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Improved method for retrieving the aerosol optical properties without the numerical derivative for Raman–Mie lidar
Optics Communications 349 (2015) 145–150
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Improved method for retrieving the aerosol optical properties without the numerical derivative for Raman–Mie lidar Wei Gong a,b,c, Wei Wang a,n, Feiyue Mao d,e, Jinye Zhang c,f a
State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China Collaborative Innovation Center for Geospatial Technology, Wuhan 430079, China c Hubei Collaborative Innovation Center for High-Efficiency Utilization of Solar Energy, Wuhan 430079, China d School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, China e School of Resource and Environmental Science of Wuhan University, Wuhan 430079, China f School of Science, Hubei University of Technology, Wuhan 430068, China b
ar t ic l e i nf o
a b s t r a c t
Article history: Received 29 January 2015 Received in revised form 19 March 2015 Accepted 20 March 2015 Available online 23 March 2015
Raman–Mie light detection and ranging (lidar) is a very useful tool for research on atmospheric aerosol optical properties with high spatial–temporal resolution. However, many uncertainties still exist in data retrieval because traditional retrieval methods need to calculate the numerical derivative for aerosol extinction coefficient (AEC), which may cause large errors, particularly with low signal-to-noise ratios. Thus, we present an improved method for retrieving aerosol optical properties. We re-formulate the N2-Raman lidar equation to obtain an unknown term which contains the AEC at the Mie wavelength. We replace the unknown term of the equation in traditional method for retrieving aerosol backscatter coefficient (ABC). Then, AEC can be retrieved by the accurate ABC and Mie lidar signal without calculating the numerical derivative. Tests on the simulated and measured signals show that results of our method and those of the traditional method have similar tendencies. However, our method is more accurate and robust, and the significant errors of AEC caused by the numerical derivative can be reduced. & 2015 Elsevier B.V. All rights reserved.
Keywords: Aerosol Raman Lidar
1. Introduction Aerosols have an important role in atmospheric processes, such as precipitation, radiation, and optical properties, and directly affect human health and the living environment. Accurate aerosol detection with high temporal–spatial resolution is critical. Compared with passive remote sensing techniques, such as sun photometry and microwave radiometry, light detection and ranging (lidar) is an effective active remote sensing tool for aerosol detection [1,2]. With the rapid development of laser technology, sophisticated spectroscopic techniques, photoelectric detection technology, and computer control technology, lidar has acquired unique advantages, including high sensitivity, high temporal– spatial resolution, and continuous monitoring [2,3]. Various useful algorithms for retrieving atmospheric properties have been proposed to improve the practicability of lidar [4–6]. Thus, lidar has been widely utilized in atmospheric aerosol detection since the 1960s [6–8]. A few lidar networks that perform routine measures, such as the Asian Dust Network [9], the European Aerosol n
Corresponding author. E-mail address: [email protected] (W. Wang).
http://dx.doi.org/10.1016/j.optcom.2015.03.050 0030-4018/& 2015 Elsevier B.V. All rights reserved.
Research lidar Network [10], and the lidar of the Atmospheric Radiation Measurement Program, have exhibited success and provide original data to significantly promote atmospheric aerosol research [11,12]. However, problems remain in the retrieval of aerosol optical properties [including the aerosol extinction coefficient (AEC) and aerosol backscatter coefficient (ABC)] via traditional methods of either Mie or Raman lidar. The signal-to-noise ratio (SNR) of the Mie lidar signal is a thousand times higher than that of the Raman signal under similar conditions. However, we need to assume the boundary value and lidar ratio (i.e., the ratio of the extinction coefficient and the backscatter coefficient) when retrieving the data of Mie lidar through the traditional Fernald method [4,13,14]. This method requires two assumptions that may cause many uncertainties [5,15]. Raman lidar can avoid these two assumptions, and the lidar ratio can be retrieved. Thus, Raman lidar has been widely utilized since its invention. For Raman lidar, the SNR of the N2 signal is very low because the N2 scattering cross section is very small. The traditional retrieval method is very sensitive to SNR because of the numerical derivative in the solution [5]. To improve the accuracy of the retrieval, a de-noise method (e.g., sliding average method) is often used, but this method involves the loss of detail information [16].
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Several researchers investigated more stable and complicated methods to accurately calculate the numerical derivative, but these methods remain very sensitive to noise [17–19]. A few researchers have proposed methods by combining N2-Raman and Mie signal, but these methods still do not completely avoid calculating the numerical derivative [20,21]. The improved method proposed by Molero and Pujadas can obtain ABC without calculating the numerical derivative for AEC, but it is affected by overlap near the ground [22]. An improved method for AEC proposed by Su with Fernald method [21], but it need to assume the lidar ratio is constant at first. Thus, the search for new or improved methods for aerosol optical properties is still important. In this paper, we present an improved method for retrieving aerosol optical properties. Firstly, we re-formulate the N2-Raman lidar equation to obtain an unknown term which contains the AEC at the Mie wavelength. Secondly, we replace the unknown term of the equation in traditional method for retrieving ABC. Thirdly, the retrieved ABC and Mie lidar equation are utilized to obtain more accuracy lidar ratio. Finally, the AEC can be obtained by the corresponding retrieved ABC and lidar ratio. The comparison of the aerosol optical properties retrieved by the traditional method and our improved method with simulated and measured lidar signal is discussed. The results verify that our method can obtain more accurate retrieval results than traditional methods without assumption or excessive de-noising means.
10 km in this study. At the reference altitude, ABC is much less than the atmosphere molecules backscatter coefficient. Thus, βm (λL , rf ) + βa (λL , rf ) ≈ βm (λL , rf ). However, we also need to determine αa (λL , r) if we want to obtain βa (λL , r). Traditionally, αa (λL , r) is obtained by the following equation [5,23].
αa (λL , r) =
d/dr ⎡⎣ln (N (r)/P (λN , r) r 2) ⎤⎦ − [αm (λL , r) + αm (λN , r)] 1 + λL /λN
,
(4)
where N(r) is the N2 molecular number density and λx is the wavelength of Mie at 532 nm and wavelength of N2-Raman backscatter at 607 nm. In Eq. (4), the numerical derivative causes a large error because of the noise of the lidar signal. Least-squares fitting is usually applied to reduce the error caused by the derivatives calculation. Thus, we propose our improved method to retrieve AEC without the numerical derivative. 2.2. Improved method 2.2.1. Aerosol backscatter coefficient The improved method can obtain βa (λL , r) without calculating αa (λL , r). Generally, the wavelength dependence of AEC is stated as αa (λL )/αa (λN ) = λN /λL [6]. Eq. (2) can be rewritten as
exp
{∫
r
0
⎡ ⎤γ P (λN , r) r 2 ⎥, [αa (λL , r‵)] dr‵ = ⎢ ⎢⎣ C (λN ) G (r) σN N (r) Tm (r) ⎥⎦
}
(5)
2. Principle and method
where
This section describes the retrieval of aerosol optical properties via the traditional method and our method.
γ=−
2.1. Traditional method
Tm (r) = exp
The equations for Mie and N2-Raman lidar with emission wavelength λL and λN can be expressed as follows:
However, a few unknown items exist in Eq. (5) and need to be eliminated. We consider rf is the reference altitude same as Eq. (3), where G (rf ) = 1. Eq. (5) can be rewritten as
P (λL , r) =
P (λN , r) =
C (λL ) r2
G (r) β (λL , r)exp
C (λN ) r2 ×
{ − 2∫
0
r
αa (λL , r ‵) + αm (λL , r ‵) dr ‵
}
(1)
G (r) β (λN , r)exp
{−∫
o
r
[αa (λL , r ‵) + αm (λL , r ‵) + αa (λN , r ‵) + αm (λN , r ‵)] dr ‵
}
(2)
where P (λx , r) is the received power from altitude r; subscripts L and N refer to the Mie and Raman backscatter of N2, respectively; C (λx ) is the lidar constant that contains all altitude-independent terms; G(r) is the geometric correction factor at r caused by the distance between the laser beam and telescope; β (λx , r) is the backscatter coefficient; and β (λN , r) = σN ⋅N (r), where σN and N(r) are the backscatter cross section and molecular number density of N2, respectively; α (λL , r) and α (λN , r) represent the extinction coefficient of Mie and N2-Raman; and subscripts a and m in α (λx , r) refer to the contribution from aerosols and molecules, respectively. ABC can be retrieved by the traditional method as follows [22,23]:
βa (λL , r) =
P (λL , r)⋅P (λN , rf )⋅N (r) P (λL , rf )⋅P (λN , r)⋅N (rf
)
⎧ exp ⎨ ⎩
λN , λN + λL
∫r
r f
{−∫
0
r
}
[αm (λL , r‵) + αm (λN , r‵)] dr‵ .
⎫ ⎡ P (λN , r) r 2⋅N (rf )⋅Tm (rf ) 1 ⎤γ ⎥, [αa (λL , r‵)] dr‵⎬ = ⎢ ⋅ ⎭ ⎢⎣ P (λN , rf ) r 2⋅N (r)⋅Tm (r) G (r) ⎥⎦
When substituted into Eq. (3), we can obtain an accurate ABC at wavelength λL by
βa (λL , r) =
P (λL , r)⋅P (λN , rf )⋅N (r) P (λL , rf )⋅P (λN , r)⋅N (rf
)
βm
⎧ ⎫ r exp ⎨ − ∫r αm (λN , r‵) dr‵⎬ f ⎩ ⎭ ⋅ (λL , rf ) ⎧ r ⎫ exp ⎨ − ∫r αm (λL , r‵) dr‵⎬ f ⎩ ⎭ ⎡ P (λ , r) r 2⋅N (r )⋅T (r ) ⎤γ N f m f 1 ⎥‵ ⎢ ⋅ ⎢⎣ P (λN , rf ) r 2⋅N (r)⋅Tm (r) G (r) ⎥⎦ − βm (λL , r)
(7) [1/G (r)]γ′
βm (λL , rf
)
⎧ ⎫ r exp ⎨ − ∫r αa (λN , r‵) + αm (λN , r‵) dr‵⎬ f ⎩ ⎭ − βm (λL , r); ⎧ ⎫ r exp ⎨ − ∫r αa (λL , r‵) + αm (λL , r‵) dr‵⎬ f ⎩ ⎭
(3)
where subscripts a and m represent aerosol and molecular scattering, respectively, and rf is the reference altitude, which is set to
(6)
where, γ′ = λL − λN /λL + λN . can be regarded as 1 where G (r) is greater than 0.8 when λL is equal 532 nm and λN is equal 607 nm. In general, altitude higher than 500 m satisfy the conditions. ABC can be retrieved by the method without the calculation of the extinction coefficient, which may cause a large error. As it will be shown latter, this improved method is more accurate than that retrieved by the traditional method described in Eq. (3). The ABC result of this method is employed in our improved method to retrieve a more accurate AEC than that of the traditional method.
W. Gong et al. / Optics Communications 349 (2015) 145–150
2.2.2. Aerosol extinction coefficient Traditional methods to retrieve AEC with a single N2-Raman signal must obtain the result of the numerical derivative which leads to larger errors. Thus, we propose an improved method to retrieve AEC based on the obtained ABC and constrained by Eq. (1), i.e the Mie lidar equation. From Eq. (1), the ratio of P (λL , ri ) and P (λL , ri + 1 ) at two adjacent points, ri and ri + 1 , can be rewritten as follows:
βa‵ (Sa‵ , λL , ri + 1 ) =
P (λL , ri + 1 ) ri2+ 1 ⎡ ⎣βm (λL , ri ) + βa (λL , ri ) ⎤⎦ P (λL , ri ) ri2
⎧ exp ⎨ − 2 ⎩
∫r
ri
i +1
(8)
where αa (λL , r) = S′a (r) ⁎βa (λL , r) and S′a (r) is the lidar ratio.
βa′ (Sa′ , λL , ri + 1 ) is ABC, and the superscript is to distinguish ABC from that in Eq. (7). Geometric correction factor G(r) in Eq. (1) is ignored. The integral term can be simply described as
∫r
i
αa (λL , r′) dr′ = 0.5⁎ ⎡⎣Sa′ (ri ) ⁎βa (λL , ri ) + Sa′ (ri + 1 ) ⁎βa (λL , ri + 1 ) ⎤⎦ (9)
⁎dr ,
where dr is the vertical resolution (equal to 7.5 m in this study) and βa is ABC obtained by the mentioned improved method. To simplify the processing of the integral term, S′a (r) is regarded as having similar values at two adjacent points (ri and ri + 1 ). Thus, Eq. (8) can be rewritten as
βa‵ (Sa‵ , λL , ri + 1 ) =
P (λL , ri + 1 ) ri2+ 1 ⎡ ⎣βm (λL , ri ) + βa (λL , ri ) ⎤⎦ P (λL , ri ) ri2 ri ⎧ ⎫ αm (λL , r‵) dr‵⎬ ⋅exp ⎨ − 2 ri + 1 ⎩ ⎭
∫
⋅exp Sa‵ (ri ) ⁎ ⎡⎣βa (λL , ri ) + βa (λL , ri + 1 ) ⎤⎦ ⁎dr
{
− βm (λL , ri + 1 )
altitude ri .
M [Sa (ri ), ri ] = βa′ [Sa (ri ), ri ] − βa (ri )
(11)
After obtaining ABC and the lidar ratio, we can obtain AEC as follows:
αa (r) = βa (r)⋅Sa (r).
(12)
3. Results and discussion
⎫ αa (λL , r‵) + αm (λL , r‵) dr‵⎬ ⎭
− βm (λL , ri + 1 )
ri + 1
147
} (10)
The lidar ratio for clear air, cloud, and aerosol is usually different, but the range of the lidar ratio is from 1 sr to 100 sr when the wavelength is 532 nm under normal conditions [13]. Thus, lidar ratios Sa′ from 1 sr to 100 sr with an increment of 0.5 sr are applied in Eq. (10). Each βa′ (Sa , ri ) can be obtained for each Sa′ (ri ) at ri . To obtain optimal lidar ratio Sa (ri ), we define the judgment function in Eq. (11). When M [Sa (ri ), ri ] in Eq. (11) is minimized, we regard the corresponding Sa (ri ) as the optimal lidar ratio at
In this section, we verify the accuracy of the proposed improved method. The experiment results retrieved from the simulated and measured signal with the improved method (for ABC and AEC) are compared with that of the traditional method. According to the simulated signal experiment, the relative errors of the two methods vary with altitude are shown. 3.1. Simulated signal We simulated the Mie signal and N2-Raman signal with wavelengths of 532 and 607 nm, respectively, and with Gaussian noise under standard atmosphere (Fig. 1). A planetary boundary layer and an optical thick layer were simulated at 0–2 km and 4– 6 km. According to its physical properties, cloud is a type of atmospheric aerosol. Therefore, we did not separate the discussion of aerosols and clouds. The simulative aerosol lidar ratio are from 70 sr to 50 sr at 0–2 km, 60 sr at 4–6 km, and 50 sr at other altitude, respectively. The SNR of the Mie lidar signal is approximately a thousand times higher than that of N2-Raman lidar signal under similar conditions. Fig. 2(a) shows the true ABC and the average and standard deviation (i.e., the error bars) of the ABCs retrieved by the traditional method and the improved method in 20 simulated experiments. The results of the two methods are in good agreement with the true value because the concepts of the two methods are similar. However, AEC must be initially calculated if the traditional method is used. AEC cannot be accurately calculated because of the numerical derivation. Lastly, the calculation errors of AEC are added to ABC. Thus, the results obtained by the traditional method are worse than the results obtained by the improved method. The error bar above 6 km shows that the uncertainty of the improved method is smaller than that of the traditional method. Fig. 2 (b) shows that the relative errors of the two methods under 6 km are almost zero because the SNR is high. However, the relative
Fig. 1. Simulated range-corrected Mie and N2–Raman lidar signals under standard atmosphere.
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W. Gong et al. / Optics Communications 349 (2015) 145–150
Fig. 2. (a) True ABC and ABCs (with error bars) retrieved by the traditional method and the improved method denoted by a blue dotted line, an orange solid line, and a red solid line, respectively. (b) Relative errors of ABCs retrieved by the traditional method and the improved method denoted by an orange solid line and a red solid line, respectively. (c) Same as (a), but for AECs. (d) Same as (b), but for AECs. (e) Same as (a), but for lidar ratios. (f) Same as (b), but for lidar ratios. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
errors rapidly increase with the decline in SNR above 6 km. In summary, the ABC of the improved method is smaller than that of the traditional method. This result indicates that the ABC retrieved by the improved method is more suitable. Fig. 2(c) shows the true AEC and the average and standard deviation (i.e., the error bars) of the AECs retrieved by the traditional method and our method in 20 simulated experiments. Before retrieving AEC by the traditional method, the N2-Raman signal was averaged with sliding windows of 375 m and 1125 m for altitudes of below 3.75 km and above 3.75 km, respectively. Fig. 2(d) shows that the uncertainty of the AEC retrieved by the traditional method becomes increasingly unacceptable with SNR decline above 4 km. However, the AEC retrieved by our method is significantly better than that of the traditional method and only has slight fluctuations around the true value. Moreover, the AEC of our method substantially coincides with the true value when an optical thick layer exists. However, the AEC of the traditional method is distorted because sliding average is used to calculate the numerical derivative. Fig. 2 (d) shows the relative errors of the AECs retrieved by the traditional method and our improved method, and the relative errors are almost zero below 2 km because the SNR is high. However, the relative error of the traditional method is greater than 100% because of the calculation of the numerical derivative where SNR is low. The range of relative errors of our method is mainly between
50 and 50 when the SNR is low and an optical thick layer exists. This result indicates that our method is more stable than the traditional method in retrieving AEC. Fig. 2(e) shows the true lidar ratios and that retrieved by the traditional method and our improved method. The ABC is smoothed with the same window length for AEC before computing the lidar ratio by traditional method. Both methods obtained accurate lidar ratios under 2 km, where the SNR is high. The result retrieved by the traditional method does not match the true value when an optical thick layer exists because the AEC of the traditional method is distorted. Fig. 2 (e) shows that the lidar ratio of our method is highly consistent with the true value. Fig. 2(f) shows that the relative errors of the two methods are basically equal to zero below 2 km. However, the relative errors of our method are from 20% to 20% above 2 km and are significantly smaller than those of the traditional method. 3.2. Measured signal Fig. 3(a) shows a Mie backscattering signal at a wavelength of 532 nm and an N2-Raman backscattering signal at a wavelength of 607 nm, which are measured and averaged from 21:51 to 22:10 Beijing time (CST) on March 15, 2014. A planetary boundary layer is below 2 km, and an optical thick layer exists from 8 km to 10 km. The SNR of the Mie signal is higher than that of the N2
W. Gong et al. / Optics Communications 349 (2015) 145–150
149
Fig. 3. (a) Mie backscattering signal at a wavelength of 532 nm and N2-Raman backscattering signal at a wavelength of 607 nm; both were measured and averaged at 21:51 to 22:10 Beijing time (CST) on March 15, 2014. (b) ABCs retrieved by the traditional method and the improved method. (c) AECs retrieved by the traditional method and the improved method. (d) lidar ratios retrieved by the traditional method and the improved method.
signal at all altitudes. The mean intensity of the N2-Raman signal is about one-thousandth of the Mie signal because the Raman scattering cross section is smaller than that of Mie. Fig. 3(b) shows the ABCs retrieved by the traditional method and the improved method. The reference altitude in the retrieval is 10 km. The quality of the ABCs of the two methods declines with the decrease in SNR. A few negative values exist in the ABC profiles at above 10 km because the SNR of the N2-Raman signal is very low. The ABC of the improved method is more stable than that of the traditional method because the improved method is less influenced by the error of AEC. Therefore, the ABC retrieved by the improved method is more suitable as the input for our improved method to retrieve AEC. Fig. 3(b) demonstrates that ABC is lower than the molecular backscatter coefficient at about 10 km. Thus, the reference altitude at 10 km is reasonable. Fig. 3(c) shows the AECs retrieved by the traditional method and our method. To retrieve a more precise AEC profile by the traditional method, the N2-Raman signal was averaged with sliding windows of 375 m and 2250 m for altitudes of below 6 km and above 6 km, respectively. The AEC retrieved by the traditional method becomes suspicious and even negative at above 6 km. In the range of 8–10 km, the local maximum value of the AEC retrieved by the traditional method is
smaller than that of our method because of excessive smoothing, similar to the simulation experiment. The profile retrieved by our method has a smaller fluctuation range and better stability than that retrieved by the traditional method. Both of the method is almost unaffected by geometric correction factor. Fig. 3 (c) indicates that our improved method has better noise immunity than the traditional method for retrieving AEC. Therefore, our improved method can provide more accurate results. Note the region below 1.5 km, the improved method for AEC is still affected by geometric correction factor of Mie lidar signal. Fig. 3(d) shows the lidar ratios retrieved by the traditional method and our improved method. The Mie signal and N2-Raman signal profiles are smoothed with same window length before computing the lidar ratio by traditional method. In general, the two lidar ratios match each other well. However, the lidar ratio of our method has smaller fluctuations than that of the traditional method. Moreover, the lidar ratios are within a reasonable range (from 20 sr to 80 sr). The region above 5.5 km is not shown because of the poor result retrieved by the traditional method.
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W. Gong et al. / Optics Communications 349 (2015) 145–150
4. Conclusion We developed an improved method to retrieve aerosol optical properties that are more accurate than those of traditional method from Raman–Mie lidar. For ABC, we re-formulate the N2-Raman lidar equation to obtain an unknown term which contains the AEC at the Mie wavelength. Then, we replace the unknown term of the equation in traditional method for retrieving ABC. To obtain the optimal lidar ratios of our method, lidar ratios from 1 sr to 100 sr with an increment of 0.5 sr were utilized in the performance function we defined. Both simulated and measured signal experiments verified that the results obtained by our method are more accurate than those of traditional methods without assumption or excessive de-noising. The advantage of the improved method for AEC retrieval is more significant because this method avoids the calculation of the numerical derivative. In particular, the results on measured signals showed that our improved method can work well at a wide range where SNR is low. Meanwhile, the aerosol details retrieved by our improved method are substantially preserved; such details may be lost or distorted when the traditional method is employed because of the de-noise methods (e.g., sliding average method). The lidar ratio of our method has smaller fluctuations than that of the traditional method. The results verify that our method can retrieve aerosol optical properties, especially AEC, with better noise immunity, stabilization, and robustness than the traditional method. The proposed method was applied to the Raman–Mie lidar system at Wuhan University. The time sequence for aerosol optical properties will be analyzed with our improved method in the future. However, our method still has room for improvement, and we will continue to search for a more effective method to retrieve aerosol optical properties.
Acknowledgments This work was supported by a Grant from 973 Programs (2011CB707106), the NSFCs (41127901, 41301372), Major Projects of Hubei Collaborative Innovation Center for High-Efficiency Utilization of Solar Energy (HBSZD2014002)
References [1] V.A. Kovalev, W.E. Eichinger, Elastic Lidar: Theory, Practice, and Analysis Methods, Wiley-Interscience, New York, 2004. [2] C. Weitkamp, Lidar: range-resolved optical remote sensing of the atmosphere, Springer Science & Business Media, 2005. [3] Raymond M. Measures. Laser remote sensing: fundamentals and applications [M]. Krieger, 1992.
[4] F.G. Fernald, Analysis of atmospheric lidar observations: some comments, Appl. Opt. 23 (1984) 652–653. [5] A. Ansmann, M. Riebesell, C. Weitkamp, Measurement of atmospheric aerosol extinction profiles with a Raman lidar, Opt. Lett. 15 (1990) 746–748. [6] D. Whiteman, S. Melfi, R. Ferrare, Raman lidar system for the measurement of water vapor and aerosols in the Earth's atmosphere, Appl. Opt. 31 (1992) 3068–3082. [7] R. Collis, Lidar: a new atmospheric probe, Q. J. R. Meteorol. Soc. 92 (1966) 220–230. [8] F.G. Fernald, B.M. Herman, J.A. Reagan, Determination of aerosol height distributions by lidar, J. Appl.Meteorol. 11 (1972) 482–489. [9] T. Murayama, N. Sugimoto, I. Uno, K. Kinoshita, K. Aoki, N. Hagiwara, Z.Y. Liu, I. Matsui, T. Sakai, T. Shibata, K. Arao, B.J. Sohn, J.G. Won, S.C. Yoon, T. Li, J. Zhou, H.L. Hu, M. Abo, K. Iokibe, R. Koga, Y. Iwasaka, Ground-based network observation of Asian dust events of April 1998 in east Asia, J. Geophys. Res. Atmos. 106 (2001) 18345–18359. [10] V. Matthais, V. Freudenthaler, A, Amodeo, et al., Aerosol lidar intercomparison in the framework of the EARLINET project. 1. Instruments[J], Applied Optics 43 (4) (2004) 961–976. [11] D.D. Turner, J. Goldsmith, Twenty-four-hour Raman lidar water vapor measurements during the Atmospheric Radiation Measurement Program's 1996 and 1997 water vapor intensive observation periods, J. Atmos. Ocean. Technol. 16 (1999) 1062–1076. [12] D.D. Turner, R.A. Ferrare, L.A.H. Brasseur, et al., Automated retrievals of water vapor and aerosol profiles from an operational Raman lidar[J], Journal of Atmospheric and Oceanic Technology 19 (1) (2002) 37–50. [13] F. Mao, W. Gong, T. Logan, Linear segmentation algorithm for detecting layer boundary with lidar, Opt. Express 21 (2013) 26876–26887. [14] F. Mao, W. Gong, C. Li, Anti-noise algorithm of lidar data retrieval by combining the ensemble Kalman filter and the Fernald method, Opt. Express 21 (2013) 8286–8297. [15] F. Mao, W. Gong, Y. MA, Retrieving the aerosol lidar ratio profile by combining ground-and space-based elastic lidars, Opt. Lett. 37 (2012) 617–619. [16] G. Pappalardo, A. Amodeo, M. Pandolfi, U. Wandinger, A. Ansmann, J. Bosenberg, V. Matthias, V. Amirdis, F. De Tomasi, M. Frioud, M. Larlori, L. Komguem, A. Papayannis, F. Rocadenbosch, X. Wang, Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio, Appl. Opt. 43 (2004) 5370–5385. [17] P. Pornsawad, C. Böckmann, C. Ritter, M. Rafler, Ill-posed retrieval of aerosol extinction coefficient profiles from Raman lidar data by regularization, Appl. Opt. 47 (2008) 1649–1661. [18] J. Zhang, C. Huang, W. Gong, An Algorithm for retrieving the atmospheric aerosol extinction coefficient via Raman lidar data, Lasers Eng. 27 (2014) 393–398. [19] P. Pornsawad, G. D'Amico, C. Bockmann, A. Amodeo, G. Pappalardo, Retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion method, Appl. Opt. 51 (2012) 2035–2044. [20] A. Ansmann, U. Wandinger, M. Riebesell, et al., Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar[J], Applied Optics 31 (33) (1992) 7113–7131. [21] J. Su, Y.H. Wu, M.P. McCormick, L.Q. Lei, R.B. Lee, Improved method to retrieve aerosol optical properties from combined elastic backscatter and Raman lidar data, Appl. Phys. B: Lasers Opt. 116 (2014) 61–67. [22] A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio, Appl. Phys. B 55 (1992) 18–28. [23] W. Gong, J. Zhang, F. Mao, J. Li, Measurements for profiles of aerosol extinction coeffcient, backscatter coeffcient, and lidar ratio over Wuhan in China with Raman/Mie lidar, Chin. Opt. Lett. 8 (2010) 533–536.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Improved method for retrieving the aerosol optical properties without the numerical derivative for Raman–Mie lidar Wei Gong a,b,c, Wei Wang a,n, Feiyue Mao d,e, Jinye Zhang c,f a
State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China Collaborative Innovation Center for Geospatial Technology, Wuhan 430079, China c Hubei Collaborative Innovation Center for High-Efficiency Utilization of Solar Energy, Wuhan 430079, China d School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, China e School of Resource and Environmental Science of Wuhan University, Wuhan 430079, China f School of Science, Hubei University of Technology, Wuhan 430068, China b
ar t ic l e i nf o
a b s t r a c t
Article history: Received 29 January 2015 Received in revised form 19 March 2015 Accepted 20 March 2015 Available online 23 March 2015
Raman–Mie light detection and ranging (lidar) is a very useful tool for research on atmospheric aerosol optical properties with high spatial–temporal resolution. However, many uncertainties still exist in data retrieval because traditional retrieval methods need to calculate the numerical derivative for aerosol extinction coefficient (AEC), which may cause large errors, particularly with low signal-to-noise ratios. Thus, we present an improved method for retrieving aerosol optical properties. We re-formulate the N2-Raman lidar equation to obtain an unknown term which contains the AEC at the Mie wavelength. We replace the unknown term of the equation in traditional method for retrieving aerosol backscatter coefficient (ABC). Then, AEC can be retrieved by the accurate ABC and Mie lidar signal without calculating the numerical derivative. Tests on the simulated and measured signals show that results of our method and those of the traditional method have similar tendencies. However, our method is more accurate and robust, and the significant errors of AEC caused by the numerical derivative can be reduced. & 2015 Elsevier B.V. All rights reserved.
Keywords: Aerosol Raman Lidar
1. Introduction Aerosols have an important role in atmospheric processes, such as precipitation, radiation, and optical properties, and directly affect human health and the living environment. Accurate aerosol detection with high temporal–spatial resolution is critical. Compared with passive remote sensing techniques, such as sun photometry and microwave radiometry, light detection and ranging (lidar) is an effective active remote sensing tool for aerosol detection [1,2]. With the rapid development of laser technology, sophisticated spectroscopic techniques, photoelectric detection technology, and computer control technology, lidar has acquired unique advantages, including high sensitivity, high temporal– spatial resolution, and continuous monitoring [2,3]. Various useful algorithms for retrieving atmospheric properties have been proposed to improve the practicability of lidar [4–6]. Thus, lidar has been widely utilized in atmospheric aerosol detection since the 1960s [6–8]. A few lidar networks that perform routine measures, such as the Asian Dust Network [9], the European Aerosol n
Corresponding author. E-mail address: [email protected] (W. Wang).
http://dx.doi.org/10.1016/j.optcom.2015.03.050 0030-4018/& 2015 Elsevier B.V. All rights reserved.
Research lidar Network [10], and the lidar of the Atmospheric Radiation Measurement Program, have exhibited success and provide original data to significantly promote atmospheric aerosol research [11,12]. However, problems remain in the retrieval of aerosol optical properties [including the aerosol extinction coefficient (AEC) and aerosol backscatter coefficient (ABC)] via traditional methods of either Mie or Raman lidar. The signal-to-noise ratio (SNR) of the Mie lidar signal is a thousand times higher than that of the Raman signal under similar conditions. However, we need to assume the boundary value and lidar ratio (i.e., the ratio of the extinction coefficient and the backscatter coefficient) when retrieving the data of Mie lidar through the traditional Fernald method [4,13,14]. This method requires two assumptions that may cause many uncertainties [5,15]. Raman lidar can avoid these two assumptions, and the lidar ratio can be retrieved. Thus, Raman lidar has been widely utilized since its invention. For Raman lidar, the SNR of the N2 signal is very low because the N2 scattering cross section is very small. The traditional retrieval method is very sensitive to SNR because of the numerical derivative in the solution [5]. To improve the accuracy of the retrieval, a de-noise method (e.g., sliding average method) is often used, but this method involves the loss of detail information [16].
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Several researchers investigated more stable and complicated methods to accurately calculate the numerical derivative, but these methods remain very sensitive to noise [17–19]. A few researchers have proposed methods by combining N2-Raman and Mie signal, but these methods still do not completely avoid calculating the numerical derivative [20,21]. The improved method proposed by Molero and Pujadas can obtain ABC without calculating the numerical derivative for AEC, but it is affected by overlap near the ground [22]. An improved method for AEC proposed by Su with Fernald method [21], but it need to assume the lidar ratio is constant at first. Thus, the search for new or improved methods for aerosol optical properties is still important. In this paper, we present an improved method for retrieving aerosol optical properties. Firstly, we re-formulate the N2-Raman lidar equation to obtain an unknown term which contains the AEC at the Mie wavelength. Secondly, we replace the unknown term of the equation in traditional method for retrieving ABC. Thirdly, the retrieved ABC and Mie lidar equation are utilized to obtain more accuracy lidar ratio. Finally, the AEC can be obtained by the corresponding retrieved ABC and lidar ratio. The comparison of the aerosol optical properties retrieved by the traditional method and our improved method with simulated and measured lidar signal is discussed. The results verify that our method can obtain more accurate retrieval results than traditional methods without assumption or excessive de-noising means.
10 km in this study. At the reference altitude, ABC is much less than the atmosphere molecules backscatter coefficient. Thus, βm (λL , rf ) + βa (λL , rf ) ≈ βm (λL , rf ). However, we also need to determine αa (λL , r) if we want to obtain βa (λL , r). Traditionally, αa (λL , r) is obtained by the following equation [5,23].
αa (λL , r) =
d/dr ⎡⎣ln (N (r)/P (λN , r) r 2) ⎤⎦ − [αm (λL , r) + αm (λN , r)] 1 + λL /λN
,
(4)
where N(r) is the N2 molecular number density and λx is the wavelength of Mie at 532 nm and wavelength of N2-Raman backscatter at 607 nm. In Eq. (4), the numerical derivative causes a large error because of the noise of the lidar signal. Least-squares fitting is usually applied to reduce the error caused by the derivatives calculation. Thus, we propose our improved method to retrieve AEC without the numerical derivative. 2.2. Improved method 2.2.1. Aerosol backscatter coefficient The improved method can obtain βa (λL , r) without calculating αa (λL , r). Generally, the wavelength dependence of AEC is stated as αa (λL )/αa (λN ) = λN /λL [6]. Eq. (2) can be rewritten as
exp
{∫
r
0
⎡ ⎤γ P (λN , r) r 2 ⎥, [αa (λL , r‵)] dr‵ = ⎢ ⎢⎣ C (λN ) G (r) σN N (r) Tm (r) ⎥⎦
}
(5)
2. Principle and method
where
This section describes the retrieval of aerosol optical properties via the traditional method and our method.
γ=−
2.1. Traditional method
Tm (r) = exp
The equations for Mie and N2-Raman lidar with emission wavelength λL and λN can be expressed as follows:
However, a few unknown items exist in Eq. (5) and need to be eliminated. We consider rf is the reference altitude same as Eq. (3), where G (rf ) = 1. Eq. (5) can be rewritten as
P (λL , r) =
P (λN , r) =
C (λL ) r2
G (r) β (λL , r)exp
C (λN ) r2 ×
{ − 2∫
0
r
αa (λL , r ‵) + αm (λL , r ‵) dr ‵
}
(1)
G (r) β (λN , r)exp
{−∫
o
r
[αa (λL , r ‵) + αm (λL , r ‵) + αa (λN , r ‵) + αm (λN , r ‵)] dr ‵
}
(2)
where P (λx , r) is the received power from altitude r; subscripts L and N refer to the Mie and Raman backscatter of N2, respectively; C (λx ) is the lidar constant that contains all altitude-independent terms; G(r) is the geometric correction factor at r caused by the distance between the laser beam and telescope; β (λx , r) is the backscatter coefficient; and β (λN , r) = σN ⋅N (r), where σN and N(r) are the backscatter cross section and molecular number density of N2, respectively; α (λL , r) and α (λN , r) represent the extinction coefficient of Mie and N2-Raman; and subscripts a and m in α (λx , r) refer to the contribution from aerosols and molecules, respectively. ABC can be retrieved by the traditional method as follows [22,23]:
βa (λL , r) =
P (λL , r)⋅P (λN , rf )⋅N (r) P (λL , rf )⋅P (λN , r)⋅N (rf
)
⎧ exp ⎨ ⎩
λN , λN + λL
∫r
r f
{−∫
0
r
}
[αm (λL , r‵) + αm (λN , r‵)] dr‵ .
⎫ ⎡ P (λN , r) r 2⋅N (rf )⋅Tm (rf ) 1 ⎤γ ⎥, [αa (λL , r‵)] dr‵⎬ = ⎢ ⋅ ⎭ ⎢⎣ P (λN , rf ) r 2⋅N (r)⋅Tm (r) G (r) ⎥⎦
When substituted into Eq. (3), we can obtain an accurate ABC at wavelength λL by
βa (λL , r) =
P (λL , r)⋅P (λN , rf )⋅N (r) P (λL , rf )⋅P (λN , r)⋅N (rf
)
βm
⎧ ⎫ r exp ⎨ − ∫r αm (λN , r‵) dr‵⎬ f ⎩ ⎭ ⋅ (λL , rf ) ⎧ r ⎫ exp ⎨ − ∫r αm (λL , r‵) dr‵⎬ f ⎩ ⎭ ⎡ P (λ , r) r 2⋅N (r )⋅T (r ) ⎤γ N f m f 1 ⎥‵ ⎢ ⋅ ⎢⎣ P (λN , rf ) r 2⋅N (r)⋅Tm (r) G (r) ⎥⎦ − βm (λL , r)
(7) [1/G (r)]γ′
βm (λL , rf
)
⎧ ⎫ r exp ⎨ − ∫r αa (λN , r‵) + αm (λN , r‵) dr‵⎬ f ⎩ ⎭ − βm (λL , r); ⎧ ⎫ r exp ⎨ − ∫r αa (λL , r‵) + αm (λL , r‵) dr‵⎬ f ⎩ ⎭
(3)
where subscripts a and m represent aerosol and molecular scattering, respectively, and rf is the reference altitude, which is set to
(6)
where, γ′ = λL − λN /λL + λN . can be regarded as 1 where G (r) is greater than 0.8 when λL is equal 532 nm and λN is equal 607 nm. In general, altitude higher than 500 m satisfy the conditions. ABC can be retrieved by the method without the calculation of the extinction coefficient, which may cause a large error. As it will be shown latter, this improved method is more accurate than that retrieved by the traditional method described in Eq. (3). The ABC result of this method is employed in our improved method to retrieve a more accurate AEC than that of the traditional method.
W. Gong et al. / Optics Communications 349 (2015) 145–150
2.2.2. Aerosol extinction coefficient Traditional methods to retrieve AEC with a single N2-Raman signal must obtain the result of the numerical derivative which leads to larger errors. Thus, we propose an improved method to retrieve AEC based on the obtained ABC and constrained by Eq. (1), i.e the Mie lidar equation. From Eq. (1), the ratio of P (λL , ri ) and P (λL , ri + 1 ) at two adjacent points, ri and ri + 1 , can be rewritten as follows:
βa‵ (Sa‵ , λL , ri + 1 ) =
P (λL , ri + 1 ) ri2+ 1 ⎡ ⎣βm (λL , ri ) + βa (λL , ri ) ⎤⎦ P (λL , ri ) ri2
⎧ exp ⎨ − 2 ⎩
∫r
ri
i +1
(8)
where αa (λL , r) = S′a (r) ⁎βa (λL , r) and S′a (r) is the lidar ratio.
βa′ (Sa′ , λL , ri + 1 ) is ABC, and the superscript is to distinguish ABC from that in Eq. (7). Geometric correction factor G(r) in Eq. (1) is ignored. The integral term can be simply described as
∫r
i
αa (λL , r′) dr′ = 0.5⁎ ⎡⎣Sa′ (ri ) ⁎βa (λL , ri ) + Sa′ (ri + 1 ) ⁎βa (λL , ri + 1 ) ⎤⎦ (9)
⁎dr ,
where dr is the vertical resolution (equal to 7.5 m in this study) and βa is ABC obtained by the mentioned improved method. To simplify the processing of the integral term, S′a (r) is regarded as having similar values at two adjacent points (ri and ri + 1 ). Thus, Eq. (8) can be rewritten as
βa‵ (Sa‵ , λL , ri + 1 ) =
P (λL , ri + 1 ) ri2+ 1 ⎡ ⎣βm (λL , ri ) + βa (λL , ri ) ⎤⎦ P (λL , ri ) ri2 ri ⎧ ⎫ αm (λL , r‵) dr‵⎬ ⋅exp ⎨ − 2 ri + 1 ⎩ ⎭
∫
⋅exp Sa‵ (ri ) ⁎ ⎡⎣βa (λL , ri ) + βa (λL , ri + 1 ) ⎤⎦ ⁎dr
{
− βm (λL , ri + 1 )
altitude ri .
M [Sa (ri ), ri ] = βa′ [Sa (ri ), ri ] − βa (ri )
(11)
After obtaining ABC and the lidar ratio, we can obtain AEC as follows:
αa (r) = βa (r)⋅Sa (r).
(12)
3. Results and discussion
⎫ αa (λL , r‵) + αm (λL , r‵) dr‵⎬ ⎭
− βm (λL , ri + 1 )
ri + 1
147
} (10)
The lidar ratio for clear air, cloud, and aerosol is usually different, but the range of the lidar ratio is from 1 sr to 100 sr when the wavelength is 532 nm under normal conditions [13]. Thus, lidar ratios Sa′ from 1 sr to 100 sr with an increment of 0.5 sr are applied in Eq. (10). Each βa′ (Sa , ri ) can be obtained for each Sa′ (ri ) at ri . To obtain optimal lidar ratio Sa (ri ), we define the judgment function in Eq. (11). When M [Sa (ri ), ri ] in Eq. (11) is minimized, we regard the corresponding Sa (ri ) as the optimal lidar ratio at
In this section, we verify the accuracy of the proposed improved method. The experiment results retrieved from the simulated and measured signal with the improved method (for ABC and AEC) are compared with that of the traditional method. According to the simulated signal experiment, the relative errors of the two methods vary with altitude are shown. 3.1. Simulated signal We simulated the Mie signal and N2-Raman signal with wavelengths of 532 and 607 nm, respectively, and with Gaussian noise under standard atmosphere (Fig. 1). A planetary boundary layer and an optical thick layer were simulated at 0–2 km and 4– 6 km. According to its physical properties, cloud is a type of atmospheric aerosol. Therefore, we did not separate the discussion of aerosols and clouds. The simulative aerosol lidar ratio are from 70 sr to 50 sr at 0–2 km, 60 sr at 4–6 km, and 50 sr at other altitude, respectively. The SNR of the Mie lidar signal is approximately a thousand times higher than that of N2-Raman lidar signal under similar conditions. Fig. 2(a) shows the true ABC and the average and standard deviation (i.e., the error bars) of the ABCs retrieved by the traditional method and the improved method in 20 simulated experiments. The results of the two methods are in good agreement with the true value because the concepts of the two methods are similar. However, AEC must be initially calculated if the traditional method is used. AEC cannot be accurately calculated because of the numerical derivation. Lastly, the calculation errors of AEC are added to ABC. Thus, the results obtained by the traditional method are worse than the results obtained by the improved method. The error bar above 6 km shows that the uncertainty of the improved method is smaller than that of the traditional method. Fig. 2 (b) shows that the relative errors of the two methods under 6 km are almost zero because the SNR is high. However, the relative
Fig. 1. Simulated range-corrected Mie and N2–Raman lidar signals under standard atmosphere.
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Fig. 2. (a) True ABC and ABCs (with error bars) retrieved by the traditional method and the improved method denoted by a blue dotted line, an orange solid line, and a red solid line, respectively. (b) Relative errors of ABCs retrieved by the traditional method and the improved method denoted by an orange solid line and a red solid line, respectively. (c) Same as (a), but for AECs. (d) Same as (b), but for AECs. (e) Same as (a), but for lidar ratios. (f) Same as (b), but for lidar ratios. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
errors rapidly increase with the decline in SNR above 6 km. In summary, the ABC of the improved method is smaller than that of the traditional method. This result indicates that the ABC retrieved by the improved method is more suitable. Fig. 2(c) shows the true AEC and the average and standard deviation (i.e., the error bars) of the AECs retrieved by the traditional method and our method in 20 simulated experiments. Before retrieving AEC by the traditional method, the N2-Raman signal was averaged with sliding windows of 375 m and 1125 m for altitudes of below 3.75 km and above 3.75 km, respectively. Fig. 2(d) shows that the uncertainty of the AEC retrieved by the traditional method becomes increasingly unacceptable with SNR decline above 4 km. However, the AEC retrieved by our method is significantly better than that of the traditional method and only has slight fluctuations around the true value. Moreover, the AEC of our method substantially coincides with the true value when an optical thick layer exists. However, the AEC of the traditional method is distorted because sliding average is used to calculate the numerical derivative. Fig. 2 (d) shows the relative errors of the AECs retrieved by the traditional method and our improved method, and the relative errors are almost zero below 2 km because the SNR is high. However, the relative error of the traditional method is greater than 100% because of the calculation of the numerical derivative where SNR is low. The range of relative errors of our method is mainly between
50 and 50 when the SNR is low and an optical thick layer exists. This result indicates that our method is more stable than the traditional method in retrieving AEC. Fig. 2(e) shows the true lidar ratios and that retrieved by the traditional method and our improved method. The ABC is smoothed with the same window length for AEC before computing the lidar ratio by traditional method. Both methods obtained accurate lidar ratios under 2 km, where the SNR is high. The result retrieved by the traditional method does not match the true value when an optical thick layer exists because the AEC of the traditional method is distorted. Fig. 2 (e) shows that the lidar ratio of our method is highly consistent with the true value. Fig. 2(f) shows that the relative errors of the two methods are basically equal to zero below 2 km. However, the relative errors of our method are from 20% to 20% above 2 km and are significantly smaller than those of the traditional method. 3.2. Measured signal Fig. 3(a) shows a Mie backscattering signal at a wavelength of 532 nm and an N2-Raman backscattering signal at a wavelength of 607 nm, which are measured and averaged from 21:51 to 22:10 Beijing time (CST) on March 15, 2014. A planetary boundary layer is below 2 km, and an optical thick layer exists from 8 km to 10 km. The SNR of the Mie signal is higher than that of the N2
W. Gong et al. / Optics Communications 349 (2015) 145–150
149
Fig. 3. (a) Mie backscattering signal at a wavelength of 532 nm and N2-Raman backscattering signal at a wavelength of 607 nm; both were measured and averaged at 21:51 to 22:10 Beijing time (CST) on March 15, 2014. (b) ABCs retrieved by the traditional method and the improved method. (c) AECs retrieved by the traditional method and the improved method. (d) lidar ratios retrieved by the traditional method and the improved method.
signal at all altitudes. The mean intensity of the N2-Raman signal is about one-thousandth of the Mie signal because the Raman scattering cross section is smaller than that of Mie. Fig. 3(b) shows the ABCs retrieved by the traditional method and the improved method. The reference altitude in the retrieval is 10 km. The quality of the ABCs of the two methods declines with the decrease in SNR. A few negative values exist in the ABC profiles at above 10 km because the SNR of the N2-Raman signal is very low. The ABC of the improved method is more stable than that of the traditional method because the improved method is less influenced by the error of AEC. Therefore, the ABC retrieved by the improved method is more suitable as the input for our improved method to retrieve AEC. Fig. 3(b) demonstrates that ABC is lower than the molecular backscatter coefficient at about 10 km. Thus, the reference altitude at 10 km is reasonable. Fig. 3(c) shows the AECs retrieved by the traditional method and our method. To retrieve a more precise AEC profile by the traditional method, the N2-Raman signal was averaged with sliding windows of 375 m and 2250 m for altitudes of below 6 km and above 6 km, respectively. The AEC retrieved by the traditional method becomes suspicious and even negative at above 6 km. In the range of 8–10 km, the local maximum value of the AEC retrieved by the traditional method is
smaller than that of our method because of excessive smoothing, similar to the simulation experiment. The profile retrieved by our method has a smaller fluctuation range and better stability than that retrieved by the traditional method. Both of the method is almost unaffected by geometric correction factor. Fig. 3 (c) indicates that our improved method has better noise immunity than the traditional method for retrieving AEC. Therefore, our improved method can provide more accurate results. Note the region below 1.5 km, the improved method for AEC is still affected by geometric correction factor of Mie lidar signal. Fig. 3(d) shows the lidar ratios retrieved by the traditional method and our improved method. The Mie signal and N2-Raman signal profiles are smoothed with same window length before computing the lidar ratio by traditional method. In general, the two lidar ratios match each other well. However, the lidar ratio of our method has smaller fluctuations than that of the traditional method. Moreover, the lidar ratios are within a reasonable range (from 20 sr to 80 sr). The region above 5.5 km is not shown because of the poor result retrieved by the traditional method.
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4. Conclusion We developed an improved method to retrieve aerosol optical properties that are more accurate than those of traditional method from Raman–Mie lidar. For ABC, we re-formulate the N2-Raman lidar equation to obtain an unknown term which contains the AEC at the Mie wavelength. Then, we replace the unknown term of the equation in traditional method for retrieving ABC. To obtain the optimal lidar ratios of our method, lidar ratios from 1 sr to 100 sr with an increment of 0.5 sr were utilized in the performance function we defined. Both simulated and measured signal experiments verified that the results obtained by our method are more accurate than those of traditional methods without assumption or excessive de-noising. The advantage of the improved method for AEC retrieval is more significant because this method avoids the calculation of the numerical derivative. In particular, the results on measured signals showed that our improved method can work well at a wide range where SNR is low. Meanwhile, the aerosol details retrieved by our improved method are substantially preserved; such details may be lost or distorted when the traditional method is employed because of the de-noise methods (e.g., sliding average method). The lidar ratio of our method has smaller fluctuations than that of the traditional method. The results verify that our method can retrieve aerosol optical properties, especially AEC, with better noise immunity, stabilization, and robustness than the traditional method. The proposed method was applied to the Raman–Mie lidar system at Wuhan University. The time sequence for aerosol optical properties will be analyzed with our improved method in the future. However, our method still has room for improvement, and we will continue to search for a more effective method to retrieve aerosol optical properties.
Acknowledgments This work was supported by a Grant from 973 Programs (2011CB707106), the NSFCs (41127901, 41301372), Major Projects of Hubei Collaborative Innovation Center for High-Efficiency Utilization of Solar Energy (HBSZD2014002)
References [1] V.A. Kovalev, W.E. Eichinger, Elastic Lidar: Theory, Practice, and Analysis Methods, Wiley-Interscience, New York, 2004. [2] C. Weitkamp, Lidar: range-resolved optical remote sensing of the atmosphere, Springer Science & Business Media, 2005. [3] Raymond M. Measures. Laser remote sensing: fundamentals and applications [M]. Krieger, 1992.
[4] F.G. Fernald, Analysis of atmospheric lidar observations: some comments, Appl. Opt. 23 (1984) 652–653. [5] A. Ansmann, M. Riebesell, C. Weitkamp, Measurement of atmospheric aerosol extinction profiles with a Raman lidar, Opt. Lett. 15 (1990) 746–748. [6] D. Whiteman, S. Melfi, R. Ferrare, Raman lidar system for the measurement of water vapor and aerosols in the Earth's atmosphere, Appl. Opt. 31 (1992) 3068–3082. [7] R. Collis, Lidar: a new atmospheric probe, Q. J. R. Meteorol. Soc. 92 (1966) 220–230. [8] F.G. Fernald, B.M. Herman, J.A. Reagan, Determination of aerosol height distributions by lidar, J. Appl.Meteorol. 11 (1972) 482–489. [9] T. Murayama, N. Sugimoto, I. Uno, K. Kinoshita, K. Aoki, N. Hagiwara, Z.Y. Liu, I. Matsui, T. Sakai, T. Shibata, K. Arao, B.J. Sohn, J.G. Won, S.C. Yoon, T. Li, J. Zhou, H.L. Hu, M. Abo, K. Iokibe, R. Koga, Y. Iwasaka, Ground-based network observation of Asian dust events of April 1998 in east Asia, J. Geophys. Res. Atmos. 106 (2001) 18345–18359. [10] V. Matthais, V. Freudenthaler, A, Amodeo, et al., Aerosol lidar intercomparison in the framework of the EARLINET project. 1. Instruments[J], Applied Optics 43 (4) (2004) 961–976. [11] D.D. Turner, J. Goldsmith, Twenty-four-hour Raman lidar water vapor measurements during the Atmospheric Radiation Measurement Program's 1996 and 1997 water vapor intensive observation periods, J. Atmos. Ocean. Technol. 16 (1999) 1062–1076. [12] D.D. Turner, R.A. Ferrare, L.A.H. Brasseur, et al., Automated retrievals of water vapor and aerosol profiles from an operational Raman lidar[J], Journal of Atmospheric and Oceanic Technology 19 (1) (2002) 37–50. [13] F. Mao, W. Gong, T. Logan, Linear segmentation algorithm for detecting layer boundary with lidar, Opt. Express 21 (2013) 26876–26887. [14] F. Mao, W. Gong, C. Li, Anti-noise algorithm of lidar data retrieval by combining the ensemble Kalman filter and the Fernald method, Opt. Express 21 (2013) 8286–8297. [15] F. Mao, W. Gong, Y. MA, Retrieving the aerosol lidar ratio profile by combining ground-and space-based elastic lidars, Opt. Lett. 37 (2012) 617–619. [16] G. Pappalardo, A. Amodeo, M. Pandolfi, U. Wandinger, A. Ansmann, J. Bosenberg, V. Matthias, V. Amirdis, F. De Tomasi, M. Frioud, M. Larlori, L. Komguem, A. Papayannis, F. Rocadenbosch, X. Wang, Aerosol lidar intercomparison in the framework of the EARLINET project. 3. Raman lidar algorithm for aerosol extinction, backscatter, and lidar ratio, Appl. Opt. 43 (2004) 5370–5385. [17] P. Pornsawad, C. Böckmann, C. Ritter, M. Rafler, Ill-posed retrieval of aerosol extinction coefficient profiles from Raman lidar data by regularization, Appl. Opt. 47 (2008) 1649–1661. [18] J. Zhang, C. Huang, W. Gong, An Algorithm for retrieving the atmospheric aerosol extinction coefficient via Raman lidar data, Lasers Eng. 27 (2014) 393–398. [19] P. Pornsawad, G. D'Amico, C. Bockmann, A. Amodeo, G. Pappalardo, Retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion method, Appl. Opt. 51 (2012) 2035–2044. [20] A. Ansmann, U. Wandinger, M. Riebesell, et al., Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar[J], Applied Optics 31 (33) (1992) 7113–7131. [21] J. Su, Y.H. Wu, M.P. McCormick, L.Q. Lei, R.B. Lee, Improved method to retrieve aerosol optical properties from combined elastic backscatter and Raman lidar data, Appl. Phys. B: Lasers Opt. 116 (2014) 61–67. [22] A. Ansmann, M. Riebesell, U. Wandinger, C. Weitkamp, E. Voss, W. Lahmann, W. Michaelis, Combined Raman elastic-backscatter lidar for vertical profiling of moisture, aerosol extinction, backscatter, and lidar ratio, Appl. Phys. B 55 (1992) 18–28. [23] W. Gong, J. Zhang, F. Mao, J. Li, Measurements for profiles of aerosol extinction coeffcient, backscatter coeffcient, and lidar ratio over Wuhan in China with Raman/Mie lidar, Chin. Opt. Lett. 8 (2010) 533–536.