Retrieval of dust aerosol properties over bright-reflecting desert surfaces with the satellite-borne Medium Resolution Imaging Spectrometer MERIS

over bright-reecting desert surfaces

with the satellite-borne Medium Resolution

Imaging Spectrometer MERIS

Dissertation

von

Dipl.-Ing. Tilman Dinter

Fachbereich Physik/Elektrotechnik

over bright-reecting desert surfaces

with the satellite-borne Medium Resolution

Imaging Spectrometer MERIS

Dissertation

von

Dipl.-Ing. Tilman Dinter

Vom Fachbereich für Physik und Elektrotechnik der Univerität Bremen zur Erlangung des akademischen Grades eines Doktor der Naturwissenschaften

(Dr.rer.nat.) genehmigte Dissertation

Ausgabetermin: 15.03.2005

Abgabetermin: 04.05.2009

Zuständige Hochschullehrer: Prof. J.P. Burrows, IUP

PD W. von Hoyningen-Huene, IUP

Institut für Umweltphysik

Fachbereich Physik/Elektrotechnik (FB 1) Postfach 33 04 40

D-28334 Bremen

Ich versichere, dass ich die Dissertation selbständig verfaÿt und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt habe.

Bremen, 04.05.2009

Abstract 9

List of Publications 11

1 Introduction 15

1.1 Motivation and objectives . . . 15

1.2 State of the knowledge . . . 16

1.3 Outline of the thesis . . . 17

1.4 Desert dust in the global context . . . 19

1.5 Saharan Mineral Dust Experiment (SAMUM) . . . 21

I Fundamentals 25 2 Optical properties of aerosol and radiative transfer 27 2.1 Processes in the atmosphere . . . 27

2.1.1 Molecular Rayleigh scattering . . . 30

2.1.1.1 Determination of the Rayleigh optical thickness . . . 31

2.1.2 Particle scattering . . . 32

2.1.2.1 Mie scattering of spherical particles . . . 32

2.1.2.2 Pollack & Cuzzi's semi-empirical theory on the scatter-ing of nonspherical particles . . . 34

2.1.3 Extinction . . . 37

2.1.3.1 Optical thickness . . . 38

2.1.3.2 Single scattering albedo . . . 39

2.2 Radiative transfer equation (RTE) . . . 40

2.2.1 Radiative transport in a scattering plane-parallel atmosphere . . . . 41

2.2.1.1 Successive order of scattering (SOS) . . . 43

2.2.2 Source terms . . . 47

2.2.3 Boundary conditions . . . 48

2.2.4 Solutions of the radiative transfer equation . . . 49

II Measurements and Retrievals 53 3 Ground-based measurements 55 3.1 Instrument (CIMEL CE-318) . . . 56

3.2 Calibration of the instrument (Schneefernerhaus Zugspitze) . . . 57

3.2.1 Langley plots . . . 58

3.2.2 Temperature stabilisation . . . 60

3.3 The SAMUM eld campaign . . . 61

3.4 Description of closure measurements . . . 62

3.5 Measurements of aerosol optical thickness with the sun photometer . . . 64

3.6 Retrieval of aerosol phase functions (CIRATRA) . . . 66

3.6.1 Retrieval of phase functions of desert dust . . . 69

3.7 Estimation of spectral single scattering albedo . . . 72

3.8 Conclusions . . . 75

4 Satellite retrieval 79 4.1 The Medium Resolution Imaging Spectrometer (MERIS) . . . 79

4.2 Sensitivity . . . 80

4.2.1 Radiative transfer calculations . . . 80

4.3 Satellite retrieval of aerosol optical thickness . . . 82

4.3.1 The Bremen Aerosol Retrieval Algorithm (BAER) . . . 82

4.3.2 Calculation of look-up tables (LUT) for desert conditions . . . 85

4.3.3 Determination of Rayleigh reectance . . . 87

4.3.4 The surface reectance model . . . 88

4.3.6 Discrimination of water, cloud, land, and desert . . . 93

5 Results and validation 97 5.1 Satellite retrieval of aerosol optical thickness . . . 97

5.2 Comparison with ground-based measurements . . . 99

5.3 Comparison with MISR . . . 101

5.4 Comparison with measurements from aircraft . . . 102

III Conclusions and outlook 105 6 Conclusions 107 6.1 Ground-based measurements . . . 107

6.2 Satellite retrievals . . . 108

7 Outlook 111 IV Appendix 113 A Additional images and appendixes 115 A.1 Tables of SAMUM results . . . 115

A.2 Minimum reectance database images . . . 117

B Acknowledgements 119

Approximately 30 % of the Earth's land surface is covered by deserts or semi-deserts, where arid conditions prevail. Aerosols originating from these regions play a signicant role in determining climate and the chemical composition of the atmosphere. Solar radiation is scattered and absorbed by dust particles in the atmosphere. Thus, these aerosols contribute signicantly to the radiation budget of the Earth-atmosphere system. Cooling and warming of the Earth-atmosphere system due to the direct aerosol eect and further secondary aerosol eects, e. g. cloud formation, are highly-discussed topics in recent climate research. Retrieving aerosol properties from space-borne platforms above deserts, where the surface reectance is usually very bright, is a challenging problem. The contribution of surface to TOA (Top-Of-Atmosphere) reectance can reach values of more than 90%, especially for wavelengths above 500 nm. For this reason, detailed knowledge of aerosol and surface optical properties from desert regions is required to distinguish atmospheric radiation from radiation resulting from surfaces that are intrinsically bright. Detailed radiative transfer calculations have been done in a sensitivity study within this thesis to yield information about the technical and physical feasibility of distinguishing between aerosol-loaded atmosphere and surface.

The main purpose of this work is to establish a retrieval technique that yields information about dust aerosol properties over source regions from satellite data. The basic quantity retrieved from satellite measurements is the Aerosol Optical Thickness (AOT).

An approach to retrieving the AOT over arid and semiarid regions based on the Bremen AErosol Retrieval (BAER) has been developed and validated within the DREAMS Project (Dust aerosol REtrievAls from space-borne instruMentS), which is part of the SAharan Mineral dUst experiMent (SAMUM) funded by the DFG (Deutsche Forschungsgemein-schaft). By combining measurements of the back-scattered radiation from the MERIS (MEdium Resolution Imaging Spectrometer) instrument aboard ENVISAT-1 and ground-based measurements during radiation closure experiments in Morocco, the aerosol optical properties were determined for selected locations.

Using the SAMUM closure experiments, we derived all important quantities that are needed to set up satellite AOT retrievals for arid and desert regions like the Sahara. For remote sensing purposes, these quantities are the optically relevant parameters of dust aerosol in the atmosphere and surface reectance.

One key characteristic is the aerosol phase function, which describes the scattering be-haviour of specied aerosol types. Uncertainties in phase function have consequences for other radiative characteristics in remote sensing. Deviations in the phase function have a

direct inuence on retrieved AOT and calculations of single scattering albedo. Therefore the rst focus in this specic SAMUM contribution lies on determination of phase function of desert dust. The application of results for phase functions will be used to derive single scattering albedo for desert dust which ranges between 0.90.99 in the wavelength region from 400 nm to 900 nm. The choice of this value leads to signicant changes in the retrieval of aerosol optical thickness (AOT). Especially remote sensing of desert dust, as described in this work and publications like Hsu et al. [2004]; Levy et al. [2007]; Dinter et al. [2009] require these basic quantities for the calculation of look-up-tables (LUT) by radiative transfer models.

Closure experiments also provide opportunities for validating the results of satellite data re-trievals. Based on the assumption of a Lambert'ian surface reectance, inter-comparisons of retrieved aerosol optical thickness from satellite and ground-based sun photometer measurements have shown systematic deviations depending on viewing geometry. Since the optical angular dependence of the aerosol-loaded atmosphere has been ascertained based on sky-brightness measurements with a sun photometer (phase function), we were able to exclude angular atmospheric eects as the source of these deviations. This lead to the assumption that surface angular eects are responsible for these deviations. Therefore we had to improve the satellite retrieval algorithm (BAER) for anisotropy eects of surface reectance. This was achieved by means of a RahmanPintyVerstraete BRDF (Bidirectional Reectance Distribution Function) model. This model is controlled by several parameters, which determine shape and absolute values of the function. The work presented here shows how BRDF parameters can be optimised on the basis of inter-comparisons of ground- and satellite-based measurements during the SAMUM campaign. The BRDF parameters are calculated using an optimal estimation method that minimises the deviations of the AOT retrieved from sun photometer and MERIS measurements. The results show that deviations for the surface reectance of 20 % occur in the specular glint region. This leads to a signicant error in the retrieved AOT, especially for wavelengths larger than 500 nm where the surface reectance is very bright (e. g. for ρsurf(412 nm) = 0.08 → ∆AOT = ±0.25; and for ρsurf(670 nm) = 0.3 → ∆AOT = ±1.2). Further comparisons of BAER results derived from the MERIS instrument aboard ENVISAT with ground-, air-, and satellite-based measurements show good agreement.

The list of publications arose during the work of this thesis:

Dinter T., von Hoyningen-Huene W., Burrows, J.P., Kokhanovsky A., Bierwirth E., Wendisch M., Müller D., Kahn R., Diouri M., (2009): "Retrieval of aerosol opti-cal thickness for desert conditions using MERIS observations during the SAMUM campaign". Tellus 61B, Special Edition Jan. 2009

Dinter T., von Hoyningen-Huene W., Kokhanovsky A., Burrows J.P., Diouri M., (2007): "Satellite Retrieval of aerosol properties over bright reecting desert regions". Pro-ceedings of the ENVISAT Symposium 2007, 2327 Apr 2007, Montreux, Switzerland, ESA Publications Division, SP-636:463371di.pdf

von Hoyningen-Huene W., Dinter T., Kokhanovsky, A., Burrows J.P., Wendisch M., Bierwirth E., Müller D., Diouri M., (2009): "Measurements of desert dust optical characteristics at Porte au Sahara during SAMUM". Tellus 61B, Special Edition Jan. 2009

Kahn R., Petzold A., Wendisch M., Bierwirth E., Dinter T., Esselborn M., Fiebig M., Heese B., Knippertz P., Müller D., Schladitz A., von Hoyningen-Huene W., (2009): "Desert dust aerosol air mass mapping in the western Sahara, using particle prop-erties derived from space-based multi-angle imaging". Tellus 61B, Special Edition Jan. 2009

Heese, B., Althausen, D., Dinter, T., Esselborn, M., Müller, T., Tesche, M., Wiegener, M., (2009): "Vertically resolved Dust Optical Properties during SAMUM: Tinfou compared to Ouarzazate". Tellus 61B, Special Edition Jan. 2009

Knippertz P., Ansmann A., Althausen D., Müller D., Tesche M., Bierwirth E., Dinter T., Müller T., von Hoyningen-Huene W., Schepanski K., Wendisch M., Heinhold B., Kandler K., Petzold A., Schütz L., Tegen I., (2009): "Dust Mobilization and Trans-port in the Northern Sahara during SAMUM 2006  A Meteorological Overview". Tellus 61B, Special Edition Jan. 2009

Bierwirth E., Wendisch M., Ehrlich A., Heese B., Tesche M., Althausen D., Schladitz A., Müller D., Otto S., Trautmann T., Dinter T., von Hoyningen-Huene W., Kahn R., (2009): "Spectral Surface Albedo over Morocco and its impact on Radiative Forcing of Saharan Dust". Tellus 61B, Special Edition Jan. 2009

Lotz W., Vountas M., Dinter T., Burrows J.P., (2009): "Cloud and surface classication using SCIAMACHY polarization measurement device". Atmospheric Chemistry and Physics. Vol.9(No.4); pp.1279-1288

G. J. Rohen, W. von Hoyningen-Huene, A. Kokhanovsky, T. Dinter, and J. P. Burrows: "Retrieval of aerosol mass load from MERIS/Envisat data". Atmos. Env. (in submission), 2008.

Ladstätter-Weiÿenmayer A., Dinter T., Heckel A., von Hoyningen-Huene W., Meyer-Arnek J., Richter A., Sfakianaki M., Wittrock F., Vrekoussis M., Burrows J.P., (2009): "Fires over Greece in summer 2007 as observed from MERIS and SCIA-MACHY". (in prep.)

Vountas, M., Dinter, T., Bracher, A., Burrows, J.P., Sierk, B., 2007: Spectral Studies of Ocean Water with Space-borne Sensor SCIAMACHY using Dierential Optical Absorption Spectroscopy (DOAS). Ocean Science 3; pp.429-440

von Hoyningen-Huene W., Rohen G., Dinter T., Kokhanovsky A., Vountas M., Bovens-mann H., Burrows J.P., WichBovens-mann-Fiebig M., (2007): "Retrieval of particulate matter concentration (PM10) from meris observation and validation over germany". Proceedings of the ENVISAT Symposium 2007, 2327 Apr. 2007, Montreux, Switzer-land, ESA Publications Division, SP-636:463312hh.pdf

Bracher, A., Vountas, M., Dinter, T., Burrows, J.P., Röttgers, R., Peeken, I., (2008): Quantitative observation of cyanobacteria and diatoms from space using PhytoDOAS on SCIAMACHY data. Biogeosciences Discussions. Vol.5(No.6); pp. 45594590 Bracher, A., Dinter, T., Sierk, B., Vountas, M., von Hoyningen-Huene, W., Richter, A.,

Burrows, J.P., 2005: Comparisons of phytoplankton concentrations from MERIS and SCIAMACHY measurements. Proceedings of the MERIS (A)ATSR Workshop 2005, ESRIN/ESA, Frascati, Italy, ESA Publications Division, ESTEC, Nordwijk, The Netherlands, SP-597

Bracher A., Vountas M., Dinter T., Röttgers R., Doerer R., Burrows J.P., 2006: Retrieval of phytoplankton distribution and light absorption from space borne SCIAMACHY data using Dierential Optical Absorption Spectroscopy. Proceedings of the Ocean Optics XVIII, 9-13 Oct 2006, Delta CentreVille, Montreal, Canada

Bracher A., Vountas M., Dinter T., Röttgers R., Peeken I., Bernitt E., Burrows J.P. (2007) Phytoplankton distribution and light absorption from space using Dierential Optical Absorption Spectroscopy. In: Proceedings of the ENVISAT Symposium 2007, 23-27 Apr 2007, Montreux, Switzerland, ESA Publications Division, Nordwijk, The Netherlands, SP-636:463496bra.pdf

Conference contributions:

Dinter, T., von Hoyningen-Huene, W. (2005): Aerosol Retrieval from Satellite. Con-stituents of Organic Aerosols ACCENT Workshop 2627 May 2005, Oslo

Dinter, T., von Hoyningen-Huene (2005): MERIS Aerosol Retrieval for desert conditions. MERIS A(A)TSR Workshop, ENVISAT-Symposium, ESA-ESRIN, 2630 September 2005, Frascati, Italy

Dinter, T., von Hoyningen-Huene, W., Burrows, J.P. (2006): Retrieval of Aerosol Prop-erties over bright reecting desert regions from top of atmosphere radiance. Tagung der Deutschen Physikalischen Gesellschaft (DPG), 1316 March 2006, Heidelberg, Germany

Dinter, T., von Hoyningen-Huene, W., Kokhanovsky, A.A., Burrows, J.P., Diouri, M. (2006): Retrieval of Aerosol Optical Thickness for desert conditions with the MERIS Instrument. Workshop on Remote Sensing of Aerosol, 45 May 2006, Berlin, Ger-many

Dinter, T., von Hoyningen-Huene, W., Kokhanovsky, A.A., Burrows, J.P., Diouri, M. (2007): Satellite retrieval of aerosol properties over bright reecting desert regions. European Geosciences Union (EGU), 1520 April 2007, Vienna, Austria

Dinter, T., von Hoyningen-Huene, W., Kokhanovsky, A.A., Burrows, J.P., Diouri, M. (2007): SAMUM and satellite aerosol retrieval over Saharan regions with MERIS. ACCENT-TROPOSAT-2 Workshop, 2122 June 2007, Bremen, Germany

Dinter, T., von Hoyningen-Huene, W., Kokhanovsky, A.A., Burrows, J.P. (2007): Satel-lite retrieval of aerosol properties over bright reecting desert regions with BAER. SAMUM-Workshop, 1516 March 2007, Mainz, Germany

Dinter, T., von Hoyningen-Huene, W., Kokhanovsky, A.A., Rohen, G., Burrows, J.P., Wendisch, M., Bierwirth, E. (2008): Improvements of satellite AOT retrieval us-ing closure experiments like SAMUM campaign. Third International Mineral Dust Workshop, 1517 September 2008, Leipzig, Germany

Günter Rohen, Wolfgang v. Hoyningen-Huene, Tilman Dinter, Alexander Kokhanovsky and John P. Burrows (2007): Retrieval of MERIS/Envisat PM10: Comparison with national AQ measurements and the Impact of Boundary Layer Height. ACCENT Satellite Aerosol Workshop, 2007, Bremen, Germany

Günter Rohen, Wolfgang v. Hoyningen-Huene, Tilman Dinter, Alexander Kokhanovsky and John P. Burrows (2007): Retrieval of Meris/Envisat PM10: Comparisons with national AQ measurements. A-Train conference, 2007, Lille, France

Günter Rohen, Wolfgang v. Hoyningen-Huene, Tilman Dinter, Alexander Kokhanovsky, and John P. Burrows (2008): Estimating Aot and PM10 over Germany. AGU Fall Meeting, 2008, Fort Lauderdale

Bracher A., Sierk B., Vountas M., Dinter T., Richter A., Burrows J.P. (2005): Determina-tion of phytoplankton concentraDetermina-tions from space-borne spectroscopic measurements. Poster: 2nd EGU General Assembly 2005, Vienna, Austria

Bracher A., Dinter T., Sierk B., Vountas M., Hoyningen-Huene W., Richter A., Burrows J.P (2005): Comparisons of phytoplankton concentrations from MERIS and SCIA-MACHY measurements. Poster: MERIS (A)ATSR USER Workshop 26-30 Sept 2005, ESRIN/ESA Frascati, Italy

Bracher A., Dinter T., Sierk B., Vountas M., Hoyningen-Huene W., Richter A., Burrows J.P. (2005): Comparisons of phytoplankton concentrations from MERIS and SCIA-MACHY measurements. Poster: MERIS (A)ATSR USER Workshop 26-30 Sept 2005, ESRIN/ESA, Frascati, Italy

Introduction

1.1 Motivation and objectives

Recognition that anthropogenic activity directly and indirectly modulates the climate has turned the attention of the scientic community to the importance of improving our understanding of atmospheric processes. Atmospheric aerosols aect Earth's climate primarily by changing the radiation budget of the Earth-atmosphere system. Aerosols can reduce the amount of radiation by backscattering incoming solar radiation or even increase the amount of radiation which is absorbed by the Earth system [IPCC, 2007]. These are the so-called direct or primary eects of aerosols.

Furthermore, aerosols aect the formation and dissipation of clouds, which have a sig-nicant impact on the Earth's radiation budget. In this process, aerosols act as cloud-condensation nuclei (CCN) or ice nuclei (IN). These eects are labelled indirect or sec-ondary aerosol eects. However estimates of the net radiative forcing due to direct and indirect eects of aerosols are highly uncertain, because information about the concentra-tion, size distribuconcentra-tion, and composition of aerosols on a global scale is limited [IPCC, 2007; Hansen et al. , 2005b].

Due to these facts and increasing interest in the eects of global warming due to trace gases, there is considerable need for accurate information on the global distribution and microphysical and optical properties of atmospheric aerosols. Retrieval of such data on a global scale is only feasible by means of satellite measurements. The resulting data is employed in aerosol/chemical transport models, which are also part of climate models. Thus, the accuracy of satellite aerosol retrievals directly aects the modelling and prediction of climate [Hansen et al. , 2005a].

In this context, airborne mineral dust plays an important role, since it has bio-geochemical impacts on the ecosystem and inuences atmospheric radiative forcing locally and globally [IPCC, 2007; Haywood & Bougher, 2000; Hsu et al. , 2000]. As several studies have reported (e.g. [Kaufman et al. , 2005]), dust from the Sahara is often transported out of the boundary layer into the free troposphere and then travels thousands of kilometres across the Atlantic or into northern Europe. This transport of dust leads to often unexpected eects. These range from aspects of air pollution to fertilisation of oceans and other ecosystems. These inuences and connections are described in greater detail in Section 1.4.

For this reason, it is especially important to understand the processes that control the formation, transport, and fate of dust aerosols originating from Saharan source regions. No ground-based measurement system can provide data on a global scale for the purposes outlined above. On a global scale, only satellite data retrieval methods are able to provide such data. Thus, adequate satellite remote-sensing observation techniques for aerosols and mineral dust are required, which can be used over a wide variety of surface conditions, including the source regions of dust.

1.2 State of the knowledge

Several algorithms for satellite remote sensing of aerosol properties over land using dierent kind of sensors have already been developed. The BAER algorithm is generic and can be applied to any calibrated measurement of backscattered radiation, yielding the top of atmosphere spectral reectance as a function of wavelength, especially those having sucient channels in the short wave region. In this context the BAER algorithm has been applied to data from the following sensors: SeaWiFS (Sea-viewing Wide Field-of-view Sensor) [http://oceancolor.gsfc.nasa.gov/SeaWiFS/], MODIS (Moderate-Resolution Imaging Spectroradiometer) [http://modis.gsfc.nasa.gov/], MERIS [Rast et al. [1981], Bézy et al. [2000]] and SCIAMACHY (SCanning Imaging Absorption SpectroMeter for Atmospheric CHartographY) [Burrows et al. [1995], Bovensmann et al. [1999]].

Most existing retrieval approaches for aerosol optical thickness work for known low-reecting surface conditions. The standard MODIS aerosol retrieval algorithm over land uses the dark target approach [Kaufman et al. , 1997a, b; Remer et al. , 2005] and assumes a xed relation between the 0.47µm or 0.64µm and the 2.1µm channels. This is a valid assumption for most vegetated land surfaces. But over desert regions the values deviate signicantly from this assumption. For these conditions, there are substantial areas with data gaps in the standard MODIS aerosol product over land.

A similar approach is the standard MERIS aerosol retrieval, based on the Dark Dense Vegetation (DDV) index [Santer et al. , 2007]. Due to restrictive threshold values of top of atmosphere reectances in the visible wavelength region and an existing NDVI (Normalised Dierential Vegetation Index) each pixel of desert conditions is excluded from the standard retrieval and no results are provided.

One possible means of distinguishing bright surface reectivity from overlying aerosol eects is the use of multiple viewing angle instruments like the Multiangle Imaging Spectro-radiometer (MISR) [Martonchik et al. , 1998, 2002] and Advanced Along-Track Scanning Radiometer (AATSR) [Veefkind et al. , 2000]. These instruments view the same scene from dierent angles and thus permit the determination of surface reectivity. But since the swath width of such instruments in a sun synchronous orbit is 400 or 500 km, global coverage takes about 9 days - a rather unsatisfactory time frame.

Another technique for obtaining more information about surface and atmospheric aerosol loading uses the polarisation features of light. Several publications have shown that the relation of polarisation properties of scattered light is highly correlated to aerosol micro-physics [Mishchenko & Travis, 1997; Waquet et al. , 2005; Hasekamp & Landgraf, 2005]. Aerosol retrievals from Polarization and Directionality of Earth's Reectance (POLDER-1

Figure 1.1: Monthly mean of June 2008 of standard products of MODIS and MERIS satellite instruments. Left: MODIS standard aerosol product shows AOT at 550 nm (taken from http://modis-atmos.gsfc.nasa.gov/). Right: Standard MERIS AOT product at 550 nm (taken from http://www.enviport.org/meris/).

and POLDER-2) exploited these facts, but unfortunately both instruments failed after about eight months life time.

The BAER algorithm as well as the Deep Blue algorithm from Hsu et al. [2004] use the blue channels of satellite instruments for distinguishing between surface and atmosphere. This is possible because of decreasing surface reectance in these spectral regions. For dark surfaces (vegetation, 'brown' bare soil) this is an appropriate approach, whereas over desert and other bright-reecting surfaces, this leads to a more than negligible overestimation of aerosol optical thickness. To avoid this problem, Hsu et al. [2004] use as an a priori knowledge a surface reectance determined from a clear-scene database for a given geolo-cation. The work presented here follows this approach and aims to improve the model for the spectral and bi-directional reecting-surface properties and integrate it into the BAER procedure. To this end, a surface reectance data set for the Saharan region based on atmospherically corrected MERIS data has been generated. Comparisons of this database with aircraft measurements during the SAMUM campaign are shown in Section 5.4.

1.3 Outline of the thesis

The main purpose of the work presented here is to develop a satellite aerosol retrieval technique for desert conditions. The following tasks arose as a result of this goal:

• Check the conditions for aerosol retrieval over bright desert surfaces by sensitivity

study. Quantify the inuence of AOT and surface to TOA reectance and investigate how the surface inuence can be factored out.

• Setup of retrieval techniques that separate the aerosol reectance and determine

the AOT from radiative transfer calculations for dierent observation and surface conditions (look-up-table approach).

• Compose required information for the retrieval. Determine the optical properties of

corresponding aerosol type (phase function and single scattering albedo) and surface properties.

• Application and test of the approach.

Because of uncertainties in microphysical and optical properties of desert dust, a measure-ment closure experimeasure-ment was initiated in a dust source region in the Saharan desert of southern Morocco within the framework of SAMUM. Main optical characteristics of desert dust, such as phase function and single scattering albedo, have been derived from combina-tions of sun-/sky-radiometer and satellite measurements during the SAMUM experiment (see Chapter 3). Scattering phase functions have been retrieved using combined data of spectral aerosol optical thickness (AOT) and spectral sky-brightness in the almucantar, under consideration of non-spherical light scattering (Section 3.6.1). The determination of spectral single scattering albedo by means of radiative transfer calculations and satellite measurements from MERIS and SCIAMACHY using scattering phase functions and AOT from ground-based observations is shown in Section 3.7.

The Bremen Aerosol Retrieval algorithm, BAER, has been developed to retrieve data on aerosol optical properties above land and ocean surfaces. Based on the BAER approach, an algorithm is developed that is adapted to the special conditions of deserts. A detailed description of the improved BAER algorithm and its application for the retrieval of aerosol properties is given in Chapter 4. The bright surfaces of desert and semiarid regions are the most challenging applications of BAER. To account for increased surface reectance associated with these very bright surfaces types, BAER had to be modied. The as-sumption of 'black' surfaces in the radiative transfer calculations of look-up-tables lead to biased AOT retrieval results. The multiple scattering terms between aerosol-surface, molecule-surface, and aerosol-molecule have to be considered in a LUT that is dependent on surface reectance. The parametrisation of this two dimensional LUT is developed and incorporated into the BAER algorithm shown in Section 4.3.2.

Inter-comparisons between ground- and satellite-based AOT retrieval results have shown clear deviations due to surface anisotropy, which is compensated for by integration of a new surface BRDF algorithm in BAER. The new BRDF surface-reectance model is introduced in Section 4.3.4. To account for high variability in surface reectance the surface model is based on a priori information from a minimum reectance database. The description of generating and using the minimum reectance database is given in Section 4.3.5. Furthermore a new discrimination technique to classify satellite measurement pixels into 'water', 'cloud', 'land', and 'desert' is introduced in Section 4.3.6.

Examples of aerosol optical thickness derived by using the BAER algorithm over the Sahara region during the SAMUM campaign in southern Morocco are shown in Sec-tion 5. The evaluaSec-tions reveal various dust sources, which are important contributors to airborne dust transported over long distances. Aerosol optical thickness and surface reectance are determined simultaneously in the algorithm using look-up tables to match the satellite-observed spectral top of atmosphere radiance. Reduced resolution level 1 data of the MEdium Resolution Imaging Spectrometer (MERIS), which is a radiometer on the ENVISAT Satellite, are used. The instrument gives top of atmosphere radiance at 15 channels in the 400 to 1000 nm wavelength range. Inter-comparisons of retrieved aerosol optical thickness from satellite and ground-based sun photometer measurements for the site of SAMUM campaign are show in Section 5.2. Also comparisons with the satellite-based instrument MISR are included. Atmospherically corrected and recalculated surface reectances by BAER are validated with airplane measurements in Section 5.4. Chapter 6

will conclude the thesis and Chapter 7 oers an brief outlook.

1.4 Desert dust in the global context

The observation of increasing desertication, which, as a consequence, results in increasing amounts of atmospheric dust, has drawn the attention of the scientic community to the importance of improving our understanding of aerosols [Tanaka, 2007].

Figure 1.2: Global map of desertication vulnerability (Natural Resources Conserva-tion Service of United States Department of Agriculture 1998).

Desertication denotes the spread of environmental conditions similar to those found in deserts to regions where they are normally not found. This problem is not only limited to Africa but poses a global threat, because all continents are aected by this phenomenon. Desertication exists not only in extremely arid regions, but also in regions where the amount of precipitation is comparable to that in Germany, e. g., Cote d'Ivoire (former: Ivory Coast). Aridity and droughts, which are typical in certain climates and are enhanced by climate change, are not the main reason for desertication. The main cause of desertication is land degradation due to irresponsible anthropogenic exploitation; the results are referred to as man-made-deserts. Desertication due to degradation of land is often irreversible. Worldwide, around two billion hectares of farmland have already been degraded to various extents. This represents 15 % of global farmland and corresponds to the combined area of the USA and Mexico. Nine million hectares have been irrepara-bly degraded. Around 5 to 7 million additional hectares are degraded per year; this is equivalent to the area of Ireland. Another 30 million square kilometres are threatened by desertication due to persistent droughts. In the Sahel, for example, around 1.5 million

hectares of farmland per year have been degraded due to droughts since 1972/73. About 46% of the land area of Africa is aected by desertication, which inuences the life of 485 million people [Reich et al. , 2001].

Figure 1.3: This schematic diagram shows the connection of dust availability and atmospheric dust loading in a complex global system (taken from [Jickells et al. , 2005]).

The major desert dust production mechanism is called 'saltation'. In this process, larger wind-blown particles bounce on the desert soil's surface and release smaller dust particles from the surface. Dust is emitted from the Sahara, Arabian, Gobi, Taklamakan, Australian, and South American deserts. The quantitatively largest amount of dust in the global atmosphere is emitted from the hyperarid northern African (5070%) and Asian (1025%) deserts.

Deserts generate dust by dynamic atmospheric processes. The lifetime of atmospheric dust ranges from less than a few hours for particles larger than 10 µ m, which are quickly

removed by gravitational settling, to 1015 days for submicron particles that are mostly removed by wet deposition [Jickells et al. , 2005]. Much of the dust travels over great distances and is deposited in non-desert areas with diverse and often unexpected eects. For example, propagation of microorganisms can be attributed to the fact that they are transported by desert dust. Uncontrolled reproduction of such exotic populations may lead to eects like the dying out of coral reefs in some regions of the world [Shinn et al. , 2000]. Far-travelled dust particles are usually less than 2 micrometres (µm) in size, and are mostly made up of aluminosilicate minerals. These are nutrient-rich materials which lead to fertilisation of vegetated land regions and eutrophication of surface water [Jickells et al. , 2005; Jickells, 2005]. Nevertheless there is also a critical discussion in the scientic community about fertilisation by dust-transported iron [Boyd & Mackie, 2008].

Dust emitted in the Sahara can be carried across the North Atlantic to North, Central, and South America, and even supply the Amazonian rain forest with nutrients [Koren et al. , 2006]. Large amounts of Asian dust are carried over the North Pacic toward the mid-Pacic islands and North America. Moreover the interference of Saharan dust with the formation of tropical cyclones in the Caribbean hurricane alley is a hot topic in scientic discussion [Evan et al. , 2006; Lau & Kim, 2007].

The schematic diagram from Jickells et al. [2005] summarises the global dust connection in a clear, representative way (see Figure 1.3). It shows the state and connection between surface and dust availability, atmospheric aerosol loading, marine productivity, and the global climatic state (here, a schematic diagram of mean global surface temperature). What state inuences another, with which sign, and to what extent is highly uncertain and not fully understood.

Frequent dust events are observed in enclosed depressions [Prospero et al. , 2002]. These are lake sediments deposited during wetter climate periods. The Bodélé Depression on the Saharan-Sahelian border (central Chad) for example, which once was part of the oor of the much larger Lake Chad, is now one of the most active dust source regions on Earth. Global annual dust emissions are estimated to range from 1000 to 5000 million tonnes per year, and about 80% of dust comes from the Northern Hemisphere [IPCC, 2001; Prospero et al. , 2002; Tanaka, 2007]. Also, intensive use of agricultural land (cropland) leads to an increase of atmospheric aerosol loading because of erosion eects. Nevertheless the anthropogenic contribution to dust direct radiative forcing of the Earth system is estimated as at most 20%, which yields a small negative value of −0.1 ± 0.2 W m−2 _{[Tegen et al. , 2004].}

1.5 Saharan Mineral Dust Experiment (SAMUM)

The Saharan Mineral Dust Experiment (SAMUM) is a joint project of several research institutes in Germany in cooperation with the Mohammed I. University (Oujda, Morocco) and is funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG).

The aim of SAMUM is to provide the full range of data on local microphysical and chemical properties of desert dust derived from laboratory and eld measurements on regional and global eects as analysed by airborne and space-borne sensors and as simulated and forecast by advanced weather and climate models. S-DREAMS (Dust aerosol REtrievals

Figure 1.4: The SAMUM research group logo shows involved institutions and institutes.

from space-borne instruMentS) is a subproject and the contribution of the Institute of Environmental Physics of the University Bremen to the SAMUM main project. It is focused on the measurement and analysis of the eect of mineral dust from the Saharan desert on the atmospheric radiation budget.

SAMUM is dedicated to the understanding of radiative eects in the source region. The eld campaign took place in MayJune 2006 and was located at two ground stations in southern Morocco on the border to the Sahara. One ground station was located at Ouarzazate airport and the second was based at Tinfou 'Porte au Sahara' on the plateau near Zagora. Further description of the eld experiment is given in Section 3.3.

The following institutes and institutions are involved in the SAMUM research group (see also Figure 1.4):

• Funded by: German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) • Institute for Atmospheric Physics, Johannes Gutenberg University Mainz

• Institute of Atmospheric Physics, Deutsches Zentrum für Luft- und Raumfahrt (DLR) • Laboratoire de Physique de l'Atmosphère, Departement de Physique, Faculté des

• Meteorological Institute, Ludwig Maximilians University Munich • Institute of Mineralogy, Technical University Darmstadt

• Institute of Environmental Physics (IUP), University of Bremen • Leibniz Institute for Tropospheric Research (IfT), Leipzig

Optical properties of aerosol and

radiative transfer

2.1 Processes in the atmosphere

On the way through the atmosphere the electromagnetic radiation of the sun is involved in many interactions. Radiation is transformed in the atmosphere substantially byabsorption and scattering. Scattering refers to the deection of radiation from the incident direction without electrical transmission; in this process, the light can be scattered not only ones but multiple times. The sum of absorption and scattering is called extinction. The mathematical approach of the change of radiation due to interactions is called radiative transport or radiative transfer theory.

On the way through the atmosphere the electromagnetic radiation of the sun hits air molecules, trace gases, and aerosols. The way they absorb, scatter, or emit the radiation of the sun is described by the radiative transfer equation (RTE). Therefore this equation plays an important role in the physics of the atmosphere. The representation of the radiative transfer problem determines the exact formulation of the RTE. The treatment of this topic is described extensively and in detail in the literature [Chandrasekhar, 1950; Sobolev, 1956, 1975; Lenoble et al. , 1985; Goody & Yung, 1989; Liou, 2002].

In Equation (2.9) the RTE is formulated to investigate the inuence of aerosols on the radiative transport. This is done by considering the so-called climate relevant aerosol parameters, which have to be known to solve the RTE. In this research, these parameters are obtained by ground-based measurements during the SAMUM campaign (see Chapter 3).

The thermal emission of radiation from aerosols will not be considered since the signicance of such emissions is negligible in the wavelength range of solar radiation.

The intensity of radiation characterised as radiance L with the unit watts per square metre per steradians W / m−2_sr−1_{. Radiance can be determined as a function of wavelength and} position of the sun. For a horizontal homogeneous and plane-parallel atmosphere, the RTE can be written for the radiance L as a deducting equation. Absorption and scattering cause radiation losses for the main propagation direction. Scattering in other directions ensures

a gain in radiation.

The losses dL− _{are described by the Beer-Lambert law (wavelength dependency is} neglected):

dL−(z, µ, φ) =−σe(z)

µ · L(z, µ, φ) dz (2.1)

The direction of the incident radiance (µ, φ) is denitely determined by the zenith distance

θ (with µ = cos θ) and the azimuth angle of the sun; z is the altitude and the volume

extinction coecient σe(z) determines how radiation is attenuated by absorption and scattering. Both processes are combined in the term extinction, according to which the volume extinction coecient is dened by the sum of volume absorption (σa) and volume scattering coecient (σs):

σe(z) = σa(z) + σs(z) (2.2)

The increase of radiance dL+ _{arises out of the radiation L(Ω}0_{), which comes from other} directions and is scattered into the light path (µ, φ) of L. This intensication is dened as:

dL+_{(z, µ, φ) =−}σs(z)

µ dz ·

∫ 4π

L(z, µ, φ, Ω0)· p(z, µ, φ, Ω0)dΩ0 (2.3)

The phase function p(z, µ, φ, Ω0_{) determines how much radiation is scattered into the light} path.

In radiative transfer calculations, usually an integrated value is taken as the vertical component. This quantity is the optical thickness:

δλ(z) = T OA∫

z

σe(z0)dz0 (2.4)

The optical thickness is a measure of the penetrability or opacity of atmospheric con-stituents like aerosols, air, and gas molecules for a given wavelength. The total optical thickness of the atmosphere is the sum of the individual optical thicknesses:

δλ(z) = δR(z) + δG(z) + δA(z) (2.5)

Therefore, if we know the ratio of air and gas optical thicknesses to the (measured) total optical thickness, we can calculate the aerosol optical thickness (AOT). One assumes at the top of atmosphere (TOA) that δλ = 0.

The ratio of scattering to total extinction is described by the single scattering albedo ω0. If ω0= 1, the medium is 100% scattering. When ω0 = 0, it is a fully absorbing medium.

ω0 =

σs

σe

= σs

σa+ σs (2.6)

The losses and gains in Equations (2.3) and (2.1) result in the following balance for the change of radiance along the light path through the atmosphere:

µ· dL dδ = µ· ( dL+ dδ + dL− dδ ) =−L(δ, µ, φ) + ω0 ∫ 4π L(δ, µ, φ, Ω0)· p(δ, µ, φ, Ω0)dΩ0 (2.7) Furthermore, it is useful to divide the radiance L into direct Ldir and diuse Ldif f so that:

L = Ldir+ Ldif f (2.8)

Then we can formulate the RTE for the diuse part as follows:

µ· dLdif f dδ =− Ldif f(δ, µ, φ) + ω0 4π 2π ∫ 0 1 ∫ −1 Ldif f(δ, µ0, φ0)· p(δ, ψ0)dµ0dφ0 + ω0 E0 4 p(δ, ψ)· e −δ µ0 (2.9)

In this integro dierential equation, E0 is the extraterrestrial irradiance of the sun at top of atmosphere. The source term is divided in a single scattering and multiscattering part. The third term on the right side of Equation (2.9) describes the single scattering, i. e. the phase function p(δ, ψ) determines which part of the direct sun beam is scattered in the direction of (µ, φ). Here, ψ stands for the scattering angle with which the sun beam is deected from its original direction. This is a function of the azimuth angle and the altitude or the zenith distance of the sun and is dened as:

cos(ψ) = 1− sin2(θ)· (1 − cos(φ)) (2.10) The second term on the right side of Equation (2.9) is the contribution of the multiple scattering in the direction (µ, φ). Here, all directions (µ0_{, φ}0_{) the diuse radiation can} come from must be considered.

In the RTE (2.9) the optical thickness δ, the single scattering albedo ω0, and the phase function p represent properties of the entire atmosphere, i. e. they reect the eects of molecules, gases, and aerosols on radiation. These values are the sums of their individual components. δλ= δR+ δG+ δA (2.11) ω0= σs σe = σ R s + σGs + σsA σR e + σGe + σeA (2.12) p = σ R spR+ σGspG+ σsApA pR_{+ p}G_{+ p}A (2.13)

The indices R, G, and A stand for the air molecules ('Rayleigh atmosphere'), gases, and aerosols respectively. Assuming a vertically homogeneous atmosphere, which means that the single scattering albedo ω0and phase function p do not depend on altitude, the volume scattering σs and volume extinction coecients σe in Equation (2.12) and (2.13) can be substituted by the respective optical thicknesses.

The RTE can only be solved by computational numerical procedures. The lower boundary condition is the relation of upward to downward ux density on the Earth's surface, which is called albedo, and the upper boundary condition is the solar irradiance on the top of the atmosphere. A common approach to solving the RTE is the matrix operator method (MOM) (Lenoble et al. [1985]; Goody & Yung [1989]). The radiative transfer code of SCIATRAN [Rozanov et al. , 2002] and Nakajima & Tanaka [1988], which are used in the work at hand, follows the approach of the discrete ordinate method [Lenoble et al. , 1985]. This program code of Nakajima & Tanaka [1988] oered a solution for a plane-parallel atmosphere and was improved by Wendisch & Hoyningen-Huene [1994] to calculate the radiative transfer for given relative air masses for the CIRATRA method (s. a. Section 3.6). 2.1.1 Molecular Rayleigh scattering

The smallest particles (or molecules) exhibit a quite simple form of scattering behaviour. This is called Rayleigh scattering because the essential colour and polarisation features of sky brightness were discovered in 1871 by Lord Rayleigh. Sometimes the Rayleigh scattering is also called molecule scattering or Cabannes scattering; Cabannes was a student of Lord Rayleigh. Rayleigh scattering applies only when the particle size is much smaller than the wavelength of the incident radiation (relation α < 0.1). Under these conditions the incident light induces a dipole moment inside of the particle, which is proportional to the power of the incident electrical eld. As an electromagnetic wave, the incident eld oscillates in a specic frequency and induces an oscillating dipole moment with the same frequency, which then emits an electromagnetic eld as a so-called Hertzian dipole. Under these conditions it can be shown that the radiance L of the scattered radiation in the far-eld (R  λ) is dened as follows:

L(ψ) = C· L0· 1 R2 · 1 λ4(1 + cos 2_{ψ) (2.14)}

with ψ the scattering angle and L0 the radiance of the incident radiation. The constant

C is given by the polarisability of the particles. For the Rayleigh scattering function we

then get: pray(ψ) = 3 4(1 + cos 2_{ψ) (2.15)} The factor 3

4 is given by the normalisation convention of the scattering function. Sometimes we nd in the literature an additional normalisation component, 1

4π. Looking into the spectrum of visible light from about 0.4µ m (violet) up to 0.8µ m (red) the extinction

σext,ray(λ)due to Rayleigh scattering is in the blue region about 16 times higher than in

the red region.

2.1.1.1 Determination of the Rayleigh optical thickness

As we know from Equation (2.11), the total optical thickness of the atmosphere is the sum of the discrete optical thicknesses of air molecules, gases, and aerosols. To calculate the aerosol optical thickness, we rst have to determine the optical thicknesses of gas absorber and air molecules. According to Bucholtz [1995] absorption by air molecules is negligible, so using Equation (2.37) and (2.49), the optical thickness due to Rayleigh scattering is:

δray(λ) = ∞ ∫ z0 σscat,ray(λ, z)dz = ∞ ∫ z0 qray· nmol(z)dz (2.16)

For the scattering cross-section of the Rayleigh scattering qray, we use an analytical solution according to Seinfeld & Pandis [1998]:

qray =

128C2π5

3λ4 (2.17)

Here, C a constant of polarisability, is a material property of the scattering particle (see also Equation 2.14). A regression line through the calculated values gives an approximation for the Rayleigh optical thickness. This is normalised by the actual air pressure p which reects the dependence of the density of the air molecules nmol(z)on altitude. Well-known approaches to calculating the Rayleigh optical thickness are given for example by Leckner [1978] (see Equation (2.18)), based on theoretical evaluations of molecule scattering by Penndorf [1957], and Fröhlich & Shaw [1980] (see Equation (2.19)):

δray = 0.008735· λ−4.08· p p0 (2.18) δray = 0.008735· λ−(3.916+0.072·λ+0.05·λ −1₎ · p p0 (2.19)

Model Coecient A p0 [hPa] λ≤ 0.5µ m λ > 0.5µ m Tropical 6.52965· 10−3 8.68094· 10−3 1013 Midlatitude Summer 6.51949 · 10−3 _{8.66735· 10}−3 ₁₀₁₃ Midlatitude Winter 6.53602· 10−3 8.68941· 10−3 1018 Subarctic Summer 6.48153· 10−3 8.61695· 10−3 1010 Subarctic Winter 6.49997· 10−3 8.64145· 10−3 1013 US Standard 1962 6.50362· 10−3 8.64627· 10−3 1013 Coecient B 3.55212 3.99668 C 1.35579 1.10298· 10−3 D 0.11563 2.71393· 10−2

Table 2.1: Coecients of Rayleigh optical thickness in Equation (2.20) according to Bucholtz [1995].

Buchholtz's approach [Bucholtz, 1995] is very similar but more sophisticated:

δray = A· λB+C·λ+Dλ −1

· p

p0 (2.20)

The coecients A, B, C, and D are determined for wavelengths where λ > 0.5µ m and smaller than λ ≤ 0.5µ m respectively. Because the air column above the observation point changes with the density prole of the atmosphere, Bucholtz [1995] varies the coecient

A for dierent conditions. This approach takes seasonal and geographical variations into

consideration. The coecients which can be used in Equation (2.20) are listed in Table 2.1. 2.1.2 Particle scattering

2.1.2.1 Mie scattering of spherical particles

The Rayleigh scattering theory cannot be applied if particle size is not small in compar-ison to the wavelength of incident radiation. In the Earth's atmosphere this is the case when light scatters on dierent kinds of aerosols. There is no analytical solution to this problem. So numerical approaches must be used. One such approach is the well-known Mie theory, which oers an exact solution of the Maxwell equations but only for the following boundary conditions:

• The scattering particles have to be spheres with the radius r

• The particles consist of homogeneous material with a complex refraction index m

Following extinction- , scattering- , and absorption-eciencies (Qe, Qs,Qa) can be derived from Mie theory [van de Hulst, 1957; Seinfeld & Pandis, 1998]:

Qs(m, α) = 2 α2 ∞ ∑ k=1 (2k + 1)·[|ak|2+|bk|2 ] (2.21) Qa(m, α) = 2 α2 ∞ ∑ k=1 (2k + 1)· Re{|ak|2+|bk|2 } (2.22) Qe(m, α) = Qs+ Qa (2.23)

The Mie coecients ak and bk are functions which depend on the size parameter α, the refractive index m, and adapted Ricatti-Bessel functions.

The extinction eciency Qe is an oscillating function of the size parameter α. For large α the functions converge at 2.

0 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100 120

Mie extinction efficiency Q

ext

Size parameter α = 2πr/λ

Refractive index 1.42 -0.015i 1.50 -0.025i

Figure 2.1: Mie extinction eciency Qe as a function of the size parameter α =

2πr/λfor two dierent refractive indices at a wavelength of 0.55 µ m.

σsλ = ∞ ∫ 0 π· r2· Qs(λ, α, m)· dN(r) d log rd log r (2.24) σaλ = ∞ ∫ 0 π· r2· Qa(λ, α, m)· dN(r) d log r d log r (2.25) σeλ = ∞ ∫ 0 π· r2· Qe(λ, α, m)· dN(r) d log rd log r (2.26) σe = σa+ σs (2.27)

2.1.2.2 Pollack & Cuzzi's semi-empirical theory on the scattering of non-spherical particles

The Mie theory oers a analytical solution of the Maxwell equations for the interaction between matter and electromagnetic radiation. These equations can only be solved analyti-cally if the matter is composed of spheroidal particles which have the size of the wavelength of radiation. This approach is an idealisation of the particles in the atmosphere. For many applications this is an appropriate solution. But strictly speaking we have to assume the existence non-spherical particles, which exhibit a random spatial orientation in order to describe the scattering behaviour of aerosols. The Mie theory is then a special case of a general scattering theory.

Pollack & Cuzzi try to circumvent this problem by describing only the optical eects of non-spherical particles to nd a parametrisation of scattering behaviour [Pollack & Cuzzi, 1980]. Therefore, they do not have to assume special particle shapes, as is the case in a closed theory like the Mie theory. We can determine which values the parameters adopt from measurements made by the CIRATRA method (see Section 3.6).

The theory of Pollack & Cuzzi is a combination of dierent physical scattering pro-cesses. It is a function of size distribution which of the physical scattering process takes eect with which intensity. Pollack & Cuzzi distinguish between ne and coarse particles by using the size parameter α0 = 2πr0/λ0. For small particles with an α < α0, the eciencies Qe,s,a and the aerosol phase function pa(ψ, λ) are calculated by the Mie theory. For coarse particles with an α > α0, the eciencies and the phase function are determined by a weighted sum of the following physical processes:

• diraction determined by the law of physical optics

• external reexion determined by the law of geometrical optics • internal transmission

The dimensionless size parameter α0 is quantied by Pollack & Cuzzi [1980] as α0 = 5. The act eciency Qe,s,a and the aerosol phase function are determined by the following equations:

Q∗_s = QL_s · F · f + QS_s · (1 − F ) (2.28) Q∗_a= QL_a · F + QS_a · (1 − F ) (2.29) Q∗_e = Q∗_s+ Q∗_a (2.30) p∗ = IS· (1 − F ) ·Q S s Q∗_s + f· F · QL_s Q∗_s · ( ID· QD QL s + IR· QR QL s + IT · QT QL s ) (2.31) Here, QS_s = α∫0 0 Qs_{d log(α)}dN(α) · πα2d log(α) α0 ∫ 0 dN(α) d log(α)· πα2d log(α) (2.32)

is the scattering eciency for particles smaller than α0 < 5. For the scattering eciency

of large particles α0, the following is valid:

QL_s = ∞ ∫ α0 Qs_{d log(α)}dN(α) · πα2d log(α) ∞ ∫ α0 dN(α) d log(α)· πα2d log(α) (2.33)

Both denitions dier only in the integration boarders. The absorption eciencies QS

a and

QL_a can be calculated analogously. The factor F is the relation of the large particles to the

total number of particles:

F = ∞ ∫ α0 dN(α) d log(α)· πα d log(α) ∞ ∫ 0 dN(α) d log(α)· πα d log(α) (2.34)

f describes the relation of an irregularly shaped particle to the sphere surface. As a

consequence, f could be seen as a value for non-sphericity and is larger than 1 because the surface of arbitrarily shaped particles is always larger than a sphere with the same volume. The rst term on the right side of Equation (2.31) determines the proportion of small particles. The second term determines the Mie scattering part and the proportion for the large particles of the aerosol phase function. The index D stands for the diraction, R for the external reexion, and T for the internal transmission. So ID,R,T are the phase functions for the discrete physical process. The coecients QD,R,T result from a normalisation of the individual contributions of the phase functions over the whole range of solid angle.

For the reexion part for large particles in Equation (2.31) the assumption is made that an ensemble of randomly orientated and irregularly shaped particles reects incident light in the same way that an ensemble of spherical particles with the same refraction index will [van de Hulst, 1957]. This means that the external reexion for all particles with α > α0 is assumed to follow the law of geometrical optics.

The part of internal transmission in Equation (2.31) is the main reason for the dierences in the scattering behaviour of irregularly shaped and spherical particles. The reason for these dierences can be obtained by illustrating the path of rays entering such particles in the limits of geometrical optics (see Figure 2.2). As indicated in this gure, a substantial part of the radiation entering the cube is reected internally and comes out as indicated, resulting in large scattering angles. On the other hand, Figure 2.2 shows that the internal transmitted radiation in at plates and spheres tends to favour the forward scattering direction.

Figure 2.2: Illustrating the path of rays entering irregularly shaped particles in the limits of geometrical optics. The situation is shown for cubes, where a substantial fraction of radiation is transmitted with large scattering angles, and at plates and spheres, where scattering in a forward direction predominates [see Pollack & Cuzzi, 1980].

To describe the transmission in Equation (2.31) Pollack & Cuzzi [1980] use an empirical parameter G which determines the relation between forward and backward scattering:

G = π/2∫ 0 IT dθ π ∫ π/2 IT dθ (2.35)

Instead of the size parameter α0 with a xed wavelength λ, a border radius rx = α0· λ/2π can be chosen, at which the sphericity and Mie theory is no longer valid. This radius

rx is one of three free selectable parameters in the semi-empirical approach of Pollack & Cuzzi. The other two parameters are the surface relation f and the transmission component G. Section 3.6 describes how this parameter is retrieved by the CIRATRA method to calculate the phase function from sun photometer measurements of desert dusts sky-brightness.

2.1.3 Extinction

The change of radiation Lλ(0) to Lλ(z) in an atmospheric layer with thickness z is the result of absorption, which converts radiation into other types of energy such as heat or produces photo-chemical reactions and scatters light away from the line of propagation. The extinction coecient comprises all absorption and scattering processes. Only under special circumstances can we neglect one contribution to the total absorption, e. g. in the microwave wavelength region it is frequently acceptable to neglect scattering.

By denition, extinction is the sum of scattering and absorption:

σext(λ) = σscat(λ) + σabs(λ) (2.36)

σscat(λ) is composed of the following components: air molecules σscat,mol(λ) (Rayleigh) aerosol particles σscat,aer(λ) (Mie and EBCM)

cloud particles σscat,cloud(λ) (Mie, EBCM, and geometric optics). Likewise, for absorption σabs(λ)we distinguish the following components:

air molecules σabs,mol(λ) (gaseous absorption lines and bands) aerosol particles σabs,aer(λ) (Mie and EBCM, dielectric loss)

cloud particles σabs,cloud(λ) (Mie, EBCM and geometric optics, dielectric loss). The relevant major theories that describe each process are listed here in parentheses. Rayleigh, Mie, and geometric optics refer to the respective theories. ECBM stands for Extended Boundary Condition Method, for example, T-Matrix method. Gaseous absorption is described by quantum mechanics.

For a homogeneously lled volume, the extinction coecient σext,mol(λ) is dened as follows:

σext,mol(λ) = n· qext,mol(λ) = n· κ(λ) + n · ε(λ) (2.37)

with n the number of molecules or the density of the medium in [m−3_{] and q}

ext,mol(λ) the extinction cross-section of one molecule in [m2_{]. This quantity can be considerably} larger than the geometrical cross-section with respect to the interaction eciency between the photon and the molecule. Applying to a mass unit κ(λ) and ε(λ) are the absorption respectively the scattering cross-section. If the medium is a mixture of gases with the densities n(i)_{, we can determine the total absorption cross-section of this composite as} follows: κ(λ) =∑ i κ(i)(λ)·n (i) n (2.38)

Corresponding relations are valid for the loss of radiation due to scattering: ε(λ) =∑ i ε(i)(λ)·n (i) n (2.39)

Using the extinction cross-section the mean free path length lλ can be calculated by:

lλ= 1

σext,mol(λ)

= 1

n· qext,mol(λ) (2.40)

The scattering coecient is dened in a similar way:

σscat,mol(λ) = n· qscat,mol(λ) (2.41)

Whereas qscat,mol(λ) is the scattering cross-section of a single molecule in [m2]. For aerosol and cloud particles we can dene the extinction coecient σext,aer(λ)as:

σext,aer(λ) = ro ∫ ru qext,aer(λ)· dN(r) dr dr (2.42)

With the integral extending over the range of particles radii for the given size distribution

N (r)in [m3], and qext,aer(λ) the extinction cross-section of a single particle in [m2]. The quantity qext,aer(λ)has to be calculated for a given particle radius by using an appropriate technique, e. g. Mie theory.

2.1.3.1 Optical thickness

The optical thickness or opacity δλ is dened by the integration over the vertical prole of extinction: δλ = z ∫ 0 σext(λ)dz = − 1 M · ln ( Lλ(z) Lλ(0) ) (2.43)

2.1.3.2 Single scattering albedo

Furthermore we have to consider the albedo due to scattering; assuming only one scattering process or the so-called single scattering albedo ω0(λ), we can write:

ω0(λ) = σscat(λ) σext(λ) = σext(λ)− σabs(λ) σext(λ) = 1−σabs(λ) σext(λ) (2.44)

This can also be interpreted as the probability of a photon being scattered. ω0(λ) = 0 represents perfectly absorbing particles, whereas ω0(λ) = 1 stands for purely scattering particles.

2.1.4 The scattering phase function

0.001 0.01 0.1 1 10 100 0 20 40 60 80 100 120 140 160 180 Phasefunction [1/sr]

Scattering angle [deg]

Phasefunction OPAC SAMUM Average LACE Average

Figure 2.3: Dierent aerosol phase functions at 870 nm wavelength, which show variable scattering behaviour depending on aerosol type. OPAC is calculated by Mie theory. LACE shows a continental (mixed) type and SAMUM a mineral desert dust type of aerosols.

The phase function p(ψ) gives the probability of light scattering in the direction of the scattering angle ψ (see Equation (2.10)). It is composed of scattering due to Rayleigh scattering of molecules and scattering by atmospheric aerosols or Mie scattering:

p(ψ) = δray(λ)· pray(ψ) + δaer(λ)· paer(ψ)

δray(λ) + δaer(λ) (2.45)

When the phase function of Rayleigh scattering is symmetrical and well-known (see Equation (2.15)), the aerosol contribution is strongly asymmetric and has high variability in the range of scattering angles. The aerosol phase function depends on aerosol type, that is size distribution, particle shape and chemical composition. In most cases it is calculated for spherical particles by Mie theory, however, experimental results have shown that in many cases strong eects due to non-spherical particles can also be observed. Especially for aerosol remote sensing, these deviations are considerable.

2.2 Radiative transfer equation (RTE)

The radiative transfer equation in a basic form (in the literature often called as Schwartzschild equation): ds z L(λ, s) dL(λ) L(λ)

Figure 2.4: Sketch of radiative transfer geometry.

dL(λ)

ds = σext(λ)· (J(λ) − L(λ)) (2.46)

It describes the change of radiance L(λ) if light is propagating through a medium. The radiance change is proportional to the product of extinction with the sources and sinks within the medium. Extinction σext(λ) describes the medium itself and is equal to the sum of absorption and scattering coecients of all atmospheric constituents. L(λ) is the radiance before entering the medium and J(λ) are the source terms within the medium. Terrestrial temperature emission occurs at wavelengths above 3 µ m; the source term is given by the Planck law. Emission is determined by the temperature state of the medium.

Spectral features which based on discrete energy states of the molecules in the medium (rotation and vibration states) lead to emission lines or bands.

Scattering (redistribution of short wave radiation) occurs by molecules, as described by Rayleigh scattering, or atmospheric particles or droplets, as described by the Mie theory for spherical particles. For non-spherical particles, e. g. ice crystals or desert dust, more sophisticated scattering formalisms must be used; these remain an important topic for current research. Finally, for particles that are very large in relation to wavelengths, e. g. precipitation or dust, geometric optics or ray tracing methods will have to be applied. 2.2.1 Radiative transport in a scattering plane-parallel atmosphere a) Plane-parallel atmosphere

Regarding a radiation beam with a spectral radiance L(λ) which travels through an atmospheric layer of the thickness dz and with an incident angle θ, Figure 2.5 shows that there is a path prolongation by the tilted path if the ray has the zenith angle θ.

dz = ds cos(θ) ds θ z L(λ) L(λ)− dL(λ)

Figure 2.5: Radiative transport through a medium in a plane-parallel atmosphere.

In this case radiation undergoes on its path ds = µ dz a change due to the extinction

σext= σscat+ σabs (scattering plus absorption) of: dL(λ) ds = µ· σext(λ)· (J(λ) − L(λ)) (2.47) with ds = 1 cos(θ)dz = µ dz and σ 0 ext(λ) = µ· σext(λ)

one gets a so-called slant path extinction σ0

ext(λ)for a tilted path as presented in Figure 2.5. In a lot of cases, the vertical path properties σext(λ) are required. This method oers sucient accuracy for θ ≤ 60◦_.

Regarding the radiance for a solar zenith angle θ and the direction φ (azimuth angle) in a plane-parallel atmosphere with the z-axis parallel to the gradient of the air density, we arrive at the following RTE:

cos θdL(λ, θ, φ) = −n · qext(λ)dz · (L(λ, z, θ, φ) − J(λ, z, θ, φ)) (2.48) If we dene the optical thickness as:

δ(z) = ∞ ∫ z σext(λ, z0)dz0 = ∞ ∫ z qext(λ)· n(z0)dz0 (2.49)

then we can substitute dδ(λ) = −(λ)ρ dz and with µ = cos θ it follows:

µ· dL(λ, δ, µ, φ)

dδ = L(λ, δ, µ, φ)− J(λ, δ, µ, φ) (2.50)

A formal solution of Equation (2.50) is obtained by separating up- and downward directed radiation.

For the upward directed radiance with µ ≥ 0 and at an altitude of δ, it follows after multiplication with e−δ/µ _{and integration from δ}0_{= δ to δ1:}

L(λ, δ, µ, φ) = L(λ, δ1, µ, φ)· e− δ1−δ µ ₊ 1 µ δ1 ∫ δ J (λ, δ0, µ, φ)· e−δ0µ−δdδ0 (2.51)

For downward directed radiance with µ < 0 and at an altitude of δ, multiplication with

eδ/µ and integration from δ0 = 0 to δ yields the following:

L(λ, δ, µ, φ) = L(λ, 0, µ, φ)· e− δ |µ| ₊ 1 |µ| δ ∫ 0 J (λ, δ0, µ, φ)· e− δ−δ0 |µ| dδ0 (2.52)

L(λ, 0, µ, φ)and L(λ, δ1, µ, φ)describe the inwards directed radiance into the atmosphere at the top of atmosphere δ = 0 and at the ground δ = δ1.

For applications in atmospheric modelling and remote sensing, it is interesting to determine the radiant uxes which comes out of the atmosphere at the top of atmosphere and on

the ground. To obtain a formal solution for such boundary conditions we have to ll in Equation (2.51) and (2.52) in an appropriate way. Doing this for the upward directed radiance at the top of atmosphere with δ = 0 leads to:

L(λ, 0, µ, φ) = L(λ, δ1, µ, φ)· e−δ1µ ₊ 1 µ δ1 ∫ 0 J (λ, δ0, µ, φ)· e−δ0µ dδ0 (2.53) The rst term on the right side represents the altitude attenuated radiation, which comes from the surface. And the second term describes the upward directed radiation from the atmosphere.

For the downward directed radiance at the ground, it follows, with δ = δ1:

L(λ, δ1, µ, φ) = L(λ, 0, µ, φ)· e− δ1 |µ| ₊ 1 |µ| δ1 ∫ 0 J (λ, δ0, µ, φ)· e−δ1−δ0|µ| dδ0 (2.54) Here the rst term on the right side is the radiation at the top of atmosphere (δ = 0), which comes from outside and propagates into the atmosphere and is attenuated by the optical thickness of δ1. The second term is the downward directed radiance, which is scattered by the atmosphere.

To reach a solution for the equations for the radiant ux densities at the top of atmosphere and on the Earth's surface, we must solve the integral on the right side of Equations (2.53) and (2.54). This is in general very complicated because the source term J within the integrals is again an integral over the product from radiance and the scattering function, along the whole range of solid angles (see Equation (2.58)). Many numerical approaches deal with this problem. Mostly they consider only homogeneous plane-parallel atmospheric layers, which means that changes in such a modelled atmosphere are only possible along the vertical line. This is a reasonable simplication for vertical layered atmospheres but could lead to problems if horizontal structures dominate (e. g. convective clouds).

2.2.1.1 Successive order of scattering (SOS)

The SOS method describes a simplied solution of the RTE in an absorbing, scattering and non-emitting atmosphere. The simplication consists of the assumption that the total scattered radiance is the sum of single, dual, and multiple scattered radiance. Therefore we can write for radiance reected in a layer (Lr or µ ≥ 0) and transmitted through a layer (Lt respectively µ < 0): Lr(λ, µ, φ) = ∞ ∑ n=1 Lr,n= Lr,1+ Lr,2+ . . . (2.55) Lt(λ, µ, φ) = ∞ ∑ n=1 Lt,n = Lt,1+ Lt,2+ . . . (2.56)