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## Equivalent black carbon

Mainly two methods are used to measure the BC light absorption: the filter based light transmission method and the photoacoustic method. Filter based photometers are relatively cheap, robust and plug and play instruments; for these reasons they are widely used for long-term measurements. Particles are continuously deposited onto a filter tape while a light beam is focused on the collecting spot. Along aerosol loading the light transmitted through the filter decreases due to increase in the optical path (Hansen et al., 1984). The absorption and thus the light-absorbing aerosol mass are assumed to be proportional to the light transmission decrease. A wide range of filter-based photometers are commercially available; despite some differences they are all based on this principle. More details about operating principles of filter based photometers will be discussed in Section 2.2. The second method available for the measurement of eBC is the photoacoustic method. The aerosol, heated up through the absorption of a pulsing laser light, heats the surrounding air and creates a sound wave that is measured by one or several microphones (Petzold and Niessner, 1996). The intensity of the sound wave is proportional to the amount of black carbon. The main advantage of the photoacoustic method is the independence of the measurement to the mixing state of BC (Lack et al., 2009). It is therefore commonly accepted as a benchmark for measuring aerosol absorption. However, its use and maintenance is rather demanding and it cannot really be used in long-term measurements. Both approaches yield an absorption coefficient, which is then converted to a black carbon mass concentration using a conversion factor called mass absorption cross-section (MAC). The MAC is an intensive optical property of BC, which describes its light absorption efficiency per mass. Thus, since this method does not allow measuring directly the mass concentration of BC, the derived mass concentration of BC is so called equivalent BC (eBC). Characterization and comparability of different absorption photometers and data treatments are under continuous development (Bond et al., 1999; Slowik et al., 2007; Collaud Coen et al., 2010; Ogren, 2010; Müller et al., 2011; Baumgardner et al., 2012; Kanaya et al., 2013).

**Refractory black carbon**

A third technique based on laser induced incandescence has been developed to measure the carbonaceous fraction of particulate matter that is insoluble and vaporizes only at temperatures near 4000 K (Moteki and Kondo, 2010). This carbonaceous fraction is called refractory black carbon (rBC). rBC is nowadays measured with the single particle soot photometer (SP2; Stephens et al., 2003) and the soot particles aerosol mass spectrometer (SP-AMS; Onasch et al., 2012). The mass of refractory black carbon is indirectly measured, in every single particle, from the amount of light emitted at the vaporization point of rBC, independently of the amount of non-refractory, internally mixed matter. In addition, the amount of non- and less refractory matter coating the rBC core can also be retrieved (Gao et al., 2007). All technical details and theoretic principles are described in Section 2.4.

**Objectives of the present study**

Black carbon represents a small fraction of the total aerosol, however, it considerably contributes to the total positive radiative forcing, playing a consistent role in climate warming. Due to its short lifetime in the atmosphere, an effective limitation of emissions would reduce the positive forcing after a relatively short period compared to the greenhouse gases. Unfortunately, a consistent number of uncertainties in its quantification and properties still exist: metrology, time-limited dataset, uncertainties on removal mechanisms and radiative forcing pathways. This work aims to contribute to a better understanding of black carbon cycle, contributing to some of the major questions:

What is the spatial and seasonal variability of light absorption properties of black carbon in the European regions?

How does aging during long-range transport modify light absorption by BC particles?

Is black carbon an active seed for formation of glaciated clouds?

Chapter 3 focuses on the investigation of BC mass absorption cross-section over Europe, considering its spatial and seasonal variability. The work is based on data collected from observation platforms being part of the Aerosol, Clouds and Trace Gases Research InfraStructure (ACTRIS) over the last 10 years. Overall, the dataset reports more than 34 years of measurements from the different stations, spread around Europe, and allows to investigate the study of the seasonal cycle of MAC and its spatial variability.

Chapter 4 addresses the issue of optical properties of BC but further away from emission sources. Despite is short lifetime, BC can be transported over long distances and, as explained in the previous sections, undergo changes of its optical properties through coating by non-absorbing material on its surface. The climate impact of short-lived pollutants and methane in the Arctic (CLIMSLIP) project aims to investigate the presence and the effects of BC during the Arctic haze in the late winter. We wanted to answer to three main challenges raised by the Summary for Policy-makers of the Arctic Climate Issues 2015 report: qualify the BC measuring techniques in the Arctic, understand the physical properties of BC after the long-range transport and provide the optical parameters needed for an accurate RF assessment in the Arctic.

**State-space modeling of beam-piezo system**

In this section, we will deduce a theoretical model of the beam-piezo system based on the Euler-Bernoulli assumptions, see the discussion in Section 3.1. In addition, the free-free boundary condition means that there will be no bending moments or shear forces at both ends of the beam. Note finally that the vibration is generated by a force disturbance applied at one end of the beam as shown in Fig. 3.2. Based on these assumptions and observations, finite element modeling is performed and leads to a coupling equation (or governing equation) that describes the beam dynamics and the electromechanical coupling between the beam and the PZT [75, 103]. However, the dimension of this governing equation is too large and it takes the displacement vector as the variable which contains an infinite number of modes. Knowing that we only choose to control a certain number of modes, we then apply Modal Displacement Method which decomposes the governing equation according to modes so that we can ignore (truncate) most of the modes that are out of interest. This leads to a much simpler governing equation which takes the modal coordinate as variable and which allows us to control the chosen modes. The commercial software COMSOL (a finite element analysis, solver and simulation software) allows us to derive an expression of the governing equation reflecting the first several number (user-chosen) of modes. In our case, the resonance frequency of the maximum number of mode have to be larger than the maximum frequency of the disturbance (i.e. 3000 rad/s) while higher modes are truncated. The error introduced by the truncation is eliminated by performing Static correction. Damping eﬀect has also to be added because we do not include damping eﬀect in COMSOL. The dynamic (diﬀerential equation) of the measurement circuit (the electric circuit used to measure the sensing voltage on the PZT pair) is also considered. For the purpose of reducing the vibration energy in the central zone (central energy), we deduce a computable expression of the central energy out of the velocities at a number of points in the central zone. The model of the beam-piezo system is finally built in form of state-space representation for the purpose of controller design.

**Governing equation deduced with COMSOL**

COMSOL performs a finite element modeling of the structure and discretizes it into multiple sections based on a standard 3D elements. In this way, we are able to consider the coupling between the beam and the piezoelectric patches. Each element contains multiple degrees of freedom (e.g. the displacements along x, y and z axis, etc). However, we only focuses on the displacement along z axis. The displacements along x and y axis are thus removed because they are not excited or coupled with those along z axis. Denote z(x, t) the displacement field along z axis with x the position and t the time, the governing equation is given as follows1 e ( ) eQ(t) R V t 0 ¨ + T M z¨(x, t) K f f 0 − e 0 V (t) E E z(x, t) = F · f(t) , (4.1).

where Mf ∈ RNe×Ne the mass matrix with Ne the number of nodes created by Fi-nite Element Analysis, Kf ∈ RNe×Ne the stiﬀness matrix, R = diag(r1, r2, · · · , rNp ) the capacitance matrix with ri the capacitance of the ith PZT pair and Np the total number of the PZT pairs2, Fe ∈ RNe the force vector and Ee ∈ RNe×Np the matrix representing the electro-mechanical coupling between the beam and the PZT. The scalar f(t) represents the force disturbance applied by the shaker. The vector V (t) = [v1(t), · · · , vNp (t)]T and Q(t) = [q1(t), · · · , qNp (t)]T represent respectively the voltage and the charge on all the PZT pairs on the beam.

**Piezoelectric capacitance correction — Static correction**

It should be noticed that the truncation will inevitably introduce static reduction error [104] into the system, which should be considered. For this purpose, we perform Static correction [28]. The ideal is that we try to modify the capacitance matrix R such that when the system is free from external constraints, i.e. f(t) = 0, the charge generated by a constant voltage, e.g. V (t) = 1, of the finite element model (Eq. (4.1)) and the truncated model (Eq. (4.4)) are the same. As the excitation voltage stays constant, there will be no dynamic deformation, which means that the derivative term in the governing equation is neglected. Thus, the finite element model gives: K T E z(x, t) = F · f(t) .

### Model improvement using Grey-box identification

In Section 4.1, a physical model has been derived for the to-be-controlled system under the form of the state-space model (4.18) relating the system inputs (the disturbance force f(t) and the actuator voltage vector Va(t)) and the system outputs (the sensor vector Vs(t) and the vector νnode(t) containing the velocity at a number of points in the central zone). As already mentioned, this physical model is parameterized by a number of physical parameters (i.e. Kmode, Rs, Ys, κa, κs, Ea, Es, F and ϕnode) for which a first estimate can be derived using COMSOL or classical tests. The first estimate is relatively accurate for Ys and Rs. However, the first estimate is much cruder for Kmode, κa, κs, Ea, Es, F and ϕnode. According to the discussion in Section 4.1.1.2, for a normalized governing equation, Kmode = diag(ω12, · · · , ωN2 ) where ωi is exactly the resonance frequency of the ith mode, which corresponds to the location of the ith peak in the fre-quency response (see for example the model response shown in Fig. 4.2). The discrepancies at peak locations can thus be easily corrected through replacing the elements of Kmode by the correct value of ωi obtained from the non parametric estimate using a frequency analyzer (i.e. the benchmark in Fig. 4.2). For the rest of the parameters (i.e. κa, κs, Ea, Es, F and ϕnode), we will introduce Grey-box identification which allows us to correct them using the measurement data from the actual setup.

#### Grey-box identification theory

Grey-box identification is a data-based optimization algorithm. It allows us to use discrete-time sampling data to optimize the parameters of a continuous model with a predefined structure, for example the state-space representation [29]. It performs iterations based on the measured input and output data to find the best group of parameters with which the discrete-time output predictions of the optimized continuous model fit best the measured output with respect to the same input. Now we consider a real continuous system Greel(s) and a candidate physical ˆ model Gmod(s, θ) with physic parameters θ. Greel(z) and Gmod(z, θ) are their corresponding discretizations. θ is the estimator composed of all the parameters to be optimized. The optimization problem is shown in Fig. 4.3.

**Table of contents :**

**1 Introduction **

1.1 The atmospheric aerosol

1.1.1 Definition, classification and sources

1.1.2 Aerosol impact on climate system

1.1.3 Aerosol impact on human health

1.2 Trend, composition and properties of the European aerosol

1.3 Soot particles

1.3.1 From emission to deposition

1.4 Impact of black carbon on climate

1.4.1 Black carbon-radiation interaction

1.4.2 Black carbon-cloud interaction

1.4.3 Snow darkening

1.4.4 Effects of mixing on optical properties of black carbon

1.5 Variability of BC concentration in the European atmosphere

1.6 Soot measuring techniques and nomenclature

1.7 Objectives of the present study

**2 Methodology **

2.1 Parametrization of the aerosol optical properties

2.2 Attenuation photometry

2.2.1 Uncertainties

2.3 Thermal optical technique

2.3.1 The OC/EC analyzer

2.3.2 Existing thermal procedures and discrepancies

2.3.3 The EUSAAR-2 protocol

2.4 Laser induced incandescence

2.4.1 The single particle soot photometer

2.5 BC measuring techniques: how do they compare?

**3 A European aerosol phenomenology-5: climatology of black carbon optical properties at 9 regional background sites across Europe **

3.1 Introduction

3.2 Method

3.2.1 Terminology

3.2.2 The ACTRIS sites

3.2.3 Experimental methods

3.3 Results and discussion

3.3.1 Spatial and seasonal variability of mEC and σap

3.3.2 Spatial variability of the MAC

3.3.3 Temporal variability and seasonal cycles of the MAC

3.3.4 Dependence of MAC on aerosol mixing degree

3.4 Conclusion

Supplementary material

**4 Mixing state and absorbing properties of black carbon during Arctic haze **

4.1 Introduction

4.2 Material and methods

4.2.1 Sampling site and meteorology

4.2.2 BC measuring techniques

4.2.3 Additional dataset and optical modelling

4.3 Arctic spring aerosol

4.3.1 Aerosol optical properties

4.3.2 Arctic black carbon

4.4 Coating effects on aerosol optical properties

4.4.1 Enhancement of black carbon mass absorption cross section

4.4.2 From particles to aerosol: estimated and observed optical properties

4.5 Conclusion

**5 Ice residual properties in mixed-phase clouds at the high Alpine Jungfraujoch site **

5.1 Introduction

5.2 Experimental: CLACE 2013 field campaign

5.2.1 Aerosol inlets: total inlet and Ice-CVI

5.2.2 Cloud probes

5.2.3 Aerosol concentration, size distribution and composition measurements

5.3 Results and discussion

5.3.1 Comparison of ice residual and small ice crystal concentrations

5.3.2 Assessment of aerosol instrument inter-comparability

5.3.3 Ice residual size distributions

5.3.4 Black carbon coating thickness

5.4 Conclusions

**6 Conclusion and outlook **

List of Figures

List of tables

**References .**