refraction index of 0.5 μm blue light through the troposphere.
Table 1 lists the atmospheric refraction index at intervals of
altitude from Earth’s surface to the stratopause.
From Table 1 and Figure 5, we can conclude that the
atmospheric refraction index is 1 along
LOS
from payload
in-orbit to the top of stratosphere at 47.35 km altitude. In the
troposphere, tropopause and stratosphere, the atmospheric
refraction index increases with the decreasing altitude. Under
the same atmospheric pressure and water vapor pressure, the
atmospheric refraction index is negatively correlated with the
atmospheric temperature. The result is that the higher the lati-
tude is, the larger the atmospheric refraction index is. The at-
mospheric refraction index is almost unchanged for the same
latitude regardless it is in the southern hemisphere or in the
northern hemisphere. For example, the mean Earth surface air
temperature at N60°, N30° and Equator is 0°, 20°, and 25° Cel-
sius degrees, respectively, the atmospheric refraction indexes
of N60° are larger than N30°, and N30° are larger than the
Equator in troposphere. The atmospheric refraction indexes
of N30° and S30° are almost equal. The atmospheric refrac-
tion index at Equator has the minimum value in troposphere.
Table 2 lists the distribution characteristics of atmospheric
refraction with regard to the atmosphere layer and altitude.
Therefore, the
ISO
eight layer atmosphere model can be
simplified into two layers:
1. Troposphere layer: geometric altitude is between 0 and
11,019 m;
2. Stratosphere layer (include tropopause): geometric
altitude is from 11,019 m to 47,350 m.
This simplification is based on the fact that the refraction
index is 1 from the stratopause to mesopause. We will use
the simplified two-layer atmosphere model to calculate the
geolocation error as shown in Figure 6.
The atmospheric refraction index in the troposphere and
stratosphere are set to be n1 and n2 respectively, and
i
is the
incident angle of
LOS
at the top of the stratosphere.
D
is the
displacement on the ellipsoid surface because of
LOS
refracted
in the troposphere and stratosphere. A weighted average
algorithm is employed to calculate the atmospheric refrac-
tion index, which is calculated at each 1,000 m interval in
the troposphere and 2,000 m interval in the stratosphere. The
weighted average algorithm in the troposphere is described as
follows:
Step 1
: Calculate the difference (
delta_atm_ref
(
i
)) of two at-
mospheric refraction indexes at every 1,000 m interval.
Step 2
: Calculate the difference (
total_delta_atm_ref
) of the at-
mospheric refraction index at the surface and top troposphere.
Step 3
: Calculate the weight of each interval:
weight
(
i
) =
delta_atm_ref
(
i
)/
total_delta_atm_ref
Step 4
: Calculate mean atmospheric refraction index (
mean_
atm_ref
) of troposphere.
mean_atm_ref
=
sum
[
weight
(
i
)
·atm_ref
(
i
)]
where
atm_ref
(
i
) is calculated by Equations 12 to 17 at any
altitude increased 1,000 m interval in troposphere.
For the 0.5 μm blue light, the atmospheric refraction index
is 1.000014132 (n2) in the stratosphere at N60°, N30°, S30°
and the Equator. The atmospheric refraction index in the
troposphere is 1.000199059 (n1) at N60° and 1.000187379
(n1) at the Equator. As for the atmospheric refraction index
of different wavelength monochromatic light, Figure 7 shows
T
able
1. A
tmospheric
R
efraction
I
ndexes
C
hange with
A
ltitude
at
the
E
quator
, N60°, N30°
and
S30°
Altitude
(m)
N60
Degrees
N30
Degrees
Equator
S30
Degrees
1000 1.000268639 1.000250154 1.000242816 1.000249707
3000 1.000221848 1.000209777 1.000204972 1.000209484
5000 1.000184809 1.000178003 1.000175255 1.000177835
7000 1.000155253 1.000152781 1.000151744 1.000152718
9000 1.000131491 1.000132614 1.000133037 1.00013264
11000 1.000112255 1.000116392 1.000118097 1.000116495
15000 1.000044223 1.000044223 1.000044223 1.000044223
20000 1.000020098 1.000020098 1.000020098 1.000020098
30000 1.000003847 1.000003847 1.000003847 1.000003847
40000 1.000000753 1.000000753 1.000000753 1.000000753
50000 1.000000003 1.000000003 1.000000003 1.000000003
60000 1.000000034 1.000000034 1.000000034 1.000000034
70000 1.000000014 1.000000014 1.000000014 1.000000014
80000 1.000000002 1.000000002 1.000000002 1.000000002
T
able
2. C
haracteristics
of
A
tmospheric
R
efraction
I
ndex
Layer
Number Layer Name
Base
Altitude
(m)
Top
Altitude
(m)
Atmospheric
Refraction Index
1 Troposphere
0
11019
Varying with
latitude and
altitude.
2
Tropopause 11019
20063
Varying only with
altitude.
3 Stratosphere 20063
32162
4 Stratosphere 32162
47350
5 Stratopause 47350
51413
The refraction
index is 1.
6 Mesosphere 51413
71802
7 Mesosphere 71802
86000
8
Mesopause 86000
—
Figure 6. Two layers atmospheric refraction model
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
June 2016
431
