This survey report points out the progress and insufficiencies in the assessment and prediction of atmospheric effects on thermal radiation from an effective point source in the troposphere to a 2-π sr receiver at the ground. Major findings of investigators during the past two decades are summarized, which also provide additional conclusions. Complicated transmission problems can, futhermore, be treated theoretically by assuming model type atmospheres and solving the radiation transfer equation by an available technique such as the Monte Carlo method. Some of the major results of this method are also presented.

Ralph G. Eldridge and John C. Johnson J. Opt. Soc. Am. 48(7) 463-468 (1958)

References

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Total thermal intensity incident on the target (denoted in this report in units. of calories/cm^{2})

F

Fraction of the total yield of the nuclear weapon (TNT equivalent) that is emitted as thermal radiation

W

Total energy yield of the nuclear weapon (expressed in calories)

T_{t}, T_{2}_{π}

Total atmospheric transmittance as commonly defined by T_{t} or T_{2}_{π} =
$$({I}_{t}/{I}_{0})\xf7({D}^{2}/{{D}_{0}}^{2})$$such that T_{t} = 1 at D = D_{0}, or, as denoted in the report, T_{t} = T_{d}(1 + H)

I_{t}

Total thermal intensity at distance D

I_{0}

Total thermal intensity at unit distance from the source

D

Source-to-target straight-line distance

D_{0}

Unit distance from the source

T_{d}

Direct atmospheric transmittance, including the square of the distance attenuation, as defined by
$${T}_{d}=\text{exp}(-aD)$$such that T_{d} = 1 at D = D_{0}

a

The direct exponential attenuation coefficient defined by
$${I}_{d}={I}_{0}\hspace{0.17em}\text{exp}(-aD)\xf7({D}^{2}/{{D}_{0}}^{2})$$(denoted in this report in units of km^{−1})

H

Indirect thermal intensity ÷ direct thermal intensity

V

Meteorological (met.) range where V = 3.9/a

aD

Optical thickness, optical depth, or optical path, which is a measure of the optical turbidity of the atmosphere

A

Albedo or the ratio of the quantity of thermal radiation reflected by a body to the quantity incident upon it

h

Source height or altitude

secθ

Geometry parameter denoted by D/h

t′

Elapsed time from beginning of nuclear detonation

t′ max

Elapsed time from beginning of nuclear dentonation to the occurrence of the second thermal maximum

T(τ)

Total thermal transmissivity of a blackbody source whose radiation distribution as a function of wavelength corresponds to a temperature τ

Ts(secθ, τ)

Scattered thermal transmissivity as a function of secθ and τ

N(λ_{i}, τ)

Fraction of the total thermal radiation emitted by a blackbody at temperature τ in the ith wavelength interval

F(λ_{i}, secθ)

Scattered radiation flux incident on a 2-π receiver in the ith wavelength interval and at a slant range corresponding to secθ

T_{wv}(λ_{i}, secθ)

Water vapor transmittance in the ith wavelength interval and at a slant range corresponding to secθ

H.O.B.

Effective source altitude or height of burst of nuclear weapon

Clear skies, hazy, low surface albedo, source to receiver distances (D) ≤ 16 km. Horizontal path measurements near water surface.

T_{2}_{π} (Extrapolated) = exp (−aD){1 + 0.5[exp(aD) − 1]} where aD ≤ 2.4. NOTE: 2_{−}_{π} = subscript refers to a 2_{−}_{π} sr or a 180° planar field of view receiver.

Clear skies, cloudy, fog patches, water fog, ice fog, and snow, high ground albedo, D ≤ 7 km. Horizontal path measurements with source 30 m above ground level receiver.

See Fig. 2. No well defined, single expression could be determined due to frequent local weather instabilities. Some evidence present, however, of high enhancement factors in the presence of clouds and a high ground albedo.

Clear skies, hazy cloudy, low ground albedo, D ≤ 12 km. Horizontal path measurements near ground level.

T_{2}_{π} = exp(−aD)[exp(0.58aD)], where H = exp(0.58aD) − 1 and 0.025 km^{−1} ≤ a ≤ 0.11 km^{−1} for the clear skies case. No transmission equation could be determined for cloudy skies due to a lack of cloud, uniformity in the local area.

Haze, mist, fog, clouds, low and high ground albedo, D ≤ 30 km. Horizontal path measurements near ground level.

T_{160°} = exp(−aD)[exp(0.55aD)], where H = exp(0.55aD) − 1 and 0.40 km^{−1} ≤ a ≤ 8.0 km for the cloudless low albedo case. In presence of clouds and high ground albedo the enhancement factor reaches peak value of about 500% (Fig. 3).

Clear skies, haze, light snow, clouds, low and high ground albedo. Air to ground, long range slant path measurements.

T_{2}_{π} = exp(−aD)[exp(aD/2)], where H = exp(aD/2) − 1 and 0.02 km^{−1} ≤ a ≤ 0.20 km^{−1} for clear skies and haze conditions. In the presence of clouds and high ground albedo the enhancement factor reaches a peak value of about 500% (Fig. 3).

Derived by I. Cantor from the data obtained by Hiser et al.

Table III

Model Atmosphere (Collins et al.16) Tropical (15°N)

Vertical humidity profile

Altitude(km)

Temp. (°C)

Rel. Humidity (%)

Absolute humidity (g/m^{3})

0.0

27

75

17

1.0

21

75

12

2.0

15

75

9

2.5

14

35

4

4.0

4

35

2

6.0

−10

35

0.8

8.0

−23

30

0.2

10.0

−36

20

0.03

Size distribution profile

Haze:

vertical distribution according to the Elterman model and with two assumed, prevailing haze concentrations and met. ranges during morning and afternoon:

Morning

Afternoon

N(r) ≈ r^{−2.5}

N(r) ≈ r^{−3.5}

Ground met. range 3 km

Ground met. range 25 km

Table IV

Model Atmosphere (Collins et al.16) Midlatitude (45°N)

Vertical humidity profile

Altitude (km)

Temp. (°C)

Relative humidity (%)

Absolute humidity (g/m^{3})

Summer

Winter

Summer

Winter

Summer

Winter

0.0

21

−1

75

77

12

3

1.0

16

−4

65

70

8

2.2

2.0

12

−8

55

65

6

1.6

3.0

6

−12

45

55

3

1.0

4.0

0

−18

40

50

2

0.55

6.0

−12

−30

30

35

0.5

0.17

8.0

−25

−42

30

35

0.17

0.04

10.0

−38

−54

30

30

0.05

—

Size distribution profile

Haze—Summer:

Vertical distribution according to the Elterman model, ground met. range 25 km N(r) ≈ r^{−4}

Haze—Winter:

Vertical distribution according to the Elterman model, ground met. range 25 km N(r) ≈ r^{−4}.

Inversion profile up to 2-km altitude, ground met. range 3 km. Above 2-km altitude Elterman model assumed, with 25-km ground met. range N(r) ≈ r^{−3}.

Snow-covered surface to 0.80 neutral reflectance in the 0.40–0.90-μ range. From 0.90 μ to about 4 μ assume a monotonically decreasing reflectance coefficient with increasing wavelength so that at 0.9 μ the reflectance = 0.80 and at 3 μ = 0.01.

Rayleigh distribution with negligible absolute humidity.

Assume following altitude distribution:

Altitude (km)

T (°C)

Td (dew point temperature °C)

Relative humidity (%)

0.2

−34

80

0.3

−26

0.4

−21

−25

70

1.0

−26

−36

1.3

−18

−27

2.8

−24

−31

58

5.1

−37

8.5

−55

11.1

−54

Tables (5)

Table I

Symbols

Q

Total thermal intensity incident on the target (denoted in this report in units. of calories/cm^{2})

F

Fraction of the total yield of the nuclear weapon (TNT equivalent) that is emitted as thermal radiation

W

Total energy yield of the nuclear weapon (expressed in calories)

T_{t}, T_{2}_{π}

Total atmospheric transmittance as commonly defined by T_{t} or T_{2}_{π} =
$$({I}_{t}/{I}_{0})\xf7({D}^{2}/{{D}_{0}}^{2})$$such that T_{t} = 1 at D = D_{0}, or, as denoted in the report, T_{t} = T_{d}(1 + H)

I_{t}

Total thermal intensity at distance D

I_{0}

Total thermal intensity at unit distance from the source

D

Source-to-target straight-line distance

D_{0}

Unit distance from the source

T_{d}

Direct atmospheric transmittance, including the square of the distance attenuation, as defined by
$${T}_{d}=\text{exp}(-aD)$$such that T_{d} = 1 at D = D_{0}

a

The direct exponential attenuation coefficient defined by
$${I}_{d}={I}_{0}\hspace{0.17em}\text{exp}(-aD)\xf7({D}^{2}/{{D}_{0}}^{2})$$(denoted in this report in units of km^{−1})

H

Indirect thermal intensity ÷ direct thermal intensity

V

Meteorological (met.) range where V = 3.9/a

aD

Optical thickness, optical depth, or optical path, which is a measure of the optical turbidity of the atmosphere

A

Albedo or the ratio of the quantity of thermal radiation reflected by a body to the quantity incident upon it

h

Source height or altitude

secθ

Geometry parameter denoted by D/h

t′

Elapsed time from beginning of nuclear detonation

t′ max

Elapsed time from beginning of nuclear dentonation to the occurrence of the second thermal maximum

T(τ)

Total thermal transmissivity of a blackbody source whose radiation distribution as a function of wavelength corresponds to a temperature τ

Ts(secθ, τ)

Scattered thermal transmissivity as a function of secθ and τ

N(λ_{i}, τ)

Fraction of the total thermal radiation emitted by a blackbody at temperature τ in the ith wavelength interval

F(λ_{i}, secθ)

Scattered radiation flux incident on a 2-π receiver in the ith wavelength interval and at a slant range corresponding to secθ

T_{wv}(λ_{i}, secθ)

Water vapor transmittance in the ith wavelength interval and at a slant range corresponding to secθ

H.O.B.

Effective source altitude or height of burst of nuclear weapon

Clear skies, hazy, low surface albedo, source to receiver distances (D) ≤ 16 km. Horizontal path measurements near water surface.

T_{2}_{π} (Extrapolated) = exp (−aD){1 + 0.5[exp(aD) − 1]} where aD ≤ 2.4. NOTE: 2_{−}_{π} = subscript refers to a 2_{−}_{π} sr or a 180° planar field of view receiver.

Clear skies, cloudy, fog patches, water fog, ice fog, and snow, high ground albedo, D ≤ 7 km. Horizontal path measurements with source 30 m above ground level receiver.

See Fig. 2. No well defined, single expression could be determined due to frequent local weather instabilities. Some evidence present, however, of high enhancement factors in the presence of clouds and a high ground albedo.

Clear skies, hazy cloudy, low ground albedo, D ≤ 12 km. Horizontal path measurements near ground level.

T_{2}_{π} = exp(−aD)[exp(0.58aD)], where H = exp(0.58aD) − 1 and 0.025 km^{−1} ≤ a ≤ 0.11 km^{−1} for the clear skies case. No transmission equation could be determined for cloudy skies due to a lack of cloud, uniformity in the local area.

Haze, mist, fog, clouds, low and high ground albedo, D ≤ 30 km. Horizontal path measurements near ground level.

T_{160°} = exp(−aD)[exp(0.55aD)], where H = exp(0.55aD) − 1 and 0.40 km^{−1} ≤ a ≤ 8.0 km for the cloudless low albedo case. In presence of clouds and high ground albedo the enhancement factor reaches peak value of about 500% (Fig. 3).

Clear skies, haze, light snow, clouds, low and high ground albedo. Air to ground, long range slant path measurements.

T_{2}_{π} = exp(−aD)[exp(aD/2)], where H = exp(aD/2) − 1 and 0.02 km^{−1} ≤ a ≤ 0.20 km^{−1} for clear skies and haze conditions. In the presence of clouds and high ground albedo the enhancement factor reaches a peak value of about 500% (Fig. 3).

Derived by I. Cantor from the data obtained by Hiser et al.

Table III

Model Atmosphere (Collins et al.16) Tropical (15°N)

Vertical humidity profile

Altitude(km)

Temp. (°C)

Rel. Humidity (%)

Absolute humidity (g/m^{3})

0.0

27

75

17

1.0

21

75

12

2.0

15

75

9

2.5

14

35

4

4.0

4

35

2

6.0

−10

35

0.8

8.0

−23

30

0.2

10.0

−36

20

0.03

Size distribution profile

Haze:

vertical distribution according to the Elterman model and with two assumed, prevailing haze concentrations and met. ranges during morning and afternoon:

Morning

Afternoon

N(r) ≈ r^{−2.5}

N(r) ≈ r^{−3.5}

Ground met. range 3 km

Ground met. range 25 km

Table IV

Model Atmosphere (Collins et al.16) Midlatitude (45°N)

Vertical humidity profile

Altitude (km)

Temp. (°C)

Relative humidity (%)

Absolute humidity (g/m^{3})

Summer

Winter

Summer

Winter

Summer

Winter

0.0

21

−1

75

77

12

3

1.0

16

−4

65

70

8

2.2

2.0

12

−8

55

65

6

1.6

3.0

6

−12

45

55

3

1.0

4.0

0

−18

40

50

2

0.55

6.0

−12

−30

30

35

0.5

0.17

8.0

−25

−42

30

35

0.17

0.04

10.0

−38

−54

30

30

0.05

—

Size distribution profile

Haze—Summer:

Vertical distribution according to the Elterman model, ground met. range 25 km N(r) ≈ r^{−4}

Haze—Winter:

Vertical distribution according to the Elterman model, ground met. range 25 km N(r) ≈ r^{−4}.

Inversion profile up to 2-km altitude, ground met. range 3 km. Above 2-km altitude Elterman model assumed, with 25-km ground met. range N(r) ≈ r^{−3}.

Snow-covered surface to 0.80 neutral reflectance in the 0.40–0.90-μ range. From 0.90 μ to about 4 μ assume a monotonically decreasing reflectance coefficient with increasing wavelength so that at 0.9 μ the reflectance = 0.80 and at 3 μ = 0.01.

Rayleigh distribution with negligible absolute humidity.