The simplified chemistry scheme with parametrized reaction rates and coefficients is based on the chemical reaction mechanism of the MAGRITTEv1.2 CTM seefor an in-depth description, which has an extensive, up-to-date isoprene oxidation chemistry primarily based on the Leuven Isoprene Model LIM, and the Caltech oxidation mechanism . As in , the isomerization rates of the δ-hydroxyperoxy radicals from isoprene oxidation by OH are enhanced, relative to the MAGRITTEv1.1 mechanism, in order to provide a better match with chamber data . The reaction network comprising the oxidation of isoprene and its intermediate products contains 243 reactions and uses 93 different compounds (Table ). The oxidation reactions of monoterpenes (i.e. α-pinene) adds another 14 reactions to this number.

The MAGRITTE CTM calculates the chemical interactions and transport of chemical compounds in the atmosphere based on a priori emission information. The model can be run in global (2°×2.5°) or regional configuration (0.5°×0.5°) using lateral boundary conditions from the global model run. The vertical resolution of the model consists of 40 levels from the surface up to the lower stratosphere at 44 hPa following a σ-level coordinate system.

Meteorological fields used in the model are taken from ERA5 reanalysis data . The aerosol optical depth data is obtained from the CAMS global reanalysis . The model uses gridded emission data from bottom-up inventories: MEGAN-MOHYCAN for biogenic emissions , CAMS-GLOB-ANTv5.3 for anthropogenic emissions , and QFEDv2.4 for biomass burning emissions , with emission factors from . The annual global NMVOC emission estimates for 2019 amount to 439 Tg for isoprene, 108 Tg for monoterpenes, 112 Tg for biogenic methanol, 193 Tg for anthropogenic VOCs, and 93 Tg for biomass burning VOCs. The model also includes oceanic emissions of methanol, acetone and acetaldehyde , and accounts for both wet scavenging by cloud and rain droplets and dry deposition .

The MAGRITTE model is run for the year 2019 with a 6-month spin-up time. It accounts for diel variations in chemical compounds through correction factors on the chemical reaction rates, photolysis rates, convective fluxes, and boundary layer diffusion coefficients computed by a simulation using a time step of 20 min . The model is run with a time step of 24 h using daily averaged chemical and dynamical parameters adjusted for the diurnal cycle using the pre-calculated correction factors.

The inversion system of MAGRITTE relies on the adjoint-based approach to optimize the gridded emissions of biogenic, anthropogenic, and pyrogenic sources, constrained by TROPOMI HCHO data over land. The setup has been described in detail in previous publications e.g.. Here we perform a global emission inversion, in which continental emissions are optimized per emission category (biogenic, anthropogenic, pyrogenic), per grid cell, per month, for a total of 3×90×144×12×0.3=139950 emission parameters. Grid cells with NMVOC emissions below 1010 molec.cm-2s-1 throughout the year are not optimized. Additionally, we require at least 10 valid satellite observations per 2°×2.5° grid cell per month. Consequently, the total number of optimized emission parameters is reduced to approximately 76 000.

Model columns are computed by running MAGRITTE in forward mode for a given set of emission parameters f. The cost function J is calculated as 1J(f)=12[(H(f)-y)TE-1(H(f)-y)+fTB-1f], where H(f) are the model columns, y are the observed TROPOMI HCHO columns, and E and B are the error covariance matrices of the emissions and observations, respectively. As in other emission inversion studies, this formulation implicitly assumes that systematic model-observation discrepancies can be reduced by adjusting the optimized emissions. Consequently, errors in the chemical mechanism or other model parameterizations may propagate into the inferred top-down emissions. In the comparison of model columns to observations, the vertical sensitivity of the satellite is taken into account by applying averaging kernels to the model profiles. Additionally, the modeled monthly columns are based on daily values at the satellite overpass time (∼ 13:30 LT), while accounting for the number of observations for each day.

The cost function in Eq. () is minimized using a quasi-Newtonian algorithm, in which its gradient with respect to the emission parameters is calculated using the adjoint of the MAGRITTE model . The convergence criterion is reached when the norm of the gradient of the cost function is reduced by a factor of 100 with respect to its initial value. This typically occurs after around 30 iterations.

One of the limitations of adjoint-based inversions of isoprene emissions is the complex chemistry involved and its associated high computational cost. Here we simplify the chemical degradation of isoprene from 93 species and 243 reactions in the MAGRITTEv1.2 mechanism to a strongly reduced network. The structure we propose is shown in Table  and consists of six reactions. The first reaction, i.e. the oxidation of isoprene by OH (Reaction R1), produces a short-lived peroxy radical, ISOPO2, and its reaction rate (k1) is well constrained from experimental data . Next, we include three reactions that represent the three main channels through which the peroxy radical can react: ISOPO2+HO2 (Reaction R2), ISOPO2+NO (Reaction R3), and an isomerization Reaction (R4). The HO2-pathway and isomerization are important in low-NOx environments, whereas the NO-pathway prevails in high-NOx conditions.

In the full MAGRITTE mechanism, the reaction channels highlighted above produce a variety of intermediate oxidation products. Here, we lump all intermediate oxidation products (besides HCHO) into a unique intermediate oxidation compound (IOX). The yields of HCHO and IOX from the reactions of ISOPO2 are parameterized using the adjustable parameters α, β, γ, δ, ϵ, and ζ (see Table ). Among these parameters, β and δ account for primary HCHO production, whereas the other parameters quantify the delayed HCHO production via IOX. The reaction rates k2 and k3 are taken from the recommendations of . The rate of the isomerization (k4) is derived from the bulk 1,6 H-shift rates of the pool of isoprene peroxy radicals adopted in the MAGRITTEv1.2 mechanism , with a similar temperature dependence. The weighted average at 298 K and typical conditions for the Amazon (30 ppt NO and 20 ppt HO2) is 0.0089 s-1. Next is the oxidation of IOX by OH (Reaction R5), to form HCHO, representing the secondary, delayed HCHO production from isoprene. The reaction rate k5, together with the coefficients α to ζ, will be optimized based on comparisons with the full MAGRITTEv1.2 chemistry model.

The final reaction, Reaction (R6), is the ozonolysis of isoprene. This reaction is the dominant isoprene sink at night, whereas it is near-negligible during daytime. Since the ozonolysis reaction only weakly affects the cumulative HCHO production and daytime HOx concentrations, we do not optimize its coefficients and rate, but estimate these based on their products and rate in the MAGRITTEv1.2 chemistry.

For simplicity, SICMA does not include an explicit representation of monoterpene oxidation. Instead, the reference box model simulations include emission sources of both isoprene and monoterpenes, whereas only isoprene emissions are represented in the SICMA parameter optimization (see Sect. ). The optimized SICMA parameters should therefore be interpreted as effective reaction yields that incorporate the contribution of monoterpene oxidation for a monoterpene-to-isoprene molar emission ratio of 10 %.

An important aspect in isoprene oxidation chemistry is its feedback on the oxidizing capacity of the atmosphere. Isoprene and monoterpene emissions have a strong impact on OH and HO2 concentrations. However, the reactions of OH and HO2 with the organic peroxy radicals generated in the mechanism are numerous, and also a significant amount of recycling takes place. In order to tackle this problem, we include a production of OH and HO2 in Reactions (R2)–(R5), with adjustable coefficients. For the ozonolysis Reaction (R6), the yields of OH and HO2 are derived from the MAGRITTEv1.2 mechanism.

In order to optimize the parameters of the chemistry network shown in Table , we use box model simulations with the kinetic pre-processor (KPP) package version 3.0.2,. The list of reactions of MAGRITTEv1.2 chemistry is loaded into the KPP system, which runs the chemical evolution over time.

The setup of the box model simulations focuses on typical Amazon conditions in terms of solar radiation, temperature, and ozone concentrations, since the majority of global BVOC emissions is released by tropical ecosystems. As such, we adopt Master Chemical Mechanism (MCM) photolysis rates based on solar zenith angles in typical Amazonian conditions (i.e., 10° S, on the 15 July), and the temperature is fixed to 298 K. The initial volume mixing ratios for H2O, CO, and ozone are set to 1 %, 150 ppb, and 15 ppb, respectively. Other initial concentrations (2 % H2O, 30 ppb O3) have been tested, but do not significantly impact the parameter optimization outcome. To avoid HCHO production from methane, its concentration is set to zero. Since isoprene oxidation pathways are NOx-dependent, we perform box model simulations at three different initial NOx concentrations: 0.03, 0.3, and 3 ppb. At every 6 min time step, we require the total NOx (=NO+NO2) to remain constant. Finally, we introduce an isoprene emission source varying diurnally with a maximum at noon and zero emissions during the night (06:30 LT sunrise and 17:30 LT sunset). The amplitude of the emission source is set to 107 molec.s-1, which corresponds to a surface emission of 1012 molec.cm-2s-1 averaged over a height of 1 km, representative of tropical isoprene source regions.

In box model simulations of the MAGRITTEv1.2 full chemistry, we include an emission flux for monoterpenes that is 10 times lower than that of isoprene, corresponding to the average monoterpene-to-isoprene molar emission ratio for Amazonia . Given the similarly short atmospheric lifetimes of isoprene and monoterpenes, the simplified chemistry scheme will therefore represent the total yield of HCHO from combined isoprene and monoterpene emissions, for the typical case of a 10 % monoterpene-to-isoprene molar emission ratio. This representation is necessarily simplified and does not explicitly account for differences in emission patterns or chemical degradation pathways between isoprene and individual monoterpene species.

We first perform box model calculations with the MAGRITTEv1.2 chemistry. The simulation starts at 06:00 a.m. LT and runs for 108 h with a time step of 6 min. We track the total HCHO production from both isoprene and monoterpenes, illustrated in Fig. , for different NOx concentrations. The cumulative HCHO production (Fig. a) increases with increasing NOx. This is mainly due to higher HCHO yields from isoprene oxidation at high NOx e.g., and to a lesser extent due to higher OH concentrations in the model, increasing VOC reactivity.

The optimization of the parameters of Table  is constrained by the MAGRITTEv1.2 chemistry run based on the HCHO production (Fig. a) and the concentrations of OH and HO2 (Fig. e and f). These parameters account for the chemical feedbacks between the organic and inorganic chemistry. Indeed, the OH concentration has a strong impact on the rates of Reactions (R1) and (R5), whereas the HO2 and NO concentrations determine the dominant reaction pathway of ISOPO2 in Reactions (R2) and (R3). The NO2 yield from the reaction of ISOPO2 with NO (Reaction R3) is set to 0.87, in order to account for organic nitrate formation . The precise value of this yield is unimportant in the box model runs with fixed NOx levels, but it will play an important role in the chemistry-transport model simulations. For OH and HO2, regeneration occurs in each reaction, hence this needs to be accounted for in Reactions (R2)–(R6). These yields are constrained in the optimization by the OH and HO2 concentrations of the full MAGRITTEv1.2 chemistry box-model simulations, and through their feedback on the HCHO chemistry (Fig. ). Likewise, the IOX production impacts the OH budget.

We used a Nelder-Mead simplex optimization method from the SciPy library to determine the minimum of the total normalized least squares difference in the cumulative HCHO distributions, OH concentrations, and HO2 concentrations simulated by MAGRITTEv1.2 and SICMA (Fig. a, e, and f). The initial values of the organic reaction coefficients (α to ζ) were set to 1.0, while the rate coefficient of the IOX oxidation reaction (k5) was initialized to 10-11 s-1. The initial OH and HO2 stoichiometric yields were both set to 0.5. The convergence tolerances in the minimization algorithm are set to 0.01 in absolute values for the parameters.

Owing to the relatively large number of free parameters and correlations between several of them, the cost function exhibits a broad minimum rather than a sharply defined optimum. Convergence was typically reached after 1000–2000 simplex iterations. A 14 d box model simulation required on average 2831 ms using the full MAGRITTEv1.2 chemistry, compared with 489 ms using SICMA, corresponding to a reduction in computational cost of approximately 83 %. Several optimizations with different initial parameter values were performed to reduce sensitivity to local minima and to identify consistently well-performing parameter sets. The existence of multiple well-performing solutions indicates that several parameter combinations can reproduce the key characteristics of the full chemistry, namely HCHO production and HOx recycling. We present the optimized isoprene chemistry of SICMA in Table .

Figure  shows the comparison of key compounds in the box model simulations. The cumulative HCHO productions of the two chemistry schemes are in excellent agreement, considering the low complexity of the SICMA scheme. The instantaneous HCHO production in Fig. b shows slight differences, with a higher HCHO production in SICMA around noontime and lower production during mornings and evenings. During the night, the absence of a formaldehyde sink highlights a small difference in nighttime HCHO production, which results in a slightly different HCHO diurnal profile shape as shown in Fig. c. However, the magnitude of HCHO concentrations is well reproduced.

The parameter optimization is also constrained by OH and HO2 concentrations. The simplified chemistry scheme performs well in reproducing the OH and HO2 concentrations. In the low-NOx regime, OH is recycled through the ISOPO2 + HO2 reaction. At high NOx, however, very little OH recycling takes place (besides HO2+NO) in the full MAGRITTEv1.2 chemistry, hence no OH recycling is needed from Reaction (R3) (Table ). Instead, the high IOX yield (4.55) in the reaction with NO (Reaction R3) leads to more OH titration, which depletes OH and forms HCHO and HO2 via Reaction (R5). As a result, the simplified chemistry scheme succeeds well in reproducing the evolution of key species of isoprene oxidation like HCHO, OH, and HO2. Also during nighttime, HOx concentrations and HCHO production in SICMA closely follows MAGRITTEv1.2, mainly through generation of HOx radicals by the ozonolysis Reaction (R6). The NO concentration is also well reproduced, except for a small overestimation due to the lower number of organic peroxy radicals considered in SICMA compared to the full chemistry. The reduced organic peroxy radical abundance results in less efficient conversion of NO to NO2 through organic peroxy radical + NO reactions, which contributes to lower ozone production (Fig. h). The resulting lower ozone concentration further reduces NO removal through the O3 + NO reaction, thereby reinforcing the higher NO-to-NO2 ratio in SICMA.

We evaluate the diurnal cycles for HCHO, isoprene, OH, HO2, NO, and NO2 in Fig. . We have selected three prominent isoprene emitting regions depicted in Fig. : the Western Amazon rain forest, the Congo Basin, and South-East US. Western Amazonia is characterized by high isoprene emissions and columns paired with generally low NOx concentrations. The Congo Basin presents a similar environment (evergreen broadleaf rain forest) but with generally higher NOx levels and therefore higher OH and lower isoprene columns. Finally, the South-East US is characterized by a strong seasonality and by the presence of anthropogenic emissions leading to high NOx and OH concentrations.

For HCHO, there is good agreement in the magnitude of the concentration in the planetary boundary layer for the different regions, especially around noon time, but with on average slightly lower concentrations using SICMA. The largest difference occurs during the evening and night. In the morning, the OH increase leads to a new equilibrium between HCHO sources and sinks, and the two chemistry schemes produce similar HCHO concentrations within several percent. The HOx and NOx concentrations show similar patterns across the regions shown in Fig. , with OH and NO generally overestimated and HO2 and NO2 underestimated. The largest differences occur in low-NOx Amazonia, with overestimations of 15 % for OH and NO. This difference is caused by the larger number of organic peroxy radicals in the full mechanism, leading to a stronger conversion of NO to NO2. This enhances the conversion of HO2 to OH through the HO2+NO reaction and contributes to the higher OH-to-HO2 ratio in SICMA. Nevertheless, the overall performance of the SICMA chemistry is adequate to replicate the full MAGRITTE results, especially during the day, despite its simplicity.

Figure  shows a comparison of annually-averaged HCHO column distributions from global model simulations using either the full or simplified chemistry. The distributions agree very well in biogenic source regions, where the isoprene chemistry matters most, as well as in anthropogenically dominated and remote regions, where isoprene plays a negligible role. The magnitude of HCHO columns are in good agreement (<10 %) over continents. Over oceans, the HCHO columns of the simplified chemistry are up to 15 % too low due to the neglect of organic nitrate and peroxynitrate formation in the SICMA mechanism. In particular, peroxyacetyl nitrate (PAN) is formed from the oxidation of many hydrocarbons including isoprene. PAN and other organic NOx reservoirs act as carriers of NOx away from the emission sources. The average westward outflow from trade winds leads to higher NOx levels over the ocean in the full chemistry run (see Fig. e and f). This in turn leads to higher OH concentrations over remote regions, and hence to larger background HCHO production from methane oxidation, which is reflected by a lower mean methane life time in the reference model (8.1 years) as compared to the SICMA simulation (8.4 years). However, the absolute difference in HCHO columns between the two models is small (<5×1014 molec.cm-2).

To evaluate the differences between the two chemical schemes in the CTM, we show difference maps for key compounds in Fig. . Over continents, the differences in OH concentrations are relatively small, generally of the order of 10 % or less. The OH concentrations of the simplified chemistry are slightly higher than those of the full chemistry, the exception being the remote desert areas where the long-range transport of NOx reservoirs leads to higher NOx levels in the MAGRITTE simulation. However, an important difference arises in boreal forests, where the SICMA OH overestimation ranges between 10 % to 20 %. This difference can be explained by the fact that monoterpene chemistry is omitted in the SICMA mechanism. Over needleleaf boreal forests, characterized by high monoterpene emissions, the isoprene-to-monoterpene emission ratio is a factor of 3 to 10 lower than assumed in SICMA. The oxidation of monoterpenes represents a significant NOx sink due to organic nitrate formation , estimated at about 1.5 TgNyr-1 globally in the MAGRITTE model run. A large fraction of the formed organic nitrate is lost through aerosol uptake or deposition, or transported away from source regions, resulting in reduced NOx and OH levels, in particular over eastern Siberia and boreal America. Moreover, the large monoterpene source in MAGRITTEv1.2 reacts directly with OH, further reducing its concentration. The general impact of using the SICMA mechanism in HCHO columns in the region is limited (Fig. a) due to competition between the lower formation of HCHO through monoterpene oxidation and the increased background source from methane due to higher concentrations of OH in SICMA. However, the higher OH concentrations also reduce the lifetime of isoprene, leading to lower isoprene columns using the SICMA chemistry in the boreal forests.

The ratio of isoprene-to-monoterpene also plays an important role in tropical regions, which are the main source of biogenic volatile organic compounds worldwide. A clear spatial correlation is found between the emission ratio of the MEGAN-MOHYCAN inventory (Fig. S1 in the Supplement), which is used as input for forward simulations, and the HCHO column discrepancy between MAGRITTE and SICMA displayed on Fig. a. In areas with high monoterpene emissions, the SICMA HCHO columns are generally underestimated, and vice versa. However, the differences are generally much lower than 10 % locally.

The differences in isoprene columns, illustrated in Fig. b, are mainly driven by differences in OH concentration, since reaction with OH is by far the main sink of isoprene . A higher OH concentration therefore increases the reactivity of isoprene and lowers the isoprene columns. The changes in isoprene columns and in OH concentrations (averaged below 1 km) are generally of opposite sign and display the same patterns, especially in high-emission areas (Fig. b and c). The correspondence is not perfect, because the isoprene column is mostly sensitive to OH levels close to the surface, such that the 1 km average might not always reflect the isoprene reactivity. In areas with low isoprene columns, like central US and the North China Plain, the impact of the SICMA mechanism is almost negligible on the 1 km OH average but might be significant near the surface, leading to large relative differences in the isoprene columns. However, the absolute difference between the two chemical schemes in these areas is small (<2×1013 molec.cm-2).

The modeled HCHO columns using the two mechanisms exhibit very similar seasonality, as shown in Fig. . The monthly variability is mainly driven by the emissions and meteorology, which are identical for both simulations. The impact of isoprene chemistry on the temporal evolution is small. Both model results show also a good agreement in temporal variation with TROPOMI HCHO observations, consistent with previous comparisons of MAGRITTE columns with TROPOMI data . In the Congo basin, both models consistently underestimate the HCHO columns by about 20 %. In Amazonia, the magnitude of the columns is very well reproduced, except for a ∼10 % underestimation during the dry season in August and September. In South-East US, we observe a clear separation of summer and winter seasons, with an amplitude of about factor of five. In North China Plain and South-East Asia, the observed HCHO columns are higher during summer/dry season conditions compared to the model. Although this is arguably caused by uncertainties in the bias correction applied to the satellite HCHO product (Sect. ), the high summertime HCHO columns are corroborated by ground-based validation campaigns, such as FTIR , MAX-DOAS , and Pandora stations. During winter/wet season, the bias between model and satellite observations is much smaller.

In this section, we show the results of emission inversions constrained by TROPOMI data (Fig. ) using either the full MAGRITTEv1.2 chemistry as reference or the simplified isoprene oxidation chemistry described in Table  in the MAGRITTE model. The emissions are constrained by the TROPOMI HCHO columns shown in Fig. . In areas where the modeled HCHO columns are higher than the observations, we can expect an emission increase, and vice versa. Consequently, the top-down emissions are sensitive to the observed HCHO columns.

In the majority of source regions, the a priori model columns are on average lower than the observed TROPOMI HCHO columns shown in Fig. . Both inversions consistently suggest a large increase of the a priori MEGAN-MOHYCAN isoprene emissions from 439 to 568 Tg (MAGRITTEv1.2) and 574 Tg (SICMA) on global scale (Fig.  and Table ). The largest emission increases are inferred in Southern Africa, in agreement with previous inversion studies e.g.. The inversion suggests increased isoprene emission fluxes in most source regions, except the Yucatan peninsula, Paraguay, Central African Republic and South Sudan, and northern Australia.

Although the inversion suggests a large increase of the fluxes (+30% globally), the annual emission total is well within the typical range for isoprene emissions from both bottom-up and top-down inventories 300–600 Tg,. Bottom-up emissions suffer from large uncertainties, mainly due to the assumed emission factors for different plant functional types. Top-down emissions also have large uncertainties, e.g. due to the presence of other contributing VOCs and due to biases in the satellite products e.g.,. A global inversion using the MAGRITTE CTM framework constrained by bias-corrected TROPOMI HCHO columns resulted in a top-down isoprene emission flux of 490 Tgyr-1 for 2021 .

Figure  shows the relative difference in top-down emissions between the inversion using the MAGRITTEv1.2 and SICMA isoprene chemistry. The overall difference is small, although locally both over- and underestimations of isoprene emissions are found, reaching up to 15 %. The relative difference of the top-down isoprene emissions is similar but of opposite sign to the relative difference in the HCHO column simulated using bottom-up isoprene emissions (Fig. a). In regions where the SICMA chemistry produces lower HCHO columns, the isoprene emission change is stronger after inversion, and vice versa, compared to the MAGRITTEv1.2 chemistry. The regional differences in the top-down emissions are therefore the direct result of the differences in the modeled HCHO columns. As discussed in Sect. , these can largely be attributed to the assumption of constant monoterpene-to-isoprene molar emission ratio in SICMA, and the absence of organic nitrates leading to differences in the NOx and HOx concentrations.

These differences can also be seen in the isoprene emission time series shown in Fig.  for selected regions. In Western Amazon, HCHO columns from SICMA are slightly lower during wet season (November to May, Fig. ). As a result, top-down isoprene emissions from SICMA are slightly higher during this period (by 4 %). In South-East US, a priori HCHO columns during summer (May to September) are lower than TROPOMI HCHO, which leads to an overall increase in isoprene emissions, and an excellent agreement between the results of the simplified and the full chemistry. In the Congo basin the emissions inferred from both inversions agree very well (Fig. c) across the seasons, and are enhanced compared to the a priori estimates. Similar conclusions are drawn for the North China Plain, a region dominated by anthropogenic VOC emissions (Fig. d). For South-East Asia, the high TROPOMI HCHO columns observed during the dry season (March to May, Fig. e) drive the strong increases of top-down isoprene emissions, which are a factor of two higher than the a priori. Biomass burning VOC emissions are also increased in this area (Fig. S2 in the Supplement). Overall, for all selected regions, the inferred isoprene emissions from the inversion using SICMA or the MAGRITTEv1.2 chemistry show a very close agreement, both in terms of magnitude and seasonal variability.

Globally, the inversion leads to a large biogenic emission enhancement of 30 % for both inversions (Table ). In spite of the small differences between the predictions of the two model simulations (Fig. ) for HCHO and isoprene columns, the difference in top-down isoprene totals is negligible (1 %). There is also good agreement with respect to biomass burning VOC emissions, both regionally and globally. The anthropogenic VOC emissions inferred from the SICMA inversions are 7 % higher compared to the full chemistry results (Table ). This can be attributed to the moderately lower a priori HCHO columns of the SICMA simulation in northern mid-latitudes, and in particular over Europe and eastern China (Fig. ), where anthropogenic VOCs are an important HCHO source. Consequently, the derived anthropogenic VOCs in SICMA are higher to compensate for the lower biogenic contribution.