the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 May 2026
Solid-particle stratospheric aerosol injection: a 2-D modeling exploration of the design space
Abstract. Solid-particle alternatives to sulfate for stratospheric aerosol injection (SAI) span a broad parameter space: particle composition and morphology, sensitivities to agglomerate microphysics, and injection strategies in latitude, altitude, and season. Spanning this space with three-dimensional chemistry--climate models is practically prohibitive. To enable such sweeps, we present a two-dimensional (2-D) zonal-mean modeling framework for SAI with solid-particle materials. ERA5-constrained stratospheric transport is coupled with explicit aerosol microphysics and a modified RRTMG radiative transfer scheme, with each component extensively validated. Focusing on silica and calcite, we use the framework to explore SAI performance across two complementary axes: material properties together with monomer and agglomerate microphysics, and injection strategies in space and time. Tropical injection maximizes radiative forcing efficacy but pays the largest in-layer heating penalty. Coagulation in the tropical confinement amplifies aggregate diameters and partially offsets the residence-time advantage. A seasonal schedule (alternating-summer-hemisphere) delivers a modest 10-20% mid-latitude gain in radiative forcing efficacy over symmetric injection, but at a comparable mid-latitude heating-cost penalty. For IR-absorbing materials such as silica, symmetric mid-latitude injection reduces stratospheric heating with limited loss of efficacy; calcite's negligible IR absorption keeps the heating penalty an order of magnitude lower across all injection strategies considered.
Competing interests: The first three authors are affiliated with Stardust Labs Ltd., a sunlight reflection technology development company. Brian E. J. Rose is advising Stardust Labs Ltd.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-2772', Ben Kravitz, 28 May 2026
- AC1: 'Reply on RC1', Yoav Lederer, 08 Jul 2026
- RC2: 'Comment on egusphere-2026-2772', Sandro Vattioni, 12 Jun 2026
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RC3: 'Comment on egusphere-2026-2772', Anonymous Referee #3, 13 Jul 2026
Summary
This manuscript presents a 2D modeling framework with explicit transport, microphysics, and radiation process representations. It is primarily designed to allow computationally feasible simulations of ensembles of solid particle SAI scenarios that are systematically varied over a parameter space encompassing injection scheme, particle size, particle material (refractive index), and fractal geometry of coagulation agglomerates.
Overall Assessment
The paper's scientific merit is high, and it makes a novel contribution to the literature.
The paper is suitable for publication in principle.
The major improvements required before publication are improvement of citations, clarification of some methodological points, addition of some caveats regarding some findings, and making the Zenodo depository described in the Data and Code Availability fully populated and live by the time of publication.
The paper is in the category of minor revisions before publication.
Major comments:
Transport
The transport in the model is driven by a climatology for the residual circulation obtained from ERA5 reanalysis (averaged over 2008 – 2017) plus mixing represented by a diagonal diffusion tensor. This averaging period averages out the QBO influence on transport, which could have implications for the fidelity of some injection schemes (see below). Regarding the diagonal diffusion tensor approximation, it is worth noting that the Chemical Lagrangian Model of the Stratosphere (CLaMS) has demonstrated that mixing and residual circulation have a comparable contribution to age of air (Ploeger et al. GRL 2015). This finding seems to raise a question regarding how well a diagonal approximation for the diffusion tensor might represent age of air. For this reason, it seems prudent to move the material regarding the diagonal approximation to the main narrative from the appendix and cite the CLaMS finding.
Aerosol Microphysics
The model uses a discrete monomer number bin scheme with power of two bins 1, 2, 4, 8, 16, 32, 64, and 128 monomers. The DDA computations to validate the volume equivalent sphere Mie approximation are rigorous, but are limited in the sense that they cover only N ≤ 5 monomers. Since this only applies to 3 of the model's 8 bins, an appropriate qualification regarding the validation of the aerosol optics should be added, or a validation for the larger aggregates should be included (likely as Supplementary Information). This is relevant because of the potential for the five larger bins (N = 8 to 128) to carry a more substantial fraction of the aerosol mass burden. For example, Figs. 6 and 8 suggest the formation of larger aggregates in high-injection-rate tropical scenarios.
Radiation Scheme and Validation
The radiation scheme uses an unmodified version of the RRTMG_LW two-stream approximation and introduces a SZA-dependent value for an optically thin-layer backscatter coefficient into the off-the-shelf RRTMG_SW solver. The assumption of optically thin layers holds well for the scenarios considered, but the dependence of this approximation on layer optical thickness should be moved to the main narrative from appendix B.
The validation of the radiative transfer scheme relies on the utilization of MODTRAN6, which is capable of high spectral resolution radiative transfer calculations as well as multi-stream representations of the polar angle radiation field. The details regarding spectral resolution and radiative transfer solver should be added to the manuscript. In particular, the meaning of using 64 moments is unclear if a multi-stream solver is not used. Boucher JAS (1998) and King (1983) should be cited regarding the phase function and number moments.
An additional point about the Modtran validation: the authors do not validate the LW heating rate profile using Modtran. This is a lost opportunity because, as Figure B1 shows, there is a large amount of spectral structure in the aerosol longwave absorption efficiencies that is averaged out in the RRTMG_LW bands. One of the paper’s main diagnostics, the stratospheric heating metric η_heating, has a potentially sensitive dependence on band-averaging, as in Sokolik et al. 1998 (JGR) for aerosols and Toon et al. (1989) for clouds. The authors note a Modtran LW heating rate profile comparison will be provided in future work. For now a qualification due to the unquantified uncertainty in η_heating would be welcome.
Results about Injection Scheme Design and Interpretation
As noted above, the transport scheme uses a climatology which averages over a decade of QBO cycles. Since the climatological averaging doesn’t capture the systematic differences in transport between hemispheres, the impact of the displacement of the NH and SH injection windows in the alternating-summer-hemisphere seasonal strategy relative to the QBO cycle is lost. Because of this, the statements in Sections 4.1.4 and 4.2 regarding the relative performance of seasonal versus symmetric injection should be qualified accordingly.
Relationship to Prior and Concurrent Literature
Recent observational work by Lyu et al. 2026 (Science) identifies the ubiquity of a small stratospheric aerosol mode with significant organic content. This new work identifies a number of significant interactions between this new mode and hypothetical SAI deployments, and is largely sulfur-centric. However, for the purposes of the authors' work, the small mode provides an additional coagulation target that would alter the effective aggregate size distribution of injected particles. For this reason Lyu et al. should be cited and its implications for the present work discussed.
Figures
Figure 1: what is the meaning of the gray shading in this figure? Please add to the caption.
Figure 2: the dimer mass fraction in Weisenstein appears to be ~0.2 to 0.25, compared to the author's ~0.05 to 0.1. This is a large relative difference and should be qualified as something less than "close agreement."
Figure 6: the third panel would more logically be tau_coagulation / tau_{no coagulation}. The effective diameter panel is suggestive as a process description but doesn't completely capture the coagulation effect's magnitude and belongs in SI.
Figure 9: While the meaning of this figure is clear, the collapse of spatial and seasonal structure into a globally- and annually-averaged TOA value hinders comparison with other work in the field. This spatial and temporal averaging makes sense for figures 11 and 12, which focus on how different injection times and locations cause well-defined scalar diagnostics to vary. However, for the purposes of understanding differences in spatio-temporal variability with analysis of other injection schemes, these figures should be modified to visualize the space and time variability in SARF for some injection scheme end-members that bookend the variation with the parameter ensemble.
Figure 13: a qualification regarding the symmetric and seasonal injection protocols producing similar profiles should be added. This is because the similar profiles are potentially a product of the model's averaged QBO transport climatology, and profiles produced under real-world QBO conditions may not be as similar. To be clear, this is to support clear conceptual interpretation of the result, not its suitability for operational SAI.References
The following citations are referenced in this review but are absent from the manuscript's reference list. The authors should consider adding them where indicated in the major comments above.Boucher, O.: On aerosol direct shortwave forcing and the Henyey-Greenstein phase function, Journal of the Atmospheric Sciences, 55, 128–134, https://doi.org/10.1175/1520-0469(1998)055<0128:OADSFA>2.0.CO;2, 1998.
King, M. D.: Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres, Journal of Quantitative Spectroscopy and Radiative Transfer, 30, 143–161, https://doi.org/10.1016/0022-4073(83)90090-2, 1983.
Lyu, M., Ahern, A. T., Schill, G. P., Lawler, M. J., Murphy, D. M., Taylor, S. J., Fodel, A., Abou-Ghanem, M., Gurganus, C., Zhu, Y., Tilmes, S., Ray, E., Thornberry, T. D., Gao, R.-S., Hintsa, E. J., Moore, F., Dutton, G., Nance, D., Hall, B., Rollins, A. W., Waxman, E. M., Zuraski, K., Diskin, G. S., Choi, Y., Pierce, R. B., Weinzierl, B., Kuderna, F., Dollner, M., Jensen, E., and Brock, C. A.: An unrecognized mode of small particles in the lower stratosphere, Science, 392, eadw8939, https://doi.org/10.1126/science.adw8939, 2026.
Ploeger, F., Abalos, M., Birner, T., Konopka, P., Legras, B., Müller, R., and Riese, M.: Quantifying the effects of mixing and residual circulation on trends of stratospheric mean age of air, Geophysical Research Letters, 42, 2047–2054, https://doi.org/10.1002/2014GL062927, 2015.
Sokolik, I. N., Toon, O. B., and Bergstrom, R. W.: Modeling the radiative characteristics of airborne mineral aerosols at infrared wavelengths, Journal of Geophysical Research: Atmospheres, 103, 8813–8826, https://doi.org/10.1029/98JD00049, 1998.
Citation: https://doi.org/10.5194/egusphere-2026-2772-RC3
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I will admit that I do not think highly of Stardust. I have moral qualms with the way they operate, and I think their conduct is inconsistent with the norms I value in the scientific research community. The currency of academic research is an honest search for how the world works, and I perceive an effort to use community-based legitimacy in support of Stardust’s broader goals. I do not expect the authors to respond to this comment, nor am I particularly interested in a response to it.
Having gotten that off my chest, as a reviewer, it is my job to assess the quality of the manuscript objectively. And my honest assessment is that, while I think there are some things in here that are interesting, ultimately this paper is just that – a collection of things. A few of those things are novel, but most are not. A few of those things are relevant to studying SAI, and many are not. A few of them cite the now ample literature, and a shocking number of them do not. A few of them are related to what I can ascertain as a potential main point of the article, but most are tangential. As such, I am recommending rejection of the article.
General comments:
1. The authors have come up with a new modeling framework, but I’m not entirely sure why. The model has an assumed climate sensitivity and no feedbacks of aerosol heating onto circulation or stratospheric water vapor, so it’s not useful for understanding climate in any capacity. (Relatedly, I don’t know why Table 1 is in the paper, considering it omits the single largest potential effect on your performance metric.) There is no mention of chemistry, although given the authors’ assertions about chemical effects on the aerosols (more on that later) I’m not sure I would trust the model to do chemistry well anyway. The active parts of the model appear to be aerosol-radiation interactions, coagulation, and sedimentation. And there’s no wet deposition, plus there’s no reliable measure of deposition locations anyway (it’s a 2-D model), so I can’t say that sedimentation is an important aspect here either. So we are left with a parameter sweep of aerosol scattering, where the most important parameter is the aerosol size distribution. (Actually a chain/agglomerate, where the agglomeration rate can change depending on atmospheric conditions or transport, but since they translate that back into equivalent Mie scattering, it’s essentially size.) Plus some window dressing of some other parameters that aren’t actually being tested because the model isn’t well suited to do so. I am calling transport window dressing, because if you look at what the model is actually capable of testing, the effect of transport is just to modify the coagulation rate, so again, size distribution. But you’re not testing this, because on lines 267-268 you’re assuming the optimal size distribution. So even then I’m confused about what you’re actually testing.
I’ll note that the fact that the coagulation model is just a means of getting to transport actually works in the authors’ favor, because the results in Figure 2 are, contrary to the authors’ description, not great until you get to very agglomerated particles (which are heavy and fall out quickly, so probably not nearly as relevant as the particles with fewer monomers). The radiation model for that parameter sweep is RRTMG, which is pretty good for GCM-scale modeling, but there are better ones if you’re testing scattering of a size distribution. Put simply, this is not an appropriate tool for what the authors are actually doing. I suppose doing this parameter sweep for silica-coated calcite aerosols hasn’t been done before, but that leads me to my next point.
2. The authors state, without evidence, that the particles are non-reactive in the stratosphere. Given what is known about stratospheric chemistry, it seems highly likely that the silica coating would simply chemically erode away, leaving hygroscopic calcite aerosols, which (according to several reputable studies by Dai et al. and Vattioni et al.) would likely get coated very quickly with background sulfate. The authors’ claim that the particles would remain non-reactive is, in my opinion, extraordinary and thus requires extraordinary evidence. And without this evidence, the authors’ parameter sweep is invalid because they’re exploring the wrong aerosol.
3. Let’s assume that the particle are pure silica. That leads me to another big problem, which is the authors’ claim about the aerosols’ “bio-compatibility”. Breathing silica is deadly – I invite the authors to read about silicosis. The authors don’t mention this anywhere in their paper, which is in my opinion a terrible oversight, considering it could make this idea a complete non-starter. More realistically, silica deposition should be quantified, but the authors have a 2-D model that cannot handle deposition adequately. Although there may not be reason that the deposition of these studies would be any different from what is reported in other studies.
4. The emphasis on radiative forcing in the paper (the bulk of Section 2.4) seems odd. The efficiency of injection is not well quantified by this model and it’s not clear the authors are using the right aerosol anyway (see point 2 above). Also, line 27 about “larger achievable radiative forcings” has no basis. One can easily get higher radiative forcings with more sulfate injection, and there is both modeling and observational evidence. I feel like most of this discussion is tangential and misguided.
5. Section 3.2 doesn’t seem particularly useful, considering other models that have more advanced capabilities have already done this work and have been doing so for about 10 years. I’m surprised to not see any citations about the relationship between injection location and residence time (e.g., Tilmes et al., Richter et al.).
6. I don’t know why the authors aren’t doing any comparisons with sulfate SAI studies. Surely it would be useful to point out that your aerosol distributions as a function of latitude of injection are similar to those, and if not, you have a mechanism as to why? In fact, the authors have not cited over ten years of literature about design in SAI, even though they specifically mention design parameters.
7. I do think the idea of ERA-derived transport in a zonal model is interesting. That strikes me as a sort of data assimilation mode of ISCA, which could be an interesting capability to add to that model. The validation of those aspects (Sections 2.1 and 3.1) are promising.
I’m not going to include any specific comments because I don’t think this paper is salvageable in its present form.