advertisement

Correlation of aerosol optical parameters for OCO channels Yu.M. Timofeyev, Ya.A. Virolainen, A.V. Polyakov Research Institute of Physics, St. Petersburg State University, 198504 St. Petersburg, Russia, Yu.M.Tim@JT14934.spb.edu 1 1. Introduction Aerosol model consists from different components which form aerosol types by external mixing. Database OPAC includes 10 components (in dry state) and 13 aerosol types. Aerosol components are characterized by: Aerosol Size Distribution Functions (SDF) for homogenous spherical particles ni(r, z), Complex refractive index (CRI) mi (, z) = ni (, z) –i ki (, z), Altitude profiles of concentration Ni(z), SDF and CRI (and optical aerosol parameters) depend on ambient conditions (humidity, wind and etc.) In reality, especially for some clouds, we need information about form and orientation of the particles. Atmospheric aerosol size distributions are often described as the sum of n log-normal distributions, (log D p log D ) 2 n N pi i n oN ( log D p ) exp 2 i 1 2 1/ 2 log i 2 log i where Ni – is the number concentration, D pi is the mean diameter, and i is the standard deviation of the i t h log-normal mode. In this case 3n parameters are necessary for the description of the full aerosol distribution. Characteristics of model aerosol distributions are presented in Table 1, following the suggestions of Jaenicke (1993). In this case for description of SDF we need 9 parameters. 2 Table 1. Parameters for Aerosol Model Distributions Expressed as the Sum of Three Log-Normal Modes Mode I Mode II log Dp (cm–3) (m) log N Dp (cm–3) (m) log N Dp (cm–3) (m Urban 9.93 x 104 0.013 0.245 1.11 x 103 0.014 0.666 3.64 x 104 0.05 0.337 Marine 133 0.008 0.657 66.6 0.266 0.210 3.1 0.58 0.396 Rural 6650 0.015 0.225 147 0.054 0.557 1990 0.084 0.266 Remote 3200 0.02 0.161 2900 0.116 0.217 0.3 1.8 0.380 129 0.007 0.645 59.7 0.250 0.153 63.5 0.52 0.425 Polar 21.7 0.138 0.245 0.186 0.75 0.300 3 x 104 8.6 0.291 Desert 726 0.002 0.247 114 0.038 0.770 0.178 21.6 0.438 Type N Mode III continental Free troposphere Source: Jaencke (1993) 3 Example of SDF for urban aerosol model o o o Fig.1. Typical urban aerosol number n N , surface n S , and volume nV distributions. 4 Altitude dependence of concentration for different aerosols Fig.2. Representative vertical distribution of aerosol number concentration [Jaenicke, 1993]. A range of concentrations is shown for marine and remote continental aerosols Different aerosol characteristics are strongly varied in space and time. Their variability have to be taken into account using satellite measurements. The statistical approach is used for developing the method for the consideration of the aerosol influence. A description of this approach is given in our papers [Biryulina and Rozanov, 1990; Polyakov et al., 2001, 2003; Virolainen et al., 2004; Timofeyev et al., 2003]. 5 2. Methods for obtaining the statistical optical characteristics of aerosols Methods for obtaining the statistical aerosol optical characteristics can be divided at five classes: 1. The first traditional method has been applied for long-term measurements of aerosol microphysical characteristics in USA [Grainger et al., 1995]. It includes calculations of optical characteristics of aerosol ensembles { ( , z ) , ( , z ) , x ( , , z ) }i by Mie algorithm from measured size distribution functions f (r ) (SDF) and given refraction index m n i . 2. The second approach [Gorchakov et al., 1976a–c] uses direct measurements of realizations of aerosol optical characteristics { ( , z ) , ( , z ) , x ( , , z ) }i for calculating the statistical aerosol characteristics K (1, 2 ) , K (1 , 2 ) , etc. 3. The third method [Timmerink, 2001; Drdla et al., 2003] applies an numerical model which takes into account the evolution and transformation of aerosol and cloud characteristics for the simulation of the ensemble of size distribution functions (SDF) and refraction indexes and further calculations of optical and statistical characteristics. 4. In the fourth method [Russel et al., 1983; Burulina et al., 1990; Gobbie, 1995; Polyakov et al., 2001], average aerosol microphysical models and variabilities are used for the simulation of initial ensemble of aerosol physical characteristics. 5. The fifth approach – the use of optical aerosol model (e.g. OPAC [Hess et al., 1998; Levoni et al., 1997] for simulating the ensemble of fraction concentrations to calculate ensembles of aerosol optical and statistical characteristics All the methods make it possible to calculate covariance and cross-covariance matrices describing the statistical relations between different microphysical and optical characteristics of aerosol and clouds and between aerosol optical characteristics and different atmospheric parameters. 6 3. Statistical model of tropospheric aerosol Model OPAC (Optical Properties of Aerosols and Clouds) [Hess et al., 1998] based on different field experiments is used for the statistical simulation of the variability of optical characteristics of tropospheric aerosol. This model includes optical aerosol characteristics (for 0.25–40 m) for 10 fractions: WASO (water-soluble aerosol from different sulphates, nitrates and other organic and compounds), INSO (insoluble particles – a mixture of dust, soil, etc.), SOOT, MINM, MIAM, MICM, MITR (mineral quart and clay participles), SSAM, SSCM (participles of sea salt) and SUSO (stratospheric sulphate participles consisting mainly from sulphuric acid droplets) (see, Table 2). Table 2. Aerosol components of the Global Aerosol Data Set and their main microphysical parameters (OPAC Model). Components of the Global Aerosol Data Set No. Aerosol Component Name rm [m] [g/cm3] 1 Water-insoluble INSO 4.71 E-1 2.51 2.0 2 Water-soluble WASO 2.12E-2 2.24 1.8 3 Soot SOOT 1.18E-2 2.00 1.0 4 Sea-salt (accumulation SSAM 2.09E-1 2.03 2.2 5 mode) (coarse mode) Sea-salt SSCM 1.75E+0 2.03 2.2 6 Mineral (nucleus mode) MINM 7.00E-2 1.95 2.6 7 Mineral (accumulation MIAM 3.90E-1 2.00 2.6 8 mode) (coarse mode) Mineral MICM 1.90E+0 2.15 2.6 9 Mineral-transported MITR 5.00E-1 2.20 2.6 10 H2SO4-Droplets SUSO 6.95E-2 2.03 1.7 On the basis of these fractions 10 regional aerosol types describing global characteristics of earth aerosol: continental (background, mean, turbid), urban, desert, sea (background, tropical, turbid), arctic, antarctic aerosols were constructed (OPAC model). 7 Аnalysis of optical aerosol characteristics Studied characteristics: the aerosol extinction coefficient (AEC), the aerosol scattering coefficient (ASC), and the parameter of asymmetry (PA) g (the mean scattering cosines). Input data: statistical ensembles of optical characteristics for different aerosol types in three spectral ranges that consist of 500 realizations of number concentration (Ni) profiles for different aerosol fractions at 25 tropospheric altitudes (0–12 km). Calculations: the characteristics. complete covariance matrix of studied Studies: spectral correlations of optical characteristics, correlation between different optical parameters, optimal parameterization of optical aerosol characteristics for three wavelengths for method for determining the aerosol type and the solution of the inverse problem. In Table 3 some characteristics of two local ensembles of tropospheric aerosol – continental and sea ones - are given. The continental model includes the models of pure and polluted continental and town aerosols, the sea model – models of pure and contaminated sea aerosol. 8 Table 3. Characteristics of local models of tropospheric aerosol (layer thickness h, height of homogeneous atmosphere H, aerosol fractions and spread of surface concentration N0). Model Continental h, H, km km 0–2 8 Fractions (spread of surface concentration N0) WASO (25–35752), INSO (0.0007–1.81), SOOT (47–212689) 2–12 8 WASO (0.8–737), INSO (0.02–0.14), SOOT (0.6–489) 0–2 Sea 1 WASO (0.5–5592), SOOT (0.9–10019), SSAM (0.3–33), SSCM (0.00001–0.005) 2–12 8 WASO (0.8–737), INSO (0.02–0.14), SOOT (0.6–489) Spectral dependence of CRI for considered measurement spectral range 1.9 1.8 SSAM WASO SOOT MITR INSO real part of CRI 1.7 1.6 1.5 1.4 1.3 1.2 0.6 0.8 1.0 1.2 1.4 Wavelength, m 1.6 1.8 2.0 2.2 Fig.3. Real part of complex refraction index (CRI) for different aerosol fractions (OPAC). 9 1 0.1 imaginary part of CRI 0.01 0.001 0.0001 SSAM WASO SOOT MITR INSO 1E-005 1E-006 1E-007 0.6 0.8 1.0 1.2 1.4 Wavelength, m 1.6 1.8 2.0 2.2 Fig.4. Imaginary part of complex refraction index (CRI) for different aerosol fractions (OPAC). 1 1 0.1 0.1 0.01 0.01 Scattering, km-1 Extinction, km-1 Spectral dependence of AEC, ASC and g for considered measurement spectral range 0.001 WASO INSO SOOT SSAM SSCM 0.0001 1E-005 1E-006 0.001 1E-005 1E-006 1E-007 1E-007 1E-008 1E-008 1E-009 1E-009 0.8 1.2 1.6 2 Wavelength, m 2.4 WASO INSO SOOT SSAM SSCM 0.0001 0.8 1.2 1.6 2 Wavelength, m 2.4 Fig.5. Spectral dependence of AEC (on the left) and ASC (on the right) for particles of different aerosol fractions involved in continental and sea models of tropospheric aerosol (see Table 1). Significant differences between AEC and ASC are only for SOOT particles, for other fractions the scattering is the main cause of radiation attenuation (see also Fig.4). AEC and ASC in the channel 2 m is less by an order of magnitude, three times and 30% that those in the channel 0.76 m for WASO, SOOT and SSAM, respectively. AEC and ASC in these channels change slightly for INSO and SSCM. 10 1 Asymmetry parameter 0.8 0.6 WASO INSO SOOT SSAM SSCM 0.4 0.2 0 0.8 1.2 1.6 Wavelength, m 2 2.4 Fig.6. Parameter of asymmetry g (AP) of the scattering indicatrix for different aerosol fractions involved in continental and sea models of tropospheric aerosol (see Table 1). Indicatrices are different for different fractions. AP values for SOOT are close to 0 (isotropic scattering, AP=0.1–0.3) especially in the long-wave range. APs are 0.45–0.65 for WASO and the indicatrices for INSO, SSAM и SSCM are most elongated ahead (AP=0.8–0.9). The AP growth at 2 m in comparison with 0.76 and 1.6 m is observed for the fraction SOOT. This peculiarity, as we will show further, will effect AP of constructed ensembles in free atmosphere where besides INSO there are only particles of fractions SOOT and WASO. 11 Optical depth (AOD) of tropospheric aerosol 0.25 Model Continental Maritime Aerosol optical depth 0.2 0.15 0.1 0.05 0 0.4 0.8 1.2 1.6 Wavelength, m 2 2.4 Fig.7. Mean value (with RMS variability) of aerosol optical depth of tropospheric aerosol in different measurement channels for different models of tropospheric aerosol. Mean AODs are maximal for the ensemble of the continental model and minimal for the maritime model. In the continental model, the essential change of the mean AOD is observed in going from the channel 0.765 m to the channel 2.016 m. The mean AOD value at 0.765 m for the continental model is twice as large in comparison with the maritime model. Mean AODs are practically the same at 2.016 m for both models. In the channel 0.765 m, the AOD RMS variability is maximal and equal to about 60% of the mean for the continental model. 12 AOD distribution in the channel 0.765 m 100 160 80 Continental aerosol 40 Number of cases Number of cases 80 120 60 Maritime aerosol 40 20 0 0 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Aerosol optical depth 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 Aerosol optical depth Fig.8. AOD distribution at 0.765 m for ensembles of continental (on the left) and maritime (on the right) models. The most part of AOD values (from 500 realizations) falls at 0.05– 0.15 and 0.045–0.065 for continental and maritime models, respectively. In the ensemble of aerosol continental model, there are more dense realizations of tropospheric aerosol. 13 4. Correlations of optical parameters 12 10 AEC 1.607 m AEC 2.061 m ASC 0.765 m ASC 1.607 m ASC 2.061 m AP 0.765 m AP 1.607 m AP 2.061 m Altitude, km 8 6 4 2 0 -0.8 -0.4 0 Correlation coefficient 0.4 0.8 Fig.9. Correlation between AEC in the channel 0.765 m and other aerosol parameters for ensemble of continental aerosol. 12 10 AEC 1.607 m AEC 2.061 m ASC 0.765 m ASC 1.607 m ASC 2.061 m AP 0.765 m AP 1.607 m AP 2.061 m Altitude, km 8 6 4 2 0 -0.8 -0.4 0 Correlation coefficient 0.4 0.8 Fig.10. Correlation between AEC in the channel 0.765 m and other aerosol parameters for ensemble of maritime aerosol. 14 Correlation coefficients (CC) are different for two models mainly in the boundary layer, as in generating the ensembles for both models in the free troposphere (above 2 km – see Table 3), we used the same statistical data. Comparing Fig.9 and 10, one can see that the AEC-ASC correlation in the layer 0–2 km is higher for the narrower ensemble of maritime model. CC between AEC at 0.765 m and AEC (ASC) in other channels exceeds 0.90–0.95 and CC between AEC and ASC is close to 1. For the continental aerosol (Fig.9), in troposphere (0–2 km), CC between AEC and ASC at 0.765 m is 0.75–0.85 depending on altitude. Similar situation is for CC between AEC at 0.765 m and ASC in other channels (0.65–0.75 and 0.50–0.65 in channels 1.607 and 2.061 m, respectively). This fact is explained by the influence of the fraction of soot particles SOOT. CC between AECs in different channels is also smaller for continental aerosol than for maritime aerosol (about 0.95 for the channel 1.607 m and 0.85 for the channel 2.061 m) due to the greater spectral AEC variability in the model of continental aerosol. Correlations between AEC and the indicatrix (AP) are practically absent for the maritime aerosol and CC equals to 0.55 (negative) on the average for the continental model. In free troposphere, CCs between AEC at 0.765 m and AEC (ASC) in channels 1.607 and 2.061 m are 0.8 and 0.6 on the average, respectively, and little variable along altitude. CC between AEC at 0.765 m and AP is negative and equals to about 0.8. High CC values in free troposphere is determined by a small variability of AP and AEC at each atmospheric level. In constructing the models, the troposphere was classified as two layers – the boundary layer (local ensembles) and the free troposphere (ensembles similar in statistical characteristics for two models). Therefore further we will consider three ensembles: the boundary continental, the boundary maritime and the free troposphere (see Table 3). 15 Correlation between AEC at 0.765 m and other optical parameters 1 0.8 Correlation coefficient 0.6 Continental Maritime Free troposphere 0.4 0.2 AEC ASC AP 0 -0.2 -0.4 -0.6 -0.8 -1 0.8 1.2 1.6 Wavelength, m 2 Fig.11. Spectral dependence of CC between AEC at 0.765 m and other optical parameters in different measurement channels for different ensembles of tropospheric aerosol. (* – CC between natural logarithms of AEC and ASC.) It is seen that there are significant correlations (CC=0.85–0.99) between AEC in the channel 0.765 m and AEC and ASD in other channels. The exception is the ensemble of the continental model for which AEC–ASD correlation coefficient decreases from 0.8 at 0.765 m to 0.55 at 2.061 m. Correlations between AEC and SP are essentially smaller and practically do not depend on wavelength (CC is close to 0 for the maritime model, CC=0.40–0.45 for the free troposphere, CC=0.55 (in an absolute value) for the continental aerosol. Spectral dependence marked by asterisks shows that there is a possibility to enhance correlations between AEC and ASD for the continental model using the connection between logarithms of parameters. For other models such increase of CC is not observed. 16 6. Optimal parameterization of spectral dependence of optical aerosol parameters Availability of a statistical ensemble of aerosol parameters gives a possibility to parameterize any spectral dependence by the expansion into eigenvectors of relevant covariance matrix (into an empirical orthogonal basis). This expansion is optimal in the sense of obtaining the minimal parameterization errors. Optimal parameterization of any parameter (AEC, ASC or AP) [Oboukhov, 1959] i : i i a p f p i p 1,n f p i are eigenvalues of spectral covariance parameter, a p are relevant expansion coefficients. Here matrix of an aerosol Parameterization based on Angstrom relation [Lenoble and Pruvost, 1983]: 0 a Here 0 and a are some parameters. 17 Comparison of two parameterizations Table 4. Errors of two parameterizations of aerosol parameters for different ensembles of tropospheric aerosol Type Angstrom Optimal Parameter Continental Maritime Free 0–2 km 0–2 km troposphere AEC 5.9% 3.9% 2.1% ASC 9.9% 4.1% 1.2% AP 5.4% 1.4% 6.5% AEC 0.3% 0.03% 0.02% ASC 0.3% 0.02% 0.02% AP 1.5% 0.04% 0.07% It is seen a significant advantage of the optimal parameterization, especially for AEC in the continental model, when the absorption plays the principal role in the aerosol extinction caused by soot particles. Errors of spectral approximation are 0.02–0.3% for AEC and ASC and 0.04–1.5% (2% for the continental ensemble) for AP in the case of optimal parameterization. Those are 1.2–9.9% for all parameters and aerosol types in the case of Angstrom parameterization. 18 7. Conclusion and recommendations 1. Global and a number of regional statistical models (continental, maritime, free troposphere) of aerosol optical characteristics have been constructed by numerical modelling. The first two moments (mean and covariance matrices) of the ensembles of optical parameters were calculated. It is shown that AEC, ASC and AP are the most variable in the continental ensemble. 2. Correlations between different aerosol parameters in the channels 0.765, 1.607 и 2.061 m have been studied. It is shown that there are significant correlations between AEC and ASC in all channels. CC between natural logarithms of these parameters is 0.7–1.0 depending on the model, the channel and the parameter. Correlations between AEC and AP are essentially less (0.05–0.55) and do not depend on wavelength. CC between values of a parameter in different channels is 0.5–1.0. 3. Errors of the approximation of AEC, ASC and AP spectral dependence by the methods of optimal parameterization and Angstrom have been analyzed. Errors of approximating the aerosol parameters averaged over three channels are 0.02–1.5% and 1.2–9.9% for optimal and Angstrom parameterizations, respectively. Errors of optimal parameterization does not exceed 0.1% in several channels for the maritime and the free troposphere models. The error of Angstrom parameterization for AEC and ASC increases with wavelength and for ASC in the channel 2.061 m ranges up to 22% for ensemble of continental aerosol. 19 Recommendations It is necessary: to proceed with the construction of statistical models of optical characteristics of tropospheric aerosol of different types (including the consideration of the polarization) and numerical studies of statistical spectral and altitudinal relations between different optical characteristics. to study variations of outgoing radiance in different OCO channels caused by variations of microphysical and optical characteristics of tropospheric aerosol. It is possible to calculate the measurement "effective noise" caused by variations of aerosol characteristics and to analyze different methods for the aerosol accounting in solving the inverse problem with respect to the column amount CO2 . to analyze available experimental data (or to organize special measurements) for studying the statistical relations (spectral, altitudinal) between different optical characteristics of tropospheric aerosol. 20 7. References Biryulina M.S., and V.V. Rozanov, 1990: The parameterization of aerosol size distribution functions for forward and inverse problems of the atmosphere remote sensing. Atm. Optics, 3, 10, 1087–1094, (Engl. transl.). Biryulina M.S., and V.V. Rozanov, 1990: The parameterization of aerosol size distribution functions for forward and inverse problems of the atmosphere remote sensing, Atm. Optics, 3, 10, 1087–1094, (Engl. transl.). Drdla K., M.R. Schoeberl, E.V. Browell, 2003: Microphysical modeling of the 1999–2000 Arctic winter: 1. Polar stratospheric clouds, denitrification, and dehydration. J.G.R, 108, D5, 8312, doi:10.1029/2001JD000782. Gobbie P.G., 1995: Lidar estimation of stratospheric aerosol properties: Surface, volume and extinction to backscatter ratio. J.G.R, 100, D6, 11219–11235. Gorchakov G.I., A.A. Isakov, M.I. Sviridenkov, 1976: Correlation between coefficients of attenuation and directional light diffusion in the 0.5–165 range. Izv. RAS, Atm. and Ocean. Phys., 12, 12, 1261–1268 (in Russian). Gorchakov G.I., A.A. Isakov, Yu.S. Georgievsky, 1976: Correlation between coefficients of attenuation and directional light diffusion in the range of small angles. Izv. RAS, Atm. and Ocean. Phys., 12, 5, 514–522(in Russian). Gorchakov G.I., M.I. Sviridenkov, 1976: Statistical analysis of light scattering matrices. Izv. RAS, Atm. and Ocean. Phys., 12, 9, 953–962 (in Russian). Grainger R.G., A. Lambert, C.D. Rodgers, et al.1995: Stratospheric aerosol effective radius, surface area and volume estimated from infrared measurements. J.G.R, 100, 16507–16518. Hess M., P. Koepke, I. Schult, 1998: Optical properties of aerosol and clouds: The software package OPAC. Bull. Americ. Meteor. Soc., 79, 5, 831–844. Jaenicke R., 1993: Tropospheric aerosols. In Aerosol-cloudsclimate interaction.Ed. by P.V. Hobbs. Academic press, Sandiego, CA, 1-31. 21 Lenoble, J. and P. Pruvost, 1983: Inference of the aerosol Angstrom coefficient from SAGE short–wavelength data. J. Climate and Appl. Meteor., 22, 10, 1717–1725. Levoni, Ch., M. Cervino, R. Guzzi, and F.Torricella, 1997: Atmospheric aerosol optical properties: a database of radiative characteristics for different components and classes. Appl. Opt., 36, 30, 8031–8041. Oboukhov, A.M., 1959: About statistically orthogonal expansions of empirical functions. Izv. RAS, Geophysics, 3, 432–459, (in Russian). Polyakov A.V., A.V. Vasil'ev, and Yu.M. Timofeev, 2001: Parametrization of the Spectral Dependence of the Aerosol Extinction Coefficient in Problems of Atmospheric Occultation Sounding from Space. Izv. RAS, Atm. and Ocean. Phys., 37, 5, 646–657 (Engl. transl.). Polyakov A.V., A.V. Vasil'ev, and Yu.M. Timofeev, 2001: Parametrization of the Spectral Dependence of the Aerosol Extinction Coefficient in Problems of Atmospheric Occultation Sounding from Space. Izv. RAS, Atm. and Ocean. Phys., 37, 5, 646–657 (Engl. transl.). Polyakov A.V.and Yu.M. Timofeyev, 2003: Potential Accuracies of Retrieving the Vertical Profiles of Atmospheric Parameters (Satellite–Based Transmittance Method): 2. Spectral Coefficient of Aerosol Extinction. Izv., Atm. and Ocean. Phys., 39, 2, 234– 239 (Engl. transl.). Polyakov A.V., Yu.M. Timofeyev, V.S. Kostsov, Ya.A. Virolainen, D.V. Ionov, A.M. Chaika, H.M. Steele, M.J. Newchurch, Trace gas and aerosol sounding of the atmosphere in the sun occultation experiment with SAGE-III device // Proceedings of the International Radiation Symposium, 2004, IRS 2004: CURRENT PROBLEMS IN ATMOSPHERIC RADIATION, eds. , Deepak Publishing, 2005, pp Polyakov A.V., Yu.M. Timofeyev, D.V. Ionov, Ya.A. Virolainen, H.M. Steele, M.J. Newchurch, Retrieval of ozone and nitrogen dioxide concentrations from Stratospheric Aerosol and Gas Experiment III (SAGE-III) measurements using a new algorithm // JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, D06303, doi:10.1029/2004JD005060, 2005 22 Russel P.B., T.J. Swissler, M.P. McCormick, et al., 1981: Satellite and correlative measurements of the stratospheric aerosol. I. An optical model for data conversion. J. Atm. Sci., 38, 1279–1294. Timmreck C., 2001: Three-dimensional simulation of stratospheric background aerosol: First results of multiannual general circulation model simulation. J.G.R., 106, D22, 28313–28332. Timofeyev Yu.M , A.V. Polyakov, H.M. Steele, M.J. Newchurch, 2003: Optimal Eigenanalysis for the Treatment of Aerosols in the Retrieval of Atmospheric Composition from Transmission Measurements. Appl. Optics, 42, 15, 2635–2646. Timofeyev Yu.M., A.V. Polyakov, Ya.A. Virolainen, V.S. Kostsov, H.M. Steele, M.J. Newchurch, K. Drdla. Statistical models of aerosols and polar stratospheric clouds (PSC) for remote sensing // Remote Sensing of Clouds and the Atmosphere VIII, Proc. of SPIE Vol. 5235 (SPIE, Bellingham, WA, 2004), pp. 347-356. Timofeyev Yu.M., Ya.A. Virolainen, A.V. Polyakov, A.V. Vasilyev, H.M. Steele, M.J. Newchurch, New method for interpreting the limb scattered solar radiance measurements // Proceedings of the International Radiation Symposium, 2004, IRS 2004: CURRENT PROBLEMS IN ATMOSPHERIC RADIATION, eds., Deepak Publishing, 2005, pp. Virolainen Ya.A., A.V. Polyakov, Yu.M. Timofeyev, 2004 Statistical Models for Tropospheric Aerosol. Izv. RAS, Atm. and Oceanic Phys., 40, 2, 216–227 (Engl. transl.). Virolainen Ya.A., Timofeev Yu.M., Polyakov A.V., Steele H., Drdla K., Newchurch M. Simulation of polar stratospheric clouds: 1. Microphysical characteristics // Atmospheric and Oceanic Optics , vol. 18, 2005, No.03, p.243-247 Virolainen Ya.A., Timofeev Yu.M., Polyakov A.V., Steele H., Drdla K., Newchurch M. Simulation of polar stratospheric clouds: 2. Spectral aerosol extinction coefficient and PSC remote sensing possibilities vol. 18, 2005, No.07, p.526-531 23