This paper presents a passive method for computation of thermal IR transmittance over slant paths. This double viewing angle technique utilizes data gathered by a radiometer or imager carried by a manned or unmanned aircraft. A sensitivity analysis showed the effect of changes or errors in input parameters on calculated transmittances. The analysis suggested the applicability and limitations of this method. Accuracies attainable through the use of the double viewing angle method appear to be similar to those from more complex techniques for many atmospheric conditions.
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Using Rs from Eq. (2) and w, compute an initial Ts.
Use the interative procedure [Eq. (3)] to compute best estimate of Ts.
Compute
using
obtained from Ta and the best estimate of Ts.
Compute k from Eq. (1) and the initial value of τ.
Compute the estimated value of R1(Re).
Obtain τ using the iterative procedure that compares Re with R1.
Descriptions of listed steps and definitions of variables are given in the text.
Table II
Difference in Transmittance (Δτ) from the Surface to Altitude Z Resulting from Use of
.a
Δτ%
z(m)
1
2
3
4
300
−0.38 (−1.06)
−0.08 (−0.24)
−0.39 (−1.09)
−0.09 (−0.25)
600
−1.65 (−5.01)
−0.34 (−1.04)
−1.74 (−5.16)
−0.38 (−1.09)
900
−3.95 (−12.93)
−0.79 (−2.98)
−4.20 (−13.38)
−0.89 (−2.61)
1200
−7.59 (−26.59)
−1.45 (−4.72)
−8.11 (−27.69)
−1.65 (−5.01)
Columns 1 and 3 had base line (truth) values of transmittance τ of 0.95/100 m (very moist), and columns 2 and 4 had values of 0.975/100 m (dry). Temperature lapse rates were −10 and −5K km−1 for columns 1,2 and 3,4, respectively. The values in parentheses were derived from Eq. (1) only.
is mean atmospheric temperature of the surface to z layer.
Table III
Difference in Transmittance(Δτ) from the Surface to Z Resulting from Use of
for Two Extreme Situationsa
Δτ (%)
z (m)
1
2
z (m)
3
4
600
−5.2(−8.5)
−0.2(−0.6)
300
−0.4(−1.1)
−0.0(−0.1)
700
5.3(4.7)
−4.5(−6.2)
400
−2.0(−3.1)
−3.9(−4.7)
900
13.7(13.7)
−12.3(−18.5)
500
4.9(4.7)
−7.0(−9.0)
1200
18.1(17.6)
−22.7(−41.1)
600
7.9(7.8)
−9.5(−13.0)
Columns 1 and 3 were computed for a simulation of a very moist layer under a dry layer separated by an inversion. Columns 2 and 4 were for a dry layer under a very moist layer. The moist layer had a lapse rate of −5 K km−1 and a layer transmittance of 0.95/100 m; the dry layer had a values of −10 K km−1 and 0.98/100 m. The inversions were 1K from 400 to 500 m for columns 1 and 2 and 0.5 K from 300 to 350 m for columns 3 and 4. Values in parentheses were derived from Eq. (1) only.
is the mean atmospheric temperature of the surface to z layer.
Table IV
Maritime Atmosphere In the Carribean Near Barbados Based on Actual Data,9a
Layer
z (m)
T(K)
τn
τ
0
301.2
1
0.9000
305
296.2
0.9000
2
0.9170
610
294.4
0.8253
3
0.9270
915
292.6
0.7651
4
0.9310
1220
290.8
0.7123
5
0.9370
1525
289.0
0.6674
6
0.9430
1830
267.2
0.6427
Temperatures T are measured values. τn are sublayer transmittances computed from sublayer emissivities (τn = 1 − ∊n) calculated for 10–12 μm.9τ is the transmittance from the surface to the listed altitude z.
Table V
1800 and 0600 CDT (2300 and 1100 Z) soundings for 26 Sept. 1980 at Dayton, OH13,a
Dry (23Z)
Moist (11Z)
z
T
RH
z
T
RH
298
15.0
43
298
8.4
86
407
14.1
40
715
6.9
93
1092
7.7
58
1091
5.4
81
1559
2.6
78
1665
4.0
23
1849
0.0
90
2123
2.2
9
2047
0.8
22
2251
2.9
9
z is altitude in meters above sea level, T is temperature in Celsius and RH is relative humidity in percent. The dewpoints for z below ~1100 m were higher by 2.4–4.8°C for the moist case. A third sounding at 1200 CDT (1600Z) was similar to the relatively dry case shown.
Table VI
Transmittance τ Errors Caused by Random Error for Various MDTa
MDT (K)
Average error (%)
Largest error (%)
0.1
1
2
0.2
2
4
0.3
3
5
MDT is defined in the text. τ errors shown are mean values derived from two τ (surface to z) profiles using input from Table IV and are relative to the simulation with no random error. MDT values listed represent random noise levels of ±0.08, 0.16, and 0.24%, respectively, at radiative temperatures near 290 K.
Table VII
Emissivities of a Number of Surfaces in the Thermal Infrareda
Surface
∊s
Wavelength (μm)
Asphalt paving
0.96
8–12
Bark
0.94–0.97
8–13
Basalt
0.90
8–12
Brick
0.92
8–14
Clay (red)
0.96
8–14
Concrete (dry)
0.97
8–12
Desert
0.90–0.93
8–14
Granite
0.82
8–12
Grass (live)
0.99
8–14
Grass (dead)
0.97
8–14
Grass (meadow fescue—dry)
0.88
8–13
Leaves
0.90–0.97
8–13
Leaves (orange)
0.99
8–14
Melting Snow
0.99
8–14
Peat
0.99
8–14
Sand
0.90–0.92
8–14
0.91–0.94
8–12
Sandy soil
0.92–0.98
8–13
Water
0.97–0.99
2–15
∊s is given to the nearest 0.01, and the nadir angle is 0° (vertical view). Mean values are presented. This table is derived from several sources.13,15,16,21–25
Table VIII
Transmittance τ Errors Caused by a Superadiabatic Layer from the Surface to 1 ma
ΔTs (K)
Dry
Moist
1
1.5
3.6
2
2.8
6.3
6
4.4
13.1
Truth values of τ were for the extremely moist (0.95/100-m) and extremely dry (0.98/100-m) atmospheres. For these simulations ∊s = 0.98, Tc = 270 K, and the lapse rate was approximately dry adiabatic (−10 K km−1) above 1 m. increase ΔTs is the temperature above 292 K (Ts for the case of no superadiabatic layer) representing lapse rates of −1, −2, and −6 K m−1, respectively.
Table IX
Computed Root Mean Square Error (Percent) for Four Categories of Sources of Error for a Moist and a Dry Atmospherea
Error source category
1
2
3
4
Dry
8.1
8.8
9.6
9.8/17.9
Moist
10.5
11.0
13.7
13.8/20.3
The source categories are (1) use of
to obtain
plus sensor error and incorrect input; (2) all of (1) plus ∊s not = 0.98 and ∊s for R1 and R2 not equal; (3) all of (2) plus superadiabatic lapse rate; (4) all of (3) plus inversion. Inversions are further divided into a low and relatively high intensity. Variables are explained in the text.
Using Rs from Eq. (2) and w, compute an initial Ts.
Use the interative procedure [Eq. (3)] to compute best estimate of Ts.
Compute
using
obtained from Ta and the best estimate of Ts.
Compute k from Eq. (1) and the initial value of τ.
Compute the estimated value of R1(Re).
Obtain τ using the iterative procedure that compares Re with R1.
Descriptions of listed steps and definitions of variables are given in the text.
Table II
Difference in Transmittance (Δτ) from the Surface to Altitude Z Resulting from Use of
.a
Δτ%
z(m)
1
2
3
4
300
−0.38 (−1.06)
−0.08 (−0.24)
−0.39 (−1.09)
−0.09 (−0.25)
600
−1.65 (−5.01)
−0.34 (−1.04)
−1.74 (−5.16)
−0.38 (−1.09)
900
−3.95 (−12.93)
−0.79 (−2.98)
−4.20 (−13.38)
−0.89 (−2.61)
1200
−7.59 (−26.59)
−1.45 (−4.72)
−8.11 (−27.69)
−1.65 (−5.01)
Columns 1 and 3 had base line (truth) values of transmittance τ of 0.95/100 m (very moist), and columns 2 and 4 had values of 0.975/100 m (dry). Temperature lapse rates were −10 and −5K km−1 for columns 1,2 and 3,4, respectively. The values in parentheses were derived from Eq. (1) only.
is mean atmospheric temperature of the surface to z layer.
Table III
Difference in Transmittance(Δτ) from the Surface to Z Resulting from Use of
for Two Extreme Situationsa
Δτ (%)
z (m)
1
2
z (m)
3
4
600
−5.2(−8.5)
−0.2(−0.6)
300
−0.4(−1.1)
−0.0(−0.1)
700
5.3(4.7)
−4.5(−6.2)
400
−2.0(−3.1)
−3.9(−4.7)
900
13.7(13.7)
−12.3(−18.5)
500
4.9(4.7)
−7.0(−9.0)
1200
18.1(17.6)
−22.7(−41.1)
600
7.9(7.8)
−9.5(−13.0)
Columns 1 and 3 were computed for a simulation of a very moist layer under a dry layer separated by an inversion. Columns 2 and 4 were for a dry layer under a very moist layer. The moist layer had a lapse rate of −5 K km−1 and a layer transmittance of 0.95/100 m; the dry layer had a values of −10 K km−1 and 0.98/100 m. The inversions were 1K from 400 to 500 m for columns 1 and 2 and 0.5 K from 300 to 350 m for columns 3 and 4. Values in parentheses were derived from Eq. (1) only.
is the mean atmospheric temperature of the surface to z layer.
Table IV
Maritime Atmosphere In the Carribean Near Barbados Based on Actual Data,9a
Layer
z (m)
T(K)
τn
τ
0
301.2
1
0.9000
305
296.2
0.9000
2
0.9170
610
294.4
0.8253
3
0.9270
915
292.6
0.7651
4
0.9310
1220
290.8
0.7123
5
0.9370
1525
289.0
0.6674
6
0.9430
1830
267.2
0.6427
Temperatures T are measured values. τn are sublayer transmittances computed from sublayer emissivities (τn = 1 − ∊n) calculated for 10–12 μm.9τ is the transmittance from the surface to the listed altitude z.
Table V
1800 and 0600 CDT (2300 and 1100 Z) soundings for 26 Sept. 1980 at Dayton, OH13,a
Dry (23Z)
Moist (11Z)
z
T
RH
z
T
RH
298
15.0
43
298
8.4
86
407
14.1
40
715
6.9
93
1092
7.7
58
1091
5.4
81
1559
2.6
78
1665
4.0
23
1849
0.0
90
2123
2.2
9
2047
0.8
22
2251
2.9
9
z is altitude in meters above sea level, T is temperature in Celsius and RH is relative humidity in percent. The dewpoints for z below ~1100 m were higher by 2.4–4.8°C for the moist case. A third sounding at 1200 CDT (1600Z) was similar to the relatively dry case shown.
Table VI
Transmittance τ Errors Caused by Random Error for Various MDTa
MDT (K)
Average error (%)
Largest error (%)
0.1
1
2
0.2
2
4
0.3
3
5
MDT is defined in the text. τ errors shown are mean values derived from two τ (surface to z) profiles using input from Table IV and are relative to the simulation with no random error. MDT values listed represent random noise levels of ±0.08, 0.16, and 0.24%, respectively, at radiative temperatures near 290 K.
Table VII
Emissivities of a Number of Surfaces in the Thermal Infrareda
Surface
∊s
Wavelength (μm)
Asphalt paving
0.96
8–12
Bark
0.94–0.97
8–13
Basalt
0.90
8–12
Brick
0.92
8–14
Clay (red)
0.96
8–14
Concrete (dry)
0.97
8–12
Desert
0.90–0.93
8–14
Granite
0.82
8–12
Grass (live)
0.99
8–14
Grass (dead)
0.97
8–14
Grass (meadow fescue—dry)
0.88
8–13
Leaves
0.90–0.97
8–13
Leaves (orange)
0.99
8–14
Melting Snow
0.99
8–14
Peat
0.99
8–14
Sand
0.90–0.92
8–14
0.91–0.94
8–12
Sandy soil
0.92–0.98
8–13
Water
0.97–0.99
2–15
∊s is given to the nearest 0.01, and the nadir angle is 0° (vertical view). Mean values are presented. This table is derived from several sources.13,15,16,21–25
Table VIII
Transmittance τ Errors Caused by a Superadiabatic Layer from the Surface to 1 ma
ΔTs (K)
Dry
Moist
1
1.5
3.6
2
2.8
6.3
6
4.4
13.1
Truth values of τ were for the extremely moist (0.95/100-m) and extremely dry (0.98/100-m) atmospheres. For these simulations ∊s = 0.98, Tc = 270 K, and the lapse rate was approximately dry adiabatic (−10 K km−1) above 1 m. increase ΔTs is the temperature above 292 K (Ts for the case of no superadiabatic layer) representing lapse rates of −1, −2, and −6 K m−1, respectively.
Table IX
Computed Root Mean Square Error (Percent) for Four Categories of Sources of Error for a Moist and a Dry Atmospherea
Error source category
1
2
3
4
Dry
8.1
8.8
9.6
9.8/17.9
Moist
10.5
11.0
13.7
13.8/20.3
The source categories are (1) use of
to obtain
plus sensor error and incorrect input; (2) all of (1) plus ∊s not = 0.98 and ∊s for R1 and R2 not equal; (3) all of (2) plus superadiabatic lapse rate; (4) all of (3) plus inversion. Inversions are further divided into a low and relatively high intensity. Variables are explained in the text.
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