Estimating aerosol emission from SPEXone on the NASA PACE mission using an ensemble Kalman Smoother: Observing System Simulation Experiments (OSSEs)

. We present a top-down approach for aerosol emission estimation from SPEXone polarimetric retrievals related to the aerosol amount, size, and absorption using a fixed-lag ensemble Kalman smoother (LETKS) in combination with the ECHAM-HAM model. We assess the system by performing Observing System Simulation Experiments (OSSEs), in order to 10 evaluate the ability of the future multi-angle polarimeter instrument, SPEXone, as well as a satellite with near perfect global coverage. In our OSSEs, the Nature Run (NAT) is a simulation by the global climate aerosol model ECHAM-HAM with altered aerosol emissions. The Control (CTL) and the data assimilation (DAS) experiments are composed of an ensemble of ECHAM-HAM simulations, where the default aerosol emissions are perturbed with factors taken from a Gaussian distribution. Synthetic observations, specifically Aerosol Optical Depth at 550nm (AOD 550 ), Angstrom Exponent from 550nm to 865nm 15 (AE 550-865 ) and Single Scattering Albedo at 550nm (SSA 550 ) are assimilated in order to estimate the aerosol emission fluxes of desert dust (DU), sea salt (SS), organic carbon (OC), black carbon (BC) and sulphate (SO 4 ), along with the emission fluxes of two SO 4 precursor gases (SO 2 , DMS). The prior emission global relative Mean Absolute Error (MAE) before the assimilation ranges from 33% to 117%. Depending on the species, the assimilated observations sampled using the satellite with near perfect global coverage, reduce this error to equal to or lower than 5%. Despite its limited coverage, the SPEXone

If I am not mistaken, the figures presenting the spatial distribution of the differences between the examined experiments present also as "mean" the mean difference (?) globally. Such an approach might result in masking of the error when positive and negative differences appear with similar frequency. I suggest also presenting the global mean of the absolute differences in order to have a more realistic overview of the differences between the experiments. Moreover, I suggest defining (in the text) the metrics used in the study (maybe as Appendix?). Indeed the global mean error (ME) may end up very close to zero with regional positive and negative error that cancel themselves out (e.g. Fig 7a). Therefore, we have added along with the ME, the mean absolute error (MAE) in all global maps that depict differences, specifically Figure  The NAT experiment represents the synthetic observations used for the assimilation. Do the authors have an estimate on how the NAT spatial variance is compared with that of the real observations? How does the comparison between the two might affect the improvement of emissions estimation? This is something that needs to be discussed in the text. Thank you for this comment. Although these nature runs were created in order to test the data assimilation system capabilities and do not aim to represent the exact differences with a specific observational dataset (as indicated in subsection 3.3), it is interesting to test if the differences between CTL minus nature runs captures some of the general patterns of the differences between CTL minus an observational dataset. As an observational point of reference for this analysis we use retrievals from POLDER, since it could provide the same variables with SPEXone. We compare the difference between (i) CTL -POLDER, (ii) CTL -NAT (collocated over POLDER) and CTL -NAT_E (collocated over POLDER). We don't show the differences CTL -NAT_M, since they are pretty similar with the differences CTL -NAT. The AOD underestimation over the biomass burning sources of Africa and South America as well as the overestimation over isolated ocean regions observed in CTL -POLDER is well represented in CTL -NAT. Further the AE global overestimation and AAOD overestimation over South America observed in CTL -POLDER is captured by CTL -NAT_E. Independent of the sign of the differences, ME and MAE for the POLDER differences and the two nature run differences is comparable for all variables. Thus, this makes the nature runs of this work a fairly good proxy to represent some of the patterns illustrated in CTL -POLDER differences. Further the differences of CTL -NAT and CTL -NAT_E are contrasting in each of the variables, making them an ideal combination to test the emission estimation system under diverse scenarios. Further we have added the underlined sentence in main manuscript on subsection 3.3. "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 -POLDER and CTL -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)."

Minor Comments
P2, L33 and where applicable: I suggest using the Oxford comma as "size, and absorption with..". Thank you for your suggestion. The lack of Oxford comma is consistent throughout the manuscript. Since this is a matter of preference according to the guidelines of GMD (as long as is consistent), we kept it as it is. P4, L106 and where applicable: Add space before nm in 700nm. Added.
P4, L107. Multiple sentences here starting with SPEXone. Please rephrase Thank you for noting it. We have rephrased the three sentences. P5, L139: taken into account -> are also taken into account Corrected. P11, L330: I suggest replacing the first sentence with " Figure 4 shows that the differences between DAS and NAT (solid lines) reach a value close to zero after 26 days." In this case you can delete " (Figure 4)" in the nest sentence. Changed as suggested.
P12, L357: "nature run" Please use the abbreviations (NAT here) throughout the manuscript Corrected.
P12, L386: from NAT -> from NAT for AOD, AE, and AAOD. Corrected. Figure 2: Maybe replace purple with green to better distinguish from blue. Changed purple with dark yellow. The green and red combination is bad for people with the most common color deficiency (deuteranopia).   Corrected the colors in the plot and made the boxes thicker. Also added the following in caption: "In subplot (d), blue and red boxes highlight regions where dust emissions are overestimated and underestimated respectively in CTL compare to NAT_E. In the first case the data assimilation can modify the emissions and correct the overestimation, while in the second case it cannot (details in the subsection 4.3.2)." Figure A 1: There seem to be some color shade areas in the scatter plot. Please indicate in the caption what they stand for. Thank you for noting this. We added on the caption: "The shaded areas represents the 2D kernel density estimation for each experiment."