AMASDU Aerosol Mapping Algorithms for Satellite

ESA Data User Programme

AMASDU Final Report

AMASDU Aerosol Mapping Algorithms for Satellite Data Users 4-D Cartography and Data Assimilation

FINAL REPORT June 10, 1999

Authors: G. Franssens D. Fonteyn Q. Errera M. De Mazière D. Fussen

Co-ordination: M. De Mazière Belgian Institute for Space Aeronomy (BIRA-IASB) Ringlaan, 3 B-1180 Brussels BELGIUM

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TABLE OF CONTENT ABSTRACT

2

EXECUTIVE SUMMARY

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ABSTRACT EXECUTIVE SUMMARY

2 3

INTRODUCTION

5

1.

1.1 1.2 1.3 1.4 2.

PROJECT INTEREST PROJECT USERS PROJECT GOALS PROJECT SCHEDULE

MULTISPECTRAL CARTOGRAPHY (WP 2100) 2.1 OBJECTIVES 2.2 PROBLEM DESCRIPTION 2.3 PROBLEM SOLUTION: SPECTRAL FITTING ALGORITHM 2.4 VARIABILITIES OF STRATOSPHERIC AEROSOL PROPERTIES 2.5 LIMITATIONS OF THE SPECTRAL INTERPOLATION ALGORITHM 2.6 ALGORITHM VALIDATION 2.7 EXAMPLES OF SAGE II SPECTRAL EXTINCTION INTERPOLATION 2.7.1 SPECTRAL INTERPOLATION AND INVERSION VERSUS ALTITUDE FOR JANUARY 1992 (POST PINATUBO PERIOD) 2.7.2 SPECTRAL INTERPOLATION AND INVERSION VERSUS TIME AT 22.5 KM ALTITUDE 2.8 EXAMPLES OF GOME TOTAL COLUMN AEROSOL EXTINCTION MAPS 2.9 CONCLUSIONS CONCERNING WP2100

3.

4D VARIATIONAL CHEMICAL DATA ASSIMILATION (WP 3100) 3.1 INTRODUCTION 3.2 SET-UP OF THE CHEMICAL BOX MODEL 3.2.1 CHEMICAL MECHANISM 3.2.2 THE CHEMICAL BOX MODEL 3.2.3 NUMERICAL IMPLEMENTATION 3.3 SET-UP OF THE ADJOINT OF THE CHEMICAL BOX MODEL. 3.3.1 ADJOINT OF THE CHEMICAL MODEL 3.3.2 IDEALISED ANALYSIS FOR A SINGLE PARTICLE 3.4 IMPLEMENTATION OF THE BOX MODEL AND ITS ADJOINT 3.4.1 3D CHEMICAL FORWARD TRANSPORT MODEL 3.4.2 ADJOINT OF THE 3D CHEMICAL BACKWARD TRANSPORT MODEL 3.5 DEMONSTRATION CASE OF 4D-VAR CHEMICAL ASSIMILATION 3.5.1 CASE SELECTION 3.5.2 ASSIMILATION ANALYSIS AND PREDICTION SET-UP 3.6 ASSIMILATION RESULTS 3.7 4D-VAR IMPLEMENTATION ISSUES

5 6 7 8 9 9 9 15 17 19 21 21 21 27 30 31 41 41 41 41 41 42 42 42 42 47 47 47 47 47 48 49 50

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CONCLUSIONS CONCERNING WP3100

REFERENCES

50 61

1. NOTATION 2. EXTINCTION 3. AN EXPLICIT INVERSION FORMULA THEOREM 4. DISCRETE BASIS FUNCTIONS 5. THE DISCRETE REPRESENTATION 6. THE DATA FITTING ALGORITHM

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Abstract The current report describes the results of the ESA Data User Programme (DUP) project, “Aerosol Mapping Algorithms for Satellite Data Users” (AMASDU, Feb. 1998 - Feb. 1999). The aim of the project was to develop tools for spectral interpolation of aerosol extinction coefficients (spectral cartography) and to upgrade the 4D variational data assimilation (4DVAR) scheme of aerosols in a pure transport model to a scheme including chemical interactions. Both tasks are the continuation of the work began in the precursor DUP project DAMS2P. The spectral interpolation exends the global 3D cartography, developed in DAMS2P, to a fourth spectral dimension. We developed a new method for spectral interpolation of aerosol extinction coefficients, based on the Anomalous Diffraction Approximation. This method simultaneously solves the spectral inverse problem, i.e., it also produces the aerosol size distribution. Examples of numerical tests as well as applications to SAGE II data are shown. The 4D-VAR method developed in this project considers 38 species and 145 chemical reactions and is representative for the chemical evolution in the stratosphere on a time scale of a season. The full chemical treatment includes a detailed microphysical model of aerosols and related heterogeneous chemistry. It was found that the 4D-VAR method can even accurately assimilate unobserved species, which are chemically coupled to the observed ones (e.g. ClONO2 from NO2 and ClO). Examples of 4D-VAR analyses applied to CRISTA 1 data are shown. The techniques and software tools developed in the DAMS2P and AMASDU projects are useful for a variety of satellite data users. The global cartography and assimilation methods developed are not limited to aerosols, but applicable to many other species. They are valuable for validation, interpretation and visualization of atmospheric data produced by satellite experiments, such as the atmospheric chemistry instruments on the future ENVISAT-1 mission.

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Executive Summary The number of satellite experiments that probe the atmosphere is growing steadily, resulting in an ever-increasing stream of observational data. Potential users of satellite data are more and more confronted with a problem of accessibility and visibility of these data. The ESA Data User Programme addresses that problem. Its goal is the enhancement of the exploitation of satellite data, through the development of tools that come up to the requirements of potential users. In this context, a first project called DAMS2P (Development of Global Aerosol Mapping from Satellites level-2 Products), aimed at developing global mapping tools for satellite level2 data. Two different approaches were followed for the production of global aerosol maps: a cartography approach and a 4D variational data assimilation method. The former approach is essentially spherical interpolation, the latter method is based on a numerical atmospheric transport model for propagation of the aerosol particles and produces a dynamically consistent map. The current project, called AMASDU (Aerosol Mapping Algorithms for Satellite Data Users), extends the work began in the first project, by incorporating also the spectral dimension (wavelength). Combining spectral information allows a user to, e.g., distinguish between aerosols, Polar Stratospheric Clouds (PSCs) and ordinary clouds. It also allows to obtain derived parameters, such as aerosol size distributions and to develop atmospheric climatologies for them (WP2100). In addition a stratospheric chemistry module has been included in the 4D variational assimilation (WP3100), giving access to a more realistic microphysical model for aerosol creation, transport and destruction, and this resulting in more reliable assimilated maps. Examples of potential users of global aerosol maps are the various remote sensing communities (e.g., ISPRA, European Environment Agency (EEA)), satellite data validation teams (e.g., GOME and ENVISAT), study groups for the assessment of the atmospheric aerosol load and evolution (e.g., WMO, UNEP assessment groups, EC DGXII), programmes/projects concerned with estimations of direct aerosol radiative forcing (e.g., IGAC, WMO/GAW and WCRP/BSRN), atmospheric chemistry and dynamics experiments (e.g., THESEO), UV modelling groups), assessment of impacts of a commercial subsonic/ supersonic aircraft fleet (e.g., IPCC, EEA BOEING, AIRBUS), the evaluation of the Montreal Protocol, etc. In both projects two approaches have been followed for the production of global aerosol maps: a direct cartography approach and a 4D variational data assimilation method. Both methods have specific advantages and are useful to the user community. Direct cartography based on spherical interpoloation is fast and justified for species that show little variation over the time span of the observations used in the interpolation (asynoptic map). On the contrary, assimilation can take into account the time at which the observations were made, and produce a map at one common moment (synoptic map). It can interpolate in time and space in a way that is consistent with the dynamics and chemistry of the atmosphere. In

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general this method will lead to more accurate maps, but is computationally very expensive. The objective of WP2100 was the development of an interpolation and/or fitting algorithm to characterise the aerosol extinction coefficient dependence on the wavelength, β(λ) . The input to the algorithm naturally consists of coefficient values, measured at a limited set of wavelengths by one or more experiments. The output is a mathematical representation of the function β(λ) . The available extinction measurements at different wavelengths are very irregularly and sparsely distributed over the UV to IR wavelength range. This makes this interpolation problem very hard to solve, because it is largely underdetermined. The nature of the available data on one hand and the mathematics on the other hand make that no off the shelf interpolation method could be used for this task. A new approach has been developed in which the function β(λ) is expanded as a linear combination of carefully chosen basis functions. The associated expansion coefficients are obtained from a least squares fit. These coefficients simultaneously yield an approximation to the aerosol size distribution. The mathematical details are given in Appendix A. The goal of WP3100 was the assimilation of chemical species, which influence the microphysical behaviour of aerosols, like nitric acid and water vapour. Since these constituents themselves are determined to a large extent by the chemical composition of the stratosphere, and also because of the increasing demand for the assimilation of “all” chemical species, the initial objectives of WP3100 were extended to include in the assimilation a fairly complete set of chemical species and their interactions. The complete list is given in Appendix B. The model dynamics are based on ECMWF wind and temperature analyses. The current developments as to spectral interpolation have been tested on both numerical examples and real SAGE-II aerosol data. Several examples of spectral interpolation and obtained size distributions under various conditions are shown (e.g. pre and post Pinatubo). In addition, efforts have been devoted to GOME/ERS-2 data (direct cartography) and CRISTA 1 (chemical assimilation). A number of example aerosol maps produced by both methods are shown and discussed. The tools developed in the framework of both projects are suitable for application to future ENVISAT data. Many ENVISAT users have expressed their interest already. In a successor project (UPSDAM, User Prototype Service for Data Assimilation and Mapping), we intend to further upgrade the software implementation of these tools. The modularitry will be increased and a WWW interface will be implemented, thus creating an operational and user-friendly version for better serving the requirements of the user community.

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1. INTRODUCTION The project AMASDU (February 1998 – February 1999) is a successor to the project DAMS2P. DAMS2P was completed by the end of February 1998. Both projects are conducted in the frame of the ESA Data User programme (DUP). By the end of DAMS2P, software tools (algorithms) were delivered for global mapping of aerosol data from satellite level-2 products, following two different methods: cartography and 4D-variational data assimilation techniques. AMASDU is developing these tools further, as follows • By extending the single-wavelength approach adopted in DAMS2P to a multi-wavelength approach, and by adding atmospheric particle microphysics and appropriate chemistry to the assimilation model which up to now included only particle transport. • Through the application/extension of some of the tools developed for the aerosol to other products, in particular H2O and the HNO3 reservoir species. • Through the development of maps of derived aerosol parameters, that may answer more directly the enquiries from specific user communities. Thereby, AMASDU is enlarging the use of these cartography and data assimilation mapping tools. Missions like ENVISAT-1 could largely benefit from them for improved visualization and interpretation of their data products. 1.1 Project interest There are many good reasons for addressing the aerosol, H2O and HNO3 products: • Aerosols or atmospheric particulate matter like PSCs affect the Earth climate directly, through their radiative effects, and indirectly, through their role in cloud formation and heterogeneous chemistry processes in the atmosphere and the latter impact on the ozone abundance. This impact on the atmospheric processes depends on various aerosol or PSC properties like the particle density, size distribution, and composition: all are highly variable with time, altitude, geolocation, etc. Stratospheric aerosols commonly are a mixture of H2O and H2SO4. PSCs mostly are a ternary solution of H2O, HNO3 and H2SO4. The aerosol and PSC formation depends mainly on temperature, the presence of condensation nuclei and of H2O vapour, and the abundance of HNO3 and H2SO4. There is still a lot of interest in establishing climatologies, temporal and spatial variability, and possible long-term evolutions of both the aerosol and the species involved. • It is found actually that there is a lack of information as to aerosol properties and climatologies. Recently, a global climatology of aerosol surface area density has been derived from the database constituted of the SAM II, SAGE and SAGE-II results, covering the 1978-1994 time frame. Their estimation of the surface area density from the extinction data is hampered to some extent by the fact that the measurements cover only a limited spectral range (4 channels in the 0.385 to 1.02 µm range) [Thomason et al., 1997]. New data are becoming available (UARS, GOME, POLDER, ADEOS, ENVISAT-1…),

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extending the time and wavelength range of the aerosol database. Their exploitation is strongly demanded by the scientific user community, for example, for improving current aerosol models and climatologies. • To this end, the multi-wavelength approach is needed, i), for enabling the combination of data resulting from optical measurements at different wavelengths which allows a more complete data set as to spatio-temporal coverage, and ii), for allowing the retrieval of a larger number of independent aerosol parameters [Box et al., 1996; Lambert et al., 1996], and a better distinction between clouds, PSCs and aerosols. The larger the number of independently determined parameters, the lesser the uncertainty or ambiguity in the results derived from a comparison between different measured optical properties or from the conversion of optical properties towards physical variables. • Many remote sensing experiments are hindered to some extent by the presence of aerosols: they are demanders of a better characterisation of the aerosol distribution, especially their optical properties.

1.2 Project Users The AMASDU project will serve the following communities: • The International Global Atmospheric Chemistry Program (IGAC) focus on direct aerosol radiative forcing (in coordination with WMO/GAW and WCRP/BSRN), which requests the global scale distribution of the aerosol radiative properties. Examples: IPCC Assessment Groups. • The THESEO scientific community, for interpretation of their measurements and for chemical modelling activities (validation, campaign support, etc.) The modellers are interested more specifically in global distribution maps of stratospheric aerosol surface area and volume density. • Assessment study groups for the long term evolution of aerosol load and PSC frequency of occurrence, their impact on long term trends of ozone and the stratospheric composition, for the assessment of the influence of volcanic eruptions under changing stratospheric composition, and for the assessment of impacts of a commercial subsonic/ supersonic aircraft fleet. At the end, policy-makers will establish international research policies based on the above assessments. Examples: WMO, UNEP assessment groups, EC DGXII. • Many atmosphere and Earth remote sensing experiments who must correct for the atmospheric opacity caused by H2O vapour and/or aerosols to extract the targeted information from the observations. Examples: JRC (Joint Research Centre), ISPRA, and European Environment Agency. • UV-monitoring, modelling and prediction groups, because they need the aerosol optical properties. Example: IPCC Assessment Groups, European Environment Agency. • The validation groups of satellite measurements of atmospheric constituents. This applies to aerosols as well as to chemical species. Example: GOME and ENVISAT validation teams.

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• Policy-makers for establishing international research policies (e.g. EC DGXII). Example: for evaluation of the Montreal Protocol.

1.3 Project Goals Essentially two goals can be distinguished: • •

Further development and extension of cartography tools for aerosol mapping (WP 2100). Further development and extension of the 4D variational data assimilation (WP 3100).

Both tools can take as input a combined set of satellite level-2 stratospheric data products. Nevertheless to a certain extent can the cartography tools address tropospheric and partial or total column data. (I)

WP 2100

DAMS2P produced cross-sections of 3D (longitude, latitude, and a vertical altitude coordinate) aerosol extinction maps, at a fixed time, within a time span set by the experiment’s spatial repeat cycle, and at a fixed wavelength [De Mazière et al., 1998]. A first goal here is to develop additional tools for combining aerosol extinction data obtained from satellite experiments in different spectral windows into a common 4D grid, the 4th dimension being wavelength. The second goal is to use this 4D interpolated data space as input for the study and implementation of methods for obtaining derived aerosol parameters. Important parameters, which represent an added value for the user community, are, e.g., effective mean radius, specific surface area and volume, and size distribution. (II)

WP 3100

DAMS2P assumed aerosol particle number density to be proportional to the extinction coefficient, according to the most simple model one can adopt for the aerosol, and propagated the particles in space and time using a pure transport model [De Mazière et al., 1998]. Herein, aerosols are treated as inert tracers. In order to make the assimilation model more realistic, the particle formation and evolution must be included. Therefore, the transport scheme in the assimilation model must be completed by chemistry and microphysics modules, requiring the additional assimilation of the most relevant species in the microphysical and heterogeneous processes, namely H2O and HNO3. The initial goal was the completion of the assimilation of H2O and HNO3, as a precursor for an aerosol assimilation in which the aerosol interacts with its environment instead of being a passive tracer. These aspects may be included in a more complete dynamical and chemical 4D variational data assimilation scheme, to be developed in a later stage.

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1.4 Project Schedule The initial proposal envisaged a 2-year schedule and the work breakdown was set up in a 2step structure. The first step aimed at the development of a spectral interpolation method and the second year step aimed towards a derivation of the aerosol size distribution. While progressing in the first year of the project, it was found that the 2-step structure could not be respected as such: the subjects of both years were found to be coupled to such an extent that a common concept or working environment had to be fixed from the beginning. Namely as to multispectral cartography, one must already take into account the final aim of inversion of aerosol parameters to define the most appropriate method for spectral interpolation. Analogously regarding 4D variational data assimilation, it turned out to be more efficient to first implement the global chemical data assimilation before addressing the particularities of the aerosol, H2O and HNO3 assimilation. Therefore, the progress actually made includes some advances that were projected initially in the AMASDU second year’s phase.

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2. MULTISPECTRAL CARTOGRAPHY (WP 2100) 2.1 Objectives The objective of this workpackage was the development of an interpolation and/or fitting algorithm to characterise the aerosol extinction coefficient dependence on the wavelength, β(λ) . The input to the algorithm naturally consists of coefficient values, measured at a limited set of wavelengths by one or more experiments. The output is a mathematical representation of the function β(λ) . It is required to serve two purposes: (i)

It should reliably predict extinction values in regions where no measurements are available.

(ii)

It should be sufficiently precise and sufficiently extensive in wavelength scope to allow the extraction of aerosol derived parameters (in first instance, the size distribution).

The extinction measurements at different wavelengths, available from the different aerosol satellite missions, are very irregularly and sparsely distributed over the UV to IR wavelength range. This makes this interpolation problem very hard to solve, because it is largely underdetermined. The nature of the available data on one hand and the mathematics on the other hand make that no off the shelf interpolation method can be used for this task. To cope with the intrinsic difficulties of the problem, a special approach has been developed, and is described in the next section. The mathematical details are given in Appendix A. 2.2 Problem description The most common quantity associated with the attenuation of light by aerosols is the spectral extinction coefficient β , usually expressed in 1/km. It is also the natural physical parameter that can be retrieved from experiments that measure optical scattering and absorption or radiances emitted by the atmosphere. This wavelength dependent extinction coefficient however is an integrated quantity: it is the integral of the particle number density distribution N (r ) times the extinction efficiency Qeff (λ, r ) , which itself is a function of wavelength λ and particle size (radius r, in the assumption of spherical particles). The extinction efficiency can be calculated with Mie-theory, if the refractive index of the particles as a function of wavelength is known. The relation between the aerosol extinction coefficient and the particle number density distribution is of the form

z

+∞

β (λ ) =

Qeff ( λ , r )πr 2 N (r )dr

(2.1)

0

The problem of spectral interpolation could be solved trivially if the problem of spectral inversion could be solved. Spectral inversion amounts to obtaining the function N (r ) from

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knowledge about the function β(λ ) . However, such problems (Fredholm integral equations of the first kind) are known to be very difficult to solve numerically and for real data subject to ill-conditioning, implying mostly the use of regularisation methods. These numerical problems could be circumvented if the function β(λ ) was known in detail. So we have a chicken-and-egg problem, which requires that we consider spectral interpolation and inversion together. This combined approach appears to be new. To solve the inversion problem the following types of solutions have been proposed in the literature. (i)

Explicit inversion formulas under the called Anomalous Diffraction Approximation (ADA) [Box et al. 1978, Smith 1982, Klett 1984, Bertero et al. 1986, Wang et al. 1996].

For these techniques to be successful one needs precise, dense and smooth varying data or at least forced to apply smoothing filters to the measured data. For most applications in atmospheric science, these methods are not very useful. (ii)

Regularised linear system inversion methods [Twomey 1975].

The integral equation is discretised and leads to a badly conditioned linear algebraic system. To alleviate the ill-conditioning of the system the inverse matrix is computed in a less direct way, using numerical regularisation methods. A drawback of these methods is that one first needs to determine the regularisation parameters. (iii)

Non-linear least squares fit [Tarantola et al. 1982].

One proposes for the size distribution a given shape (e.g. a log-normal) and one tries to determine the parameters of the distribution. This requires minimising a non-linear functional, depending on refractive index and the parameters of the proposed distribution. One ends up with a non-linear system. This method thus needs either an algorithm to solve a non-linear system or equivalently a non-linear minimisation algorithm to minimise the functional. Either way this is a time consuming method and the procedure may fail to converge. For inversion to be successful, it is necessary to have a sufficient number of measurements over a wide enough wavelength range and which are not too irregularly sampled. In cases where the measurements of the β(λ ) function are very sparse, one will need a special kind of interpolation. This interpolation scheme must be able to provide the missing information. This is only possible if the method is given additional information about the physical behaviour of a typical β(λ ) function. It is clear from (2.1), that the spectral dependence of the extinction coefficient will be largely influenced by the spectral dependence of the scattering efficiency kernel Qeff (λ, r ) . Also, different surface density distributions S ( r ) = 4πr 2 N ( r ) will lead to different β(λ ) curves. In the next section, a special interpolation scheme is described that is able to take this kind of

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information to parametrise the interpolant. In doing so, one can assure that interpolated values will remain within an envelope of a bundle of physical acceptable β(λ ) curves. In this way, it is even possible to fine tune the interpolation method for different kind of aerosols, e.g. background conditions, volcanic conditions, special mixtures, etc. An intelligent interpolation of measured β(λ ) values is interesting in its own right, for reasons already explained elsewhere. But in addition, it is a necessary step for improving the accuracy of the inversion procedure, necessary to obtain the aerosol size distribution. The extinction efficiency Qeff (λ, r ) in (2.1) has been calculated in the framework of Mie scattering theory, and is a complicated function. For many practical computations, an approximation to this general theory can be used, called Anomalous Diffraction Approximation (ADA), that is capable of representing all the major features of the scattering and absorption of light by spherical particles within certain limits of application [van de Hulst 1981]. Under the ADA, the extinction efficiency Qeff (λ, r ) is given by: (i)

For lossless particles with real refractive index n (only scattering takes place) :

Qeff (λ, r ) = 2 − 4

1 − cos(ρ) sin(ρ) , +4 ρ ρ2

(2.2)

ρ = 2 keff r keff = (n − 1)

(ii)

2π λ

For lossy particles with complex refractive index m = n − in' (particles that scatter and absorp light) :

Qeff (λ, r ) = 2 − 4 cos(β)e − ρ tan(β )

sin(ρ − β) cos(2β) − e − ρ tan(β ) cos(ρ − 2β) + 4 cos 2 (β) , ρ ρ2

ρ = 2 keff r

(2.3)

2π λ n' β = Arctan n −1 keff = (n − 1)

The parameter ρ represents the phase shift of the ray travelling through the full diameter of the particle; ρ' = ρ tan β represents the amplitude decay (lossy case). The ADA was developed under the assumptions that n − 1 n − 1 . It is readily seen, from (2) and (3) that the limit behavior lim Qeff (λ, r ) = 2 λ→0 reproduces the geometrical scattering limit, loosing any physical information about the refraction index and the aerosol composition. When λ increases, some oscillatory structures express the diffraction interferences. Also, one find by series expansion, that lim Qeff ( λ , r ) → 0 λ →∞

as λ−2 (Rayleigh-Gans scattering limit) in the non-lossy case. As a consequence, the scattering cross section does not contain anymore information about the particle radius. In the lossy case, lim Qeff ( λ , r ) → 0 as λ−1. λ →∞

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We will use these ADA forms (2.2 and 2.3) in the following section. In figures 1a,b below, we have represented the typical behaviour of the ADA scattering efficiency kernel Qeff(r,λ) versus the wavelength, for the lossless and lossy case, respectively.

Fig. 1a. ADA kernel Qeff(λ), for r=1.0 µm, nr=1.43, ni=0.0

Fig. 1b. ADA kernel Qeff(λ), for r=1.0 µm, nr=1.43, ni=0.1

Figures 2a,b below, show the ADA scattering efficiency kernel Qeff(r,λ) versus the radius, for the lossless and lossy case, respectively.

Fig. 2a. ADA kernel Qeff(λ), for λ=1.0 µm, nr=1.43, ni=0.0

Fig. 2b. ADA kernel Qeff(λ), for λ=1.0 µm, nr=1.43, ni=0.1

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Figures 3a,b-5a,b show respectively a log-normal size distribution and its associated extinction function, in the lossless case.

Fig. 3a. S(r), for rm=0.25, σ=1.2

Fig. 3b. β(λ), for nr=1.43, ni=0.0

Fig. 4a. S(r), for rm=1.0, σ=1.2

Fig. 4b. β(λ), for nr=1.43, ni=0.0

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Fig. 5a. S(r), for rm=1.0, σ=2.0

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Fig. 5b. β(λ), for nr=1.43, ni=0.0

Figures 6a,b show a trimodal size distribution (sum of three log-normal distributions) and its associated extinction function, in the lossless case.

Fig. 6a. S(r), Trimodal

Fig. 6b. β(λ), for nr=1.43, ni=0.0

In the UV-visible range, the extinction cross section is dominated by the scattering and the

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absorption may be considered negligible. On the other hand, the absorption cross section becomes dominant in the infrared. It dominates by far the pure scattering cross section and is proportional to the volume of the particle. Some examples hereof will be given in section 2.3.2. Therefore, the general spectral matching problem between both wavelength ranges is a difficult one. The absorption in the IR range is dominantly characterised by the spectral dependence of the refractive index. Interpolation (and inversion) in this range requires information about the spectral behaviour of the refractive index and therefore of the composition of the aerosol particles. During the one-year time span of this project, we concentrated on the UV-visible case (dominantly scattering), and formulated a practical solution for this problem. Due to time limitation we could not address the IR case (dominantly absorption) fully. The complexity of the mathematics involved and the higher physical complexity demands for a separate study. However, the insight gained by solving the UV-visible case is of great value to tackle the absorption case. 2.3 Problem solution: spectral fitting algorithm Our method is also based on the Anomalous Diffraction Approximation (ADA). It is valid for spherical particles, with radius r and real refractive index n, when n − 1