SPEXone is a passive remote sensing MAP instrument, part of the NASA Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission (Werdell et al., 2019), scheduled for launch in 2023/2024. It was developed by the Netherlands Institute for Space Research (SRON) and the Airbus Defense and Space Netherlands (ADS-NL) with optical expertise from the Netherlands Organization for Applied Scientific Research (TNO). SPEXone can measure intensity and polarization of backscattered sunlight at multiple wavelengths and discrete viewing angles for a specific pixel on the ground. Specifically, it can measure radiance and polarization at five viewing angles (+57, +20, 0, -20, -57∘ on ground) with high accuracy (0.003) in the degree of linear polarization (DoLP). SPEXone is a spectrometer, measuring a continuous spectrum (at 2 nm resolution for radiance and 10–25 nm for polarization) between the spectral range from 385 to 770 nm. The sensor's horizontal resolution is ∼ 5.4 × 4.6 km for all viewing angles, and the swath is 100 km. The aerosol-retrieved parameters include column AOD, AE, SSA, aerosol layer height, effective radius, effective variance (of the size distribution), complex refractive index, particle number for a fine- and a coarse-mode aerosol, and a shape parameter for the coarse mode. Detailed information on the optical and technical attributes and the retrieval capabilities of SPEXone can be found in Hasekamp et al. (2019a​​​​​​​) and van Amerongen et al. (2019).

The sixth generation of the general circulation model ECHAM6, developed at the Max Planck Institute for Meteorology (MPI-M) in Hamburg, Germany (Stevens et al., 2013), and the second version of the Hamburg Aerosol Model (HAM2) (Stier et al., 2005; Tegen et al., 2019; Zhang et al., 2012) are used to simulate the physical and chemical processes of aerosol in the atmosphere.

The M7 aerosol module used in HAM2 considers five aerosol species, dust (DU), sea salt (SS), organic carbon (OC), black carbon (BC), and sulfates (SO4) (Vignati et al., 2004). Aerosols are partitioned into seven unimodal lognormal particle size distributions (nucleation, Aitken, accumulation, coarse) called modes and separated into two hygroscopic classes (hydrophobic and hydrophilic). Six of these modes contain several aerosol species (internally mixed modes). Each mode is characterized by the number concentration and the mass concentration by species. Aerosol number and mass are used in order to calculate the median radius for each mode (Tegen et al., 2019). The mode width (standard deviation of the lognormal distribution) is assumed and fixed as equal to 1.59 for the nucleation, Aitken, and accumulation modes and 2.00 for the coarse mode. The cloud and aerosol optical properties are computed using Mie theory and derived from lookup tables (Tegen et al., 2019) using the prognostic concentrations of aerosol tracers (Schultz et al., 2018).

All aerosol species are emitted, transported, deposited, and take part in aerosol–radiation interactions (scattering and absorption) and aerosol microphysical processes (e.g., nucleation, coagulation, aerosol water uptake, and cloud activation). The natural aerosol types (DU, SS) are introduced to the atmosphere by utilizing the simulated information of wind and certain surface and ocean characteristics. Other aerosol species (OC, BC) or aerosol precursor gases (SO2, DMS) that are emitted from both natural (e.g., forest fires) and anthropogenic sources use predefined emission inventories (Zhang et al., 2012). For a description of the importance of individual processes, see the budget sorted by species in Schutgens and Stier (2014).

Two SS emission schemes are used in this study. The first and default scheme in ECHAM-HAM parameterizes sea salt emissions based on laboratory measurements (Keene et al., 2007) using the wind velocity at 10 m and the sea surface temperature (SST) (Long et al., 2011; Sofiev et al., 2011). Low SST results in lower sea salt emissions with smaller particle size (Sofiev et al., 2011). The second scheme (previously the default option) in ECHAM-HAM calculates the sea salt flux mass and number through tables of wind speed classes and fits to two lognormal distributions based on Guelle et al. (2001 and reference therein). Note that sea salt particles are emitted only in the soluble accumulation and coarse mode in both schemes.

Dust emissions are based on the dust source scheme developed by Tegen et al. (2002). Wind velocity at 10 m is the main driver of dust aerosol particle production, while soil properties are also taken into account. The preferential dust emission sources are consist of arid or sparsely vegetated areas and are predefined based on Tegen et al. (2002). Improvements in the surface aerodynamic roughness length, soil moisture, and soil properties over East Asia specifically were made by Cheng et al. (2008). The threshold friction velocity depends on the soil size distribution, vegetation cover, and soil moisture (Cheng et al., 2008). Further, updates related to the representation of Saharan dust sources were made using infrared dust index from the SEVIRI instrument on board the Meteosat second-generation satellite by Heinold et al. (2016).

The emission for the remaining aerosol types and aerosol precursors are defined using emission inventories derived for 14 sectors. Each sector may include one or more aerosol types or aerosol precursors (Schultz et al., 2018; Tegen et al., 2019). The Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP) dataset is used for the anthropogenic, biomass burning, and aerosol precursor emissions, consisting of monthly mean estimates at a horizontal resolution 0.5∘ × 0.5∘ (Lamarque et al., 2010). The Community Emissions Data System (CEDS) is used as an alternative for the anthropogenic aerosol and aerosol precursor (Hoesly et al., 2018). The first version of Global Fire Assimilation System (GFAS) is also used for the biomass burning emissions coming from grass and forest fires consisting of daily gridded estimates at 0.5∘ × 0.5∘ horizontal resolution based on the fire radiative power measurements of the MODIS instrument (Kaiser et al., 2012). A more detailed description of both ECHAM6 and HAM2 can be found in Tegen et al. (2019).

The local ensemble transform Kalman smoother (LETKS) is used to estimate aerosol emission fluxes. This method has been previously used by Schutgens et al. (2012) for aerosols emission estimation and earlier by Bruhwiler et al. (2005), Peters et al. (2005), and Feng et al. (2009) for CO2 emission estimation. It requires a model to produce background information based on assumed emissions and observations that are assimilated to estimate analysis emissions. In data assimilation studies the terms analysis or posterior are used to describe the improved state of the system due to assimilation, although in this study we reserve the term analysis for cases where the aerosol emissions were estimated by a fraction of the total observations that are going to affect them in the end (more details follow).

The data assimilation occurs in assimilation cycles, where each cycle contains a background and an analysis step as depicted in Fig. 1. Dashed boxes indicate the default emission where no assimilation took place yet, while filled boxes indicate emission changed based on observations. The background step consists of an 8 d (ΔTb) forward simulation of the model that will initially (first cycle) create the simulated background observations. Following this, all the available observations within the last 2 d (ΔTs) of the forward simulation are assimilated in order to estimate the analysis emission for the last 6 d (ΔTa=ΔTb-ΔTs) of the forward simulation. Note here that the term analysis is used to indicate the updated emissions affected by n days of observations (where n<ΔTa), while the term posterior is used to indicate updated emissions affected by ΔTa days of observations (Fig. 1). This is where the first cycle ends. In the second cycle, background emissions are set as equal to the analysis emissions of the first cycle, and the respective steps of the background and assimilation steps are then performed for the second cycle. This process continues until the end of the assimilation experiment.

The assimilation window (ΔTs) defines the shift (step) in time of the forward simulation in each cycle, the period of the assimilated observations, and the period during which emissions are estimated. A ΔTs=2 d allows the aggregation of more satellite observations that provides a better constraint on emission estimates globally, but it also assumes that emissions do not change considerably over this period. Undoubtedly this is not always the case, for example dust emissions may vary a lot from day to day. The smoother lag (ΔTa) determines how many days are going to be affected by the assimilated observations in one assimilation cycle. In our setup this is equal to 6 d, but we conduct experiments to see its impact when reduced to 4 and 2 d.

Note that it is assumed that the observations of a certain day contain only a fraction of the available information to change the emissions and that the rest is contained in observations of subsequent days. Thus, emissions should be estimated iteratively, allowing observations up to 6 d after to correct the emissions. The posterior emission perturbations, corrected by 6 d of observations, are derived after three assimilation cycles and are indicated with an asterisk (*) in Fig. 1. For example, the posterior emission perturbations for days 7 and 8 are estimated in the third assimilation cycle and are corrected from the assimilated observations of days 7 to 12.

Background emissions come with uncertainties. The uncertainty of background emissions are represented by an ensemble that is generated by perturbing the default emissions. The perturbations are not globally constant but vary from grid cell to grid cell. Each grid cell has a distinct prior emission distribution. Changes in neighboring grid cells of each member are not abrupt but smooth. This spatial correlation of the prior perturbations was generated using spatial smoothing, a method where data points are averaged with their neighbors. A step-by-step description of how our spatially correlated perturbations are created can be found at Sect. 3.2 of our preceding work (Tsikerdekis et al., 2021a). The spatial correlation length scale of the generated perturbations is approximately 25∘ omnidirectionally. The perturbations are uniquely created and distinctively estimated by the data assimilation system for each aerosol species and sulfate precursor gas. The resulting 2D spatially correlated perturbations are multiplied with the model's emissions for each aerosol species and each member, resulting in an ensemble of simulations. In our experiments the ensemble size is 32. Note that the mean and the standard deviation of background distribution is equal to 1. Furthermore, it is noted that the perturbations are uniquely defined every ΔTs=2 d (different colors in the boxes of Fig. 1). The rationale here is that the simulated observations and emissions at day D (where D is any integer number) will be more correlated than the simulated observations at day D+ΔTs and emissions at day D. Consequently, changes in emissions caused by assimilated observations of day D will be stronger compared to changes in emissions by assimilated observations of day D+ΔTs. This design is based on the fact that observations on the day of the emissions carry more information about the emissions than observations in subsequent days.

More info regarding the emission perturbations and the ensemble can be found in our preceding work (Tsikerdekis et al., 2021a). New emission estimates are obtained by estimating new perturbed emission factors based on the assimilated observations by solving the Kalman filter equations: 1xa=xb+Pa⋅HT⋅R-1⋅(y-H⋅xb),2Pa=(I+Pb⋅HT⋅R-1⋅H)-1⋅Pb, where xb is the background state vector and represents the variables aimed to be improved. It includes emission perturbations of five aerosol species (DU, SS, OC, BC, SO4) and the emission perturbations of two aerosol precursor gases (SO2, DMS). xa is the analysis state vector, which is the improved version of xb based on the assimilated observations (y). The background and analysis uncertainty and correlations of emission are represented by the model error covariance matrix Pb and Pa respectively, using the ensemble. The observational uncertainties are represented by the error covariance matrix R. We assume R to be diagonal (i.e., correlations between observational errors are assumed to always be zero). The observational operator H translates the emission perturbations (x) to the simulated observations (H⋅x) and is entirely handled by the model (emission, transport, deposition, aerosol processes, and optical properties code). T stands for the matrix transpose operator.

The ensemble Kalman filter assumes that prior emissions in the model are unbiased. In reality this is not necessarily the case, since emission inventories or emission schemes in models may suffer from biases that are often higher than the defined background uncertainty. Past studies have demonstrated that optimizing prior emissions based on previous assimilation cycles can improve data assimilation performance (Bruhwiler et al., 2005; Peng et al., 2017; Peters et al., 2005). Based on that we have developed a method, hereafter called the “prior correction”. Prior correction updates the prior emission based on estimated emissions from the previous assimilation cycles, thus correcting biased emissions of the model as the data assimilation experiment progresses in time. Specifically, the ensemble mean (Emean) of the new emission perturbations of each cycle is defined according to the analysis results of the previous assimilation cycle. For example, the Emean of the newly created perturbations at B (Fig. 1) will be equal to the Emean of the perturbation at A (Fig. 1). Consequently, the filter corrects the emissions bias based on the estimated emissions of previous assimilation cycles.

Although prior correction fixes the problem of potentially biased model prior emissions, it may introduce unwanted negative emission perturbations when the Emean drops below 1. One way of addressing this issue would be to set all negative produced perturbations to zero, but this will affect the distribution of the perturbations and make it less Gaussian. Hence, the ensemble standard deviation (Estd) is adjusted according to the Emean: 3Emean≤1.1→Estd=1,4Emean>1.1→Estd=Emean⋅0.9. As an example, three distributions with different Emean and adjusted Estd are depicted in Fig. 2. Note that even under this design there is <0.5 % chance to generate a negative value in the distribution when Emean is lower than 1, which in that case is set to zero. The adjusted Estd method implies that emissions will have lower relative background uncertainty when Estd<1.1. This might not benefit the data assimilation system for some dust sources where emissions can differ substantially from day to day, although we have not noticed examples where this is a problem.

The prior correction approach has two optional settings where the background Emean can reach a maximum or a minimum threshold. Under the framework of OSSEs, these background minimum and maximum values are known, since the background and the nature emissions can be compared. However, in reality these values can only be approximated using observations; for example, this can be done by using the ratio of background simulated observations to real observations. The majority of the experiments with the prior correction option use a minimum and a maximum threshold equal to 0.3 and 3.6, respectively, based on the AOD ratio of NAT to CTL. It is noted, however, that AOD is just one of the assimilated observations that constrains the emissions and that further work is needed in case background minimum and maximum settings are used in a data assimilation experiment with real observations. The effect of prior correction is tested by conducting two data assimilation experiments (with and without prior correction) that are presented in Appendix A.

Observing system simulation experiments (OSSEs) are data assimilation experiments in which synthetic observations are used that themselves are generated by a model. The synthetic observations of an OSSE can be modified to match the spatiotemporal coverage and observational uncertainty of any satellite sensor. Hence, with OSSEs it is possible to assess the potential impact of past, present, and future satellite missions on aerosol top-down emission estimation. The unique advantage of OSSEs is that the “truth” is perfectly known for all times, locations, and climate and aerosol components and can be used to evaluate the performance of an experiment.

There are three parts of an OSSE, (i) the nature run (NAT) that represents the “true” conditions of the aerosol state in the atmosphere, (ii) the control (CTL) run of the model, which sets the baseline performance of the model without data being assimilated, (iii) and the data assimilation run (DAS) where synthetic observations are assimilated in a model identical to the CTL model in order to improve aerosol emissions. The intercomparison of the differences between CTL and NAT and DAS and NAT can provide the added value of the assimilated observations, identify limitations of the data assimilation system, or quantify the role of some processes on the estimated emissions. The main goal of the present paper is to assess the ability of different satellite observations for quantifying aerosol emissions. Therefore, for all experiments we use the same physical model for the NAT, CTL, and DAS because otherwise we cannot attribute differences between NAT and DAS to either limitations of the satellite observations or model differences. We also perform some additional experiments with different nature runs (NAT_M, NAT_E) to assess different causes of uncertainty in emission estimation (e.g., biased meteorology) in addition to the standard nature run (NAT) and partially address the OSSE identical twin problem (Arnold and Dey, 1986; Timmermans et al., 2015). Note that the meteorology of all experiments is nudged to the ensemble mean of the 10 analysis members of ERA5 (Hersbach et al., 2020), except the nature run NAT_M (details below).

The standard nature run (NAT) only changes the emissions in comparison to CTL, by multiplying the default emissions of DU and SS by 0.5; the default emissions of OC and BC by 2; and the default emission of SO4, SO2, and DMS by 1.5. These emission factors are within the current range of uncertainty of aerosol emissions (discussed in Tsikerdekis et al., 2021a) and create a distinct difference in the global and regional distribution of AOD, AE, and SSA in comparison to CTL. These emission factors are chosen arbitrary, aiming to test if the data assimilation is able to estimate them correctly (test the system), rather than to reduce biases between NAT and a specific set of observations of an existing satellite (e.g., POLDER-3). Nevertheless the differences between CTL and POLDER and CTL and NAT exhibit similarities in the biomass burning region in the tropics and the global ME and MAE of these differences are on the same scale (not shown). The second nature run (NAT_M) uses the same altered emissions as NAT but its meteorology is nudged to reanalysis ERA-Interim. Consequently, the assimilated observations sampled from NAT_M can show the impact of biased meteorology on emission estimation. To investigate whether the scaling of emissions in NAT represents a too simple difference between nature and data assimilation run, a new nature run (NAT_E) was performed that changes emission parameterizations schemes for DU and SS and uses different emission inventories for the other species. This approach creates distinct spatiotemporal differences between the two runs in each species. An overview of all the NAT emission choices is depicted in Table 1.

The SPEXone spatial coverage at native resolution (∼ 5.4 × 4.6 km) was simulated using an orbit simulator for cloud-free pixels based on the MODIS cloud product. In our case, we would like for SPEXone spatial coverage to be consistent with ECHAM clouds; thus, we modified the SPEXone spatial coverage to match ECHAM cloud mask. The goal of this post-processing was to create an ECHAM cloud-based SPEXone mask that provided a similar amount of observations to that of the MODIS cloud-based SPEXone mask (more details are given in Appendix B).

An ideal sensor in terms of spatial coverage was assumed in order to test the data assimilation system and act as a benchmark for the SPEXone ability to estimate aerosol emissions. This sensor, hereafter referred to as SUPER, is able to retrieve AOD550, AE550–865, and SSA550 over the whole globe every 2 d. The 2 d global coverage was based on the step of the data assimilation set which estimates the emissions every 2 d. In addition, the SUPER sensor is able to get aerosol observations even over cloudy pixels and over very high latitudes.

The spatial coverage for a 2 d period for these two satellites is shown in Fig. 3. Note that SUPER has a fixed number of observations in time and space, while the number of SPEXone observations fluctuates in time and space depending on cloud cover and orbit characteristics. The total number of grid cell observations (each grid cell includes an AOD550, AE550–865, and SSA550 value) assimilated for the period 20 July to 20 September 2006​​​​​​​ is more than double in SUPER (139 872) compared to SPEXone (61 086). The observations we are using are super-observations, meaning that all the high-resolution SPEXone observations were aggregated to the model resolution (1.875∘ × 1.875∘). At the original resolution of SPEXone, our SUPER sensor would provide approximately 6 times the observations. Note that in that case these observations would be very closed together and highly spatially correlated. In addition, with super-observations the swath of SPEXone appears larger than 100 km, since only one high-resolution SPEXone resolution within each grid box is needed to provide a value for the whole grid box of a size 1.875∘ × 1.875∘ (∼ 250 km).

An instrument and retrieval simulator was used to generate estimates of observational errors. Retrievals for 4 individual days were used for this purpose. To be more specific, the estimated uncertainty is based on the difference between the retrieved and the true values, following a similar method to that of Tsikerdekis et al. (2021a). More details can be found in Appendix C. Note that these observational uncertainties were used for both satellites (SUPER and SPEXone).

All of the experiments span 2 months in the summer of 2006 (20 July to 20 September 2006). This year and period was chosen based on our previous work (Tsikerdekis et al., 2021a). Prior to this period the model was spun up for 3 months (1 April to 1 July 2006), and the ensemble background emissions were spun up for 20 d (1 July to 20 July 2006). We employ a grid resolution T63L31 (1.875∘ × 1.875∘ , with 31 hybrid-sigma vertical layers concentrated in the troposphere).

There are a few LETKS parameters that can be adjusted. In this study we keep these parameters fixed in all of our experiments. The description, discussion, and sensitivity experiments of these parameters (ensemble size, inflation local patch size, and the horizontal localization) was presented in our preceding study (Tsikerdekis et al., 2021a). The data assimilation ensemble size consists of 32 members. The local patch size and the horizontal localization are set to eight and four grid cells, respectively, while the inflation is set to 1. The inflation parameter is essentially deactivated with the value equal to 1, since under the emissions estimation setup of the data assimilation system the background uncertainty remains large enough throughout the experiment for the data assimilation to work. The local patch size is deliberately chosen to be high (8) in order to let observations that are far away from the source (up to 15∘) impact the emission estimation.

Table 2 shows the list of experiments related to SPEXone. The experiment where the assimilated observations are based on the SUPER spatiotemporal sampling is used mainly as a benchmark for the performance of the experiments that use the SPEXone sampling. The experiments where the assimilated observations use the SPEXone satellite coverage intend to evaluate the added value provided by the SPEXone instrument's ability to estimate emissions under different observational uncertainty and data assimilation options. Specifically, the experiment SPX used the default errors estimated for SPEXone retrievals (Appendix C). The experiment SPX_2U doubles the uncertainty of the assimilated observations, and SPX_2URE doubles the uncertainty and adds random errors (with standard deviation equal to the observational uncertainty) to the assimilated observations. Finally, SPX_W1 and SPX_W2 reduce the ΔTa length to 4 and 2 d respectively (from 6 d originally); hence, fewer observations are used to derive the analysis emissions in each assimilation cycle and only one and two assimilation cycles (instead of three) are used to calculate the analysis emission perturbations. Consequently, the data assimilation experiment is faster and less computationally expensive, but fewer observations are used to obtain the analysis emission.

Sensor SUPER is further used in other sensitivity experiments that aim to assess issues related to the nature run complexity and development of the data assimilation system (Table 3). The SUP0_M experiment points out the degradation in emission estimation purely due to biased wind by assimilating observation from NAT_M. SUP_E assimilates observation from NAT_E and shows that even under totally different emission schemes and emission inventories between the nature run and the data assimilation experiment, the emission errors are reduced.

The prior emissions may be overestimated or underestimated, and the smoother (+ prior correction) will take time to adjust them. The smoother's time window of 6 d suggests that correct estimation of emissions does not happen until a multiple of that number of days has passed. During this period, the smoother is adjusting to the major biases present in the CTL emissions. We define this period based on the results of our data assimilation experiment in order to exclude it from the evaluation that follows in Sect. 4.

Figure 4 shows that the differences between DAS and NAT (solid lines) reach a value close to zero after 26 d. From that point until the end of the experiment, these differences fluctuate around zero. For comparison the emission differences of CTL–NAT (dashed lines) are also shown. Note that the day-to-day dust and sea salt emission differences can fluctuate a lot in CTL, but SUP is able to estimate them adequately.

The duration of the initialization phase may be expected to be a multiple of the longest of two timescales: the aerosol lifetime (that determines how quickly aerosol are deposited) and the DA window (that determines how quickly we can adjust emissions based on observations).

This is shown in Fig. 5, where after approximately 26 d the differences in aerosol optical properties and column burden relative differences between DAS and NAT reach a value close to zero and start fluctuating around this value until the end of the assimilation experiment. Consequently, we choose the period of 26 d as the data assimilation initialization period, and only the remaining 36 d, spanning from 15 August 20 September 2006, are evaluated in Sect. 4. Note that the data assimilation initialization varies for each experiment depending on the amount of the assimilated observations, the differences with nature run, and the assimilation options used. Nevertheless, 26 d is sufficient as a data assimilation initialization period for all experiments (not shown) (except SUP_E for SS emissions in the coarse mode); thus, it is kept constant throughout the paper.

The ability to estimate the true aerosol state using SPEXone is compared to an experiment in which observations were assimilated based on a sensor like SPEXone (meaning that it can retrieve the same type of observations with the same accuracy) but with an almost perfect global coverage. In order to understand the simulated aerosol state for the examined period, the aerosol optical properties of the CTL experiment are shown and discussed in Fig. 6. High AOD is evident over Sahara and Arabian Peninsula mainly due to dust; over tropical forests (Amazon, Africa, Indonesia) mainly due to organic and black carbon; and over Europe, North America, and China mainly due to sulfates. AE is small over isolated ocean areas that are dominated by sea salt and shows high values over land, excluding desert areas where large dust particles prevail. High AAOD (low SSA) highlights high black carbon concentrations, either from natural (biomass burning) or anthropogenic (fossil fuel) sources, and intermediate values over high sources of dust. Note that SSA (not AAOD) is the quantity that is assimilated in our system (for details on the differences between SSA and AAOD assimilation, see Tsikerdekis et al., 2021a), but AAOD is shown in the plots since it is easier to interpret.

The ability of SPEXone and SUPER sensors to recreate the NAT are summarized in Fig. 7, where the differences between the experiments CTL, SUP, and SPX from NAT are depicted for AOD, AE, and AAOD. In both data assimilation experiments the modeled aerosol is improved when compared to the CTL experiment, and the global mean error (ME) and the global mean absolute error (MAE) are almost zero. The ME and MAE equations can be found in Appendix B of our preceding publication (Tsikerdekis et al., 2021a). The performance of SPX is as good as the SUP, which suggests that the spatial coverage of SPEXone is sufficient to constrain the emissions in a similar fashion to the SUPER satellite.

An important advantage of OSSEs is that we are able to evaluate the estimated emissions of the data assimilation experiments with the emissions of the nature run. Figures 8 and 9 depict the emission of aerosol species for NAT and the emission differences for CTL, SUP, and SPX from NAT. In both data assimilation experiments the estimated emissions are improved compared to the emissions of the CTL. The overestimated dust emissions in the CTL are constrained in the data assimilation experiments, and the ME is not close to zero only in the western part of the Sahara desert where emissions are high. For both data assimilation experiments the relative ME averaged for the same region is lower than 10 % (not shown). The overestimated sea salt emissions in CTL are constrained globally in both data assimilation experiments, though in SPX the sea salt emission over the Indian Ocean shows high ME with relative ME in some grid cells that exceeds 50 %. This is caused by the limited observations by SPEXone due to cloudiness over India and the surrounding seas (see Fig. B2). The ME and the relative ME emission for organic and black carbon over high sources, mainly over the tropics in South America, Africa, and Indonesia but also over eastern China, reach almost zero in the data assimilation experiments. Sulfates in the model are mainly produced from SO2 precursor emissions, and only a small fraction (2.5 %) of sulfates are directly emitted to the atmosphere. For all other species (DU, SS, OC and BC) the assimilated aerosol optical and microphysical observations directly constrain the emission of the particles that form these observations in the atmosphere. Despite that, the SO2 + SO4 emissions are constrained reasonably well, especially over high anthropogenic sources (North America, Europe, India, and China), where the relative ME per grid cell does not exceed 10 % (not shown) in both data assimilation experiments. These results suggest that SPEXone limited observational coverage can estimate global aerosol emission in a similar manner to a sensor that would have an almost perfect observational coverage. However, it is noted that local error due to cloudiness deteriorates the performance of SPEXone in comparison to SUPER. Further, we assume that the 1.875∘ aggregate of SPEXone contains a non-significant representation error and that the observations of both sensors are unbiased.

A series of data assimilation experiments were conducted in order to explore less optimistic (SPX_2U) scenarios for the SPEXone retrievals and also to check what the effect is of adding actual noise to the observations (SPX_2URE) instead of relying purely on the uncertainty descriptions of the measurements. Further, we vary the ΔTa length (SPX_W1, SPX_W2) of the data assimilation system. The differences of these two data assimilation experiments from NAT for AOD, AE, and AAOD are depicted in Fig. 10. In all cases the observations improve compared to the CTL experiment (Fig. 7a–c), although not to the extent of the default experiment SPX, which was discussed in the previous subsection (Fig. 7g–i).

Specifically, SPX_2U, where the assimilated observation uncertainty was doubled, shows similar results for AOD and AE, whereas the AAOD bias is increased slightly in comparison to SPX (Fig. 10a–c). SPX_2URE, where the assimilated observations uncertainty was doubled and random errors (with standard deviation equal to the observational uncertainty) were added to the assimilated observations, the bias increases over northeastern China for AOD, over the Sahara, Arabian Peninsula, and northern Indian ocean for AE, and over tropical Africa and the Amazon basin for AAOD (Fig. 10d–f). We can quantify the effect of an observation's random error on emission estimations by comparing the experiments SPX_2U and SPX_2URE. The data assimilation performance does not degrade significantly when taking into account random errors in the assimilated observations. Specifically the dust emission global MAE increases by 5 percentage points due to random errors, while for other species the increase is even lower (Fig. 13).

SPX_W1 and SPX_W2 reduce the ΔTa length to 4 and 2 d (from 6); hence, fewer observations are used to derive the analysis emissions in each assimilation cycle, and only one and two assimilation cycles (instead of three) are used to calculate the analysis emission perturbations. The results reveal that ΔTa=4 d (SPX_W1) is sufficient to constrain the AOD, AE, and AAOD in a similar manner to ΔTa=6 d (SPX) (Fig. 11a, b, c). In other words, under the current experimental setup, observations 5 to 6 d after the emissions probably hold very little information for the correction of these emissions, and their exclusion has a very limited impact on the data assimilation performance. In contrast, the experiment SPX_W2 shows a degradation in performance over the western Sahara and northern Atlantic for AOD and AE (Fig. 11d, e, f), indicating that observations during the subsequent days 3 and 4 hold useful information for the correct estimation of emissions at day 1 and 2, as will be discussed below. Note that SPX_W1 and SPX_W2 need ∼ 33 % and ∼ 66 % fewer computational resources than SPX, respectively, since the background step in each assimilation cycle is shorter.

Figure 12 shows the mean and standard deviation of errors per grid cell. These errors are averages for the evaluation period of the difference between an experiment (CTL or DAS) and NAT. Both SUP and SPX errors are significantly smaller than CTL in both global (mean) and local errors (spread). The global AOD MAE of SPX_2U and SPEX_2URE remains very low, while AE and AAOD global ME slightly increase. Note that SPEXone AOD uncertainty range (Appendix C) is very low (lower than 10 % over ocean and 15 % on average over land), and doubling this uncertainty only has a limited effect on the analysis. On the other hand, the uncertainty in AE and SSA observations is higher than AOD; hence, the data assimilation performance is affected to a larger extent. Overall, it can be concluded that in these less optimistic assessments (doubled uncertainty), the assimilated observations based on SPEXone spatial coverage are still able to estimate the emissions with reasonable accuracy. Further, the experiment where actual noise is added to the measurements shows similar results to the experiment where no noise was added. This illustrates that the system is not “overfitting” the observations but takes the specified uncertainty correctly into account even when there is no noise added to the measurements.

In terms of estimated emissions, the four sensitivity experiments rank a bit lower in comparison to both SUP and SPX, as indicated in Fig. 13, where the global relative MAE for various species is shown. Specifically, SPX has similar emission errors to SUP but differs in the SS-estimated emission, which is caused by the limited observations in SPEXone due to cloudiness over India and surrounding seas (see Fig. B2), as discussed in the previous subsection. SPX_2U and SPX_2URE emission biases for all species are increased by no more than 10 percentage points in comparison to SPX, which indicates that increased (double) uncertainty and adding random errors in the observations has a small but noticeable negative effect on the global relative differences in the emissions. Finally, SPX_W1 emission bias increases by no more than 6 percentage points in comparison to SPX in all species. However, dust emission error grows to 54 % in SPX_W2 from 17 % in SPX_W1, indicating that the information content of observations 3 and 4 d after the emissions is very rich and should be used to correct these emissions, especially for Saharan dust plumes that extend over the Atlantic Ocean and last for several days. The emissions of OC, BC, and SO2 + SO4 are estimated very accurately by all of the data assimilation experiments, with relative MAE ranging from 0 % to 5 %, which indicates that, in terms of the global mean emission estimation, these emissions are unaffected by the sensor spatial coverages and observational uncertainty increases that were tested. The global maps of emission differences from NAT for the four sensitivity experiments of these subsection are shown in Fig. S1.

OSSEs also allow us to quantify the uncertainty due to assumptions in nudging meteorology or emission source locations. The first relates to the assumption that the meteorological parts of the model and specifically the wind components (U and V) are perfect. The second factor relates to complex spatiotemporal change of aerosol emission in the nature run compare to the data assimilation run and test if the system is able to estimate the correct emissions when the data assimilation and nature runs emissions differ by more than just an emission factor (per species) that is constant in time and space.