Vol.3, No.3, 193-198 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.33025
Retrieval of the ground surface reflectance along coast
zone and island with MODIS image*
Jinji Ma#, Xiaofan Li
College of Physics and Electronic Information, Anhui Normal University, Wuhu, China;
#Corresponding Author:
Received 26 December 2010; revised 27 January 2011; accepted 29 January 2011.
ABSTRACT
A new method based on lookup tables (LUTs)
for retrieval of the ground surface reflectance
along coastal zones and islands with MODIS
(Moderate-resolution imaging spectroradiome-
ter) image was described. Through simulation
of the AHMAD radiative transfer model, we can
retrieve the aerosol optical character with water
pixels of MODIS image. Postulating the back-
ground is cloudless and the atmosphere on the
water is the same as that on the island, we can
use the 6S radiative transfer model to compute
the LUT about the ground surface reflectance,
then use the interpolate method to get the re-
flectance of the ground surface along coastal
zones and islands through the reflectance of the
land pixels of MODIS image, the geometric
condition and the aerosol optical thickness. The
LUT method is applied to determine the ground
surface reflectance in Xiamen’s zone from the
MODIS image. At last, the results were analyzed
and its expectation errors were reported.
Keywords: MODIS Image; Reflectance;
Optical Thickness; Aerosol; Remote Sensing
1. INTRODUCTION
How to get the ground surface reflectance is the key
technology for remote sensing because it is important to
use the image of satellite to retrieve ration and the
ground information. Because the image of satellite in-
cludes not only the ground information but also the at-
mosphere information, so we must correct the errors
from the atmosphere effect to the image. There are many
kinds of methods for correcting error, but the most valid
method is the direct correction from the image of satel-
lite. In the beginning, people wanted to evade atmos-
phere correction [1] through calculating the Normalized
Difference Vegetation Index (NDVI) and synthesizing
the DVI by the biggest value of the row of time [2]. Now,
we mainly adopt the radiative transfer measurement ac-
cording as atmospheric parameter to correct atmosphere
[3]. For example, we usually use the dark object method
[4] and the dark object subtraction method [5] to retrieve
the optical character of the aerosol. The aim of these
methods is to minimize the error due to the retrieval of
the ground surface reflectance.
Since the ocean surface is simpler than the land sur-
face, and the atmospheric signal is almost 90% of the
apparent reflectance over the ocean [6], so we think the
atmospheric optical character cannot be significantly
changed by the variation of ocean surface reflectance.
Based on this property, and using the AHMAD radiative
transfer model [7], we determine the aerosol optical
character over the ocean through water pixels of MODIS
image based on the LUT method [8]. If we think the
atmospheric condition over the ocean is the same as that
on the ground under cloudless condition, we can deter-
mine the aerosol optical character, using the 6S model [9]
on computing of the LUT about the ground surface re-
flectance. Using the interpolation method to retrieve of
the ground surface reflectance along coastal zones and
islands with the LUT, aerosol optical character can be
determined from the MODIS image.
2. METHOD
2.1. Retrieval of the Aerosol Optical
Character from Pixel of MODIS Image
There are different methods to retrieve of the aerosol
optical character on the land and over the ocean from
pixel of MODIS image. The aerosol optical character on
the land is retrieved based on the dark method, and the
aerosol optical character over the ocean is retrieved
based on the LUT method.
*National Natural Science Foundation, No. 40701132; Anhui Provincial
N
atural Science Founda
t
ion, No.070412042.

J. J. Ma et al. / Natural Science 3 (2011) 193-198 194
2.1.1. Calculation of Lookup Tables
Using the LUT method to retrieve the aerosol optical
character over the ocean with the MODIS image has
been proposed by Tanré et al. [10]. The LUT is calcu-
lated by the AHMAD radiative transfer model based on
the size of different particles. This paper use the aerosol
model proposed by the Leavy et al. [11], which have
five coarse particles and four fine particles. Errors in the
retrieved aerosol optical character over the ocean derive
chiefly from the size distribution of particles and spectral
distribution [12], so choosing seemly aerosol models is
of great importance. Leavy et al. have discussed the
large variation of about the radiation of coast [11]. For
simplicity, we choose the Cox model to compute the
reflectance of the ocean surface [13]. We take nine parti-
cles as nine kinds of aerosol models. For each kind of
aerosol model, we use AHMAD’s radiative transfer code
to calculate the LUT that have five parameters [10].
2.1.2. Method and Theory to Retrieval of the
Aerosol Optical Character
The simplified method proposed by Wang and Gordon
is the base for calculation of LUT and retrieval of aero-
sol optical character. The advantage of this method is
that we only need calculate 9 models not 4 × 5 × 11
models for two different absorption models.
If the total reflectance measured from the satellite is
expressed



cs
svv svv
l
svv
,, ,,
1,,


  



 (1)
where

s
svv
,,


 is the spectral reflectance of the
fine models,

l
svv
,,


 is the spectral reflectance
about the coarse models, and

is the fraction of the
two models. The superscript c denotes calculation, s de-
notes the fine model and l denotes the coarse model. The
subscript

denotes central wavelength. How to choose
the aerosol model and confirm the optical thickness is
defined by minimizing the error
s
l

:
2
1
1
0.01
mcsl
n
sl csl
n










 (2)
where n is the sum of pixels, m


is the measured
MODIS reflectance at wavelength

, and csl


is cal-
culated from the combination of modes in the LUT and
is defined by Eq.1. The small number 0.01 prevents di-
vergence for the longer wavelengths under clean condi-
tions. The best aerosol model and the optical thickness at
0.55 m

will be obtained when
s
l

has reached its
the least value.
2.2. Retrieval of the Ground Surface
Reflectance
2.2.1. RTE of 6S Model
The 6S is a radiative transfer model proposed by
Ver mo te et al. If the geometrical conditions, atmospheric
model, aerosol model, aerosol optical thickness and the
ground surface reflectance are known, we can calculate
apparent reflectance at the atmosphere top and other
characters about atmosphere, such as atmospheric trans-
mission, etc.
We can suppose that the ground surface is a Lamber-
tian, the ground surface reflectance is
  

*,,,, 1
,,
c
svsva svsvsv
c
gass v sv
TT
s
T

  











(3)
where


*,,
s
vsv

 is apparent reflectance at the at-
mosphere top,


,,
asvsv

 is the intrinsic reflec-
tance of the aerosol, c

is the bottom surface reflec-
tance,


s
T

, [respectively

v
T

] is the total trans-
mission of the atmosphere between the sun and the sur-
face, (respectively between the surface and sensor),


,,
g
ass v sv
T

 is the total atmosphere transmission of
the sun to the surface and the sensor, s is the spherical
albedo of the atmosphere.
2.2.2. Using 6S Model to Calculate the LUT
The required parameters can be calculated according
to 6S-model, choosing midlatitude summer (determined
by MODIS image) as the atmospheric model, using the
best of result by the front retrieval as aerosol model. Al-
titude of target is zero and the bottom of surface is
Lambertian and its reflectance is chosen from 0.02 to
0.18 with a step of 0.02. We use the 6S model to calcu-
late the LUT for retrieval of the ground surface reflec-
tance at 550nm, for six optical thickness (a

= 0.0, 0.2,
0.5, 1.0, 2.0, 3.0), six zenith angles of sun
(00
s18.2 21.2
  step is 0.50), six relative azimuth
angels (the step is 50) and five zenith angles of view
(v


150, 200, 250, 300, 350) in central of the front
MODIS band. Table 1 shows a part of the LUT.
2.2.3. Retrieval of the Ground Surface
Reflectance
We can use the line of interpolation method to retrieve
the ground surface reflectance base on Table 1 that have
been calculated by the 6S model, the geometrical condi-
tions (according the MODIS image, we can determine
zenith angle of sun, zenith angle of view, relative of
azimuth angle and the apparent reflectance), the best
aerosol model and the optical thickness that have been

J. J. Ma et al. / Natural Science 3 (2011) 193-198
195195
retrieved in Subsection 2.1.
2.3. Process of the Retrieval
The method based on the LUT to retrieve the ground
surface reflectance is feasible when the ocean surface
reflectance is known and the aerosol model over the
ocean is same as that on the coast. When both conditions
are satisfied, we can retrieve the ground surface reflec-
tance. The steps are
1) Supposing there are nine kinds of particle models,
including four fine particle models and five coarse parti-
cle models.
2) Using the Cox’s model to calculate the ocean sur-
face reflectance.
3) Based on conditions 1) and 2), the LUT (A) for re-
trieval of the aerosol optical character can be calculated
by using the AHMAD’s radiative transfer code.
4) Using the Formulas (1) and (2) and the clear ocean
pixel of MODIS, the best of aerosol model and the opti-
cal thickness can be retrieved.
5) Using the best aerosol model and the 6S model, we
can get the LUT (B) for retrieval of the ground surface
reflectance.
6) Based on the LUT (B) and the step 4) retrieval
aerosol optical thickness, and the geometrical conditions
and the clear ocean of pixels that were given from
MODIS image, the ground surface reflectance can be
retrieved from the line of interpolation method.
2.4. Estimation of the Error in Retrieval of
Result
In order to verify the influence of the variation of
validate the aerosol optical thickness on the ground sur-
face reflectance, we have performed the analog compu-
tation. In the simulation calculation, we chose the zenith
angle of sun and the azimuth angle to be 19 and 95, the
zenith angle of view of sun and azimuth angle to be 280
and 900, the aerosol optical thickness to be 0.28 at 0.55
nm. The simulation is based on the LUT (B) and these
conditions. Table 2 shows the influence of increasing
5%-10% or decreasing 5%-10% of the aerosol optical
thickness on the retrieval of the result.
From Table 2, we see that the error is increasing with
the increase of relative of aerosol optical thickness in
visible band from retrieval of the ground surface reflec-
tance. While in infrared band its influence relatively
smaller. When the variation of the retrieved of aerosol
optical thickness is about ten percent, the error is less
than five percent for all band retrieved from the ground
surface reflectance. Therefore, after adding the line of
interpolation of error, the total error in the retrieved the
ground surface reflectance is less than ten percent.
Usually, the aerosol optical thickness on the land is
thicker than that over the ocean. Chlorophyll of water,
speed and direction of wind are sources of error in re-
trieval of the aerosol optical thickness. They deviates the
retrieved optical thickness from the actual value. In
some areas, the assumption that the atmospheric condi-
tion over the ocean is the same as that on the land may
make the retrieved optical thickness be less than the true
value. This is the major source error of the retrieved
ground surface reflectance.
3. APPLICATION OF THE MODIS IMAGE
AND ANALYSIS OF THE RETRIEVED
RESULT
We choose the MODIS image in south ocean of China
on May 282 003 as our research area. This research area
is 30 × 30 pixels cloudless. (Figure 1(a) shows the re-
search area.) The long-lat coordinates of the four top
points are (24.682, 118.199), (24.637, 118.563), (24.414,
118.142), (24.369, 118.505). With the dark aim’s method,
all the water pixels in Figure 1(b) are picked-up. With
these water pixels, the aerosol thickness and the aerosol
model are retrieved. The best result of the retrieval is
that the aerosol model is Multimodal Log Normal dis-
tribution, with three fine and one coarse particle in ratio
of four to one.
Figure 2(a) shows the average value of the retrieved
aerosol optical thickness. We use the retrieved average
value to retrieve the ground surface reflectance, if an
island separates the row, we choose two average values
in the row. Figure 2(b) shows the relative error in the
average of the aerosol optical thickness, the standard
value (


a550 nm0.264
 ) comes from the ground
measurement at the same time. Figure 2 shows that the
aerosol varies little on the space and the atmosphere is
uniform in the research of area.
Figure 3 and Figure 4 show the reflectance curve of
every pixels marked in the Figure 1(b). Figure 3 show
the ocean water reflectance curve, its value is almost
zero from 870 nm to 2100 nm. In the Figure 3, curves T,
T1 and T2 are the ocean pixel reflectance, among there
curves T1 and T2 are the retrieval results with the same
method of land, and curve of T is the calculation result
using the Cox’s model [13]. In the model, the wind
speed is 6 m/s, the chlorophyll of concentration is 0.5
mg/ m3 and the salt concentration is 35 ppt. From these
curves in the Figure 3, we find that the retrieval results
tally with the calculation result.
Figure 4 shows the ground surface reflectance curves
on the coast and the island. These curves tally with the
type spectrum of vegetation that the reflectance on the
visible band is very small and the reflectance quickly
increases from 670 nm to 1240 nm with little variation

J. J. Ma et al. / Natural Science 3 (2011) 193-198 196
Table 1. Lookup table for calculating the reflectance of the ground.
Zenith of sun
angle (degree)
Zenith angle of
view (degree)
relative azimuth
angle (degree)
Aerosol optical
thickness
Apparent
reflectance
Reflectance of the
ground
… … … … … …
19.2 25.0 2.0 0.27 0.1545 0.1400
19.2 25.0 2.0 0.27 0.1713 0.1600
19.2 25.0 2.0 0.27 0.1882 0.1800
19.2 25.0 2.0 0.28 0.0557 0.0200
19.2 25.0 2.0 0.28 0. 0802 0.0500
… … … … … …
Table 2. Error in the retrieved the ground surface reflectance with the aerosol optical thickness of the relative error.
aerosol optical thickness
wavelength (550nm) Increase 10% Increase 5% Decrease 5% Decrease 10%
0.47 μm 2.60 1.10 0.90 1.86
0.55 μm 1.30 0.45 0.39 1.20
0.66 μm 1.50 0.84 0.67 1.45
0.86 μm 1.41 0.76 0.78 1.55
1.24 μm 1.20 0.47 0.59 1.02
1.64 μm 0.80 0.45 0.30 0.79
Relative Error (%)
2.13 μm 0.49 0.29 0.29 0.50
(a) (b)
Figure 1. MODIS image. (a) Region of interesting; (b) T 30 × 30 pixels at band 2.
(a) (b)
Figure 2. Result of the row of MODIS image. (a) The aerosol optical thickness; (b) The relative error.

J. J. Ma et al. / Natural Science 3 (2011) 193-198
197197
Figure 3. Reflectance curve of the ocean water marked in Fig-
ure 2(a).
on the infrared band.
The four curves in Figure 4(a) show the ground sur-
face reflectance spectrum along the coast of land, among
them curves B and F maybe mixture pixel (contain water
pixel) reflectance curve. The eight curves in Figure 4(b)
show the surface reflectance spectrum on the coast of
island, among the curve G maybe the mixture pixel of
ocean and land, curve O is the typical reflectance spec-
trum of green vegetation. The curves in Figure 4(c) and
(d) are the ground surface reflectance spectrum on the
inside of land and from island far away of the coast.
From these curves, we can see that the ground matter is
complex on the inside of land and the ground matter is
uniform on the island.
4. RESULTS AND EXPECTATION
According to the characteristic of the ground matter
on the coast near the ocean, this paper uses the retrieved
aerosol optical thickness over the ocean to retrieve the
ground surface reflectance of the land. For every pixel of
land, we use the geometrical conditions, the retrieved
aerosol optical thickness and LUT (B) from 6S model
calculation based on the retrieved aerosol model and the
interpolation method to retrieve the ground surface re-
flectance. Simulation shows that the error of retrieved
the ground surface reflectance is less than ten percent
when the error of retrieved aerosol optical thickness is
less than ten percent.
The method is fast and accurate in retrieval the ground
surface reflectance because of using the synchronized of
aerosol model. However, the method is only applicable
to near coast and Small Island; the method needs to be
further researched to the land to the ocean beyond 30
kilometer. The water near the coast is Case II water, but
there is no good model to calculate the Case II water of
reflectance. It influences the precision of the retrieved of
(a)
(b)
(c)
(d)
Figure 4. The reflectance curve of the land marked in Figure
1(b).

J. J. Ma et al. / Natural Science 3 (2011) 193-198 198
aerosol optical thickness so that the precision of the re-
trieved ground surface reflectance would be inflected.
The further works are to build a good model to calculate
the reflectance of the Case II water and to use the ASD
to measure the ground surface reflectance at real time in
comparison with the retrieved result from the MODIS
image.
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