Seasonal Variations of the Relative Optical Air Mass Function for Background Aerosol and Thin Cirrus Clouds at Arctic and Antarctic Sites

New calculations of the relative optical air mass function are made over the 0°–87° range of apparent solar zenith angle θ, for various vertical profiles of background aerosol, diamond dust and thin cirrus cloud particle extinction coefficient in the Arctic and Antarctic atmospheres. The calculations were carried out by following the Tomasi and Petkov (2014) procedure, in which the above-mentioned vertical profiles derived from lidar observations were used as weighting functions. Different sets of lidar measurements were examined, recorded using: (i) the Koldewey-Aerosol-Raman Lidar (KARL) system (AWI, Germany) at Ny-Ålesund (Spitsbergen, Svalbard) in January, April, July and October 2013; (ii) the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite-based sensor over Barrow (Alaska), Eureka (Nunavut, Canada) and Sodankylä (northern Finland), and Neumayer III, Mario Zucchelli and Mirny coastal stations in Antarctica in the local summer months of the last two years; (iii) the National Institute of Optics (INO), OPEN ACCESS Remote Sens. 2015, 7 7158 National Council of Research (CNR) Antarctic lidar at Dome C on the Antarctic Plateau for a typical “diamond dust” case; and (iv) the KARL lidar at Ny-Ålesund and the University of Rome/National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA) lidar at Thule (northwestern Greenland) for some cirrus cloud layers in the middle and upper troposphere. The relative optical air mass calculations are compared with those obtained by Tomasi and Petkov (2014) to define the seasonal changes produced by aerosol particles, diamond dust and cirrus clouds. The results indicate that the corresponding air mass functions generally decrease as angle θ increases with rates that are proportional to the increase in the pure aerosol, diamond dust and cirrus cloud particle optical thickness.


Introduction
Regular sun-photometer measurements are currently conducted at numerous Arctic and Antarctic sites to determine the spectral values of aerosol optical thickness τa(λ) at visible and near-infrared wavelengths [1].These measurements are conducted using different sun-photometer models such as the Cimel CE-318 of the Aerosol Robotic Network (AERONET) network [2], the Prede POM-01L and POM-02L sun/sky-radiometers of the SKYNET network [3], the hand-held Microtops sun-photometers of the Maritime Aerosol Network (MAN) [4], the EKO MS-110 model [5] used by the Japan Meteorological Agency (Tokyo, Japan) at Syowa (Antarctica), and various sun-photometer models employed by the POLAR-AOD partners [6,7].An extensive list of the multispectral sun-photometers employed at numerous Arctic and Antarctic sites to carry out the routine activities planned by various networks to measure the aerosol optical depth τa(λ) during the past two decades is given in Table 1, providing also the peak-wavelengths of the narrow-band interference filters mounted on the sun-photometers, and the references where the technical characteristics of these instruments are available.
Following the criteria established by the multispectral sun-photometry method [18], each measurement of direct solar irradiance J(λ) (performed at a window-wavelength λ for a certain apparent solar zenith angle θ on a cloudless day) is examined in terms of the Lambert-Beer law to determine the total optical thickness τ(λ) of the atmosphere in terms of the following analytical form obtained by inverting the well-known Lambert-Beer law: where: m is the relative optical air mass of the atmosphere for angle θ, D is the factor taking into account the day-to-day variations in the direct solar irradiance due to the changes in the Earth-Sun distance throughout the year [19], and Jo(λ) is the output voltage that would be measured by the sun-photometer outside the atmosphere.The spectral values of Jo(λ) are usually determined by applying the Langley plot method to measurements carried out at high-altitude sites on days characterized by stable atmospheric turbidity conditions [20].Equation (1) shows that the instantaneous values of m need to be accurately known in order to determine the monochromatic value of τ(λ) with the best precision.This is particularly important in the polar regions, where the aerosol optical thickness τa(λ) is often very low [6], and aerosol radiative effects may be not negligible [21].A set of appropriate values of m was calculated by Tomasi and Petkov [22] (hereinafter referred to as TP2014) at Arctic and Antarctic sites over the 0° ≤ θ ≤ 87° range.The dependence of air refractive index on the vertical profiles of pressure p(z), temperature T(z) and water vapor partial pressure e(z) in the polar atmospheres was taken into account by using the algorithm of Tomasi et al. [23] applied to the average vertical profiles of p(z), T(z) and e(z) derived from the radiosounding data collected at Ny-Ålesund (~79°N) in Spitsbergen (Svalbard) during June and July in the years from 2000-2003 [24], and from those recorded at Mario Zucchelli (~75°S) during the austral summer season from 1987 to 1998 [25].

Model Arctic Stations Antarctic
Wehrli [8] Carter Scott SP01, SP01-A,  As pointed out by TP2014 22, the product m τ(λ) is equal to the sum of the following contributions: (i) the product of the atmospheric relative optical air mass m by the Rayleigh scattering optical thickness τR(λ), (ii) the product of the relative optical air mass ma for aerosol extinction by the aerosol optical thickness τa(λ), and (iii) the sum of the products of relative optical air mass mj for the j-th atmospheric gaseous constituent by the corresponding optical thickness τj(λ), where j identifies each gaseous constituent causing weak absorption within the sun-photometer spectral channels.
Therefore, τa(λ) can be calculated as where the subscript j refers to atmospheric water vapor, ozone, nitrogen dioxide (together with its dimer N2O4), and oxygen dimer (O4).Simulations of the atmospheric absorption spectrum of incoming solar radiation made over the 0.30-1.10µm wavelength range by using the MODTRAN 2/3 code and the LOWTRAN 7 model [26] for the Subarctic Summer atmospheric model [27] indicate that: (i) numerous absorption bands of water vapor are centered at the 591, 650, 695, 702, 720, 730, 820, 906, 936, 950 and 975 nm wavelengths, with intensities gradually increasing with wavelength; (ii) the strong wing of the ozone Huggins band is present from 0.30 to 0.35 µm and the wide Chappuis band covers the 407-750 nm wavelength range, presenting semi-continuous absorption features having the maximum at the 602 nm wavelength; (iii) the semi-continuum of nitrogen dioxide NO2, superimposed with the absorption effects of its dimer N2O4, exhibits a spectral absorption curve gradually decreasing from 400 to 660 nm; and (iv) the oxygen dimer (O4) displays a sequence of six absorption bands from 430 to 1140 nm, centered at the 446, 476, 532, 577, 628 and 1065 nm wavelengths [28].
In order to calculate τa(λ) with a good accuracy, we recommend to use in Equation ( 2): (i) the values of m for Rayleigh scattering determined separately for the Arctic and Antarctic atmosphere [22], and (ii) the values of mj defined for the four minor absorbing gases separately for the Arctic atmosphere (at Ny-Ålesund, ~79°N latitude) and the Antarctic atmosphere (Mario Zucchelli, ~75°S latitude).
The relative optical air mass ma for aerosols was derived for 0° ≤ θ ≤ 87° 22 and the following vertical profiles of aerosol extinction coefficient: (i) background Arctic aerosol observed in summer; (ii) average haze observed at Ny-Ålesund in winter−spring 2002; (iii) dense Arctic haze observed at Ny-Ålesund on 2 May 2006; (iv) Kasatochi volcanic particles observed at Ny-Ålesund in late August and early September of 2008 [29]; (v) background Antarctic aerosol measured at coastal sites during the austral summer; and (vi) aged volcanic particles measured by a lidar located at McMurdo on 1 June 1993, two years after the Pinatubo eruption.
These calculations describe the mean behavior of ma for different atmospheric turbidity conditions in the Arctic and Antarctic atmospheres.Therefore, seasonal changes of ma(θ) or its dependence on the measurement site are not discussed by TP2014 [22].Moreover, no information was given on the behavior of ma(θ) in cases of upper tropospheric thin cirrus cloud layers or marked diamond dust loads close to the surface.These aspects are examined in the present study.
In particular, the main purpose of the present calculations is to (1) ascertain the variability of ma(θ) for different vertical profiles of the aerosol volume extinction coefficient ka(z) at various Arctic and Antarctic sites and (2) estimate the values of ma(θ) to be used when particulate matter layers are suspended at various tropospheric altitudes (such as a diamond dust close to the ground or a thin cirrus cloud layer in the mid-or upper troposphere).The values of ma(θ) obtained in the different cases are compared with the calculations made by TP2014 [22], which provide reference cases for background summer aerosol loads in the two polar atmospheres.The new calculations of ma(θ) given in the present study and those provided by TP2014 [22] may be usefully employed to determine more accurately the atmospheric turbidity parameters given by polar aerosols and improve the analysis of the ground-based sun-photometer data collected during the new field campaigns conducted by the AERONET, AEROMAN, AEROCAN, GAW-PFR, SKYNET and Japan Meteorological Agency (JMA) networks mentioned in Table 1.The present results may be also used in order to implement more accurate radiative transfer calculations in the polar atmospheres for thin cirrus clouds or diamond dust layers at tropospheric layers.

The Atmospheric Model used to Calculate the Relative Optical Air Mass Functions and Determination of the Vertical Profiles of Aerosol Volume Extinction Coefficient
The present calculations of ma(θ) were made following the TP2014 [22] procedure based on the general scheme of the Earth-atmosphere system proposed by Thomason et al. [30].The calculations apply to an incoming direct solar radiation beam propagating through a spherical atmosphere.The wet-air refraction effects closely related to the pressure and temperature variations with height, and the Earth's curvature are taken into account.In the specific cases of aerosol or cloud particle extinction, the relative optical air mass ma(θ) has been calculated over the 0° ≤ θ ≤ 87° range by using the following formula: where: (i) ka(z) is the vertical profile of the volume extinction coefficient produced by aerosols or cloud particles, calculated in km −1 over the altitude range from the mean sea-level zo to the atmospheric top-level z  (assumed to be of 120 km in all cases); (ii) Ka is the integral of ka(z) made over the zo  z  z  altitude range, which in practice equal to the aerosol optical thickness τa(λ) measured at a certain wavelength λ; (iii) no is the air refractive index at sea-level zo; and (iv) n(z) is the air refractive index varying as a function of z.It can be clearly seen in Equation (3) that ka(z) is used as a weighting function to evaluate the solar radiation extinction effects versus altitude.TP2014 [22] used vertical profiles of p(z), T(z) and e(z) derived from radiosoundings to better characterize the dependence of n(z) on altitude.The radiosounding datasets were based on measurements made at Ny-Ålesund (~79°N) during June-July of 2000-2003 [24], and at Mario Zucchelli (~75°S) during the austral summer season from 1987 to 1998 [25].Above 30 km altitude, the profiles were completed with (i) monthly mean vertical profiles of the three thermodynamic parameters obtained by Tomasi et al. [31] from multi-year Michaelson Interferometer for Passive Atmospheric Sounding (MIPAS)-Environmental Satellite (ENVISAT) limb-scanning measurements over the 33-60 km altitude range at 80°N in July and at 75°S in January, and (ii) the vertical profiles p(z) and T(z) defined in the AFGL Subarctic Summer model over the 70-120 km altitude range [27].The combined average vertical profiles of p(z), T(z) and e(z) were used in the Tomasi et al. [23] algorithm to calculate the vertical profiles of n(z) in the Arctic and Antarctic atmospheres.The values of no were determined for the ground-level measurements of the air thermodynamic parameters.
The analysis of the various datasets produced monthly mean vertical profiles of p(z), T(z) and e(z), which were used to determine the average vertical profiles of n(z) at the various polar sites for the different months.As shown by Tomasi et al. [24], the monthly mean vertical profiles of pressure p(z) regularly decrease in an exponential fashion as a function of altitude over the whole range, while relative humidity decreases in general with height until reaching values of a few percent at the tropopause level and low stratosphere altitudes [25].The rather low values of e(z) correspondingly found usually in both polar atmospheres for cloudless conditions exert a weak influence on n(z).Conversely, appreciable variations in the monthly mean temperature profiles are observed during the local summer months at all the Arctic and Antarctic sites, in agreement with the results by Tomasi et al. [24].The monthly mean vertical profiles of T(z) obtained from the radiosounding datasets at the eight polar sites are presented in Figure 1, showing that T(z) gradually decreases with altitude until reaching a minimum at the tropopause level found between 8 and 10 km.The temperatures measured in April and October at Ny-Ålesund are appreciably lower (by more than 10 K) than those measured in July at Ny-Ålesund and the other Arctic sites.The values measured in January are close to those of October at all the tropospheric levels, and are considerably lower than in October at all stratospheric levels z > 8 km.The summer profiles of T(z) measured at the four Arctic sites differ by less than 10 K, and display similar vertical gradients.The changes are larger in the lower stratosphere than in the troposphere.In Antarctica, the January (austral summer) profiles of T(z) are similar at all four sites, both in the troposphere and in the lower stratosphere.The temperature profiles at Dome C, which is a high altitude sites, is characterized by a significant thermal inversion in the lowest atmospheric layers, differently from the other sites.The values of ka(z) and its integral Ka used in Equation (3) were calculated by TP2014 [22] for various particle extinction profiles.Coefficient ka(z) was obtained from lidar measurements of the volume backscattering coefficient Bbs(0.532m) multiplied by the value of lidar ratio for tropospheric aerosols derived from inelastic scattered lidar returns of N2 molecules, according to Ansmann et al. [32].
The integral of Ka(z) was calculated and compared with the measured value of τa(0.532m), as made by Hoffmann et al. 29.A value of lidar ratio equal to 40 sr at the 0.532 m wavelength was used in the present study: A possible error in estimating the lidar ratio should cause an uncertainty in Ka(z) not exceeding 10%.
Vertical profiles of ka(z) were selected at various Arctic and Antarctic sites to represent the average extinction of background aerosols in the troposphere and low stratosphere during the local summer months.The background aerosol cases do not include volcanic particles in the lower stratosphere, nor Arctic haze, biomass burning smoke or Asian dust layers in the lower troposphere.More precisely, the following aerosol and cloud particle extinction profiles were considered in the present study: (1) The mean profile of ka(z) derived from monthly or multi-monthly average Bbs(0.532m) profiles measured at Ny-Ålesund with the AWI (Alfred Wegener Institute, Germany) KARL (Koldewey-Aerosol-Raman Lidar) lidar-system (described by Hoffmann et al. [33]) in January, April, June−July and October−December of 2013 (see also [1]).
(2) Multi-month average vertical profiles of ka(z) derived from observations by the CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) lidar onboard the CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) satellite.Profiles over 2° latitude  5° longitude sectors centerd at Barrow, Eureka and Sodankylä were selected.The Level-3 satellite data for the summer (June−September) months of the last two years were taken from the https://eosweb.larc.nasa.gov/project/calipso/cal_lid_l3_apro_combined-beta-v1-30_table and http://reverb.echo.nasa.gov/reverb websites, as a part of the "Cloud-Free + Above (Combined) Aerosol Extinction Profiles", Version 1.30, Beta (codex CAL_LID_L3_APro_Combined-Beta-V1-30) dataset.It is worth mentioning that for cloud-free conditions in the planetary boundary layer the vertical profiles of aerosol extinction coefficient derived from CALIOP measurements were evaluated by Kim et al. [34] to agree with those obtained from ground-based lidar measurements within about 2 × 10 −2 km −1 .A pixel of 2° latitude  5° longitude have sizes of 223  154 km 2 at a latitude of 75°N.Therefore, the vertical profiles collected above a certain Arctic site during the summer months pertain to similar background aerosol conditions, as demonstrated by Tomasi et al. [1] who defined the Arctic and Antarctic maps of the seasonal average Level-3 aerosol optical thickness τa(0.55 μm) derived from MODIS/Aqua, MODIS/Terra and MISR satellite data recorded from 2005 to 2012 during the summer three-month period, showing that variations smaller than 0.02 can affect the seasonal average values of τa(0.55 μm) within pixels of the above sizes.
(3) Multi-month average vertical profiles of ka(z) determined from the vertical profiles of (5) Five vertical profiles of ka(z) determined from measurements of Bbs(0.532m) made in the presence of cirrus clouds at Ny-Ålesund, with the AWI KARL lidar-system on three days of April, July and October 2013, and at Thule (76°39'N, 68°46'W, 225 m a.m.s.l.) in northwestern Greenland using the University of Rome/ENEA lidar-system [35] on two distinct observation days in June 2012 and January 2014.The five cases are relative to clouds of different depths located at middle and high tropospheric levels.
The vertical profiles of ka(z) for the five datasets are presented in the following sections.

Calculations of Relative Optical Air Mass Function for Various Aerosol Types and Cloud Particle Layers
The behavior of ma(θ) for the different sets of meteorological data and ka(z) vertical profiles are discussed in the following sections.assumed by TP2014 [22] at Ny-Ålesund for the vertical profile of ka(0.532m) is equal to 50 km, while that assumed in the present study for all the four monthly (or multi-monthly) mean vertical profiles of ka(0.532m) obtained from the field measurements is equal to 90 km.
The values of ka(0.532m) at all the tropospheric levels are appreciably lower than those calculated by TP2014 22 or the summer background Arctic aerosol at Ny-Ålesund, yielding a ground-level visual range V0 = 50 km (calculated according to the Koschmieder theory [36]) The monthly mean vertical profiles of ka(0.532m) determined in January, April, June-July and October-December are shown in Figure 2.They provide a value of V0 = 90 km in all cases.Therefore, the dataset pertains to considerably higher atmospheric transmittance conditions in the visible than those assumed by TP2014 [22].In fact, the extinction coefficients of the four monthly or multi-monthly mean vertical profiles of ka(0.532m) in Figure 2 are appreciably lower than those defined for the summer background Arctic aerosol for z  8 km.In particular, the vertical profiles determined in January and October-December are very similar, with values of ka(0.532m) decreasing from 10 −3 to 3 × 10 −4 km −1 as z increases from 3 to 10 km.Appreciably higher values were measured in June−July, mainly in the upper troposphere; this profile more typically represents the summer background aerosol vertical distribution.The highest values of ka(0.532m) are found in April at all the tropospheric levels, presumably due to the frequent episodes of Arctic haze observed in early spring at this site.The KARL mean vertical profiles of ka(0.532m) were determined up to levels varying between 8.5 and 12 km from the lidar observations, and were completed up to 50 km altitude with the extinction coefficient data determined by TP2014 [22] for summer background Arctic aerosol.The values of τa(0.532m) were equal to 0.016 in January, 0.020 in April, 0.017 in June-July and 0.015 in October-December, therefore considerably less than the value of Arctic summer background aerosol optical thickness τbaa(0.532m) = 0.072 determined by TP2014 [22] for the average summer background Arctic aerosols.
In order to obtain reliable estimates of ma(θ), the vertical profiles of ka(0.532m) shown in Figure 2 were extended to the whole stratospheric altitude range with the vertical profiles defined by TP2014 [22].These were derived from KARL lidar measurements performed at Ny-Ålesund in summer 2009 over the 12-50 km altitude range, and are representative of background Arctic aerosol without volcanic particles in the lower stratosphere.The values of ma(θ), calculated using the four complete vertical profiles of ka(0.532m) from the surface to 50 km height, are given in Table 2.They are appreciably lower than the values of Arctic summer background relative optical air mass mbaa(θ) calculated by TP2014 [22].The differences are equal to about −1% at around θ = 82° for January, at about θ = 81° for April and June-July, and at θ = 82° for October-December, and are at θ = 87° equal to about −4% in January and October-December (corresponding to values of τa(0.532m) close to 0.015) and nearly equal to −6% in April and June-July for slightly higher values of τa(0.532m).This shows that the present estimates of ma(θ) are lower by 4% to 6% than those given by TP2014 [22], being associated with values of τa(0.532m) ranging between 0.015 and 0.020, which are considerably lower than τbaa(0.532m).

Table 2.
Values of the relative optical air mass functions ma(θ) calculated for 25 selected values of apparent solar zenith angle θ ranging from 0° to 87°, as obtained in the present study for background summer Arctic aerosol using as weight functions in Equation (3) the average vertical profiles of ka(z) shown in Figure 2 for Ny-Ålesund in April, June-July and October of 2013, and in Figure 3 for Barrow, Eureka, and Sodankylä, obtained by averaging the CALIPSO data collected during the summer months from June to October of the last 2 years.The present results are compared with the TP2014 [22] evaluations of relative optical air mass function mbaa(θ) determined at Ny-Ålesund for background Arctic aerosol in summer, which are reported in the last column for comparison.

Background Summer Arctic Aerosol Cases based on the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations over Barrow, Eureka and Sodankylä
The seasonal average vertical profiles of ka(0.532m) shown in Figure 3a were derived from the CALIOP/CALIPSO satellite datasets collected in summer during 2013 and 2014 at Barrow, Eureka and Sodankylä.As above, these profiles were used as weighting functions in Equation (3).It is interesting to note that ka(0.532m) is significantly smaller than the values given by TP2014 [22] in the lowest two kilometers.In particular, very similar values of ka(0.532m) were determined at the surface at Barrow and Sodankylä, corresponding to values of V0 of 57 and 60 km, respectively.At both sites ka(0.532m) slowly decreases with altitude until reaching the TP2014 [22] profile at about 2 km altitude.Conversely, the vertical profile of ka(0.532m) at Eureka displays values considerably lower than those of Barrow and Sodankylä at z < ~2 km, the surface-level value yielding V0 = 56 km.The vertical profile of ka(0.532m) was completed above the 5 km level with a profile typical of background polar aerosol, which remains stable at Eureka, Ny-Ålesund and Sodankylä during the summer months, as shown by the lidar measurements conducted at these Arctic sites.On the basis of these measurements, we assumed that ka(0.532m) gradually increases with height to reach the TP2014 [22] rofile at about 5-km altitude.The three CALIPSO vertical profiles of ka(0.532m) shown in Figure 3a were then extended up to 50 km altitude by using the summer background Arctic aerosol profile defined by TP2014 [22] in the upper part of the troposphere and the whole stratosphere.The corresponding summer average values of τa(0.532m) were 0.053 at Barrow, 0.045 at Eureka, and 0.046 at Sodankylä, which are all considerably lower than the TP2014 [22] value of τbaa(0.532m) equal to 0.072 for atmospheric turbidity conditions typical of background Arctic aerosol in summer.The values of ma(θ) calculated using these three CALIPSO vertical profiles of ka(0.532m) are given in Table 2, for comparison with the values of ma(θ) determined from the KARL measurements at Ny-Ålesund, and with those of mbaa(θ) by TP2014 [22].The comparison indicates that the CALIPSO-derived values of ma(θ) at the three Arctic sites gradually increase as a function of solar zenith angle θ differing only slightly from those calculated by TP2014 [22].The percent differences at θ = 87° are −1.3% at Barrow, −0.7% at Eureka, and −1.8% at Sodankylä.These small discrepancies can be plausibly attributed to the relatively lower values of τa(0.532m) obtained for the CALIPSO observations, which are 26%, 37% and 36% lower than τbaa(0.532m).

Background Austral Summer Antarctic Aerosol Cases at Neumayer III, Mirny and Mario Zucchelli from CALIPSO Observations
The calculations of ma(θ) for the three Antarctic coastal sites were carried out as explained in the previous section, using the average vertical profiles of ka( 0 3b were completed with the TP2014 [22] vertical profile of summer background Antarctic aerosol over the altitude range from ~1.5 to 50 km.The corresponding average values of τa(0.532m) were evaluated to be equal to 0.026 at Neumayer III, 0.057 at Mirny, and 0.042 at Mario Zucchelli.Among these mean values of τa(0.532m), the estimate obtained at Neumayer III is therefore lower by 26% than the value of 0.035 estimated by TP2014 [22] for austral summer background Antarctic aerosol at coastal sites over the altitude range from the surface to the stratopause-level, and those here determined at Mirny and Mario Zucchelli are higher by 63% and 20%, respectively, than the value of τbAa(0.532m) calculated by TP2014 [22].
The summer average values of ma(θ) were calculated for the vertical profiles of ka(0.532m) at the three sites.The results are given in Table 3 for θ ranging from 0° to 87°.The comparison with the values of mbAa(θ) determined by TP2014 [22] for austral summer background Antarctic aerosol at coastal sites indicates that the values of ma(θ) determined at Neumayer III are slightly lower than mbAa(θ) by ~1% at θ = 85° and ~2% at θ = 87°.The value of τa(0.532m) at Neumayer III is 0.026, which is equal to about 74% of τbAa(0.532m).Conversely, ma(θ) evaluated at Mirny is higher than mbAa(θ) by ~1% at θ = 84.5°and nearly 3% at θ = 87°.The value of τa(0.532m) is equal to 0.057, which is 63% higher than τbAa(0.532m), suggesting that higher values of ma(θ) are associated with higher values of τa(0.532m).The Mario Zucchelli values of ma(θ) are slightly higher by about 1% than mbAa(θ) for θ = 87°, for the value of τa(0.532m) which is 20% higher than τbAa(0.532m).Tomasi et al. 6 have shown that many diamond dust episodes occur at Amundsen-Scott South Pole base (89°59'S, 139°16'E, 2835 m a.m.s.l.), examining the spectral series of aerosol optical thickness τa(λ) carried out at visible and near-infrared wavelengths by Global Monitoring Division (GMD)/National Oceanic and Atmospheric Administration (NOAA) [9] using the SP02 Carter Scott sun-photometers.The values of τa(0.500m) were found to vary mainly from less than 0.02 to 0.08 and the values of the Ångström [37] exponent  range from less than 0.3 to about 1.2.The low values of  are often due to the presence of significant concentrations of diamond dust particles near the ground.
The mobilization of diamond dust by winds is also very frequently observed at the Dome C base on the Eastern Antarctic Plateau, as confirmed by the INO-CNR Antarctic lidar observations.Diamond dust particles are often present in the lowest 100-200 m of the atmosphere, with values of ka(0.532μm) decreasing with height.Background values typical of the free troposphere are reached at 400-500 m altitude.A sharp increase in the particulate extinction at the ground level is usually observed during these events.In these cases, specific estimates of air mass function mdd(θ) are needed to analyze the sun-photometer measurements of direct solar irradiance for these particularly dense optical turbidity conditions.For this purpose, a diamond dust event observed at Dome C with the INO-CNR Antarctic lidar on 7 February 2008 (from 00:30 to 01:20 UTC) is considered here.The vertical profile of ka(0.532m) is shown in Figure 4.The volume extinction coefficient ka(0.532m) decreases slowly with height in the first 120-140 m above the surface, and rapidly above reaching values typical of the diamond dust-free upper troposphere at altitudes z > 0.4 km.The measured vertical profile of ka(0.532m) up to the altitude of 0.4 km was connected with the austral summer background aerosol profile by TP2014 [22].The overall value of τdd(0.532m) is 0.056, and the ground-level visual range is 7.7 km.close to the ground is due to wind-mobilized diamond dust particles.The corresponding visual range V0 is 7.7 km and the overall value of the aerosol optical thickness τa(0.55 m) is 0.056.
The values of relative optical air mass function mdd(θ) for the diamond dust case are given in Table 3.The values of mdd(θ) are appreciably higher than those of TP2014 [22] pertaining to background Antarctic austral summer aerosol, with differences exceeding + 1% for θ ≈ 81.5°, and up to about + 6.5% for θ = 87°.Such high values of mdd(θ) are attributed to the higher aerosol optical thickness, with τdd(0.532m) about 60% higher than τbAa(0.532m).The present results show that the diamond dust extinction involving the lowest atmospheric layer implies a marked increase of the sun-path length through the ground layer.Therefore, the values of mdd(θ) are in general expected to vary proportionally to the increase of τdd(0.532m), associated with the decrease in the ground-level visual range.

Various Tropospheric Cirrus Cloud Cases from Lidar Measurements at Ny-Ålesund and Thule
Five vertical profiles of ka(0.532m) were considered to calculate the relative optical air mass function for cirrus clouds, mcc(θ).The following cirrus cloud cases, whose profiles are shown in Figure 5, were selected:  (15:10 UTC).The vertical profile of ka(0.532m) is characterized by a marked peak located at about 8.7 km.The cloud layer was superimposed to the monthly average vertical profile of ka(0.532m) for April shown in Figure 2. The overall value of τcc(0.532m) is 0.098, i.e., about five times higher than the value of τa(0.532m) = 0.020 measured in April 2013, indicating that about 80% of the overall particulate extinction along the atmospheric path is produced by cloud particles, and only 20% by polar aerosols.
(ii) Case (b), from the KARL lidar measurements conducted at Ny-Ålesund on 12 July 2013 (14:49 UTC).The vertical profile is characterized by a marked peak centered at z ≈ 5 km, and significant extinction structures at other tropospheric levels.This profile has been assumed to be superimposed to the June−July 2013 average vertical profile of ka(0.532m) shown in Figure 2. In this case, an overall value of τcc(0.532m) = 0.044 has been obtained, about five times higher than the June-July 2013 mean value of τa(0.532m) (= 0.017), indicating that about 60% of the overall atmospheric particulate extinction is due to cloud particles suspended in the middle troposphere.
(iii) Case (c), from the KARL lidar measurements conducted at Ny-Ålesund on 15 October 2013 (12:49 UTC).The measurements exhibit minor extinction features in the 2 to 6 km altitude range and a pronounced bicuspid maximum between 8 and 9 km, which has been assumed to be superimposed over the October-December 2013 average vertical profile shown in Figure 2. A value of τcc(0.532m) = 0.028 has been determined in this case, which is about twice the value of τa(0.532m) = 0.015, determined as October-December 2013 average at Ny-Ålesund, clearly indicating that about 46% of the overall particulate extinction is due to cloud particles.
(iv) Case (d), obtained from the University of Rome/ENEA lidar measurements conducted at Thule on 12 June 2012 over the time interval from 11:09 to 12:14 UTC.The profile shows a very marked multi-layered structure of thick cirrus clouds, extending from about 6 km to more than 10 km altitude, as can be seen in Figure 5.This lidar-derived profile was superimposed to the June−July average vertical profile shown in Figure 2 and assumed to be valid also at Thule.The overall value of τcc(0.532m) = 0.048 is considerably higher than the value of τa(0.532m) = 0.017 estimated for June-July 2013 at Ny-Ålesund.In this case, about 44% of the overall particulate extinction in the atmosphere is produced by cloud particles.
(v) Case (e), derived from the University of Rome/ENEA lidar measurements conducted at Thule on January 30, 2014, over the period from 19:12 to 20:42 UTC.Similarly to the previous cases, the monthly average aerosol profile at Ny-Ålesund for the month of January 2013, derived from the KARL lidar measurements, was added to the cirrus data.The obtained profile is shown in Figure 5.A marked extinction peak exists at z ≈ 10 km.The overall value of τcc(0.532m) was estimated in this case to be equal to 0.036, while a value of τa(0.532m) = 0.016 has been determined at Ny-Ålesund from the KARL lidar measurements conducted in January 2013, indicating that about 56% of the overall atmospheric particulate extinction is due to cloud particles and the remaining 44% to aerosols.
The values of mcc(θ) were calculated for the above five cases by using in Equation (3) the composite vertical profiles of ka(0.532m) shown in Figure 5 as weighting functions.The resulting values of mcc(θ) are given in Table 4.The ratio mcc(θ)/ma(θ) is reported in Table 4 as a function of θ, to highlight the influence of the cirrus cloud layers shown in Figure 5.The values of ma(θ) used in the ratio are derived from Table 2 for the Ny-Ålesund lidar observations made in April 2013 (for case (a)), June-July 2013 (for cases (b) and (d)), October−December 2013 (for case (c)) and January 2013 (for case (e)), respectively.It can be seen that the values of mcc(θ) are 1% lower at θ = 76° for case (a), at θ ≈ 86° for case (b), at θ = 84° for case (c), at θ = 78° for case (d), and at θ = 77° for case (e).Considerably lower values of mcc(θ) with respect to ma(θ) were found for θ = 87°.The reduction is about 15% in case (a), 2% in case (b), 4% in case (c), 12% in case (d) and 13% in case (e).These results also provide evidence that the presence of cirrus clouds at mid and/or high tropospheric levels may lead to significant reductions of mcc(θ) with respect to mbaa(θ), evaluated to increase with a rate proportional to the fraction of optical thickness due to cloud particles.

Conclusions
The multispectral sun-photometry method [18] requires accurate values of the relative optical air mass functions for Rayleigh scattering, aerosol, minor gases and thin clouds as a function of the apparent solar zenith angle θ (see Equations ( 1) and ( 2)).The calculations of ma(θ) for Arctic and Antarctic cases of background polar aerosol made in this study indicate that for θ > 75° ma(θ) appreciably decreases with respect to the TP2014 [22] estimates when τa(0.532 m) is smaller than 0.07 at the Arctic sites and smaller than 0.03 at Antarctic sites.The present analysis of field data has demonstrated that ma(θ) percent variations are proportional to the changes of aerosol optical thickness with respect to the background standard values.The percent changes of ma(θ) become gradually larger as θ increases, up to θ = 87°, which constitutes the upper limit for rigorous sun-photometry applications.
The present results also provide evidence that the formation of an optically dense diamond dust layer near the surface, such as that shown in Figure 4, can cause a marked decrease in mdd(θ) with respect to ma(θ).The difference reaches several percent for θ > 80°.A pronounced relative increase exceeding 6% has been found for θ = 87° in the diamond dust case described in Figure 4.This large increase is attributed to the marked particulate extinction occurring within the lowest atmospheric layers, also involving the thermal and pressure characteristics of the ground layer and their effects on the air refractive index n(z).
Finally, five cases with cirrus cloud layers presenting different depths at various tropospheric altitudes were examined.The calculated values of the corresponding relative optical air mass function mcc(θ) decrease for increasing θ with respect to ma(θ) for pure background aerosol.The increase of mcc(θ) with respect to ma(θ) ranges from 2% to more than 10% as the overall optical thickness τcc(0.532m) increases from 0.028 to 0.098 because of the cirrus cloud contributions, which add to the pure background aerosol contribution, estimated to be equal to 0.02 on average at Dome C. In the five cases, the cirrus clouds produce an increment of the background aerosol optical thickness varying between 50% and about 80%, which enhances the effects of high-altitude pressure and temperature conditions observed at these high levels on both sun-path length and air refractive index, causing considerable decreases of mcc(θ) with respect to mbaa(θ) for pure background aerosol.
Tatiana di Iorio analyzed the University of Rome/ENEA lidar measurements performed at Thule (northwestern Greenland).Massimo del Guasta analyzed the INO-CNR lidar measurements conducted at Dome C (Antarctica).All the authors contributed to writing the manuscript.

:
Ångström (1964) exponent derived from spectral series of τa(λ) over the visible and near-infrared wavelength range; θ: apparent solar zenith angle; τ(λ) total optical thickness of the atmosphere at wavelength λ; τa(λ) aerosol optical thickness at wavelength λ; τa(0.532m) aerosol optical thickness derived from lidar measurements at wavelength λ = 0.532 m; τbaa(0.532m) optical thickness derived from lidar measurements for summer background Arctic aerosols; τbAa(0.532m) optical thickness derived from lidar measurements for austral summer background Antarctic aerosols; τcc(0.532m) optical thickness derived from lidar measurements for cirrus cloud particles; τdd(0.532m) optical thickness derived from lidar measurements for diamond dust at the Antarctic high-altitude sites; τj(λ) optical thickness produced at wavelength λ by absorption of the j-th atmospheric gaseous constituent; τR(λ) rayleigh scattering optical thickness at wavelength λ, Bbs(0.532m) volume backscattering coefficient measured by the lidar-systems employed at Ny-Ålesund (Spitsbergen, Svalbard), onboard the CALIOP/CALIPSO satellite, at Thule (north-western Greenland) and Dome C (Antarctic Plateau); D correction factor used in the Bouguer-Lambert-Beer law applied to the Sun-photometry method to take into account the day-to-day variations in the direct solar irradiance associated with the Earth-Sun distance changes; e(z) water vapor partial pressure at altitude z; J(λ) ground-level direct solar irradiance at wavelength λ; Jo(λ) extra-terrestrial output voltage of the sun-photometer at wavelength λ; Ka integral of ka(z) made over the zo ≤ z ≤ z  altitude range; ka(0.532m) aerosol volume extinction coefficient derived from lidar measurements; ka(z) aerosol volume extinction coefficient at altitude z; m(θ), m relative optical air mass of the atmosphere for a certain solar zenith angle θ; ma(θ), ma relative optical air mass for aerosol extinction at solar zenith angle θ; mbaa(θ) relative optical air mass calculated at solar zenith angle θ for summer background Arctic aerosols; mbAa(θ) relative optical air mass calculated at solar zenith angle θ for austral summer background Antarctic aerosols; mcc(θ) relative optical air mass calculated at solar zenith angle θ for cirrus cloud particles; mdd(θ) relative optical air mass calculated at solar zenith angle θ for diamond dust at Antarctic high-altitude sites; , 1627, 2200 Shiobara et al. [10],di Carmine et al.[11]

Figure 1 .
Figure 1.Monthly mean vertical profiles of wet air temperature T(z) derived over the 0  z  30 km altitude range from the multi-year radiosounding datasets collected at Ny-Ålesund in four different months and at three other Arctic sites in July (left-hand side), and at four Antarctic sites in January (right-hand side).Note that the vertical profile of T(z) (solid triangles) measured at Dome C on the Antarctic Plateau starts at the (surface-level) altitude of 3.233 km.

Bbs( 0
.532 m) measured by the CALIOP/CALIPSO lidar in the austral summer months over the 2°  5° sectors centered at (i) the German Neumayer III base, (ii) the Russian Mirny base and (iii) the Italian Mario Zucchelli base.The data collected during the summer months of the last two years were used from the same CALIPSO/NASA websites mentioned above, presenting collocation, retrieval and overpass times similar to those defined at the previous point(2).(4)A vertical profile of ka(z) for a diamond dust particle layer calculated from measurements of Bbs(0.532m) carried out at the French-Italian Dome Concordia base (~75°S) using the INO-CNR depolarization lidar, which is an automatic prototype operating at wavelength λ = 532 nm, equipped with a 10 cm refractive telescope, and having vertical resolution of 7.5 m, altitude measurement range from 30 to 8 × 10 3 m, and time resolution of 5 minutes.Regular INO-CNR lidar measurements were made during a strong event of diamond dust mobilization by surface winds observed on 7 February 2008 (from 00:30 to 01:20 UTC) and completed with the vertical profile of ka(z) derived from the Bbs(0.532m) lidar measurements carried out at altitudes z > 0.4 km.

3. 1 .
Background Arctic Aerosol Cases based on the Koldewey-Aerosol-Raman Lidar-System Measurements at Ny-Ålesund Monthly mean vertical profiles of aerosol extinction coefficient ka(z) measured with the KARL lidar in four different periods of the year are shown in Figure 2. As discussed above, ka(z) is calculated from the measured values of Bbs(0.532m) using appropriate values of the lidar ratio [1].

Figure 2 .
Figure 2. Monthly or multi-monthly average vertical profiles of aerosol volume extinction coefficient ka(0.532m) determined from the corresponding monthly or multi-monthly average vertical profiles of aerosol volume backscatter coefficient Bbs(0.532m) determined by Tomasi et al. 1 and obtained from the AWI KARL lidar system measurements conducted at Ny-Ålesund (~79°N, Spitsbergen, Svalbard) in January, April, June-July and October−December 2013.Note that the ground-level visual range V0

Figure 4 .
Figure 4. Vertical profile of volume aerosol extinction coefficient ka(0.532m) obtained from the INO-CNR lidar measurements conducted at Dome C on 7 February 2008 (00:40 UTC).The relatively large values of the measured backscattering coefficient Bbs(0.532m)

Figure 5 .
Figure 5. Left-hand side: Vertical profiles of volume extinction coefficient ka(0.532m) obtained from the KARL lidar measurements conducted at Ny-Ålesund (~79°N) for thin cirrus clouds at various tropospheric altitudes and measured on 11 April (15:10 UTC) (case (a)), 12 July (14:49 UTC) (case (b)), and 15 October (12:49 UTC) (case (c)).Each of these three profiles was superimposed to the corresponding monthly (or multi-monthly) mean vertical profile of ka(0.532m) shown in Figure 2 obtained from the KARL lidar measurements conducted in April, June−July and October-December 2013, respectively.Right-hand side: as in the left-hand side, but for the vertical profiles of ka(0.532m) derived from the University of Rome/ENEA lidar measurements conducted at Thule (77°N) on June 12, 2012 (from 11:09 to 12:14 UTC) (case (d)) and January 30, 2014 (from 19:12 to 20:42 UTC) (case (e)).The cirrus cloud profiles were superimposed over the corresponding monthly or bi-monthly mean vertical profile of coefficient ka(0.532m) shown in Figure 2 for June-July 2013 in case (d) and for January 2013 in case (e).
(i) Case (a), relative to measurements made at Ny-Ålesund with the KARL lidar on 11 April 2013
.532 m) derived from the CALIOP/CALIPSO observations made in the summer months of 2013 and 2014, and shown in Figure 3b.Reliable values of ka(0.532m) were found only in the lowest atmospheric layers, approximately below 1.4 km.The ground-level extinction coefficient values correspond to values of V0 equal to 42 km at Mirny, 72 km at Mario Zucchelli, and largely more than 100 km at Neumayer III.At all these sites, the sea salt aerosols, generated by winds over the ocean surfaces and then transported toward the coastal regions 7, are the predominant particulate constituent in the boundary layer.The vertical profiles of ka(0.532m) shown in Figure

Table 3 .
[22]es of the relative optical air mass functions ma(θ ) calculated for 25 selected values of apparent solar zenith angle θ ranging from 0° to 87°, as obtained in the present study for background summer Antarctic aerosol used as weight functions in Equation (3) the average vertical profiles of ka(z) shown in Figure3bfor Neumayer III, Mirny and Mario Zucchelli, as obtained by averaging the CALIPSO data collected during the summer months from November to February of the last 2 years, and values of the relative optical air mass functions mdd(θ) calculated for diamond dust particles obtained for the average vertical profile of ka(0.532m)shown in Figure4for a diamond dust ground layer observed at Dome C on 7 February 2008 (00:40 UTC) using the INO-CNR Antarctic lidar.The present results are compared with the TP2014[22]evaluations of relative optical air mass function mbAa(θ) determined at Mario Zucchelli for background Antarctic aerosol in austral summer, which are reported in the last column for comparison.

Table 4 .
Values of the relative optical air mass functions mcc(θ) calculated for 25 selected values of apparent solar zenith angle θ ranging from 0° to 87°, as obtained using as weighting functions in Equation (3) the average vertical profiles of ka(z) shown in Figure5for three thin cirrus cloud cases observed at Ny-Ålesund on 11 April (15:10 UTC) (case (a)), 12 July (14:49 UTC) (case (b)), and 15 October (12:49 UTC) (case (c)) using the KARL lidar system, and two cirrus cloud cases observed at Thule (76°39'N, 68°46'W, 225 m a.m.s.l.m.) on 12 June 2012 (from 11:09 to 12:14 UTC) (case (d)), and 30 January 2014 (from 19:12 to 20:42 UTC) (case (e)), using the Rome University LiDAR.The last five columns provide the values of ratios mcc(θ)/ma(θ) to give a measure of the percentage variations caused by the thin cirrus clouds with respect to the monthly mean values of ma(θ) determined for background Arctic aerosol extinction features.