Abstract

This paper, Part 2, presents additional atmospheric optical data, comparable to the data presented in Part 1, but for a different type of day, and for four descents instead of two. All descents were before local apparent noon. Simultaneous spectral irradiance data were recorded at the surface of Crater Lake. Data presented are altitude profiles of heading of aircraft, temperature, relative humidity, equilibrium luminance, horizontal path function, attenuation length, nadir luminance, upwelling and downwelling illuminances and their ratios, reflectance calculated from nadir luminance, atmospheric beam transmittances for vertical path of sight as a function of solar zenith angle, and downwelling illuminance as a function of solar zenith angle.

© 1968 Optical Society of America

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References

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  1. R. C. Smith, J. E. Tyler, J. Opt. Soc. Amer. 57, 589 (1967).
    [CrossRef]
  2. J. E. Tyler, R. C. Smith, J. Opt. Soc. Amer. 57, 595 (1967).
    [CrossRef]
  3. S. Q. Duntley et al., Appl. Opt. 3, 549 (1964).
    [CrossRef]
  4. J. I. Gordon, P. V. Church, Appl. Opt. 5, 793 (1966).
    [CrossRef] [PubMed]
  5. A. R. Boileau, J. I. Gordon, Appl. Opt. 5, 803 (1966).
    [CrossRef] [PubMed]
  6. J. I. Gordon, P. V. Church, Appl. Opt. 5, 919 (1966).
    [CrossRef] [PubMed]
  7. A. R. Boileau, Appl. Opt. 7, 407 (1968).
    [CrossRef] [PubMed]

1968

1967

R. C. Smith, J. E. Tyler, J. Opt. Soc. Amer. 57, 589 (1967).
[CrossRef]

J. E. Tyler, R. C. Smith, J. Opt. Soc. Amer. 57, 595 (1967).
[CrossRef]

1966

1964

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Figures (21)

Fig. 1
Fig. 1

Aircraft heading, magnetic, during descents. True heading is magnetic heading plus 20°. The change of heading at 6200 m during second descent was made in order to cross the center of Crater Lake; the change at 4900 m was made in order to resume original heading. During the third descent it became necessary to change aircraft heading at 3400 m to avoid clouds.

Fig. 2
Fig. 2

Altitude profiles of dry air temperature. Only minor changes in these profiles, which are of little significance, occurred during the nearly 4 h elapsed time between the start of the first descent and the termination of the fourth descent.

Fig. 3
Fig. 3

Altitude profiles of relative humidity. These profiles show no change in relative humidity during the time of the four descents except for the stratum between 3250 m and 2250 m.

Fig. 4
Fig. 4

Aircraft altitude as a function of time during the four descents. Changes in the attitude of the aircraft during descent can be inferred from these plots. It appears that the attitude of the aircraft remained virtually unchanged once a descent was started.

Fig. 5
Fig. 5

Profiles of equilibrium luminance Bq (z, 90°, ϕ). The values of ϕ for the four descents were 133°, 46°, 148°, and 22°. The random fluctuations with altitude are believed to be spurious with the true equilibrium luminance profiles being approximated by the envelopes of the maximum values. There seems to be no discernible change owing to the various values of ϕ.

Fig. 6
Fig. 6

Profiles of horizontal path function B* (z, 90°, ϕ). The four values of ϕ for the four descents are the same as listed for Bq (z, 90°, ϕ), Fig. 5. The large change in the value of B* (z, 90°, ϕ) at 3250 m during the third descent is attributed to the relatively large increase of relative humidity measured at that altitude during the same descent.

Fig. 7
Fig. 7

Profiles of attenuation length L(z) and equivalent attenuation length L ¯(z) for the first descent. The random fluctuations in the L(z) profile are primarily due to similar fluctuations of the equilibrium luminance profile.

Fig. 8
Fig. 8

Profile of L(z) and L ¯ (z) for the second descent. This profile and the profile of horizontal path function in Fig. 6 show an increase in attenuation in the strata at 3600 m and below.

Fig. 9
Fig. 9

The third descent profiles for L(z) and L ¯ (z). A comparison of this profile with that in Fig. 8 shows that the attenuation in the lower altitudes had continued to increase with elapsed time.

Fig. 10
Fig. 10

Attenuation length profiles for fourth descent. The L(z) profile and the L ¯ (z) profile for the third descent appear to be quite similar, but the transmittance calculated from these profiles (see Fig. 20) shows that the transmittance for the vertical path of sight during the fourth descent was higher than the transmittance during the third descent.

Fig. 11
Fig. 11

Nadir luminance Br (z, 180°, ϕ) during first descent. The apparent luminance of Crater Lake during the four descents is that between the arrows in Figs. 1114.

Fig. 12
Fig. 12

Nadir luminance during second descent.

Fig. 13
Fig. 13

Nadir luminance during third descent.

Fig. 14
Fig. 14

Nadir luminance during fourth descent.

Fig. 15
Fig. 15

Downwelling and upwelling illuminances, E(z, −) and E(z, +), respectively, during first and third descents. The solid line profiles are for the first descent, the broken line profiles are for the third descent.

Fig. 16
Fig. 16

Downwelling and upwelling illuminances for second and fourth descents. The solid line profiles are for the second descent, the broken line profiles are for the fourth descent.

Fig. 17
Fig. 17

Profiles of ratios of upwelling and downwelling illuminances during first and third descents and during second and fourth descents. These reflectances are found by the equation Rr(z, 180°, ϕ) = E(z, +)/E(z, −).

Fig. 18
Fig. 18

Profiles of terrain reflectance for first and third descents calculated from nadir luminances and downwelling illuminances by the equation Rr(z, 180°, ϕ) = πBr(z, 180°, ϕ)/E(z, −).

Fig. 19
Fig. 19

Profiles of terrain reflectance for second and fourth descents calculated in the same manner as the profile in Fig. 18.

Fig. 20
Fig. 20

Beam transmittance for the vertical path of sight as a function of the solar zenith angle. The data shown by filled circles were calculated from ground based data and the equation T ( 2070 , , ) = [ B s ( 2070 , θ s , ϕ s ) / B s 0 ] cos θ s .The data shown by elongated data points were from extrapolated aircraft data and the equation T(2070, 0°, 0°) = exp [− ∑Δz/L(z)]. During the forenoon, the beam transmittance for the vertical path of sight decreased as the solar zenith angle decreased. At 1315 (local apparent noon) the solar zenith angle was 25.75°.

Fig. 21
Fig. 21

Downwelling illuminance E(2070, −) as a function of solar zenith angle. The data indicated by the filled circles are those recorded by ground based irradiometer; the elongated data points are from extrapolated aircraft irradiometer data and the open box □, from spectroradiometric data weighted by the luminance efficiency function, recorded at the surface of Crater Lake. The ground station location was at an altitude of 2070 m. The surface of Crater Lake is at an altitude of 2020 m.

Equations (1)

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T ( 2070 , , ) = [ B s ( 2070 , θ s , ϕ s ) / B s 0 ] cos θ s .

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