1. Introduction

Mineral dust is the most abundant natural source of aerosol particles of continental origin. Dust has considerable influence on the radiation budget of Earth [1–3]. We still have little understanding of the optical, microphysical, and radiative properties of mineral dust due to its complexity in, for example, mineralogy, particle shape, size, refractive index, and the mixing state of the chemical compounds, which lead to a strong variability of optical and radiative properties [4,5]. Most of the observations of mineral dust are done by in situ observations in which we collect particles and analyze them according to their optical properties, their chemical composition, and mineralogical and morphological properties. With regard to remote sensing methods, passive remote sensing still is the main method of choice for particle dust characterization [6]. Just as with any other method, passive remote sensing has its limitations regarding the characterization of mineral dust particles, and we need new methods that can fill the gaps in the particle characterization.

Multiwavelength lidar offers such a possibility. First of all, lidar is the only remote measurement method that can give vertically resolved information on aerosol particle properties (in contrast to passive remote sensing methods). Second, lidar offers optical properties that can be backscatter coefficients from simple backscatter lidars or extinction coefficients acquired with advanced Raman lidar and high-spectral-resolution lidar (HSRL), as discussed for instance in [7–13]. The depolarization ratio (DR) of dust qualitatively describes particle shape. It can be measured directly with depolarization lidar without critical assumptions on particle shape in the data analysis chain [14,15].

The development of multiwavelength polarization Raman lidar in the mid 1990s was one important step in our ability to characterize mineral dust particles [16,17]. The configuration of a Raman lidar that emits laser wavelengths at 355, 532, and 1064 nm allows us to derive profiles of particle backscatter coefficients at these wavelengths. If we employ the Raman lidar technique we may also measure extinction coefficients at 355 and 532 nm with reasonable accuracy. From such a data set of backscatter and extinction coefficients we may derive microphysical properties with data inversion algorithms that have been specifically developed for this purpose [18–20].

The algorithms have been extensively tested and applied to lidar data in the past 10 years, for instance in [19–27]. However, the constraint of particle sphericity always kept us from applying the algorithm to the inversion of optical data that describe mineral dust particles. The main reason for not using these algorithms for mineral dust data is rooted in our poor understanding of how to describe the light-scattering properties of particles of irregular (nonspherical) shape, especially for the 180° scattering angle, which is crucial for lidar applications.

It is extremely complicated to model the optical properties of mineral dust particles. The mathematical methods that are used to compute scattering properties of nonspherical particles have been in development for more than a decade [28–31]. Enormous progress has been made regarding the computation of light-scattering properties of particles with edges and corners, with rough surfaces, and with inclusions. There are attempts to develop a forward model that allows us to describe optical properties of particles with diverse geometrical shapes and morphologies, for example [32]. Still, there is a lack in the adequate description of light-scattering properties of nonspherical (mineral dust) particles. Numerical methods such as the discrete dipole approximation [33], are extremely time consuming even for the case of forward modeling, saying nothing about their implementation to the inverse-problem algorithms.

Numerous studies have demonstrated that the scattering properties of nonspherical desert dust particles can be mimicked by spheroids of random orientation [6,28,30,31]. In this simplified approach the aerosols are modeled as a mixture of two components: one composed only of spherical and the second one composed of nonspherical particles. The nonspherical component is an ensemble of randomly oriented spheroids with size-independent aspect-ratio distribution. The aspect ratio is defined as the ratio of the longest axis to its shortest axis. The orientation of the particle in space is not considered. Thus, the aspect ratio is always $\ge 1$. Another possibility is the use of the axis ratio, which can be $\ge 1$ or $\le 1$. It describes the ratio of the longest to the shortest length of the symmetry axis (perpendicular to the longest axis) of a particle and takes account of the orientation of the particle in space.

This concept of describing the nonspherical component as an ensemble of randomly oriented spheroids with size-independent aspect-ratio distribution has been successfully employed in the operational retrieval algorithm of the Aerosol Robotic Network (AERONET) [6,34], and it may also be used for inversion of lidar observations to retrieve particle parameters. In regard of using the AERONET model for our purposes (application to lidar data) we are still at the very beginning. We still search for theoretical models that allow us to link specific features of a particle’s shape to its specific optical properties. This is particularly true as lidar provides particle backscatter coefficients and particle DRs, which on the one hand are sensitive to particle shape; on the other hand, these parameters cannot be measured in this form by any other instrument technology.

Irregularly shaped particles may lead to lower backscatter coefficients [28], which are one of the main data products in lidar observations. Computations point to the reduction of the particle backscatter coefficients by a factor of up to 3 compared to what a volume-equivalent spherical particle may deliver. As a consequence, the so-called particle-extinction-to-backscatter (lidar) ratio may be considerably higher for nonspherical (mineral dust) particles than for spherical particles. Lidar observations [9,25,35,36] corroborate this finding.

An accurate description of the scattering of nonspherical particles is also important in view of separating spherical from nonspherical particles in mixed pollution plumes. Several attempts are under way in that regard [6,37–42]. An accurate description of the content (concentration) of spherical and nonspherical particles allows for better retrievals of, for instance effective radius and the complex refractive index [CRI] (size and wavelength dependent) of the particle size distribution (PSD).

Spherical particles can be largely attributed to aerosol types like smoke (though low relative humidity may have some effect on the depolarization properties of smoke; see Section 4.B), sulfates, and urban haze. Nonspherical particles mainly are mineral dust, but also volcanic ash can episodically be a major component [41,43]. The eruption of the Eyjafjallajökull and Grimsvötn volcanoes in 2010 and 2011, respectively [32,41–44], in an impressive way showed the need for identifying the physical and chemical properties of the particles in these plumes. The portion of the size distribution that describes the nonspherical component was considered extremely hazardous to aircraft engines, and led to severe restrictions in air traffic over Europe during the eruptions.

Particle depolarization channels installed in multiwavelength Raman lidar can provide us with additional information on particle shape in a very straightforward manner. However, this information is only qualitative in terms of using it for a description of the deviation of particle shape from sphericity. We may infer under certain circumstances whether the particles are highly irregular or still somewhat resemble a spherical shape. The particle DR does not give us a physically quantifiable measure of nonsphericity in a direct way, for instance, the axis ratio.

We consider the model used by AERONET as a good starting point in our search for developing a particle model appropriate for the use in the inversion of lidar data. For this purpose we adapted the model from [6], which, as mentioned above, successfully applied it to the inversion of AERONET Sun photometer data into microphysical properties.

Sun photometer measurements of almucantar usually end at a 150° scattering angle, although the AERONET model was extended to a phase function angle of 173° on the basis of laboratory measurements of light-scattering by dust [45]. One key question in using this specific model for the inversion of lidar data is whether particle backscatter coefficients, which describe the phase function at exactly 180° scattering angle, can be used. The same question of applicability refers to the particle DR measured by lidar at 180°. We need to keep in mind that prolates and oblates, which describe the particle shape, are only an approximation of the true shape of mineral dust particles. The exact shape of the dust particles cannot be prescribed in this way. Ellipsoids have smooth surfaces, in contrast to the dust particles. Inclusions of various minerals in the dust grains and heterogeneous chemical composition are also not accounted for.

For the first time, [40] applied an inversion algorithm to retrieve microphysical properties of a pollution plume that consisted of a mixture of mineral dust and anthropogenic haze that was transported from Northwest Africa across Spain to the southwest of Germany in the summer of 2007 [40,46]. The original inversion methodology used by [19] was modified for this purpose. Following the approach of [6], the authors modeled the dust as a mixture of spherical particles and randomly oriented spheroids. Reference [19] used optical data of the standard configuration of a multiwavelength aerosol Raman lidar, namely, particle backscatter coefficients at 355, 532, and 1064 nm and particle extinction coefficients at 355 and 532 nm. In addition, the authors included information on the linear particle DR at 532 nm in their data analysis in order to find out if such information on particle nonsphericity affects the quality of the retrieval results. The entire methodology and developed retrieval scheme could not be tested for cases of pure mineral dust plumes. Furthermore, no airborne in situ observations of dust optical, microphysical, or chemical properties were available for comparison for this study.

In order to make any conclusion about the feasibility of the algorithm that is based on the spheroid model, more measurement cases need to be considered. It is furthermore desirable to apply the method to measurements performed near the source. The Saharan Mineral Dust Experiment (SAMUM) [1,4] to date provides the best available data set that can be used for such validation purposes.

We collected data with several lidar systems during a one-month period near one of the source regions of Saharan dust in Morocco in May/June 2006 [9,11,14,47]. The dust plumes were largely unaffected by contribution from anthropogenic pollution. This could be verified by chemical analysis of particles sampled aboard aircraft and at ground and in the greater area around the lidar site [5]. Another campaign took place in the Republic of Cape Verde (tropical North Atlantic) in January/February 2008. During that campaign we observed mineral dust that was mixed with marine aerosol and biomass-burning smoke for the most part of the measurement period [10,15,48,49].

The aircraft used in SAMUM carried instrumentation for in situ characterization of optical, microphysical, and morphological particle properties [5,50–53]. The aircraft also carried an HSRL [11,54]. On several days we collected dust optical, microphysical, chemical, and morphological information when the aircraft passed over the ground-based lidars. The overpasses in part also occurred during nighttime, which allowed us to make use of the full measurement capability of Raman lidar. In daytime lidar measurements were carried out during overpasses, too, and we have AERONET Sun photometer data available. HSRL measurements provided us with extinction coefficients at 532 nm [11]. One rotational Raman channel of one of the Raman lidars [9] also provided us with extinction coefficients at 532 nm from ground during daytime. In summary, we selected four measurement days of SAMUM, and we have a set of lidar data that can be used by our inversion algorithm. The inversion results can be compared to data retrieved from AERONET Sun photometer observations. We also show some results of independently measured in situ data products for comparison. In view of the amount of data collected during SAMUM-1 and SAMUM-2, we leave a more detailed comparison of lidar and Sun photometer results to results from in situ observations to a future contribution.

In Section 2 we provide an overview on the inversion methodology. Section 3 gives an overview on SAMUM. In Section 4 we present and discuss the results of our study. In Section 5 we summarize our results and we give recommendations for future measurements of mineral dust.

2. Inversion Methodology

The inversion methodology is described in detail by [19,40,55]. Briefly, we use as input particle backscatter coefficients measured at 355, 532, and 1064 nm and extinction coefficients measured at 355 and 532 nm. This data set, which is denoted as a $3b+2a$ data set (in other literature it sometimes is also referred to as a $3+2$ data set or $2\beta +2\alpha$ data set) provides the information that is conventionally used in the inversion of lidar data. The linear particle DRs at 355 and 532 nm can be included as input in our data analysis, too, which extends the conventional input to the $3b+2a+1d$ data set (also denoted as a $3+2+1$ data set or $3\beta +2\alpha +1\delta$ data set). The atmospheric model is represented by a mixture of two fractions: spheres (s) and spheroids (ns). The volume fraction of spheroids is assumed to be size independent.

The linear particle DR gives us preliminary information about the observed particle type. For a high DR ($\approx 30\%$), which is the case for pure dust, the aerosol can be modeled with the spheroids ensemble only. In contrast, for a low DR (below $\approx 10\%$) the particles can be considered as spheres. For the intermediate values of DR the use of the DR becomes important because otherwise the volume fraction of the spheroids cannot be determined. It should be noted that the errors in the spheroids volume fraction (SVF; see following text), influences mainly the retrieval of the CRI [40]. SVF is the ratio of the volume attributed to spheroids to the total particle volume.

The PSD and the particle CRI are derived in the inversion process. The mean properties, such as particle effective radius and integral properties, namely number, surface-area, and volume concentration, are calculated from the PSD.

We need to define a reasonable lower and upper particle size limit within which we want to carry out the inversion. This can be achieved by the so-called gliding inversion window [56]. In this study, the boundary of the inversion window has been set to the particle radius $r_{\min }=75\mathrm{nm}$ as lower limit and to the particle radius $r_{\max }=15\mathrm{\mu m}$ as upper limit. As described by [19,56], the lower and upper limit can be varied within a range of values; this means $r_{\min }$ and $r_{\max }$ have variable boundaries, which causes a variable width of the inversion window. This approach allows for a better identification of the position of the investigated PSD. In this study, we select five or six base functions within this inversion window for the reconstruction of the PSD. Furthermore, we set as a constraint that the PSD has to have the number concentration $0{\mathrm{cm}}^{-3}$ at the outer borders of the inversion-window range.

This upper value of 15 μm has been chosen to account for the large particle size of mineral dust; see for instance [51]. We need to consider that the measurement wavelength of 1064 nm certainly is not high enough to allow for an accurate identification of large particles above 2–3 μm radius [19]. For this reason retrieval uncertainties may result in the underestimation of particle concentration at large particle radii. We assume that this underestimation may also be caused by the restriction of the maximum particle radius that we can apply in our inversion methodology. There may be measurement situations that show a significant concentration of dust particles with radii larger than 15 μm.

Except for one study [40], all previous applications of the inversion methodology [18–20,55,56] were performed under the assumption of spherical particle shape. The input optical characteristics of aerosol particles are related to the particle volume distribution via Fredholm integral equations of the first kind as follows:

Here the index $p$ labels the type of optical data $(i)$ and wavelength ${\lambda }_k$. The terms $K_p^s(m,r)$ and $K_p^{ns}(m,r)$ are the kernel functions for spheres and spheroids, respectively. The parameter $m$ denotes the real part (mR) and imaginary part (mI) of the CRI. The parameter $r$ denotes the particle radius. The term $\eta$ is the SVF. According to [6,28], we assume an equal number concentration of aspect-ratio-equivalent prolate and oblate spheroids. We denote the aspect ratio as $ϵ$. The detailed description of choosing the aspect ratio distribution for the spheroidal kernels can be found in [6].

Equation (1) can be solved numerically by transforming it into a system of linear equations. This is done by approximating the distribution $\partial V(r)/\partial \ln r$ by a linear combination of the base functions $B_j(\ln r)$, which are triangles in our case [16,18]. We obtain

The optical data are represented by the vector $g=[g_p]$, and the weight factors by the vector $\mathbf{C}$. The matrices $A^s(m)$ and $A^{ns}(m)$ consist of the following elements:

This inverse problem is underdetermined, also called ill-posed. The number of input optical data is very limited (only five data points), and this number is not sufficient to uniquely describe the properties of the aerosol within the atmospheric layer. Therefore, we use an intermediate approach. Using the fact that the system of Eq. (2) is linear with respect to $\mathbf{C}$, one can generate a family of linear solutions for different values of $\eta$, $m$, and inversion intervals $[r_{\min },r_{\max }]$ that provides the best fit to the observations. At the same time, we use a priori constraints in identifying this family of solutions. Specifically, we limit the range of considered values of the refractive index and the interval of particle radii $[r_{\min },r_{\max }]$. Although these constraints do not provide uniqueness of the final solution space, they help us to significantly reduce the number of members in this solution family. Once the solution family is identified the results are averaged and the mean solution and the uncertainty are provided.

We note that we have an additional fitting parameter—SVF, denoted as $\eta$—when a mixture of spheres and spheroids is used. Numerical simulations demonstrate that this parameter cannot be accurately estimated from $3\beta +2\alpha$ data, and the particle DR is needed. The DR is used in the calculation of the so-called discrepancy $\rho$, for example [18,19], when we use the $3\beta +2\alpha +1\delta$ data set. The SVF ($\eta$) is varied from 0 to 1 with a step size of 0.2. That is, we use a grid of SVF values. We also use a search grid to identify the CRI. The results that deliver the most suitable discrepancy for the SVF are taken as the final solution space.

Because there is no a priori knowledge about the PSD and the CRI, we find the discrepancy $\rho$ for all predefined values of $[r_{\min },r_{\max }]$, and for the set of values mR and mI in the interval [1.35, 1.65] and [0, 0.02], respectively, just as we describe in [40]. Based on our previous experience [19], we prefer to average the solutions near the minimum of the discrepancy rather than taking a single solution. The averaging interval is chosen by arranging the solutions according to their discrepancy from their minimum value ${\rho }_{\min }$ to their maximum value ${\rho }_{\max }$. Normally 1% of all solutions are averaged.

From previous studies we carried out with the spheroids model we could show that the most stable parameters (in terms of accuracy) in the retrieval are the surface-area and volume concentration and particle effective radius. We can estimate these parameters with an accuracy of 25%–30%, at least for particles of spherical shape, which means that particle depolarization has to be less than 10%, and for pure dust particles. The number concentration is characterized by higher uncertainties of up to 40%–50%. The retrieval accuracy degrades for mixtures of particles. The multiwavelength lidar technique allows us to estimate the particle CRI, too, but the accuracy depends significantly on a priori constraints that we need to introduce. This constraint in particular refers to the maximum value of the imaginary part mI, which was 0.02 in our case. We estimate the uncertainty of the retrieved real part mR to be $\pm 0.05$. The uncertainty of the imaginary part is about 50% for $\mathrm{mI}>0.005$.

3. SAMUM

We tested the performance of the inversion methodology by comparing our results to data products from AERONET measurements that were carried out at the SAMUM field sites. For some of the data products we also show results from other measurement platforms (in situ measurements aboard aircraft and at ground). Any data comparison that involves remote sensing and in situ measurements is a very complex task. In this contribution we can only show a few data products for this comparison. We will carry out a more thorough comparison study in a future contribution. There we will present a comprehensive overview of profiles of dust microphysical properties derived from the inversion of the SAMUM data acquired with our lidar systems.

The data were collected with several lidar systems during SAMUM-1 and SAMUM-2. The first SAMUM campaign took place in Morocco in May/June 2006. The second SAMUM campaign took place in the Republic of Cape Verde in 2008. The core period was in January/February 2008. A smaller campaign with a reduced set of instruments followed in May/June 2008. A detailed description of the scopes and results of SAMUM-1 is given in the special issue of Tellus B, Vol. 61, 2009. The results of SAMUM-2 are presented in the special issue of Tellus B, Vol. 63, 2011. For the purpose of this study we selected two measurement days of SAMUM-1 and two measurement days of SAMUM-2.

During SAMUM-1 we operated three ground-based Raman lidars at Ouarzazate airport (30.93°N, 6.9°W, 1133 m above sea level [asl]) and one HSRL, which was installed aboard the research aircraft Falcon of the German Aerospace Agency. The data from all four systems provided us with profiles of particle backscatter coefficients at 355, 532, and 1064 nm and particle extinction coefficients at 355 and 532 nm (i.e., a $3b+2a$ data set) from near ground to the top of the troposphere. An overview on the lidar measurements, a discussion of the main findings, the data analysis procedure, and the error analysis can be found in several SAMUM-1-related publications, for instance [9,11,14,47]. We also measured linear particle DRs at 355, 532, 710, and 1064 nm [14]. Instrument performance, however, did not allow us to measure this parameter on more than a few days; particularly we nearly never measured simultaneously at all four measurement wavelengths. For our study we therefore selected only the particle DR profile measured at 532 nm. Adding this data extends the conventional input data set to $3b+2a+1d$.

The aircraft flew on several days over the ground site. It carried in situ instrumentation, which allowed us to measure PSDs across a wide range of particle radii. The instruments, data analysis, and measurements are presented by [50,51]. Mineralogical analysis of particles collected aboard the aircraft furthermore allowed us to infer the CRI and the axis ratio distribution of dust particles [5]. There was also a ground site at Tinfou near Zagora (30.23° N, 5.6° W), which is nearly 200 km away from the remote-sensing site. Data from Tinfou provided us with additional valuable information on the mineralogical composition of the particles. The data from this site allowed us to investigate to what extent the ground-based measurements of particle mineralogy are similar to particle mineralogy measured aboard the aircraft; see for instance [5,57,58].

For our validation study we selected two measurement days, 18 and 19 May 2006. On these two days we have a comparably complete set of optical data from all four lidar instruments. We also have optical, microphysical, and chemical data and information on particle morphology from the in situ observations. The main results of 19 May 2006 are described in detail in various publications of the SAMUM special issue in Tellus B, Vol. 61. References [57–59] present a detailed quality-assurance study on optical and microphysical dust properties for 19 May 2006.

The second SAMUM campaign took place at Praia Airport (15°N, 23.5°W, 75 m asl) in the Republic of Cape Verde [4]. During the main campaign in January/February 2008 the complete set of instrumentation as in SAMUM-1 was available. During several measurements we observed plumes of biomass burning mixed with mineral dust on top of a mineral dust layer that was immersed into the marine boundary layer [10,15,48,49,52,60]. In several cases a biomass-burning layer was observed on top of the mixed marine/dust layer. The biomass-burning aerosol originated from fires in West Africa.

As in the case of SAMUM-1, we operated an aircraft for in situ observations of optical, microphysical, mineralogical, and morphological properties of these pollution layers [52,60,61]. We operated two lidar systems at ground [10,15,49] and the airborne HSRL [52].

For our comparison study of the SAMUM-2 cases we selected the measurements of 22 and 31 January. The results of these two days are discussed in [10,48]. These days are characterized by mixtures of mineral dust and biomass-burning aerosols. The results of in situ observations of PSDs and optical properties are given by [52,61]. Results of particle mineral composition and morphology are presented by [60].

In both campaigns we operated an AERONET Sun photometer at the field sites, respectively. The AERONET instruments are described by [34]. Further details relevant to understanding the AERONET results presented in this contribution are given by [57] We briefly summarize the main points.

The AERONET instrument that we used during SAMUM-1 is usually installed at the Leibniz Institute for Tropospheric Research (instrument no. 234). The instrument was calibrated at NASA Goddard Space Flight Center before it was taken to Morocco, and it was calibrated once more after the campaign. During SAMUM-1 the AERONET Sun photometer was placed on the rooftop of one of the sea containers that housed the lidar instrumentation at Ouarzazate airport.

The instrument measured the direct solar radiation at 339, 379, 441, 501, 675, 869, 940, and 1021 nm. For the SAMUM-1 campaign the instrument was furthermore equipped with a measurement channel at 1638 nm wavelength. The signals at 339, 379, 441, 501, 675, 869, and 1021 nm are used to compute optical depth. In the present study we do not use data from the channel at 940 nm (used for inferring precipitable water) and at 1638 nm. The sky radiance (almucantar) measurements are carried out at 441, 675, 869, and 1021 nm.

In SAMUM-2 we used a mobile version of the AERONET Cimel Sun photometer (instrument no. 90). It measured direct Sun light at 340, 380, 441, 500, 675, 870, and 1020 nm. The four channels at 441, 675, 870, and 1020 nm were used for the sky radiances collected in the almucantar and the principal plane. The instrument was again placed on the rooftop of one of the lidar containers.

In both campaigns direct Sun measurements were carried out every 15 min with a higher measurement frequency at sunrise and sunset. Sky radiances were measured every hour. Aerosol phase function and PSD were retrieved from the data according to the algorithm described in [62]. Reference [6] describes the mineral dust model that is used for the analysis of the AERONET data. For all inversion calculations of the optical quantities we use the spheroid particle model and standard distributions of the aspect ratio as employed in the standard AERONET retrieval algorithm [6]. A discussion on errors of the data products can be found in [6,63]. Except for the measurement on 31 January 2008, all data products are derived from level 1.5 data. Level 1.5 data passed automated cloud screening, as described by [64].

The particle volume size distribution covers the radius range from 0.05 to 15 μm. Effective radii, number, surface-area, and volume concentrations are computed from the retrieved PSDs. The CRI can be inferred in the range from 1.33 to 1.6 (real part) and from 0.0005i to 0.5i (imaginary part). Results on the CRI are given as a wavelength-dependent quantity at 441, 675, 869, and 1021 nm.

4. Results

A. SAMUM-1: Case Studies of 18 and 19 May 2006

Figure 1 shows the vertical profiles of the particle backscatter coefficients and the particle DR on 18 May (nighttime measurement) and 19 May (morning measurement). The measurements are described in detail in [10]. The dust layer extends up to approximately 5 km height asl, which is equivalent to 4 km above ground level. Note that the lidar station was 1133 m asl. On 18 May 2006 the backscatter coefficient is nearly constant to the top of the dust layer. Some variation of the backscatter coefficient exists on 19 May 2006. The linear particle depolarization varies around 30%–35%. The lidar ratios measured at 355 and 532 nm at nighttime on 18 May 2006 are wavelength independent. We also estimated the lidar ratio at 1064 nm [9]. We find no significant difference to the values at the other two wavelengths. The daytime measurement of the lidar ratio at 532 nm, measured with the rotational Raman channels of the Backscatter Extinction Lidar-Ratio Temperature Humidity Profiling Apparatus (BERTHA) and the HSRL aboard the Falcon aircraft agree within the measurement uncertainty [11]. The lidar ratios do not vary significantly between 18 and 19 May. The extinction-related and backscatter-related Ångström exponents are less than 0.5 during both measurement times, indicating the presence of large dust particles up to 5 km height asl. Note that measurement errors of the Ångström exponents are estimated to be around 20%–30%.

 

Fig. 1. Lidar measurements from 2016-2222 UTC on 18 May 2006 (upper row) and from 0959-1116 UTC on 19 May 2006 (lower row). The lidar site was located at 1133 m height asl. Shown are (a), (d) the particle backscatter coefficient (green) and the particle DR (black); (b), (e) the lidar ratios; and (c), (f) backscatter- and extinction-related Ångström exponents for the wavelengths and wavelength pairs given in the respective plot. The circles mark the 500-m mean value used to obtain the optical input data set for the microphysical inversion calculations. The black vertical line in (c) and (f) denotes the column-mean Ångström exponent from AERONET observations of aerosol optical depth (AOT) at 441 and 869 nm. The legend also names the instrument with which the respective profiles were measured. Details on the in situ results for effective radius from measurements aboard the Falcon aircraft are found in [51,57,58].

Download Full Size | PDF

We show for comparison the column-mean Ångström exponents (with respect to optical depth measured at 441 and 869 nm), measured with the AERONET Sun photometer. The column-mean value is within the uncertainty of the vertical profile of the extinction-related Ångström exponent measured with lidar on 18 May 2006 [Fig. 1(c)]. A direct comparison between AERONET and lidar results is not possible for the measurement on 19 May 2006, as we do not have the profile of the extinction-related Ångström exponent.

One of the goals of this study is the comparison of retrievals obtained from the extended set of the optical data ($3\beta +2\alpha +1\delta$) and from the conventional set of optical data ($3\beta +2\alpha$), where we exclude the linear particle DR at 532 nm. The data sets used in this study represent 500 m mean values of the lidar profiles and are shown by the circles in the plots. The SVF estimated from the $3\beta +2\alpha +1\delta$ data sets is $\eta =100\%$ in the whole height range. The SVF can be estimated also from the $3\beta +2\alpha$ set, but the numerical simulations demonstrate that excluding the particle DR from the input data normally leads to an underestimation of the SVF. So in the case of pure dust, we used $\eta =100\%$ for the $3\beta +2\alpha$ data set as well.

The difference between the results of the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets exists because real dust is not a mixture of spheroids, and the forward model (especially for the computation of the linear particle DR) causes uncertainties. But from our retrievals we can conclude that the results for the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets are reasonably consistent. Thus, the spheroids model is acceptable, at least for the cases considered in this study.

The vertical profiles of particle physical parameters retrieved from the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets are shown in Figs. 2–4. We show the results of 18 and 19 May 2006. For comparison, we also show the results obtained from the $3\beta +2\alpha$ data set under the assumption of spherical particles. Furthermore, we show in Figs. 2 and 4 the results from the AERONET retrievals. In the case of 18 May 2006 the comparison needs to be taken with caution, as there is a considerable time difference between the last AERONET measurement (at 0712 UTC) and the start of the Raman lidar measurement (at 2016 UTC). In the case of 19 May 2006 the comparison is easier as there is a smaller time gap between the times of the AERONET (0830 UTC) and the lidar (0959-1116 UTC) measurements.

We use the DR as one of our input data. The spheroids model can reproduce the measured DR, as we showed in one of our previous publications [40]. However, that measurement case was characterized by small values of the mI, and mR was $<1.5$. It is still under discussion how well the spheroid model describes the dust depolarization properties in general. In our retrievals we use only the DR at one wavelength as input data.

We find a height-independent effective radius from the inversion of the lidar data taken on 18 May 2008. Values vary around 1 μm, if we apply the spheroidal particle model. We find larger effective radii if we use the spherical particle shape in data inversion. We obtain two different results for the AERONET-derived effective radius. One can be computed from the complete size distribution (fine and coarse mode fraction of the PSD). The other value describes only the coarse mode fraction of the size distribution.

The volume concentration is comparably constant in the section of the dust plume that we used in the data inversion. This result agrees nicely with the constant particle backscatter coefficient. In that regard we assume that particle volume qualitatively follows the profile of the particle backscatter coefficient.

We find much higher values of the volume concentration if we assume spherical particles in the retrieval. The results from the AERONET Sun photometer retrievals (volume concentration of the total size distribution and the volume concentration of the coarse mode fraction only) agree rather well with the results of the lidar data inversion, if we use the spheroidal model and the $3\beta +2\alpha$ and the $3\beta +2\alpha +1\delta$ data sets as input, respectively. Figures 2 and 4 show the comparison between lidar and AERONET results and allow us to quantify the agreement respectively disagrement.

 

Fig. 2. Volume concentration and effective radius from the inversion of the lidar data on (a) 18 May 2006 and (b) 19 May 2006. Results are shown for $3\beta +2\alpha$ (star) and $3\beta +2\alpha +1\delta$ (squares). The spheroidal kernels were used for the retrieval. Results assuming sphericity of the particles (circles) and results from the inversion of the AERONET Sun photometer data are shown, too. The measurement time was from $0711:50$ to $0829:46$ UTC. In the case of the AERONET data we show the results for the total size distribution and for the coarse mode fraction of the volume size distribution (black dashed vertical lines) and effective radius (red dashed vertical lines). The AERONET results are derived from level 1.5 data, which are used in all other figures, except for Figs. 12–14 (level 2). The red diamonds represent the results for effective radius measured aboard the Falcon during overflights in two height levels on 19 May 2009 [51,57].

Download Full Size | PDF

The $3\beta +2\alpha$ data set seems to give a little better agreement between AERONET and lidar results. Note that the way AERONET uses spheroids for the retrieval of dust properties is quite different from the way we apply this particle model to the inversion of our lidar data. In the case of the algorithm used by AERONET the complete phase function is fitted to the almucantar sky-brightness data such that the phase function reproduces the almucantar data. In contrast, we use the lidar backscatter data in our retrieval. The backscatter data are representative of the sky brightness at exactly 180° scattering angle. The inversion of $3\beta +2\alpha$ data seems to deliver results that are closer to the AERONET results than the use of the $3\beta +2\alpha +1\delta$. However, within the uncertainty of our retrievals we cannot claim that this data set of $3\beta +2\alpha$ gives us results that are closer to the AERONET results.

For the computation of the column-integrated volume concentration we need the dust layer height as scaling factor. We assumed a dust layer height of 5 km; see Fig. 1(a). We find values of $0.14{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$ and $0.15{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$ for the $3\beta +2\alpha$ and the $3\beta +2\alpha +1\delta$ data sets, respectively. The inversion of the AERONET data results in $0.13{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$ and $0.11{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$ for the total volume distribution and the coarse mode fraction of the volume distribution, respectively. The inversion of the $3\beta +2\alpha$ data set thus agrees a bit better to the AERONET results. We need to keep in mind, though, that the retrieval uncertainties are high and that there is overlap between the results from the inversion of the two sets of lidar data.

On 19 May 2006 the volume concentration $V$ [Fig. 2(b)] increases with height. It reaches its maximum value at approximately 4 km height asl, which is near the top of the dust layer. We find the same behavior (increase with height) for both the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets. The profile corresponding to the $3\beta +2\alpha +1\delta$ data set is shifted by 20%–30% toward larger particle volumes. This difference, however, is comparable in magnitude to the uncertainty of our retrievals, which we estimate to be approximately 30%.

We computed the column-integrated volume concentration from the lidar data. We assumed a constant volume concentration below 2 km height asl. The column-integrated values are $0.16{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$ and $0.19{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$ for the $3\beta +2\alpha$ and the $3\beta +2\alpha +1\delta$ data set, respectively. The volume concentration provided by AERONET is $0.21{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$ for the total volume distribution. The coarse mode fraction results in a slightly lower value of $0.19{\mathrm{\mu m}}^3/{\mathrm{\mu m}}^2$. Thus, in this case the inversion of the $3\beta +2\alpha +1\delta$ data set shows a slightly better agreement to the AERONET results.

Effective radius $r_{\text{eff}}$ increases with height from 0.6 to 1 μm for the $3\beta +2\alpha +1\delta$ set. For the $3\beta +2\alpha$ data set, effective radii are slightly larger. Again, the difference is within the uncertainty of the method. The column-integrated effective radius provided by AERONET is approximately 0.65 μm for the total size distribution. This value is a little lower than the value we obtain from the inversion of the lidar optical data. However, the lidar profiles are processed starting with optical data at 2250 m height asl. We do not have sufficient information on particle effective radius below that height. The AERONET result for the coarse mode fraction is approximately 1.6 μm.

Our four lidar instruments do not provide us with a complete set of $3\beta +2\alpha$ data down to ground level. However, we were still able to measure some optical data in the near range of the lidars. Radiosonde data taken during the measurement provide information on the mixing state of the dust plume. Details are shown in [9]. From the available information we draw the conclusion that the mineral dust plume was homogeneously mixed and that it is very unlikely that there was a significant drop of particle effective radius below 2.2 km height asl (about 1 km height above ground level).

We note that the airborne in situ measurements (Falcon aircraft) result in an effective radius that is about twice as large [51] as the values we obtain from the inversion of the Sun photometer and the lidar data [57], respectively. The airborne measurements of effective radius resulted in considerably larger effective radii than what the AERONET results showed during SAMUM-1 [58]. In view of the results from the inversion of the lidar (Fig. 2) there remains the question why there is such a large difference, namely a factor of 2 between Sun photometer and lidar results on the one hand and airborne in situ results on the other hand. See also the results presented in [57,58], which show this factor-2 difference.

Figure 3 shows the profiles of the surface-area ($S$) and the number ($N$) concentration. The surface-area concentration of the large particles is usually the most stable parameter in the retrieval because the scattering cross section (expressed in terms of extinction in this case) is proportional to the particle surface-area. Surface-area concentration behaves in a similar fashion to the volume concentration on 18 May 2006. It slightly drops with height, which results in the constant profile of particle effective radius on that day. The number concentration gradually drops with increasing height above ground, but the retrieval uncertainties mask this effect. The profiles of the surface-area and the number concentrations that we obtained from both types of input data are close.

 

Fig. 3. Surface-area concentration and number concentration on (a) 18 and (b) 19 May 2006. The meaning of the symbols is the same as in Fig. 2.

Download Full Size | PDF

The profiles of the real (mR) and the imaginary (mI) part of the refractive index are shown in Fig. 4. On 18 May 2006 the real part varies from 1.45 to 1.6, depending on what kind of data combination we use as input and whether we assume spherical particles or spheroids in our retrievals. The real part remains relatively constant with height, given the uncertainty bars. The error bars are only shown for the profile of the $3\beta +2\alpha +1\delta$ data.

 

Fig. 4. Real (mR) and imaginary (mI) part of the refractive index on 18 and 19 May 2006. The meaning of the symbols is the same as in Fig. 2. The real part (dashed black line represents the measurement wavelength at 675 nm) and the imaginary part (dashed red line for the measurement wavelength at 675 nm) from AERONET Sun photometer retrievals are shown for comparison. The gray-shaded boxes (real part) and red-shaded boxes (imaginary part) display the AERONET maximum and minimum values of the real and imaginary part in the wavelength range from 441 to 1021 nm. The boxes show the significant enhancement of the imaginary part toward shorter wavelengths (441 nm) and the comparably low wavelength dependence of the real part. The individual values of the CRI for the case of 19 May 2006 are shown in Fig. 5 of [57]. The AERONET results are only for level 1.5 data on 18 and 19 May. The gray and red bars at the bottom of the $x$ axis show the real and imaginary parts we obtained from ground-based mineralogical analysis of the dust particles [5,57]. The bars at 3246 and 4853 m represent the real and imaginary parts and the flight levels of the Falcon aircraft on 19 May 2006. Each bars denote the minimum and maximum values in the wavelength range from 441 to 1021 nm.

Download Full Size | PDF

On 19 May [Fig. 4(b)], mR retrieved from the $3\beta +2\alpha +1\delta$ data drops slightly with height from 1.55 to 1.5. In view of the retrieval uncertainties, this drop may not be significant. The values that we obtain for mR from the $3\beta +2\alpha$ measurements are higher (approximately 1.6) and remain nearly constant inside the dust layer. The decrease of the real part, when depolarization measurements are used in the retrieval, follows from the spheroid particle model. A DR above 30% can be obtained only if $\mathrm{mR}<1.6$ and for low values of mI [40]. For this reason we obtain approximately 0.006 for mI from the inversion of the $3\beta +2\alpha$ measurements. In contrast, the use of the full data set ($3\beta +2\alpha +1\delta$) results in $\mathrm{mI}=0.001$.

The values that we obtain for mR from the full as well as from the reduced data sets seem reasonable. We compare our results to AERONET and in situ observations. The results from the two methods differ, as we show in the following.

AERONET provides wavelength-dependent values of the real and imaginary part of the CRI. In contrast, the lidar inversion provides only a wavelength-independent refractive index. We assume that this wavelength-independent value represents the visible part of the wavelength range that we consider in the lidar data inversion (355, 532, 1064 nm).

The dashed line (black for the real part and red for the imaginary part) shows the AERONET values at 675 nm. We obtain $\mathrm{mR}=1.44$ on 18 May and 1.47 on 19 May 2006. The AERONET result for 18 May is lower than the results (profile) of the inversion of the lidar data regardless of which data combination and particle model we use. The closest match is given for the spherical particle model and the $3\beta +2\alpha$ data. In the case of 19 May the results from AERONET (at 675 nm) are close to the inversion results of the $3\beta +2\alpha +1\delta$ data.

The gray-shaded areas show the minimum and maximum values we obtain from the inversion of the AERONET data in the wavelength range between 441 and 1021 nm; see also Fig. 5 in [57]. With regard to 18 May 2006 the results from lidar are always larger than the results from AERONET. With regard to 19 May 2006, the AERONET results are in between the lidar inversion results for the $3\beta +2\alpha$ data set (spherical particle model) and the $3\beta +2\alpha +1\delta$ data set (spheroidal particle model).

We obtain a more consistent set of results if we compare the real part from the lidar inversion to the real part obtained from the mineralogical analysis of the particles. The gray bar at the bottom of the $x$ axis represents the real part that results from the ground-based measurements at Tinfou [5]. We obtain values of 1.56 to 1.61 across the wavelength range considered in this study (441–1021 nm); see also [5,57] for comparison.

This wavelength dependence is comparably low, and it overlaps with the values we obtain from the inversion of the $3\beta +2\alpha$ lidar data and the use of the spheroidal particle model on both days. We also have results for mR from particles collected aboard the Falcon aircraft. It flew over the lidar site at several flight levels during the lidar measurements. The real parts of the airborne measurements do not differ from the real parts of the ground-based measurements.

The imaginary part varies considerably depending on the particle-shape model we use for the data inversion. On 18 May, the highest values occur if we assume spherical particles for the $3\beta +2\alpha$ data set. The imaginary part drops when we replace the spherical particle model with the spheroid model for this data combination. The error bars represent the average uncertainty of the inversion results. When we add the particle linear DR, mI drops further, and it is near 0 for all heights. This drop to values near 0 is a specific feature of the spheroid model in our data inversion scheme. Reference [32] offers some explanation on this behavior.

The imaginary part at 675 nm ($\mathrm{mI}=0.004$) from AERONET is in between the lidar data inversion results that we obtained with the spheroid model for the $3\beta +2\alpha$ and the $3\beta +2\alpha +1\delta$ data sets, respectively. The red-shaded box shows the strong wavelength dependence of the imaginary part in the range from 441 to 1021 nm. The largest imaginary part is at 441 nm (0.008) for the AERONET measurement on 18 May 2006. This box covers the profile of the imaginary part obtained from the inversion of the $3\beta +2\alpha$ data set with the spheroidal particle model.

For comparison, we also show the imaginary part that we obtained from the mineralogical analysis of single particles at the Tinfou ground site on 18 May 2006 [5]. The red box at the bottom of the $x$ axis represents the imaginary parts between 441 nm (highest values at around 0.013) and 1021 nm. The wavelength dependence (values of the imaginary part for several wavelengths between 355 and 1638 nm) is shown in Fig. 5 of [57,58]. The in situ results overlap nearly all the mI values from AERONET and lidar except the numbers obtained with the $3\beta +2\alpha +1\delta$ data set, and only if we neglect the retrieval uncertainties for this data combination. The results of the AERONET retrievals and the $3\beta +2\alpha$ data are rather well centered in the variability given by the in situ measurements.

The results from the inversion of the lidar data on 19 May slightly differ from the inversion results for 18 May. The highest imaginary parts are found from the inversion of the $3\beta +2\alpha$ data sets if we use the spheroidal model. The next lower values of mI follow from the inversion of the $3\beta +2\alpha$ data if we use the spheroid model. However, if we consider the retrieval uncertainties we cannot distinguish these two profiles. The lowest values again result from the inversion of the $3\beta +2\alpha +1\delta$ data with the spheroidal model.

The red dashed curve shows the results from AERONET at 675 nm. The red-shaded box shows the variation of the imaginary part in the wavelength range between 441 nm (highest imaginary part) and 1021 nm. The red bar at the bottom of the $x$ axis in Fig. 4(b) shows the variation of the imaginary parts that we obtain from the mineralogical particle analysis at Tinfou. The same variation of the imaginary part is obtained for two flight levels of the Falcon aircraft.

The wavelength dependence is significantly stronger compared to the case from 18 May 2006. The in situ values not only cover the complete range of imaginary parts from AERONET and lidar but also stretch toward significantly higher imaginary parts.

We list some key points that follow from the discussion of Fig. 4:

As was shown in [40], the application of kernels that describe spherical scatterers can actually provide a reasonable estimation of particle size and concentration. This is corroborated by Figs. 2 and 3. The figures show that the values of $V$, $S$, $N$, and $r_{\text{eff}}$ obtained with the use of kernels that describe spheroidal and spherical particles are reasonably close to each other. Reference [40] concluded that this approach may considerably underestimate the real part of the refractive index. The inversion results for the mR presented in this study and the comparison to the AERONET and in situ results clearly call for a reevaluation of this statement on the basis of more case studies.

The inversion of the multiwavelength lidar data can also be used to reproduce to some limit the main features of the PSD. Figure 5 shows the results for one height layer of the measurements of 18 and 19 May 2006, respectively. In both cases we find a high volume concentration above 1 μm particle radius. The coarse mode that we obtain from the inversion of the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets are rather similar. The maximum volume concentration is obtained for particle radii between 3 and 4 μm.

 

Fig. 5. Particle volume size distribution retrieved from the lidar data for the height layer at (a) 3023 m on 18 May and (b) 3773 m on 19 May 2006. The results follow from the inversion of the $3\beta +2\alpha$ data set (dashed–dotted line) and the $3\beta +2\alpha +1\delta$ data set (solid line). The column-mean PSD obtained from the AERONET Sun photometer measurements are shown for comparison (solid line with squares). The last measurement time for the Sun photometer data was 0712 UTC on 18 May 2006 and 0830 UTC on 19 June 2006.

Download Full Size | PDF

The figure also shows the column-integrated PSD obtained from the inversion of the AERONET measurements. The coarse mode of this PSD is shifted toward smaller radii compared to the coarse mode obtained from the lidar measurements. The maximum volume concentration is around 2 μm. The size distribution obtained from the Sun photometer measurements shows a fine mode, which is centered at approximately 0.1 μm particle radius. In contrast, this fine mode is absent in the results from the lidar retrieval if we treat the slight oscillations around 0.2–0.3 μm as artifact that may be the result of the retrieval uncertainties. Ground-based measurements do not indicate a significant contribution of particles in the fine mode fraction of the PSD. Another reason for the discrepancy of the PSD obtained from AERONET and lidar may be the fact that the lidar retrieval uses only five or six observations (optical data), which might be insufficient to reproduce detailed features of the PSD. More comparisons also with airborne in situ observations will be needed in order to evaluate the uncertainties.

Figure 6 shows another example of the volume size distribution that we obtain from the inversion of the lidar data taken on 18 and 19 May 2006. In this case the PSDs were derived on the basis of three different assumptions of the wavelength dependence of the imaginary part of the CRI. In the first case we assumed that the mI is wavelength independent. In another case we assumed that the mI at 355 nm is two times higher than the mI at 532 nm. The mI was set to 0.01 at 355 nm, and we assumed that the mI at 532 and 1064 nm is 0.005 at both wavelengths. In the third case we assumed that the mI at 355 nm is 10 times higher than at 532 nm. Thus, mI was set to 0.05 at 355 nm. The assumptions regarding the wavelength dependence follow from the observation that mineral dust was considerably absorbing at ultraviolet wavelengths, for instance [5,58]; see for example the values for mI shown in Fig. 5 of [57].

 

Fig. 6. PSDs (volume concentration) retrieved from lidar measurements (a) at 3023 m height on 18 May and (b) at 2243 m height on 19 May 2006, assuming a spectrally resolved independent imaginary part mI (solid line) and a spectral dependence of the imaginary part. We show the results for the ratio $\mathrm{mI}(355)/\mathrm{mI}(532)=2$ (dotted line) (maximum value of $\mathrm{mI}=0.01$) and 10 (dashed–dotted line) (maximal value of $\mathrm{mI}=0.05$). In both cases the values of mI(532) and mI(1064) were set to 0.005. The intermediate case of $\mathrm{mI}(355)/\mathrm{mI}(532)=5$ coincides with the case of $\mathrm{mI}(355)/\mathrm{mI}(532)=10$. This means that the solutions at very high mI had a large discrepancy and were excluded. The discrepancy is a measure of the quality of the inversion results; see [18,19,40] for further explanations. The retrieval was done for the $3\beta +2\alpha$ data set.

Download Full Size | PDF

The details of incorporating the spectrally variable imaginary part into the inversion scheme can be found in [40]. We note that all other results presented in this contribution were derived under the assumption of a spectrally independent imaginary part of the CRI. We generally apply the inversion algorithm without any use of the spectrally dependent imaginary part of the CRI as we usually do not have reliable information on the wavelength dependence of this parameter. Figure 6 is intended to give an estimate of the possible contribution of this effect to the uncertainty in the retrieval.

Figure 6 shows that the shape of the retrieved PSDs does not change significantly for the two cases of the wavelength-dependent mI. We note that the spectral dependence of the mI affects only one optical input data point in a significant way (backscattering at 355 nm).

On 18 May 2006 the volume concentration of the coarse mode fraction is 29 μm for the wavelength-independent case and 24 μm for both cases of the wavelength-dependent mI (factor 2 and 10 of the wavelength dependence). The effective radius is 1.1 μm in the wavelength-independent case and 0.9 μm in the case of the wavelength-dependent mI that uses the factor 2. The effective radius is 0.82 μm for the case of a wavelength dependence of factor 10. The mR is 1.6 in all three cases.

For the measurement of 19 May 2006 we find a total volume concentration of 45 μm for the wavelength-independent case and 47 and 46 μm in the case of the wavelength-dependent mI (factor 2 and 10 of the wavelength dependence, respectively). This means, in contrast to the first case, the wavelength dependence of the mI does not significantly influence the results for the volume concentration. The effective radius is 0.82 μm in the wavelength-independent case. It is 0.93 μm in case of the wavelength-dependent mI (factor 2 and 10). The mR differs insignificantly, namely 1.62 (wavelength-independent case) versus 1.58 and 1.59 for the wavelength-dependent cases (factor 2 and 10, respectively).

B. SAMUM-2: Case Studies of 22 and 31 January 2008

We obtain consistent results with the full ($3\beta +2\alpha +1\delta$) and the conventional ($3\beta +2\alpha$) input data sets for the two measurement cases of pure mineral dust observed during SAMUM-1; see Fig. 5. We also find reasonable agreement between our inversion results and the results of the AERONET retrievals regarding particle size and volume concentration.

The situation becomes more complicated when the aerosol layers consist of a mixture of dust and biomass-burning particles. In that case the particles are represented by a mixture of spheroids and spheres in our retrieval scheme. Thus, we have to consider one more unknown parameter, which is the volume fraction of spheroids. In principle, this parameter can be estimated even from a $3\beta +2\alpha$ data set, but the retrieval uncertainty will be significant. We note that the spheroid aspect-ratio distribution is optimized for dust and not for smoke or mixtures of dust with smoke. The volume fraction of spheroids is usually underestimated; thus the use of the particle DR is essential in the retrieval. More details on this effect can be found in [40].

Another problem in the retrieval of the microphysical parameters of a dust–smoke mixture is the fact that we have to deal with different values of the imaginary part of the refractive index for the two components. There is a strong wavelength dependence of this parameter across the investigated wavelength range for the dust component. It is strongly absorbing at ultraviolet wavelengths. The mI is quite low at visible wavelengths, for instance, below $0.005i$ at 532 nm. In contrast, the mI of smoke may exceed $0.02i$ [65] at visible wavelengths. The imaginary part of the refractive index is one of the most difficult parameters to estimate from multiwavelength lidar data as the kernels are not very sensitive to changes in the value of this parameter.

The inverse problem of multiwavelength lidar sounding is strongly underdetermined, which means that we have to infer many parameters from a comparatively small set of optical input data. The inversion solution depends on the constraints used in the retrieval, in particular on the range of the imaginary part of the refractive index that we consider in the retrieval. In the case of pure dust this range can usually be limited by the interval $0i<\mathrm{mI}<0.015i$, whereas in the case of the smoke it should be extended to $0i<\mathrm{mI}<0.03i$ [65]. This range extension does not significantly influence the accuracy of $V$, $S$, $N$, and $r_{\text{eff}}$ [40], but it enhances the uncertainty of the mR retrieval. We estimate for this case an absolute uncertainty of $\pm 0.07$, whereas we assume an uncertainty of $\pm 0.05$ for the reduced search range.

To illustrate the use of the spheroids model we apply it to measurements of the dust–smoke mixtures observed on 22 and 31 January 2008 during SAMUM-2 [10,49].

Figure 7 shows the measurement on 22 January 2008. The profiles represent a combination of BERTHA and multiwavelength lidar system (MULIS) [14] measurements. Dust from northern Africa dominates at heights below 1 km asl. The aerosol particles above 1 km height are composed of a mixture of mineral dust and biomass-burning smoke from southern West Africa [10]. This mixed smoke–dust layer extends up to 3.5 km height. The 532 nm linear particle DR in this layer varies between 15% and 20%, which is lower than the values typically measured for pure dust [14]. The lidar ratios are 60 sr in the center of the plume (2–3 km asl) and are as large as 90 sr, indicating strongly absorbing particles. The extinction-related Ångström exponents are above 0.5, which indicates a significant contribution of fine-mode particles.

 

Fig. 7. Same as Fig. 1 but for the measurement from 2005 to 2231 UTC on 22 January 2008.

Download Full Size | PDF

We show for comparison the column-mean Ångström exponents measured with the AERONET Sun photometer. The column-mean value is within the uncertainty of the vertical profile of the extinction-related Ångström exponent above approximately 2 km height.

Figure 8 shows the vertical profiles of the particle volume concentration and the effective radius. We show the results for the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ retrievals. The vertical distribution of the volume concentration, as well as surface-area and number concentration, follow the vertical structure of the profiles of the backscatter coefficients shown in Fig. 7. The minimum concentration is reached at 1750 m height, and the maximum concentration within the lofted dust–smoke layer is observed at approximately 2500 m height.

 

Fig. 8. Volume, surface-area and number concentration, and effective radius on 22 January 2008. The meaning of the symbols is the same as in Fig. 2. Note the large time gap of the AERONET results (level 1.5), which were taken at 0915 UTC on 23 January 2008. Pink boxes denote results for smoke (0.5–4.3 km) and pure dust (0–1 km). Details are given in the text.

Download Full Size | PDF

As we have already mentioned, one of the key problems in the retrieval of the parameters is estimating the SVF. We obtain nearly 100% for the SVF from the $3\beta +2\alpha +1\delta$ measurements at 1260 m height, that is, within the pure dust layer (not shown). This value slightly decreases with height, and it reaches the minimum value of 80% at 2300 m height. It then rises again to 95% at 3250 m height, which indicates that above 2500 m height the contribution of dust to the aerosol mixture probably increases again. The particle DR [Fig. 7(a)] increases above 2600 m height and corroborates this assumption. We note that backscattering by spheres is higher than backscattering by irregularly shaped particles. Thus, even a relatively small increase of the concentration of the spherical particles in this mixture may cause a significant change in the particle DR of the mixture. In other words, the uncertainty of the SVF is high for such mixtures.

The SVF estimated from our $3\beta +2\alpha$ measurements is about 40% at all heights. The numerical simulations demonstrate that excluding the DR from the input data set usually leads to a lower SVF compared to the use of the $3\beta +2\alpha +1\delta$ data set, which sometimes leads to a higher SVF. Thus, the most reasonable profiles of the retrieved parameters should be somewhere between the results obtained for these two sets of optical input data. From Fig. 8(a) we see that the profiles that we obtain from the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets are similar in shape. However, the use of the $3\beta +2\alpha$ data set leads to 20%–30% higher volume concentrations compared to the volume concentration that we obtain when using the $3\beta +2\alpha +1\delta$ data set. Figure 8(a) shows that the results for surface-area concentration and number concentration do not differ significantly regardless of the model and data combination we use.

The particle effective radius increases with height from approximately 0.35 to 0.6 μm if we use the $3\beta +2\alpha +1\delta$ data for the inversion. Effective radii are 10%–20% higher if we use the $3\beta +2\alpha$ data sets in the inversion regardless whether we use the spheroid or spherical particle model. The difference to the results from the $3\beta +2\alpha +1\delta$ data are still inside the retrieval uncertainty.

The inversion of the Sun photometer measurements on 22 January 2008 results in a column-integrated value of the effective radius of 0.42 μm for the total size distribution (dust and smoke and marine particles). If we only take the coarse mode fraction we obtain an effective radius of approximately 1.6 μm.

The value of 0.42 μm for the total size distribution is in reasonable agreement with the inversion results from lidar, even though the profile of effective radius shows a slight increase of this parameter with height. Note that there was a significant time lag between the lidar and the Sun photometer measurements. The lidar measurement time was 2005–2231 UTC; the Sun photometer measurement time was 0915 UTC.

For comparison we also show the range of effective radius of the coarse mode of pure dust observed during SAMUM-1 (open pink box). The short vertical line represents the result for 19 May 2006 (observed with AERONET). The top of this box indicates the height up to which we find a significant concentration of dust particles on 22 January 2008. The pink box that extends from 0.5 to 4.3 km denotes the region of high concentration of smoke particles. The box also shows the minimum and maximum effective radius of the smoke particles. The combined information of the two boxes shows that the effective radius derived by the lidar inversion method is realistic.

Figure 9 shows the height variation of the refractive index. At low altitudes, where the mixture is represented mainly by the dust component, we obtain $\mathrm{mR}=1.57$ if we use the $3\beta +2\alpha +1\delta$ data set for the retrievals. At higher altitudes, where the content of the biomass-burning particles in the mixture is enhanced, the mR drops to slightly lower values of approximately 1.5–1.52. The mR estimated from the $3\beta +2\alpha$ data set slightly increases with height from 1.4–1.43 to 1.47.

 

Fig. 9. Real and imaginary part of the refractive index on 22 January 2008. The meaning of the symbols that represent the lidar and AERONET results is the same as in Fig. 4. In addition we show campaign-mean values of the real part (vertical gray box) and the imaginary part (vertical red box) of the dust. The values were derived from the mineralogical analysis of dust collected aboard the Falcon aircraft during several flights [52,60]. The real (horizonal gray box) and imaginary (horizontal red box) part of the smoke particles were taken from [38] (T11b) (representative of the measurement on 22 January 2008) and [66] (D02). The horizontal gray and red bars represent the findings for pure dust observed during SAMUM-1 [5,58].

Download Full Size | PDF

We obtain $\mathrm{mR}=1.47$ at 675 nm from the Sun photometer data. Note that the AERONET results show a wavelength-dependent real part that varies between 1.41 and 1.53 (gray-shaded box, wavelength range from 441 to 1021 nm) in this mixed smoke–dust plume. Within the uncertainty bars of $\pm 0.07$ the profiles of the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ inversion are within the results from the Sun photometer measurements. The model that uses spherical particles in the lidar data inversion lies outside the AERONET results.

Reference [60] reports on a value of 1.57–1.58 that was derived from the mineralogical analysis of dust particles collected aboard the Falcon aircraft during SAMUM-2, the same way it was done during SAMUM-1. We do not have results that match exactly the measurement times of lidar or Sun photometer. The mean value represents the campaign-mean, wavelength-dependent value (wavelength range 441–1021 nm) for the height interval from 0.6 to 3.6 km [60].

We show the results for the real part of dust as vertical gray open box in Fig. 9. The numbers are within the variation of the real part we found during SAMUM-1 [5,58]. The SAMUM-1 results for pure dust are shown as a gray horizontal bar at the bottom of the $x$ axis in Fig. 9.

The airborne measurements did not provide us with data for the smoke in the plume. Reference [48] presents results for smoke within the elevated dust–smoke layers on the basis of lidar measurements. The contribution of dust was removed from the measured optical properties of this mixed plume using the approach presented in [38]. In this way we can derive the properties of the smoke particles. Mean values of the effective radius of $0.22\pm 0.08$ were found for the smoke particles in the lofted layers.

Reference [48] obtained mR values between 1.42 and 1.67 for the smoke layer. The mean value is $1.54\pm 0.06$. These results are shown by the horizontal gray open box at the bottom $x$ axis in Fig. 9. The large variation of the real part includes the variation of the real part in the vertical profile of the smoke, and it also includes the retrieval uncertainties of the real part. Details can be found in [38].

For comparison, Table 1 of [66] reports on mean values of 1.47–1.52 for the real part of the refractive index of various types of biomass-burning particles. These results are shown by the gray open box (dashed) at the bottom of Fig. 9. The values summarize the results for smoke observed in boreal forests ($1.5\pm 0.04$), the Amazonian forest ($1.47\pm 0.03$), the South American cerrado ($1.52\pm 0.01$), and the African savannah ($1.51\pm 0.01$).

We can combine this rather inhomogeneous information, namely, real parts from dust and smoke from different methods, column-mean and vertically resolved values, and wavelength-dependent and wavelength-independent values [38,60,66]. We expect that mR decreases with increasing height because the smoke content increases with height in the mixed layer and because smoke seems to have on average a lower real part than pure dust. Thus, the profile of mR that we obtain from the inversion of the $3\beta +2\alpha +1\delta$ data seems to be in better accordance with the results presented by [38,60,66] than the mR profile that we obtain from the $3\beta +2\alpha$ data.

With regard to the profiles of the imaginary part we obtain the following results. The mI is 0.002–0.004 from the inversion of the $3\beta +2\alpha +1\delta$ data. An evaluation of the vertical variation of mI is not possible due to the large uncertainty. If we exclude the linear particle DR from the input data we obtain higher values of $\mathrm{mI}=0.004–0.012$. Note that the error bars of this profile are also representative for the error bars of the other profiles of the imaginary part. The profile that results from the inversion of the $3\beta +2\alpha$ data set using the spherical particle model is in between the other two profiles.

The results for the imaginary part from lidar are at the lower range of values provided by AERONET observations. The red-shaded box shows the range of imaginary parts between 441 and 1021 nm. The red dashed curve shows the imaginary part at 675 nm.

Table 4 of [60] reports values of 0.012 (at 441 nm) to 0.0034 (at 1021 nm) for the imaginary part of dust observed during SAMUM-2. We show the airborne results for the dust part as a red box in Fig. 9. For comparison, the red bar at the top of Fig. 9 represents the imaginary part of pure dust observed during SAMUM-1 [5,58].

With respect to smoke, mI varies between 0.014 and 0.044 with a mean value of $0.029\pm 0.01$ according to the method described by [48]. These values are shown by the horizontal, open red box on the upper $x$ axis in Fig. 9. We note again that this value is wavelength independent and the range of 0.014–0.044 includes the uncertainty of mI and the variation of mI with height of the smoke in the dust–smoke plume.

Reference [66] reports on imaginary parts between 0.00093 and 0.021 for various types of smoke particles. In detail, these are as follows: boreal forests ($0.0094\pm 0.003$), the Amazonian forest ($0.00093\pm 0.003$), the South American cerrado ($0.015\pm 0.004$), and the African savannah ($0.021\pm 0.004$). The values for the African savannah are closest to the results obtained by [48] for smoke.

This comparison of the lidar inversion results to the data from the other methods neither proves nor rejects whether our inversion scheme is able to derive a trustworthy imaginary part. First, the other methods have their uncertainties, too. Second, there were no airborne in situ measurements of the imaginary part (absorption) of the smoke content in these plumes. Thus we lack a very important piece of information in our comparison. Third, we again compare a rather inhomogeneous (incomplete) set of data of the imaginary part: vertically resolved measurements of smoke (imaginary part) from lidar, literature values on smoke observed in other regions on the globe, column-mean values of the dust–smoke mixture observed during SAMUM-2 with the AERONET Sun photometer, campaign-mean imaginary parts from mineralogical analysis of particles collected aboard the Falcon during SAMUM-2, and imaginary parts of pure dust observed considerably closer to the source regions during SAMUM-1.

If we assume that our lidar-inversion method is not able to derive the imaginary part to sufficient accuracy, our goal is to achieve at least 50% accuracy. There also remains the question of whether this underestimation is caused by the strong wavelength dependence of Northwest African mineral dust toward ultraviolet (UV) measurement wavelengths. Other types of dust might be less critical in that respect if they contain less or no iron oxides, which are the cause for the comparably strong light absorption at UV wavelengths.

Figure 10 shows the PSDs obtained from the lidar measurements on 22 January 2008. We show the results from the $3\beta +2\alpha +1\delta$ retrievals for 1770, 2790, and 3270 m height asl; we find similar results for the $3\beta +2\alpha$ retrievals. The PSD is bimodal with significant contributions of the fine and coarse mode at all three heights. The coarse mode is shifted toward larger radii when we exclude the DR from the data inversion, that is, when we keep the conventional $3\beta +2\alpha$ data set (not shown). For comparison, the same figure shows the column-averaged PSD that we obtain from the inversion of the Sun photometer measurements on 23 January 2008; data for 22 January are not available. The PSDs provided from the inversion of the lidar and Sun photometer data are similar. However, the fine mode that we obtain from the inversion of the Sun photometer data is again centered at 0.1 μm (see Fig. 5). The maximum value of the fine mode obtained from the lidar measurements is centered at about 0.2 μm. This offset of the center value between the two fine-mode fractions may be due to an insufficient number of optical input data that are needed to properly extract particle radii for the range from 0.075 to 15 μm in the lidar data inversion.

 

Fig. 10. PSDs on 22 January 2008 obtained from $3\beta +2\alpha +1\delta$ measurements at 1770, 2790, and 3270 m. For comparison the AERONET column-integrated volume distribution on January 23 is also shown (solid line with squares).

Download Full Size | PDF

To further investigate the performance of the inversion algorithm that uses the spheroid model, we analyzed another measurement. On 31 January 2008 [10,38,48]. The aerosol below 1500 m height was dominated by mineral dust, whereas particles above this dust layer were again composed of a mixture of mineral dust and biomass-burning smoke. As in the case of 22 January 2008, this day has been extensively analyzed [48] including a retrieval of smoke microphysical properties that followed after the separation of the individual optical properties of the dust and smoke particles in the mixture [38,48].

Figure 11 shows the vertical profiles of the optical particle properties measured with lidar. The linear particle DR is above 30% within the dust layer. Above 1250 m it drops to approximately 14%, which indicates that the contribution of the smoke becomes more dominant. The lidar ratios on average increase from around 50–70 sr below 3 km height to 80 sr around 3.6 km height asl.

 

Fig. 11. Same as Fig. 1 but for the measurements between 2015 and 2232 UTC on 31 January 2008.

Download Full Size | PDF

The column-mean Ångström exponent measured with the AERONET Sun photometer is on average 0.2 lower than the values of the vertical profile of the extinction-related Ångström exponent. Note that the profile starts at 1.5 km height asl. One possible cause of the lower value measured by AERONET may be large particles in the marine boundary layer. For instance, large sea-salt particles produce lower Ångström exponents, sometimes close to zero, which decreases the column-mean value.

Figure 12 presents the height distribution of the particle-number, surface-area, and volume concentrations and of effective radius. The vertical variation of the parameters maybe be explained as follows. The SVF that is estimated from the $3\beta +2\alpha +1\delta$ data set is close to 100% inside the dust layer, and it decreases to 85% at 4250 m height (not shown). The inversion of the $3\beta +2\alpha$ data delivers a lower SVF of 50% below 1250 m. We have good reason to expect that the SVF of 85% that we obtain from the $3\beta +2\alpha +1\delta$ data inside the smoke layer is overestimated. The SVF that we obtain from the $3\beta +2\alpha$ data inside the smoke layer is in the range of 20%–40%, which may be too low.

 

Fig. 12. Volume, surface-area and number concentration, and effective radius on 31 January 2008. The meaning of the symbols is the same as in Fig. 2. The results from AERONET represent the measurement at 18:25 UTC on 31 January 2008. The AERONET results are derived from level 2.0 data (also in Fig. 13 and Fig. 14). We marked with big gray symbols the data points for the $3\beta +2\alpha +1\delta$ data in the lower part of the aerosol layer that seems mainly determined by mineral dust (nonspherical particles). There is one transition height, and the upper four points more likely describe smoke, for which we used the spherical particle model in data inversion. More explanations are given in the text.

Download Full Size | PDF

We believe that the true profiles of the particle parameters should be between the results obtained from the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets. We marked the most trustworthy results by gray symbols in the profiles of the volume concentration. The same applies of course also to the profiles of effective radius and the number and surface-area concentration.

We expect that the most reliable results are the first three points [gray-filled squares below 2 km height in Fig. 12(a)] that result from the inversion of the $3\beta +2\alpha +1\delta$ data within the dust layer. The fourth point (open square at around 2.4 km height) represents the intermediate stage at which the inversion model changes from dust-dominated (spheroids) to smoke-dominated (spheres) particle size parameters. The next four points (gray-filled circles) thus result from using the $3\beta +2\alpha$ data set and the assumption of spherical scatterers within the smoke layer. It seems reasonable to use just spheres in the retrieval when the linear particle DR stays below 10%.

The backscatter profile is quite complex so it is not easy to compare the volume concentration derived from the inversion of the lidar data to the AERONET results. All microphysical profiles obtained from the $3\beta +2\alpha +1\delta$ and the $3\beta +2\alpha$ data sets are quite similar. The difference on average does not exceed the uncertainty of the retrieval, which means that these parameters are not very sensitive to the ambiguity of the SVF estimation in the dust–smoke mixture. In other words: the particle depolarization data may not add information in the lidar data inversion for such complicated cases of dust–smoke mixtures, given the measurement and retrieval uncertainties.

The volume concentration decreases with increasing height above 1250 m height asl. It reaches its minimum values near 2750 m height and then starts rising again. The number and surface-area concentrations are strongly enhanced in the lower part of the pollution layer and reach their maximum values at 1750 m. The number concentration remains comparably constant above 3000 m, whereas surface-area concentration, just like volume concentration, increases again above 3300 m. There is an offset of approximately 500 m in the height where volume concentration and surface-area concentration start to increase.

It is unclear to us why there is a vertical offset of 500 m between the maximum value of the volume concentration and the maximum values of surface-area and number concentration on the one hand, and the 500 m offset between the decrease of volume concentration and surface-area concentration on the other hand. We will check if this behavior (offset) appears in the profiles of the other SAMUM-1 and SAMUM-2 data. We plan to carry out a comprehensive analysis (inversion) of the optical data sets.

Effective radius is between 0.4 and 0.6 μm at the bottom of the profiles, which is the region mostly dominated by dust. The different values result from the two different data combinations and the use of the spheroidal and spherical particle model, respectively. Effective radius decreases with height. This indicates the presence of a high amount of smaller particles, which is typical for biomass-burning products. The effective radius reaches its minimum value of 0.2 μm between 2800 and 3000 m. It increases with increasing height and reaches 0.4–0.5 μm at the top of the smoke–dust layer.

The increase of the volume and surface-area concentration and the effective radius above 3000 m height may be explained by particle hygroscopic growth of the mixed dust–smoke plumes; note that for pure dust considered in this study it is not an issue as hygroscopic growth factors were insignificant in view of the overall uncertainties of our inversion results. Thin clouds formed at the top of the aerosol layer (5 km height asl) after 2232 UTC. This assumption of hygroscopic growth is also corroborated by the fact that number concentration remains comparatively constant above 3000 m.

The AERONET result of the column-mean effective radius is 0.36 μm for the total size distribution. If we only take the coarse mode fraction, we obtain $\sim 1.41\mathrm{\mu m}$ for effective radius, which is similar to the value obtained from AERONET retrievals of pure dust observed during SAMUM-1. We need to keep in mind, though, that this value certainly is influenced by marine particles. The mean effective radius from AERONET represents quite well the vertical profile of effective radius that we derived from our inversion scheme.

A point that is noteworthy in the context of effective radius is [24] and our comment in the introduction section regarding zero depolarization of smoke particles. The authors present inversion results of an aged smoke plume (measured with multiwavelength Raman lidar) that was transported from West Canada to Central Europe in August 1998. The authors found linear particle DRs of approximately 7% in that plume. A similar version of the inversion algorithm [18,67] used in our study was applied in that study. However, only spherical particle shape could be used in this inversion scheme. We found a value of approximately 0.24–0.27 μm (standard deviation of 0.04 μm) in that smoke plume. Results for effective radius matched very well to airborne in situ measurements of effective radius (0.25 μm) [19,24]. This value of 0.24–0.27 μm was measured under comparatively dry conditions of the aged biomass-burning plume.

Figure 13 shows that the real part of the refractive index changes significantly if we add the particle DR to the input data set. The value of mR inside the dust layer is $1.52\pm 0.05$. We already mentioned that the SVF obtained from the $3\beta +2\alpha +1\delta$ data set in the smoke layer is probably overestimated. Hence, the inversion of the $3\beta +2\alpha +1\delta$ data set leads to relatively high values of mR in the 1.5–1.6 range for all heights (i.e., within the dust layer and within the mixed dust–smoke layer). The values of mR obtained with the $3\beta +2\alpha$ data set are around 1.43 in the dust-dominated part of the plume, increase to 1.52 at 2.8 km height, and then decrease again. The profile that we obtain from the $3\beta +2\alpha$ data and the use of the spherical particle model looks the same except for the fact that each value is slightly lower than the respective value from the spheroidal model.

 

Fig. 13. Real and imaginary parts of the refractive index on 31 January 2008. The meaning of the symbols and the references is the same as in Fig. 9.

Download Full Size | PDF

The real part of the refractive index provided by AERONET is about 1.5 at 675 nm. The gray-shaded box again denotes the variation with wavelength (441–1021 nm). The imaginary part obtained from the $3\beta +2\alpha +1\delta$ observations is about $0.006\pm 0.003$ in the smoke layer. In contrast, the AERONET result gives a higher value of $\mathrm{mI}=0.01$ at 675 nm. The variability is 0.003–0.013, depending on measurement wavelength (441–1021 nm).

For completeness, Fig. 13 also shows the results from the airborne measurements of the CRI of dust and the results from [38,66]. The numbers and meaning of the symbols are the same as those in Fig. 9.

The vertical variation of the real part seems to follow in an inverse manner the vertical variation of effective radius (see Fig. 12) regardless of the model we apply and the data combination we use in the data inversion. The real part increases with height from low values (1.4–1.53, depending on model and data combination) to maximum values of 1.46–1.6 at 2750 m height, where the concentration of smoke particles may have reached its maximum compared to the concentration of dust particles. At this height effective radius reaches its minimum value. The real parts then tend to decrease again with height to values of 1.38–1.5 at the top of the smoke–dust plume. This decrease of the real part could again be caused by hygroscopic growth of the smoke particles, just like what may have caused the increase of particle effective radius; see Fig. 12. Note that the particle DR (Fig. 11) significantly drops between 1.5 and 2.2 km height from 32% to 15%, then stays fairly constant nearly to the top of the smoke–dust layer, where its drops to slightly lower values of 12%. Thus it seems unlikely that the increase of effective radius and decrease of the real part above 3 km height is caused by the increase of the dust-particle concentration.

Figure 14 shows the PSDs obtained with the spheroid model for the $3\beta +2\alpha$ data sets at two heights. We note that we obtain similar results for the PSDs if we invert the $3\beta +2\alpha +1\delta$ data (not shown). Though the size distributions obtained with our inversion technique have significant uncertainties, we can retrieve the main features of the PSDs with height. Inside the smoke–dust layer the coarse mode is visible in both size distributions. This mode is centered at 3 μm. For comparison, the same figure shows the PSD provided by the AERONET instrument. Again we see that the maximum of the coarse mode is shifted toward a slightly lower effective radius of 2 μm. Just as on 22 January 2008, the fine mode obtained from the lidar measurements is slightly shifted toward larger radii compared with the results provided by AERONET.

 

Fig. 14. PSDs on 31 January 2008 obtained from $3\beta +2\alpha$ measurements at 3750 and 4260 m. For comparison the AERONET column-integrated volume size distribution acquired on 31 January 2008 is also shown.

Download Full Size | PDF

The extinction profiles provide us with the Ångström exponent for the wavelength pair $355/532\mathrm{nm}$. We obtain approximately $1-1.5$ between 2.5 and 3.2 km height asl (see Fig. 11). The Ångström exponent drops to $\approx 1$ below 2.5 km, which is in accordance with the assumption that the dust concentration is higher below 2.5 km height. The Ångström exponent also drops to $\approx 1$ above 3.2 km height, which is also in agreement with the assumption of particle hygroscopic growth rather than an increase of the dust concentration.

5. Conclusions

Our study shows that optical data derived from multiwavelength lidar measurements of dust can be inverted to particle microphysical properties. The inversion algorithm is based on the use of randomly oriented spheroids. We have applied the algorithm to invert several cases of lidar measurements performed during SAMUM-1 and SAMUM-2. The inversion results are in reasonable agreement with the results provided by the inversion of AERONET Sun photometer data. Our study shows that we are making progress particularly regarding the retrieval of size parameters (effective radius and extensive parameters) of the PSDs. The major challenge lies in the trustworthy retrieval of the CRI, particularly of the imaginary part that shows a strong spectral dependence. The investigated dust is strongly absorbing at UV wavelengths.

The main findings of our study can be formulated as following:

In view of the above statements we carried out another test of our inversion results. Figure 15 gives an impression of the quality of our inversion results for effective radius and for volume and surface-area concentration in terms of correlation plots. We show the results we obtained for all four measurement days for the data combination $3\beta +2\alpha +1\delta$ and $3\beta +2\alpha$ and the use of the spheroid model. In general it is accepted in published literature, see for instance [23], that there exists a correlation between the extinction-related Ångström exponent and the particle effective radius. Surface-area concentration is expected to correlate with particle extinction [68]. Simulations indicate that nonspherical particle shape may not significantly alter the extinction coefficient compared to surface-equivalent spheres, as extinction is mainly influenced by the projection of the particle onto the two-dimensional plane (projected area). Reference [28], for example, shows for the case of ellipsoids that extinction changes by 5% compared to spheres of the same projected surface.

 

Fig. 15. Correlation plots show (a) effective radius (from inversion of lidar data) versus Ångström exponent (wavelength pair $355/532\mathrm{nm}$) and (b) surface-area concentration versus extinction coefficient at 355 nm, and (c) volume concentration versus backscatter coefficient at 355 nm for all four measurement days. The symbols and colors (white and gray) denote the different data combinations and measurement days. In all cases only the results obtained with the spheroid particle model are shown. The coefficients from linear regression are shown in (a) and (b) together with the correlation coefficients $R^2$. The horizontal line in (c) denotes the minimum volume concentration we found from all the SAMUM-1 data sets (18 and 19 May, spheroid particle model, $3\beta +2\alpha +1\delta$ and $3\beta +2\alpha$ data combination) that we processed in this study. The dashed line (from origin to top $x$ axis) indicates the upper limit of the maximum volume concentration that may exist for given particle backscatter coefficient. The dashed line (from the origin to the right $y$ axis) indicates the limit of the minimum volume concentration that may exist for given particle backscatter coefficient. Note that these lines rest upon the analysis of four measurement cases only and that we considered the four triangles below the lower dashed line as outliers. In this sense this dashed lines only serve as a guideline and must be verified by more measurement cases.

Download Full Size | PDF

Volume concentration correlates with the backscatter coefficient in the case of spherical scatterers. However, particle shape leads to significant variations of the particle backscatter coefficients. Thus we cannot expect a significant correlation of the dust-related backscatter coefficient to the dust particle volume in our study for several reasons:

Figure 15(a) shows a comparatively strong correlation of effective radius with the extinction-related Ångström exponent. From the linear regression analysis we find a correlation $R^2$ of 0.85 if we consider all results, regardless of data combination we used for the inversion with the spheroid model. Figure 15(b) shows an exceptionally strong correlation of surface-area concentration versus particle extinction at 355 nm. $R^2$ is 0.98. Figure 15(c) shows the variation of the volume in dependence of the backscatter coefficient at 355 nm. As expected, there is a rather broad spread, and we cannot identify a clear correlation due to the above-mentioned reasons. However, it is worth noting two features in this plot.

First, we find on average higher volume concentrations for lower backscatter coefficients in the case of pure dust (SAMUM-1) compared to the results from the two SAMUM-2 cases, which present a mix of spherical and nonspherical particles. Backscatter coefficients measured during SAMUM-2 are on average larger for the same volume concentration; see all the data points about $20{\mathrm{\mu m}}^3/{\mathrm{cm}}^3$ for which we have results from both campaigns (horizontal line). This feature points to the reduction of the backscatter coefficient by a factor of up to 3 in the case of nonspherical particles.

Second, the dashed lines denote the maximum and minimum volume concentrations that were found for given backscatter coefficients. We are aware that these limiting lines can be only a first guess in view of the limited data set we processed in this study. As we want to process all SAMUM-1 and SAMUM-2 cases in the near future, we will be able to verify this finding on the basis of a more statistical data analysis.

This study is our first real attempt of deriving microphysical properties of pure mineral dust and mixtures of mineral dust with smoke from lidar observations. In view of this task, we consider our results very promising for future work with this particle model.

The linear particle DR can improve the retrieval if it is used as input in the data inversion. Dust particles strongly depolarize the backscattered laser light, and the spectral particle DR definitely contains information about particle microphysics [13]. This means the ensemble of spheroids should be able to mimic the optical properties of the (volume-equivalent) nonspherical particles. The Raman technique allows us to calculate the optical data (extinction and backscattering) from lidar data with an uncertainty of approximately 10%. This low error, however, requires careful data analysis and strong backscatter signals. Hence, the forward model should provide comparable accuracy of the computations if we want to achieve an improved retrieval in data inversion.

The dust particle DR measured with lidar during SAMUM-1 was above 30% [14], and we should recall that the spheroid model can provide such high values only for small values of the imaginary part of the refractive index ($\mathrm{mI}<0.001$) and $\mathrm{mR}<1.5$ [6,28,40]. Note that mineral dust may be highly absorbing at UV wavelengths. Besides this fact, the maximum values of the particle DR are obtained for size parameters of $x\sim 10$, which for 532 nm radiation corresponds to a particle radius of $\sim 1\mathrm{\mu m}$. Thus, the analysis of the SAMUM measurements provides us with an opportunity to check whether the retrievals performed with and without the use of the linear particle DR as input are consistent. Our results demonstrate that retrievals performed with and without depolarization are reasonably consistent, at least for the cases considered in the present study.

The spheroidal model is the only model available today that can be used for retrieval of dust particle properties from lidar measurements. This model works well for the AERONET inversion. The model also proves useful for the lidar inversions, though there still remain many open questions to answer regarding lidar applications. Some of the main questions and tasks are as follows:

In summary we note that the use of the spheroidal model may be a candidate for the application to lidar measurements in the framework of the European Aerosol Research Lidar Network. Particularly, stations in South Europe are regularly affected with mineral dust from North Africa [70]. In our contribution we made the first step toward a microphysical characterization of dust and mixtures of dust with other pollution, which is a common phenomenon in South Europe. Still, our study needs to be further expanded, and more efforts are needed to improve the forward model that is used to describe the light-scattering properties of nonspherical (mineral dust) particles.