Black carbon (BC) is a product of incomplete combustion of carbonaceous matter (fossil fuel, biomass and biofuels) that has an impact on both air quality and climate. Atmospheric particles affect the climate both directly by intercepting incoming solar radiation and scattering a portion back to space and absorbing a fraction, heating the local atmosphere and indirectly by changing cloud albedo and lifetimes. The present best estimate of the net climate forcing by anthropogenic particles is about –1.
2 W/m2 (IPCC, 2007), not including aerosol lifetime effects, compared with the climate forcing by the anthropogenic CO2 of +1.6 W/m2 , however, the uncertainty in the estimate of the aerosol forcing is much larger. Black carbon is the principal light absorbing component of atmospheric particles that heat the atmosphere.Locally the sign of the radiative effect of this heating depends upon the underlying surface albedo, but globally black carbon is estimated to cause a radiative forcing of 0.20±0.15 W/m2 (IPCC, 2007); furthermore Stier et al. (2007) has demonstrated the strong sensitivity of the topof-atmosphere aerosol radiative forcing to BC absorption.
When deposited on snow, black carbon containing aerosol particles reduce the albedo, thereby enhancing heating of the snow and causing a more rapid melting, which in turn can lead to an even larger albedo change.To assess the impact of black carbon at the global scale Chemistry Transport Models and General Circulation Models are used even though the resulting studies contain large uncertainties due to both the black carbon emissions and the treatment of physical and chemical processes affecting black carbon (Cooke and Wilson, 1996; Liousse et al., 1996; Jacobson, 2002; Chung and Seinfeld, 2002; Stier et al., 2005; Koch and Hansen, 2005; Reddy and Boucher, 2007; Koch et al., 2007; Stier et al., 2007). To evaluate the effect of future emission reductions these uncertainties in the atmospheric black carbon cycle need to be better understood and quantified.
It is not always clear what is meant by “black carbon” in models. Primary carbonaceous particles that are the product of the fuel combustion, often called soot, consist of a mixture of elemental and organic carbon; while other elements such as oxygen, hydrogen and nitrogen are also frequently present in the structure (Seinfeld and Pandis, 1998; Bond and Bergstrom, 2006). The chemical and physical properties of these primary aerosol particles evolve when transported in the atmosphere due to a number of competing processes such as condensation, absorption and coagulation as well as surface reactions, whereby the primary part becomes increasingly imbedded in other organic and inorganic components changing light absorption and refractory properties of the particles.Diverse measurement methods have been developed and utilized for the quantification of this aerosol component on a routine basis making use of some characteristic properties of soot particles. These methods have created new operational definitions such as black carbon and elemental carbon (EC) depending whether they respectively take advantage of the light absorbing or refractory properties, (i.
e. the resistance to the exposure to high temperatures without reacting). Dozens of inter-laboratory comparison studies have been conducted and BC and EC concentrations are found to differ considerably, up to a factor 7 among different methods, reducing to a factor of 2–3 among optical methods and a factor of 4 among thermal methods (Chow et al., 2001; Schmid et al.
, 2001; Currie et al., 2002; Jeong et al., 2004; ten Brink et al.
, 2004; Watson et al., 2005; Hitzenberger et al., 2006; Reisinger et al., 2008).However given that the chemical composition of soot particles is not uniform, while the physical properties of the particles are neither constant nor conserved during the lifetime of individual particles, neither of these methods can provide consistently accurate measures of soot and both elemental and black carbon can only be regarded as proxies for its concentration. Regrettably however, these discrepancies are usually disregarded in the modelling studies and the terms elemental carbon and black carbon are used interchangeably as synonyms of soot.
Only in a few cases have the differences between the parameters been considered in model evaluations (Schaap et al., 2004; Tsigaridis and Kanakidou, 2003). Of the three, the term black carbon is the one most commonly used in the climate modeling community for soot/black carbon/elemental carbon, as it derives from the optical property, which is that relevant for climate.
In the following, we also use the name black carbon for this “substance” that is emitted, transported and transformed in the model studies, however when comparing with observations, we also use the appropriate operational name for the observations themselves (BC for optical and EC for thermo-optical measurements, respectively).When BC is emitted it undergoes chemical and physical transformations, which are commonly referred to as “ageing”. The ageing process results in an overall shift from a more hydrophobic to a more hydrophilic state. The processes contibuting to the ageing are condensation of soluble material on BC particles (Weingartner et al., 1997), coagulation with soluble particles (Fassi-Fihri et al., 1997; Strom et al., ¨ 1992) and oxidation (e.g.
by O3, see Poschl et al., 2001) of ¨ organic material that coats the particles. The ageing by O3 is a slow process compared to the ageing due to the aerosol dynamics (Croft et al.
, 2005).Apart from the fact that these processes are not yet fully known, their explicit numerical treatment is time consuming in large-scale models. The time-scale of the conversion from the hydrophobic to the hydrophilic state affects the BC lifetime, by enabling more efficient removal by wet and dry deposition. The conversion depends on the initial state of the BC, as well as on the presence of other particles and gases in the atmosphere and it is not constant in space and time: the conversion time scale remains uncertain. Some models assume that this conversion can be approximated by an exponential decay process with fixed half-life, called the “ageing time” (e.
g. Cooke and Wilson, 1996 proposed 1.15 days).
Independently of how the ageing is described assumptions are always required, such as how much soluble material needs to be added to a hydrophobic core “to define” a particle as hydrophilic and thus capable of being taken up into clouds and wet deposited. This adds uncertainty to the model estimates (Wilson et al., 2001; Croft et al., 2005).Another important uncertainty is in the emission inventories of BC, which show large differences in global emission estimates due to differences in emission factors and/or activity data both for fossil fuel (4.7–8 TgC/yr) and biomass burning (3.
6–6 TgC/yr) (Bond et al., 2004; van der Werf, 2004; Cooke et Wilson, 1996; Liousse et al., 1996; Penner et al., 1993; Junker and Liousse, 2008). The quality of the inventories cannot easily be checked by models, since the resulting concentrations are highly model dependent, but are estimated conservatively to have an uncertainty of a factor of two (Bond et al., 2004).The first attempts to model aerosols in global models used simple mass based models and assumed external mixtures of components and constant size distributions (e.g.
Haywood and Shine, 1995; Tegen et al., 1997). Subsequently more elaborate approaches were developed including size resolved descriptions and the inclusion of aerosol dynamics, with the consequent improved descriptions of the aerosol optical properties, of their interactions with clouds, and of the nonlinearities of the aerosol system (Jacobson, 2001; Gong et al., 2003; Wilson et al.
, 2001; Stier et al., 2005; Stier et al., 2006; Spracklen et al.
, 2007; Guillaume et al., 2007). Size resolved aerosols and a more explicit treatment of atmospheric processes involving BC may not be important in certain conditions or areas, where other processes determine the concentrations, e.g. close to the source regions. In these regions, simplified descriptions can be sufficiently accurate for certain applications.Thus, models of the atmospheric black carbon cycle are highly uncertain, consequently the results are difficult to evaluate as they are influenced by: emission inventories that can have an uncertainty of a factor of 2 (Bond et al.
, 2004); the inclusion of black carbon ageing processes that can change BC lifetime by an order of magnitude (Croft et al., 2005); and finally by wet deposition that is perhaps the most uncertain process in the models (Textor et al., 2006).The purpose of this study is to investigate important sources of uncertainties in the global BC estimates, by examining firstly the effect of using two different approaches to represent BC (bulk versus size resolved, dynamics versus more simplified approach to BC ageing) in the global Transport-Chemistry model TM5 (Krol et al., 2005), then by looking at the impact of the wet removal on BC properties and finally by analysing the consequences of the unclear BC definition and subsequent quantification, information which is used in both the emission inventories, through the emission factors and in measurements used for the model evaluation.
In this study the Transport-Chemistry Model TM5 is used for the evaluation of uncertainties related to BC processing parameterisations. The model is briefly described in the following section.
The second section gives an overview of the emission inventories used in the simulation, while the last section introduces the dataset used in the model evaluation.
2.1 The Chemistry-Mransport Model TM5
1 Model set-up
The TM5 model is an off-line global transport chemistry model (Krol et al., 2005) that uses the ECMWF ERA-40 meteorological data. It has a spatial global resolution of 6 ?×4 ? and a two-way zooming algorithm that allows regions (e.g. Europe, N. America, Africa, and Asia) to be resolved at a finer resolution of 1?×1 ? . To smooth the transition between the global 6?×4 ? region and the regional 1?×1 ? domain, a domain with a 3?×2 ? resolution has been added. In the present application the zoom is over Europe, therefore outside the European domain the resolution of the model is 6 ?×4 ? .
In the current version, the model has a vertical resolution of 25 layers, defined in a hybrid sigma-pressure coordinate system with a higher resolution in the boundary layer and around the tropopause. The height of the first layer is approximately 50 m.TM5 uses the slope scheme for the advection calculations (Russell et al., 1981; Petersen et al., 1998). The model transport has been extensively validated using 222Rn and SF6 (Peters et al., 2004; Krol et al., 2005) and further validation was performed within the EVERGREEN Project (Bergamaschi et al.
, 2006).Gas phase chemistry is calculated using the CBM-IV chemical mechanism (Gery et al., 1989a, b) modified by Howeling et al. (1998), solved by means of the EBI method (Hertel et al., 1993). Dry deposition is calculated using the ECMWF surface characteristics and the resistance method (Ganzeveld and Lelieveld, 1995).Wet deposition is the dominant removal process for most aerosols and therefore is a major source of uncertainty in aerosol modelling (Textor et al., 2006).
Removal occurs in convective systems (convective precipitation) and in largescale stratiform systems that are associated with weather fronts. The in-cloud removal rates, which depend on the precipitation rate are differentiated for convective and stratiform precipitation and are calculated following Guelle et al. (1998) and Jueken at al. (2001). Aerosol below-cloud scavenging is parameterised according to Dana and Hales (1976). Wet removal is describe in more detail in Appendix A.
2.1.2 Aerosol description and processes
TM5 has been run with two different schemes for the aerosols. In the first set-up, common for bulk models, (hereafter called BULK) only the masses of the aerosol compounds are considered. The inorganic compounds, sulphate, nitrate and ammonium, are internally mixed, while organic carbon, sea salt and dust are externally mixed. Black carbon is also assumed to be externally mixed and resides in the accumulation mode with a mass mean radius of 0.
14 µm for wet and dry removal. BC is considered hydrophobic and it does not uptakeTable 1. Boundaries (dry radii, r), standard deviations (?), particle number (N) and mass (M) tracers of the modes in M7.2.2 Emission inventories
The available emission inventories of BC, Particulate Organic Matter (POM) and primary sulphate are for mass only.
Some assumptions are therefore required to calculate the emitted number of particles. Sulphuric acid is the only gaseous compounds interacting with the particles though the dynamics therefore details on the sulphur emissions are reported in a following paragraph. Sea salt is emitted using an on-line emission function following Gong (2003). Dust and the remaining gaseous emission inventories as well as emission heights are from the AEROCOM model inter-comparison exercise (Dentener et al., 2006) (http://nansen.ipsl.
jussieu.fr/AEROCOM/). Global emission fields are reported in Table 2.
1 BC and POM emissions
The BC and POM emission inventories used in the present application are from Bond et al. (2004) for the anthropogenic contributions (fossil and bio fuels) and from van der Werf (2004) for large scale biomass burning areas. The emission factors used in the BC anthropogenic emission inventories are predominantly based on thermal-optical measurements and therefore they represent a more EC-like carbonaceous compound rather than BC (T. Bond, personal communication, 2008). Similarly biomass burning emission inventories are also based on emission factors (Andreae and Merlet, 2001) derived mostly from thermal-optical techniques.In both simulations black carbon is assumed to be insoluble when emitted. In the DYNA case the number of BC and POM emitted particles is calculated assuming the freshly emitted particles ever number median radii of 0.
03 and 0.075 µm, for fossil/bio fuel and biomass burning, respectively, and emitted in the insoluble Aitken mode with standard deviation ?=1.59 (Stier et al.
, 2005). 65% of the emitted POM is considered soluble.The model does not contain a module for the calculation of Secondary Organic Aerosols (SOA) therefore monthly emission fields of SOA are used following the recommendations of Dentener et al. (2006). A factor of 1.4 is used to convert OC to POM.
2.2 Sulphur emissions
Anthropogenic emission inventories from transport, production and industrial processes, and domestic use are from IIASA (Dentener et al., 2005; Cofala et al., 2007). Biomass burning sulphur emissions are from van der Werf (2004), volcanic emissions from Dentener et al. (2006). While 97.
5 % of sulphur of anthropogenic sources is emitted as SO2, 2.5% is considered sulphate, to take into account the SO4 production in plumes, as sub-grid process, and emitted in the following modes: SO4 from industrial sources in the accumulation soluble mode (number mean radius of emission = 0.075 µm); sulphate from domestic, transport and biomass burning is emitted 50% in the Aitken mode with number mean radius = 0.03 µm and 50% in the accumulation mode and number mean radius = 0.075 µm (Stier et al., 2005).
DMS fluxes are estimated following the parameterisation proposed by Liss and Merlivat (1986), they are function of the wind speed and temperature and are calculated from DMS sea water concentrations from Kettle et al. (1999).
2.3 EC and BC datasets used for model evaluation
Modelled concentrations are compared with an extensive data set of observations distinguished by measurement method, season and region. The dataset contains network measurements of EC: EMEP (Yttri et al., 2007) and IMPROVE1 , as well as long-term and campaign measurements of both EC and BC. The long-term measurements were collected at the Arctic stations of Alert (Sharma et al., 2004, 2006: aethalometer) and Barrow (Bodhaine, 1995: aethalometer), in the Amazon basin (Echalar et al.
, 1998:Table 2. Global annual aerosol (Tg yr?1 ) emissions (sulphur in TgS yr?1 ).light reflectance technique), and at Halley, Antarctica (Wolff and Cachier, 1998: aethalometer).
The observations are chosen as representative of regional background levels to be coherent with the model scale, even though not all the EMEP sites participating in the 2002–2003 campaign have this characteristic. The network measurements were taken in a few samples per week and the model output has been sampled to represent exactly those days and sampling hours. All other measurements, other than EMEP and IMPROVE, were selected only if the collection density was high enough to allow a comparison with monthly modelled averages (this means almost continuous measurements during the month). For the sites where observations are not from the run years (2002– 2003) the model results are averaged over the two year simulations for the corresponding observational periods.Measurement inter-comparison studies showed that when the same sample is analysed with both optical techniques and thermo-optical analysis the mass of BC varies from 1 or little less to 3 times the mass of EC, with the higher BC/EC ratios found in urban areas (ten Brink, 2004; Jeong et al., 2004). It is therefore important to consider EC and BC measurements separately. The measurement sites used are shown and identified in Fig.
1. Most of the EC measurements are made in Europe and in USA, close to anthropogenic sources; whereas the optical observations of BC are typically found in areas where thermal-optical methods cannot be operated as monitoring techniques.The modelled black carbon vertical profiles are also compared to aircraft measurements made by Single Particle Soot absorption Photometers (SP2s) (Schwarz et al., 2006; Slowik et al., 2007) onboard NASA and NOAA research aircraft. The campaigns are at tropical and middle latitudes and high latitudes over North America. Observational data and averaging methodology are as in Koch et al. (2009).
Fig. 1. Map of the measurement sites used for model evaluation
3.1 Burdens and concentrations
The comparison of surface mean BC concentrations of the BULK and DYNA cases (Fig.
2) shows similar concentrations and gradients over the source regions (Europe, North and South America, Asia and Africa), while the gradients towards the most remote regions (the Poles and Oceans) are stronger for BULK than in the DYNA case, due to higher scavenging rate during the transport. Inspecting the annual zonal means (Fig. 3) reveals that in TM5-DYNA the transport of BC to the higher levels of the atmosphere and to remote regions is favoured, while in the BULK case BC remains more confined to the lower atmosphere above the source regions.Over the continents where emissions are taking place there is still a large percentage of freshly-emitted insoluble black carbon.
The global BC burden reflects the features of the surface concentrations. The burden is lower in the BULK case (0.11 TgC) than the DYNA case (0.14 TgC), corresponding to BC lifetimes of 4.
7 and 6.2 days, respectively. Other global models using different formulations for black carbon processing and emission inventories have reported burdens ranging from 0.
11–0.25 TgC and lifetimes of 4–15 days (Liousse et al., 1996; Cooke and Wilson, 1996; Chung and Seinfeld, 2002; Croft et al., 2005; Koch and Hansen, 2005; Stier et al., 2005; Textor et al.
, 2006, 2007).TM5 estimates dry and wet deposition around 0.16 and 8 TgC y?1 , respectively, for both approaches; as expected wet deposition is by far the predominant mechanism of removal.Fig. 2.
Annual mean surface layer modelled BC (ng/m3 , ambient conditions).3.2 Comparison with measurements
Given that BC can be 1 to 3 times the EC for the same sample and that the emissions used are more characteristic of EC, comparisons with the observations are inevitably qualitative. However it would be reasonable to expect agreement between observed EC and the modelled concentrations and agreement or under-prediction of observed BC concentrations, but by no more than a factor of 3 and less in remote areas.The scatter-plots of the modelled concentrations versus the EMEP and IMPROVE EC observations are displayed in Fig. 4.
The evaluation shows that the two results differ very little among each other, confirming that close to the sources emissions and synoptic scale mixing are the dominant processes influencing the modelled concentrations. Over Europe the model represents better the concentrations (spatial correlation coefficient R 2=0.78 and 0.
79) while over UnitedFig. 4. Scatter-plots of model (squared-TM5-BULK, triangle-TM5- DYNA) BC and observed EC concentrations measured by EMEP and IMPROVE networks (ambient conditions).Table 3. Daily correlation coefficients for the EMEP stations.
Table 4. Daily correlation coefficients for the IMPROVE stations.
Table 5. Comparison of modelled versus observed near-surface elemental carbon (EC) measurements.
Comparison of modelled versus observed near-surface black carbon (BC) measurements.
Table 7. Comparison of modelled and measured BC values spitted in dry and wet seasons for biomass burning sites.
4.1 Uncertainties related to the aerosol and wet removal schemes
The differences between the results from the two models depend on the distance from the black carbon sources: in fact the ratio between BULK and DYNA surface concentrations goes from about 1 over the continents to more than 10, up to orders of magnitude at the Antarctic area.
The crude assumption in the BULK approach of 30% of black carbon being interstitial and 70% being in-cloud removed very probably overestimates the wet removal since it does not take into account the hygroscopic state and the actual size of the particles and considers BC particles to be always totally soluble in clouds. In the case of coupling to M7Fig. 7. Modelled and measured BC mass profiles in ng/kg at tropical and middle latitudes (a–d) and in high latitudes over North America (e–f).Fig. 9. Scatter-plot of modelled BC versus observations at remote stations.between the DYNA and the BULK case. At high latitudes the 60% interstitial profile gets closer to the BULK case profile. Looking again at Fig. 8 it is clear that closer to high latitudes the DYNA approach estimates an interstitial fraction larger than 60–70% up to more than 90% therefore the 60% hypothesis leads again in those areas to an overestimation of the wet removal.
The major difference between the DYNA and BULK results in remote regions is due to the variable interstitial fraction and the fixed fraction, respectively.Wet removal is the dominant sink for black carbon and the choice of the scheme in the model will determine BC burden and lifetime. The wet removal parameterisations used in TM5 have been evaluated in the AEROCOM intercomparison exercise (Textor et al., 2006) and found to be one of the strongest removal schemes among the 16 participant models.Precipitation is taken from the ECMWF ERA-40 data, which have been evaluated using satellite and gauge measurements and reported in Hagermann et al.
(2005) and in more recent works. Precipitation over the oceans is overestimated compared to measurements, which are uncertain. Over land precipitation is much closer to the observations although slightly overestimated.
Betts et al. (2009) compared the ERA-40 data with observations in the Amazon Basis and found that the model underestimates precipitation during the wet season and overestimates in the dry season. Another precipitation evaluation was done for China and ERA-40 underestimates precipitations in most years (Ma et al., 2009). Betts et al. (2009) also evaluated the cloud cover using satellite measurements and showed that it has the same seasonal cycle of the retrieved data although underestimating it in the second part of the year.To study the sensitivity of the BC burden and lifetime to wet removal, some simulations were performed using the DYNA model.
In these tests, the wet removal due to large scale and convective precipitation were decreased by 30%. In an additional test the below cloud scavenging by large scale precipitation was neglected. These sensitivity tests were performed for one month (May) with one month spin-up, but the results are considered representative, at least for a global analysis performed here.Reduction of either scale or convective precipitation by 30% resulted in the same effect on BC lifetime. The burden and lifetime go up by approximately 10% (Table 8).
Logically, the reduction of both large scale and convective removal by 30% produces the largest effect, the burden increases by 16% and lifetime goes up to 7.85 days (+22%). Below cloud scavenging has a negligible effect on BC concentrations, since most of the BC is in the aitken and accumulation mode, for which below cloud removal is slow.
The reduction of the wet removal has consequences for the transport of BC to the oceanic and remote areas: BC concentrations further away from the source regions increase by 10–20%.
4.2 Uncertainties related to the EC/BC measurement technique
How well the model simulates real BC levels can be evaluated by comparison with measurements, as long as the model output is comparable to the measurements. As discussed above, this is not always the case for black carbon. The DYNA results are consistent with both the emission inventories being EC rather than BC and the coincident BC measurements being equal or larger than EC: the good agreements with EC over Europe; the ability to capture the seasonal trends in BC observations in polar regions, while not always reproducing the magnitude of the signal. In Alert the BC to EC ratio is equal to 1 in winter and to 1.
5 in the summer (Sharma et al., 2004) while in Zeppelin the ratio is slightly less than 1 (Nyeki et al., 2005) therefore a slight under-prediction of observed BC in polar regions is consistent with our understanding.The absolute uncertainty related to each measuring method is unknown; therefore no optical and thermal method can give the “real” amount of soot. Thermal and thermooptical methods estimate elemental carbon and are affected by uncertainties due to different protocols of temperature steps and use of the optics to monitor the charring used to separate the organic from the elemental fraction. The presence of salts in the sample can influence the estimation as well. Black carbon is quantified by optical methods which can measure only a signal proportional to the absorbing material collected on the sample.
Dust and organic material can absorb light and if they are present the concentration of BC estimated with the assumption that the absorption is only due to soot can be overestimated (Andreae and Gelencser, ´ 2006), specially in the biomass burning and dust source regions.Not only it is not possible to put an error bar around the black carbon/elemental carbon observations, but up to now no method is sufficiently ubiquitous to allow consistent comparable data set to be built at global scale, rendering the quantification of the “absolute” bias of the model compared to the whole dataset impossible; only a “relative” bias for each of the sub-datasets collected using a common method would be possible. As a consequence it is difficult to improve the model from an evaluation by comparison with such disparate and inconsistent observations.
Conclusions and recommendations
The aim of this study is to investigate important sources of uncertainties in the global BC estimates, by comparing the results of two common BC aerosol set-ups in a global model, by varying the strength of wet removal schemes and by their evaluation using measurements.The global Chemistry-Transport Model TM5 has been applied to evaluate the sensitivity of the model to the black carbon description and processing using a bulk and a dynamical approach, respectively. The bulk scheme is very simple to include in a large scale model and very common, but with the wet removal scheme used in TM5 underestimates the concentrations far away from the sources compared to measurements. The crude assumption of a constant removal by rain is probably the main reason for this difference.
Using the results of the dynamical model to calibrate the interstitial fraction in the bulk scheme doubles the fraction of aerosols assumed to be interstitial, but the transport to remote stations does not improve much and equally at all sites, pointing to the importance of the size dependent description of BC and its removal. Similarly, the dynamical model is relatively insensitive to feasible changes in efficiency of wet deposition: reducing both large scale and convective precipitation by 30% the increase of BC concentrations at remote regions is up to 20%.The observations available for an evaluation of a global model are sparse, and both measurements of EC and BC have to be used. The evaluation and further improvements of the modelled BC concentrations are not easy due to the quantifi- cation of the model bias to measurements, due to different methods used for their collections and analysis.Increased understanding of not just the observational dataset and the uncertainties therein, but also the terminology surrounding black carbon is required not only to give a more coherent phenomenology of BC at global scale but also to underpin better model development.
Model output and observations used for comparison should be more consistent: emission inventories are representative of EC-like substance therefore a harmonized dataset of EC measurements is required, for which the factor of difference among the thermal methods is accounted for. For sites and regions where the ratio of BC to EC mass is known, this ratio should be taken into account in the model comparison with BC observations.For applications of the optical properties of BC, such as climate studies, it may be better to calculate the optical property (light absorption coefficient) from the model output, as this is directly comparable with the observed aerosol property. In this case emission inventories should also take into account the mass of absorbing organic material which contributes to the total absorption but not considered yet in the current inventories. However, the radiative properties of organics, including the imaginary part of the refractive index important for absorption, are barely known and measurements are required to include them in models.