Abstract

Systematics of the Novaya Zemlya (NZ) effect are discussed in the context of sunsets. We distinguish full mirages, exhibiting oscillatory light paths and their onsets, the subcritical mirages. Ray-tracing examples and sequences of solar images are shown. We discuss two historical observations by Fridtjof Nansen and by Vivian Fuchs, and we report a recent South Pole observation of the NZ effect for the Moon.

© 2003 Optical Society of America

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References

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  1. A. T. Young, G. W. Kattawar, P. Parvainen, “Sunset science. I. The mock mirage,” Appl. Opt. 36, 2689–2700 (1997).
    [CrossRef] [PubMed]
  2. G. De Veer, Waerachtige Beschryvinge van drie seylagiën ter werelt noyt soo vreemt ghehoort, Cornelis Claesz, ed. (Amsterdam, 1598).
  3. G. De Veer, The True and Perfect Description of Three Voyages, so Strange and Woonderfull That the Like Hath Never Been Heard of before; translation of Ref. 2 by William Phillip, ed. (Pauier, London, 1609).
  4. F. Nansen, Fram over polhavet: den Norske polarfaerd 1893–1896; med en tillaeg af Otto Sverdrup, H. Aschehoug, ed. (Kristiania, Oslo, 1897).
  5. E. Shackleton, South: The Story of Shackleton’s Last Expedition 1914–1917 (MacMillan, New York, 1920).
  6. Sir Vivian Fuchs, Sir Edmund Hillary, The Crossing of Antarctica, The Commonwealth Trans-Antarctic Expedition 1955–1958 (Cassel, London, 1958).
  7. S. Y. van der Werf, G. P. Können, W. H. Lehn, F. Steenhuisen, W. P. S. Davidson, “Gerrit de Veer’s true and perfect description of the Novaya Zemlya effect, 24–27 January 1597,” Appl. Opt. 42, 379–389 (2003).
    [CrossRef] [PubMed]
  8. S. Y. van der Werf, “Ray tracing and refraction in the modified US1976 atmosphere,” Appl. Opt. 42, 354–366 (2003).
    [CrossRef] [PubMed]
  9. L. H. Auer, E. M. Standish, “Astronomical refraction: computational method for all zenith angles,” Astron. J. 119, 2472–2477 (2000).
    [CrossRef]
  10. D. R. Lide, Handbook of Chemistry and Physics, 81st ed. (CRC Press, Boca Raton, Fla., 2000).
  11. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

2003

2000

L. H. Auer, E. M. Standish, “Astronomical refraction: computational method for all zenith angles,” Astron. J. 119, 2472–2477 (2000).
[CrossRef]

1997

Auer, L. H.

L. H. Auer, E. M. Standish, “Astronomical refraction: computational method for all zenith angles,” Astron. J. 119, 2472–2477 (2000).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

Davidson, W. P. S.

De Veer, G.

G. De Veer, Waerachtige Beschryvinge van drie seylagiën ter werelt noyt soo vreemt ghehoort, Cornelis Claesz, ed. (Amsterdam, 1598).

G. De Veer, The True and Perfect Description of Three Voyages, so Strange and Woonderfull That the Like Hath Never Been Heard of before; translation of Ref. 2 by William Phillip, ed. (Pauier, London, 1609).

Fuchs, Sir Vivian

Sir Vivian Fuchs, Sir Edmund Hillary, The Crossing of Antarctica, The Commonwealth Trans-Antarctic Expedition 1955–1958 (Cassel, London, 1958).

Hillary, Sir Edmund

Sir Vivian Fuchs, Sir Edmund Hillary, The Crossing of Antarctica, The Commonwealth Trans-Antarctic Expedition 1955–1958 (Cassel, London, 1958).

Kattawar, G. W.

Können, G. P.

Lehn, W. H.

Lide, D. R.

D. R. Lide, Handbook of Chemistry and Physics, 81st ed. (CRC Press, Boca Raton, Fla., 2000).

Nansen, F.

F. Nansen, Fram over polhavet: den Norske polarfaerd 1893–1896; med en tillaeg af Otto Sverdrup, H. Aschehoug, ed. (Kristiania, Oslo, 1897).

Parvainen, P.

Shackleton, E.

E. Shackleton, South: The Story of Shackleton’s Last Expedition 1914–1917 (MacMillan, New York, 1920).

Standish, E. M.

L. H. Auer, E. M. Standish, “Astronomical refraction: computational method for all zenith angles,” Astron. J. 119, 2472–2477 (2000).
[CrossRef]

Steenhuisen, F.

van der Werf, S. Y.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

Young, A. T.

Appl. Opt.

Astron. J.

L. H. Auer, E. M. Standish, “Astronomical refraction: computational method for all zenith angles,” Astron. J. 119, 2472–2477 (2000).
[CrossRef]

Other

D. R. Lide, Handbook of Chemistry and Physics, 81st ed. (CRC Press, Boca Raton, Fla., 2000).

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University, Cambridge, UK, 1999).

G. De Veer, Waerachtige Beschryvinge van drie seylagiën ter werelt noyt soo vreemt ghehoort, Cornelis Claesz, ed. (Amsterdam, 1598).

G. De Veer, The True and Perfect Description of Three Voyages, so Strange and Woonderfull That the Like Hath Never Been Heard of before; translation of Ref. 2 by William Phillip, ed. (Pauier, London, 1609).

F. Nansen, Fram over polhavet: den Norske polarfaerd 1893–1896; med en tillaeg af Otto Sverdrup, H. Aschehoug, ed. (Kristiania, Oslo, 1897).

E. Shackleton, South: The Story of Shackleton’s Last Expedition 1914–1917 (MacMillan, New York, 1920).

Sir Vivian Fuchs, Sir Edmund Hillary, The Crossing of Antarctica, The Commonwealth Trans-Antarctic Expedition 1955–1958 (Cassel, London, 1958).

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Figures (10)

Fig. 1
Fig. 1

Illustration of the ray-tracing procedure. The observer is in A at height h obs above sea level. The ray enters from the right and passes through point P, with polar coordinates (R, ϕ) at height h above sea level, where its angle with the local horizontal is β. At P a local frame of reference is defined with unit vectors û x (horizontal) and û h (vertical).

Fig. 2
Fig. 2

Left, the modified US1976 atmosphere, shifted in the troposphere to match the sea-level temperature. At low heights an additional temperature profile may be added, indicated by the insets and shown enlarged in the middle diagrams: A, standard atmosphere, sea-level temperature T 0 = 288.15 K (15 °C). B, a warm layer as could produce a desert mirage for an observer above it. T 0 = 300.15 K (27 °C), h ciso = 4 m, a = 0.5 m, and ΔT = -2 °C. C, a cold layer as could produce the NZ effect. T 0 = 250.15 K (-23 °C), h ciso = 45 m, a = 4 m, and ΔT = 5 °C. The diagrams on the right show the corresponding terrestrial ray-curvatures in the lower atmosphere for near-horizontal rays.

Fig. 3
Fig. 3

Light paths for the standard atmosphere (inset A of Fig. 2) traced backwards from an observer’s height at 15 m, up to an apparent altitude of 50′. The corresponding images of the Sun are shown along the top, for equidistant steps in altitude. The scale of the horizontal distance along the Earth (x axis) has been compressed by a factor 500 relative to the y axis.

Fig. 4
Fig. 4

Transformation curves for the standard atmosphere, the desert mirage atmosphere and the NZ mirage atmosphere shown in Fig. 2, for an observer at h = 15 m. If there were no atmosphere, the true and the apparent altitudes would be equal (upper curve).

Fig. 5
Fig. 5

Light paths for the desert mirage atmosphere (inset B of Fig. 2), observer’s height at 15 m, and corresponding images of the Sun in equidistant steps up to 50′ apparent altitude. The desert mirage arises if there is a sufficiently warm layer below the observer (inferior mirage).

Fig. 6
Fig. 6

Light paths for the NZ mirage atmosphere (inset C of Fig. 2), observer’s height at 15 m, and corresponding images of the Sun. The strong temperature inversion is here above the observer (superior mirage). For apparent altitudes, β, larger than a given value, the backwards traced rays (indicated by A) break through the inversion. Also, rays of sufficient negative β, which (just) miss the ground, break through the inversion on their upward course (indicated by B). In a limited range of apparent altitudes, around β = 0, rays follow oscillatory paths (indicated by C). Eventually they escape in a region where the inversion is less strong. The Sun’s images on top arise from rays A and B; rays C are missing, which causes the gap. Rays C may produce images when the Sun is well below the horizon (images to the right).

Fig. 7
Fig. 7

A, Temperature profile of an inversion, ΔT = 5.0 °C, centered around h ciso = 40 m with a width parameter a = 3 m. B, Terrestrial ray-curvature, showing the heights h 1 and h 2, between which c T is negative. For an observer at h = 45 m: C, full inferior NZ mirage, ΔT = 5.0 °C. D, Subcritical inferior NZ mirage, ΔT = 1.5 °C. For an observer at h = 15 m: E, full superior NZ mirage, ΔT = 4.0 °C. F, Subcritical superior NZ mirage, ΔT = 3.7 °C.

Fig. 8
Fig. 8

Transformation curves between apparent altitude and true altitude, for red (650 nm), yellow (580 nm), and green light (520 nm). The vertical axes show the true altitude, ϕ(∞), and the horizontal axes the apparent altitude, β, both in minutes of arc. Left, Inferior NZ mirages for an observer at h = 45 m. From top to bottom: ΔT = 0.5, 1.0, 1.5 (subcritical), and 5.0 °C (full mirage). Right, Superior NZ mirages for an observer at h = 15 m. From top to bottom: ΔT = 3.7 (subcritical), 4.0, and 7.0 °C. Note the enormous color dispersion of the (just) subcritical superior mirage.

Fig. 9
Fig. 9

Images of the Sun for (from left to right) subcritical NZ mirages: superior, ΔT = 3.7 °C (column 1); inferior, ΔT = 1.5 °C (column 2). Full NZ mirages: superior, ΔT = 7.0 °C (column 3); inferior, ΔT =5.0 °C (column 4). For the subcritical mirages the colors may be realistic; for the full mirages only the red will survive. Note the large green flash in column 1.

Fig. 10
Fig. 10

Drawing by Fridtjof Nansen of the NZ effect as he observed it on 16 February 1894 at 80° 01′ N and approximately 135° E.

Tables (1)

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Table 1 Observation of the Novaya Zemlya Effect for the Moon at South Pole Station on 7–8 May 1998

Equations (34)

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1r=1nh, xcosβnh, xh-sinβnh, xx,
cTh, βd2h/dx21+dh/dx23/2=1r+1Rcosβ1+sin2β,
d2hdx21r+1RE=cTh, β=0.
dRdϕ=R tanβ,
dβdϕ=1+1rRcosβ.
nh, x=1+AλP0, xTh, x×exp-B 0hghg0dhTh, x.
Th, x=TMUSA76h-ΔTx+ΔTx1+exp-h-hcisox/ax.
flatteninghor.axis-vert.axishor.axis=dϕ-βdϕ=-dξdϕ.
flatteningβ=01-REcTβ=0=AλP0RET02dTdh0+B.
flatteningβ=00.211+29.2dTdh0.
dTdh-B=-3.4 10-2 °C/m.
dTdh>Th2AλPhRE-B,
d2h-h1dx2=dcTdhh=h1h-h1.
ax=a0, xx0,
ax=a01+αx-x02, x>x0,
1r=1nνˆ · n,
νˆ=cosβûh-sinβûx,
n=nhûh+nxûx,
1r=1ncosβnh-sinβnx.
β=arctan1RdRdϕ,
dβdϕ=11+1RdRdϕ21Rd2Rdϕ2-1R2dRdϕ2.
dβdϕ=1+Rr1cosβ=1+Rr1+1RdRdϕ21/2.
1Rd2Rdϕ2-1R2dRdϕ2=1+Rr1+1RdRdϕ21/2×1+1RdRdϕ2.
d2hdx2=1R+1r1+dhdx21/2×1+dhdx2+1Rdhdx2,
cTβd2hdx21+dhdx23/2=1r+1Rcosβ1+sin2β.
d2hdx21r+1RE=cTh, β=0,
nλh, x=1+AλPh, xTh, x,
Ph, x=P0, xexp-mk0hghdhTh, x,
gh=g0RERE+h2.
nλh, x=1+AλPh, xTh, x×exp-B 0hghg0dhTh,
1r=1nhdndh=-AλP0T01ThdThdh+BTh.
dϕ=dxRE=dβ1+RE/r.
flattening=1-dβdϕ=-RE/r.
flattening-RErβ=0=AλP0RET02dTdh0+B,

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