Biomass burning (BB) constitutes a major source of particulate and gaseous atmospheric pollutants with a significant impact on air quality and climate . As a consequence of climate change, natural BB events are expected to increase in frequency and intensity, thereby gaining even further significance in the coming decades . Particles emitted from BB primarily consist of black carbon (BC) and organic carbon (OC) , while emitted gases include carbon monoxide, nitrogen oxides, a plethora of volatile organic compounds, and greenhouse gases such as CO2, CH4, and N2O . During daytime, both BB particles and gases undergo photochemical processing in the plume, leading to the removal and transformation of emitted gases, formation of secondary pollutants, and changes in particle properties . The main driver for these processes is photochemistry inside the plume, which is often optically thick and highly inhomogeneous. Consequently, the accurate quantification of the photochemical drivers is crucial to assessing the impact of biomass burning emissions on the environment.

Understanding and predicting the photochemistry in a given environment require knowledge of the speed at which the involved reactions proceed. For a photochemical reaction, 1A+hν→B+C, initiated by a photon hν, the reaction rate, 2d[A]dt=-J[A], is determined by the photolysis frequency J (expressed in Hz), which can be calculated according to 3J=∫σ(λ)Φ(λ)F(λ)dλ. The absorption cross-section σ(λ) of A describes the probability of photons being absorbed, while the quantum yield Φ(λ) is the probability of absorbed photons undergoing the reaction. σ(λ) and Φ(λ) are typically known from laboratory measurements. The actinic flux F(λ) describes the spherically integrated, directionally independent number of photons at wavelength λ. F(λ) is controlled by environmental factors, such as altitude, solar position, cloudiness, aerosols, and Earth surface properties. All of these conditions are temporally and spatially variable. Consequently, F(λ) is highly variable and its determination can be challenging.

Direct measurements of F(λ) can be performed with high accuracy using instruments with direction-insensitive reception optics and spectrometers that cover the required spectral and dynamic range (e.g., ). However, such in situ measurements are limited in spatiotemporal coverage and are not performed on all aircraft missions studying trace gases or aerosols. Another, often complementary, approach is to simulate actinic fluxes using radiative transport (RT) models. With such models, continuous spatial distributions of actinic fluxes can be derived. RT models need to be constrained with detailed information on the atmospheric conditions, in particular on the spatial distribution and properties of clouds and aerosols. In chemical transport models the inputs for the built-in RT models are driven by the chemical transport simulation itself. For the interpretation of field experiments and observations, the compilation of adequate RT model input data is more challenging.

Over the past 50 years, both direct measurements of actinic fluxes and RT simulations have been applied to obtain a complete picture of the radiative conditions for clear-sky conditions (e.g., ) and above, below, and inside clouds (e.g., ). In contrast, for BB plumes, corresponding studies rely on observations only, whereas the modeling of actinic fluxes and photolysis frequencies and their spatial distribution has received less attention. For instance, many current experimental BB plume chemistry studies are based on directly measured actinic fluxes or irradiances (e.g., ) or on the deduction of actinic fluxes from concentration measurements of gases involved in well-known proxy reactions . Such measurements are, however, limited in spatiotemporal coverage as they can only provide information at a single location and time. For atmospheric chemistry studies in BB plumes, a more complete picture is desirable, as the high spatial variability of actinic fluxes and photolysis frequencies significantly impacts plume processing (e.g., ). Continuous distributions of actinic flux and photolysis frequencies with the required accuracy and spatial resolution can only be inferred using RT models. and performed such RT modeling, but only for a synthetic BB plume created with a 3D chemical transport model. To our knowledge, similar studies for real plume scenarios do not currently exist. This is not surprising, as modeling is typically challenged by a lack of information to constrain the RT model, arising from the complex and variable nature of such plumes, in particular when they are young (hours old) and optically dense. The RT in BB plumes is dominated by aerosol, for which the spatial distributions and optical properties are often not well-known. A peculiarity in BB plumes is the optically active fraction of OC, typically referred to as “brown carbon” (BrC), which becomes strongly absorbing towards shorter wavelengths . It dominates the RT in the ultraviolet (UV) spectral range, where photochemistry is most responsive. Its concentrations and optical properties are difficult to assess, as they depend on the burned fuel, burning phase, and smoke age .

In addition, challenges arise from the modeling side. In the presence of optically thick clouds or plumes, horizontal transport effects such as side illumination and shadowing can significantly impact the radiation field, particularly when spatial scales on the order of the cloud size or smaller have to be resolved . Considering such effects requires 3D RT models (e.g., ), which are computationally expensive. Most models, including the model used in this study, therefore assume a horizontally homogeneous atmosphere; they solve the radiative transfer equation in one dimension and are thus referred to as “1D RT models”. This assumption strongly increases efficiency but can introduce errors due to the inability to simulate RT in the horizontal dimension. Investigations of these effects have been performed based on synthetic data , showing the significance of shadowing. 1D RT models, and to a certain extent 3D models, often suffer from incomplete knowledge and a simplified description of the input data, particularly in complex environments where atmospheric inhomogeneities can introduce uncertainties in the model initialization. These inhomogeneity effects and challenges with horizontal RT in real BB plume scenarios have not been well-studied. There is thus a need to better understand how well 1D RT models can describe actinic fluxes and photolysis frequencies in these plumes.

The accuracy of modeled actinic fluxes and photolysis frequencies can only be ensured by comparison with established models or with measurements. While such comparisons have been conducted extensively for well-defined atmospheric scenarios (e.g., ), they have not been performed for the complex radiative conditions encountered in optically dense BB plumes.

In the present study we derive continuous spatial distributions of actinic flux and photolysis frequencies in a real and optically dense BB plume by means of RT simulations. The key objectives of the study are the following:

Introduce and validate a recently developed radiative transfer model (VPC) for photochemical and remote sensing applications in BB plumes.

VLIDORT for photochemistry (VPC) is built around the Quasi-Spherical Vector Linearized Discrete Ordinate Radiative Transfer (VLIDORT-QS) code (Sect. ). The VLIDORT family of RT codes is widely used in the trace gas remote sensing community . These codes have been tested for many different atmospheric conditions and are thus well-suited for the study and interpretation of field observations. While there are other well-established and efficient RT models for the calculation of photolysis frequencies, such as the Tropospheric UV and Visible (TUV) radiation model Fortran code or Fast-J , VPC particularly facilitates the interpretation of field observations of BB plumes. To allow the study of dense BB plumes, VPC has to meet the following requirements: (1) a suitable and flexible representation of BB plume particles in the model, (2) efficient retrieval and sensitivity analyses common in remote sensing studies, (3) accurate RT results for a wide variety of geometries, including high solar zenith angles (SZAs) and limb viewing directions, (4) simulation of the light's polarization state, allowing for retrieval of aerosol information from polarimetric remote sensing data (which will be explored in future studies), and (5) the simultaneous calculation of radiances and actinic fluxes, useful for applications where actinic fluxes are deduced from radiance observations or where photochemistry and remote sensing are closely linked (e.g., for plume composition measurements from a satellite).

An overview of the model is depicted in Fig. . On the input side, VPC features the so-called “aerosol module”, designed to describe complex aerosol mixtures in a flexible way: the module allows usage of an arbitrary number of aerosol types, each with individual properties that are described either via bulk optical or microphysical parameters (see Sect.  for details). On the output side, a module has been added to convert the RT-simulated actinic flux spectra to photolysis frequencies for various chemical reactions (Sect. ). VLIDORT-QS, the photolysis frequency module, and parts of the aerosol module are implemented in Fortran but have been embedded in object-oriented Python wrappers to obtain a structured and modular user interface, including useful functions for data pre- and post-processing as well as visualization. The package supports not only combined use but also stand-alone individual use of the aerosol, VLIDORT-QS, and photolysis frequency modules. The current model default configuration is optimized for tropospheric applications in the wavelength range between 295 and 650 nm. Extension to stratospheric applications requires adding additional absorbers (e.g., O2 absorption in the deep UV).

The present study is based on data from the 2019 NOAA/NASA FIREX-AQ measurement campaign . In the course of this 6-week airborne campaign, more than 90 BB plumes were sampled in situ as well as remotely from the NASA DC-8 research aircraft. For our purpose, the FIREX-AQ observations offer a unique opportunity, as they provide a view of plume composition and radiative conditions of unprecedented comprehensiveness and accuracy. An overview of all of the instruments aboard the aircraft and the raw data is available in the NASA FIREX-AQ data archive . This section provides basic information on the flight selected for our analysis and instrumentation relevant for our study.

To initialize our model, the measurements introduced in Sect.  were pre-processed and combined with literature and satellite data as described in the following subsections. An overview of the input data is provided in Table . We use a vertical grid of 87 layers extending from the ground to 62 km above ground level (a.g.l.). The layer thickness was set to 100 m between 0 and 6 km (approximately covering the altitude range of the flight), 250 m between 6 and 9 km, 3000 m between 9 and 42 km, and 5000 m between 42 and 62 km altitude a.g.l. The spectrum by was used for the extraterrestrial solar irradiance. All literature spectra were spectrally smoothed prior to simulation (Δλ = 2 nm) as described in Sect. , which was found to approximately match the resolution of the CAFS instrument. Full simulations were performed on an irregular wavelength grid with 23 nodes (see Sect. S2), with denser sampling towards UV wavelengths. The grid was optimized for the interpolation approach described in Sects.  and S2. The final actinic flux spectra were calculated from these simulations using the aforementioned interpolation approach with a spectral sampling interval of 0.2 nm. For the VLIDORT scattering RT solver, the number of discrete ordinate streams in the polar half-hemisphere was set to 8. In addition, the “delta-M scaling” ansatz was used to deal with sharply peaked forward-scattering characteristic of aerosols.

Spatial distributions (2D plume cross-sections) of actinic flux and photolysis frequencies are modeled for each of the 20 transects highlighted in the lower panel of Fig. . The horizontal resolution of the modeled distributions is determined by the speed of the aircraft and the temporal resolution at which input data are available. As indicated in Table , different model input parameters are updated at different temporal intervals, depending on the parameter's data availability, variability, and relevance for the RT.

10 s: the temporal resolution of the model simulations is ultimately limited by the resolution of the lidar backscatter profile measurements (10 s). All model input data available at shorter time spans are therefore averaged to at least 10 s intervals prior to simulation, which corresponds to an approximate horizontal resolution of 1.5 km.

We ran the VPC model for the 20 transects indicated in Fig. . Simulation runs were performed at 10 s temporal resolution (corresponding to a horizontal spatial resolution of ≈ 1.5 km) and 100 m vertical resolution at flight altitude, roughly matching the resolution of the lidar observations (Sect. ). For each run, the model was constrained as described in Sect.  based on the plume composition and vertical distribution observed at the respective time and location. In total, 350 model runs (10 to 30 runs per transect) were performed. Each run provides vertical profiles for the actinic flux and photolysis frequencies.

For the investigation of photolysis frequencies, we will focus on four important atmospheric reactions with different spectral sensitivity. O3+hν→O2+O(1D)HONO+hν→OH+NONO2+hν→NO+O(3P)NO3+hν→NO2+O(3P) Figure  illustrates the spectral sensitivity by showing action spectra (actinic flux spectrum × reactant absorption cross-section × quantum yield) for each reaction, assuming typical modeled actinic flux spectra with and without the plume present. The action-spectra-weighted average wavelengths for the four reactions are approximately 310, 360, 375, and 550 nm.

The major features in the observed actinic flux and photolysis frequency time series (Figs.  and ), as well as in the actinic flux spectra (Fig. ), are well-reproduced by the model. RMSDs over the entire dataset are on the order of 10 % to 20 % in both actinic fluxes and photolysis frequencies. Systematic differences in our comparison are on the order of a few percent, as illustrated by the regression slope of 0.98 and negligible intercept between measured and modeled actinic fluxes (Fig. ) as well as slopes between 0.99 and 1.02 in the measured and modeled photolysis rates (Fig. ). These differences are smaller than the uncertainty in the CAFS measurements (Figs. , , ).

Generally we find surprisingly good model–measurement agreement, considering the complexity, heterogeneity, and variability of BB plumes and the large variations in actinic flux and photolysis frequencies over more than an order of magnitude on short spatial and temporal scales. To put our results into perspective, similar airborne and ground-based model–measurement comparisons for less polluted and nearly homogeneous clear-sky atmospheres typically achieve agreement on the order of 10 %.

Besides the relatively small CAFS measurement error, model–measurement differences arise for two major reasons: errors in the model input parameters and simplifications taken in the modeling approach.

Errors in model input parameters partly arise from instrumental measurement errors and uncertainties in the literature data that were used to constrain the model (Sect. ). Furthermore, the limited spatiotemporal coverage and limited resolution of these data do not fully encompass real variations in the inhomogeneous plume, thereby adding considerable uncertainty to the model constraints. Nonlinear relations between plume properties and actinic fluxes might also hinder exact simulations when using averaged parameters.

Model simplifications are the representation of aerosol (as spherical particulates and externally mixed) and the application of a 1D model, which cannot account for horizontal RT effects. The latter are caused by the horizontal inhomogeneities of the scenario. Such effects comprise, for instance, side illumination and shadowing, especially at the edges of the plumes. But also on smaller scales and within the plume, horizontal RT can affect the results. For instance, the fact that the lidar aerosol extinction profile was measured in the zenith direction, while the RT calculation was performed for nonzero SZA can introduce inconsistencies in the aerosol extinction profiles.

For our sensitivity studies (Sect. ), we estimated the uncertainties in the model input parameters, considering both instrumental errors and uncertainties due to limited coverage and resolution of the measurements. Propagating these uncertainties through the model yields model uncertainties very similar to the observed model–measurement differences, not only in magnitude but also in wavelength and AOD dependence (compare Figs.  and ). We conclude that, at least as average behavior over the dataset, the model–measurement differences are dominated by uncertainties in the model input. Hence, even with comprehensive state-of-the-art measurements as performed during FIREX-AQ, the information on the plume environment is still the limiting factor for accurate modeling of actinic fluxes and photolysis frequencies in BB plumes. Most critical is the uncertainty in brown carbon aerosol properties (refractive indices and PSD), which dominates the model uncertainties in the UV (Fig. ), where photochemistry is most sensitive. BrC properties are difficult to assess as they are highly variable and the mechanisms affecting the absorption's spectral dependence are not yet fully understood (e.g., ). A recent comparison study revealed inconsistencies between different approaches to derive BrC optical properties from FIREX-AQ data , presumably in part due to insoluble BrC components that the SAEB technique (Sect. ) cannot detect . In our study, this effect is likely reduced, since we combine the SAEB observations with direct in situ optical measurements of the SSA (Sect. ). However, the absence of SSA observations in the UV and the inhomogeneity of the plume hinder an accurate consideration of BrC in the modeling process. We propose that further investigation of the discrepancies between in situ extractive BrC sampling and remotely sensed actinic flux or radiance spectra may shed light on this issue and ultimately better constrain radiative transport and photochemistry in BB plumes.

Considering that most of the model–measurement differences can be explained by uncertainties in the model input, simplifications in the model are unlikely to limit the modeling accuracy under typical conditions. However, horizontal radiative transport effects might become problematic for specific cases. These effects – in particular side illumination and shadowing – are expected to be most pronounced when the SAA is not aligned with the plume axis, i.e., the sun illuminates the plume from the side (first and third sketch in Fig. a), and when SZAs are large. Indeed, we observe a dependence in model–measurement differences, matching these expectations (Fig. b). Furthermore, horizontal radiative transport effects are likely to occur at the plume edges, where horizontal inhomogeneity is large. An extreme case, where all three conditions are fulfilled, is represented by the plume edges of transect 20. The actinic flux time series indicates strong underestimations and overestimations (black boxes in Fig. c), which can be explained by plume side illumination and shadowing, respectively. It should be noted that the Shady fire dataset is favorable in this context, since the sun is almost aligned with the plume axis over the entire flight (Sect. ). Plumes under less favorable geometries might lead to larger horizontal radiative transport effects. On the other hand, corrections, for example based on additional measurements of direct solar AOD, might reduce these effects in the future .

With the confidence that we can model actinic fluxes and photolysis frequencies accurately, it is worth discussing the modeled spatial distributions of actinic fluxes and photolysis frequencies. Figure  shows actinic flux vertical profiles for case 1 during transect 5 (black box in Fig. g). We separated contributions from direct, diffuse downwelling, and diffuse upwelling flux and investigated two wavelengths close to the lower and upper end of the photochemically relevant wavelength range (320 and 600 nm in panels a and b, respectively). For the wavelengths in between these values, the profiles were found to transition steadily into each other.

Below the plume, the contribution from direct sunlight is considerably reduced in the UV and Vis, leading to a net reduction in the actinic fluxes, despite the enhancement of the diffusive radiation fields (e.g., the Vis downwelling contribution in Fig. b). Above the plume, the behavior is very different for UV and Vis. In the Vis (Fig. b), more light is scattered upwards, as the plume albedo is larger than the typically dark Earth surface (LER ≲ 10 %). This leads to an enhancement of the Vis diffuse upwelling flux on the order of 20 % for the example in Fig. b and up to 60 % over other parts of the Shady fire. The enhancement decreases only slightly with altitude for the infinitely horizontally extended plume in our 1D model. This behavior is very similar to the one reported for cloud layers, which are known to have substantially (> 100 %) increased (decreased) actinic fluxes and photolysis frequencies above (below) the clouds (e.g., ).

This behavior changes significantly in the UV. While upwelling radiation from clouds is similar in the UV and Vis spectral range, actinic fluxes above BB plumes remain similar to those in a pure Rayleigh atmosphere. This is due to increased darkening of the plume by BrC absorption. For wavelengths below 320 nm, actinic fluxes above the plume are even reduced by a few percent (light gray shading above the plume in Fig. b), indicating that the plume appears even darker than the combined reflectance of the surface and atmosphere in a clean atmosphere. Within and below the plume the shape of the profile is similar for UV and Vis, but reductions are much stronger in the UV.

For chemical studies, the spatial distribution of photolysis frequencies in the plume is of most interest. Figure  shows such distributions, as obtained from the VPC model based on data from transect 5. The distributions mostly reflect the findings on the actinic flux vertical profiles. Photolysis frequencies for UV-driven reactions such as O₃ photolysis (Fig. b) remain unchanged (or are slightly lower) above the plume and drop to near zero towards the center or bottom of the plume. For Vis-driven reactions like NO₃ photolysis (Fig. d), photolysis frequencies are enhanced by up to 40 % above the plume, while the reduction within and below the plume by up to 60 % is much weaker than that in the UV. The ultimate impact of these spatial and spectral features on the plume processing should be investigated with high-resolution chemical models in the future.

We have introduced and validated VPC, a VLIDORT-based quasi-spherical 1D RT model. VPC can calculate radiances, radiative fluxes, and photolysis frequencies for a wide range of atmospheric conditions, including high loads of complex aerosol mixtures as they occur in BB or other plumes. VPC also efficiently calculates Jacobians of the simulated quantities with respect to the input parameters, facilitating its use as a forward model in remote sensing retrievals or similar inversion problems.

We have constrained the model by a comprehensive set of aerosol measurements performed during FIREX-AQ and calculated actinic fluxes and photolysis frequencies in BB plumes with an accuracy of 10 %–20 % compared to direct measurements. Previous model–measurement comparisons in clean atmospheres have found differences of < 10 %. Considering the highly complex and inhomogeneous RT environment in dense BB plumes, the agreement between VPC and the observations is remarkably good. The average difference of actinic fluxes over the entire dataset is 17 %, with larger values (≈ 40 %) at ≈ 300 nm and for large plume AODs (≈ 10 at 300 nm). For the resulting photolysis frequencies, RMSRDs range between 13 % and 21 %, with lower (higher) errors for Vis-driven (UV-driven) reactions. A further analysis of the comparison results shows very small systematic differences on the order of ≈ ±2 % between the model and the observations. Our sensitivity studies suggest that most of the RMSD can be explained by the uncertainties in the model input data, mostly arising from the limited spatiotemporal coverage and resolution of the corresponding measurements. In the UV, the model error is dominated by the uncertainty in the properties of the strongly absorbing BrC. These uncertainties can stem from the variability of refractive indexes as well as size distribution inside the plume. In the Vis, the amount and properties of black carbon dominate the model error. Due to the decrease in both strong BrC absorption and plume optical density towards the Vis, the model error in the Vis is lower by about a factor of 3 compared to the error in the UV. Given these findings and considering that photochemistry is particularly sensitive to the UV spectral range, more research on BrC optical properties in BB plumes is needed to better constrain radiative transport and photochemistry in BB plumes.

The model–measurement comparison also provides insights into the potential limitations of the 1D approximation in the RT simulations. We observe a systematic increase in the model–measurement difference by a factor of 2 for solar geometries with high SZA and when the SAA is not aligned with the plume direction. In addition, occasional outliers at the plume edges, where horizontal gradients of environmental parameters are largest, can be identified. Both of these considerations indicate that, under certain conditions, 3D RT effects can have a significant impact.

The model results also provide insights on how photochemistry is affected within and in proximity to BB plumes. Despite the absorption of BC, BB plumes appear bright in the nadir at the visible wavelength compared to the typical Earth surface. Accordingly, the additional upward-reflected light leads to enhancements of actinic fluxes in the Vis above the BB plume of up to ≈ 60 % compared to fluxes in a Rayleigh atmosphere. This enhancement can reach the upper troposphere and the stratosphere and resembles the impact of clouds on actinic fluxes reported in previous studies. However, the increase in BrC absorption significantly darkens the BB plume towards the UV. Consequently, the observed above-plume enhancement gradually disappears towards shorter wavelengths and actinic fluxes can even be reduced compared to fluxes in a Rayleigh atmosphere for wavelengths ≲ 310 nm. Inside the plume, actinic fluxes steadily decrease from top to bottom and remain approximately constant in the atmosphere below. The decrease is more pronounced in the UV than in the Vis.

Our results show good agreement between observations and measurements in the Shady fire. However, our results also highlight the challenges in describing actinic fluxes in complex dense BB plumes. The Shady fire has been selected for its favorable conditions, such as the large plume size, clear-sky conditions, comprehensive sampling, and the alignment of the sun with the plume axis. An expansion of our analysis to other FIREX-AQ plumes would allow assessment of actinic fluxes and RT modeling challenges in a wider variety of BB plumes. From the 90 fires sampled during FIREX-AQ, about five other fires provide similarly favorable conditions. Prevailing challenges for the study of other fires are scarce sampling and the presence of clouds. Identifying the most critical unknowns from additional sensitivity studies might be of great value in the future to constrain actinic fluxes in and around BB plumes with fewer measurements and less effort.

The availability of a linearized RT model, such as VLIDORT-QS, together with our sensitivity results also opens the opportunity to use actinic flux and other remote sensing observations to study aerosol optical properties. The increasing disagreement of measured and modeled actinic fluxes towards lower wavelengths strongly implies that the BrC optical properties from the in situ SAEB observations may not fully represent the true properties of the plume aerosol. The next application for VLIDORT-QS is to retrieve BrC aerosol optical properties from the measured actinic flux spectra.

Further applications are conceivable in the context of chemical transport models (CTMs). To improve computational efficiency, CTMs typically run at relatively coarse spatial resolution (several kilometers) and resort to simplifications (e.g., 1D RT modeling) and parameterizations to account for photochemical processes. Detailed modeling based on accurate measurements of the atmospheric state, similarly as presented in this study, can help us to understand the magnitudes and origins of the uncertainties introduced into CTMs by these approximations.

Adding the capacity to calculate actinic fluxes to VLIDORT-QS allows us to improve trace gas remote sensing retrievals of BB plumes. These retrievals depend on the trace gas vertical concentrations profiles, which for many of the target gases, such as O₃, NO₂, HCHO, and HONO, depend on the vertical profiles of the respective photolysis frequencies. By combining actinic flux profiles from VLIDORT-QS with a CTM, self-consistent retrievals of trace gases should be possible.