In the present study, we performed retrievals for three fires: Shady, Lefthand, and Williams Flats. These fires evolved under clear-sky ambient conditions; this consideration simplifies the radiative transfer modeling. Table provides an overview of the fire occurrences and their key characteristics, such as plume aerosol optical depth (AOD), burned fuel, and meteorological conditions.

Figure  shows a typical flight path through the Shady fire. The aircraft crossed the plume in transects perpendicular to the wind direction, and in sequentially increasing distances (steps of ≈10km) to the fire. At a distance of about 100 km from the fire, the aircraft returned to the original starting point, repeating the transect pattern over the plume.

The key FIREX-AQ observations for the present study are the actinic flux spectra from which aerosol absorption properties are retrieved. However, ancillary FIREX-AQ measurements were used to constrain other relevant environmental parameters; these include atmospheric conditions, particle size and plume geometry. The following paragraphs introduce the most relevant instruments. Assimilation of the data into the retrieval is described in Sect. .

Actinic flux spectra were recorded by the CAFS instrument onboard the NASA-DC8 aircraft . This instrument combines data from two channels with upward and downward-facing entrance optics, to capture radiation over the full 4π steradian solid angle. The instrument was calibrated in the laboratory to provide absolute actinic flux density spectra in units of photonss-1cm-2nm-1. It covers the spectral range from 298 to 640nm at a resolution of 1.7nm (FWHM) at 297nm and ≈0.8nm sampling. Typical spectra are shown in Fig. . Its limit of detection is 6×1010photonss-1cm-2nm-1, a value determined from noise analysis under low light conditions. The error in sensitivity was estimated to be 5% and arises from uncertainties in the instrument’s calibration.

The aerosol spatial distribution was constrained using Lidar observations from the aircraft, from an instrument called DIAL-HSRL, which combines a High Spectral Resolution Lidar (HSRL, ) and an ozone DIfferential Absorption Lidar (DIAL, ). The Lidar observations were complemented by in situ measurements of the aerosol extinction, absorption, and scattering coefficients, using TSI Nephelometers, a Radiance Research Particle Soot Absorption Photometer (PSAP), and the NOAA Aerosol Optical Properties Suite AOP, . The data were combined and processed as described in to infer vertical profiles of the aerosol extinction coefficient at 532 nm, at a temporal resolution of 10 s (equivalent to a horizontal spatial resolution of 1.5 km at the average speed of the aircraft of about 150ms-1) and a vertical resolution of 30 m (Fig. ). Time series of these profiles (Lidar curtains) for the individual transects are shown in panel A of Fig. , and in Figs. S3 and S4 in the Supplement.

A TSI model 3340 laser aerosol spectrometer measured aerosol size distributions at 1s temporal resolution, at aircraft cabin temperature and dry humidity. Hygroscopic growth effects were neglected, since relative humidities during the investigated flights were <40% (Table ). Under these conditions, scattering enhancements for BB aerosol are reported to be ≲1% .

For the physical plume age, i.e. the residence time of the smoke in the atmosphere since emission, we use data from the FIREX-AQ database . These are the “wind uncorrected” plume ages, calculated as described in by backtracking upwind trajectories from the aircraft to the source fire location using the NOAA HYSPLIT model .

The DC-8 aircraft meteorology and navigation systems provided temperature, pressure, humidity, wind speed, wind direction, geolocation, altitude above sea level, ground speed, and radar measured altitude above ground at 1 s temporal resolution.

We use the 1D radiative transfer model VPC (VLIDORT for PhotoChemistry, ), built around the Quasi-Spherical Vector Linearized Discrete Ordinate Radiative Transfer (VLIDORT-QS) code . The model simulates actinic fluxes for a given atmospheric state, solar geometry, and observer altitude. The atmospheric state is described in terms of various model input parameters, including aerosol properties and aerosol vertical profile (details in Sect.  and ). For plumes that are several kilometers wide and for solar zenith angles ≲75°, showed that the application of 1D radiative transfer models such as VPC, is highly successful: Comparisons between modeled and measured actinic fluxes showed that 3D radiative effects can occasionally be significant for individual data points (10 s temporal resolution) in areas with large extinction gradients, such as plume edges. However, transect-averaged measurements agreed very well with the model, confirming minimal 3D effects in this approach.

In the model, we approximate plume particles as an ensemble of homogeneous spherical particles of uniform composition. For their representation we make use of VPC's “microphysical aerosol” module , which characterizes the ensembles in terms of a bimodal log-normal PSD, the complex refractive index n(λ)+ik(λ) of the particle material and a vertical extinction coefficient profile E(λ0) at a predefined reference wavelength λ0. This simplified aerosol representation was chosen to (1) best accommodate available FIREX-AQ measurements, (2) minimize the number of retrieved parameters, given the limited information in the spectra, and (3) align with the Mie aerosol representation commonly used for radiative transfer calculations in current chemical transport and climate models . The description is complete in the sense that all bulk optical properties (extinction coefficient, SSA and scattering phase function) can be calculated for arbitrary wavelengths and altitudes by running VPC's integrated Mie model. The imaginary RI is the parameter of primary interest in this study and the target quantity of the retrieval (Sect. ).

It should be noted that the retrieved imaginary RI represents a “Mie equivalent” value. RI values for actual particles may differ due to specific mixing state and particle morphology. At the same time, this Mie-equivalent RI value is “radiatively correct” in the sense that the Mie code will yield optical bulk properties (extinction cross-section, SSA, scattering phase function) that are close to reality. Furthermore, the homogeneous sphere representation underlying the Mie-equivalent approach is often used in satellite retrievals and chemical transport models. This makes our results directly transferrable.

Nevertheless, we performed sensitivity studies for more complex particle representations, to estimate direction and approximate magnitude for the biases induced by our homogeneous sphere assumption. For particles with a core-shell morphology (core is BC, shell is BrC, BrC / BC volume ratio and PSD same as in the homogeneous case), our retrieval overestimates the particle average imaginary RI by ≈10% and underestimates its Angstrom coefficient by ≈0.15. For particles that are externally mixed (pure BC particles, pure BrC particles), our retrieval underestimates the particle average imaginary RI by ≈10% and overestimates its Angstrom coefficient by 0.3. These numbers are within the uncertainties of our retrieval. Furthermore, we investigated potential impacts of ammonium nitrate (NH₄NO₃) coating on the aerosol optical properties, as reported, e.g., by . High-resolution Aerosol Mass Spectrometer measurements (see FIREX-AQ database, ) during the three analyzed flights imply NH₄NO₃ volume fractions of 1.9 %–2.4 %. Assigning all particulate nitrate to NH₄NO₃ gives conservative upper bounds of 2.4 %–3.3 %, with a transect-averaged maximum of 7 %. Core-shell Mie calculations using 2.5%, 3.5%, and 7% volume fractions of non-absorbing NH₄NO₃ shells (n=1.55) changed absorption by at most 6% and single-scattering albedo by equal to or less than 0.01. As illustrated in Sect. S2, these changes are about an order of magnitude smaller than the changes introduced by the size uncertainties assumed in our error propagation scheme (see Sect. ) and thus have no significant impact on the retrieval results.

The goal of the retrieval is to infer the wavelength dependent imaginary refractive index k(λ) of the aerosol material. To reduce the number of retrieved parameters, we do not retrieve independent values k(λ) at multiple wavelengths. Instead, we assume an Angstrom wavelength dependence 2k(λ)=k(λ0)λ0λαk and we then retrieve the Angstrom coefficient αk, plus magnitude k(λ0) at a reference wavelength of λ0=387nm. These two parameters constitute the parameter vector x=(k(λ0),αk). Adding higher order terms to Eq. 2 had only a small impact and was thus not implemented.

The retrieved state vector elements combined with information on the size distribution and real RI (see Sect. ), enable calculations of the imaginary refractive index, and the SSA and VAC at other wavelengths.

The measurement vector y in our retrieval scheme contains m=18 values: these are the logarithm of CAFS upwelling and downwelling actinic fluxes, each at 9 selected wavelengths (308, 313, 322, 332, 347, 364, 387, 405, 440 nm). Instead of the full spectra provided by the CAFS, this reduced set of wavelengths has been selected to improve computational efficiency, while still capturing the spectrally smooth aerosol signal. The wavelengths are specially chosen to avoid interference with strong solar Fraunhofer lines. To temporally match the CAFS and the Lidar, the 1Hz CAFS data was averaged over the 10s Lidar measurement window. The logarithmic transformation of y improves model linearity, numerical stability, and representativeness of uncertainties, considering the exponential nature of the Beer-Lambert law.

The fixed model inputs were constrained with ancillary FIREX-AQ aircraft measurements, satellite observations and literature data. We distinguish between uncritical and critical fixed inputs, based on their relevance to the modeled actinic fluxes and ultimately to the retrieval results.

Uncritical fixed parameters have a negligible impact on the modeled actinic flux (<3% when uncritical input is varied within its uncertainty) and are not considered in the retrieval error propagation scheme (Sect. ). They comprise the pressure profile, temperature profile, NO₂ profile and background aerosols, and are constrained following the procedures described in detail in . Table provides an overview of all uncritical fixed inputs, along with short descriptions of the respective sources of information (FIREX-AQ instrument or literature reference).

Critical fixed parameters have a higher impact on modeled actinic flux and are considered in the retrieval error propagation scheme (Sect. ). Critical fixed inputs are the PSD, the aerosol vertical profile, the ozone vertical profile, the surface albedo and the real part of the plume aerosol RI. Except for the real RI, the critical fixed inputs are constrained following the procedures in , a summary of which is provided in the following paragraphs.

PSDs were measured in situ by a laser aerosol spectrometer on the aircraft. For the retrieval we use transect-averaged data, to reduce measurement noise, while still capturing changes in particle size with plume age (Sect. S1). The Mie module of VPC describes particle sizes in terms of a normalized multi-modal log-normal size distribution, described via median radii, modal widths, and modal fraction for each mode. These model input parameters were inferred by fitting a bimodal distribution to the observed PSDs. The bimodal distribution describes the observed PSDs accurately (see Sect. S2). The amount and spatial distribution of aerosols are described through vertical profiles of the aerosol extinction coefficient at 532 nm. These are inferred combining Lidar observations and in situ measurements, both performed on the aircraft (Sect. ). Conversion to the actual retrieval wavelengths in the UV-Vis (Sect. ) is performed on-the-fly at each inverse-model iteration, based on derived aerosol microphysical properties from the current iteration. The surface albedo is constrained using the TROPOMI database for monthly Lambertian-equivalent reflectivity LER,, which is integrated into the VPC model. The O₃ tropospheric profile is inferred from O₃ in situ measurements during ascent and descent of the corresponding flight. For the stratospheric profile we assumed the 1976 US Standard Atmosphere, scaled according to OMI satellite observations .

The most critical fixed parameter in our retrieval is the real RI n(λ) of the aerosol. During FIREX-AQ, no direct measurements of n(λ) were performed. Based on literature review and FIREX-AQ related investigations presented in , we choose a fixed value of n=1.52 for all wavelengths.

Finding a realistic uncertainty estimate for the retrieval results x^, based on the various uncertainties and assumptions involved in the retrieval, constitutes a major challenge. Sources of uncertainty are present in both the parameter space (e.g. errors in the critical fixed parameters) and the measurement space (e.g. CAFS measurement error). Combining these requires propagation of error contributions through the radiative transfer model F in both the forward direction (from the parameter to the measurement space) and the backward direction (from the measurement to the parameter space). For this purpose, we resort to the most general approach for linear propagation of statistical errors: the formalism for error propagation with covariance matrices e.g.. This approach is based on the equation 3Cf=JCβJT where Cf is the covariance of some function or model f(β), resulting from covariances Cβ in the input parameters β, propagated using the Jacobian matrix 4J=∂f∂β Here, the “T” suffix denotes matrix transpose.

This formalism is applicable to any vector-valued function and considers potential correlations between errors, represented by the off-diagonal elements of the covariance matrices. It should be noted that for a multivariable scalar function f(β) and uncorrelated errors, Eq.  reduces to the much more familiar equation for error propagation: 5Δf2=∑i∂f∂βi2Δβi2 For our retrieval, we consider the following error contributions: (1) uncertainties in the CAFS measurements, (2) uncertainties in the fixed model parameters, (3) errors arising from model simplifications, and (4) the fit residual to capture potential failures in convergence of the fit. For these initial uncertainties, we construct covariance matrices, assuming the errors to be uncorrelated, i.e. the off-diagonal elements of these covariance matrices are identically zero. The measurement covariance matrix Cy is constructed based on the CAFS measurement uncertainties Δy (see Sect. ). The covariance of the fixed model parameter Cb is constructed similarly, assuming the uncertainties Δb listed in Table . Uncertainties arising from model simplifications are considered by additional uncertainties in distinct model input parameters, which lead to similar errors in the modeling results as one would expect from the actual model simplifications. These errors, Δb′, are listed in Table and are represented by the covariance matrix Cb′. They are applied to (1) the PSD radii to account for the simplified representation of aerosols as homogeneous and spherical particles, (2) the aerosol optical depth to account for horizontal inhomogeneity of the plume and related 3D radiative transfer effects, and (3) the surface albedo to account for horizontal inhomogeneity in surface properties. The fit residual is represented by the covariance matrix Cr, with the squared residual elements (Fi(x^)-yi)2 on the diagonal. It captures the cases in which the simplified model cannot reproduce the real observations, most noteworthy in scenarios where the assumption of a simple angstrom dependence of k does not hold.

The complete error propagation scheme is qualitatively illustrated by the blue arrows and symbols in Fig. . The scheme unfolds in two major steps, indicated by the upper and lower light-blue arrows, respectively. In the first step, we forward propagate Cb and Cb′ through the model to obtain a “model covariance” CF in the measurement space. This covariance describes the uncertainties in the modeled actinic fluxes that arise from uncertainties in the critical fixed model inputs and model simplifications. In accordance with equation , it is calculated as 6CF=Jb(Cb+Cb′)JbT using the radiative transfer model Jacobians with respect to the fixed input parameters: 7Jb=∂F(x,b)∂b. In the second step, the covariances in the measurement space (CF, Cr and Cy) are combined and propagated back through the model to obtain the fit result covariance 8C^x=J¯x(CF+Cr+Cy)J¯xT, using the weighted Moore-Penrose inverse (also referred to as weighted generalized inverse or gain matrix in literature): 9J¯x=(JxTCy-1Jx)-1JxTCy-1. Here, Jx are the Jacobians with respect to the retrieved parameters 10Jx=∂F(x,b)∂x. With the retrieval state vector having just two elements, C^x is a 2×2 matrix providing the uncertainties for the retrieved imaginary RI and its Angstrom coefficient 11Δk^(λ0)=C^x,11andΔα^k=C^x,22. as well as their correlation coefficient 12r^=C^x,12C^x,11C^x,22.

In a first step, we apply the retrieval scheme described in Sect.  to each Lidar profile where (1) vertical gaps in the Lidar profile are absent or can reliably be interpolated and (2) the AOD is >0.2. This results in 10–20 individual retrievals per plume transect at 10s temporal resolution. For all three fires, we perform nearly 900 retrievals (see Table ). As these retrievals include any data with a notable plume signal, they cover a broad range of conditions. We use this set of results to assess (1) the ideal conditions for accurate and stable retrievals, (2) the reliability of propagated errors, and (3) the contribution from various error sources to the total uncertainty in the retrieval results.

Figure  shows a time series of the lidar profiles and the imaginary RI retrieval results in terms of k0 (at λ0=387nm) and αk for the Shady fire. Section S3 provides similar plots for the Lefthand and Williams Flats fire.

At first glance, the retrieval results show significant variability within and between transects (Fig. B and C). However, there are clear indications that the quality of the retrieval strongly depends on the geometrical configuration and the underlying atmospheric conditions and that particularly large variations originate from retrieval artifacts rather than from any real variations of the plume aerosol properties.

Based on our sensitivity studies in Sect. S4 and and considering the limitations of the 1D radiative transfer model, most reliable results are expected when the aircraft is inside the plume, the AOD is moderate, the horizontal variability is low, and the sun is relatively high in the sky (SZA<75°). For retrievals where these conditions are met, the variability in the retrieval results is relatively small and the propagated errors in k(λ0) and αk are on the order of 20 % and 15 %, respectively. A few examples of such retrievals are highlighted by the green shading in panels B and C of Fig. . For the imaginary RI k(λ), this translates into uncertainties of about 20 % in the UV and 25 % in the visible (example shown in Fig. S7, top row). In these cases, the errors are dominated by uncertainties in the critical fixed parameters CF (Fig. E), with the highest contributions from the real RI of the aerosol and the plume AOD (green and blue areas in Fig. F). Interestingly, the sensitivity to the PSD (red, Fig. F) is relatively small, i.e., similar retrievals for other plumes are conceivable in the future, even in scenarios where the PSD is not as well constrained as was the case during FIREX-AQ.

On the other hand, there are scenarios where conditions are less favorable. For example, for low AODs, the aerosol signal in the spectra is small, rendering the retrieval susceptible to inaccurate assumptions about surface properties, the presence of thin clouds, or horizontal inhomogeneities. Furthermore, when the aircraft is far above, well below, or close to the edge of the plume, 3D radiative transfer effects not captured by the model, such as shadowing and side-illumination, become increasingly probable. As a result, the retrieval occasionally becomes unstable and yields extreme or even unrealistic values for k0 and αk. Such scenarios are sometimes captured by the error propagation scheme, in terms of correspondingly large associated uncertainties (example indicated by the orange shading in Fig. ), which provides confidence in our error propagation scheme to reflect the quality of the conditions and results well. However, accounting accurately for all detrimental effects is impractical and, for extreme scenarios, the non-linearity of the problem can cause the error propagation scheme to fail (example indicated by the red shading in Fig. ). Consequently, it becomes necessary to apply additional filters, as described in detail in Sect. .

The error magnitudes shown in Fig. E indicate that the contribution of the fit residual Cr to the propagated retrieval error typically stays below the contribution of the model error CF, indicating a successful convergence of the fit within the limits of the model. During in-plume observations at high SZAs, the retrieval error is dominated by the increasing measurement noise Cy of the CAFS measurements (Fig. E, transects 17–20) due to low-light conditions.

To obtain the final absorptivity results discussed in the result sections, we calculate average values for each transect from the time series in Fig. . The averaging smoothes out small-scale variability and retrieval instabilities, thereby providing more reliable results, while major dependencies, e.g., on the plume age, can still be investigated.

To reduce biases introduced by extreme outliers, we apply additional filtering, as noted above in Sect. . We generally find that unrealistic retrieval results occur when we obtain very large values in k0 and very low values in αk, or vice versa. We therefore apply a filter based on the k0/αk ratio. We discard retrieval results where k0/αk deviates from the k0/αk median by more than a factor of 5 or 0.2 in the upper or lower direction, respectively. In our dataset for all three fires, this filtering removes 14 % of the retrievals. Allowing for larger or smaller deviations in k0/αk affects the variability of our results, but does not introduce significant biases in the transect-averaged values (Fig. S9). During transect averaging of the filtered data, individual retrievals are weighted by their propagated error, such that the averages are driven by the most reliable retrievals. We use the weighted average of the propagated errors of the individual retrievals to represent the uncertainties of the transect averages. This is a conservative approach, but quite reasonable, considering that many of the contributing errors are expected to systematically bias individual retrievals in a common direction (such as biases arising from the fixed real RI, PSD size calibration, Lidar ratio estimates for the current transect, etc.).

In the Supplement (Fig. S7) we present examples showing how the averaging process successfully calculates transect-averaged spectrally resolved RI, VAC, and SSA for a case where retrievals vary little during a transect and one where larger systematic variations are encountered.

Based on the approach described in Sect. , we derive transect-averaged imaginary RI and Angstrom exponents for all three investigated fires (Fig. A). The retrieved imaginary RIs vary between 0.02 and 0.03 between transects with uncertainties below 0.01. The Angstrom exponents vary between 3 and 5, with uncertainties below 1. Outliers in k0 and αk, as for instance occurring for transects 5 and 6 during the Lefthand fire (Fig. A), can be attributed to non-ideal conditions such as low AOD, which are partly captured by the error propagation scheme and associated with correspondingly large uncertainties in αk.

To further illustrate our results, we calculate VACs and SSAs at three wavelengths (Fig. B and C). We observe the expected strong increase in absorption towards shorter wavelengths. Although the different transects comprise varying numbers of individual retrievals and variability among them (e.g. Fig. S7A and C), the transect averages are mostly consistent, within the uncertainty estimates (Fig. ). Surprisingly, the values are similar between the three different fires, in particular towards shorter wavelengths (Fig. B and C). The dependence of the optical properties on plume age (the latter is shown in Fig. D), will be analyzed in more detail in Sect. .

Transect-averaged imaginary RI and Angstrom exponents, as well as VAC and SSA derived from them, are in line with previous studies (as, for example, reviewed in ) and coincident aircraft-based comparison measurements, which we will discuss further in Sect. .

During the Shady fire flight, our retrievals coincided with two independent aircraft-based UV-visible aerosol absorption datasets: filter samples analyzed offline by spectral analysis of extracted BrC chromophores (SAEB), and real-time in situ measurements by photoacoustic spectroscopy (PAS). These datasets provide complementary points of comparison with our remote sensing results.

The first comparison dataset, referred in the sequel to as SAEB (spectral analysis of extracted BrC chromophores), is based on aircraft filter collection followed by offline solvent extraction and spectrophotometric analysis, and is therefore not strictly an in situ measurement in the same sense as PAS. Particles were collected on separate filters for each transect. The filters were then extracted with water and afterwards with methanol. While most organic material dissolves in either of these solvents, insoluble black carbon remainders can be removed from the solution using pore filters. The absorption coefficients of the solutions between 300 and 700nm were determined using a Liquid Waveguide Capillary Cell. Detailed descriptions of the procedure can be found in . Following , we combined this data with BC measurements from a single-particle soot photometer and sizing information from the laser aerosol spectrometer, to reconstruct the absorption coefficient of the original particle ensemble and to estimate uncertainties (≈30%) for the full measurement and analysis procedure.

The second comparison dataset is based on in situ PAS. The PAS instruments during FIREX-AQ provided real-time measurements of the dry aerosol absorption coefficient at wavelengths of 405, 532 and 664 nm. Given the low humidity conditions during the Shady fire (<35%), dry absorption can be considered representative of ambient absorption . In contrast to SAEB, PAS observations measure directly the total absorption of aerosol in its particulate state. Uncertainties for the direct PAS measurements are estimated to be 20 % . However, since the measurements were limited to three wavelengths in the visible, UV absorption properties were determined as described in , a process based on log-linear spectral extrapolation, something that potentially introduces considerable biases .

performed a detailed comparison of absorption coefficients from SAEB and PAS and reported substantial inconsistency (as also evident in Figs.  and S8 in the present study). In the following, we perform a similar comparison, this time including our remote sensing results. For this purpose, absorption coefficients from PAS and SAEB were converted to VACs, assuming the same aerosol PSDs from the laser aerosol spectrometer (Sect. ) that were used in our retrieval. For 14 transects during the Shady fire, all three absorption datasets (Remote sensing, SAEB and PAS) contain sufficient data and enough temporal overlap for meaningful comparisons to be made. Comparing data for individual transects shows that, within the specified uncertainties, our remote sensing results agree with at least one of the aircraft-based comparison datasets for nearly all transects and wavelengths (Fig. S8).

Figure  summarizes this comparison over all transects in the form of VAC box-plots at five UV-Vis wavelengths and VAC Angstrom exponents, thereby revealing general systematic features. On average, our retrieved VACs and Angstrom coefficients are between the SAEB and PAS results. In the UV spectral range, VACs are closer to the SAEB data but stay slightly below, whereas in the visible, our results tend towards the PAS data. These trends agree well with the recent analysis by . In the UV, they expect the SAEB measurements to be most reliable, since soluble BrC dominates the absorption. At the same time, they postulate a potential overestimation in SAEB measurements due to the alteration of the chromophores through the extraction process, such as change in pH or direct reaction with the solvent. The UV PAS measurements suffer from uncertainties introduced by the UV extrapolation. Since the Angstrom exponent is inferred in the visible, where BC weakens the absorption wavelength dependence, PAS is expected to increasingly underestimate the real VAC towards shorter wavelengths. The situation changes in the visible spectral range. Here, SAEB excludes potentially relevant absorption from insoluble compounds and thus underestimates the VAC, whereas the PAS provides direct reliable measurements. However, while our results confirm the assumptions by , it should be noted that the propagated errors of the retrieval (with a large systematic contribution from uncertainty in the fixed real RI) could allow for other outcomes and further measurements would be beneficial to increase confidence in the validity of the results.

Our remote sensing results feature remarkably low variability (cf. small box sizes in Fig. ), which is about three times less than in the corresponding aircraft-based comparison datasets. As demonstrated in Fig. S9, this low variability is not artificially imposed by our filtering (Sect. ) but likely related to the enhanced spatial averaging inherent to remote sensing. This indicates that aircraft-based comparison measurements averaged over a single plume transect may suffer from biases due to variations associated with the specific height at which the plume was probed and variability in the plume geometry during the transect. Therefore, these values are not necessarily representative for the entire plume cross-section. This effect may be in part responsible for the large variability in absorption properties reported in the literature, and for the current consensus that a simple parameterization of the aerosol absorption properties of BB cannot be found .

Based on the data from all three investigated fires, we find a dependence of imaginary RI, VAC and SSC on physical plume age (Figs.  and S10), with Pearson correlation coefficients of ≈0.5. Fitting an exponential decay to data of strongly absorbing wavelengths (308 to 347nm), yields half-lives τ1/2 of 13±3, 16±4 and 17±4 h for imaginary RI, VAC and SSC, respectively. The fit result for VAC is indicated by the gray dashed line in Fig. . The values obtained are in good agreement with previous studies investigating the oxidative and photochemical bleaching of BB aerosol (which leads to a decay of BrC absorption with plume age). While laboratory studies with synthetic organic aerosol have reported a wide range of absorption half-lives from a few minutes to several hours , measurements in real plumes report values between 9 and 24 h . Given the limited amount of data and the relatively large uncertainties, we could not identify a dependence of τ1/2 on the exposure to sunlight in terms of solar zenith angle (dot size in Fig. ).

Given the uncertainty limits in our retrievals, we find no significant differences in imaginary RI, VAC and SSA between the three fires (Fig. ). This is surprising considering that aerosol absorption properties have been reported to vary significantly between different fires for a variety of reasons (Sect. ). The small differences might be partly explained by the similarity in combustion conditions. A common proxy for combustion conditions is the modified combustion efficiency (MCE), defined as ΔCO2/(ΔCO+ΔCO2), where ΔCO and ΔCO2 are background-corrected concentrations of carbon monoxide and carbon dioxide, respectively . For both the Shady and the Williams Flats fires we find little variation in MCE throughout the plumes and average values close to 0.9 (see Table ), representing approximately equal contributions from flaming and smoldering combustion . For the Lefthand fire, the enhancement ΔCO is too small to calculate a reliable MCE value.

We have seen that the aerosol UV absorption properties depend on wavelength and plume age, while the variation among the three investigated fires is insignificant within the retrieval uncertainties. Our retrieved absorption properties might therefore be applicable to other fires, for which comprehensive measurements similar to FIREX-AQ are not available. Example applications are chemical transport modeling, assessment of BB radiative forcing, or other remote sensing applications such as trace gas retrievals from satellite-based measurements. For such purposes we consolidate our results into a parameterization, that considers the relevant dependencies according to: 13A(λ,t)=A0⋅λ0λα⋅exp⁡-tln⁡2τ1/2. A(λ,t) is the absorption property of interest (either k, VAC or SSC), that is a function of wavelength λ and physical smoke age t. A0 is the value of the property at λ0=400nm and t=0h. The wavelength parameterization is given by an Angstrom dependence with exponent α, while plume age is characterized by an exponential decay with half-life τ1/2. Table provides the values for A0, α and τ for each absorption property. These values were determined by fitting Eq. to correspondingly binned averages of our retrieval results. It should be pointed out that this parameterization is intended for plume ages between 0.5 and 8 h, and a wavelength range from 308 to 440 nm; it is probably only valid for fires with fuel and MCE values similar to those for the three fires treated in the present study (see Table ).