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Atmospheric temperature dependence of the aerosol backscattering coefficient
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Atmospheric temperature dependence of the aerosol backscattering coefficient Binglong Chen, Siying Chen ∗ , Yinchao Zhang, He Chen, Pan Guo, Hao Chen Key Laboratory of Photoelectronic Imaging Technology, Beijing Institute of Technology, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 29 July 2015 Received in revised form 15 December 2015 Accepted 17 December 2015 Available online xxx Keywords: Lidar Atmospheric temperature Aerosol Raman scattering Backscattering coefficient
a b s t r a c t In extracting vertical profiles of aerosol backscattering coefficient from lidar signals, the effects of atmospheric temperature are usually ignored. In this study, these effects are analyzed using a rotational Raman–Mie lidar system, which is capable of simultaneously measuring atmospheric temperature and vertical profiles of aerosols. A method is presented to correct the aerosol backscattering coefficient using atmospheric temperature profiles, obtained from Raman scattering signals. The differences in the extracted aerosol backscattering coefficient with and without considering temperature effects are further discussed. The backscattering coefficients for scattering off clouds are shown to be more sensitive to temperature than that of aerosols and atmosphere molecules; the aerosol backscattering coefficient is more sensitive to temperature in summer due to higher atmospheric temperatures. © 2016 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
Introduction Aerosols play an important role in global climate change and have a leading role in the formation of regional atmospheric haze pollution. The coefficients dictating scattering are important in determining aerosol optical properties and thus an accurate measurement of the scattering coefficients of aerosols is crucial in gaining awareness and understanding of aerosols. Various methods have been developed to measure the scattering coefficient for atmospheric aerosols, including the use of radiosondes, optical particle counters, sun photometers, and satellite remote sensing detectors. Regarding satellite remote sensing detection, it has included the use of high-resolution imaging spectrometers such as MODIS (Engel-Cox, Holloman, Coutant, & Hoff, 2004), multiangle imaging spectrometers such as MISR (Diner et al., 2001), and spaceborne lidar systems, such as the CALIPSO satellite monitor (Jean & Philippe, 2006). These methods have their own advantages and disadvantages; for instance, the accuracy obtained with satellite remote sensing detection is not sufficiently high, and continuous detection is difficult to achieve using a radiosonde. In contrast to these methods, lidar technology for extracting atmospheric aerosol scattering data has advanced in recent years and has high temporal-spatial resolution and detection sensitivity because
∗ Corresponding author. Tel.: +86 10 68918398. E-mail address: [email protected] (S. Chen).
the laser is of short wavelength and oriented. Because elastic scattering from aerosol particles is strong, Mie scattering lidar is mainly used to detect atmospheric aerosol scattering data. Klett (1981, 1985) and Fernald (1984) both assumed a relationship between aerosol backscattering and extinction, and presented their methods for calculating both the backscattering and extinction coefficients of atmospheric aerosols using elastic backscattering signals. Kim and Cha (2005) obtained the backscattering coefficient of aerosols using rotational Raman backscattering and elastic backscattering signals without making any assumption. Using a chi-square test in simulations, Russo, Whiteman, Demoz, and Hoff (2006) found the minimum numerical uncertainty for the extinction coefficient of aerosols extracted using the Raman method. In these methods to determine on the backscattering coefficient of aerosols, correction from variational effects of atmospheric temperature with height has been ignored. We present a method to analyze the effect of atmospheric temperature on the backscattering coefficient of aerosols and to correct for atmospheric temperature variations. The method involves using a rotational Raman–Mie lidar system. Raman–Mie lidar The Raman–Mie lidar system designed by the Lidar Laboratory of Beijing Institute of Technology is located at the Beijing Institute of Technology in Beijing, China. This system enables vertical profiles of aerosols and temperature in the troposphere to be
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R, M, a, and m denote rotational Raman, Mie scattering, aerosol, and atmospheric molecule, respectively. Because the rotational Raman frequency shift is small (only 1–3 nm at 532 nm), the rotational Raman scattering frequency can be assumed to be approximately the same as the laser frequency (10–9 error in magnitude). This also means that the rotational Raman and Mie scattering signals yield the same extinction coefficient. Taking the ratio of their expressions, we obtain PM (z) C2 ˇa (z) + ˇm (z) = . C1 PR (z) ˇR (z)
(3)
Because molecular number density varies, both the rotational Raman and Rayleigh backscattering coefficient are sensitive to atmospheric temperature. The aerosol scattering coefficient ˇa can be solved from Eq. (3) after the rotational Raman backscattering coefficient ˇR and the molecular Rayleigh backscattering coefficient ˇm are calculated. The procedure is given below. Integrating the aerostatics equation and the ideal gas state equation, we can obtain an expression for the atmospheric molecular number density:
⎡
Fig. 1. Schematic of the rotational Raman–Mie scattering lidar system.
obtained by measuring Mie elastic scattering return signals and rotational Raman return signals, respectively. The lidar system is non-coaxial and consists of a laser, receiving optics, spectrometer, signal detection, and data acquisition units. Laser pulses are emitted from the Nd:-YAG laser with a pulse energy of 60 mJ at 20 Hz. The wavelength is 532 m after frequency doubling from the original 1064 nm. The laser beam divergence is 0.2 mrad following 4 × beam expansion. The receiving optics unit contains a 400-mm Newtonian telescope with field of view of 0.9 mrad, that is adjustable from 0.1 to 1.5 mrad using a diaphragm. The spectrometer comprises a multichannel double-grating monochromator, which selectively separates the rotational Raman returns of N2 and O2 molecules (529.05, 530.40, 533.77, and 535.13 nm) and the Mie scattering return (532 nm). The spectral resolution of the spectrometer unit is 0.23 nm. The rotational Raman and the Mie scattering return signals are detected by a photomultiplier tube (PMT) and collected separately using a photon counter card and an analog-to-digital card. The vertical resolutions of the Raman and Mie scattering paths in the lidar system are 30 and 2.5 m, respectively. Fig. 1 shows the system configuration. Method The rotational Raman return is associated only with atmospheric molecules at certain rotational quantum numbers. To obtain strong rotational Raman scattering spectral lines, we used the rotational Raman signals J = 6 and 12 of O2 molecules and J = 9 and 17 of N2 molecules. The Mie scattering return is associated with aerosols and atmospheric molecules. The return power (P) for the rotational Raman and the Mie elastic lidar signals are given by PR (z) =
⎧ ⎨
z
C1 ˇR (z) exp −2 z2 ⎩
[˛m (r) + ˛a (r)] dr
⎫ ⎬ ⎭
,
(1)
PM (z) =
⎩
⎧ ⎨
z
C2 ˇa (z) + ˇm (z) exp −2 z2 ⎩
[˛m (r) + ˛a (r)] dr
⎫⎫ ⎬⎬ .
⎭⎭
0
(2) here ˛, ˇ, and C are the extinction coefficient, the scattering coefficient, and a constant that does not depend on altitude; subscripts
Mg dz ⎦ , RT (z )
(4)
0
where N0 (2.55 × 1019 molecules/cm3 ) is the atmospheric molecular number density at mean sea level, T0 the real atmospheric temperature at ground where the lidar system located, and T the atmospheric vertical temperature retrieved with the rotational Raman signal (Behrendt & Reichardt, 2000; Cooney, 1972) using T (z) =
1 A[ln M(z)]2 + B ln M(z) + C
(5)
.
here M(z) is the ratio of the higher-order and lower-order channel return signals for rotational Raman scattering; A, B, and C are constants, which can be calibrated by fitting the ratio M(z) with the measured temperature profiles (radiosonde) using the least squares method. Because the atmospheric molecular Rayleigh scattering occurs as an independent scattering (Sun, 1986), it can be written as ˇm (z) = 3.439 × 10−7
2 Nm (z) 4 N02
(6)
.
Combining Eqs. (4)–(6), the molecular Rayleigh backscattering coefficient ˇm can be obtained. The relationship between the rotational Raman spectrum strength of molecules and temperature obeys a Boltzmann distribution; the rotational Raman scattering coefficient for molecules is related to the rotational quantum number J, which is expressed as ˇR (z) = ˇJ = n(z)FJ J−J ,
(7)
where n(z) is the number density of N2 or O2 molecules, which can be obtained using Eq. (4) with the volume ratio of N2 or O2 molecules in air; J–J is the differential scattering cross section; the physical meaning of FJ is the percentage of molecules in the initial rotational quantum state J, which is written as
0
⎧ ⎨
⎤
z
N0 T0 Nm (z) = exp ⎣− T (z)
FJ =
2hcB0 2
(2I + 1) kT
B hc 0
gI (2J + 1) exp −
kT
J(J + 1) .
(8)
here h, k, gI , B0 , and I are the Planck constant, the Boltzmann constant, the statistical weight factor determined by the nuclear spin, the rotational constant, and the nuclear spin quantum number, respectively. For diatomic molecules (N2 or O2 ), the rotational Raman transitions need to meet J = ± 2, where the plus and minus signs
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Table 1 Parameters for nitrogen and oxygen (Penney et al., 1974). Gas
I
gI (J is even)
gI (J is odd)
B0 (cm–1 )
D0 (cm–1 )
␥2 (cm6 )
N2 O2
1 0
6 0
3 1
1.989500 1.437682
5.48 × 10−6 4.85 × 10−6
0.51 × 10−48 1.27 × 10−48
represent Stokes and anti-Stokes scattering, respectively. The rotational Raman frequency shift (Vaughan, Wareing, Pepler, Thomas, & Mitev, 1993) can be written as
3 ωJ→J = (4B0 − 6D0 ) J + 3 − 8D0 J + 3 , 2
(9)
2
where ωJ-J is the frequency shift wave number of the rotational Raman scattering when the rotational quantum level changes from J to J ; D0 is the centrifugal distortion constant. The strength of the rotational Raman scattering signal depends on the differential scattering cross section ( J–J ) (Penney, Peters, & Lapp, 1974), which is given as J−J =
644 4 bJ−J (ω0 + ωJ−J ) 2 , 45
(10)
where bJ–J is the Placzek–Teller coefficient for a paired linear molecule, ω0 the laser wave number (18796 cm−1 ) at 532 nm, and the anisotropic part of the molecular polarizability tensor. The corresponding values obtained from Eqs. (8)–(10) are shown in Table 1. Even though the full rotational Raman spectrum is temperature independent (Whiteman, 2003), the magnitude of the rotational Raman signal depends on temperature (Nedeljkovic, Hauchecorne, & Chanin, 1993). From the above expressions, the aerosol backscattering coefficient ˇa , which depends on atmospheric temperature, can be obtained (Cohen, Cooney, & Geller, 1976; Arshinov, Bobrovnikov, Zuev, & Mitev, 1983), and is given by ˇa (z) = =
C1 PM (z) ˇR (z) − ˇm (z) C2 PR (z) T0 T (z)
N0 FJ J−J
⎡
z
exp ⎣−
3.439 × 10−7 2 C1 PM (z) − C2 PR (z) N0 4
(11)
0
bJ→J+2 =
3(J + 1)(J + 2) (Stokes), 2(2J + 1)(2J + 3)
bJ→J−2 =
3J(J − 1) (anti − Stokes). 2(2J + 1)(2J − 1)
here is the volume ratio of N2 or O2 molecules in the air. Temperature T(z) is obtained from Eq. (5). We use in this study the relative error ı to characterize the effects of atmospheric temperature on the aerosol backscattering coefficient. We write it as ı=
ˇa (z) − ˇa∗ (z) ˇa (z)
× 100%.
Fig. 3. Profiles of the aerosol backscattering coefficient with and without considering temperature effects (ˇa , ˇa *, respectively), based on data measured at 19:00–21:00 on February 10, 2012, in Beijing.
Results
⎤
Mg dz ⎦ , RT (z )
Fig. 2. (a) Temperature profile retrieved from the lidar signals was compared with that of the radiosonde. (b) Absolute error of the results between the two different methods, based on data measured at 19:00–21:00 on February 10, 2012, in Beijing.
(12)
where ˇa is the aerosol backscattering coefficient taking into consideration the atmospheric temperature obtained with the rotational Raman scattering signal and ˇa * the aerosol backscattering coefficient, without regard to atmospheric temperature, obtained using the method of Kim and Cha (2005).
Fig. 2(a) and (b) compares the atmospheric temperature profile retrieved with the rotational Raman signal from ground to 9 km with the radiosonde temperature profile. Even though there is a peak (4.3 K) at 0.9 km resulting from the blind zone near the ground using the non-coaxial Raman–Mie lidar, the mean absolute error over the total altitude range from 0 to 9 km is also only 1.13 K. The rotational Raman lidar can retrieve the real atmospheric temperature profile with an acceptable accuracy. Fig. 3 shows a comparison of aerosol backscattering coefficient profiles between ˇa and ˇa * . Aerosol backscattering coefficients obtained from data of cloudy sky (5.5 to 6.8 km) are more sensitive to temperature than that of non-cloudy sky. Cloud extent is assessed from the aerosol attenuated scattering ratio dˇa /ˇm , where dˇa and ˇm are the attenuated backscattering coefficient of aerosol and the backscattering coefficient for atmospheric molecules, respectively (Platt, Winker, Vaughan, & Miller, 1999; Young, 1995). Fig. 4 shows respectively the absolute error dı between ˇa and ˇa * and the relative error ı obtained using Eq. (12). Using the assessment of the cloud extent dˇa /ˇm , we calculated the mean absolute error and relative error for cloudy sky from 5.5 to 6.8 km, obtaining 1.58 × 10−5 km−1 sr−1 and 36.77%, respectively; the mean absolute error and relative error for non-cloudy sky (the total altitude not including clouds) are 1.02 × 10−4 km−1 sr−1 and 12.21%, respectively. The result shows that the backscattering coefficient for
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Fig. 4. (a) Absolute error dı between ˇa and ˇa *. (b) Relative error ı between ˇa and ˇa *. The data were measured at 19:00–21:00 on February 10, 2012, in Beijing. Fig. 6. Variations of mean relative error between ˇa and ˇa * with season in summer and winter, based on data measured at night in 2013 in Beijing.
skies (Fig. 5). Date and associated meteorological factors related to this data are listed in Table 2; here, ground surface temperatures were obtained from local meteorological data. Moreover, as there are differences in atmospheric temperature in summer and winter, we analyzed the dependence of aerosol backscattering coefficient on temperature over the two seasons. The number of days of chosen data during summer and winter 2013 in Beijing is 55 and 43, respectively. Among the chosen data, days of cloudy weather are 25 and 17, respectively. The dependence of aerosol backscattering coefficient on temperature (Fig. 6) is stronger on average by 17.55% in summer than in winter. Conclusions
Fig. 5. Variations of mean values of the relative errors between ˇa and ˇa * for cloudy and non-cloudy skies of the temperature profile, respectively, based on data measured at night from February to May 2013 in Beijing.
cloud is more sensitive to temperature than aerosol and molecules because of multiple scattering effects of the laser beam in clouds. To verify further the reasonableness of the result, we chose data obtained during cloudy weather from February to May 2013 in Beijing and calculated the mean values of ı for cloudy and non-cloudy Table 2 Date and the associated meteorological factor of chosen data from February to May 2013 in Beijing, China. Date
Cloud-base height (km)
Cloud-top height (km)
Ground surface temperature (K)
Feb 10 Feb 15 Feb 17 Feb 25 Mar 7 Mar 17 Mar 24 Mar 27 Apr 8 Apr 16 Apr 26 May 7 May 10 May 17 May 20
4.9 5.3 5.9 6.7 6.2 3.0 5.8 6.1 3.5 3.7 5.9 4.3 4.4 6.2 8.1
7.1 6.4 8.0 9.8 8.5 4.9 7.6 8.2 4.5 5.0 6.5 6.4 5.6 8.5 11.7
267–272 267–277 269–280 270–274 275–290 278–292 272–284 277–290 279–286 280–293 281–296 290–303 287–303 289–300 287–304
With atmospheric temperature depending on height, we proposed a method to correct the aerosol backscattering coefficient using the atmospheric temperature profile extracted from Raman lidar data. By analyzing rotational Raman–Mie lidar return signals, we obtained the dependence of aerosol backscattering coefficient on temperature. The results of the experiments show that the backscattering coefficient for cloudy sky is more dependent on temperature than that for aerosol and atmosphere molecules. The relative difference between aerosol backscattering coefficients with and without correction of atmospheric temperature in cloudy sky (36.77%) is much larger than in non-cloudy sky (12.21%); the temperature dependence of the aerosol backscattering coefficient is stronger on average by 17.55% in summer over that in winter due to higher atmospheric temperatures. The method presented in this paper can be applied to extract aerosol backscattering coefficient profiles in real atmosphere conditions with greater precision. Acknowledgment This work was funded by the National Natural Science Foundation of China under Grant No. 61178072. References Arshinov, Y. F., Bobrovnikov, S. M., Zuev, V. E., & Mitev, V. M. (1983). Atmospheric temperature measurements using a pure rotational Raman lidar. Applied Optics, 22, 2984–2990. Behrendt, A., & Reichardt, J. (2000). Atmospheric temperature profiling in the presence of clouds with a pure rotational Raman lidar by use of an interferencefilter-based polychromator. Applied Optics, 39, 1372–1378.
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Cohen, A., Cooney, J. A., & Geller, K. N. (1976). Atmospheric temperature profiles from lidar measurements of rotational Raman and elastic scattering. Applied Optics, 15, 2896–2901. Cooney, J. (1972). Measurement of atmospheric temperature profiles by Raman backscatter. Journal of Applied Meteorology, 11, 108–112. Diner, D. J., Abdou, W. A., Bruegge, C. J., Conel, J. E., Crean, K. A., Gaitley, B. J., et al. (2001). MISR aerosol optical depth retrievals over southern Africa during the SAFARI-2000 Dry Season Campaign. Geophysical Research Letters, 28, 3127–3130. Engel-Cox, J. A., Holloman, C. H., Coutant, B. W., & Hoff, R. M. (2004). Qualitative and quantitative evaluation of MODIS satellite sensor data for regional and urban scale air quality. Atmospheric Environment, 38, 2495–2509. Fernald, F. G. (1984). Analysis of atmospheric lidar observations: Some comments. Applied Optics, 23, 652–653. Jean, B., & Philippe, L. (2006). CALIPSO small satellite flight commissioning. In In 57th International Astronautical Congress, IAC-06-B5, 4, 9. Klett, J. D. (1981). Stable analytical inversion solution for processing Lidar returns. Applied Optics, 20, 211–220. Klett, J. D. (1985). Lidar inversion with variable backscatter/extinction ratios. Applied Optics, 24, 1638–1643. Kim, D., & Cha, H. (2005). Rotational Raman lidar for obtaining aerosol scattering coefficients. Optics Letters, 30, 1728–1730.
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Nedeljkovic, D., Hauchecorne, A., & Chanin, M.-L. (1993). Rotational Raman Lidar to measure the atmospheric temperature from the ground to 30 km. IEEE Transactions on Geoscience and Remote Sensing, 31, 90–101. Penney, C. M., Peters, R. L., & Lapp, M. (1974). Absolute rotational Raman cross sections for N2 , O2 , and CO2 . Journal of the Optical Society of America, 64, 712–716. Platt, C. M. R., Winker, D. M., Vaughan, M. A., & Miller, S. D. (1999). Backscatterto-extinction ratios in the top layers of tropical mesoscale convective systems and in isolated cirrus from LITE observations. Journal of Applied Meteorology, 38, 1330–1345. Russo, F., Whiteman, D. N., Demoz, B., & Hoff, R. M. (2006). Validation of the Raman lidar algorithm for quantifying aerosol extinction. Applied Optics, 45, 7073–7088. Sun, J. Q. (1986). Laser atmospheric detection. Beijing: Science Press., in Chinese. Vaughan, G., Wareing, D. P., Pepler, S. J., Thomas, L., & Mitev, V. M. (1993). Atmospheric temperature measurements made by rotational Raman-scattering. Applied Optics, 32, 2758–2764. Whiteman, D. N. (2003). Examination of the traditional Raman lidar technique. I. Evaluating the temperature-dependent lidar equations. Applied Optics, 42, 2571–2592. Young, S. A. (1995). Analysis of lidar backscatter profiles in optically thin clouds. Applied Optics, 34, 7019–7031.
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Contents lists available at ScienceDirect
Particuology journal homepage: www.elsevier.com/locate/partic
Atmospheric temperature dependence of the aerosol backscattering coefficient Binglong Chen, Siying Chen ∗ , Yinchao Zhang, He Chen, Pan Guo, Hao Chen Key Laboratory of Photoelectronic Imaging Technology, Beijing Institute of Technology, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 29 July 2015 Received in revised form 15 December 2015 Accepted 17 December 2015 Available online xxx Keywords: Lidar Atmospheric temperature Aerosol Raman scattering Backscattering coefficient
a b s t r a c t In extracting vertical profiles of aerosol backscattering coefficient from lidar signals, the effects of atmospheric temperature are usually ignored. In this study, these effects are analyzed using a rotational Raman–Mie lidar system, which is capable of simultaneously measuring atmospheric temperature and vertical profiles of aerosols. A method is presented to correct the aerosol backscattering coefficient using atmospheric temperature profiles, obtained from Raman scattering signals. The differences in the extracted aerosol backscattering coefficient with and without considering temperature effects are further discussed. The backscattering coefficients for scattering off clouds are shown to be more sensitive to temperature than that of aerosols and atmosphere molecules; the aerosol backscattering coefficient is more sensitive to temperature in summer due to higher atmospheric temperatures. © 2016 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
Introduction Aerosols play an important role in global climate change and have a leading role in the formation of regional atmospheric haze pollution. The coefficients dictating scattering are important in determining aerosol optical properties and thus an accurate measurement of the scattering coefficients of aerosols is crucial in gaining awareness and understanding of aerosols. Various methods have been developed to measure the scattering coefficient for atmospheric aerosols, including the use of radiosondes, optical particle counters, sun photometers, and satellite remote sensing detectors. Regarding satellite remote sensing detection, it has included the use of high-resolution imaging spectrometers such as MODIS (Engel-Cox, Holloman, Coutant, & Hoff, 2004), multiangle imaging spectrometers such as MISR (Diner et al., 2001), and spaceborne lidar systems, such as the CALIPSO satellite monitor (Jean & Philippe, 2006). These methods have their own advantages and disadvantages; for instance, the accuracy obtained with satellite remote sensing detection is not sufficiently high, and continuous detection is difficult to achieve using a radiosonde. In contrast to these methods, lidar technology for extracting atmospheric aerosol scattering data has advanced in recent years and has high temporal-spatial resolution and detection sensitivity because
∗ Corresponding author. Tel.: +86 10 68918398. E-mail address: [email protected] (S. Chen).
the laser is of short wavelength and oriented. Because elastic scattering from aerosol particles is strong, Mie scattering lidar is mainly used to detect atmospheric aerosol scattering data. Klett (1981, 1985) and Fernald (1984) both assumed a relationship between aerosol backscattering and extinction, and presented their methods for calculating both the backscattering and extinction coefficients of atmospheric aerosols using elastic backscattering signals. Kim and Cha (2005) obtained the backscattering coefficient of aerosols using rotational Raman backscattering and elastic backscattering signals without making any assumption. Using a chi-square test in simulations, Russo, Whiteman, Demoz, and Hoff (2006) found the minimum numerical uncertainty for the extinction coefficient of aerosols extracted using the Raman method. In these methods to determine on the backscattering coefficient of aerosols, correction from variational effects of atmospheric temperature with height has been ignored. We present a method to analyze the effect of atmospheric temperature on the backscattering coefficient of aerosols and to correct for atmospheric temperature variations. The method involves using a rotational Raman–Mie lidar system. Raman–Mie lidar The Raman–Mie lidar system designed by the Lidar Laboratory of Beijing Institute of Technology is located at the Beijing Institute of Technology in Beijing, China. This system enables vertical profiles of aerosols and temperature in the troposphere to be
http://dx.doi.org/10.1016/j.partic.2015.12.004 1674-2001/© 2016 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
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R, M, a, and m denote rotational Raman, Mie scattering, aerosol, and atmospheric molecule, respectively. Because the rotational Raman frequency shift is small (only 1–3 nm at 532 nm), the rotational Raman scattering frequency can be assumed to be approximately the same as the laser frequency (10–9 error in magnitude). This also means that the rotational Raman and Mie scattering signals yield the same extinction coefficient. Taking the ratio of their expressions, we obtain PM (z) C2 ˇa (z) + ˇm (z) = . C1 PR (z) ˇR (z)
(3)
Because molecular number density varies, both the rotational Raman and Rayleigh backscattering coefficient are sensitive to atmospheric temperature. The aerosol scattering coefficient ˇa can be solved from Eq. (3) after the rotational Raman backscattering coefficient ˇR and the molecular Rayleigh backscattering coefficient ˇm are calculated. The procedure is given below. Integrating the aerostatics equation and the ideal gas state equation, we can obtain an expression for the atmospheric molecular number density:
⎡
Fig. 1. Schematic of the rotational Raman–Mie scattering lidar system.
obtained by measuring Mie elastic scattering return signals and rotational Raman return signals, respectively. The lidar system is non-coaxial and consists of a laser, receiving optics, spectrometer, signal detection, and data acquisition units. Laser pulses are emitted from the Nd:-YAG laser with a pulse energy of 60 mJ at 20 Hz. The wavelength is 532 m after frequency doubling from the original 1064 nm. The laser beam divergence is 0.2 mrad following 4 × beam expansion. The receiving optics unit contains a 400-mm Newtonian telescope with field of view of 0.9 mrad, that is adjustable from 0.1 to 1.5 mrad using a diaphragm. The spectrometer comprises a multichannel double-grating monochromator, which selectively separates the rotational Raman returns of N2 and O2 molecules (529.05, 530.40, 533.77, and 535.13 nm) and the Mie scattering return (532 nm). The spectral resolution of the spectrometer unit is 0.23 nm. The rotational Raman and the Mie scattering return signals are detected by a photomultiplier tube (PMT) and collected separately using a photon counter card and an analog-to-digital card. The vertical resolutions of the Raman and Mie scattering paths in the lidar system are 30 and 2.5 m, respectively. Fig. 1 shows the system configuration. Method The rotational Raman return is associated only with atmospheric molecules at certain rotational quantum numbers. To obtain strong rotational Raman scattering spectral lines, we used the rotational Raman signals J = 6 and 12 of O2 molecules and J = 9 and 17 of N2 molecules. The Mie scattering return is associated with aerosols and atmospheric molecules. The return power (P) for the rotational Raman and the Mie elastic lidar signals are given by PR (z) =
⎧ ⎨
z
C1 ˇR (z) exp −2 z2 ⎩
[˛m (r) + ˛a (r)] dr
⎫ ⎬ ⎭
,
(1)
PM (z) =
⎩
⎧ ⎨
z
C2 ˇa (z) + ˇm (z) exp −2 z2 ⎩
[˛m (r) + ˛a (r)] dr
⎫⎫ ⎬⎬ .
⎭⎭
0
(2) here ˛, ˇ, and C are the extinction coefficient, the scattering coefficient, and a constant that does not depend on altitude; subscripts
Mg dz ⎦ , RT (z )
(4)
0
where N0 (2.55 × 1019 molecules/cm3 ) is the atmospheric molecular number density at mean sea level, T0 the real atmospheric temperature at ground where the lidar system located, and T the atmospheric vertical temperature retrieved with the rotational Raman signal (Behrendt & Reichardt, 2000; Cooney, 1972) using T (z) =
1 A[ln M(z)]2 + B ln M(z) + C
(5)
.
here M(z) is the ratio of the higher-order and lower-order channel return signals for rotational Raman scattering; A, B, and C are constants, which can be calibrated by fitting the ratio M(z) with the measured temperature profiles (radiosonde) using the least squares method. Because the atmospheric molecular Rayleigh scattering occurs as an independent scattering (Sun, 1986), it can be written as ˇm (z) = 3.439 × 10−7
2 Nm (z) 4 N02
(6)
.
Combining Eqs. (4)–(6), the molecular Rayleigh backscattering coefficient ˇm can be obtained. The relationship between the rotational Raman spectrum strength of molecules and temperature obeys a Boltzmann distribution; the rotational Raman scattering coefficient for molecules is related to the rotational quantum number J, which is expressed as ˇR (z) = ˇJ = n(z)FJ J−J ,
(7)
where n(z) is the number density of N2 or O2 molecules, which can be obtained using Eq. (4) with the volume ratio of N2 or O2 molecules in air; J–J is the differential scattering cross section; the physical meaning of FJ is the percentage of molecules in the initial rotational quantum state J, which is written as
0
⎧ ⎨
⎤
z
N0 T0 Nm (z) = exp ⎣− T (z)
FJ =
2hcB0 2
(2I + 1) kT
B hc 0
gI (2J + 1) exp −
kT
J(J + 1) .
(8)
here h, k, gI , B0 , and I are the Planck constant, the Boltzmann constant, the statistical weight factor determined by the nuclear spin, the rotational constant, and the nuclear spin quantum number, respectively. For diatomic molecules (N2 or O2 ), the rotational Raman transitions need to meet J = ± 2, where the plus and minus signs
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Table 1 Parameters for nitrogen and oxygen (Penney et al., 1974). Gas
I
gI (J is even)
gI (J is odd)
B0 (cm–1 )
D0 (cm–1 )
␥2 (cm6 )
N2 O2
1 0
6 0
3 1
1.989500 1.437682
5.48 × 10−6 4.85 × 10−6
0.51 × 10−48 1.27 × 10−48
represent Stokes and anti-Stokes scattering, respectively. The rotational Raman frequency shift (Vaughan, Wareing, Pepler, Thomas, & Mitev, 1993) can be written as
3 ωJ→J = (4B0 − 6D0 ) J + 3 − 8D0 J + 3 , 2
(9)
2
where ωJ-J is the frequency shift wave number of the rotational Raman scattering when the rotational quantum level changes from J to J ; D0 is the centrifugal distortion constant. The strength of the rotational Raman scattering signal depends on the differential scattering cross section ( J–J ) (Penney, Peters, & Lapp, 1974), which is given as J−J =
644 4 bJ−J (ω0 + ωJ−J ) 2 , 45
(10)
where bJ–J is the Placzek–Teller coefficient for a paired linear molecule, ω0 the laser wave number (18796 cm−1 ) at 532 nm, and the anisotropic part of the molecular polarizability tensor. The corresponding values obtained from Eqs. (8)–(10) are shown in Table 1. Even though the full rotational Raman spectrum is temperature independent (Whiteman, 2003), the magnitude of the rotational Raman signal depends on temperature (Nedeljkovic, Hauchecorne, & Chanin, 1993). From the above expressions, the aerosol backscattering coefficient ˇa , which depends on atmospheric temperature, can be obtained (Cohen, Cooney, & Geller, 1976; Arshinov, Bobrovnikov, Zuev, & Mitev, 1983), and is given by ˇa (z) = =
C1 PM (z) ˇR (z) − ˇm (z) C2 PR (z) T0 T (z)
N0 FJ J−J
⎡
z
exp ⎣−
3.439 × 10−7 2 C1 PM (z) − C2 PR (z) N0 4
(11)
0
bJ→J+2 =
3(J + 1)(J + 2) (Stokes), 2(2J + 1)(2J + 3)
bJ→J−2 =
3J(J − 1) (anti − Stokes). 2(2J + 1)(2J − 1)
here is the volume ratio of N2 or O2 molecules in the air. Temperature T(z) is obtained from Eq. (5). We use in this study the relative error ı to characterize the effects of atmospheric temperature on the aerosol backscattering coefficient. We write it as ı=
ˇa (z) − ˇa∗ (z) ˇa (z)
× 100%.
Fig. 3. Profiles of the aerosol backscattering coefficient with and without considering temperature effects (ˇa , ˇa *, respectively), based on data measured at 19:00–21:00 on February 10, 2012, in Beijing.
Results
⎤
Mg dz ⎦ , RT (z )
Fig. 2. (a) Temperature profile retrieved from the lidar signals was compared with that of the radiosonde. (b) Absolute error of the results between the two different methods, based on data measured at 19:00–21:00 on February 10, 2012, in Beijing.
(12)
where ˇa is the aerosol backscattering coefficient taking into consideration the atmospheric temperature obtained with the rotational Raman scattering signal and ˇa * the aerosol backscattering coefficient, without regard to atmospheric temperature, obtained using the method of Kim and Cha (2005).
Fig. 2(a) and (b) compares the atmospheric temperature profile retrieved with the rotational Raman signal from ground to 9 km with the radiosonde temperature profile. Even though there is a peak (4.3 K) at 0.9 km resulting from the blind zone near the ground using the non-coaxial Raman–Mie lidar, the mean absolute error over the total altitude range from 0 to 9 km is also only 1.13 K. The rotational Raman lidar can retrieve the real atmospheric temperature profile with an acceptable accuracy. Fig. 3 shows a comparison of aerosol backscattering coefficient profiles between ˇa and ˇa * . Aerosol backscattering coefficients obtained from data of cloudy sky (5.5 to 6.8 km) are more sensitive to temperature than that of non-cloudy sky. Cloud extent is assessed from the aerosol attenuated scattering ratio dˇa /ˇm , where dˇa and ˇm are the attenuated backscattering coefficient of aerosol and the backscattering coefficient for atmospheric molecules, respectively (Platt, Winker, Vaughan, & Miller, 1999; Young, 1995). Fig. 4 shows respectively the absolute error dı between ˇa and ˇa * and the relative error ı obtained using Eq. (12). Using the assessment of the cloud extent dˇa /ˇm , we calculated the mean absolute error and relative error for cloudy sky from 5.5 to 6.8 km, obtaining 1.58 × 10−5 km−1 sr−1 and 36.77%, respectively; the mean absolute error and relative error for non-cloudy sky (the total altitude not including clouds) are 1.02 × 10−4 km−1 sr−1 and 12.21%, respectively. The result shows that the backscattering coefficient for
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Fig. 4. (a) Absolute error dı between ˇa and ˇa *. (b) Relative error ı between ˇa and ˇa *. The data were measured at 19:00–21:00 on February 10, 2012, in Beijing. Fig. 6. Variations of mean relative error between ˇa and ˇa * with season in summer and winter, based on data measured at night in 2013 in Beijing.
skies (Fig. 5). Date and associated meteorological factors related to this data are listed in Table 2; here, ground surface temperatures were obtained from local meteorological data. Moreover, as there are differences in atmospheric temperature in summer and winter, we analyzed the dependence of aerosol backscattering coefficient on temperature over the two seasons. The number of days of chosen data during summer and winter 2013 in Beijing is 55 and 43, respectively. Among the chosen data, days of cloudy weather are 25 and 17, respectively. The dependence of aerosol backscattering coefficient on temperature (Fig. 6) is stronger on average by 17.55% in summer than in winter. Conclusions
Fig. 5. Variations of mean values of the relative errors between ˇa and ˇa * for cloudy and non-cloudy skies of the temperature profile, respectively, based on data measured at night from February to May 2013 in Beijing.
cloud is more sensitive to temperature than aerosol and molecules because of multiple scattering effects of the laser beam in clouds. To verify further the reasonableness of the result, we chose data obtained during cloudy weather from February to May 2013 in Beijing and calculated the mean values of ı for cloudy and non-cloudy Table 2 Date and the associated meteorological factor of chosen data from February to May 2013 in Beijing, China. Date
Cloud-base height (km)
Cloud-top height (km)
Ground surface temperature (K)
Feb 10 Feb 15 Feb 17 Feb 25 Mar 7 Mar 17 Mar 24 Mar 27 Apr 8 Apr 16 Apr 26 May 7 May 10 May 17 May 20
4.9 5.3 5.9 6.7 6.2 3.0 5.8 6.1 3.5 3.7 5.9 4.3 4.4 6.2 8.1
7.1 6.4 8.0 9.8 8.5 4.9 7.6 8.2 4.5 5.0 6.5 6.4 5.6 8.5 11.7
267–272 267–277 269–280 270–274 275–290 278–292 272–284 277–290 279–286 280–293 281–296 290–303 287–303 289–300 287–304
With atmospheric temperature depending on height, we proposed a method to correct the aerosol backscattering coefficient using the atmospheric temperature profile extracted from Raman lidar data. By analyzing rotational Raman–Mie lidar return signals, we obtained the dependence of aerosol backscattering coefficient on temperature. The results of the experiments show that the backscattering coefficient for cloudy sky is more dependent on temperature than that for aerosol and atmosphere molecules. The relative difference between aerosol backscattering coefficients with and without correction of atmospheric temperature in cloudy sky (36.77%) is much larger than in non-cloudy sky (12.21%); the temperature dependence of the aerosol backscattering coefficient is stronger on average by 17.55% in summer over that in winter due to higher atmospheric temperatures. The method presented in this paper can be applied to extract aerosol backscattering coefficient profiles in real atmosphere conditions with greater precision. Acknowledgment This work was funded by the National Natural Science Foundation of China under Grant No. 61178072. References Arshinov, Y. F., Bobrovnikov, S. M., Zuev, V. E., & Mitev, V. M. (1983). Atmospheric temperature measurements using a pure rotational Raman lidar. Applied Optics, 22, 2984–2990. Behrendt, A., & Reichardt, J. (2000). Atmospheric temperature profiling in the presence of clouds with a pure rotational Raman lidar by use of an interferencefilter-based polychromator. Applied Optics, 39, 1372–1378.
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