Abstract

In recent years, a new technique has been proposed to measure path-averaged rain rates by observing the rain-droplet-induced irradiance scintillation of a laser beam. The theoretical formulation was developed under the assumption that the detector is in the far-field region of the raindrop-induced scattering patterns. Preliminary experimental results for an optical link of 200 m supported this theory. For shorter path-lengths, the droplets in the near-field region effect the raindrop-induced scintillation. This paper discusses the modification to the theory to include the near-field effects. A 30-m laser link has been set up to measure path-averaged rain rates at COMSAT Laboratories, Clarksburg, Md., for more than 1 yr. The preliminary sample data indicate good agreement with the averaged rain rates measured by two tipping-bucket rain gauges that are 20 m apart and deployed along the path. The correlation of the optically measured rain rates with the average of the two individual bucket rain rates is better than the correlation of the rain rates measured by the two individual tipping-bucket rain gauges.

© 1983 Optical Society of America

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References

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  1. T. Wang, K. B. Earnshaw, R. S. Lawrence, Appl. Opt. 17, 384 (1978).
    [CrossRef] [PubMed]
  2. T. S. Marshall, W. M. Palmer, J. Meteorol. 5, 165 (1948).
    [CrossRef]
  3. R. Gunn, G. D. Kinzer, J. Meteorol. 6, 243 (1949).
    [CrossRef]
  4. T. Wang, G. R. Ochs, W. D. Cartwright, B. W. Guderian, S. Y. Simpson, NOAA Technical Memorandum ERL WPL-95, (Jan.1982).
  5. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

1978 (1)

1949 (1)

R. Gunn, G. D. Kinzer, J. Meteorol. 6, 243 (1949).
[CrossRef]

1948 (1)

T. S. Marshall, W. M. Palmer, J. Meteorol. 5, 165 (1948).
[CrossRef]

Cartwright, W. D.

T. Wang, G. R. Ochs, W. D. Cartwright, B. W. Guderian, S. Y. Simpson, NOAA Technical Memorandum ERL WPL-95, (Jan.1982).

Earnshaw, K. B.

Guderian, B. W.

T. Wang, G. R. Ochs, W. D. Cartwright, B. W. Guderian, S. Y. Simpson, NOAA Technical Memorandum ERL WPL-95, (Jan.1982).

Gunn, R.

R. Gunn, G. D. Kinzer, J. Meteorol. 6, 243 (1949).
[CrossRef]

Kinzer, G. D.

R. Gunn, G. D. Kinzer, J. Meteorol. 6, 243 (1949).
[CrossRef]

Lawrence, R. S.

Marshall, T. S.

T. S. Marshall, W. M. Palmer, J. Meteorol. 5, 165 (1948).
[CrossRef]

Ochs, G. R.

T. Wang, G. R. Ochs, W. D. Cartwright, B. W. Guderian, S. Y. Simpson, NOAA Technical Memorandum ERL WPL-95, (Jan.1982).

Palmer, W. M.

T. S. Marshall, W. M. Palmer, J. Meteorol. 5, 165 (1948).
[CrossRef]

Simpson, S. Y.

T. Wang, G. R. Ochs, W. D. Cartwright, B. W. Guderian, S. Y. Simpson, NOAA Technical Memorandum ERL WPL-95, (Jan.1982).

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

Wang, T.

T. Wang, K. B. Earnshaw, R. S. Lawrence, Appl. Opt. 17, 384 (1978).
[CrossRef] [PubMed]

T. Wang, G. R. Ochs, W. D. Cartwright, B. W. Guderian, S. Y. Simpson, NOAA Technical Memorandum ERL WPL-95, (Jan.1982).

Appl. Opt. (1)

J. Meteorol. (2)

T. S. Marshall, W. M. Palmer, J. Meteorol. 5, 165 (1948).
[CrossRef]

R. Gunn, G. D. Kinzer, J. Meteorol. 6, 243 (1949).
[CrossRef]

Other (2)

T. Wang, G. R. Ochs, W. D. Cartwright, B. W. Guderian, S. Y. Simpson, NOAA Technical Memorandum ERL WPL-95, (Jan.1982).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

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Figures (7)

Fig. 1
Fig. 1

Temporal power spectrum of rain-induced amplitude scintillation vs temporal frequency for different rain rates (from calculation based on Marshall-Palmer distribution for raindrop sizes).

Fig. 2
Fig. 2

Bandpass-filtered variance for amplitude scintillation (f0 = 1 kHz) vs path-averaged rain rates for 30-m path (with asymptotic solutions for far-field and near-field cases plotted for comparison).

Fig. 3
Fig. 3

Normalized bandpass-filtered variance (f0 = 1 kHz) for amplitude scintillation vs path-averaged rain rates for various path lengths.

Fig. 4
Fig. 4

Curve-fitting parameters α and β [Eq. (24)] vs path length.

Fig. 5
Fig. 5

Comparison of laser-measured rain rates with averaged tipping-bucket rain rates.

Fig. 6
Fig. 6

Scatter diagram of laser-measured rain rates vs averaged tipping-bucket rain rates.

Fig. 7
Fig. 7

Scatter diagram of measured rain rates of two tipping-bucket rain gauges 20 m apart.

Equations (25)

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I ( y , z ) = I 0 [ 1 exp ( y 2 + z 2 a 2 ) ] ,
η ( z ) = { I 0 l π a I 0 exp ( z 2 a 2 ) ; if | y | l / 2 ; I 0 l ; if | y | > l / 2.
χ ( z ) η ( z ) I 0 l I 0 l = { π a l 1 exp ( z 2 a 2 ) ; if | y | l / 2 ; 0 ; if | y | > l / 2 .
C ( τ ) = 1.47 × 10 7 π l 1 0 L dxR ( x ) 0 d a υ 1 p ( a , x ) exp [ υ 2 τ 2 2 a 2 ] ,
p ( a , x ) = N ( a , x ) a 3 υ 0 d a N ( a , x ) a 3 υ .
ω ( f ) exp ( 2 π i f τ ) C ( τ ) d τ .
ω ( f ) = 2.08 π × 10 7 l 1 0 L dxR ( x ) 0 dap ( a , x ) a υ 2 exp ( 4 π 2 f 2 a 2 2 υ 2 ) .
ω ( f ) = 2.08 π × 10 7 l 1 L R 0 dap ( a ) a υ 2 exp ( 2 π 2 f 2 a 2 υ 2 ) .
N ( a ) = N 0 exp ( 2 Λ a ) ,
p ( a ) = Γ 1 ( 9 / 2 ) ( 2 Λ ) 9 / 2 a 7 / 2 exp ( 2 Λ a ) ,
υ = 200 a .
ω ( f ) = 0.52 π × 10 11 R L l 1 ( 1 + 10 4 π 2 f 2 4 Λ ) 9 / 2 .
ω N ( f ) 6.12 × 10 10 R 1 L 1 l ω ( f ) = ( 1 + 6.02 × 10 8 f 2 R 0.21 ) 9 / 2 .
σ f 2 = 0.52 π × 10 11 R L l 1 f 0 Δ f / 2 f 0 + Δ f / 2 d f ( 1 + 10 4 π 2 f 2 4 Λ ) 9 / 2 ,
σ f 2 = G R ( 1 + 6.02 × 10 8 f 0 2 R 0.21 ) 9 / 2 ,
G = 0.52 π × 10 11 L l 1 Δ f .
R = σ f 2 G [ 1 6.02 × 10 8 f 0 2 ( σ f 2 G ) 2 / 9 ] 9 / 2 .
C T ( τ ) = R 4.8 π × 10 6 0 d a a 1 υ 1 p ( a ) { 2 π k l L m L dxx d z sin ( k z 2 2 x + π 4 ) sin [ k ( z + υ τ ) 2 2 x + π 4 ] J 1 ( η z / x ) z J 1 ( η [ z + υ τ ] / x ) z + υ τ + π l 0 L m d x a π / 2 exp ( υ 2 τ 2 2 a 2 ) } ,
ω T ( f ) = 2.08 π × 10 11 l 1 R 0 dap ( a ) [ ( L L m ) J 1 2 ( π f a / 100 ) ( π f a / 100 ) 2 + L m 4 exp ( 10 4 π 2 f 2 a 2 ) ] .
ω T ( f ) = 2.08 π × 10 11 l 1 R ( 2 Λ ) 9 / 2 Γ ( 9 / 2 ) 0 d a a 7 / 2 exp ( 2 Λ a ) [ ( L L m ) J 1 2 ( π f a / 100 ) ( π f a / 100 ) 2 + L m 4 exp ( 10 4 π 2 f 2 a 2 ) ] .
ω T ( f ) = 2.08 π × 10 11 R L Γ ( 9 / 2 ) l 0 2 Λ L / k d u u 7 / 2 exp ( u ) J 1 2 [ π f u / ( 100 2 Λ ) ] [ π f u / ( 100 2 Λ ) ] 2 × ( 1 k u 2 4 L Λ 2 ) + k L 1 16 Λ 2 0 2 Λ L / k d u u 11 / 2 × exp [ u ( 1 + 2.5 × 10 5 π 2 f 2 Λ ) ] + 1 4 2 Λ L / k d u u 7 / 2 exp [ u ( 1 + 2.5 × 10 5 π 2 f 2 Λ ) ] ,
σ f 2 G = 4 R Γ ( 9 / 2 ) { 0 2.6 R 0.21 L 1 / 2 d u u 7 / 2 exp ( u ) J 1 2 ( 3.47 × 10 4 f 0 u 1 / 2 R 0.105 ) 1.2 × 10 7 f 0 2 u R 0.21 ( 1 0.148 u 2 R 0.42 L 1 ) + 0.037 R 0.42 L 1 0 2.6 R 0.21 L 1 / 2 d u u 11 / 2 exp [ ( 1 + 6.02 × 10 8 f 0 2 R 0.21 ) u ] + 0.25 2.6 R 0.21 L 1 / 2 d u u 7 / 2 exp [ ( 1 + 6.02 × 10 8 f 0 2 R 0.21 ) u ] } ,
σ f 2 R L ( 1 0.135 × 10 6 f 0 2 R 0.21 ) ,
R = σ f 2 G [ 1 α f 0 2 ( σ f 2 G ) β ] 4.5 ,
R ( mm / h ) = K σ f 2 [ 1 0.035 ( K σ f 2 ) 0.29 ] 4.5 ,

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