Spectral signatures

In late June Grant's crew spent two days in the service area with a borrowed field spectroradiometer, a white reference panel and a list of fields chosen by Leah: irrigated alfalfa, spring wheat, winter wheat nearing harvest, malt barley, canola coming into bloom, dryland stubble, a fallow field of bare clay, the canal and a stock pond. At each site they measured the reflected spectrum from 350 to 2500 nm, photographed the field, noted its condition and recorded the time and the cloud. Leah wanted to know, before buying or downloading any imagery, which wavelengths could tell the district's crops apart and which could tell an irrigated field from a dry one. This lesson explains spectral signatures: why vegetation, soil, water and other surfaces reflect as they do, how those patterns change with condition and season, how they are measured, and how they are condensed into spectral indices.

The idea of a spectral signature

A spectral signature, or spectral reflectance curve, is a plot of a surface's reflectance against wavelength. Different materials absorb and scatter light differently at different wavelengths, so their curves have different shapes, and a sensor that measures reflectance in several bands records a sample of that curve for every pixel. The word signature is a little optimistic: a signature suggests something unique and fixed, while real reflectance varies with condition, moisture, growth stage, viewing geometry and the mixture of materials inside a pixel. It is more accurate to think of each class as having a family of curves, with a typical shape and a spread. Classification, in Lesson 7, works only where the families of different classes are separated by more than their spread.

Vegetation

The reflectance of a green leaf is controlled by three things: pigments in the visible, the internal structure of the leaf in the near infrared, and water in the shortwave infrared. In the visible, chlorophyll a and b absorb strongly in the blue near 0.45 µm and in the red near 0.67 µm, and carotenoids absorb in the blue. Green light is absorbed less, giving a small reflectance peak near 0.55 µm, typically 0.08 to 0.15, which is why leaves look green. The red reflectance of a dense healthy canopy is very low, often 0.02 to 0.05.

Beyond about 0.7 µm, pigments stop absorbing, and the reflectance rises steeply in a narrow interval called the red edge. In the near infrared a leaf reflects 40 to 60 % and transmits most of the rest, because light is scattered many times at the boundaries between hydrated cell walls and the air spaces of the spongy mesophyll. A canopy of several leaf layers reflects even more, since light transmitted by one leaf is partly reflected by the leaves below. Near infrared reflectance therefore rises with leaf area and biomass, which is the physical basis of vegetation indices. The position of the red edge shifts slightly toward longer wavelengths as chlorophyll content increases and toward shorter wavelengths under stress, which is why some sensors carry narrow bands between 0.70 and 0.78 µm.

In the shortwave infrared, liquid water in the leaf absorbs strongly, with absorption bands near 1.45 and 1.95 µm, and reflectance at 1.6 and 2.2 µm falls as leaf water content rises. A crop that is short of water first shows a rise in SWIR reflectance, and only later, as cells collapse and chlorophyll breaks down, a rise in red and a fall in near infrared reflectance. Shortwave infrared bands are therefore sensitive to the early stages of water stress that matter for irrigation scheduling.

A canopy is more than a stack of leaves. Its reflectance depends on leaf area index, the one-sided leaf area per unit ground area; on leaf angle, with erect leaves such as wheat reflecting differently from flat leaves such as sugar beet or alfalfa; on the soil visible between the rows, which dominates early in the season; on flowers, seed heads and senescent leaves; and on the sun and view angles, which control how much shadow is seen. Canola in full bloom, for example, is bright yellow and has a much higher green and red reflectance than canola before flowering, so its spectrum changes completely for three weeks in July. Alfalfa is cut several times a year, so a field can go from dense canopy to stubble and back again within a month.

Soil, water, snow and built surfaces

Bare soil generally has a smooth reflectance curve that rises gradually with wavelength, without the sharp red edge of vegetation. Its overall level depends mostly on moisture, organic matter, texture and surface roughness. Moist soil is darker at all wavelengths than the same soil dry, by up to half, and has deeper water absorption features at 1.45 and 1.95 µm. Organic matter darkens soil in the visible; the dark brown and black chernozems of the prairies are darker than the light brown soils of the drier south. Iron oxides produce a reddish color and absorption features near 0.5 and 0.9 µm, and clay minerals have absorption features near 2.2 µm. A freshly cultivated field is rougher and darker than a crusted one, because of its shadows.

Clear water has a low reflectance of a few percent in the blue and green, falling to almost nothing in the near infrared and beyond, where water absorbs strongly. This makes the near infrared and shortwave infrared the best bands for mapping water boundaries: even a shallow flooded field stands out sharply as a dark area. Suspended sediment raises reflectance in the green, red and even near infrared, so the canal after a storm, carrying silt from the coulees, looks brighter and browner than the clear water at the headworks. Chlorophyll in algae raises green reflectance and lowers blue and red, and high concentrations produce a near infrared bump similar to vegetation, which allows algal blooms in reservoirs to be monitored. Surface glint from waves can make water appear bright in any band.

Fresh snow is very bright in the visible, often above 0.9, and much darker in the shortwave infrared because ice absorbs there; clouds are bright in both. The contrast between visible and SWIR reflectance is therefore used to tell snow from cloud in winter and spring images. Concrete, asphalt, gravel and roofs have mostly flat curves at levels that depend on their age and color; new asphalt is dark and becomes lighter with age, and metal roofs can be very bright with strong directional effects. Burned areas show low near infrared and high shortwave infrared reflectance, a combination used in Lesson 8.

Measuring spectra in the field and the laboratory

A field spectroradiometer measures radiance in hundreds of narrow channels. Reflectance is obtained by measuring a reference panel of known, nearly Lambertian reflectance immediately before and after the target, so that the ratio cancels the illumination: \(\rho_{target} = (L_{target}/L_{panel}) \, \rho_{panel}\). The panel must be clean, level and fully lit, and the sky stable, because a cloud passing between the two readings changes the illumination and corrupts the ratio. Measurements are usually made within two hours of solar noon to keep the sun high and shadows short, and several readings over each target are averaged. The instrument's field of view and height determine the footprint, which must be large enough to sample the canopy and soil in their true proportions; a reading of one alfalfa plant is not a reading of an alfalfa field.

Spectral libraries collect measured spectra of minerals, soils, vegetation and man-made materials, and are used to design classifications and to unmix hyperspectral pixels. Library spectra are useful references but rarely match local conditions exactly, so local field spectra like Grant's are preferred for calibrating a project. Field spectra also serve as ground truth for checking atmospheric correction: if the satellite surface reflectance of a large uniform field agrees with the field measurement on the same day, the correction is working.

From spectra to bands

A multispectral sensor does not record a continuous spectrum but integrates the incoming radiance over each band, weighted by the band's spectral response function. The reflectance in a band is therefore an average over the band, and two sensors with slightly different band positions and widths record slightly different reflectances for the same surface. When Leah compared the field spectra with images, she convolved each field spectrum with the response functions of each sensor's bands to simulate what the sensor would see. The differences between sensors are small for broad smooth features and larger where a band falls on a steep part of a curve, such as the red edge.

import math
# Surface reflectance (0-1) at six band centres, typical mid-July values for the canal service area
bands = ["blue 0.49", "green 0.56", "red 0.665", "NIR 0.842", "SWIR1 1.61", "SWIR2 2.19"]
lib = {
    "irrigated alfalfa": [0.030, 0.075, 0.035, 0.480, 0.200, 0.090],
    "irrigated wheat":   [0.035, 0.070, 0.045, 0.390, 0.230, 0.120],
    "canola in bloom":   [0.050, 0.150, 0.060, 0.420, 0.240, 0.120],
    "dryland stubble":   [0.090, 0.130, 0.170, 0.250, 0.340, 0.270],
    "bare clay soil":    [0.100, 0.140, 0.180, 0.230, 0.300, 0.250],
    "canal water":       [0.060, 0.070, 0.040, 0.020, 0.008, 0.005],
}
def nd(a, b): return (a - b) / (a + b)
print(f"{'cover':18s}  NDVI    NDWI   NDMI")
for name, r in lib.items():
    print(f"{name:18s} {nd(r[3], r[2]):6.3f} {nd(r[1], r[3]):6.3f} {nd(r[3], r[4]):6.3f}")

def sam(a, b):
    dot = sum(x * y for x, y in zip(a, b))
    na = math.sqrt(sum(x * x for x in a)); nb = math.sqrt(sum(y * y for y in b))
    return math.degrees(math.acos(min(1.0, dot / (na * nb))))

print()
print("Spectral angle (deg) between covers")
names = list(lib)
for i in range(len(names)):
    for j in range(i + 1, len(names)):
        print(f"  {names[i]:18s} vs {names[j]:18s} {sam(lib[names[i]], lib[names[j]]):5.1f}")

# Which single band separates alfalfa from wheat best, relative to a 0.015 field-to-field spread?
print()
a, w = lib["irrigated alfalfa"], lib["irrigated wheat"]
for bnd, x, y in zip(bands, a, w):
    print(f"{bnd:11s} difference {x - y:+.3f}  separability {abs(x - y) / 0.015:4.1f} spreads")

cover               NDVI    NDWI   NDMI
irrigated alfalfa   0.864 -0.730  0.412
irrigated wheat     0.793 -0.696  0.258
canola in bloom     0.750 -0.474  0.273
dryland stubble     0.190 -0.316 -0.153
bare clay soil      0.122 -0.243 -0.132
canal water        -0.333  0.556  0.429

Spectral angle (deg) between covers
  irrigated alfalfa  vs irrigated wheat      9.3
  irrigated alfalfa  vs canola in bloom     12.2
  irrigated alfalfa  vs dryland stubble     38.7
  irrigated alfalfa  vs bare clay soil      39.8
  irrigated alfalfa  vs canal water         68.6
  irrigated wheat    vs canola in bloom      8.4
  irrigated wheat    vs dryland stubble     30.0
  irrigated wheat    vs bare clay soil      31.6
  irrigated wheat    vs canal water         67.2
  canola in bloom    vs dryland stubble     29.4
  canola in bloom    vs bare clay soil      30.1
  canola in bloom    vs canal water         60.3
  dryland stubble    vs bare clay soil       4.1
  dryland stubble    vs canal water         57.7
  bare clay soil     vs canal water         54.0

blue 0.49   difference -0.005  separability  0.3 spreads
green 0.56  difference +0.005  separability  0.3 spreads
red 0.665   difference -0.010  separability  0.7 spreads
NIR 0.842   difference +0.090  separability  6.0 spreads
SWIR1 1.61  difference -0.030  separability  2.0 spreads
SWIR2 2.19  difference -0.030  separability  2.0 spreads

The output shows which bands carry the information. Alfalfa and wheat differ hardly at all in the blue, green and red bands, by less than the field-to-field spread of about 0.015, but by six spreads in the near infrared and by two in each shortwave band. The spectral angle, which compares the shape of two curves regardless of brightness, separates the vegetated covers from soil and water by 30 to 70 degrees but alfalfa, wheat and canola by only 8 to 12 degrees, and dryland stubble from bare soil by only 4 degrees. A single date is therefore enough to separate green from not green, but the crops themselves need several dates, which the classification lesson will use.

Spectral indices

A spectral index combines two or more bands into a single number that emphasizes one property and suppresses others, such as illumination differences and some atmospheric effects. The most widely used is the normalized difference vegetation index:

NDVI ranges from −1 to +1. Water usually has negative values, bare soil and rock values near 0.1 to 0.2, sparse vegetation 0.2 to 0.5 and dense green canopies 0.6 to 0.9. Because it is a ratio, NDVI partly cancels differences in illumination caused by slope and sun angle. It has known weaknesses: it saturates over dense canopies, rising little once leaf area index exceeds about 3, and it is affected by the color and brightness of the soil beneath sparse canopies. Many alternatives have been proposed to address these weaknesses.

How signatures change over time

A crop's spectrum follows a seasonal path called its phenology. A spring wheat field is bare soil in May, shows rising NDVI from emergence in late May to a peak at heading in early July, and then falls as the crop ripens and turns golden before harvest in August. Canola emerges later, peaks in July with a distinctive yellow flowering stage, and is swathed in late August. Alfalfa is green from early spring, falls sharply at each cut and recovers within two or three weeks. Winter wheat greens up early, ripens by late July and is often harvested before spring crops peak. Irrigated fields stay green later into the season than dryland fields of the same crop.

These differences in timing are often more diagnostic than any single-date spectrum. An NDVI profile through the season, built from many cloud-free images, is a signature in time as well as wavelength. The district's crop map would be built from such profiles, and the dates of the field visits would be chosen to coincide with the stages at which the crops differ most: canola flowering, the wheat and barley ripening, and the regrowth of alfalfa after a cut.