Modeling of the Diffuse Sky RadianceField based on Sun Photometer Retrievals

Tanya RodriguezAdvisors: Dr. Johannes Kaiser, Jurg Schopfer

Professor: Dr. Klaus I. Itten

Master ThesisSpectroLab, RSL

Department of GeographyUniversity of Zurich

September 2005

Contents

1. Introduction 91.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2. Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3. Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2. Radiative Transfer Elements 122.1. Interaction of radiation and atmosphere . . . . . . . . . . . . . . . . . . . . . 12

2.1.1. Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.2. Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.3. Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2. Radiative transfer/ Radiation field properties . . . . . . . . . . . . . . . . . . . 13

3. Tools 163.1. IDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2. MODTRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3. Sunphotometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4. Data 194.1. Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2. Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5. Method 245.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.2. Inversion: anar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.2.1. Retrieving water vapor, ozone and visibility . . . . . . . . . . . . . . . 255.2.2. Retrieving the aerosol model . . . . . . . . . . . . . . . . . . . . . . . 275.2.3. Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.3. Forward Modeling Radiances: anar fwdmod . . . . . . . . . . . . . . . . . 29

6. Results 316.1. Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.2. Forward Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

7. Conclusions 357.1. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.2. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Bibliography 38

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A. Outputs 40A.1. Results of anar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40A.2. Sample of the results of anar fwdmod . . . . . . . . . . . . . . . . . . . . . 41

B. Programs 42B.1. anar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

B.1.1. RSL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42B.1.2. Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

B.2. anar fwdmod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43B.2.1. Own . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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List of Figures

1.1. The shadow-band sunphotometer MFR-7. . . . . . . . . . . . . . . . . . . . . 9

2.1. Polar diagram of the directionality of the Rayleigh scattering [28]. . . . . . . . 132.2. Polar diagram of the directionality of the Mie scattering [28]. . . . . . . . . . . 132.3. Sun radiance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4. Differential volume element containing material which alters a beam of radiation

passing through it. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5. Vertical optical depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1. An example of the MODTRAN input file tape5. . . . . . . . . . . . . . . . . . 163.2. An example of MODO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3. The Reagan sunphotometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1. Sample of a standard Reagan sunphotometer file. . . . . . . . . . . . . . . . . 204.2. Sample of the converted data file with the header and the observations. . . . . . 204.3. DN of channel 1 (383 nm), 5 (669 nm) and 10 (1033 nm). . . . . . . . . . . . . 214.4. Transmittances for all 10 channels as output of spm read. . . . . . . . . . . . 214.5. τslant for all 10 channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.6. τvert for all 10 channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.1. Overview of the method [own graphic]. . . . . . . . . . . . . . . . . . . . . . 245.2. The main principle of anar [27]. . . . . . . . . . . . . . . . . . . . . . . . . 265.3. Anar graphical user interface. . . . . . . . . . . . . . . . . . . . . . . . . . . 285.4. Anar fwdmod graphical user interface. . . . . . . . . . . . . . . . . . . . . . 30

6.1. Results from anar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.2. Results from anar fwdmod: radiance for two different zenith angles at the

same azimuth angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.3. Logarithmic plots of the radiance for 382nm and 940nm. . . . . . . . . . . . . 33

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List of Tables

3.1. Technical information for the Reagan sunphotometer [8] . . . . . . . . . . . . 18

4.1. Collected information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5.1. MODTRAN Aerosol Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6.1. Table of the results classed by decreasing best fitting aerosol model . . . . . . . 31

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Thanks

During the course of this work, many people have been of assistance to me in various ways. Iwould like to thank the following, in no particular order:

• Prof. Dr. Klaus I. Itten

• Dr. Johannes Kaiser

• Jurg T. Schopfer

• Dr. Daniel Schlapfer

• Dr. Stefan Dangel

• SpectroLab-Team

• Sven Werlen

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List of abbreviations

AERONET Aerosol Robotic NetworkBRDF Bidirectional Reflectance Distribution FunctionBRF Bidirectional Reflection FactorCNES Center d’Etudes SpacialesDN Digital NumbersFOV Field Of ViewFWHM Full Width at Half-MaximumIDL Interactive Data LanguageJAXA Japan Aerospace Exploration AgencyGIUZ Geographical Institute of the University of ZurichGUI Graphical User InterfaceHCRF Hemispherical Conical Reflectance FactorLUT Look Up TableMFR-7 Multi-Filter Rotating Shadowband RadiometerMODTRAN Moderate Resolution Transmittance CodeNASA National Aeronautics and Space AdministrationRSI Research Systems IncorporatedRSL Remote Sensing LaboratoriesSPM Sun Photometer

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Abstract

Spectrodirectional surface reflectance properties are important quantities in remote sensing re-search and applications. They are by definition characterized by the Bidirectional ReflectanceDistribution Function (BRDF), or equivalently, the Bidirectional Reflectance Factor (BRF), anddepend only on the surface properties [18]. However, spectrodirectional field experiments withgoniometer systems are only able to observe approximations of the bidirectional reflectance fac-tor. By following the well known method proposed by Martonchik and others [17] [16], theBRDF can be retrieved. For this procedure, the incoming diffuse radiation has to be known overthe complete hemisphere at the same angular resolution as the reflected radiation from the target.Only a few instruments can measure the incoming diffuse radiation at angular resolution. Forthis reason, a simplified approach is then used, measuring the average diffuse irradiance withan MFR sunphotometer. This leads to the aim of the thesis, which is to develop a model of thediffuse sky radiance field.

The available tools are a sunphotometer and the radiative transfer model MODTRAN [7]. Themethod consists of measuring the direct irradiance with a sunphotometer, retrieving the state ofthe atmosphere from the observations so as to input them in the radiative transfer model in or-der to finally find the diffuse irradiance distribution. The observations were performed on theroof of the University on a clear sunny day. The sunphotometer was measuring permanentlyfrom 8:15 to 16:45. The raw data was transformed to transmittances and then to vertical opticaldepth. The process of the inversion consists of comparing the observed vertical optical depthwith the simulated vertical optical depth in order to retrieve the most accurate values for watervapor, ozone, visibility and the best aerosol model. For this purpose the IDL routine anar,calling MODTRAN, was developed. Anar compares the observed vertical optical depth withthe simulated one. The routine is based on the so called curvefit function [23] which usesa gradient-expansion algorithm to compute a non-linear least squares fit to a user-applied func-tion, in this case a MODTRAN simulation, with an arbitrary number of parameters, here three.Iterations are performed until the chi square changes by a specific amount, or until a maximumnumber of iterations has been performed.

Water vapor, ozone, visibility and the aerosol model serve as input for MODTRAN in or-der to simulate the diffuse irradiance. The simulation is achieved using a second routine,anar fwdmod. The program allows the user to choose a minimum and a maximum sensorzenith and azimuth angle with an adequate increment. By using the resulting values of wa-ter vapor, ozone, visibility and the MODTRAN aerosol model that was previously retrieved, itsimulates the real total irradiance for each angle.

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1. Introduction

1.1. Motivation

Spectrodirectional surface reflectance properties are important quantities in remote sensing re-search and applications. They are by definition characterized by the Bidirectional ReflectanceDistribution Function (BRDF), or equivalently, the Bidirectional Reflectance Factor (BRF), anddepend only on the surface properties [18]. However, spectrodirectional field experiments withgoniometer systems are only able to observe approximations of the bidirectional reflectancefactor. The directly observed quantity in field experiments is called Hemispherical Conical Re-flectance Factor (HCRF), corresponding to hemispherical illumination, which depends on theatmospheric conditions and conical observation [26].

By following the well known method proposed by Martonchik and others [17] [16], the BRDFcan be retrieved. For this procedure, the diffuse radiation has to be measured over the completehemisphere at the same angular resolution as the reflected radiation of the target. At the mo-ment, the incoming diffuse radiation can be measured at angular resolution with the CIMELCE318 [5] [14], but this apparatus is not available at the Remote Sensing Laboratories (RSL)of the University of Zurich. A simplified approach is then used, measuring the average diffuseirradiance with the MFR-7 sunphotometer [26] that can be seen in figure 1.1.

Figure 1.1.: The shadow-band sunphotometer MFR-7.

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A more accurate BRDF can be retrieved, if the incoming radiation is known at the sameangular resolution as the reflectance is measured. The aim of the thesis is to derive the angu-lar dependent incoming radiation from measurements of the Reagan sunphotometer, using theradiative transfer model MODTRAN.

1.2. Approach

The radiative transfer model MODTRAN is used for modeling the diffuse irradiance, so initially,the input requirements must be discussed. The input file for MODTRAN (tape5) asks for thestate of the atmosphere and specially for the total column amounts of water vapor, ozone, andthe visibility, and for the aerosol model. Those values can be retrieved from the measuredtransmittances. For this purpose, the transmittances are transformed into vertical optical depthsso as not to depend on the sun position. The idea is to compare the observed vertical opticaldepths with the ones modelled by MODTRAN with varying values for water vapor, ozone,visibility and the aerosol model. The problem is to know how to vary those four parameters inorder to find the best approximations. Various possibilities are considered:

• At the outset, the same or approximately the same algorithm as AERONET (AerosolRobotic Network) [9] [14] for the atmospheric retrievals [11] wanted to be used. TheAERONET program is an inclusive federation of ground-based remote sensing aerosolnetworks initiated by the NASA (National Aeronautics and Space Administration) [29],developed to support NASA, CNES (Centre d’Etudes Spaciales) [10] and JAXA’s (JapanAerospace Exploration Agency) [4] Earth satellites systems. The goal is to assess aerosoloptical properties and validate satellite retrievals of aerosol optical properties. The net-work imposes standardization of instruments, calibration and processing. Data from thiscollaboration provides globally distributed observations of spectral aerosol optical depths,inversion products and precipitable water in geographically diverse aerosol regimes. TheUniversity of Bern takes part in this program and runs instruments at the Lageren researchsite, which is on the south slope of the Lageren mountain (866 m a.s.l.), approximately 15km northwest of Zurich, Switzerland. The instrument is mounted on a 45m tower, about15m above the top of the forest canopy. The vegetation cover around the research site ismixed forest dominated by beech and spruce. The raw data taken by the Lageren’s instru-ment are directly sent to the AERONET main center at the Goddard Space Flight Centerin the US, where they are processed and sent back to Bern. The process used to convertand transform the raw data was unfortunately not accessible.

• A second possibility was to use a Look Up Table (LUT). The principle of this method isthe following: a table with different parameter combinations is built and stored. MOD-TRAN runs with those combinations and the results are compared to the observations;the smaller the difference the better the solution. The problem is that the difference canstill be important and no truly close values can be found. The LUT could be the easiestsolution but also the less accurate. Furthermore, the LUT becomes multi-dimensional andvery large when all possible observational scenarios are accounted for. This poses large

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demands on the available computer processing power during the creation of the LUT aswell as on the storage afterwards.

• The chosen solution is the use of an iterative algorithm. It is more powerful but alsomore difficult, as the problem can have multiple solutions. Its main advantage is that theparameters can be retrieved with a self-defined error, which means that the results may bemore accurate than with the LUT. More details can be found in chapter 5. Additionally,the method can be applied to varying observational set-ups in a generic way.

1.3. Thesis organization

Chapter 2 gives the needed theory for a good understanding of this work. The first sectiondescribes the interaction of the radiation and the atmosphere, and the second section the radiativetransfer and the radiation field properties. In the next chapter, the available tools are presented.Chapter 4 describes the data, the conditions of observation and the first processing steps. ThenChapter 5 is about the method and the two developed routines: anar and anar fwdmod. InChapter 6 the results are discussed and finally, in Chapter 7 a summary and an outlook are given.

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2. Radiative Transfer Elements

2.1. Interaction of radiation and atmosphere

When the solar radiations reach the atmosphere of the earth, they are affected by three maineffects: reflection, absorption and scattering.

2.1.1. Reflection

The first effect describes the fact that part of the incoming electromagnetic sun radiation isreflected at the Earth’s surface. More precisely, the surface reflectance is the fraction or percentof a particular frequency or wavelength of electromagnetic radiation that is reflected from thesurface of the Earth without being absorbed or transmitted [2].

2.1.2. Absorption

The second effect is the atmospheric absorption, which occurs through two principal media:gases and aerosols, and leads to a loss of energy. Under gases we include O3, CO2 and H2O asvapor. Aerosol, excluding weather and clouds, is any small particle that tends to stay in the air,such as smoke, dust, salt and pollen [2]. The absorption follows the Beer-Lamber law for purelyabsorbing media [20]:

dIλ = −Iλ · σaλ · ds, (2.1)

where Iλ is the irradiance, σaλ the absorption coefficient and s the distance. Ozone mainlyabsorbs the UV-range waves and water vapor in the IR-range waves.

2.1.3. Scattering

The third effect is known as scattering and no loss of radiative energy occurs. A scatteredradiation is a radiation that has been reflected from particles, disrupting the original direction ofthe beam [2]. There are two types of scattering: Rayleigh scattering and Mie scattering.

In Rayleigh scattering the particle’s diameter d is much smaller than the wavelength λ:

d

λ¿ 10−1. (2.2)

A polar diagram of its directionality can be seen in figure 2.1, were, as for figure 2.2, Iλ is theradiance, θ the angle of scattering and iλ the scattering intensity.

When the diameter of the particle is almost equal to the wavelength, the Mie scattering hap-pens with aerosols (figure 2.2).

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Figure 2.1.: Polar diagram of the directionality of the Rayleigh scattering [28].

Figure 2.2.: Polar diagram of the directionality of the Mie scattering [28].

As for absorption, a scattering coefficient is found, σsλ, which is the addition of the aerosoland Rayleigh coefficients. The addition of the absorption and scattering coefficients give us theextinction coefficient:

σaλ + σsλ = σeλ. (2.3)

The Beer-Lambert law describes the attenuation of light in an arbitrary medium using the ex-tinction coefficient:

dIλ = −Iλ · σeλ · ds. (2.4)

2.2. Radiative transfer/ Radiation field properties

Radiation arriving from the sun, as measured by a ground based radiometer, can be written inmathematical form as:

E = dt · dλ · dA · I(−→x ,−→Ω , λ0, t0), (2.5)

where E is the energy, t is the time, λ the wavelength, and A the surface (figure 2.3).From this equation, the radiance can be defined in words as the amount of electromagnetic

radiation leaving or arriving at a point on a surface [1]. In mathematical form:

L(−→x ,−→Ω , λ0, t0) = lim

dA→0dλ→0dt→0dΩ→0

Energy

dt · dλ · dA · dΩ[

W

s ·m2 · sr · nm]. (2.6)

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dA

dΩ

Figure 2.3.: Sun radiance.

Figure 2.4.: Differential volume element containing material which alters a beam of radiationpassing through it.

The irradiance, I , which is proportional to the radiance can now be introduced as the rate atwhich radiant energy arrives at a specific area of surface during a specific time interval:

I =∫

LdΩ. (2.7)

A typical unit is [W/m2] [2].In the preceding section, Lambert’s theory 2.4 was presented with the following formula:

dIλ = −Iλ · σaλ · ds. (2.8)

It implies that the rate of decrease in the intensity of radiation as it passes through a mediumis proportional to the intensity of the radiation itself (figure 2.4) [15]. The formal solution ofequation 2.8 is:

Iλ = I0 · e−R b

a σeλds, (2.9)

where Iλ is the measured irradiance, I0 the solar irradiance, σeλthe extinction coefficient and s

the distance along the path (figure 2.4).

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The transmittance Tλ which is the fraction of radiant energy that passes through a substance[1], can now be calculated:

Tλ =transmitted radiance at λ

incident radiation at λ=

Iλ

I0. (2.10)

Beer’s law states:

Tλ =I0 · e−

R ba σeλds

I0= e−

R ba σeλds, and Tλ ∈ [0, 1] (2.11)

which yields the slant optical depth τslλ as:

τslλ =∫ b

aσeλds. (2.12)

As seen before, the extinction coefficient is the addition of the absorption and scattering coef-ficients where the scattering coefficient is itself the addition of the aerosol and Rayleigh coeffi-cients. Thus the extinction coefficient can be written:

∫ b

aσeλds =

∫ b

a(σaeroλ + σRayleighλ + σaλ)ds (2.13)

=∫ b

aσaeroλds +

∫ b

aσRayleighλds +

∫ b

aσaλds, (2.14)

which is the addition of aerosol slant optical depth with the Rayleigh slant optical depth and theabsorption slant optical depth. When the way between a and b is arbitrary this is called the slantoptical depth, τslt, and when the way between a and b is directly vertical this is called the verticaloptical depth, τvert. The aerosol’s vertical optical depth (figure 2.5), which can be approximatedfrom the slant component, is important for this work. Under the assumption that the atmosphereis plane-parallel and horizontally stratified, it is:

τvert aeroλ =τaeroλ

cos θ. (2.15)

z

θ

dz

ds =

dz/

cosθ

Figure 2.5.: Vertical optical depth.

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3. Tools

3.1. IDL

IDL is for Interactive Data Language [13]. It is an array-oriented data analysis and visualizationenvironment developed and marketed by Research Systems, Incorporated (RSI) of Boulder, Col-orado [3]. The first version of IDL was released in 1981 by RSI founder David Stern. Since then,IDL has emerged from its roots in the astronomical and space sciences to become a widely usedtool in research, educational, and commercial settings in areas as diverse as the earth sciences,medical physics, and engineering test and analysis. IDL is used at the RSL of the University ofZurich and a well furnished IDL routines library is available. For this reasons, the processingand the development of the routines has been done in this programming language.

3.2. MODTRAN

MODTRAN is the abbreviation of Moderate Resolution Transmittance Code. It is an integratedcomputer code for predicting atmospheric radiance and transmittances. In particular it calculatesatmospheric transmittance, atmospheric background radiance, single-scattered solar and lunarradiance, direct solar and lunar irradiance and multiple-scattered solar and thermal radiance [7].

The MODTRAN resolution is 2cm−1 FMWH (Full Width at Half-Maximum) in averagesteps of 1cm−1. Three parameters are used for molecular line absorption: pressure, temperatureand a line width. The effects of molecular continuum-type absorption, molecular scattering,aerosol and hydrometeor absorption and scattering are all included. Representative atmosphericaerosol, cloud and rain models are provided within the code with options to replace them withuser-modeled or measured values.

The input file is called tape5. An example of it can be seen in figure 3.1. The tape5 is neither

Figure 3.1.: An example of the MODTRAN input file tape5.

easy to understand nor easy to edit. The best way to become familiar with it is to use MODO(figure 3.2). MODO is a tool providing access to most of the functionality of MODTRANthrough a graphical user interface [25].

The output file of MODTRAN is called tape6. It contains not only the wanted simulation but

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Figure 3.2.: An example of MODO.

also an overview of the input parameters. This implies for the program developed in this thesisthat the tape6 had to be read and that the wanted values have to be extracted.

3.3. Sunphotometer

The atmospheric data used in this project were acquired with the Reagan sunphotometer (figure3.3). It is a sun-looking ground-based instrument. In Remote Sensing applications, it is mainlyused for atmospheric observations in order to characterize the state of the atmosphere and im-prove atmospheric correction algorithms. Its continuous monitoring allows further conclusionson atmospheric stability and daily developments of aerosol contents [12].

This sunphotometer was manufactured by the University of Arizona, Tucson, USA [8]. Itis simple to set up and can make observations during an entire day without interruption. Itsspecifications can be found in table 3.1.

Ten parallel FOV telescopes are pointed towards the sun via an active auto sun-tracking sys-tem. The optical head contains these assemblies, associated electronics, heater, and the quad-cell

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Figure 3.3.: The Reagan sunphotometer.

Parameter DescriptionManufacturer University of Arizona, Tucson, USASpectral Range 382 - 1033 nmChannel 10, parallel coalligned FOV tube

382, 410, 501, 611, 669, 721, 780, 872, 940 and 1033 nmBandwidth 10 nmField of View 3.2

Size, Weight (only Head) 28.3 cm x 21.6 cm x 16.5 cm, 7.7 kgDigitization 16 BitOperating Environment Temperature stability at 43 ± 5 by heater

Table 3.1.: Technical information for the Reagan sunphotometer [8]

tracking device. The head is moved by an altitude-azimuth tracking mount fastened to the base.The power supply and data logger/control electronics are also mounted to the base. The instru-ment operator starts the data logger and enters appropriate information such as data collectioninterval and start/stop time. The optical head is pointed at the sun and the tracker then takes overpointing. The data is easily downloaded by connecting a laptop to the data logger and runningthe appropriate program. This has to be done only once a day.

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4. Data

4.1. Measurements

The Reagan sunphotometer was set up on the roof of the University of Zurich (Irchel) in Septem-ber 2003. The weather was sunny and clear: only a few streaky cirrus and contrails but none infront of the sun. Contrails are the condensation trails left behind jet aircrafts which may affectirradiance measurements as described in [6] [22] [19] [21]. Observations started at 8:15 localtime and continued until 16:45 without interruption. The time interval beetween two measure-ments was set to 30 seconds. Ancillary information such as the date, the air pressure, the airtemperature, the relative humidity, the longitude and the latitude was also collected (table 4.1).

date 09.19.2003pressure 1013 mbar (assumed)air temperature 25

relative humidity 60%longitude −8.55 Wlatitude 47.4 Nhours west of GMT 2

Table 4.1.: Collected information

This ancillary information is needed for the conversion of the raw data as it is explained insection 4.2.

4.2. Processing

The data that is downloaded from the Reagan sunphotometer is depicted in blocks separatedby the time of the measurement (figure 4.1). The first given value is the temperature of theinstrument followed by the channels and the measurements associated in Digital Numbers (DN).The last value is the time of the measurement.

In this format, the data cannot to be used by IDL without transformation. For this a headerfile has to be edited with: calibrations coefficients for the incident radiation, date, pressure,air temperature, relative humidity, longitude, latitude, etc. Those data were collected on theday of measurement (table 4.1). The calibration values used were made on the fourteenth ofAugust 2002 at Murtel Corvatsch in the canton of Graubunden. The IDL routine spm conv, asestablished by Schlapfer (1998) [24], reads the header and converts the raw data as read fromthe sunphotometer into a *.rad standard Reagan sunphotometer file including the header file(figure 4.2).

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Figure 4.1.: Sample of a standard Reagan sunphotometer file.

Figure 4.2.: Sample of the converted data file with the header and the observations.

The first six lines of figure 4.2 belong to the header. The measurement times can be found inthe first two columns, the temperature of the apparatus in the third. The next ten columns arethe DN for each of the ten channels. Figure 4.3, gives an overview of the measurements overthe day with the plots of three channels as example. Channel 1 (383 nm) is in blue, channel5 (669 nm) in green and channel 10 (1033 nm) in orange. The x-axis represents the time ofmeasurement and the y-axis the raw data in DN. For the three wavelengths, the observations aresmooth until 12:00, then perturbations occurred. They can be explained by some light cirrus and

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contrails which scatter and reflect solar radiation [21]. Those perturbations are stronger at 669nm and 1033 nm than at 383 nm because the clouds induce Mie scattering (see section 2.1.3). Inthe blue curve it can be clearly seen that the values of the observations increase as the sun risesand then decrease as the sun descents. This reflects the longer path through the atmosphere forlarger solar zenith angles.

Figure 4.3.: DN of channel 1 (383 nm), 5 (669 nm) and 10 (1033 nm).

At this point, no calculation has been done yet. The next step is to transform the DN intotransmittance by applying the above-mentioned calibration coefficients. For that the IDL routinespm read, with the option /trans, is used. The output is an array containing the measuredtransmittances. They can be seen in figure 4.4. The ten channels can be found on the x-axis

Figure 4.4.: Transmittances for all 10 channels as output of spm read.

as wavelengths, the times of measurements on the y-axis and the transmittances on the z-axis.Between 382 nm and 611 nm, there are smaller transmittances than by the others wavelengths,

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because of the Rayleigh scattering. At 940 nm, the water vapor absorption is strong, as it can beclearly seen in the plot. Along the time axis, the sun zenith angle can be seen: the transmittanceincreases until the sun reaches the highest positions and then decreases. This dependency canbe corrected in two steps. The first one is to transform the transmittances Tλ into slant opticaldepth τslant with equation 4.1:

τslant = −lnTλ. (4.1)

The intermediate results can be seen in figure 4.5. The 10 channels are on the x-axis aswavelengths, times of measurements on the y-axis and the slant optical depths on the z-axis.Comparing this plot (figure 4.5) with the plot of the transmittances (figure 4.4) the values areinverted: the lower values are now the higher. For example, the strong water vapor absorptionappears now as a peak.

Figure 4.5.: τslant for all 10 channels.

The second step is to transform the slant optical depths, τslant, into vertical optical depths,τvert, with equation 4.2:

τvert =τslant

cos θ, (4.2)

where θ is the angle between the sun position and the vertical (see figure 2.5).

22

The results are plotted in figure 4.6. As before, the 10 channels are on the x-axis, timesof measurements on the y-axis and the vertical optical depths on the z-axis. The zenith angledependency no longer appears along the y-direction.

Figure 4.6.: τvert for all 10 channels.

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5. Method

5.1. Overview

As shown in figure 5.1 the method of this work consists of three main steps: observation, inver-sion and forward modeling.

Figure 5.1.: Overview of the method [own graphic].

Observation

As described in section 4.1, irradiance observations were made with the Reagan sunphotometer.The data were collected on the roof of the University of Zurich over an entire sunny day in

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September 2003. The sunphotometer measures raw data for ten channels each 30 seconds. Theobservations must be converted into transmittances in order to be used by IDL routines (section4.2).

Inversion

The second step is the inversion which is performed using the IDL routine anar. Anar wasdeveloped in order to retrieve important parameters which describe the state of the atmosphere.The retrieved parameters are: water vapor, ozone, visibility and an aerosol model. Those specificvalues are required by MODTRAN as input.

Forward modeling

The third step is the forward modeling for which another IDL routine, called anar fwdmod,was developed. It is based on the radiative transfer model MODTRAN and calculates the in-coming diffuse irradiance for specific azimuth and zenith angles.

In order to provide an easy use of the routines for people not familiar with MODTRANand/or IDL, a Graphical User Interface (GUI) has been created for both programs, anar andanar fwdmod (figures 5.3 and 5.4).

5.2. Inversion: anar

The retrieval of the four parameters is divided in two steps: first a routine using an algorithmto find the best values for water vapor, ozone and the visibility; and second a loop calling theprecedent program, running with the different aerosol models proposed by MODTRAN, in orderto find the most adequate aerosol model.

5.2.1. Retrieving water vapor, ozone and visibility

MODTRAN is used in the retrieval of the parameters of the atmosphere at the time of the mea-surements. This program can simulate transmittances for different states of the atmosphere,which can be converted into vertical optical depths as seen in section 2.2. The main parame-ters needed are water vapor, ozone, the visibility in kilometers and the MODTRAN’s aerosolmodel (table 5.1). Anar compares the simulated and observed vertical optical depth using angradient-expansion algorithm (figure 5.2).

25

Figure 5.2.: The main principle of anar [27].

The first task is to acquire the observed vertical optical depth for the desired zenith angle. Forthis purpose, the raw data is converted into transmittances, as explained in section 4.2, and theninto slant optical depths (Equations 4.1). Then, the time of measurement must be transformedinto degrees angles. This is done by using the IDL routine zenith [24]. This routine asks forthe time in decimal units, hh.xxxx, and a standard auxiliary structure, which is composed of:

• date of data caption

• pressure

• air-temperature

• relative humidity of the air at the ground

• decimal longitude, west of Greenwich

• decimal latitude

• hours west of Greenwich

• date of calibration

• processing flag

This information is found in the header of the standard Reagan sunphotometer file (section4.2). The corresponding slant optical depths for each of the ten channels are now transformedinto vertical optical depths (equation 4.2). Those observed vertical optical depths serve as ref-erence values for the retrieval process. The simulated vertical optical depths must be modelled,using MODTRAN and varying the values of the wanted parameters, water vapor, ozone and thevisibility, with an adequate algorithm.

In order to determine this adequate algorithm for the core of anar the problem had to beclearly defined. In this case the function may have multiple solutions and it has more thanone variable parameter. The solution is found in the IDL function: curvefit [23], whichuses a gradient-expansion algorithm to compute a non-linear, least-squares fit to a user-suppliedfunction with an arbitrary number of parameters. The user-supplied function may be any non-linear function where the partial derivatives are known or can be approximated. In this case, theuser-supplied function is an IDL routine.

26

The supplied function generates first the MORTRAN input file tape5 with the user inputvalues such as: the MODTRAN geographical-seasonal model, the zenith angle and a first guessfor the visibility and the scaling factors for water vapor and ozone. Then the radiative transfermodel MODTRAN is called up. In the output file tape6, more information than needed is given.So the next task is to locate the wanted values and to extract them in a matrix. The simulatedtransmittances are then transformed into vertical optical depth and compared with the measuredvalues: the difference between both of them is calculated. If this difference is not small enough,curvefit asks for the partial derivatives so as to find new values for the parameters. Watervapor, ozone and the visibility are then updated and input in a new tape5 in order to go throughthe procedure again. This process is repeated until the difference between the observed and thesimulated vertical optical depth is small enough, but stops after 200 iterations. The results arestored in a matrix and at this point, the second part of the program (retrieving the aerosol model)starts.

5.2.2. Retrieving the aerosol model

As mentioned at the beginning of this section, the second part of the program is a loop whichcalls the retrieval routines for water vapor, ozone and the visibility, and runs several times, eachwith a different aerosol model. Six models have to be evaluated (table 5.1).

Number Description1 Rural3 Navy Maritime4 Maritime5 Urban6 Tropospheric10 Desert

Table 5.1.: MODTRAN Aerosol Models

Anar searches the best values for water vapor, ozone and visibility for all those models. Eachtime, when the program has retrieved the parameters, the norm (|(−→a − −→b )|) of the differencebetween the measured (−→a ) and the simulated (

−→b ) vertical optical depths is calculated and stored:

−→a = (a1, a2, ..., an) and−→b = (b1, b2, ..., bn) (5.1)

|(−→a −−→b )| =√

(a1 − b1)2, (a2 − b2)2, ..., (an − bn)2 (5.2)

The smallest norm indicates the smallest difference between the measured and the simulatedvertical optical depths, and hence the best fitting aerosol model.

For each aerosol model, the output file of anar gives:

• the norm,

27

• the scaling factor of water vapor,

• the scaling factor of ozone,

• the visibility in kilometers,

• the observed vertical optical depth for the ten channels,

• the simulated vertical optical depth for the ten channels

• and the difference between the observed and the simulated vertical optical depth for theten channels

Further details of the output are presented in chapter 6.

5.2.3. Graphical User Interface

The anar GUI has several editable text fields and buttons as shown on figure 5.3.

Figure 5.3.: Anar graphical user interface.

The on-screen components of a GUI, such as buttons and sliders, are known collectivelyas widgets [13]. The first one allows to browse for the appropriate data file containing theobservations of the Reagan SPM. Then a MODTRAN geographical-seasonal model has to bechosen from the droplist. The possibilities are:

• Tropical Atmosphere (15 North Latitude)

• Mid-Latitude Summer (45 North Latitude)

28

• Mid-Latitude Winter (45 North Latitude)

• Sub-Arctic Summer (60 North Latitude)

• Sub-Arctic Winter (60 North Latitude)

• 1976 Standard Atmospheres

On the next line the user needs to indicate a sun zenith angle in degrees which correspondsto a measurement time. The next block asks for an initial guess of the parameters. If the userhas no idea, the default button can also be used. It fills the field of the angle, water vapor, ozoneand visibility with standard values. If possible, known parameters should be entered since thenthe accuracy is improved, the number of iterations is decreased and hence the running time ofthe program is shortened. The MODTRAN input file is set for clear weather, without cloudsor volcanic extinction, and for ground altitude of 500m. Those hard-coded parameters can bemanually changed in the source, if necessary.

5.3. Forward Modeling Radiances: anar fwdmod

The final purpose of this work is to have a model of the sky radiance field which is done withthe routine anar fwdmod. For this purpose the state of the atmosphere is important and it hasbeen retrieved by the routine anar. The forward modeling program also has a user-friendlyGUI which is described hereafter.

The first task accomplished by anar fwdmod is the storing of the user’s values which are:zenith and azimuth angles with an increment, for the definition of the diffuse radiance field, aMODTRAN geographical-seasonal model, a sun angle which must be the same one as for anarand the retrieved results for water vapor, ozone, visibility and aerosol model. Then the loop overthe angles starts. For example, if the user chooses 0 to 90 zenith angles with an incrementof 10 , and -180 to -180 azimuth angles with an increment of 30 , the first loop will befor 0 zenith angle and 0 azimuth angle, the second for 0 and 30 , the third for 0 and60 and so on. The MODTRAN input file tape5 is generated with the user’s values and the firstangles. The output file tape6 is read and the radiances are extracted. The results of the same tenwavelengths as for the Reagan SPM are then stored in a matrix. Then, a subsequent iterationstarts for the next angles and the results are added to the previous matrix. The final output isthe total radiance field, L, in the form of a 3-dimensional L(θ ∗ φ ∗ λ) matrix (see annex A.2),where θ is the zenith angle, φ the azimuth angle and λ the ten different channels. The unit is[W/cm2/sr/µm].

Further details of the output are to be found in Chapter 6.

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Graphical User Interface

MODTRAN requires many different parameters; some are fixed and some can be determined bythe user through the GUI of anar fwdmod that can be seen in figure 5.4.

Figure 5.4.: Anar fwdmod graphical user interface.

The first fields allow the user to choose the zenith angles and the azimuth angles with theadequate increment for each. Then, as for anar, a MODTRAN geographical-seasonal modelhas to be chosen from the droplist. This should of course be the same one as in the precedingroutine (anar). The next five fields must be carefully filled in: the angle for the sun positionmust be the same as the azimuth angle used for the retrieval. For H2O, O3, visibility and theaerosol model, the results of anarmust be given. It is important to notice that the aerosol modelis given as a number and not as a name. The meaning of those numbers can be found in table5.1. The Default button fills the fields with possible values. When everything is ready the usercan click on Run to start the program.

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6. Results

6.1. Retrieval

Anar retrieves the scaling factors for water vapor, ozone and the visibility in kilometers for eachdifferent aerosol model. The results can be seen in table 6.1. The scaling factors are required byMODTRAN and they multiply the standard values of the water column and the ozone column.The results tell that the atmosphere was dryer than the standard values: the defaults value forwater vapor is multiplied by an average of 0.5. The same occurs to the ozone.

TYPE VAPOR [-] OZONE [-] VISIBILITY [km] NORM [-]Tropospheric 0.501233 0.643494 34.6636 0.051024Desert 0.498746 0.560439 34.0150 0.053405Rural 0.486319 0.565760 34.7922 0.059277Urban 0.474789 0.477981 34.5923 0.068977Navy maritime 0.438880 0.410367 34.2777 0.107504Maritime 0.427019 0.352966 34.5017 0.120706

Table 6.1.: Table of the results classed by decreasing best fitting aerosol model

Concerning the MODTRAN aerosol model, the best fitting one has to be determinated by theuser. In the output file of anar (see annex A.1), the norm of the difference between the observedand the modelled vertical optical depths is given (table 6.1). The smallest norm (Equation 5.2)indicates the best model, but the result can seem odd because the MODTRAN’s description doesnot always correspond to the actual situation. For example, for the observations made on theroof of the University of Zurich in September 2003, the second best fitting model, surprisingly,is desert. An explanation might be that the program is considering only one moment of the dayand not the entire time of measurement.

Figure 6.1 is a plot of the results of anar for the tropospheric model. The horizontal axisrepresents the wavelengths and the vertical axis the vertical optical depth. The initial guessedvalues are in blue, the simulated in red and the observed in green. The difference between theobserved and the simulated optical depths is in orange. The blue, red and green curves haveapproximately the same shape. This means that the MODTRAN’s simulations correspond tothe measurements. The vertical optical depth is higher at smaller wavelengths because of theRayleigh scattering as explained in section 2.1. Two peaks are noticeable: they show the strongwater vapor absorption at those wavelengths (730nm and 940nm). The guessed values (blue) aremuch higher, which shows that the user’s parameters were actually not the real ones. It is veryimportant to see that the measured and the simulated optical depths are very similar becauseit means that the retrieved parameters are close to the reality. This is confirmed by the orange

31

Figure 6.1.: Results from anar.

curve, which features the difference between the observed (green) and the simulated (red) opticaldepths. It shows that the retrieved parameters are satisfactory.

6.2. Forward Modeling

The results of anar fwdmod are given in a file in which, for each wavelength a table is pro-duced that contains the zenith angles in rows, and the azimuth angles in columns (see annexA.1). The values of two different zenith angles for the same azimuth angle are plotted in figure6.2.

Figure 6.2.: Results from anar fwdmod: radiance for two different zenith angles at the sameazimuth angle.

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The x-axis shows the wavelengths and the y-axis the radiances in [W/cm2/sr/µm]. Theblue curve represents the radiances for the 60 zenith and the red the 30 zenith. In this case,the zenith is the angle over the horizon. As more scattering occurs at lower wavelengths, theradiance values are larger. On the blue curve, the two strong water vapor absorption spots arerecognizable by a sudden decrease of the radiance values. More important is that the greater thezenith angle, the greater the radiances. This is explained by the fact that, when the sun angle issmall, the path through the atmosphere is longer and so the radiance encounters more reflection,absorption and scattering. This can be even better seen in the logarithmic plots (figure 6.3). Thevalues of the radiances are small, as it can be seen on annex A.2.

In order to produce a plot were the difference between the values are more distinguishable,the logarithmic function has been applied. In figure 6.3, the zenith angles are on the x-axis from

Figure 6.3.: Logarithmic plots of the radiance for 382nm and 940nm.

0 to 100 , the azimuth angles on the y-axis from -200 to 200 with the 0 in the middle andthe logarithms of the radiance on the z-axis. The sun position can be read at the highest zenithof the 0 azimuth line. In the case of figure 6.3, it is 65 . Symmetrical values are found on bothside of the 0 azimuth line, because the model is isotropic. There is a large variability between

33

low and high values, which indicates that the angular dependency of the diffuse irradiance ishigh and considering it, an added value for the BRDF retrieval is expected.

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7. Conclusions

7.1. Summary

Spectrodirectional surface reflectance properties are important quantities in remote sensing re-search and applications. They are by definition characterized by the BRDF, or equivalently,the BRF, and depend only on the surface properties [18]. However, spectrodirectional fieldexperiments with goniometer systems are only able to observe approximations of the bidirec-tional reflectance factor. The directly observed quantity in field experiments is called HCRF,corresponding to hemispherical illumination, which depends on the atmospheric conditions andconical observation [26].

By following the well known method proposed by Martonchik and others [17] [16], the BRDFcan be retrieved. For this procedure, the diffuse radiation has to be measured over the completehemisphere at the same angular resolution as the reflected radiation of the target. At the moment,the incoming diffuse radiation can not be measured at angular resolution. A simplified approachis then used, measuring the integrated diffuse irradiance with the MFR-7 sunphotometer [26].But a more accurate BRDF can be retrieved, if the incoming radiation is simulated at the sameangular resolution as the reflectance is measured. A possible solution was presented in thiswork. Based on the measured direct incoming illumination, a model of the diffuse sky radiancefor each zenith and azimuth angle over a defined spectral range could be provided.

The radiative transfer model MODTRAN is used for modeling the diffuse irradiance. Theinput file for MODTRAN asks for the state of the atmosphere and specially for water vapor,ozone, visibility and the aerosol model. Those values could be retrieved from the measuredtransmittances. For this purpose, the transmittances were transformed into vertical optical depthsso as not to depend on the sun position. The idea was to compare the observed vertical opticaldepths with the modelled vertical optical depths by varying the values for water vapor, ozone,visibility and the aerosol model. The problem was to know how to vary those four parametersin order to find the best approximations. Various possibilities were considered (see section 1.2).The use of an inversion algorithm was selected and implemented.

The data used in this project was acquired with the Reagan sunphotometer, which is a sun-looking ground-based instrument. In Remote Sensing applications, it is mainly used for at-mospheric observations in order to improve atmospheric correction algorithms. The Reagansunphotometer was set up on the roof of the University of Zurich (Irchel) in September 2003.Observations started at 9:15 and continued until 16:45 without interruption and a time intervalbeetween two measurements of 30 seconds. Ancillary information such as the date, the air pres-sure, the air temperature, the relative humidity, the longitude, the latitude and the number ofhours west of GMT was also collected for the same day (table 4.1) because it is needed for theconversion of the raw data.

The data that is downloaded from the Reagan sunphotometer could not be used by IDL with-

35

out transformation. For this a header file had to be edited and inserted in the new standardReagan sunphotometer file. At this point, no calculation had been done. The next step was toconvert the DN into transmittance and then into vertical optical depth, as explained in section4.2.

The retrieval of the four parameters (anar) was divided into two steps. The first is a routineusing an algorithm to find the best values for water vapor, ozone and the visibility. The time ofmeasurement had to be transformed into degrees angles, in order to find the desired observedvertical optical depths, which serve as reference values for the retrieval process. The simulatedvertical optical depths had to be modelled, using MODTRAN and varying the values of thewanted parameters (water vapor, ozone and the visibility) with an adequate algorithm. In orderto discover this adequate algorithm for the core of anar the problem had to be clearly defined.In this case the function was not linear and it had more than one variable parameter. The solutionwas found in an IDL function which uses a gradient-expansion algorithm to compute a nonlinear,least-squares fit to a user-supplied function with an arbitrary number of parameters. The user-supplied function may be any non-linear function where the partial derivatives were knownor could be approximated [23]. In this case, the function was an IDL routine. The functiongenerated first the MORTRAN input file with the user input values. The radiative transfer modelMODTRAN was called up. The wanted values were located in the output file, and extracted.The simulated transmittances were then transformed into vertical optical depth and comparedwith the measured values: the difference between both of them was calculated. If this differencewas not small enough, the procedure would start again with different parameters values. Thisprocess was repeated until the difference between the observed and the simulated vertical opticaldepth was small enough, but stopped after 200 iterations. The results were stored in a matrixand at this point, the second part of the program started.

The second step of the program was a loop calling the retrieval of water vapor, ozone and thevisibility, and running with the six different aerosol models proposed by MODTRAN. The normof the difference between the measured and the simulated vertical optical depths was calculatedand stored. The smallest norm indicates the smallest difference between the measured and thesimulated vertical optical depths, and hence the best fitting aerosol model. The four parameterswere retrieved and the forward modeling could start with the program anar fwdmod. TheMODTRAN input file was generated with the user’s values and the first desired angles. Theoutput file was read and the radiances extracted. The results were then stored in a matrix. Asubsequent iteration started for the next angles. The new results were then added to the previousmatrix. The final output was the total radiance field.

The results of anar were satisfactory: the difference between the observed and the simulatedvertical optical depth were small. As for the aerosol model, the smallest norm indicated the bestfitting model but it had to be selected manually by the user. The model did not always behaveintuitively, as discussed previously (section 6.1). The model produced by anar fwdmod wasalso satisfactory. The angular dependency of the diffuse radiance was appearing clearly.

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7.2. Outlook

The results are already usable in the process of retrieving the BRDF from goniometer observa-tions, but some potential improvements could be made:

1. Currently, anar reads only morning angles. The user is asked for an angle which deter-mines the time of the day. Because the sun rises to its zenith and then descend over thecourse of a day, the same angles are observed twice: once in the ascent (morning) andonce in the descent (afternoon). The routine looks for the user’s chosen angle and takesthe first one in the row, which normally is the morning angle. This could be changed byadding an option in the GUI which asks the user to choose between AM and PM. Anothersolution would be to have two observation files: one with the morning measurements andone with those from the afternoon.

2. anar fwdmod calculates only radiances for the ten channels of the Reagan sunphotome-ter: 382, 410, 501, 611, 669, 721, 780, 872, 940 and 1033 nm. Three options of furtherimprovement are possible. The first is to model the radiances for a continuous spectrumuntil 1000 nm. As the goniometer measures until 2500 nm it would also be interesting toexpand the range. But it is important to notice that the method would extrapolate between1000 nm and 2500 nm. The second would be to keep a definite number of wavelengthspossible, currently there are ten, but to let the user choose them. The third would be tomake possible to input a minimum and a maximum wavelength as bounds in the GUI per-haps also with an interval, but this would require that the wavelength variable is dynamicin the program. Its implementation would be more complicated.

3. In the simulation of the radiance, the albedo is significant. Currently it is assumed at0.4[a.u.] in the MODTRAN input file tape5. An accurate value could be retrieved by usingobservations made with the shadow-band rotating sunphotometer MFR-7 and comparingthem with MODTRAN simulations.

4. The MODTRAN input file tape5 asks for many different parameters. The GUI of bothroutines, anar and anar fwdmod, allows the user to choose only some of those param-eters. In order to be more complete, a GUI such as MODO [25] should be available.

5. The result of the simulated diffuse radiance should be validated. For this, previous obser-vations made simultaneously with the Reagan and the MFR-7 sunphotometer are avail-able. The MFR-7 gives an average value of the diffuse light for six different channels.The idea would be to integrate the modelled diffuse sky radiance field, obtained out ofthe SPM radiances, and to compare it to the hemispherical irradiance from the MFR-7. Asecond method would be to measure the incoming radiance at a certain angular resolutionover the whole hemisphere by using an upward looking spectroradiometer and to comparethem with the modelled values.

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Bibliography

[1] Hyper Dictionary. http://www.hyperdictionary.com, 08/31/2005.

[2] Renewable Resource Data Center. http://rredc.nrel.gov/solar/glossary, 08/31/2005.

[3] Research Systems Incorporated, Boulder, Colorado, USA, 08/31/2005.http://www.rsinc.com.

[4] Japan Aerospace Exploration Agency. http://www.jaxa.jp, 09/06/2005.

[5] CIMEL Electronique, France. http://www.cimel.fr, 09/12/2005.

[6] S. Ackerman. Cooperative Institute for Meteorological Satellite Studies, University ofWisconsin-Madison Space Science and Engineering Center, USA.http://cimss.ssec.wisc.edu/wxwise/class/contrail.html, 08/31/2005.

[7] A. Berk, G. P. Anderson, and P. K. Acharya et al. MODTRAN4 Version 3 Revision 1User’s Manual. Air Force Research Laboratory, Hanscom AFB, 2003.

[8] C. Brinker. Remote Sensing Group, Optical Sciences Center University of Arizona, USA.http://www.optics.arizona.edu/rsg, 08/31/2005.

[9] D. Giles, B. Holben. Aerosol Robotic Network (AERONET).http://aeronet.gsfc.nasa.gov, 08/31/2005.

[10] Direction de la Communication Externe, de l’Education et des Affaires Publiques. CentreNational d’Etudes Spaciales (CNES), France. http://www.cnes.fr, 08/31/2005.

[11] O. Dubovik and M. D. King. A flexible inversion algorithm for rertrieval of aerosoloptical properties from sun and sky radiance measurements. Journal of GeophysicalResearch, 105:20,673–20,696, August 2000.

[12] A. R. Ehsani, J. A. Reagan, and W. H. Erxleben. Design and Performance Analysis of anAutomated 10-Channel Solar Radiometer Instrument. Journal of Atmospheric andOceanic Technology, 15(3):697–707, 1998.

[13] L. E. Gumley. Practical IDL Programming. Morgan Kaufmann, 2002.

[14] B. N. Holben, T. F. Eck, I Slutsker, D. Taure, J.P. Buis, A. Setzer, E. Vermote, J. A.Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov.AERONET- A Federated Instrument Network and Data Archive for AerosolCharacterization. Remote Sensing Environment, Elsevier Science Inc., 66:1–16, 1998.

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[15] S. Q. Kidder and T. H. Von der Haar. Satellite Meteorology: An Introduction. AcademicPress, 1995.

[16] A. I. Lyapustin and J. L. Privette. A new method of retrieving surface bidirectionalreflectance from ground measurements: Atmospheric sensitivity study. Journal of RemoteSensing, 1:131–136, 1999.

[17] J. V. Martonchick. Retrival of Surface Directional Reflectance Properties using GroundLevel Multiangle Measurements. In Remote Sensing of Environment, volume 50, pages303–316. 1994.

[18] J. V. Martonchick, C. Bruegge, and A. Strahler. A Review of Reflectance Nomenclatureused in Remote Sensing. In Remote Sensing Reviews, volume 19, pages 9–20. 2000.

[19] R. Meerkoeter, U. Schumann, D. R. Doelling, P. Minnis, T. Nakajima, and Y. Tsushima.Radiative forcing by contrails. Annales Geophysicae, 17:1080–1094, 1999.

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[22] K. Wyser (Regional Climate Group, Earth Sciences Center, Goeteborg University) andW. O’Hirok (Institute of Computational Earth System Sciences, UC Santa Barbara).Modeling radiation effects of contrails with high spatial resolution.http://www.gvc.gu.se/ngeo/rcg/flyklim/Intern/F2001-gvc-3.pdf, November 2001.

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A. Outputs

A.1. Results of anar

40

A.2. Sample of the results of anar fwdmod

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B. Programs

This appendix gives a list of all the routines used in anar and anar fwdmod. They can befound, with further description, on the attached CD.

B.1. anar

B.1.1. RSL

• curvefit.pro

• spm conv.pro

• spm read.pro

• zenith.pro

B.1.2. Own

• anar.pro

• anar create param input.pro

• anar diff.pro

• anar ev browse.pro

• anar ev cleanup.pro

• anar ev clear.pro

• anar ev default.pro

• anar ev handler.pro

• anar ev quit.pro

• anar ev run.pro

• anar function.pro

• anar get info.pro

• anar procedure.pro

• anar tauvert.pro

42

• anar tp5.pro

• anar tp6.pro

• anar tp6 find.pro

B.2. anar fwdmod

B.2.1. Own

• anar fwdmod.pro

• anar fwdmod create param input.pro

• anar fwdmod create param multi.pro

• anar fwdmod ev cleanup.pro

• anar fwdmod ev clear.pro

• anar fwdmod ev default.pro

• anar fwdmod ev handler.pro

• anar fwdmod ev quit.pro

• anar fwdmod ev run.pro

• anar fwdmod get info.pro

• anar fwdmod tp5.pro

• anar fwdmod tp6.pro

• anar fwdmod tp6 find.pro

43