IEEE Geoscience and Remote Sensing Magazine - December 2023 - 55

soil moisture content for the ith element, respectively. The
NRMSE can then be computed by dividing the RMSE [defined
in (7)] by the maximum value of the measured soil moisture
content {}X
meas 1## [127].
,ii n
PLANT LEAVES: PROSPECT
The well-known PROSPECT model [49], [75] has been designed
to describe the optical properties of plant leaves, in particular,
spectral properties (0.4-2.5
nm ). Leaves are any generally
flattened green outgrowth of the stem of a vascular plant.
They are the primary organs of photosynthesis that significantly
affect important global biogeochemical cycles. The optical properties
of leaves are particularly difficult to simulate due to the
complexity of their internal structure and their complicated and
sophisticated interaction with light. It is well settled that the reflectance
and transmittance spectra of leaves are dependent on
both the concentration of light-absorbing components [for example,
the pigments (like chlorophylls or carotenoids), water,
dry matter, and proteins] and the internal scattering of light.
The original PROSPECT model [49], also known as
PROSPECT-3, was developed to simulate leaf reflectance
and transmittance in the solar domain. This model requires
only three input parameters: the structure parameter or the
number of layers N, the total chlorophyll content
C ,ab
and
the equivalent water thickness (EWT) C .w PROSPECT has
undergone multiple upgrades since its creation, including
new biochemical elements [76], [77], [78], [79], [80], [81],
[82], expanding its abilities [83], [84], [85], and incorporating
new wavelengths [86]. A detailed evolution is presented
in a book by Jacquemoud and Ustin [75].
In its latest versions, PROSPECT-Pro [78] simulates the total
reflectance and transmittance spectra of a leaf as a function
of the following biochemical and biophysical parameter values:
chlorophyll a content, chlorophyll b content, carotenoid
content, anthocyanin content, cellulose and lignin content,
water content, and dry matter content. PROSPECT-PMP+ [80],
[81], [82] can separate between the contributions of the photosynthetic
pigments (chlorophyll a, chlorophyll b, and carotenoids)
and photo-protective pigment (anthocyanins) to the
leaf spectrum in the visible domain (400-800 nm).
The leaf is modeled as a stack of N identical homogeneous
layers of refractive index n separated by N 1layers
of air [cf.
Figure 4(c)]. The incident light arrives perpendicularly to the
plant leaf surface. The plant leaf surface is rough, and at a microscopic
scale, the angle of incidence of the light is therefore
different from 0° for numerous incident points. This plant leaf
roughness is modeled by considering a perfectly flat surface and
by considering that the incident light consists of the continuous
superposition of rays whose incidence angle is contained in the
cone [; ]
0 i [cf. Figure 4(c)]. Inside the plant leaf, after having
passed through the external leaf interface, the light is supposed
to be diffuse and isotropic. The light arriving at the first internal
interface and the light arriving at all the following interfaces
therefore have an angle of incidence between 0° and 90°.
Furthermore, the path of light in the interior of one dielectric
layer is modeled by a transmission coefficient x that
DECEMBER 2023 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
depends on leaf biochemical and biophysical parameter values
(namely pigment content, water content, and dry matter
content). This coefficient verifies (5) with Lw
a replaced
by (),am the spectral absorption coefficient of the internal
part of the leaf. The authors of the PROSPECT model then
derived the leaf reflectance and transmittance model by first
calculating the reflectance and transmittance of a unique
layer using Allen's plate model [(2) and (3)] and then determining
the reflectance and transmittance of the N-homogeneous
layer stack using well-known Stokes expressions [65]
[cf. Figure 4(c)].
PROSPECT has been used to evaluate the content of pigments
(chlorophyll, carotenoid, and anthocyanin); leaf mass
per area (LMA); EWT; nitrogen-based constituents (protein);
and carbon-based constituents (including cellulose, lignin,
hemicellulose, and starch). PROSPECT has been shown to
be precise when applied to databases containing only dicotyledon
leaves, such as the Angers database in which a 5-8%
NRMSE on plant leaf biochemical parameter prediction has
been achieved [76], [77], except for the carotenoid content
(NRMSE of 15-17%) (cf. Table 1). Between 5% and 21%
NRMSE has been achieved on other databases containing dicotyledons
only: VIRGINIA, MAPLE, DOGWOOD, HAZEL,
CALMIT, and HAWAII. Currently, one unique database containing
monocotyledons has also been used for PROSPECT
testing: the LOPEX database. The normalized error in plant
leaf content prediction by PROSPECT on this later database is
as high as 33-68%, but it is currently not determined whether
this low accuracy is inherent to improper data in the database
or to the limitations of the current PROSPECT version for
modeling monocotyledons [76].
FRUITS AND VEGETABLES: FARRELL
Fruits, such as apples, are seed-bearing structures usually developed
from the ovary of a flowering plant. Vegetables, on
the other hand, are all other edible plant parts, such as roots
(like potatoes), leaves (like spinach), and stems (like broccoli).
Both fruits and vegetables are very high in nutrition as they
contain many vitamins and are low in fat and calories. They
also contain pigments and aroma substances of importance
to sensory quality.
A diffusion theory model that describes the radially dependent
diffuse reflectance of light from tissue was developed
[106]. To find an analytical solution to the diffusion
approximation equation, the authors studied the diffuse
reflectance at the surface of a turbid material assimilated to
a homogeneous semi-infinite layer (infinite in the direction
r and finite in the direction z) over the visible and shortwave
NIR region (0.5-1
nm ) [cf. Figure 4(d)]. The incident
white light passes through the diffuse medium in such a
way that at each z there exists a point source then reflected
from the surface. The absorption and scattering of the light
inside the considered turbid biological material are modeled
through the introduction of an absorption coefficient
a
n and a reduced scattering coefficient snl [128]. The reduced
scattering coefficient snl denotes isotropic scattering
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IEEE Geoscience and Remote Sensing Magazine - December 2023

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