A 2.5-year data set of Raman lidar measurements performed in Lecce within the European Aerosol Research Lidar Network and a numerical model are used to characterize continental aerosols over southeast Italy. Continental conditions are selected by means of back trajectories, limiting the data set to cases of advection from the European continent. The model is used to constrain the relevant aerosol microphysical parameters needed to reproduce the altitude-resolved optical properties measured by lidar, namely, aerosol extinction (α), backscatter (β), and lidar ratio (LR = α/β) at 351 nm. The observed variability of α, β, and LR is simulated by randomly varying, within appropriate ranges, all the microphysical parameters describing the aerosol composition and size distribution (assumed as bimodal). An optimal model configuration capable of reproducing within ±10% the mean optical properties retrieved by lidar, including their vertical pattern, is presented and discussed with sensitivity studies. Results indicate rather clean continental aerosols to characterize the site, with water-soluble fine-mode aerosols (dry modal radius of 0.05–0.10 μm) accounting for 98–99% of the total number of particles. The (dry) imaginary refractive index of fine-mode particles is extended up to 0.02 to better fit the lidar data. This suggests some mixing of water-soluble substances with more absorbing material. Coarse-mode particles (modal radius 0.4–0.5 μm) are shown to play a crucial role in determining the observed vertical profile of β and LR. Finally, an altitude-resolved relationship linking α to β is derived. This could be usefully employed in continental conditions to invert the lidar measurements when only the elastic signal is available (for example, in daylight).
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 Aerosols affect the Earth-atmosphere radiation budget by several processes. They scatter solar radiation and absorb both solar and thermal radiation [aerosol direct effect, e.g., Haywood and Boucher, 2000]. They alter microphysical properties and lifetime of clouds [first and second aerosol indirect effect, e.g., Lohmann and Feichter, 2005], thus modifying cloud radiative properties. A good characterization of atmospheric aerosols is therefore needed to achieve a better understanding of the climate system [Intergovernmental Panel on Climate Change, 2001]. However, the complexity of the processes involved and the great spatiotemporal variability of the atmospheric particulate strongly complicate this task and requires continuous acquisition of aerosol data in the different regions of the world. The several aerosol-dedicated instruments onboard satellite missions (e.g., MODIS [Kaufman et al., 1997; Tanré et al., 1997], POLDER [Deuzé et al., 2000, 2001], and CALIPSO [Winker et al., 2003]), the worldwide network of sun photometers (AERONET [Holben et al., 1998]), and the establishment of networks of aerosol lidar systems (e.g., Micro Pulse Lidar Network (MPLNET) [Welton et al., 2001], European Aerosol Research Lidar Network (EARLINET) [Bosenberg et al., 2003], and Commonwealth of Independent States Lidar Network (CISLINET) [Chaikowsky et al., 2006]) represent the best evidence of the effort paid in this respect by the international scientific community.
 The Mediterranean region is certainly one of the most interesting regions in terms of atmospheric particulate due to the significant input of particles (and/or particle precursors) from both natural (Mediterranean Sea, North African arid regions) and anthropogenic (European continent) sources. The contribution of pollution-related aerosols and mineral dust over the Mediterranean basin has been demonstrated to be relevant particularly in summer [e.g., Lelieveld et al., 2002; Barnaba and Gobbi, 2004a; Antoine and Nobileau, 2006].
 In this study we investigate a 2.5-year data set of aerosol optical properties measured by a Raman lidar in southern Italy under advection conditions from the European continent. The main purpose is to constrain the altitude-resolved variability of the aerosol microphysical properties in such “continent-affected” conditions. To this aim, we perform a closure study between the observed aerosol optical properties and the numerical simulations explaining those properties on the basis of aerosol microphysical parameters.
 The aerosol optical properties (measured and simulated at the lidar wavelength of 351 nm) addressed in this study are the following: the aerosol extinction, α (km−1), the aerosol backscatter, β (km−1sr−1), the extinction-to-backscatter ratio, α/β (sr, also referred to as “lidar ratio”, LR), and their dependence on the altitude, z. Lidar measurements of α(z), β(z), and LR(z) have been collected in Lecce (Italy, 40°20′ N; 18°06′ E) between May 2000 and August 2002 in the framework of the EARLINET project. Origin and pathway of 4-day analytical back trajectories have been used to select measurement days characterized by advection of air masses from the European continent. Selection criteria of continental cases and relevant lidar data are described in section 2.
 The lidar unique capability to provide vertically resolved information has thus been exploited in this study, and a numerical model capable of simulating the aerosol vertical variability has been set up (section 3). The model assumes a bimodal lognormal aerosol size distribution. Vertical variability is introduced in the model through both altitude scaling of the particle number density and dependence of aerosol size and refractive index on relative humidity (RH) (which is also assumed to vary with z). The aerosol microphysical parameters describing both aerosol size and composition are initially chosen according to continental aerosol climatology data available in literature [Hess et al., 1998]. Then the variability of the different parameters is tuned to achieve a good accordance with experimental data. A specific model configuration capable of reproducing the lidar-observed aerosol optical properties within 10% is proposed and discussed (section 4). The relevant aerosol microphysical properties needed as input to the optical simulations are believed to provide a useful indication on the variety of particles contributing to the aerosol load observed in the “continent-affected” aerosol conditions over the central-eastern Mediterranean.
 Through the investigation of the α versus z and the β versus z behavior, a further result of this study is the definition of a mean functional relationship, α = f(β, z), specific for the continental aerosols characterizing the Lecce site (section 5). This relationship could be usefully employed in the inversion of the lidar elastic signal when the Raman channel cannot be used (for example, in daylight).
2. Continental Aerosol Optical Properties by Lidar Measurements
 Lidar measurements presented in this study have been performed between May 2000 and August 2002 at the Physics Department of Lecce’s University in the framework of the EARLINET project [Bosenberg et al., 2003; Matthias et al., 2004a; Guibert et al., 2005]. A detailed description of the lidar system can be found in the paper of De Tomasi and Perrone . We only remind here that the instrument employs an XeF excimer laser (at 351 nm) and an f/4 Newton telescope with a 30-cm-diameter mirror. In accordance to the EARLINET’s protocol, lidar observations have been performed 2 days per week and include two measurements after sunset and one around 1300 UT (each of about 30 min duration). However, only nighttime measurements are considered in this work since daylight conditions do not allow the independent retrieval of backscatter and extinction vertical profiles (and hence of lidar ratios).
 A first data quality selection has been applied by discarding lidar-derived extinction and backscatter coefficients associated with errors larger than 50%. In particular, we have rejected extinction and backscatter coefficients with statistical relative uncertainties ≥50% for α(z) > 0.1 km−1 and β(z) > 0.2 × 10−3 km−1 sr−1. The lidar data fulfilling the conditions −0.02 < α(z) < 0.1 km−1 and 0.5 × 10−4 < β(z) < 0.2 × 10−3 km−1 sr−1 have been kept if the absolute errors on α and β were lower than 0.05 km−1 and 0.1 × 10−3 km−1 sr−1, respectively.
 A thorough analysis of the complete nighttime lidar data set collected in the same period at Lecce within EARLINET (168 measurement days, including all aerosol conditions, i.e., continental, maritime, Saharan dust transport episodes) can be found in De Tomasi et al. . Here we specifically focus on continental aerosol conditions. Selection of the latter has been performed on the basis of analytical back trajectories. Namely, the 4-day backward trajectories arriving over Lecce have been calculated on a three-dimensional grid and with a time resolution of 6 hours by the German Weather Service. These are based on wind fields of the European numerical weather prediction model [e.g., Kottmeier and Fay, 1998] and are provided at six distinct arrival pressure levels (950, 850, 700, 500, 300, and 200 hPa). Since nighttime lidar measurements have typically been performed in the time interval of 1900 ± 0200 UT, the origin and pathway of the 4-day back trajectories reaching Lecce at 1900 UT have been considered. We have assumed that continental-type aerosols have been observed over Lecce on days characterized by advection patterns coming from western, northern, and eastern Europe. In fact, air masses coming from these regions have the common property to travel across several industrialized European areas before reaching Lecce. We have thus discarded measurements associated with air masses traveling prevalently over the Mediterranean Sea and North Africa to limit lidar data contamination by maritime and desert dust aerosols, respectively. More specifically, we have only selected trajectories having more than 60% of their points above 40°N, and more than 60% of their points at an altitude higher than 980 hPa when traveling over the sea. A total of 76 days passed this double-selection criterion. Note that, Lecce being located in a rural area not far from the sea (about 20 km away from both the Adriatic and the Ionian Sea), any selection of data based on back trajectories could not exclude some “contamination” by marine aerosol. Nevertheless, we believe that the selection criterion adopted guarantees rejection of all the measurement days significantly affected by this type of particles.
 The back trajectories corresponding to the 76 days selected as “continental” are summarized in Figure 1 for the three arrival levels: 950, 850, and 700 hPa. Note that only tracks corresponding to lidar-observed aerosol layers at the trajectory arrival altitude are shown in each panel.
Figure 2 shows the number of continent-affected measurement days per year (grey histograms) and the corresponding total number of measurement days (white histograms). Overall, the former represents about 45% of the total, with small fluctuations year by year.
 To give a view of the observed aerosol properties in the above defined continental conditions, we show in Figures 3a–3c the scatterplots of β, α, and LR versus the altitude z, respectively. Figures 3d and 3e show the scatterplots of α versus β and LR versus β, respectively. As evident in Figures 3a–3c, aerosol optical properties undergo a rather marked variability with z which reflects the variation of aerosol concentration and microphysical properties. Figures 3a and 3b show backscatter and extinction coefficients to decrease more than 50% within the lowermost 1.5–2.0 km [the decrease of α(z) being somewhat more pronounced than that of β(z)]. Conversely, lidar ratios (Figure 3c) tend to increase above 1.5–2.0 km, suggesting a change of aerosol characteristics at those levels. Nonetheless, it is worth noting the wide spread of lidar ratios at all altitudes, which is indicative of a corresponding high variability of the aerosol microphysical properties at each level. As expected, Figure 3d shows that extinction coefficients increase with β. Conversely, the relationship between LR and β is less obvious in Figure 3e although a slight LR tendency to decrease with β can be identified. In fact, high values of β are mostly associated with the presence of poorly absorbing coarse particles, which conversely have a minor impact on α, thus leading to smaller extinction-to-backscatter ratios. This aspect, as well as the general results of Figure 3, will be clearer after the comparison of the lidar measurements with simulations presented in section 4. Presentation of the model setup to simulate the observed aerosol properties is given in the next section.
 Obviously, the approach adopted in this study implicitly assumes the experimental data set of Figure 3 to be statistically representative of the continental aerosol properties we intend to reproduce (this represents an intrinsic, unavoidable limit of this work). The rather large statistics used (559-point data set) makes us confident in the validity of such assumption (this being weaker only for those z and β regions having a limited number of experimental data, for example, z < 0.5 km, z > 3.5 km, β < 10−3 km−1 sr−1, and β > 10−2 km−1 sr−1; see Figure 3).
3. Aerosol Model Setup
 Given the aerosol size distribution, n(r), the aerosol extinction (α) and backscatter (β) coefficients are derived by the following relationships (based on the Mie theory for spherical particles, e.g., Bohren and Huffman, 1983):
where Qext and Qbks are the Mie extinction and backscatter efficiencies, respectively, for a particle of radius r and a refractive index m at the wavelength λ (in our case, the lidar wavelength λ = 351 nm). On this basis, aerosol models available in literature [e.g., d’Almeida et al., 1991; Volger et al., 1996; Hess et al., 1998] generally assume precise aerosol size distributions and compositions to derive mean aerosol optical properties of specific aerosol types. Aerosol conditions ranging from “continental clean” to “continental polluted” are addressed by summing up the contribution of different aerosol components namely, water-soluble and water-insoluble substances (plus soot in polluted conditions). A similar method (aerosol external mixing) is used here. In our case, however, it is clear that variable aerosol microphysical properties should be considered in order to reproduce the whole range of α, β, and LR values observed by the lidar (Figure 3). A numerical model has then been developed that allows simulating a wide range of “expected” α, β, and LR by varying, within appropriate ranges, the aerosol microphysical parameters describing the aerosol size distribution and composition [i.e., n(r) and m in equations (1) and (2)]. For each computation, a random choice procedure selects, within the relevant range, the actual value of the different parameters to be employed. A large number of computations (typically 10,000) are performed to achieve a statistically representative variability of modeled aerosol optical properties.
 A bimodal lognormal size distribution is assumed in the present study:
The two modes (indicated with i = 1, 2 and also referred to in the following as fine and coarse modes, respectively) are intended to reproduce particles of anthropogenic and natural origin, respectively. To define n(r), the following parameters are therefore needed for each aerosol mode: the modal radius, rmi, the width, σi, and the particle number density, Ni. In our model, the values Ni are obtained by scaling the total number of particles, N (per cubic centimeter), for the ith mode mixing ratio, Ni% (i.e., Ni = N × Ni%). Then, the particle refractive index, m, defined by both its real (mRe) and imaginary (mIm) parts, is required to compute the α and β values [equations (1) and (2)].
 Having no precise hint for the variability ranges of the different aerosol microphysical parameters, these have at first been chosen taking into account the continental aerosol climatology data set summarized in the Optical Properties of Aerosol and Clouds (OPAC) database by Hess et al. . Then, several model configurations have been tested varying this “first-guess” assumption.
 To simulate the vertical variability of α, β, and LR (Figure 3), a further random choice is introduced in the model to select, for each computation, the altitude z to which the corresponding optical data (α, β, and LR) should be referred. The vertical dependence of the aerosol microphysical parameters assumed in the model is described in the next section. The z range considered in this study is 0–5 km, which includes the whole lidar data range (0.3–4.5 km).
3.1. Modeled Aerosol Variability With Altitude and Relative Humidity
 As mentioned, the two modes are intended to represent particles from different sources. In continental conditions, fine mode particles are expected to be mainly of anthropogenic origin and mostly composed of water-soluble substances (sulfates, nitrates, and carbonaceous material). Conversely, coarse particles are principally of natural origin (as sea salt), and in continental sites, these are expected to be mainly insoluble soil-derived aerosols. Hence the two modes not only represent particles with different microphysical characteristics (concentration, size distribution, and refractive index) but are also expected to have a different vertical distribution within the atmosphere and different hygroscopic properties. These last two features are taken into account in the model as described below.
 Soil-derived particles are assumed to be nonhygroscopic, whereas for the fine-mode particles, we assume a dependence on the relative humidity (RH) of both the aerosol size and the refractive index [i.e., rm = rm(RH) and m = m(RH)]. On the basis of the results by Hanel  and d’Almeida et al. , the following relationships are used:
with rm,RH and mRH being the RH-corrected modal radius and refractive index, respectively; rm,0 and m0 being the particle dry modal radius and refractive index, respectively; and mw being the water refractive index (assumed as mw = 1.34–i6.5 × 10−9 at 351 nm).
 At each run, given the randomly selected altitude z, the RH value to be employed in equations (4) and (5) is determined through the following relationship:
where dRH is randomly chosen between −0.6 and +0.6. That is, we allow a maximum variability of ±60% with respect to the mean RH(z) profile (this gives, for instance, RH in the range of 20–80% at 1.5 km and in the range of 13–50% at 4 km). The RH(z) profile and the associated variability of equation (6) were chosen in order to include the whole range of measured RH(z) values in the Lecce region [e.g., De Tomasi and Perrone, 2003]. To avoid divergence problems in equation (4), an upper threshold of RH = 98% was fixed (which only affects the lowermost levels, z < 0.3 km).
 In addition to the RH dependence of the aerosol parameters, an exponential decrease with height of the particle number density is assumed for both the fine and the coarse aerosol modes. This is expressed as:
where Ni,z0 is the number of particles of the ith mode at the ground [1 = fine mode (f) and 2 = coarse mode (c)], and Hi is the relevant scale height. In particular, we used the following parameterizations in the model: Hc = 0.8 km and Hf = 5.5 km to rescale the fine and coarse-particle number density, respectively.
 A further dependence on z was introduced for the fine-mode width, σf , which is forced to slightly increase with altitude as:
 Overall, it is clear that equations (4), (5), (7), and (8) affect the vertical distribution of the aerosol microphysical properties and hence the vertical profiles of α, β, and LR.
4. Simulation Results and Comparison With Observations
 The performance of the model is assessed by evaluating its capability to reproduce both the observed vertical variability of β, α, and LR (i.e., the scatterplots in Figures 3a–3c, respectively) and the mutual link between these properties (i.e., the scatterplots in Figures 3d and 3e). In fact, this multiple accordance better guarantees for an appropriate model reproduction of the experimental data and thus for trustworthy model assumptions of the relevant aerosol microphysical properties.
 As mentioned, several model configurations were tested, varying the aerosol microphysical parameters. A total of 10,000 points was generated for each configuration. We proceed by first presenting the model configuration that better fits the experimental results. As detailed in section 4.1, such “optimal model configuration” (OMC) was selected as able to reproduce within ±10% both the mean aerosol vertical variability and the reciprocal link between the aerosol optical properties observed by lidar. After that (section 4.2), we give a summary of the model response to deviations from the OMC to (1) provide an overview of the role played in the simulations by the different parameters and (2) quantify the performance of the OMC with respect to other configurations.
4.1. Optimal Model Configuration
 The best agreement between model and measurements is reached for the aerosol parameter variability reported in Table 1 (OMC). For direct comparison, we also give in Table 1 the OPAC values of the corresponding parameters (“clean continental” aerosol type [Hess et al., 1998]).
Table 1. Values of the Aerosol Parameters Adopted in the Optimal Model Configuration (OMC)a
 OMC simulations in terms of α, β, and LR vertical variability are shown in Figure 4 (grey crosses) together with the experimental data (black dots). Figure 4 shows the OMC results to include the whole α and β ranges observed by lidar. Only a few (high) lidar ratios (≥100 sr) are not reproduced by the model. In this respect, it is worth noticing that an agreement between the modeled and the measured α and β ranges does not necessarily imply an accordance in the LR range. This is because, being defined as α/β, each LR value depends on the particular combination of the two variables. The agreement between the observed and the simulated LR values is therefore a real added value of the model since it indicates a similar combination of the α and β variables in both data sets. As evident in Figure 4, this LR agreement is generally met along the vertical, with few exceptions particularly at the lower altitudes. Figure 5 shows model and lidar results (grey crosses and black dots, respectively) as α versus β and LR versus β scatterplots. Also in this case, model data points are shown to well envelop the values retrieved by lidar and to follow a dependence on β rather similar to that of experimental values.
 To illustrate the results of Figure 4 in terms of mean vertical profiles of α, β, and LR, data from both model and observations have been averaged over different bins of z. The following average values have been defined for each bin of z: 〈αmod〉binz, 〈βmod〉binz, 〈LRmod〉binz (from model data) and 〈αobs〉binz, 〈βobs〉binz, 〈LRobs〉binz (from lidar observations). These are reported in Figure 6 (grey bullets and black empty squares for model and measurement-derived values, respectively; error bars are ±1 s. d.). A total of 10 bins of z have been considered covering the range of 0.6–4.5 km (altitudes lower than 0.6 km have been excluded to avoid lidar retrievals possibly affected by the lidar system overlap problems [e.g., Matthias et al., 2004b]). The altitude range of 0.6–3.3 km has been divided into nine, equally spaced (0.3 km wide) bins. The first bin thus refers to the altitude range of 0.6–0.9 km (i.e., 0.75 ± 0.15 km), while the ninth bin refers to the range of 3.0–3.3 km (i.e., 3.15 ± 0.15 km). A further, larger bin (1.2–km wide) has been chosen for the higher levels (>3.3 km) to include a number of data greater than 1% of the total. The number of experimental data points available in each bin is given in Figure 6d, which clearly shows the decreasing number of measurements with height. The good correspondence between the OMC and the lidar-derived aerosol optical data is evident in Figure 6. Since LR values are generally considered representative of specific aerosol types, it is worth to compare the lidar ratio mean values in Figure 6c to the results derived from similar wide statistics of Raman lidar data (at 350 nm) in other continental sites. A mean LR of 68 ± 12 sr was derived by Ferrare et al.  in north central Oklahoma, USA (1 year data set, average in the altitude range 1-7 km), while a mean LR of 58 ± 12 sr was obtained by Mattis et al.  in Leipzig, Germany (3-year data set, average in the altitude range of 1–3 km). If averaged over analogous layers, lidar ratios of continent-affected aerosol observed in Lecce are comparable although slightly lower: mean lidar ratios of 50 ± 24 and 48 ± 23 sr are obtained, averaging the Lecce data in the ranges of 1–7 and 1–3 km, respectively. Figure 6c shows, however, that the LR vertical variability is not negligible over the Lecce site so that, in this case, averages over such broad layers could be misleading. A wide, altitude-resolved LR statistics (4-year data set) can be found in the paper of Amiridis et al.  based on lidar measurements performed in Thessaloniki (Greece). That study also highlights a marked LR vertical variability. Their 4-year average (which includes all types of aerosol conditions) shows mean LRs of about 80 sr in the lowermost levels (<1000 m), decreasing with altitude and stabilizing around 40 sr above 2 km. In that case, the LR vertical behavior is therefore rather different from the one observed in Lecce (Figure 6c). Amiridis et al.  attribute such high LR values in the lowermost levels to local sources of pollution (particularly affecting the summer months).
Figure 7 shows mean values of α and LR per bin of β (grey bullets and black squares for model and measurement-derived values, respectively; error bars are ±1 s. d.). In this case, the region β < 10−2 km−1 sr−1 has been divided in 10, equally spaced bins (0.001 km−1 sr−1 wide each), and the following quantities have been computed: 〈αmod〉binβ, 〈LRmod〉binβ and 〈αobs〉binβ, 〈LRobs〉binβ. Again, also from this point of view, the good model-measurement correspondence is evident in Figures 7a and 7b. Figure 7c shows the number of experimental data points available in each bin.
 The mean values reported in Figures 6 and 7 can be used to quantify the model-measurement accordance shown in the plots. In fact, for each aerosol optical property, P, we can evaluate a mean model-measurement difference as:
(valid for both z and β bins), where N is the total number of defined bins. For example, in the case of aerosol extinction, we can evaluate the model-measurement mean discrepancy by both:
For the OMC, the 〈dP/P〉bin mean differences are as follows: 〈dα/α〉binz = −2%, 〈dβ/β〉binz = −7%, 〈dLR/LR〉binz = −3%, and 〈dα/α〉binβ = 1%, 〈dLR/LR〉binβ = 0%. These values are summarized in Table 2. As able to reproduce within ±10% both the mean aerosol vertical variability and the reciprocal link between the aerosol optical properties (i.e., all the five 〈dP/P〉bin lower than ±10%), this configuration has thus been selected as “optimal.” Deviations from the OMC produce worse model-measurement correspondence as widely detailed hereafter.
Table 2. Mean Discrepancies Between Model Results and Measurements Evaluated Following Equation (9)a
Values obtained for the optimal model configuration (OMC) are compared to those related to the different sensitivity cases discussed in the text. The asterisk identifies configurations whose results are also shown in figures.
MC1a* (Nc% = 0, i.e., no coarse)
MC1b (Nc%: 0.00–0.02)
MC2a (rmc: 0.3–0.5 μm)
MC2b (rmc: 0.8–1.0 μm)
MC3a* (rmf: 0.025–0.05 μm)
MC3b (rmf: 0.05–0.07 μm)
MC3c (rmf: 0.07–0.10 μm)
MC4a* (mRef: 1.45–1.55)
MC4b (mImf: 0.0025–0.005)
MC5 (N: 1000–2000 cm−3)
OMC_s1* (Hc = 1.0 km)
OMC_s2* (Hc = 0.5 km)
OMC_s3 (z-independent σf)
4.2. Model Sensitivity and Results Discussion
 To better evaluate the proposed optimal model configuration, it is necessary to provide a more general view of the model response and, particularly, to discuss its sensitivity to the variability of the parameters employed. An overview of the impact on model results produced by variations in the OMC input parameters is therefore given hereafter.
4.2.1. Impact of Coarse-Mode Particle Parameters
 The role of the coarse-particle mixing ratio is exemplified in Figure 8, which shows model results obtained removing the contribution of this mode (Nc% = 0). We will refer to this case as model configuration MC1a. The comparison of Figures 8a–8c with Figure 4 makes evident the impact of coarse-mode particles on both aerosol backscatter and extinction values: assuming Nc% = 0, the variability range of α and β extends toward lower values with respect to the OMC. Nevertheless, Figure 8 shows that the effect of Nc% is more marked on the modeled β than on α (reducing Nc% to 0, the lower limit of β decreases more than 1 order of magnitude at z < 1 km). This effect can be quantified through the mean model-measurement differences, 〈dP/P〉bin, introduced in section 4.1. In the MC1a case, we obtain 〈dβ/β〉binz = −39%, while 〈dα/α〉binz = −8% (Table 2). As a consequence, the variability range of LR in Figure 8c extends toward larger values with respect to the one in Figure 4. Besides the latter results, the comparison of Figure 8e to the LR versus β data in Figure 5 very well highlights the important role of the coarse-particle concentration in generating the low LRs retrieved by lidar. Finally, the comparison of Figure 8d to both the OMC and the experimental α versus β scatterplots in Figure 5 allows inferring that contribution of coarse particles is also responsible of the large spread of data observed by lidar. Coarse-mode particles are, on average, characterized by smaller extinction coefficients than fine-mode particles with similar β values. Overall, the MC1a configuration is particularly useful to illustrate the effect of coarse-particle concentrations on simulations, but it certainly represents a rather drastic change with respect to the OMC (in which Nc% ranges between 0.01 and 0.02). However, though in a less pronounced manner, similar results are also obtained if, rather than setting it to zero, we simply extend to zero the Nc% variability adopted in the OMC (configuration indicated as MC1b). For conciseness, model data provided by the MC1b run are not shown in the paper. However, we provide in Table 2 the relevant 〈dP/P〉bin values. These show that the downward extension of the Nc% range to 0 has little effect on the aerosol extinction (〈dα/α〉binz = −3%) but produces a noteworthy underestimation of β (〈dβ/β〉binz = −16%) and an overestimation of LR (〈dLR/LR〉binz = +11%). In conclusion, the above presented sensitivity studies show that if no (or too few) coarse particles are included in the model, we obtain too low β values and, thus, too high LRs. This is one of the main differences we found with respect to the climatological (OPAC) data of Table 1, which propose a very low mixing ratio of these particles.
 Since the scale height Hc regulates the exponential decrease of the coarse particles in the atmosphere (section 3.1), it affects the modeled vertical variability of the aerosol optical properties, and particularly β(z). Reproduction of the way β reduces with height as observed by the Lecce lidar has indeed been particularly intricate. Having no precise hint for evaluating Hc, we have proceeded by the trial and error technique, considering a reasonable particle concentration reduction of about one third in the first 500- to 1000-m altitudes. We give in Table 2 the 〈dP/P〉bin values corresponding to model simulations performed with Hc = 1.0 km (OMC_s1 run) and with Hc = 0.5 km (OMC_s2 run). The value of Hc = 0.8 km allowed us to get the best correspondence between observed and simulated β(z), α(z), and LR(z) profiles and is therefore implemented in the model. Note that Hc = 0.8 km is used for the OMC run and for all the other model configurations (MC) presented here (except, evidently, for the OMC_s1 and OMC_s2 cases, which are therefore named in such different way). Table 2 shows that increasing Hc from 0.8 to 1.0 km (OMC_s1 run) produces, on average, larger β(z) values (〈dβ/β〉binz = +10%), while α(z) is poorly affected by this modification (〈dα/α〉binz = +1%). As a consequence, LR(z) mean values tend to be underestimated (〈dLR/LR〉binz = −16%). Consistently, the decrease of Hc from 0.8 to 0.5 km (OMC_s2 run) leads to smaller β(z) mean values (〈dβ/β〉binz = −27%) and larger LR(z) mean values (〈dLR/LR〉binz = +16%). To better illustrate these effects on the vertical scale, in Figure 9 we compare the altitude-binned OMC values of β(z) and LR(z) (grey bullets) to the corresponding OMC_s1 and OMC_s2 ones (black triangles and black diamonds, respectively). Minor variations are found for α(z) that is thus omitted in Figure 9. The lidar-derived, altitude-binned β and LR are also shown in Figure 9 for direct comparison (black empty squares). Figure 9 clearly explains the 〈dP/P〉bin values commented above and further allows to evaluate the model-measurement discrepancies along the vertical in the different configurations.
 Changes in the size of coarse-mode particles also have their main impact on the aerosol backscatter. Modal radius (rmc) values higher (lower) than the OMC ones increase the contribution of model-generated points with higher (lower) β. Results from two different model configurations, obtained modifying the OMC-rmc variability, are provided in Table 2 (MC2a and MC2b). In the MC2a configuration, the OMC-rmc range (i.e., 0.4–0.5 μm) is extended to 0.3–0.5 μm, thus including coarse particles of smaller size. Differently, the MC2b configuration has been obtained shifting the OMC-rmc variability range toward quite large sizes (rmc range of 0.8–1.0 μm in this case). As evident from Table 2, the presence of smaller coarse particles (MC2a) produces, on average, β values slightly lower than the ones measured by lidar (〈dβ/β〉binz = −13%). Conversely, α and LR are weakly affected by the rmc variability extension adopted in MC2a (〈dα/α〉binz = −3% and 〈dLR/LR〉binz = +1%). The MC2b assumption of larger coarse particles leads to too high β and α values (〈dβ/β〉binz = +21%; 〈dα/α〉binz = +16%), which however combine into a minor effect on LR (〈dLR/LR〉binz = −6%). For brevity, scatterplots of MC2a and MC2b results are not shown here. It is however worth mentioning that these sensitivity cases also highlight a dependence of the α versus β data dispersion on rmc. In particular, Figure 5 shows the α versus β lidar data dispersion to reduce for β > 10−2 km−1 sr−1 and the OMC to well reproduce this trend. This feature is partly altered for the rmc variability of MC2a and is completely lost for MC2b.
4.2.2. Impact of the Fine-Mode Particles Parameters
 The effect of the fine-particle modal radius (rmf) on the model response is illustrated in Figure 10. This shows the results obtained, reducing by 50% both the lower and the upper limits of the OMC rmf variability range (which we recall to be 0.05–0.10 μm). This configuration (referred to as MC3a) thus assumes the (dry) rmf to vary in the 0.025- to 0.05-μm range. As expected, compared with the OMC, MC3a leads to lower α and β values which, in this case, combine producing LR values lower than those observed. Results in Figures 10a–10c highlight α to be more affected by rmf changes than β. Table 2 also provides the quantitative evaluation of the remarkable model-measurement differences found in the MC3a case (these are the following: 〈dα/α〉binz = −85%, 〈dβ/β〉binz = −61%, and 〈dLR/LR〉binz = −61%). Moreover, Figures 10d and 10e show the assumption of smaller fine-mode particles to significantly alter the dependence of both α and LR on β. Evidently, the MC3a case does not simulate correctly the observed behavior of α versus β and LR versus β, and it completely fails in providing the high α and LR values retrieved by lidar measurements for 10−3 km−1sr−1 < β < 10−2 km−1sr−1. Again, the MC3a sensitivity case is certainly instructive but is based on a significant modification of the OMC input data. Therefore we include in Table 2 the results from two other cases in which the OMC rmf variability range (0.05–0.10 μm) is only reduced: this is 0.05–0.07 μm in the MC3b and is 0.07–0.1 μm in the MC3c. The first sensitivity test shows that the decrease of the OMC rmf upper limit from 0.10 to 0.07 μm (MC3b) produces a remarkable model underestimation of the lidar data (mean model-measurement differences as large as −49, −38, and −21% for α(z), β(z), and LR(z) values, respectively). On the contrary, the increase of the OMC rmf lower limit from 0.05 to 0.07 μm (MC3c) leads to quite high, positive mean model-measurement differences (+50, +28, and +15% for α(z), β(z), and LR(z) values, respectively).
 Sensitivity studies on the impact of the real part of the fine-mode refractive index (mRef) are rather useful to illustrate how model input changes producing minor effects on β(z) and α(z) can still affect significantly the α versus β relationship (and thus the α-to-β ratio). Figure 11 shows the data obtained by replacing the (dry) OMC mRef variability range (1.35–1.55) with the narrower one (1.45–1.55; configuration indicated as MC4a). Figures 11a and 11b show the modeled α(z) and β(z) data to well envelop the corresponding experimental data, so that a dependence on z similar to the observed one is derived for MC4a (〈dβ/β〉binz = +4%; 〈dα/α〉binz = +6%, see Table 2). Nonetheless, the comparison of Figures 11d and 11e with Figure 5 highlights some noteworthy differences. The upper limit of the modeled extinction is lower in the whole β range. As a consequence, MC4a gives a reduced dispersion of LR values (which are mostly confined below ≈ 85 sr). Figure 11c reveals this LR underestimation to mainly occur at the higher altitudes, where, due to the lower RHs [equation (5)], mRef values actually used in the computations are closer to the dry ones. In conclusion, the reduction of the OMC mRef variability range to 1.45–1.55 translates into 〈dP/P〉bin values slightly larger than those of the OMC, with maximum model-measurement discrepancies of −10% for the 〈dLR/LR〉binz parameter (Table 2). The critical point of the MC4a configuration is therefore its inability to correctly simulate the several observed high (>85 sr) lidar ratios.
 A similar effect on LR is also obtained reducing the mImf variability (not shown), since this implies less particle absorption (thus less extinction) and a higher backscatter. As an example, in Table 2, we include the 〈dP/P〉bin results calculated for the MC4b configuration in which the mImf upper limit has been set at 0.005 (i.e., equal to one fourth of the OMC one and equal to the climatological mImf value in the study of Hess et al. ). Again, the MC4b configuration provides maximum model-measurement discrepancies of −10% for the 〈dLR/LR〉binz parameter (Table 2), and it fails in providing the highest observed LRs (>100 sr). As a matter of fact, the mImf upper limit of the OMC is quite higher than the recommended OPAC value. However, we need to include such high mImf in our model to better describe the measurements (i.e., generate the highest LR observed). We believe this partly overcome the omission in our model of a third aerosol mode describing soot particles. In fact, the contribution of soot particles in moderately to highly polluted regions is generally accounted for by introducing a third mode of nonhygroscopic, very fine (rm ≈ 0.01 μm), highly absorbing (mImf > 0.4) particles [e.g., Hess et al., 1998; Barnaba and Gobbi, 2004b]. To simulate the Lecce’s lidar measurements under continental conditions, this further element of complexity is revealed to be unnecessary, provided that moderately absorbing properties are included in the water-soluble fine-mode aerosols (reasonably simulating internal mixing of water-soluble substances with more absorbing material). In fact, some supplementary sensitivity tests have shown that an addition of a third aerosol mode described by such particle properties (rm ≈ 0.01 μm, mImf ≈ 0.4), even if accounting for 50% of the total number of particles N, does not improve the accordance between modeled and experimental data. Conversely, this leads to too low α and β values and does not even contribute to generate the high LRs derived by lidar measurements at the lower altitudes (as one could expect, given the high mImf value of these particles). This is because the main fine-mode parameter driving α (and thus LR) values is the particle size (see the above discussion on rmf variations). Therefore contribution of absorbing particles on the extinction of externally mixed aerosols strongly depends on the relative size of the different particle types. If absorbing particles are too small with respect to the ones of the water-soluble mode, their impact on the total extinction can still be negligible. In fact, the OMC results in Figures 4 and 5 well prove that high LRs (>75 sr) are not necessarily related to the presence of (externally mixed) small, highly absorbing (pollution-associated) particles. We can thus assume that the good results obtained with the OMC indicate an internal mixing of water-soluble fine-mode aerosols with absorbing material in the Lecce case (simulated by allowing water-soluble aerosols to be described by mif values as high as 0.02).
 The width of the fine-mode size distribution, σf, also merits a comment. As indicated in Table 1, the σf variability range at the ground is 1.35–1.7, but a slight increase of σf with altitude has been introduced in the model [see section 3.1; scale height of 30 km in equation (8)]. If no increase of σf with altitude is assumed (sensitivity case referred to as OMC_s3), we obtain vertical distributions of the aerosol optical parameters similar to those of OMC and lidar data (Figure 4) only in the first 2 km. Conversely, for z > 2 km, a faster decrease with altitude of the α(z)- and β(z)-range lower limit is derived. This effect is more pronounced on the aerosol extinction, so that the LR(z) lower limit also tends to decrease with altitude more quickly than observed. 〈dP/P〉bin values for the OMC_s3 configuration are given in Table 2. To the best of our knowledge, a very scarce information exists on changes of the size distribution width with altitude. Our results indirectly suggest a broadening of the particles size distribution with altitude. This is possibly a consequence of particle processing acting more efficiently when increasing distance from the main aerosol sources (expected to be located in the planetary boundary layer).
 As done for Hc, some sensitivity tests on Hf were performed. Results comparable to those provided by the OMC run are obtained, for example, by increasing Hf from 5.5 to 6 km or by decreasing it down to 5 km.
 A last case is provided in Table 2 (MC5) which quantifies the effect of changing the total particle number density at the ground, N. In general, as one expects, the increase (decrease) of N increases (decreases) the mean α(z) and β(z) values with respect to those of Figure 4, leaving almost unaffected the lidar ratio values. In the MC5 case, the N variability range has been limited to 1000–2000 particles/cm3 (it is 1000–3000 particles/cm3 in the OMC). We observe from Table 2 that this produces 〈dβ/β〉binz = −27% and 〈dα/α〉binz = −30% (while 〈dLR/LR〉binz = −3%).
5. The Altitude-Dependent Relationship Between α and β
 The relationship linking aerosol extinction to its backscatter is important when aerosol optical properties are investigated by means of elastic lidars rather than more complex systems such as Raman lidars. In fact, while the two-wavelength Raman lidar configuration allows the independent retrieval of α and β [e.g., Ansmann et al., 1992], a predefined link between these is necessary to invert single-wavelength (elastic) lidar signals. On the other hand, elastic lidars are simpler and generally more compact instruments with respect to Raman ones and are becoming widely employed (e.g., MPLNET [Welton et al., 2001] and ADNET [Murayama et al., 2001]). Generally, a constant, z-independent lidar ratio (α/β) is assumed to solve the mentioned inversion problem, the value of LR being chosen on the basis of data available in literature [e.g., Pappalardo and The EARLINET Lidar Ratio Team, 2005). To improve the retrieval of aerosol optical properties from elastic lidars, an original approach has been developed in the last years [Barnaba and Gobbi, 2001; Barnaba and Gobbi, 2004b]. This approach employs aerosol simulations to link the aerosol extinction to its backscatter and takes advantage of this link (i.e., a functional relationship between α and β) to avoid the choice of a predefined, constant LR. For the Lecce lidar, such functional relationships have already been derived and tested for measurements affected by Saharan dust and maritime aerosols [Barnaba et al., 2004]. Since the OMC data provide a rather good representation of the aerosol properties observed over southeast Italy in continent-affected conditions, these have been fitted to obtain a “continental,” altitude-dependent relationship between α and β (α = f(β, z)). The double dependence of α on β and z avoids the typical choice of a z-independent LR value (which, on average, is not the case in Lecce, as shown in Figures 4 and 8).
 The following relationship has been found to describe the OMC data quite well (fit correlation coefficient r = 0.92):
with a = 1.5079, b = 1.0169, and c = 0.0993.
 In Figure 12, we compare the vertical variability of the aerosol extinction as derived from the observations (black squares), the OMC simulation (grey crosses), and the fit-derived relationship [i.e., equation (12)] using the OMC values of β and z (black circles). The fit-derived, α-average values per bin of z, 〈αfit〉binz, are given in Figure 13 (black triangles). The corresponding model and lidar-derived average values, 〈αmod〉binz and 〈αobs〉binz, are also displayed in the plot for direct comparison (grey bullets and black empty squares, respectively). Figure 13 shows the fit-derived mean values of extinction to well follow the measurement-derived trend, with some underestimation between 1.5 and 3 km. The mean discrepancy between the fit- and the measurement-derived average values is −15% (i.e., 〈dα/α〉binz = (1/10) × Σbinz [(〈αfit〉binz − 〈αobs〉binz)/〈αobs〉binz] = −15%). Figure 14 shows α-average values per bin of backscatter (〈αfit〉binβ) (black triangles) together with 〈αmod〉binβ and 〈αobs〉binβ (grey bullets and black squares, respectively). Again, the fit is shown to well follow the lidar-derived trend, with some underestimation of the lidar measurements for β > 7 × 10−3 (which, however, is the region with a limited number of measurements; see Figure 7). In this case, the mean discrepancy between fit- and measurement-derived average data is -6%.
 These results propose the derived relationship α = f(β, z) [equation (12)] as a useful tool in the inversion of elastic lidar signals in aerosol conditions similar to those addressed in the present study.
6. Summary and Conclusions
 A closure study between observed and simulated aerosol optical properties has been performed with the main aim of constraining the relevant microphysical properties of the aerosol particles monitored by lidar at Lecce (southeast Italy) in continental conditions. A 2.5-year Raman lidar data set of aerosol optical data (aerosol extinction, α; backscatter, β; and lidar ratio, LR = α/β at 351 nm) collected in the framework of the EARLINET project has been employed. Selection of continental conditions in the data set has been performed on the basis of back trajectory analysis. A total of 76 measurements days have been selected as related to advection of air masses from the European continent. A total of 559 lidar data points have been employed.
 A specific numerical model has been set up to reproduce the observed vertical variability of the aerosol optical properties [i.e., α(z), β(z), and LR(z)] and their mutual link. Optical computations have been performed on the basis of aerosol microphysical properties (for example, particle size distribution and refractive index). Wide ranges of simulated α, β, and LR have been obtained by randomly varying, in each computation, the aerosol microphysical parameters within appropriate ranges. Vertical variability has been introduced in the model through particle number density scaling with altitude (z) and particle property dependence on relative humidity [which also has a vertical dependence, RH(z)]. Several tests have been performed by modifying the variability range of all the aerosol microphysical properties describing the aerosol size distribution and composition. An optimal model configuration (OMC) has been determined which reproduces within ±10% the mean continental aerosol optical properties observed, including their vertical pattern. The aerosol microphysical properties which define this OMC (Table 1) are believed to provide a useful indication of the type of particles characterizing the continent-affected cases investigated.
 Results indicate that continental aerosols over Lecce can be well described by a bimodal lognormal size distribution, with a fine mode representing water-soluble substances (likely sulfates, nitrates, and organics), and with a coarse mode representing nonhygroscopic soil-derived particles. The OMC fine mode has a dry modal radius (rmf) in the range of 0.05–0.10 μm [the dependence of rmf on RH(z) modulates its vertical variability], while the OMC coarse mode has a modal radius (rmc) of 0.4–0.5 μm. The variability of rmf in the model is shown to impact the simulated aerosol extinction more than the corresponding backscatter. As a consequence, the assumed variability of rmf is crucial in determining the variability range of the lidar ratio. The OMC rmf variability allows to well reproduce the lidar-derived α, β, and LR variability, with the exception of few points, associated to very high (>100 sr) LRs. Although the fine mode accounts for the quasi totality of the particle number density (98–99% at the ground level), the optical role of the coarse particles has been found to be relevant. A coarse-mode particle number density contribution between 1 and 2% (at the ground level) has been necessary to well fit the lidar data, with its vertical scaling being decisive in reproducing the observed β(z) vertical behavior. The rapid decrease with altitude of the number of coarse particles (a scale height Hc = 0.8 km is adopted in the model) mainly drives the observed increase of LR with z.
 On average, rather “clean” continental aerosols characterize southeast Italy even under the influence of the European air masses. A satisfactory agreement between simulations and observations has indeed been found assuming the (dry) fine-mode imaginary refractive index (mImf) to be variable in the range of 0.0025–0.005 [this latter being the typical “climatological value” for water-soluble substances, e.g., Hess et al., 1998]. However, in the OMC, the mImf variability is extended to 0.02 since this allows generating some of the high LRs observed by lidar (thus optimizing the general model-measurement comparison). This result, combined with sensitivity tests on the effects of external mixing with soot-like spherical particles, allows us to infer cases of internal mixing of water-soluble substances with more absorbing material in the Lecce conditions. Results of this study also suggest a broadening of the size distribution with height.
 As a further result of this investigation, an altitude-dependent functional relationship linking α and β (α = f(β, z)) has been determined based on the OMC results. When the lidar Raman channel cannot be used (for example, in daylight conditions), the use of this “continental aerosol” relationship can help solve the elastic channel equation, avoiding the choice of a fixed, preassigned LR value as often done.
 Recent results demonstrate that the statistics of aerosol optical depth derived by ground-based instrumentation in the Lecce site is in very good accordance with the corresponding satellite-based statistics obtained for a 300 × 300-km region centered in Lecce [Santese et al., 2007]. We therefore believe that the aerosol properties discussed in this study can be considered representative of such an extended area of the central-eastern Mediterranean and, more in general, of central-eastern Mediterranean coastal regions far away from large cities and/or industrial areas. In fact, results different from the Lecce ones have been obtained by Amiridis et al.  using a similar, wide lidar statistics in Thessaloniki (Greece). In particular, mean lidar ratios larger than those observed in Lecce have been found to characterize the lowermost levels (<1500 m) in Thessaloniki due likely to the larger impact of local pollution in such industrialized coastal site.
Asian Dust Network
Aerosol Robotic Network
Cloud Aerosol Lidar and Infrared Pathfinder Satellite Observations
Commonwealth of Independent States Lidar Network
European Aerosol Research Lidar Network
Moderate-Resolution Imaging Spectroradiometer
Micro Pulse Lidar Network
Optical Properties of Aerosol and Clouds (software package)
Polarization and Directionality of the Earth Reflectance
 This work has been supported by the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca” (Programma di Ricerca 2004, Prot. 2004023854) and by the EARLINET project (European Commission grant EVR1-CT1999-40003). Back trajectory analysis was performed by the German Weather Service using an IDL code provided by I. Mattis (IFT, Germany).