IEEE Geoscience and Remote Sensing Magazine - December 2023 - 54

In fact, the water is not pure. It may contain
soil particles in suspension. Assuming
that these particles are much smaller than the
wavelength of light and homogeneously distributed
in the water layer, x is determined,
in MARMIT-2, thanks to the extension of the
Beer-Lambert law to diffuse light (proposed in
Allen's plate model [65])
xa a^^ L 2
=- Le- wa L
w
with w
+
w
1 hh# e dx
3
-x
a L
w
x
(5)
a and L identical to the previous equation.
The total reflectance of the water-soil system
Rw is also used from Allen's plate model [65]
and verifies (2). In the first approximation, the
authors of the MARMIT model consider that
rR ,d
23 =
r
soil, and that the diffuse radiation is neglected
().
12 0= Considering that the soil may be an
aggregation of dry areas and of areas covered
by water, the authors introduce a coefficient
e representing the proportion of soil covered
with water 0
# 1#e
(e 0= for the dry soil
and e 1= for fully wet soil). The modeled reflectance
Rmod
of the wet soil is given by [73]
RR ()R
mod = ee` +- d
1
o
w
1
1 o
o j
(6)
where o is an empirical parameter.
The parameter o allows one to take into account
the fact that light can penetrate the soil in
a given area type (dry or water-covered area) and
exit in a different area type (the Yule-Nielsen effect).
In MARMIT-2, o is generally greater than 1.
o 1= corresponds to the extreme case in which
the Yule-Nielsen effect is neglected (which corresponds
to the hypothesis of MARMIT-1).
The MARMIT-1 and MARMIT-2 models
were applied to several datasets (Liu02, Lob02,
Whit04, Les08, Mar12, Phil14, Bab16, and
Dup20) containing different experimental data
of different soil types [72], [73] to measure
the soil moisture content. They show good accuracy
in the prediction; the normalized rootmean-squared
error (NRMSE) is between 2%

IEEE Geoscience and Remote Sensing Magazine - December 2023

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