at the area on the ground and recorded what they saw, including when the cause stayed unclear?