## Abstract

A technique to determine the aerosol extinction-to-backscatter ratio (lidar ratio) as well as extinction and backscatter coefficients from simultaneous ground-based and space-borne lidar measurements is proposed. This technique can be applied in presence of more than one aerosol layer. To test the reliability of this technique, a numerical simulation has been performed. Moreover, the technique has been applied to an actual case by analyzing data from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and Napoli-Earlinet lidar measurements. The results show that the values of lidar ratio and backscatter coefficient retrieved by this technique are in good agreement with the ones obtained from Raman measurements.

© 2011 OSA

## 1. Introduction

Lidar is considered to be one of the leading techniques for remotely studying characteristics and properties of aerosols, which play an important role in the Earth’s radiative budget by both extinction of solar and planetary radiation and by acting as condensation nuclei of clouds [1]. In order to retrieve aerosol optical properties from elastic backscatter lidar returns, a traditional way is to assume a functional relationship between extinction and backscatter coefficients to overcome the problem of one equation containing two unknowns [2,3]. The relationship is known as aerosol extinction-to-backscatter ratio or lidar ratio, which is a key parameter to describe the physical nature of aerosols.

It is well known that the value of lidar ratio is highly variable for different aerosol types depending strongly on the aerosol composition, size distribution and refractive index as well as on the lidar wavelength [4]. The lidar ratio can be obtained from elastic lidar measurements when supplemented by other measurements, such as by sun photometry, optical particle counter etc [5]. It can also be directly determined from a High Spectral Resolution Lidar (HSRL) [6,7], an elastic-Raman lidar [8], or by two counter-looking lidar measurements [9–12]. Some of these methods have been recently applied to simultaneous ground-based and space-borne lidar measurements. In particular the Counter-propagating Elastic Signals Combination (CESC) [11] is, in principle, able to determine the aerosol extinction and backscatter coefficients independently, but the retrieval of the extinction coefficient is very sensitive to the signal to noise ratio. On the other hand, the method proposed in [12] assumes a single value of lidar ratio in the whole probed range, and requires an independent knowledge of the backscatter vertical profile.

In this paper a new method to determine the aerosol lidar ratio, as well as the aerosol extinction and backscatter coefficients from simultaneous ground-based and space-borne lidar measurements is proposed. Compared with the previous methods [12], the new one is applicable to two-component (i.e., aerosol and molecule) atmospheres in the presence of more than one aerosol layer. The feasibility of this method has been demonstrated by using a numerical simulation case. A direct comparison with results of Raman measurements has also been performed by applying this method to an actual case, by using the data from simultaneous ground-based and space-borne lidar measurements. The ground-based measurements were carried out at the Napoli lidar station in southern Italy (40.838° N, 14.183° E, 0.118 km above mean sea level) [11], which is part of the European Aerosol Research LIdar NETwork (EARLINET) [13]. As for the space-borne lidar measurements, we used the total attenuated backscatter signal (ABS) at 532 nm, as available from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) level 1 products [14]. In Section 2 the technique is described. Section 3 gives the application of the technique to a numerical simulation and to an actual case and shows the results obtained by this new method. The findings are briefly summarized in Section 4.

## 2. The technique

The technique is based on the assumption that the two counter-looking lidars probe the same atmospheric column during the measurement time. Therefore, the total volume backscatter and extinction coefficients of atmospheric molecules (β_{m} and α_{m}) and aerosol particles (β_{p} and α_{p}), measured by the two lidars must be the same. The range corrected signals (RCS) and the attenuated backscatter (ABS) simultaneously available from ground-based (subscript g) and CALIPSO (subscript s) lidars can then be written as:

where z is the altitude (z = 0 is the sea level, z = z_{s} is the CALIPSO lidar calibration altitude), and C_{g} is the system constant of ground-based lidar, which can be determined by normalizing the lidar signal to the molecular backscatter signal in an aerosol free region. The backscatter and extinction coefficients of molecules can be obtained from either radio sounding or standard atmosphere models.

Since the lidar ratio S(z) depends on the different aerosol types, we suppose that a number k of different aerosol layers are present in the sounded path, and that the lidar ratio S_{k} of the k^{th} aerosol layer is constant within its layer boundaries.

The actual procedure for the technique is as follows. First, an iterative procedure to calculate the backscatter coefficients β_{p,g}(z) and β_{p,s}(z) is applied by using a series of trial values of the lidar ratio for each aerosol layer. Then, a performance function is employed to determine the best values of the aerosol lidar ratio for each aerosol layer.

In addition to the analytical lidar solutions, iterative procedures have been already used in the lidar signal inversion [15,16]. In the technique described in the present paper, the iterative procedure described in [17,18] is used. In particular, with a trial value of the lidar ratio for each aerosol layer, the backscatter coefficients β_{p,g}(z) and β_{p,s}(z) are determined through an iteration process starting by assuming α_{p,g}
^{0}(z) = α_{p,s}
^{0}(z) = 0m^{−1}, where the superscript 0 stands for the initial iteration step. From Eqs. (1) and (2), the backscatter and extinction coefficients at iteration step i (i≥1) are determined by the following formulas:

where the subscript j in Eq. (5) refers to either ground-based (g) or space-borne (s) lidar signals. A new vertical profile of the extinction coefficient is then obtained by Eq. (5), and it is used to calculate new values of the backscatter coefficients by Eqs. (3) and (4) at the next iteration step. With the new values of backscatter coefficients, a new profile of extinction coefficient is retrieved and a new iteration starts. The iteration procedure is stopped when the new backscatter profile converges to the previous one within the set error margin. The number of iterations required for convergence is a function of the signal to noise ratio. Usually, for the ground-based lidar returns 9–10 iteration steps are required for the convergence, while 18-20 iteration steps are needed for space-borne lidar data.

With the final values of β_{p,g}(z) and β_{p,s}(z) retrieved from the iterative process for each trial lidar ratio value, we construct a performance function F(S_{k}) as in [12]:

where z_{b} and z_{t} correspond to the lowest and highest altitudes of the considered range, and the subscript k indentifies different layers. Generally, we chose the altitude where the overlap function of the ground-based lidar is equal to unity as z_{b}, and the altitude of the aerosol free range as z_{t}.

If the correct values of lidar ratio for each aerosol layer are chosen, Eqs. (3) and (4) will give correct values of backscatter coefficients β_{p,g}(z) and β_{p,s}(z), and thus the value of F(S_{k}) obtained from Eq. (6) will be zero.

In our application of the procedure, the values of lidar ratio of each layer are varied from 15 to 90sr with an increment of 1sr. For any value of the lidar ratio of each aerosol layer, the inversion process starts from the iterative process to calculate the backscatter coefficients β_{p,g}(z) and β_{p,s}(z), and then a value of F(S_{k}) is retrieved. Finally, we search for the minimum value of F(S_{k}), and the corresponding lidar ratios are the expected solutions for the considered aerosol layers.

## 3. Application to the numerical simulation and actual lidar measurements

The reliability of the proposed technique has been checked with a numerical simulation. To further test its reliability, this technique has also been applied to an actual lidar measurement performed by the Napoli and CALIPSO lidars. The Napoli lidar is based on a Nd:YAG laser source and the fundamental emitted wavelength is at 1064nm, but the working ones are the Visible and UV wavelengths, respectively at 532nm and 355nm [19]. The receiving system collects UV and Visible elastic backscattered light as well as Raman radiation backscattered from atmospheric nitrogen molecules at 607nm (532nm primary wavelength) and 387nm (355nm primary wavelength) and water vapor molecules at 407nm (355nm primary wavelength), therefore aerosol properties retrieved by the algorithm mentioned above can be compared with the ones obtained by Raman method. In the CALIPSO spacecraft, the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) consists of a laser transmitter and a receiver subsystem [14]. The Diode-pumped Nd:YAG laser of the transmitter subsystem produces simultaneous pulses at 1064nm and 532 nm. A 1-meter diameter telescope in the receiver subsystem with field of view of 130μrad is used to detect the backscattered photons. Here in the analysis of the real case, we have considered the total attenuated backscatter signals (calibrated, range-scaled, energy and gain normalized) at 532nm as available from CALIPSO level 1 V1.20 products, and the range corrected signals at 532nm from Napoli lidar measurements.

#### 3.1 Numerical simulation

The RCS_{g}, ABS_{s} used for the numerical simulation are shown in Fig. 1(a)
. Below 1.5km, a typical polluted planetary boundary layer (PBL) aerosol (β = 1-5 × 10-6 sr^{−1}m^{−1}, S = 75sr) is simulated. From 3 to 5.5km two aerosol layers (β = 3 × 10-6sr^{−1}m^{−1}, S = 40sr) are included in order to simulate lofted layers of Saharan desert mineral dust. Lidar signals are simulated with statistical errors comparable to those of actual experimental signals obtained from ground and space measurements. The error bars in Figs. 1(a) account for statistical errors which are about 2-10%.

To retrieve aerosol lidar ratio by the described technique, we considered two layers from 0 to 1.5km (S = S_{1}) and from 1.5 to 6km (S = S_{2}), respectively. The color coded curtains of performance function F(S_{k}) for lidar ratios S_{1} and S_{2} in full scale is shown in Fig. 2(a)
, and its small scale is shown in Fig. 2(b). From the color coded curtains in Fig. 2, it can be found that the performance function has only one minimum value for lidar ratios S_{1} and S_{2} changing from 15 to 90sr. The values of 74 ± 6sr and 41 ± 2sr corresponding to the minimum value of the performance function can be easily determined from Fig. 2(b) for the lidar ratios of S_{1} and S_{2}, respectively. The retrieved backscatter coefficients are shown in Fig. 1(b). From the results it can be seen that vertical profiles of both the backscatter coefficients β_{p,g}(z) and β_{p,s}(z), as well as the retrieved lidar ratio values agree quite well with the assumed ones. The errors on S_{1} and S_{2} are determined as the values corresponding to the fluctuations of the performance function around its minimum value, and an approximate expression for the errors on aerosol lidar ratio retrieved by the new method is given by:

where ${\sigma}_{S}^{}$is the standard deviation of the aerosol lidar ratio, ${\sigma}_{F}^{}$is the standard deviation of the performance function around its minimum value and $\frac{\partial F}{\partial S}$represents the first derivative of performance function on the value of lidar ratio. For this ideal case with typical values of PBL aerosol and Saharan desert layer, the errors of lidar ratio are within 10%.

An analysis of the accuracy of the proposed method in obtaining the values of lidar ratio has been performed by evaluating the fluctuations of the retrieved values of lidar ratio by changing the assumed values of the lidar ratio of S_{1} and S_{2} by ± 10%. Our results indicate that the retrieved values of lidar ratio deviate from the assumed values by less that 5%.

#### 3.2 Application to the actual lidar measurements

To further test the reliability of this technique, it has been applied to the lidar measurements performed by Napoli and CALIPSO lidars at the wavelength of 532nm. For the application to actual measurements, the range corrected signals RCS_{g} measured from 01:11 to 01:21 GMT on July 22 2007 by the Napoli lidar and the ABS_{s} averaged value of 16 seconds measurements by CALIPSO lidar when the satellite nearly overpassed the Napoli lidar site (at a nearest distance of about 50km) have been used. Figure. 3 shows the signals RCS_{g} and ABS_{s}. From Fig. 3
, it can be found that at altitude below 5km the standard deviations of RCS_{g} and ABS_{s} do not exceed 2% and 10%, respectively.

For this study, the slope of the attenuated backscatter profiles on altitude z was used to define the aerosol layer boundaries. Two layers are considered for the case of Fig. 3, corresponding to altitude ranges of 0-1km and 1-5km, with lidar ratios S_{PBL} and S_{D}, respectively. The values of the performance function as a function of the lidar ratios of the two layers are reported in Fig. 4(a)
as a contour plot. The performance function has only one minimum value for the lidar ratios changing from 15 to 90sr, thus only the relationship between the performance function F(S_{k}) and lidar ratios S_{PBL} and S_{D} of a small scale is shown in Fig. 4(a). From the contour plot, lidar ratio values of 45 ± 4sr and 48.0 ± 0.5sr corresponding to the minimum value of the performance function can be easily determined for the altitude ranges 0-1km and 1-5km, respectively. The lidar ratio values of 41 ± 17sr and 46 ± 9sr are determined from the Napoli Raman simultaneous measurements for the two layers. From the results, it can be found that the lidar ratios retrieved by the described technique are in excellent agreement with those obtained by the Raman method.

The retrieved backscatter coefficients β_{p,g}(z) and β_{p,s}(z) are presented in Fig. 4(b); they are also in good agreement with results obtained from Raman measurements simultaneously performed by the Napoli lidar. While the differences between the backscatter coefficients by the Raman and the present method at lower altitude are due to the horizontal distance (50km) between CALIPSO ground track and Napoli lidar site. In fact, the optical properties of the atmosphere near the ground are strongly affected by local sources and usually they are not homogeneous in the horizontal direction.

## 4. Conclusion

In conclusion, a technique allowing the direct determination of aerosol lidar ratio of multiple aerosol layers from elastic backscatter signals simultaneously measured by ground-based and space-borne lidars is proposed. The feasibility of this technique was analyzed by a numerical simulation. An actual case of aerosol lidar ratio determination from the Napoli and CALIPSO lidar simultaneous measurements was also performed. The results are in very good agreement with those obtained from Raman technique.

## Acknowledgments

The authors wish to thank the CALIPSO team at NASA Langley Research Center for providing the data used in our calculations. This work is funded by National Natural Science Foundation under grant no. 40571097 and supported by the 2010 Innovation Foundation of BUAA for PhD Graduates.

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