Corresponding author: Y. Derimian, LOA, Université de Lille1/CNRS, Bat. P5, Universite Lille1, F-59655 Villeneuve d'Ascq, France. (email@example.com)
 In this work we characterize optical properties and assess the direct radiative effect of an ash plume observed on April 17, 2010 by AERONET, lidar and broadband solar flux measurements collocated on the roof of the Laboratory of Atmospheric Optics in Lille, northern France. These measurements allowed experimental evaluation of ash radiative impact and validation of simulations. The derived aerosol model of ash is characterized by a bi-modal size distribution dominated by coarse mode centered at a radius of 1.5 μm and by relatively strong absorption at short wavelengths (single scattering albedo of 0.81 ± 0.02 at 440 nm as opposed to 0.92 ± 0.02 at 670, 870 and 1020 nm). Due to relatively low aerosol optical thickness during the ash plume transport (∼0.26 at 440 nm), which is unfavorable for AERONET retrievals, the uncertainties in derived ash aerosol model were additionally evaluated. The complex refractive index of ash was derived assuming that effective refractive index retrieved by AERONET for externally mixed bi-component aerosol can be approximated as an average of refractive indices of two components weighted by their volume concentrations. Evaluation of the accuracy of this approximation showed acceptably small errors in simulations of single scattering albedo and aerosol phase function over the range of scattering angles observed by the AERONET almucantar. Daily average radiative forcing efficiency of ash calculated for a land surface reflectance representing Lille was about −93 ± 12 Wm−2τ550−1 and −31 ± 2 Wm−2τ550−1 at the bottom and top of the atmosphere; the values for an ocean surface reflectance are also provided.
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 In April 2010 a plume of volcanic ash from the Eyjafjallajökull volcano eruption in Iceland significantly affected the European airspace. The numerous flight cancellations, consequent inconvenience and impact on economy from this event had drew attention to the need for forecasting of the volcanic ash dispersion and concentrations, and for detecting and characterizing volcanic ash using different types of measurements, including space-borne, airborne and ground-based remote sensing [e.g., Emeis et al., 2011; Francis et al., 2012; Kristiansen et al., 2012; Leadbetter et al., 2012; Schumann et al., 2011; Stohl et al., 2011]. Despite significant experience in remote sensing observations of natural and anthropogenic atmospheric aerosol particles, such as mineral dust, sea salt, biomass burning, urban and industrial pollution, volcanic ash particles are still poorly characterized. Among the requirements necessary for accurate forecasting of the volcanic ash dispersion and concentrations are the microphysical and optical properties of the aerosol particles such as size distribution, shape of particles and complex refractive index. In addition, due to abilities of volcanic particles to absorb and scatter light, an ash layer can perturb incoming and outgoing solar radiation, and modify surface temperature or gradient of atmospheric temperature and therefore affect atmospheric dynamics. In the past, it was also found that during the long-range transport in the stratosphere the volcanic particles can significantly affect global climate. For instance, after the Pinatubo eruption in 1991 a large amount of volcanic aerosols were ejected into the stratosphere and had forced the Earth's climate during the consequent years. A peak of the global mean of the Pinatubo eruption aerosol radiative forcing at the top of the atmosphere was estimated of about −4.5 Wm−2 [Hansen et al., 1992]. A recently published study by Solomon et al.  suggests that even in the absence of major volcanic eruptions volcanic plumes significantly contribute to climate cooling while supplying aerosol to the stratosphere. Therefore, characterization of optical properties and radiative forcing of volcanic airborne particles is of interest for studies on local and global scales. In addition, evaluation of optical properties of volcanic airborne particles can improve the ability to detect volcanic events and estimate their significance by satellite or ground-based remote sensing techniques.
 Present activity of Iceland's volcanoes suggests probable new eruptions with the atmospheric conditions similar to those of April 2010. At the same time, it has to be noted that different eruptions and even different stages of the same eruption may supply particles of different size and composition [e.g., Ilyinskaya et al., 2011]. Nevertheless, we need detailed studies of particular eruptions to begin to understand volcanic ash properties. In this work we investigate optical properties and radiative forcing derived from remote sensing observations of ambient volcanic aerosol during the Eyjafjallajökull eruption. The analyzed observations were conducted by several instruments collocated on the roof of the Laboratory of Atmospheric Optics (LOA) in Villeneuve d'Ascq, vicinity of Lille, northern France, during the fourth day of the volcano eruption (April 17, 2010) when the plume reached the area. This work is conducted in conjunction with other studies at LOA dedicated to detection and characterization of ash plumes by ground-based (A. Mortier et al., manuscript in preparation, 2012) and satellite (D. Tanre et al., manuscript in preparation, 2012) remote sensing during the period from April to May, 2010. In the present study we focus on detailed analysis of ash optical properties and radiative impact using ground-based observations during favorable clear-sky atmospheric conditions. In addition, accurate and well-characterized observations of aerosol before and after arrival of the volcanic plume allowed us to test an approximation for calculating complex refractive index of externally mixed aerosol. The simultaneous measurements by a sun/sky photometer (part of the AERONET/PHOTONS network), a broadband solar flux at the surface, and a lidar system operated by LOA are employed in the experimental part of this study. Then, the rigorous numerical simulations of aerosol optical characteristics, atmospheric radiances, and broadband solar fluxes are employed to explain and interpret the measurements. Finally, we provide a derived microphysical model and assess the direct radiative forcing and forcing efficiency of the observed volcanic ash aerosol.
2. Instrumentation and Numerical Modeling
 The instrument setup that we use is located on the roof of the LOA and includes: (i) a CIMEL sun/sky photometer, (operated in the framework of the AERONET/PHOTONS program; (ii) a Kipp and Zonen CM22 pyranometer and CH1 pyrheliometer; and (iii) a CIMEL micro-pulse backscattering lidar system.
 In addition, some specific numerical simulations of atmospheric radiation characteristics were conduced using modifications of the AERONET operational code.
2.1. Numerical Simulations
 The AERONET operational inversion code and some adaptations of this code are used here in a research mode. The code is described in Dubovik and King  and Dubovik et al. [2002b, 2006, 2000]. Additionally some aspects of the latest modifications of the code, such as, accounting for particle non-sphericity in the operational version, were reviewed and summarized in the recent paper by Dubovik et al. . The code retrieves the aerosol size distribution and complex refractive index from the angular and spectral intensity distribution of atmospheric radiation measured by a sun/sky photometer from the ground. The retrieval algorithm simultaneously fits spectral optical thickness and spectral and angular distribution of atmospheric radiances. The aerosol single scattering properties in this algorithm are modeled using a subset of kernel look-up tables produced for a set of size parameters, complex refractive indices and fraction of spherical particles [Dubovik et al., 2011] using an assumed aspect ratio distribution of prolate/oblate spheroids [Dubovik et al., 2006]. The aspect ratio distribution used can closely reproduce single-scattering matrices of mineral dust measured in the laboratory by Volten et al. . The multiple scattering effects, required for modeling the angular distribution of atmospheric radiances, are accounted for using discrete ordinates radiative transfer code (DISORT) [Nakajima and Tanaka, 1988; Stamnes et al., 1988]. The employed numerical inversion uses a multiterm Least Squares Method concept [Dubovik, 2004; Dubovik and King, 2000].
 In addition, we use the forward simulation module of the AERONET inversion code for modeling atmospheric radiances in specific atmospheric conditions. Namely, the forward simulation module was adopted for modeling a scenario of externally mixed aerosol particles. Externally mixed aerosol is composed of two types of aerosol mixed together within the same plume/layer, but with no interactions between particles. In the case of internally mixed particles all individual particles are mixtures of several originally different aerosol components. In this paper we study the observations of two separate layers that can, for optical reasons, be assumed as externally mixed at the same height. The external mixture was modeled as a composition of two aerosol components with different size distributions and complex refractive indices.
 The broadband solar fluxes were simulated using an aerosol model derived from the AERONET observations. A module of the radiative transfer model GAME (Global Atmospheric ModEl) [Dubuisson et al., 1996, 2006; Roger et al., 2006] that is integrated into the operational AERONET inversion code provides the fluxes and aerosol radiative forcing values as a part of the AERONET operational product. This module of GAME accurately accounts for the molecular scattering and the gaseous absorption (mainly H2O, CO2, and O3). Gaseous absorption is calculated by utilizing the correlated k-distribution [Lacis and Oinas, 1991] that allows broadband fluxes simulations with acceptably short computational time. The coefficients of the correlated k-distribution have been estimated from reference calculations using a line-by-line code [Dubuisson et al., 2004]. The gaseous content in the atmospheric column is assessed from: (1) AERONET retrieval of the instantaneous water vapor content using the absorption differential method at the 0.94 μm channel [Smirnov et al., 2000]; (2) the monthly climatology values of the total ozone content obtained from NASA Total Ozone Mapping Spectrometer (TOMS) measurements from 1978 to 2004; and (3) the atmospheric gaseous profiles of U.S. standard 1976 atmosphere model. Since we are estimating the aerosol impact at different times for the same day, the uncertainties resulting from the profile or ozone concentration are expected to be minor.
 The broadband flux was obtained by integration of spectral irradiances computed for more than 200 spectral intervals in the range of wavelengths from 0.2 to 4.0 μm. Hence, the extinction, single scattering albedo and phase function were calculated for these spectral intervals using the retrieved size distribution, complex refractive index and nonsphericity fraction. The values of the complex refractive index were linearly interpolated or extrapolated from the values retrieved at AERONET operational wavelengths. The effects of multiple scattering in broadband integration were accounted by discrete ordinates radiative transfer code. The details of the aerosol phase function were taken into account using a 12-moment expansion of Legendre polynomials. The surface spectral reflectance was modeled using climatological values provided by the MODIS space instrument that are spectrally interpolated or extrapolated in a similar manner to what was done for the complex refractive index.
 The calculated broadband fluxes were compared with surface flux measurements collected during the AMMA campaign by Derimian et al.  and with measurements of the global SolRad-Net and BSRN solar networks by Garcia et al. . Both comparisons found rather good agreement between AERONET simulated fluxes and the measurements (generally within about 10%).
 Finally, the inversions of the almucantar scans on April 17 were processed offline in order to provide analysis of the retrievals errors. The computed errors include two components: a random and a systematic error. The covariance matrix was calculated using equation (15) from the paper by Dubovik . The detailed description of the random component is given by equation (5) in the paper by Dubovik et al. . The measurement biases needed to estimate the systematic component were modeled by the known values of calibration errors for both sun and sky-scanning observations. The values of model biases were accounted by misfit of observations by the model. The systematic component was estimated using two scenarios with adding and subtracting of the measurement biases caused by calibration uncertainty. These errors are computed as a part of the inversion scheme, but they are not currently available at the AERONET website. The errors for each parameter of average model including concentration of aerosol size distribution bins and spectral values of complex refractive indices were estimated using the equation: , where Δxi is the error of each individual retrieval.
2.2. Sun/Sky Photometer
 A CIMEL sun/sky photometer of PHOTONS, which is the French part of AERONET [Holben et al., 1998] is used in this study. The photometer performs direct sun measurements at the 440, 500, 675, 870, 940, and 1020 nm nominal wavelengths. The 940 nm channel is used to retrieve water vapor content. The angular distribution of sky radiance is also measured at 440, 670, 870, and 1020 nm. These sky radiances, together with aerosol optical thickness (AOT or τ) measured at the same wavelengths, are used to retrieve aerosol size distribution, complex refractive index etc., as described by Dubovik and King . The latest retrieval scheme also considers aerosol mixture of polydisperse, randomly oriented homogeneous spheroids [Mishchenko et al., 1997] with a fixed distribution of aspect ratios [Dubovik et al., 2006, 2011] and provides the fraction (here we use percentage) of spherical particles. The AERONET retrieval products used in this study were collected under cloud-free conditions as labeled on the AERONET web site as “Version 2 (V2) inversion products” using the Smirnov et al.  cloud-screening algorithm.
2.3. Pyranometer and Normal Incidence Pyrheliometer
 The downward broadband solar radiative flux at the surface is measured in the spectral range from 200 to 3600 nm using the Kipp and Zonen CM22 pyranometer with a time step of 1 min. In order to measure the diffuse radiation, a 60 mm diameter sphere shadower tracks the sun and intercepts the direct solar radiation. The downward broadband solar direct radiative flux, in the spectral range from 200 to 4000 nm, is measured by the Kipp and Zonen CH1 pyrheliometer in a full angle of 5° ± 0.2°. The total radiative flux at the surface is then calculated as the sum of the measured diffuse and direct fluxes. The calibration tests are periodically applied to these instruments. The pyranometer and pyrheliometer sensitivity to the temperature is corrected for. The relative error between the total flux that can be measured by the pyranometer with the shadower removed and the one resulting from the sum of the diffuse and direct flux is normally expected to be within 1%. The reasons responsible for this discrepancy are the minor derivations in proper shadowing of the pyranometer, and the differences in the upper spectral range of the pyranometer and the pyrheliometer.
2.4. Lidar Observations
 Lidar measurements are performed continuously by LOA using a CIMEL 532 nm micro-pulse backscattering eye-safe lidar. The lidar measurements were conducted and processed in coordination with the collocated co-incident photometer observations. The collected data are available at http://www-loa.univ-lille1.fr/Instruments/lidar/. Inversions of lidar data are performed following the classical Klett/Fernald method. For daytime processing, Sun photometer AOT is used to retrieve the extinction profiles and lidar ratio. However, since no Sun photometer data are available during nighttime, a prescribed lidar ratio is used for retrieval of the extinction profiles. In order to minimize impact of this a priori assumption, we use the last in the evening and the first in the morning lidar ratios that are retrieved using the AERONET AOT measurements. These assumptions remain reasonably valid if there is no significant change in the aerosol properties between the two inversion times (daytime and nighttime, as considered here). Usually the AERONET AOT measurements are available a short time before (after) sunset (sunrise). Therefore, the described approach allows us to derive AOT at 532 nm during nighttime through the vertical integration of extinction coefficient as provided by the lidar. Good matching of the lidar AOTs before and after midnight (based on last and first AERONET AOTs from two successive days) can be used as an indication of the approach validity. According to our results, the continuity criterion was well satisfied for observations presented in this work. More detailed description of the lidar data processing and ash observations are in preparation by Mortier et al. (manuscript in preparation, 2012).
3. Case Study Description
 Active eruption of the Eyjafjallajökull volcano started on April 14 producing a gray ash-rich cloud that lofted to 5–10 km in height and was carried by winds toward the southeast and Europe. This phase of the eruption lasted until midnight on April 17, afterwards the character and intensity of the eruption changed, but continued in different phases until May 23, e.g. [Schumann et al., 2011; Zehner, 2010]. Figure 1 shows the AERONET and lidar observations over Lille during three consecutive days, April 16, 17 and 18, 2010. It presents AOT at 500 nm and Angstrom exponent calculated between 870 nm and 440 nm as measured by AERONET, as well as AOT at 532 nm derived from the lidar measurements and the total lidar backscatter signal at 532 nm. The lidar signal during April 16 is strongly attenuated during almost the whole day by an opaque layer at an altitude of about one kilometer, which is the typical situation when clouds are present. Due to the presence of clouds there were no AERONET aerosol data available on that day. In the evening of April 16th the lower layer becomes transparent to the lidar, which then detected an aerosol layer at the altitude of about 2 km with AOT of 0.2–0.4 retrieved from the lidar data. However, there are no AERONET observations at this time (after the sunset) and it is not possible to obtain information on the details of aerosol model. On April 17, lidar observations show arrival of an aerosol layer at the altitude of about 2 km that sharply modified aerosol properties as observed by AERONET. In this event the background aerosol that predominantly consists of fine particles from urban/industrial pollution was perturbed by the significant presence of coarse particles. In the bottom panel of Figure 1 a sharp decrease of Angstrom exponent (from about 1.2 to 0.7) is associated with an increase in AOT at 500 nm (from about 0.15 to 0.23) at 15:30 UTC, which indicates possible change in the aerosol type over the site. The lidar signal, presented in Figure 1a), unfortunately has a gap in the data acquisition exactly during this time; however, the measurements exist starting from about 18:20 UTC and continue throughout the night and into the next day. These measurements clearly show an aerosol layer transported at the altitude of about 2 km with the lidar-derived AOT reaching 0.75. A backward trajectory in Figure 2 that ends at Lille at 15:00 UTC (agreeing with trajectories ending at 18:00 UTC) indicates the air originated from the northwest having passed over Iceland and suggests a volcanic ash aerosol origin. Relatively low Angstrom exponent values observed during the next day of April 18 (0.6–0.8 in the beginning of the day) also show the significant presence of coarse particles. However, AOT on April 18 is quite variable and there are no low AOT values that may refer to the background aerosol. Alternatively, a sharp change in the measured AOT before and after the entrance of the plume on April 17 can be identified and the AOT values before and during the plume are fairly steady. Therefore, we choose April 17 as an episode with favorable conditions for deriving optical characteristics and radiative forcing of ash airborne particles. Identification of the analyzed episode is also based on analysis of a longer period of observations and conclusions provided by Tanre et al. (manuscript in preparation, 2012) and Mortier et al. (manuscript in preparation, 2012).
 It should be mentioned, however, that the aerosol loading during the analyzed period is not high. Consequently, the accuracy of the AERONET retrievals, in particular the complex refractive index and single scattering albedo, is rather limited [see Dubovik et al., 2000, 2002a]. Therefore, in this work we also quantified uncertainties of the derived aerosol optical properties based on errors of every individual retrieval that are calculated in the AERONET inversion procedure (as described in section 2.1). In addition, the parameters designed to control quality of the inversion indicate fairly favorable conditions for deriving aerosol characteristics during the analyzed episode of the volcanic ash. Specifically, the sky was homogeneous and the fitting of the observed angular and spectral measurements of photometer was always very accurate (3% or better), and no anomalies were observed.
4. Analysis of Observations and Simulations
4.1. Combination of AERONET and Surface Solar Flux Observations
 In order to identify the ash aerosol impact on the radiative flux from experimental data, the collocated and simultaneous measurements of broadband solar flux, AERONET AOT at 500 nm and Angstrom exponent (870/440 nm) were analyzed as shown in Figure 3. The flux data are presented as a function of solar zenith angle (SZA) because the solar flux depends on the SZA and not only on the atmospheric composition (concentration and type of aerosols and gases). Therefore, Figure 3 enables tracking of the perturbation of downward solar radiation resulting from the change in aerosol regime. In particular, the observed changes in the measured flux for the same SZA before solar noon and after solar noon are due only to the change in aerosol concentration and type (given that the concentration of gases is stable). As can be seen in Figure 3, there is remarkable stability of AOT (around 0.15 at 500 nm) before and after noon, up to SZA of about 60°. The Angstrom exponent during this time is high and indicates dominance of small particles. However, after noon for SZA >60°, the AOT at 500 nm increases fairly rapidly to about 0.23; the Angstrom exponent decreases indicating the presence of coarse mode particles. Based on the time series of AOT, Angstrom exponent and lidar observations (later on in the day), the identified change in the aerosol conditions is due to the advection of the volcanic ash plume over the site. The arrival of the volcanic ash plume can also be identified in records of the ground measured solar flux. Figure 3 shows that for the same solar geometry the decrease in flux at the surface due to volcanic ash layer is, for example, about 25 Wm−2 at SZA of 60°, as illustrated in the figure. The observed shift in the flux is experimental evidence of the volcanic ash radiative forcing. These experimental data are further used for comparison and validation of the simulated fluxes and radiative effect of the volcanic ash aerosol.
4.2. Total Column Aerosol Model
 In an attempt to characterize the volcanic ash aerosol model we rely on aerosol characteristics retrieved by the AERONET inversion algorithm. The retrieved aerosol model accurately fits aerosol spectral optical thickness, and spectral and angular sky radiances measured from the ground. As demonstrated by sensitivity studies by Dubovik et al.  the AERONET retrieval is practically insensitive to the vertical structure of the atmosphere. Therefore, the AERONET retrieval provides only total column properties even in the case of multilayer structure. During the volcanic ash episode, the lidar data clearly showed a two-layer structure over Lille. Based on these observations we investigated the possibility to differentiate the aerosol optical properties of ash and background aerosol assuming an external aerosol mixture. Specifically, in order to derive the properties of pure ambient volcanic ash, we used the hypothesis that the background aerosol did not change during the analyzed period and we subtracted the properties of the background aerosol. This hypothesis is supported by fairly steady behavior observed before and after the ash plume for AOT and Angstrom exponent (see Figure 3), as well as, the retrieved detailed aerosol properties. Figures 4 and 5 show the averaged values of the retrieved aerosol size distribution, single scattering albedo (SSA), and complex refractive index from seven successful AERONET retrievals for before-plume and during-plume. The associated standard deviations and the range of the AERONET retrieval errors are indicated by vertical bars and dashed lines correspondingly. It shows quite small standard deviation for size distribution of the background aerosol. After entrance of the plume the coarse mode is significantly changed and, despite the standard deviations are larger, they do not overlap with the coarse mode of the background aerosol. Although standard deviations of the fine mode are also larger after the plume entrance, its magnitude shows only a small increase relative to the background aerosol, showing that the ash plume consists mostly coarse mode particles in terms of aerosol volume.
 The retrieved complex refractive index is less stable than size distribution, as can be seen from standard deviations in Figure 5. At the same time, retrievals of the refractive index are generally more uncertain than those of other parameters [Dubovik et al., 2002a, 2000]. This can explain the observed higher variability. It is interesting to note that standard deviations (vertical bars) in Figures 4 and 5 are sometimes similar or larger than the range of the retrieval errors (dashed lines). It indicates that some variability of aerosol model is a likely result from the influence of random errors on individual retrievals.
 The AERONET inversion also provides retrieval of fraction (we express it via percentage) of spherical particles. The non-spherical aerosol fraction is modeled by an ensemble of randomly oriented spheroids with size independent aspect ratio distribution. The ratio is fixed equal to a value that provided the best fit of single-scattering matrices of mineral dust by an ensemble of spheroids as described in studies by Dubovik et al. . The same study demonstrated very low sensitivity of angular dependence of aerosol phase function to the details of the shape of the aspect ratio distribution. Therefore, even if nonspherical volcanic ash may differ from desert dust in its distribution of particle shape, the utilization of the same spheroid mixture is not expected to produce important uncertainty. Moreover, aircraft in situ volcanic ash observations give values of the aspect ratio (1.8 and 2.0 for fine and coarse mode) [Schumann et al., 2011] that are well represented by the distribution used in the AERONET inversion.
 The fraction of spherical particles retrieved on April 17 shows sensitivity to ash and sharply decreases after the plume arrival, from about 70% to 40% and even less in some cases, indicating high nonsphericity of ash. Further on in our simulations we assume that ash consists only of nonspherical particles.
4.3. Assessment of the Volcanic Ash Aerosol Model
 The mean models of the background aerosol and aerosol after the volcanic ash arrival described in the previous section are now used for derivation of ash aerosol optical properties. The vertically separated aerosol layers can be considered in this case as an external mixture. Therefore, the size distributions of the aerosol in the total atmospheric column can be considered as a simple additive combination of background aerosol and ash. The size distribution of ash aerosol derived by this approach (Figure 4a, black solid line) is bi-modal with a dominant coarse mode centered at about 1.5 μm radius. The scattering and absorption AOTs of externally mixed particles can be determined and the single scattering albedo of externally mixed aerosols can be calculated as weighted average using the expression:
where ω0back(λ), ω0ash(λ) and τback(λ), τash(λ) are spectral SSA and AOT of background aerosol and ash, respectively. The spectral AOT of the ash layer is calculated here as a difference between the mean AOTs after the plume entrance and before. The derived single scattering albedo of ash (Figure 4b, black solid line) has strong spectral dependence with important absorption at short wavelengths. In Figure 4 we also provide standard deviations (vertical bars) and range of retrieval errors (dashed lines) for the “Before plume” and “During plume” mean aerosol models. The standard deviations and range of retrieval errors for the “Ash only” aerosol model were calculated as propagation of standard deviations and retrieval errors of before and after plume models.
 In this study we also make an attempt to estimate the complex refractive index of ash particles, which is important for the accurate computing of phase function and polarization. The detailed angular shape of these aerosol characteristics is particularly important for interpretation of satellite measurements or lidar signals. The difficulty is that the refractive index of mixed aerosol is not a linearly additive combination of involved aerosol species and thus some approximations are required for deriving the index of refraction of ash aerosol. In order to make sure that our extra assumptions do not contradict the observations, we conducted simulations of aerosol characteristics and sky-radiation observed by AERONET using an external mixture of aerosol where the complex refractive indices were defined using several simple scenarios. Specifically, we considered that AERONET retrieved refractive index for the total column aerosol can be related to refractive indices of each aerosol component as an average weighted by volume fraction. Thus, the complex refractive indices of “background” and “ash” aerosol components can be related to AERONET derived values of complex refractive index ( mix) as follows:
where back(λ), ash(λ) and Vback, Vash are spectral complex refractive indices and volume concentrations of background aerosol and ash, respectively. Using simple algebraic manipulation the real and imaginary parts of the complex refractive index of ash can be derived from equation (2) and are shown in Table 1 and Figure 5 (solid black line). In Figure 5 the standard deviations (vertical bars) and range of errors (dashed lines) were calculated as propagation of standard deviations and retrieval errors of mix(λ) and back(λ). The range of errors obtained for the complex refractive index of the observed ash plume is quite large. For instance, at wavelengths 440 nm and 670 nm it is 1.52 ± 0.12 and 1.54 ± 0.07 for the real part and 0.015 ± 0.004 and 0.006 ± 0.002 for the imaginary part. As shown in sensitivity studies by Dubovik et al.  such high level of uncertainty in retrieved complex refractive index is not surprising for the fairly low AOT (0.1 at 440 nm) observed for this ash event.
Table 1. Summary of Aerosol Microphysical and Optical Properties Derived From the AERONET Observations of a Volcanic Ash Plume Over Lille on April 17, 2010a
Value ± Absolute Error
Notation: rV is median radius and σ is standard deviation of lognormal volume size distribution, CV is volume concentration; n and k are real and imaginary parts of spectral complex refractive index, reff is effective radius, ω0 is spectral single scattering albedo, 〈g〉 is spectral asymmetry parameter, S532nm(sr) and δ532nm are lidar and depolarization ratios at 532 nm, respectively. The indices f and c denote fine and coarse modes, T denotes total size distribution.
 In spite of the previously mentioned uncertainties, the ash model provides a good fit to the radiation field measured by AERONET with these values of complex refractive index serving as useful additional information. For example, the derived complex refractive index of this study (1.53 ± 0.07 real part and 0.007 ± 0.002 imaginary part interpolated for 630 nm) agrees reasonably well with a high absorbing case (1.59–0.008i at 630 nm) reported in the in situ study of Schumann et al. . Although, this study did not discuss the spectral dependence of absorption at shorter wavelengths where we found an increase of absorption, the Schumann et al. analysis showed the dominant presence of spectrally neutral silicate component along with some presence of iron oxide known as strong absorber in short wavelengths. The fact that iron oxide is present can explain the spectral dependence of ash absorption derived in our study. In fact, the low single scattering albedo of 0.81 at 532 nm presented in Schumann et al. [2011, Figure 25] for the absorbing case and for an effective diameter of 1.22 μm, that corresponds to our result, reasonably agrees with the decrease of single scattering albedo in our work (0.85 ± 0.02 at 532 nm). It should be noted, however, that in a number of other studies volcanic ash is considered as less absorptive. At the same time, those studies relied on assumptions of the dominance of weakly absorbing components in ash particles or used a refractive index for mineral dust [e.g., Marenco et al., 2011; Turnbull et al., 2012]. For example, complex refractive index of andesite, a volcanic rock that is often used for volcanic ash characterization, has a relatively low imaginary part of refractive index (e.g., 1.47–0.0013i at 440 nm) [Pollack et al., 1973]. It is noteworthy that despite low imaginary refractive index, andesite also contains iron oxide [Pollack et al., 1973]. This presence of even a few percents of iron oxide (or other form of iron that further can be oxidized in the atmosphere [Cwiertny et al., 2008; Meskhidze et al., 2003]) in volcanic ash can produce spectral absorption similar to mineral dust [Lafon et al., 2006; Sokolik and Toon, 1999]. Finally, dark, gray or brownish appearances of the volcanic plume were reported in visual observations [e.g., Schumann et al., 2011; Zehner, 2010]. In this context, strong spectral dependence and enhanced absorption of ash appears reasonable.
 In order to check validity and limitations of equation (2) we compare results of two different simulations of AOT, SSA and phase function. In the first simulation we calculate spectral AOT, SSA and phase function using an external mixture of two aerosol components (the first component has size distribution and complex refractive index of the background aerosol and second has those of the volcanic ash, as derived above). In the second simulation we make the same calculations but use aerosol size distribution and complex refractive index retrieved by AERONET for the total column measurements (the same total aerosol model that was initially used for distinguishing between ash and background aerosol models). The differences obtained (shown in Figure 6) therefore represent uncertainty in spectral AOT, SSA and phase function due to the assumption that the complex refractive index of externally mixed particles can be assessed as in equation (2). The results of these simulations show that the relative error in aerosol phase function (Figure 6a) can be within 15% over the entire range of scattering angles and wavelengths, and within 5% over the range of scattering angles observed by the AERONET photometer during the almucantar scans (up to 140°). The spectral phase functions themselves are shown for 440 nm and 1020 nm in Figure 7 for: (i) the background aerosol model; (ii) during presence of the ash plume; and (iii) ash only. The calculated atmospheric radiances driven by aerosol phase functions had much smaller relative errors (about 3%). This can be explained by the fact that observed radiances are the products of the multiple scattering interaction in the atmosphere that smooth out angular features observed in phase matrices. The absolute differences in AOT and SSA are within 0.008 and 0.004, respectively, at 440 nm and about zero at 1020 nm (Figure 6b). Note that AOT = 0.008 is below the level of calibration uncertainty. Thus, it can be concluded that the assessment of the complex refractive index of externally mixed particles as presented in equation (2) seems to be an acceptable approximation for computation of AOT and SSA. However, simulations of the aerosol phase function at large scattering angles may have unacceptably high uncertainty for some applications. Since this approach produces low uncertainties in simulated AOT and SSA, the obtained model of ash can be used for the broadband flux simulations and estimation of aerosol radiative forcing. In addition, we also tested assumption that the AERONET retrieved refractive index for total column aerosol can be related to the refractive indices of each aerosol component as an average weighted by AOT fraction. This alternative assumption is based on the idea that manifestation of optical properties of each aerosol component is proportional to AOT of each component. The obtained results were very similar to weighting by volume fraction, however, showed slightly higher uncertainties.
 Considering the importance of the ash layers characterization by lidar [e.g., Ansmann et al., 2010, 2011; Chazette et al., 2012; Gasteiger et al., 2011; Groß et al., 2010] we also calculated the lidar ratio and the depolarization ratio at the wavelength of 532 nm using the derived ash aerosol model (refractive index was linearly interpolated for 532 nm) and compare them with those reported in the literature. Using the total size distribution and the coarse mode only we obtained lidar ratios of 42.0 sr and 48.0 sr, respectively. These values are typical for large nonspherical particles [Cattrall et al., 2005] and agree well with 50 ± 10 sr in [Ansmann et al., 2011]. The calculated depolarization ratios using the total size distribution and coarse mode only are 0.21 and 0.29, respectively, which is however somewhat lower than the value of 0.36 ± 0.02 measured for the ash layer in April 2010 over Munich by polarization lidar [Ansmann et al., 2010, 2011; Groß et al., 2010].
 In Table 1 we summarize the microphysical and optical properties derived for the observed volcanic ash plume. We also provide parameters of bimodal lognormal size distribution and effective radii, which are optical equivalents of those presented in the Figure 4 volume size distribution of ash. The asymmetry parameter or average cosine of phase function (〈g〉) is also provided. We have noted a spectrally flat dependence of 〈g〉 with a local decrease at 670 nm, which is different from what is usually observed for mineral dust particle [e.g., Dubovik et al., 2002a].
4.4. Surface Flux Simulations
 The retrieved aerosol models are employed to simulate the broadband solar flux at the surface in the spectral range from 0.2 to 4.0 μm. The comparison of the simulated flux with the measured ones is also used as an additional validation of the derived ash aerosol model. As described in section 2.1, the simulations of the flux are conducted using a part of the AERONET operational code. Figure 8a shows the fluxes measured before noon, after noon, and after the ash plume arrival (same as in Figure 3), and fluxes simulated with a 5° step of SZAs using a mean aerosol model derived for the periods before and after the ash plume arrival. The simulated fluxes slightly overestimate the measurements; however, they reproduce the differences similar to those observed between fluxes measured before and after the ash plume influence, which basically represents the radiative forcing of the ash plume as was mentioned in section 4.1. The quantitative comparison of the simulated and measured flux is presented in Figure 8b. The simulated fluxes in Figure 8b are adjusted to exactly the same SZAs as the measured fluxes using interpolation of simulations presented in Figure 8a. The quantitative comparison shows a bias of about 3% and an increase up to 10% in the relative error with increase in solar zenith angles. Note that the expected accuracy of the flux measurements themselves are about 3%, and it is known that the measurement accuracy decreases for low sun, which may explain the increase of the error. Thus, given the possible uncertainty in the measurements, the observed discrepancy between the simulated and measured flux is indeed acceptable.
4.5. Direct Ash Radiative Forcing
 The direct radiative forcing of the volcanic ash particles assessed in this study relies on flux simulations and ground-based measurements. Figure 9 (red dotes) presents differences in the measured downwelling flux for the same solar zenith angles, but for the aerosol type and concentration changed due to arrival of the ash particles. Therefore, it demonstrates the measurement-based evaluation of the ash radiative impact on downwelling flux at the surface. For small SZAs the difference in the flux between morning and afternoon is around zero because the plume was observed starting from about 15:30 UTC, i.e., for larger SZAs. Therefore, at about 60°, during arrival of the plume front, we observe an increase in the difference between fluxes. Note, that in Figure 3 this period is presented by only one observational point because the sun/sky photometer observations have lower time resolution than pyrano- and pyrheliometer. Noteworthy is also a decrease of the difference after SZA of 60°, despite that the AOT has not changed during this time. Except for a bias, which can be explained by the use of an averaged aerosol model from limited number of AERONET retrievals and by the retrieval uncertainties, the shape of the experimentally observed angular dependence is in good agreement with the results of the simulations (Figure 9, black solid line) and is related to the dependence of the aerosol radiative forcing on SZA. The angular dependence of aerosol radiative forcing is known from theoretical atmospheric radiative transfer computations, e.g., it was reported by Boucher and Tanré  and used by Remer and Kaufman  for satellite-based and by Derimian et al. [2006, 2008] for ground-based estimations of aerosol radiative forcing.
 The difference in the downwelling flux discussed above is the loss of radiation reaching the surface due to aerosol presence. In some studies, depending on application, it is defined as aerosol radiative forcing at the bottom of the atmosphere (BOA) as follows:
where and are the downwelling fluxes at the BOA for aerosol-free and aerosol-laden conditions, respectively. The aerosol radiative forcing at the top of the atmosphere (TOA) then is defined as:
where and are the upwelling fluxes at the TOA in aerosol-free and aerosol-laden conditions, respectively.
 However, in climate applications the net radiative forcing is often used, which is defined at the BOA as
where FBOA0 and FBOA are the net (downwelling minus upwelling) fluxes in aerosol-free and aerosol-laden conditions, respectively. Therefore, the net BOA forcing accounts for interaction with the surface and depends on the surface reflectance. At the TOA the values of the net forcing are identical to what can be found from the equation (3b) because at the TOA the downwelling (extraterrestrial) flux is the same either for aerosol-free or aerosol-laden conditions. Difference between TOA and net BOA forcing is defined as atmospheric forcing and represents the energy trapped in the atmospheric layer due to the aerosol presence.
 In this study we provide the instantaneous and 24-h averaged net radiative forcings and forcing efficiencies calculated over land and some values over ocean. Similarly to the AERONET operational code, the land spectral surface reflectance was adopted from the MODIS climatology. For instance, at the wavelength of 555 nm, over Lille, France, the surface reflectance is nominally 0.12, which is assumed to represent the regional surface reflectance and hence is used in the forcing calculations below. The daily average radiative forcing is calculated by integration of instantaneous radiative forcings over the period of daylight duration and dividing by 24 h. For the given day and location the daylight duration is 13.7 h and the maximum of sun elevation is at SZA of 40°. Calculations of the net radiative forcing and forcing efficiency were conducted using the mean aerosol models of: (i) “Before plume”; (ii) “During plume”; (iii) “Ash only”; and for (iv) external mixture of “Before plume” plus “Ash only.” The instantaneous net radiative forcings are presented in Figure 10 along with indication of the 24 h averages. As can be seen, the impact of the volcanic ash plume is significant at the BOA and TOA. After the ash plume arrival the daily average BOA forcing increases from −10.5 Wm−2 to −17.6 Wm−2 and at TOA from −4.0 Wm−2 to −6.2 Wm−2. In general, the difference between forcings of the “During plume” and “Before plume” aerosol models provide an approximation of the radiative forcing of “Ash only.” However, the difference between “Ash only” and the simpler approximation is about 1 Wm−2, e.g., for daily average forcing at BOA and TOA. The 1 Wm−2 difference may be due to either an error in estimating the volcanic ash aerosol model (section 4.3. and Figure 6) or to contributions of multiple scattering effects that are not simply additive. In order to check the impact of the error in the ash aerosol model we calculate radiative forcing using an external mixture of the “Ash only” and the “Before plume” aerosol models. Then, the obtained results (blue dashed line in Figure 10) are compared to forcing calculated using the “During plume” aerosol model. The obtained difference is minor (e.g., see the 24 h average values in Figure 10), suggesting that the major contribution to the 1 Wm−2 mentioned above is due to different impacts of the multiple scattering effects.
 In general, the effect of vertical aerosol structure can also have an impact on flux simulations. However, based on some conducted tests, the vertical structure is expected to be insignificant for the bottom of the atmosphere. It can be somewhat more important for top of atmosphere, but may depend on surface reflectance and AOT. We also found that our conclusions are in agreement with Guan et al. . In our current simulations we assumed negligible impact of aerosol vertical structure.
 The radiative forcing efficiency is defined as radiative forcing per unit of aerosol optical thickness and is calculated here with respect to AOT at 550 nm. Despite the daily average radiative forcing of ash being lower than the background aerosol (Figure 10), its radiative efficiency is higher at BOA and comparable to the background at TOA as shown in Figure 11. It means that the atmospheric forcing efficiency of ash is stronger, which is a result of stronger absorption by ash. The daily average forcing efficiency of the ash plume is −93 ± 12 Wm−2τ−1 at the BOA and −31.2 ± 2 Wm−2τ−1 at the TOA.
 The error provided for the values of radiative forcing efficiency is calculated using a cumulative error of complex refractive index and size distribution under assumption that errors are not correlated. This is a worst case scenario. We have chosen this approach because the exact error estimate for the simulated forcing requires utilization of the full covariance matrix, which are not available in the present inversion outputs. In reality, the errors of refractive index and of size distribution are negatively correlated, which should result in a lower cumulative error. Indeed, both increase of particle concentration and increase of index of refraction result in increase of AOT. Therefore, the effects of measurement errors usually lead to anti-correlative changes of particle concentration and refractive index, since AOT is always fitted well in the AERONET inversion. However, using our assumption of non-correlated errors suggests simple addition of effects from errors in particle concentration and refractive index. That leads to high uncertainty in the calculated AOT that would propagate to unrealistically high values of calculated uncertainty in radiative forcing (alternatively to forcing efficiency that is normalized by AOT value). At the same time, AOT is directly measured by AERONET with accuracy of about ±0.01. Therefore, in our estimation of ash radiative forcing we assumed uncertainty of ±0.01 in AOT while the uncertainty in AOT spectral dependence, phase function and SSA were calculated using errors of the derived ash aerosol model.
 According to our additional simulations, the same ash particles over the sea surface produce a daily average forcing efficiency of −115 ± 13 Wm−2τ−1 at the BOA and −58 ± 4 Wm−2τ−1 at the TOA. The sea spectral surface reflectance selected in these computations was derived for an area in the North Sea that in the path of the ash transport (as in Figure 2). The SeaWiFS 8-day average product for April 15 in the 2° × 4° box between UK and Northern Europe provided the reflectance values of 0.01/0.013/0.003 at the wavelengths 443/555/670 nm, respectively.
5. Summary and Conclusions
 The detailed optical properties and radiative forcing of the volcanic ash originating from the Eyjafjallajökull volcano eruption were analyzed using the ground-based remote sensing observations collected in northern France on April 17, 2010. Both the measurements of the sun/sky-scanning AERONET photometer and the lidar permanently installed on the roof of the Laboratory of Atmospheric Optics in Lille were used for identification of detailed optical characterization of ambient volcanic ash. The derivations of the ash optical model significantly relied on AERONET total column aerosol properties retrieved from atmospheric radiances measured in the solar almucantar scan. In addition, the derived optical model of volcanic ash was validated by numerical tests and co-incident broadband solar flux measured independently. The obtained ash size distribution demonstrates domination by coarse mode aerosol; however the radius of the mode was 1.5 μm compared to that of ∼2.5 μm which has been observed from long-term AERONET measurements of desert dust [Dubovik et al., 2002a]. The observations of this value of mode radius over Lille are consistent with AERONET observations in other European sites during April 2010 [e.g., Ansmann et al., 2011]. The spectral values of complex refractive index of ash were estimated and summarized in a table along with other microphysical and optical characteristics. The spectral single scattering albedo suggested stronger absorption at shorter wavelengths (0.81 at 440 nm as opposed to a relatively high value of 0.92 at 1020 nm). The AERONET retrieved fraction of spherical particles notably decreases after the plume arrival suggesting the nonspherical character of the ash particles. The lidar ratio and depolarization ratio calculated for coarse mode of ash were 48.0 sr and 0.29, respectively. The derived ash aerosol model was then used for simulations of the fluxes and radiative forcing. The results of these calculations showed good agreement with available ground-based measurements of broadband fluxes. The radiative forcing efficiency for ash was simulated both over land and ocean surfaces. The simulations imply that an ash plume with moderate AOT of 0.1 at 550 nm could produce a daily cooling effect at bottom of atmosphere of about 9 to 12 Wm−2 while transported from Iceland to the European continent over land and ocean for the given latitude and time. This cooling effect is about 10% stronger than can be produced by background urban/industrial pollution in the study region. Based on the presence of two vertically distinct aerosol layers observed by lidar, the aerosol assumed in modeling was an external mixture composed of background near-surface aerosol and elevated volcanic ash aerosol. The complex refractive index of such mixture was approximated using weighting of the refractive indices by corresponding volume fractions of the background and ash aerosol components. This approximation yielded an error within 0.008 and 0.004 in calculation of spectral AOT and SSA, respectively. At the same time, computations of spectral phase function had somewhat higher uncertainty, in particular at large scattering angles that are beyond the scattering angle range observed by AERONET photometers. The angular dependence of phase function in that angle range manifested notable sensitivity to the assumption used for modeling of complex refractive index of mixed aerosol.
 Also, we would like to mention that similarly to the mineral dust, coarse mode ash particles might have significant effect on the outgoing long-wave (thermal IR) radiation. We tried to examine the ash impact on simultaneous pyrgeometer measurements, however, for the evidently low atmospheric loading of ash the effect of ash presence was not evident, it was probably masked by variability in meteorological conditions.
 We thank the members of the AERONET/PHOTONS team for theirs effort in establishing and maintaining the Lille site. We are also thankful to Gerard Brogniez, Thierry Podvin, Frederique Auriol and Christine Deroo of Laboratoire d'Optique Atmospherique in Lille, France, for making possible the continuous collection of broadband solar flux at a high level of data quality. The authors acknowledge the NOAA Air Resources Laboratory (ARL) for the provision of the HYSPLIT transport and dispersion model and/or READY website (http://www.arl.noaa.gov/ready.php) used in this publication. Analyses used in this paper were produced with the Giovanni online data system, developed and maintained by the NASA GES DISC. Finally, we appreciate constructive comments made by anonymous reviewers, which significantly contributed to improving the quality of this study.