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Abstract
Multi-wavelength Raman lidar has been widely used in profiling aerosol optical properties. The accuracy of measured aerosol optical properties largely depends on sophisticated lidar data retrieval algorithms. Commonly to retrieve aerosol optical properties of Raman lidar, the extinction-related Ångström exponent (EAE) is assumed (to be 1). This value usually generally differs from the true value (called EAE deviation) and adds uncertainty to the retrieved aerosol optical properties. Lidar-signal noise and EAE-deviation are two important error sources for retrieving aerosol optical properties. As the measurement accuracy of Raman lidar has been greatly improved in recent years, the influence of signal noise on retrieval results becomes relatively small, and the uncertainty of retrieved aerosol optical properties caused by an EAE-deviation becomes nonnegligible, especially in scenes that EAE deviation is large. In this study, an iteration retrieval algorithm is proposed to obtain more reliable EAE based on multi-wavelength Raman lidar. Results from this iteration are more precise values of aerosol optical properties. Three atmospheric scenarios where aerosol distribution and the values of EAE vary widely were simulated with a Monte Carlo method to analyze the characteristics and robustness of the iterative algorithm. The results show that the proposed iterative algorithm can eliminate the systematic errors of aerosol optical properties retrieved by traditional retrieval method. The EAEs after iteration does converge to the true value, and the accuracy of aerosol optical properties can be greatly improved, especially for the particle backscatter coefficient and lidar ratio, which has been improved by more than 10% in most cases, and even more than 30%. In addition, field observations data of a three-wavelength Raman lidar are analyzed to illustrate the necessity and reliability of the proposed iterative retrieval algorithm.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Aerosol lidar is an effective measurement method for investigations of the distribution and transport of aerosols [1–4]. Research on optical and microphysical properties of aerosol can be combined with the advantages of high spatial and temporal resolution and long detection range [5–7]. How to improve the accuracy of retrieved result has been a research hotspot, which is of great significance for improving the accuracy of meteorological forecast and models, etc. [8,9].
Aerosol optical properties mainly include particle extinction, backscatter coefficients, lidar ratio (the ratio of particle extinction coefficient and backscatter coefficient) and Ångström exponent. Particle extinction and backscatter coefficients are extensive parameters. They reflect particle concentration in the atmosphere. Lidar ratio [10–12] and Ångström exponent [13,14] are intensive parameters which reflects the type of particle, which are important parameters in studies of atmospheric pollution with lidar.
Raman lidar is used for detecting two types of light signals. One type of signal is caused by elastically scattered light, which means the wavelength of the emitted laser light is not changed during the scattering process. The other type of light is inelastically scattered light which is the results of Raman-scattering. Compared with elastic-backscatter lidar, aerosol optical properties can be derived by a Raman lidar without assuming the lidar ratio. Raman lidar emits laser light into the atmosphere. A Raman channel then is used to detect the Raman-shifted photons. In order to obtain the particle extinction coefficients at the emission wavelength, wavelength conversion is needed. Therefore, a parameter that represents the wavelength dependence of particle extinction coefficients is introduced, called extinction-related Ångström exponent (EAE) [13,14]. The EAE is closely related to the type, size of the aerosol particles and wavelength, whose values are distributed over a certain range (-1 ∼ 3) [15–19]. However, the value of EAE is assumed in traditional retrieval method for Raman lidar, and the assumed value is often different from the true value, which is called EAE deviation.
Lidar-signal noise and EAE-deviation are two important error sources in algorithms that are used for calculating aerosol optical properties. When the signal-to-noise ratio (SNR) of a lidar signal is poor, the influence of the EAE deviation on retrieved aerosol optical properties is relatively small compared with the random error caused by lidar signal noise. However, with the improvement of lidar system performance, the lidar signal noise becomes smaller and smaller. In this way, the optical-data error caused by the EAE deviation becomes nonnegligible, and can even much larger than the random error caused by lidar signal noise. In addition, particle microphysical properties, which can be retrieved from aerosol optical properties, are very sensitive to the uncertainties of aerosol optical properties [20].
Multi-wavelength Raman lidar allows for measuring aerosol spatial information (height-dependent distribution) at emission wavelengths simultaneously. It has the ability to retrieve EAE. However, at present, the relationship between measured aerosol spatial information at emission wavelengths is not fully used. Same as a simple backscatter lidar, the EAEs are still assumed to obtain aerosol optical properties. This method is imperfect.
A lot of work in lidar data retrieval has been done in European Aerosol Research Lidar Network (EARLINET), such as, testing the accuracy of retrieval algorithm by algorithm inter-comparison [21], developing an automatic lidar analysis tool, single calculus chain (SCC) [22–24], to assure the homogenous of the retrieval results. In the calculation of particle extinction coefficients with Raman method in EARINET, the EAE is assumed [24]. In addition, Ansmann, et. al., Whiteman, et. al. usually assumes the EAE 1 when retrieving the particle extinction coefficient for Raman lidar [25–28]. However, there are still many types of particles in the atmosphere whose EAE vary greatly from 1, such as, dust, cirrus cloud, sea salt, biomass burning [29,30], etc. Whiteman discussed the influence of EAE deviation on retrieved particle extinction coefficient at 351 nm, and results showed that when the EAE changed from 0 to 2, the value of particle extinction coefficient increases by about 8% [31]. Ansmann, et. al. presented that when the assumed EAE is 0.5 or 1 different from the true value, the relative uncertainty of particle extinction coefficient will be 2% and 4%, respectively [32]. Veselovskii, I. et al. discussed the effect of EAE deviation both on particle extinction and backscatter coefficients, the results showed that the EAE deviation could cause relatively large uncertainty when the EAE deviation was large [33]. However, they do not discuss how to improve the accuracy of EAE used in data retrieval, and further improve the accuracy of retrieved aerosol optical properties.
In this contribution, we discuss the influence of EAE-deviation on aerosol optical properties for the case of multi-wavelength Raman lidar. We propose an iterative retrieval algorithm to obtain more accurate values of EAE. We show that the accuracy of aerosol optical properties can be improved. Section 2 presents the theoretical background of the relationship between EAE deviation and the relative uncertainties of aerosol optical properties. The iterative retrieval algorithm is introduced. Section 3 presents the numerical verification of the iterative algorithm. Section 4 presents the application of iterative algorithm to measured data. Section 5 presents conclusions.
2. Methodology
2.1 Theoretical background
For Raman lidars, the particle extinction and backscatter coefficient can be calculated independently [12,13,21,26] according to the following 2 equations:
Aα and Aβ are the extinction-related Ångström exponent (EAE) and backscatter-related Ångström exponent (BAE), respectively [13,18,34]. The formulas of EAE and BAE can be expressed as:
Equations (1) and (2) show that particle extinction and backscatter coefficients are related to the EAE. That is to say, any deviation of the EAE from the true value (labeled as ΔAα) will lead to uncertainties of the aerosol optical properties. The relative uncertainties of the particle extinction coefficient (${\delta _\alpha }$) and the backscatter coefficient (${\delta _\beta }$) [33] can be expressed as
Figure 1 shows the simulation of the influence of EAE deviation on the particle extinction coefficients based on Eq. (5). The commonly used emission wavelengths of Raman lidar are 355 nm, 532 nm and 1064 nm, and the corresponding Raman scattering wavelength of nitrogen are 386 nm, 607 nm, and 853 nm [35]. In this study, these emission and Raman wavelengths are used for simulation. The EAE is assumed to be 1. When the EAE deviation changes from -2 to 2, the maximum relative uncertainties (absolute value) of the particle extinction coefficients can reach about 8%, 12% and 25% at 355 nm 532 nm and 1064 nm, respectively. The result is consistent with previous researches [31,32].
Fig. 1. The influences of the extinction-related Ångström exponent (EAE) deviation on the relative uncertainties of the particle extinction coefficients at 355 nm, 532 nm and 1064 nm.
2.2 Iterative retrieval algorithm for multi-wavelength Raman lidar
An iterative retrieval algorithm is proposed to obtain more accurate EAE and aerosol optical properties based on multiwavelength Raman lidar with more than two Raman detection channels. Figure 2 is the flow chart of the iterative retrieval algorithm. The data preprocessing is needed before retrieval. The layers boundaries are identified for signal profiles, which is based on differential zero-crossing method [36]. The value of EAE keep same in the same layer. As the EAE deviation caused by the assumed initial value of EAE is the main error source for data retrieval, and the differences between the values of EAE at different wavelength pairs (such as, 355/532 nm, 355/386 nm, 532/607 nm) are small. Therefore, in our iterative retrieval algorithm, we assume that the values of EAE at different wavelength pairs are the same. The iterative process is as follows.
- (1) Assume the initial value of EAE (to be 1), labeled it A0. Calculating the particle extinction coefficients at emission wavelengths with the assumed EAE using the Raman method (see Eq. (1)).
- (2) Calculate the EAE with the particle extinction coefficients derived from step (1) using Eq. (3), and labeled it A1.
- (3) In every layer, compare A1 with A0. If the absolute value of the difference between A1 and A0 (called EAE difference) is less than threshold, the EAE in this layer is convergent. At present, the relative uncertainty of retrieved particle extinction coefficient from lidar is difficult to reach 0.5%. As can be seen from Fig. 1, when the relative uncertainty of particle extinction coefficient is less than 0.5%, the EAE deviations at 355 nm, 532 nm and 1064 nm should be less than about 0.09, 0.13 and 0.04, respectively. In this study, we set the threshold of EAE difference to 0.01. Otherwise, if the EAE difference is larger than threshold, the input value of EAE need to be adjusted in the next iteration. That is, A0(j + 1) =A0(j)+k*(A1(j)-A0(j)), where j is the number of iterations, and the k represents the amplification factor. The newly calculated A0 will be used to calculate particle extinction coefficients and repeat steps (1-3). The amplification factor k affects the convergence speed and direction of iterative calculation. If k is too large, the iterative calculation will diverge easily. The judgment condition of divergence is that the EAE difference in this iteration is larger than the EAE difference of the previous iteration. In this case, the amplification factor k is multiplied by 0.5 to ensure the convergence of iterative calculation. If k is too small, the convergence process will be slow. In this study, the k value is set as 1 according to lots of experiments.
- (4) If the calculated EAE at all layer meet the convergence condition, the iterative calculation ends; otherwise, repeat steps (1-4).
3. Numerical verification and analysis
We simulated three typical scenarios that included two layers, three layers and mixture layer to verify and analyze the proposed iterative algorithm. In these scenarios, the EAE of aerosols differ greatly. The first scenario contains two aerosol layers and describes a transported biomass-burning smoke in urban environment, which comprises of fine-mode particles with large EAE. The second scenario contains three aerosol layers, and describes transported desert dust in urban environment. Urban aerosol is comprised of fine-mode anthropogenic particles that usually can be described by a relatively large EAE. Desert dust is mainly comprised of particle in the coarse mode which has a small EAE. The third scenario is a mixture of two different types of aerosols.
We simulated signals for the case of a three-wavelength Raman lidar for scenarios analysis. Table 1 shows the main parameters of the lidar used in the simulations. The temporal resolution of a single lidar signal is 1 minute, and the time for signal accumulation (accumulate time) is 30 minutes.
Table 1. Values of main simulation parameters of a three-wavelength Raman lidar
3.1 Simulation of scenario with two layers
In the scenario with two aerosol layers, the polluted planetary boundary layer (PBL) and another particle layer is simulated.
Table 2 shows the values of main simulation parameters of scenario with two aerosol layers. We assume that the main component of the aerosols in the PBL are anthropogenic aerosol. The anthropogenic aerosols are mainly distributed in 0-3 km, and the lidar ratios at 532 nm mainly range from 50 sr to 80 sr. Their EAEs and BAEs are mainly distributed in 1-2 and 1-2, respectively [29,30,37]. In regard to the lofted particle layer, we assume that smoke particles from biomass burning comprises the main component of the aerosol. The biomass burning smoke is mainly distributed between 4 and 7 km, and the lidar ratios at 532 nm mainly range from 55 sr to 95 sr, while their EAEs and BAEs are mainly distributed in 1.2-2 and 1.3-1.8, respectively [29,38–40]. The particle extinction coefficients at 532 nm are chosen with the typical values in the city. All the simulation parameters in Table 2 are assumed according to the literatures above. The particle extinction coefficient and backscatter coefficients at the remaining wavelengths (355 nm, 386 nm, 607 nm and 1064 nm) are derived from Eqs. (3) and (4).
Table 2. Values of main simulation parameters of scenario with two layers. (α-532 nm is particle extinction coefficient at 532 nm. LR-532 nm is the lidar ratio at 532 nm. The same below).
The lidar signals were simulated according to the lidar equation and the Monte Carlo method described in Refs. [41,42]. Figure 3 shows the example of simulated range-corrected signals (RCS) at 355 nm, 386 nm, 532 nm, 607 nm and 1064 nm. The signal accumulative time is 30 minutes. The signal differs at the different wavelengths. These simulated signals are used to retrieve aerosol optical properties with the Raman method [21,26].
Fig. 3. The simulated range-corrected signals (RCS) of scenario with two layers at (a) 355 nm and 386 nm, (b) 532 nm and 607 nm, (c) 1064 nm. The temporal and spatial resolution are 30 min and 15 m, respectively.
To evaluate the effect of EAE deviation on the particle backscatter coefficient, the simulated lidar signal is retrieved with the true EAE and in another case with the assumed EAE (value 1). We obtain two different profiles of the particle backscatter coefficients. Then we calculate the two scattering ratios (the ratio of the sum of molecular and particle backscatter coefficients to the molecular backscatter coefficient). We calculate the difference between the two scattering ratios for each height level. We call this new profile the differential scattering-ratio (DSR) profile. The larger the DSR, the larger is the effect of the EAE deviation on the profile of the particle backscatter coefficient. In addition, we also calculated the relative uncertainty of the particle backscatter coefficient for the complete profile.
Figure 4 shows the influence of the EAE deviation on the particle backscatter coefficient at 355 nm and 532 nm, respectively. Both the DSRs at 355 nm and 532 nm are larger than 1. The maximum DSR at 532 nm is larger than that of 355 nm in each layer.
Fig. 4. The influence of an EAE deviation on particle backscatter coefficients. Shown are the (a) differential scattering ratio (DSR) and relative uncertainty of particle backscatter coefficient at 355 nm, and (b) at 532 nm.
The maximum relative uncertainties of particle backscatter coefficients of layer1 and layer2 at 355 nm are larger than 15% and 30%, respectively. The maximum relative uncertainty of the particle backscatter coefficient in the PBL at 532 nm is also larger than 15%. The simulation result shows the need for accurate EAEs which requires improving the accuracy of retrieved aerosol optical properties.
The random noise of a lidar signal is an important factor that affects the quality of the measured aerosol optical properties. And it also affects the convergence behavior of the iterative retrieval algorithm. A poor SNR will directly increase the number of iterations and convergence accuracy of the algorithm. We run 200 times to obtain lidar signals with random noise using Monte Carlo method [41]. For every lidar signals with random noise, we obtained the aerosol optical properties with the improved retrieval algorithm proposed in this study. Since the true value of aerosol optical properties is known, we discuss the convergence of the algorithm and present result of our statistical analysis.
Figure 5 shows the retrieval result from traditional and iterative algorithm. The red lines represent the true value assumed in simulation. The green line, orange dotted line and blue dotted line represent the retrieval results during the 1st, 2nd and 3rd iterations, respectively. In this example, convergence is achieved after 3 iterations. The retrieval results during the first iteration are obtained with the initial value of EAE, which is the same as the traditional algorithm. The aerosol optical properties retrieved with assumed EAE (green line) have a relatively large differences from the true values (red line). The results for the profiles of the aerosol optical properties retrieved with the proposed iterative algorithm (blue dotted line) converge towards the true values.
Fig. 5. The retrieval result from iterative algorithm. Shown are (a, e) particle extinction coefficients, (b, f) particle backscatter coefficient and (c, g) lidar ratio at 355 and 532 nm, respectively. Results are shown (d) EAE and (h) BAE. “Iter” is the abbreviation for iteration.
Figure 6 show the statistics of 200 retrieved particle extinction and backscatter coefficients at 355 nm and 532 nm, respectively. What we present is the difference values between the retrieval results from the two retrieval algorithms (orange-red presents traditional algorithm, while light blue represents iterative algorithm) and the true value. The statistics show that the different values are relatively large. Compared with the traditional retrieval method, the iterative algorithm can reduce the systematic error in the retrieval process and does not change the random error in the retrieval process. The retrieved results from the iterative algorithm converge to the truth value. The average retrieved particle extinction coefficients at 355 nm have been improved by 19 Mm-1 and 26 Mm-1 (relative uncertainties 3% and 3%) in layer 1 and layer 2, respectively. The average retrieved particle extinction coefficients at 532 nm have been improved by 14 Mm-1 and 19 Mm-1 (relative uncertainties 5% and 5%) in layer 1 and layer 2, respectively. For particle backscatter coefficient, the average value has improved by 2.1 Mm-1sr-1 and 0.7 Mm-1sr-1 (relative uncertainties 26% and 8%) in layer 1, layer 2 at 355 nm, and 0.6 Mm-1sr-1, 0.2 Mm-1sr-1 (relative uncertainties 13% and 4%) in layer 1, layer 2 at 532 nm.
Fig. 6. The statistics of difference between retrieved result and true value for particle extinction and backscatter coefficients. The difference of (a, c) particle extinction coefficients at 355 nm and (e, g) 532 nm. The difference of (b, d) particle backscatter coefficients at 355 nm and (f, h) 532 nm. The red dashed line marks the position of value 0. AVG, STD and STE are the abbreviations for average, standard deviation and standard error, respectively.
The statistical results show a Gaussian distribution. That result indicates the proposed iterative algorithm can be used to improve the accuracy of retrieved aerosol optical properties.
Figure 7 shows the statistics of the differences between retrieved lidar-ratio (the iterative, and the traditional method) and the true values. The differences are large. The retrieved lidar ratio from the iterative algorithm converge to the truth value. The average lidar-ratio at 355 nm can be improved by as large as about 17 sr and 9 sr (relative uncertainties 23% and 10%) in layer 1 and layer 2, respectively. The average lidar-ratio at 532 nm can be improved by as large as about 11 sr and 7 sr (relative uncertainties 16% and 9%) in layer 1 and layer 2, respectively.
Fig. 7. The statistics of the difference between the retrieved lidar ratios and the true values at (a, c) 355 nm and (b, d) 532 nm. The meaning of abbreviations is the same as in Fig. 6.
Figure 8 shows the statistics of the differences between the retrieved EAE, BAE and their true values. Figure 8(a) and (c) shows the statistical results of the differences of the EAEs. Both the true values of the EAEs of layer 1 and layer 2 are 1.8, respectively. The statistical results of the EAEs of layer 1 and layer 2 are 1.7999 ± 0.0001 and 1.800 ± 0.001.
Fig. 8. The statistics of the difference between the retrieved EAE, BAE and the true values. Shows are the results for the (a, c) EAE difference and the (b, d) BAE difference. The meaning of abbreviations is the same as in Fig. 6.
Figure 8(b) and (d) shows the statistical results of the differences of the BAEs. We find a distribution that is similar to the one obtained for the EAE. In layer 1 and layer 2, the true values of the BAEs are 1.6 and 1.5 respectively. The 200 statistical results in values for the BAEs for layer 1 and layer 2 are 1.607 ± 0.004 and 1.505 ± 0.004, respectively. The differences show a normal distribution which is related to the random errors of the signals. The iterative algorithm can improve the accuracy of EAEs and BAEs.
3.2 Simulation of scenario with three layers
In the scenario with three layers, a planetary boundary layer (PBL), a dust layer, and a cirrus layer are assumed.
Table 3 presents the values of main simulation parameters of scenario with three layers. The main component of the PBL is anthropogenic aerosol. We set the EAE and BAE to 1.2 and 1.5, respectively [29,37]. The desert dust is mainly distributed between 1 and 8 km, and the lidar ratio at 532 nm mainly range from 45 sr to 70 sr, while their EAEs and BAEs are mainly distributed in 0-1 and -0.2-0.6, respectively [43]. The cirrus cloud is mainly distributed between 8 and 14 km, and the lidar ratios at 532 nm mainly range from 10 sr to 30 sr, while their EAEs and BAEs are around 0. Therefore, We set both the EAE and BAE to 0 [44,45], and lidar ratio to 20 sr [45] in the cirrus layer. All the simulation parameters in Table 3 are assumed according to the literatures above. The particle extinction and backscatter coefficients at the other wavelengths (355 nm, 386 nm, 607 nm and 1064 nm) are calculated using Eqs. (3) and (4).
Table 3. Values of main simulation parameters of scenario with three layers
Same as in section 3.1, the lidar signals were simulated and retrieved with the true EAE and in another case with the assumed EAE (value 1).
Figure 9 shows the influence of the EAE deviation on the particle backscatter coefficients at 355 nm and 532 nm respectively. Both the differential scattering ratios (DSR) at 355 nm and 532 nm are larger than 1. The DSR shows the maximum value at the cirrus layer, even larger than 2.5 at 532 nm. The maximum DSR at 532 nm is larger than that of 355 nm in each of the three layers.
Fig. 9. The influence of an EAE deviation on particle backscatter coefficients. The meaning of symbols, lines, and colors is the same as in Fig. 4.
Both the relative uncertainties of the particle backscatter coefficient of layer 1 and layer 2 at 355 nm and 532 nm are larger than 10%, which is comparably large. The simulation result shows the necessity to obtain a more accurate EAE and improve the accuracy of aerosol optical properties.
In the same way as mentioned above, we run 200 times to obtain lidar signals with random noise using Monte Carlo method [41] to discuss the convergence of the algorithm and present result of our statistical analysis.
Figure 10 shows an example of the retrieval result of proposed iterative algorithm. Same as Fig. 5, the red lines represent the true value assumed in simulation. The green line and blue dotted line represent the retrieval results during the first and final iterations, which correspond to the traditional retrieval algorithm and iterative retrieval algorithm, respectively. The aerosol optical properties retrieved with assumed EAE have a relatively large differences from the true values, especially in particle backscatter coefficient and lidar ratio. The results for the profiles of the aerosol optical properties retrieved by proposed iterative algorithm converge towards the true values.
Fig. 10. The retrieval results. The meaning of symbols, lines, and colors is the same as in Fig. 5. “Trad” and “Iter” are the abbreviation for traditional and iteration, respectively.
Figure 11 show the statistics of 200 retrieved particle extinction and backscatter coefficients at 355 nm and 532 nm, respectively. We can draw conclusions similar to the ones in regard to Fig. 6. The average particle extinction coefficients at 355 nm retrieved from iterative algorithm have been improved by 3 Mm-1, 12 Mm-1 and 17 Mm-1 (relative uncertainties 1%, 4% and 4%) in layer 1, layer 2 and layer 3, respectively. And the average particle extinction coefficients at 532 nm have been improved by 2 Mm-1, 19 Mm-1 and 26 Mm-1 (relative uncertainties 1%, 6% and 7%) in layer 1, layer 2 and layer 3, respectively. For particle backscatter coefficient at 355 nm retrieved from iterative algorithm, the average value has improved by 0.9 Mm-1sr-1, 0.6 Mm-1sr-1 and 0.3 Mm-1sr-1 (relative uncertainties 18%, 9% and 2%) in layer 1, layer 2 and layer3, respectively. And the average particle backscatter coefficients at 532 nm have been improved by 0.5 Mm-1sr-1, 0.5 Mm-1sr-1 and 0.5 Mm-1sr-1 (relative uncertainties 17%, 10% and 2%) in layer 1, layer 2 and layer3, respectively.
Fig. 11. The statistics of the difference between retrieved results and true values. The meaning of symbols, lines, and colors is the same as in Fig. 6.
In addition, from the distribution of retrieval results at layers 1,2 and 3, when the SNR of the signal is relatively small, the random noise of retrieval result is relatively large, and when the SNR of the signal is better, the distributions of retrieval results around the true value are more concentrated, and the advantages are more obvious compared with the traditional algorithm.
Figure 12 shows the statistics of the differences of retrieved lidar-ratio (the iterative, and the traditional method) and the true values. The differences are large, especially in layer 1 and layer 2.
Fig. 12. The statistics of the difference between the retrieved lidar ratios and the true values. The meaning of symbols, lines, and colors is the same as in Fig. 7.
The average lidar ratio at 355 nm retrieved from iterative algorithm have been improved by 14 sr, 7 sr, and 1 sr (relative uncertainties 21%, 15% and 6%), respectively. The average lidar ratio at 532 nm retrieved from iterative algorithm have been improved by 15 sr, 10 sr, and 2 sr (relative uncertainties 20%, 18% and 9%), respectively.
Figure 13 shows the statistics of the differences between the profiles of the EAE, BAE obtained with the iterative, traditional method and the true values. In the case of the EAE (Fig. 13 (a), (c), and (e)), the statistical results show that the distributions of retrieved EAEs around the true value are more concentrated for layer 1 and layer 2. This may be due to the high SNR of layer 1 and layer 2. The SNR of layer 3 (cirrus layer) is relatively poor, and the distribution of the results for EAE obtained with the iteration algorithm, is relatively dispersed.
Fig. 13. The statistics of the difference between the retrieved EAE, BAE and the true values. The meaning of symbols, lines, and colors is the same as in Fig. 8.
In more detail we obtain the following results. The true values of the EAEs are 1.2, 0 and 0 respectively, in layer 1 layer 2 and layer 3. The 200 statistical results in values of 1.1999 ± 0.0002, 0.0003 ± 0.0006 and 0.003 ± 0.004 for layer 1, layer 2 and layer 3, respectively.
Figure 13 (b), (d), and (f) show the statistical result of the differences of the BAE. The distribution of the statistics is similar to the one we obtain for the EAE. In layer 1, layer 2 and layer 3, the true values of the BAE are 1.5, 0.4 and 0, respectively. The results for the 200 statistical results are 1.505 ± 0.004, 0.405 ± 0.003 and 0.007 ± 0.003 for the three layers, respectively.
3.3 Simulation of scenario with mixture layers
We simulated a scenario with mixture layers, in which the boundaries of mixture layers are hard to distinguish. We assume an anthropogenic aerosol layer in 0-2 km agl, and place a dust layer in 1-3 km agl. The values of lidar ratio, EAE and BAE of these two types of aerosols are shown in Table 3.
Figure 14 show the simulated value of aerosol optical properties. The particle extinction and backscatter coefficients at the other wavelengths (355 nm, 386 nm, 607 nm and 1064 nm) are calculated using Eqs. (3) and (4).
Fig. 14. The simulated value of (a, b, c) particle extinction, backscatter coefficients and lidar ratio at 532 nm. (d) EAE, (e) BAE. Anthro. Stands for anthropogenic aerosol.
In data retrieval, we take the signal at 0-3 km as a layer, and the same value of EAE is used in this layer. Figure 15 shows the influence of an EAE deviation on particle backscatter coefficients at 355 nm and 532 nm. The maximum differential scattering-ratio (DSR) at 355 nm and 532 nm are 1.2 and 1.9, respectively. The maximum relative uncertainties at 355 nm and 532 nm are 11.0% and 11.7%, respectively. We can draw the same conclusions as Fig. 4 and Fig. 9.
Fig. 15. The influence of an EAE deviation on particle backscatter coefficients. The meaning of symbols, lines, and colors is the same as in Fig. 4.
Figure 16 present the retrieval result obtained with the traditional and iterative retrieval algorithm. The meaning of symbols, lines, and colors is the same as in Fig. 10. The result show that the retrieval result obtained from iterative retrieval algorithm is closer to the true value compared with the traditional retrieval algorithm, especially in particle backscatter coefficient and lidar ratio. Compared with the traditional algorithm, the iterative algorithm shows obvious advantages.
Fig. 16. The retrieval results from traditional and iterative algorithms. The meaning of symbols, lines, and colors is the same as in Fig. 10.
Figure 17 shows the statistics (statistical method is the same as above) of the difference between retrieved results and true values for particle extinction and backscatter coefficients. The difference between particle extinction coefficients from traditional retrieval algorithm and true values at 355 nm and 532 nm are 7.5 and 13.9 Mm-1, respectively, while they become -4.9 and -0.5 Mm-1 with iterative algorithm. The difference between particle backscatter coefficients from traditional retrieval algorithm and true values at 355 nm and 532 nm are -1.0 and -0.9 Mm-1sr-1, respectively, while they become -0.3 and -0.4 Mm-1 with iterative algorithm. Both the accuracies of particle extinction and backscatter coefficients have improved.
Fig. 17. The statistics of the difference of (a, c) particle extinction and (b, d) particle backscatter coefficients. The meaning of symbols, lines, and colors is the same as in Fig. 6.
Figure 18 show the statistics of the difference between retrieved lidar ratio and true values. The differences of lidar ratio from traditional retrieval algorithm and true values at 355 nm and 532 nm are 5.3 and 8.3 sr, respectively. While the differences from iterative algorithm at 355 nm and 532 nm becomes 0.4 and 2.1 sr, respectively. The accuracy of lidar ratio has also been greatly improved.
Fig. 18. The statistics of the difference between retrieved lidar ratio and true values. The meaning of symbols, lines, and colors is the same as in Fig. 7.
The results of the three simulation scenarios show that the iterative retrieval algorithm can be applied to different aerosol scenarios, such as, multi-layer aerosols and mixed aerosol layers, and the accuracy of retrieved aerosol optical properties can be greatly improved, especially for the particle backscatter coefficient and lidar ratio, which can be improved by more than 10% in most cases, and even more than 30%. In addition, the values of assumed EAE in the three simulation scenarios vary widely (such as, 0 and 1.8). Even so, the retrieved aerosol optical properties can converge to the true value, which reflects the practicability and robustness of the proposed iterative retrieval algorithm. Moreover, in simulation, the lidar parameters is same, as the aerosol loadings in the three scenarios are different, the SNRs of simulated signals are different. The simulation results show that when the SNR of the lidar signal is high, the convergence of the retrieval results show well, and the accuracy of retrieved aerosol optical properties can be greatly improved. When the SNR of the lidar signal is poor, the accuracy of aerosol optical properties retrieved by iterative retrieval algorithm is comparable to that of traditional algorithm. With the improvement of lidar system performance, the proposed iterative retrieval algorithm becomes more and more important.
4. Results and discussion
We tested our algorithm with data collected from lidar observations by the multi-wavelength Raman Polarization Lidar (AMPLE) [46,47]. The AMPLE system has 8 detection channels: 355 nm parallel polarization channel (E355P), 355 nm cross polarization channel (E355S), 532 nm parallel polarization channel (E532P), 532 nm cross polarization channel (E532S), nitrogen Raman channel (R386) corresponding to the laser emission wavelength at 355 nm, nitrogen Raman channel (R607) corresponding to the laser emission wavelength at 532 nm, 1064 nm elastic scattering channel (E1064) and the water vapor channel (R407) corresponding to the laser emission wavelength at 355 nm. The repetition frequency of the laser is 1000 Hz. The multiwavelength lidar has undergone a lidar self-calibration test [48]. Two observations scenes are selected in this study. One scene describes cirrus observed over Beijing (39°48’ N, 116° 28’ E). The second scene is dust observed in Beijing and Tianjin (39°03’ N, 117° 43’ E), respectively.
4.1 Cirrus case
Cirrus is widespread in the atmosphere and plays an important role in the global energy budget and atmospheric radiation balance [49]. According to previous studies, the EAE value of cirrus is relatively small, close to 0 [44,45]. If the EAE is still assumed to be 1 in the data processing, the uncertainty will be transmitted to the retrieved optical properties of cirrus. In this study, we select a cirrus scene to test the iterative algorithm.
Figure 19 shows the lidar signal observed over Beijing on 28 October 2021 LT (local time). Figure 19(a) and (b) are the time-height distribution of RCS and volume depolarization ratio at 532 nm, respectively. Cirrus was observed between 00:00 and 20:00 LT and between about 3 and 9 km height above ground. Figure 19 (c), (d), (e), and (f) shows the RCS of the elastic-backscatter (355 nm, 532 nm) and the Raman channels (386 nm, 607 nm) for the time between 2:00 and 3:00 LT on 28 October 2021. During the selected observation period, there were two layers of cirrus between about 5-9 km. The lidar signal show a good agreement with Rayleigh-fitting profiles. Both the elastic and Raman channels could detect signals above the cirrus cloud.
Fig. 19. Lidar signal on 28 October 2021 LT. Time-height plot of (a) RCS, (b) volume depolarization ratio at 532 nm. The profile of RCS at (c, d, e, f) 355 nm, 386 nm, 532 nm and 607 nm taken between 2:00-3:00 LT as the red box marked in (a, b). The red line represents the profiles of the Rayleigh fit (molecular signal). The temporal and spatial resolution are 1 minute and 30 m for (a, b), 60 minutes and 60 m for (c-f), respectively.
To test the proposed iterative algorithm, we used two methods to retrieve the lidar data for this measurement case. One method was the traditional data processing method by assuming the EAE to be 1. The other method is the iterative method proposed in this study.
Figure 20 shows the retrieval results at 2:00-3:00 LT on 28 October 2021. We see differences between the retrieved particle extinctions (Fig. 20 (a), (e)) and backscatter coefficients (Fig. 20 (b), (f)) at 355 nm and 532 nm, respectively, obtained with the two methods. In the aerosol layer between 0-2 km agl, the average (maximum) relative uncertainties of the particle backscatter coefficient at 355 nm and 532 nm are 42% (64%) and 21% (28%), respectively. Both the deviations of the retrieved particle backscatter coefficients from two methods at 355 nm and 532 nm are greater than 1-standard deviation. In the cirrus layer, the retrieved lidar ratio at 355 nm and 532 nm are both around 20 sr, and the average (maximum) relative uncertainties of the lidar ratio at 355 nm and 532 nm (Fig. 20 (c), (g)) are 7% (10%) and 9% (12%), respectively. which shows the necessity of the algorithm proposed in this study. The cirrus cloud is divided into one layer, and the boundary of cloud layer is between 6510 m and 8910 m. In the cirrus layer, the particle depolarization ratio retrieved by iterative algorithm at 355 nm and 532 nm (Fig. 20 (d), (h)) are around 0.4. The EAE obtained with the iterative algorithm is quite different from the initial value of 1. The EAE after iteration calculation is 0.05 ± 0.04. All the values of lidar ratio, particle depolarization ratio and EAE are in agreement with the typical value of cirrus [50,51], which verifies the reliability of the proposed algorithm.
Fig. 20. The retrieval result at 2:00-3:00 LT on October 28, 2021. (a, e) particle extinction coefficients, (b, f) particle backscatter coefficients, (c, g) lidar ratio with traditional and iterative algorithm at 355 nm and 532 nm, respectively. (d, h) volume and particle depolarization ratio retrieved by iterative algorithm at 355 nm and 532 nm, respectively. The temporal resolution and spatial resolution are 60 minutes and 60 m, respectively.
4.2 Dust case
Figure 21 shows an example of dust case observed over Tianjin on 11 April 2023 LT. Figure 21(a), (b) are the time-height distribution of RCS at 1064 nm and volume depolarization ratio at 532 nm. In this case, the aerosol was mainly distributed in the near field 0-2 km agl. At about 07:00-11:00 LT, clouds were detected in a height of approximately 8-9 km agl. Figure 21 (c), (d), (e), and (f) shows the RCS of the elastic-backscatter (355 nm, 532 nm) and the Raman channels (386 nm, 607 nm). Data were taken from 03:00-04:00 LT on 11 April 2023, which is marked in the red box in Fig. 21(a), (b). The profiles indicate the presence of an obvious aerosol layer from ground to approximately 3 km height. Also shown is the molecular signal.
Fig. 21. Lidar signal on 11 April 2023 LT. The meaning of symbols, lines, and colors is the same as in Fig. 19.
Figure 22 shows the retrieval result at 03:00-04:00 LT on April 11, 2023. Again, we see difference between the aerosol optical properties retrieved with the two methods. In the aerosol layer between 0-2 km agl, the average (maximum) relative uncertainties of the particle extinction coefficient at 355 nm and 532 nm (Fig. 22(a, e)) are 4% (4%) and 6% (6%), respectively. The average (maximum) relative uncertainties of the particle backscatter coefficient at 355 nm and 532 nm (Fig. 22(b, f)) are 14% (23%) and 12% (17%), respectively. Meanwhile, there is a large area where both the deviations of particle extinction, backscatter coefficients and lidar ratio are greater than 1-standard deviation. The average (maximum) relative uncertainties of the lidar ratio at 355 nm and 532 nm (Fig. 22(c, g)) are 21% (34%) and 20% (28%), respectively. The particle depolarization ratio at 355 nm and 532 nm are around 0.3 and 0.2, respectively. The EAE of aerosol layer between 0-3 km obtained by iterative algorithm was 0.14 ± 0.01. From the backward trajectories (Fig. 25(a)) of NOAA HYSPLIT MODEL [52], the aerosols passed through Mongolia (average elevation about 1500 m). Combined with the particle depolarization ratio of dust [53], the aerosol type was most probably dust. The retrieval results from iterative algorithm are in agreement with the typical values of dust [29,30], which proves the reliability of the algorithm.
Fig. 22. The retrieval result between 03:00-04:00 LT on April 11, 2023. The meaning of symbols, lines, and colors is the same as in Fig. 20.
Figure 23(a) shows the RCS at 1064 nm observed over Beijing on 18 October 2021 LT. In this case, the aerosol content in the lower part of the troposphere (0-4 km agl) was high, and contained more than one aerosol layer. Another aerosol layer was observed in a height of 5 to 7 km agl between 00:00 and 16:00 LT. There was also a layer at around 12 km before the clouds appear. Clouds appeared between approximately 05:00-09:30 and 08:30-12:30 LT in heights between 8-9.5 km and 5-7 km, respectively.
Fig. 23. Lidar signal on 18 October 2021 LT. The meaning of symbols, lines, and colors is the same as in Fig. 19.
Figure 23(c-f) shows the RCS of the elastic-backscatter (355 nm, 532 nm) and Raman channels (386 nm, 607 nm). The profiles describe the situation between 21:00 and 22:00 LT on 18 October 2021. During this time period, it was obvious that there were two aerosol layers. Aerosol optical depth was 0.45 at 355 nm between 0-5 km agl. The profiles from Rayleigh fitting at 355 nm and 532 nm agreed well.
Figure 24 shows the retrieval results of two methods as mentioned above at 21:00-22:00 LT on October 18, 2021. In this scenario, the lidar signal is identified as two aerosol layers, and the boundary of the two layers are 1230-2130 m and 2130-3810 m, respectively. The EAEs of the two-layer aerosols obtained by iterative algorithm were 1.95 ± 0.03 and 1.98 ± 0.04, respectively, which was quite different from its assumed value of 1. Further, the deviation of particle extinction and backscatter coefficients were caused. In the aerosol layer between 0-2 km agl, the average (maximum) relative uncertainties of the particle extinction coefficient at 355 nm and 532 nm (Fig. 24(a, e)) are 5% (6%) and 7% (9%), respectively. The average (maximum) relative uncertainties of the particle backscatter coefficient at 355 nm and 532 nm (Fig. 24(b, f)) are 6% (10%) and 2% (2%), respectively. In aerosol layer between 0-1 km, there is a large area where both the deviations of particle extinction, backscatter coefficients, and lidar ratio are greater than 1-standard deviation. The average (maximum) relative uncertainties of lidar ratio at 355 nm and 532 nm (Fig. 24(c, g)) are 11% (15%) and 9% (11%), respectively. The aerosols passed through Mongolia (Fig. 25(b)); therefore, it was most probably dust. The conclusion is the same as Fig. 22.
Fig. 24. The retrieval result between 21:00-22:00 LT on 18 October, 2021. The meaning of symbols, lines, and colors is the same as in Fig. 20.
Fig. 25. The backward trajectories of NOAA HYSPLIT MODEL at (a) 03:00-04:00 LT on April 11, 2023 in Tianjin, (b) 21:00-22:00 LT on October 18, 2021 in Beijing.
5. Conclusion
In the data retrieval of Raman lidar, in order to obtain the particle extinction coefficients at the emission wavelength, the wavelength conversion is needed, therefore, the extinction-related Ångström exponent (EAE) is introduced. In traditional data retrieval method, the EAE is usually assumed (to be 1). In this study, we analyzed the limitations of the traditional method in which the assumed value of EAE is usually different from the true value depending on the type of particle, and it can introduce uncertainties to the aerosol optical properties. Numerical simulations show that when the EAE deviation (the difference between the assumed value and true value) changes from -2 to 2, the maximum relative uncertainties of the particle extinction coefficients can reach 8%, 12% and 25% at 355 nm, 532 nm and 1064 nm, respectively. The relative uncertainty of particle backscatter coefficient increases with the increase of AOD and EAE deviation.
In this study, we proposed an iterative retrieval algorithm based on multiwavelength Raman lidar to settle the issue mentioned above. We simulated three scenarios with differ layers and EAEs to analyze and verify the proposed iterative algorithm. The first one is a two layers scene, which denotes as biomass-burning smoke in urban environment with big EAEs. The second one is a three layers scene, which denotes as transported dust in urban environment which has relatively small EAE. The third one is a mixture of anthropogenic aerosol and dust. The simulation result shows that deviations and relative uncertainties of retrieved aerosol optical properties due to EAE deviation is large. The relative uncertainties are larger than 10% in many cases, and the maximum relative uncertainty is even larger than 30%. The Monte Carlo Method was used to analyze and discuss the convergence of the iterative algorithm. Results show that the retrieved EAE and aerosol optical properties with the proposed iterative algorithm does converge to the true value, and their accuracies are improved. Compared with the traditional retrieval method, the proposed iterative algorithm can reduce the systematic error in the retrieval process and does not change the random error in the retrieval process. We tested the iterative algorithm for experimental data. Examples of cirrus cloud and dust are used to illustrate the usefulness of the proposed iterative algorithm.
In addition, the lidar signal noise and the signal layering are important factors affecting the iterative algorithm. When the SNR of lidar signal is poor, the error of aerosol optical properties caused by EAE-deviation is relatively small compared to the random error caused by lidar signal noise. In this case, the accuracy of aerosol optical properties retrieved by iterative retrieval algorithm is comparable to that of traditional algorithm. Moreover, the signal layering needs to be accurate, which directly reflects the distribution of aerosols. Ideally, one layer contains one type of aerosol. For mixture of aerosol layer, a comprehensive EAE can be obtained with the iterative retrieval algorithm. In this study, we verified the applicability of the iterative algorithm in the scenario with three aerosol layers, and the scenario with more aerosol layers need to be further verified.
Funding
National Natural Science Foundation of China (42205130, 62105248, 62275202).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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