. The other nine wavelengths give the AOD and are used. The instrument is calibrated regularly in pristine conditions in Izaña, Tenerife via the Langley method. A cloud screening based on short scale fluctuations of the AOD is used as in Alexandrov et al. (2004). The AOD uncertainty for this instrument is generally around 0.01 (Stock, 2010;Toledano et al., 2012). The time resolution of the instrument is 1 minute.
The multi-wavelengths Raman lidar KARL ('Koldewey Aerosol Raman Lidar') consists of a Nd:YAG laser with 10 W in each of the wavelengths k ¼ 355 nm, 532 nm and 1064 nm. The first two wavelengths are recorded in polarisation states parallel and perpendicular to the laser. Additionally, the Raman shifted lines from N 2 at 387 nm and 607 nm and water vapour at 407 nm and 660 nm are recorded by a 70 cm mirror. The overlap is complete after about 700 m altitude, while below a qualitative estimation of the backscatter coefficient using a Vaisala CL51 ceilometer was performed. More technical details on the system are given in Hoffmann (2011). The evaluation was done according to Ansmann et al. (1992) with 30 m vertical and 10 min temporal resolution. No further smoothing of the lidar profiles has been performed as this can easily lead to wrong results as the derivation of extinction coefficients 2 C. RITTER ET AL.
from lidar is an ill-posed problem (Pornsawad et al., 2008). Intensive parameters derived from the lidar measurements are the lidar ratio (LR), the colour ratio (CR) and the particle linear depolarisation ratio (d): where a aer and b aer are the aerosol extinction coefficient [m À1 ] and aerosol backscatter coefficient [m À1 sr À1 ], respectively. The LR also depends on size and shape of the aerosol (slightly larger for small and non-spherical aerosol, Doherty et al., 1999;Ferrare et al., 2001), but mainly on the refractive index, i.e. the chemical composition of the aerosol and is large for soot and low for cirrus clouds. The colour ratio is a rough measurement of the size of the aerosol. For very small particles, compared to the employed wavelengths, the Rayleigh limit holds true and the backscatter is proportional to k À4. Contrary, for large particles ('grey approximation') the backscatter becomes independent of the wavelengths. Hence, when calculated for k 1 ¼ 355 nm and k 2 ¼ 532 nm the colour ratio shows values between approximately 5 (for small particles) and 1 (for large ones).
The particle linear depolarisation ratio (PLDR) is defined as where b aer? and b aer | are the aerosol backscatter coefficients in polarisation planes perpendicular and parallel to the laser, respectively. As spherical particles do not alter the polarisation during a scattering event it holds b aer? ¼ 0 for them. Contrary, ice crystals in cirrus clouds can have a depolarisation of d > 0.5 (Chen et al., 2002).
Surface radiation measurements at Ny-Ålesund are operated in the frame of the Baseline Surface Radiation Network (BSRN) (Maturilli et al., 2015), providing direct radiation measured by a Kipp & Zonen CH51, while diffuse, global and reflected radiation components are recorded by Kipp & Zonen CMP22 pyranometers. The longwave up-and downward radiation is measured by Eppley PIR pyrgeometers. All radiation data is given with a temporal resolution of 1 minute (Maturilli, 2016).
Finally, on UT 10:48 a Vaisala RS-92 radiosonde was launched, providing vertical profiles of temperature (T), relative humidity (RH), pressure, wind speed and direction. The retrieved air number density has been applied in the lidar evaluation.
The BB event started over our site on 9 July 2015, but measurements with KARL were available first on 10 July. Air temperature was around þ10 C at 2 m above ground, and the surface was free of snow and ice. Fig. 1 gives an overview of the vertical aerosol backscatter coefficient on that day (similar to Markowicz et al., 2016).
White stripes indicate excluded data due to multiple scattering in the figure. Only the structures around 12 UTC in 10-12 km altitude and between 14 and 22 UTC at about 5 km altitude are clouds. This can be seen from the colour ratio in Fig. 2 which shows small values (large particles) for the clouds. All other features are BB aerosol. This aerosol occurs mainly below 4 km altitude in distinct structures and shows backscatter coefficients of more than 10 Mm À1 sr À1 for k ¼ 532 nm. A clear transition between very polluted and relative clean air masses below 4 km altitude before noon can be clearly seen. Details on the origin of the event and its distribution in time are described in Markowicz et al. (2016). Exemplarily some lidar profiles for the time of the radiosonde launch (UT 10:48) are shown in Fig. 3. The clear, abrupt transition between very polluted and quite clear conditions at about 3.5 km altitude is again evident. Due to the high extinction coefficients of the event a retrieval of the extinction coefficients from the Raman shifted wavelengths was possible up to that altitude.
The (volumetric) backscatter and extinction coefficients derived from the lidar data for the time of the launch of the radiosonde are presented in Fig. 4. Again, the sharp transition between polluted and clean conditions in about 3.5 km altitude is evident. Moreover, a layered structure below about 2.1 km altitude is visible, while above that no more layers but rising values with altitude are found.
Generally, the backscatter and extinction coefficients are extremely high for the European Arctic. Ritter et al. (2016) derived for 355 nm typical aerosol extinction coefficients around 20 Mm À1 for the generally more polluted spring time in about 2 km altitude. Hence, this event increased the backscatter and extinction coefficients roughly by a factor of 20. This extreme air pollution allowed a detailed analysis of the lidar data. It can be also estimated from Fig. 4 that the noise in the extinction coefficient at 532 nm (the weakest channel), is around 20 Mm À1 in 3 km altitude and hence the error is below 10%, which is required for the derivation of aerosol microphysics from lidar data (Veselovskii et al., 2002).
The profiles of potential temperature and relative humidity (RH) over water from the radiosonde measurements are given in Fig. 5. The altitude of the (elevated) temperature inversion in about 3.5 km coincides precisely with the top of the aerosol plume in Fig. 4, revealing how this inversion effectively traps the aerosol and inhibits most vertical exchange. Moreover, several moist layers were present up to 10 km altitude above the range shown in Fig. 5. The aerosol rich altitudes between 2.1 km and 3.5 km altitude are characterised by an almost neutral potential temperature gradient, while the RH increases from about 50% to 90% giving an excellent opportunity to study any hygroscopic effects of the aerosol. The local boundary layer was very low, about 100 m altitude, see blue curve in Fig. 4 and Markowicz et al. (2016).

Mathematical preliminaries for the inversion
In this section, it is described how aerosol microphysical properties are derived from lidar data. The model relating the optical parameters C(k) with the volume size distribution v(r) is described by a Fredholm integral operator T of the 1st kind where k is the wavelength, r is the radius, m is the complex refractive index, C(k) denotes either the extinction or backscatter coefficients, K is a kernel function and Q stands for either the extinction or the backscatter (dimensionless) Mie efficiencies respectively, i.e. the particle cross sections divided by the geometrical cross section of a sphere. The integral limits r min and r max are appropriate lower and upper radii which are describing the specific measurement event but have also to respect the restriction of the physical model. Therefore, here for the lower limit 0.001 mm and for the upper one 2 mm were used. This upper limit was chosen, because sometimes in the calculations a mode in the transition between fine and coarse around 1 mm has been found, hence our chosen upper limit includes this mode without extending the calculation interval too much. We will call this mode in the transition region 'coarse mode' later for simplicity. As the input data is provided by the KARL lidar, 5 discrete values of input data can be provided: the 3 backscatter coefficients at 355 nm, 532 nm and 1064 nm and 2 extinction coefficients at the former 2 wavelengths.
Identifying C(k) as our measurement data and v(r) as the unknown distribution, the problem reduces to the inversion of the operator T. Knowing the volume size distribution, we can then extract the following microphysical parameters: total surface-area concentration s t ¼ 3 Ð vðrÞ r dr (mm 2 cm À3 ) total volume concentration v t ¼ Ð v r ð Þdr (mm 3 cm À3 ) effective radius r eff ¼ 3 v t /a t (mm) total number concentration n t ¼ 3 4p Ð vðrÞ r 3 dr (cm À3 ). In addition, the complex refractive index m ¼ m R þ i m I with the real part Re(m) ¼ m R and imaginary part Im(m) ¼ m I as well as the single scattering albedo (SSA) in 355 nm and 532 nm are retrieved. Note that