Abstract

The statistical properties of atmospheric water vapor mixing ratio (WVMR) determined as the ratio of Raman lidar signals backscattered from water vapor and nitrogen molecules are studied. It is shown that WVMR estimates can be biased by a small percentage at low signal photon-counting rates due to fluctuations in the nitrogen signal in the denominator of the ratio, the magnitude of the bias being linked to the signal-to-noise ratio of the nitrogen signal. This is particularly important when unbiased estimates are required as in the case of climate studies and global positioning system (GPS) signal calibration. Different bias corrections and a modified ratio formulation are proposed in order to correct or eliminate this bias. The method is successfully applied in processing signals obtained with an experimental Raman lidar system devoted to calibrate GPS signals for slant path delays. It is shown to reduce biases into negligible values in both WVMR and wet path delay estimates in the range interval of 0–7 km.

© 2007 Optical Society of America

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    [CrossRef]
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  20. D. D. Turner, R. A. Ferrare, L. A. Heilman Brasseur, W. F. Feltz, and T. P. Tooman, "Automated retrievals of water vapor and aerosol profiles from an operational Raman lidar," J. Atmos. Ocean. Technol. 19, 37-50 (2002).
    [CrossRef]
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2007 (1)

H. Vömel, H. Selkirk, L. Miloshevich, J. Valverde, J. Valdés, E. Kyrö, R. Kivi, W. Stolz, G. Peng, and J. A. Diaz, "Radiation dry bias of the Vaisala RS92 humidity sensor," J. Atmos. Ocean. Technol. 6, 953-963 (2007).
[CrossRef]

2006 (1)

L. M. Miloshevich, H. Vömel, D. N. Whiteman, B. M Lesht, F. J. Schmidlin, and F. Russo, "Absolute accuracy of water vapor measurements from six operational radiosonde types launched during AWEX-G and implications for AIRS validation," J. Geophys. Res. 111, doi:1029/2005JD00683 (2006).
[CrossRef]

2004 (1)

B. J. Soden, D. D. Turner, B. M. Lesht, and L. M. Miloshevich, "An analysis of satellite, radiosonde, and lidar observations of upper tropospheric water vapor from the Atmospheric Radiation Measurement program," J. Geophys. Res. 109, D04105, doi:10.1029/2003JD003828 (2004).
[CrossRef]

2003 (5)

L. Bengtsson, G. Robinson, R. Anthes, K. Aonashi, A. Dodson, G. Elgered, G. Gendt, R. Gurney, M. Jietai, C. Mitchell, M. Mlaki, A. Rhodin, P. Silvestrin, R. Ware, R. Watson, and W. Wergen, "The use of GPS measurements for water vapor determination," Bull. Am. Meteorol. Soc. 84, 1249-1258 (2003).
[CrossRef]

H. E. Revercomb, D. Turner, D. Tobin, R. Knuteson, W. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Line, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The atmospheric radiation measurement (ARM) programs water vapor intensive observation periods: overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

J. Wang, D. J. Carlson, D. B. Parsons, T. F. Hock, D. Lauritsen, H. L. Cole, K. Beierle, and E. Chamberlain, "Performance of operational radiosonde humidity sensors in direct comparison with a chilled mirror dew-point hygrometer and its climate implication," Geophys. Res. Lett. 30, 1860, doi:10.1029/2003GL016985 (2003).
[CrossRef]

D. D. Turner, B. M. Lesht, S. A. Clough, J. C. Liljegren, H. E. Revercomb, and D. C Tobin, "Dry bias and variability in Vaisala RS80-H radiosondes: The ARM experience," J. Atmos. Ocean. Technol. 20, 117-132 (2003).
[CrossRef]

D. N. Whiteman, "Examination of the traditional Raman lidar technique; I. evaluating the temperature-dependent lidar equations," Appl. Opt. 42, 2571-2592 (2003).
[CrossRef] [PubMed]

2002 (2)

D. D. Turner, R. A. Ferrare, L. A. Heilman Brasseur, W. F. Feltz, and T. P. Tooman, "Automated retrievals of water vapor and aerosol profiles from an operational Raman lidar," J. Atmos. Ocean. Technol. 19, 37-50 (2002).
[CrossRef]

J. Tarniewicz, O. Bock, J. Pelon, and C. Thom, "Raman lidar for external GPS path delay calibration devoted to high accuracy height determination," Phys. Chem. Earth Part A Solid Earth Geod. 27, 329-333 (2002).

2001 (2)

O. Bock, J. Tarniewicz, C. Thom, J. Pelon, and M. Kasser, "Study of external path delay correction techniques for high accuracy height determination with GPS," Phys. Chem. Earth Part A Solid Earth Geod. 26, 165-171 (2001b).
[CrossRef]

O. Bock, J. Tarniewicz, C. Thom, and J. Pelon, "Effect of small-scale atmospheric inhomogeneity on positioning accuracy with GPS," Geophys. Res. Lett. 28, 2289 (2001a).
[CrossRef]

1998 (1)

1992 (1)

1991 (1)

R. Santerre, "Impact of GPS satellite sky distribution," Manuscr. Geod. 16, 28-53 (1991).

1985 (1)

J. L. Davis, T. A. Herring, I. I. Shapiro, A. E. E. Rogers, and G. Elgered, "Geodesy by radio interferometry: effects of atmospheric modeling errors on estimates of baseline length," Radio Sci. 20, 1593-1607 (1985).
[CrossRef]

1976 (1)

1974 (1)

G. Thayer, "An improved equation for the radio refractive index of air," Radio Sci. 9, 803-807 (1974).
[CrossRef]

Appl. Opt. (3)

Bull. Am. Meteorol. Soc. (2)

L. Bengtsson, G. Robinson, R. Anthes, K. Aonashi, A. Dodson, G. Elgered, G. Gendt, R. Gurney, M. Jietai, C. Mitchell, M. Mlaki, A. Rhodin, P. Silvestrin, R. Ware, R. Watson, and W. Wergen, "The use of GPS measurements for water vapor determination," Bull. Am. Meteorol. Soc. 84, 1249-1258 (2003).
[CrossRef]

H. E. Revercomb, D. Turner, D. Tobin, R. Knuteson, W. Feltz, J. Barnard, J. Bosenberg, S. Clough, D. Cook, R. Ferrare, J. Goldsmith, S. Gutman, R. Halthore, B. Lesht, J. Liljegren, H. Line, J. Michalsky, V. Morris, W. Porch, S. Richardson, B. Schmid, M. Splitt, T. Van Hove, E. Westwater, and D. Whiteman, "The atmospheric radiation measurement (ARM) programs water vapor intensive observation periods: overview, initial accomplishments, and future challenges," Bull. Am. Meteorol. Soc. 84, 217-236 (2003).
[CrossRef]

Geophys. Res. Lett. (2)

O. Bock, J. Tarniewicz, C. Thom, and J. Pelon, "Effect of small-scale atmospheric inhomogeneity on positioning accuracy with GPS," Geophys. Res. Lett. 28, 2289 (2001a).
[CrossRef]

J. Wang, D. J. Carlson, D. B. Parsons, T. F. Hock, D. Lauritsen, H. L. Cole, K. Beierle, and E. Chamberlain, "Performance of operational radiosonde humidity sensors in direct comparison with a chilled mirror dew-point hygrometer and its climate implication," Geophys. Res. Lett. 30, 1860, doi:10.1029/2003GL016985 (2003).
[CrossRef]

J. Atmos. Ocean. Technol. (3)

D. D. Turner, B. M. Lesht, S. A. Clough, J. C. Liljegren, H. E. Revercomb, and D. C Tobin, "Dry bias and variability in Vaisala RS80-H radiosondes: The ARM experience," J. Atmos. Ocean. Technol. 20, 117-132 (2003).
[CrossRef]

D. D. Turner, R. A. Ferrare, L. A. Heilman Brasseur, W. F. Feltz, and T. P. Tooman, "Automated retrievals of water vapor and aerosol profiles from an operational Raman lidar," J. Atmos. Ocean. Technol. 19, 37-50 (2002).
[CrossRef]

H. Vömel, H. Selkirk, L. Miloshevich, J. Valverde, J. Valdés, E. Kyrö, R. Kivi, W. Stolz, G. Peng, and J. A. Diaz, "Radiation dry bias of the Vaisala RS92 humidity sensor," J. Atmos. Ocean. Technol. 6, 953-963 (2007).
[CrossRef]

J. Geophys. Res. (2)

L. M. Miloshevich, H. Vömel, D. N. Whiteman, B. M Lesht, F. J. Schmidlin, and F. Russo, "Absolute accuracy of water vapor measurements from six operational radiosonde types launched during AWEX-G and implications for AIRS validation," J. Geophys. Res. 111, doi:1029/2005JD00683 (2006).
[CrossRef]

B. J. Soden, D. D. Turner, B. M. Lesht, and L. M. Miloshevich, "An analysis of satellite, radiosonde, and lidar observations of upper tropospheric water vapor from the Atmospheric Radiation Measurement program," J. Geophys. Res. 109, D04105, doi:10.1029/2003JD003828 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

Manuscr. Geod. (1)

R. Santerre, "Impact of GPS satellite sky distribution," Manuscr. Geod. 16, 28-53 (1991).

Phys. Chem. Earth Part A Solid Earth Geod. (2)

O. Bock, J. Tarniewicz, C. Thom, J. Pelon, and M. Kasser, "Study of external path delay correction techniques for high accuracy height determination with GPS," Phys. Chem. Earth Part A Solid Earth Geod. 26, 165-171 (2001b).
[CrossRef]

J. Tarniewicz, O. Bock, J. Pelon, and C. Thom, "Raman lidar for external GPS path delay calibration devoted to high accuracy height determination," Phys. Chem. Earth Part A Solid Earth Geod. 27, 329-333 (2002).

Radio Sci. (2)

J. L. Davis, T. A. Herring, I. I. Shapiro, A. E. E. Rogers, and G. Elgered, "Geodesy by radio interferometry: effects of atmospheric modeling errors on estimates of baseline length," Radio Sci. 20, 1593-1607 (1985).
[CrossRef]

G. Thayer, "An improved equation for the radio refractive index of air," Radio Sci. 9, 803-807 (1974).
[CrossRef]

Other (4)

R. M. Measures, Laser Remote Sensing: Fundamentals and Applications (Wiley-Interscience, 1984) 521 pp.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 2002).

J. Tarniewicz, "Étude d'une méthode de sondage de la vapeur d'eau dans la troposphère appliquée à la correction de mesures GPS pour l'altimétrie de haute précision," Université de Versailles-Saint-Quentin (2005).

E. P. Shettle and R. W. Fenn, "Models for the aerosols of the lower atmosphere and the effects on humidity variations on their optical properties," Optical Physics Division, Air Force Geophysics Laboratory in Environmental Research Papers (1979).

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Figures (11)

Fig. 1
Fig. 1

Comparison of WVMR retrievals from Raman lidar and simultaneous radiosoundings (Vaisala, RS92) during the VAPIC campaign on: (a) 26 May 2004 01:49 UTC and (b) 24 May 2004 23:14 UTC. The error bars on the radiosonde profiles correspond to a 5% relative humidity uncertainty as specified by the manufacturer. The error bars on the lidar profiles correspond to the variability (minimum and maximum) of the four 5 min lidar profiles.

Fig. 2
Fig. 2

Raman lidar signals simulated from radiosonde profile of 26 May 2004. (a) Molecular and background signal components in nitrogen and water vapor channels expected for 5 min measurements with a 30 m range resolution. (b) SNR on nitrogen and water vapor signals (molecular + background). (c) Average error in WVMR estimates (computed from ratio of simulated water vapor over nitrogen signals). The gray surface indicates the expected accuracy of the bias estimate ( ± 1 σ / N ) . (d) Average error and ± one standard deviation (error bars) in incremental ZWD and IWV (integrated between the surface and a given altitude).

Fig. 3
Fig. 3

Same as Fig. 2 but with signals summed over an irregular range resolution grid, as defined in Table 1, before computing WVMR.

Fig. 4
Fig. 4

Comparison of bias correction coefficient as a function of mean molecular signal, μ y , (lower abscissa) and SNR (upper abscissa). The curves show results from simulations (SIM), PDF, Eq. (15), SE2 and SE6 [second and sixth order series expansions, Eqs. (12) and (14), respectively] for different values of the background signal β y = 0.25 , 0.5, and 0.75, from top to bottom.

Fig. 5
Fig. 5

Bias (a) and RMS error (b) of the bias correction coefficient computed from realizations of signal, y ˜ c , instead of the true mean, μ y , for the different methods (PDF, SE2, and SE6). Background signal mean is β y = 0.25 .

Fig. 6
Fig. 6

Bias (a) and RMS error (b) of signal ratio estimates, x / y , for the different methods: simple (uncorrected) ratio estimator (SRE), bias corrected estimators (PDF, SE2, and SE6) and MRE, as a function of the mean of signal y, μ y , (lower abscissa) and SNR (upper abscissa). Mean of signal x is μ x = 60 . Background signal means are β x = 10 and β y = 0.25 .

Fig. 7
Fig. 7

Mean error in (a) WVMR and (b) ZWD and IWV estimates for simulation S1 (Poisson fluctuations in WV signal only), for 24 May 2004 profile, using the SRE method (no fluctuations in N 2 signal). Error bars in plot (b) have similar signification as in Figs. 2 and 3. Vertical resolution of WVMR (Table 1) provides SNR superior to 10 on N 2 channel.

Fig. 8
Fig. 8

Similar to Fig. 7, but for simulation S2 (Poisson fluctuations in nitrogen signal only) and using SRE and MRE methods (see text). SNR [ N 2 ] 2 plotted in (a) is an approximate bias estimate computed from Eq. (12).

Fig. 9
Fig. 9

Similar to Fig. 8, but for simulation S3 (Poisson fluctuations in N 2 and water vapor signals).

Fig. 10
Fig. 10

Similar to Fig. 9, but for 26 May 2004 profile.

Fig. 11
Fig. 11

Observed (STD) and predicted (EST) uncertainty in WVMR estimates using MRE method (dotted lines, lower abscissa). STD is the standard deviation of WVMR estimates and EST is predicted from Eq. (13). The dotted lines indicate the SNR (upper abscissa) of the signals. Left plot (a) is for 24 May 2004 and right plot (b) for 26 May 2004.

Tables (1)

Tables Icon

Table 1 Spatial Resolution of the Irregular Spatial Integration Grid

Equations (26)

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ZWD = r H 2 O ( z ) ε + r H 2 O ( z ) P ( z ) T ( z ) ( k 2 + k 3 T ( z ) ) d z ,
S X ( z ) = [ E ν 0 h ν 0 d σ ( ν 0 , ν X , π ) d Ω T ( ν 0 , ν X , z ) Σ X ( z ) A z 2 K X ( T ) ] × N X ( z ) + B X ,
SNR X ( z ) = n [ S X ( z ) B X ] n S X ( z ) ,
r H 2 O ( z ) = r N 2 M H 2 O M d d σ ( ν 0 , ν N 2 , π ) d Ω d σ ( ν 0 , ν H 2 O , π ) d Ω T ( ν 0 , ν N 2 , z ) T ( ν 0 , ν H 2 O , z ) × K N 2 ( T ) K H 2 O ( T ) Σ N 2 ( z ) Σ H 2 O ( z ) S H 2 O ( z ) ¯ B H 2 O ¯ S N 2 ( z ) ¯ B N 2 ¯ ,
x ˜ s = x ˜ m + b ˜ x ,
y ˜ s = y ˜ m + b ˜ y .
x ˜ c = x ˜ s β x ,
y ˜ c = y ˜ s β y .
{ Pr [ x ˜ c ] = Pr [ x ˜ s = x ˜ c + β x ] , E [ x ˜ c ] = μ x , V [ x ˜ c ] = λ x = μ x + β x , SNR [ x ˜ c ] = μ x λ x
{ Pr [ y ˜ c ] = Pr y ˜ s = y ˜ c + β y , E [ y ˜ c ] = μ y , V [ y ˜ c ] = λ y = μ y + β y , SNR [ y ˜ c ] = μ y λ y ,
Pr [ x ˜ c ] = λ x x ˜ c + β x ( x ˜ c + β x ) ! e λ x , Pr [ y ˜ c ] = λ y y ˜ c + β y ( y ˜ c + β y ) ! e λ y .
r ^ SRE = x ˜ c y ˜ c .
E ( r ^ SRE ) = E ( x ˜ c y ˜ c ) = μ x μ y E ( μ y y ˜ c ) = r c ( μ y , β y ) .
μ y y ˜ c = 1 1 + δ y c / μ y 1 δ y c μ y + ( δ y c μ y ) 2 ,
c ( μ y , β y ) ( 1 + λ y μ y 2 ) = ( 1 + SNR [ y ˜ c ] 2 ) .
V ( r ^ SRE ) r 2 ( λ x μ x 2 + λ y μ y 2 ) = r 2 ( SNR [ x ˜ c ] 2 + SNR [ y ˜ c ] 2 ) .
c SE ( μ y , β y ; N ) = n = 0 N ( 1 ) n μ y n m y ˜ s , n ,
c PDF ( μ y , β y ) = E ( μ y y ˜ c ) = n = 0 μ y n β y λ y n n ! e λ y .
c ( μ y , β y ) c ^ ( y ˜ c , β y ) .
r ^ MRE = λ y μ y 1 1 e λ y ( x ˜ c 1 + y ˜ s ) .
E [ g ( x ˜ ) ] = R g ( x ) f x ˜ ( x ) d x .
m y ˜ s , n = k = 0 n C n k ( 1 ) n k m y ˜ s , 1 n - k m y ˜ s , k .
m y ˜ s , k = M y ˜ s ( k ) ( 0 ) .
M y ˜ s k ( 0 ) = i = 1 k M y ˜ s ( i , k ) y ¯ k ,
M y ˜ s ( i , k ) = { 1 i · M y ¯ s ( i , k 1 ) + M y ˜ s ( i 1 , k 1 ) 0 if   i = k   or   k = 1 if   i < k otherwise
M y ˜ s ( 0 ) ( 0 ) = 1 .

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