Geoengineering, also referred to as climate engineering, encompasses specific techniques and methods that have been proposed to mitigate the consequences of climate change e.g.,. Stratospheric aerosol injections (SAI), i.e the injection of, for example, sulphur dioxide into the stratosphere, are one idea in the field of solar radiation management (SRM) to mitigate the effects of global warming . Other ideas include the injection of sulphuric acid (H2SO4) e.g., or carbonyl sulphide (COS) e.g., as well as solid materials such as alumina (Al2O3) or calcite (Ca3CO3), as these particles absorb less terrestrial infrared radiation e.g.,.

Possible future SAI applications above a certain size can probably be observed with satellite occultation instruments. The SAGE III/ISS instrument (Stratospheric Aerosol and Gas Experiment III), mounted on the International Space Station (ISS) is a currently active satellite solar occultation instrument, which measures the attenuation of the solar radiation due to scattering and absorption of atmospheric components such as aerosols, ozone, nitrogen dioxide and water vapour. SAGE III/ISS observes around 15 sunrises and 15 sunsets in 24 h and covers a possible latitude range between 70° S and 70° N . The instrument has nine spectral channels with aerosols as target species. These specific wavelengths are 384, 448, 520, 601, 676, 755, 869, 1021, and 1543 nm .

A previous study showed that it is possible to detect stratospheric aerosols formed from continuous emissions of 1 and 2 TgSyr-1 in the quasi-steady-state phase from the perspective of a typical satellite solar occultation instrument, taking into account the natural variability . However, 1 and 2 TgSyr-1 are comparatively small emission rates in the context of possible SAI applications. Depending on the progression of climate change and increasing damage and costs, as well as future goals regarding the reduction of the global mean surface temperature of the Earth, large-scale SAI applications (here defined as injection rates >10 TgSyr-1) might be considered.

A problem that was already highlighted by the eruption of Mt. Pinatubo in June 1991, which injected about 20 TgSO2 into the stratosphere, was the occurrence of measurement gaps in areas with high aerosol loadings e.g., due to the resulting low transmission (“zero transmission problem”) from the perspective of a satellite solar occultation instrument. This refers to the transmission of the radiation from the Sun through the atmosphere to the instrument. The corresponding aerosol plume caused so much extinction of the solar signal that no retrievals were possible e.g.,. The SAGE II dataset shows gaps in aerosol measurements for the period June–August 1991 in the region 15° S to 20° N below 22 km e.g.,, and during the first year after the eruption, the instrument only provided measurements above ≈ 23 km altitude at wavelengths of 1020 nm and shorter e.g.,. It should be noted, however, that the eruption of Mt. Pinatubo serves as a natural analogue here, but does not represent continuous emissions. Continuous emissions lead to much lower injection amounts per time compared to a volcanic eruption with the same amount injected. Notably, the relationship between injected sulphur dioxide mass and the resulting stratospheric aerosol burden is non-linear due to aerosol microphysical processes e.g.,.

The aim of this study is to investigate the so-called zero transmission problem using MAECHAM5-HAM simulations and the SCIATRAN radiative transfer model. More specifically, the question is which wavelengths, depending on the latitude, are necessary for a physically meaningful stratospheric aerosol extinction profile retrieval result, assuming continuous tropical emissions of 30 TgSyr-1 (radiative forcing of about -4 Wm-2, ), i.e. hypothetical large-scale SAI deployments. In this context, “physically meaningful” means that not only a retrieval result exists, but that it is also close to the true profile (i.e. based on the MAECHAM5-HAM simulation).

For achieving this, MAECHAM5-HAM simulations for the SRM scenario of 30 TgSyr-1 were used. This injection rate is analysed as a deliberately high, upper-end SAI scenario to probe the zero-transmission problem under conditions where radiative forcing effects are most pronounced. Although it appears to be a comparatively high emission rate, the upper limit in the context of possible SAI applications depends, for instance, on the specific goal, such as specific radiative forcing effects.

The simulations provided vertical profiles of aerosol extinction coefficients at different wavelengths for an altitude range of 10–27 km. The aerosol extinction coefficient profiles were used for the transmission calculations with SCIATRAN from the perspective of a typical solar occultation instrument, which were then used for the aerosol extinction profile retrievals using SCIATRAN. Although the following study analyses the zero transmission problem for a typical satellite solar occultation instrument like SAGE III/ISS, the SAGE retrieval algorithm was not used.

The paper is structured as follows. Section 2 provides an overview of the relevant methods, such as MAECHAM5-HAM and SCIATRAN. Section 3 presents the results, followed by the discussion and conclusions.

Figure  shows aerosol extinction coefficients at 550 nm (1/km) for January (Jan) based on the MAECHAM5-HAM simulations for the continuous injection of 30 TgSyr-1 (upper panel) and the corresponding aerosol optical depth (AOD) at 550 nm (lower panel) in the quasi steady-state phase.

The maximum in AOD near the Equator (lower panel of Fig. ) is due to the continuous injection of 30 TgSyr-1 in this region (compare Sect. 2.1). Figure , i.e. the latitude dependence of the aerosol extinction coefficients and the corresponding AOD, highlights the fact that the minimum wavelength required to obtain a physically plausible retrieval result depends on the specific latitude. Note that this depends not only on the AOD but also on the vertical profile of the aerosol extinction coefficients. Nevertheless, the AOD (550 nm) for the corresponding latitudes is given in the following for better contextualisation.

Figure a shows as an example the aerosol extinction profile retrieval result for 5° N if performed for a wavelength of 520 nm. With the retrieved aerosol extinction profile in blue, the apriori profile in black and the true profile (MAECHAM5-HAM simulation result) in orange. Figure b shows the averaging kernels resulting from the retrieval of the aerosol extinction profile at 520 nm and 5° N (blue line in panel a).

As expected, the retrieved aerosol extinction profile (blue line in Fig. a) shows below ≈ 17 km a behaviour similar to the apriori profile (black line in Fig. a), above ≈ 25 km a good agreement with the true profile (orange line in Fig. a), and in between oscillations of the profile. Overall, the retrieved aerosol extinction profile is not in good agreement with the true profile. Consistent with these findings, the averaging kernels (Fig. b) show very small values close to zero below about 24 km. At these altitudes, the retrieval exhibits little to no sensitivity to the measurement. The lack of good agreement can be attributed to the high AOD (0.45 at 550 nm) near the latitude of the injection, resulting in high aerosol extinction and low transmission from the perspective of the satellite solar occultation instrument.

Figure  illustrates, on the one hand, the correspondingly low transmission values from the perspective of a typical solar occultation instrument, which are ≈ 10⁻¹⁴ at a minimum (TH=18 km), based on the true vertical profile of the aerosol extinction coefficients at 520 nm and 5° N (orange line in Fig. a). On the other hand, it highlights the poor agreement between the retrieved and true profile. The black line in Fig. a represents the true transmission values (Ttrue) based on the true aerosol extinction profile (MAECHAM5-HAM simulation), and the blue line the transmission values based on the retrieved aerosol extinction profile (Tsim). Figure b illustrates the corresponding relative residuals (Ttrue-Tsim/Ttrue) of the transmission values in %. Consistent with expectations and the averaging kernels (Fig. b) the minimum transmission values of ≈ 10⁻¹⁴ fall below the detection threshold where measurement noise dominates the signal, preventing the retrieval algorithm from extracting meaningful information about the vertical profile of aerosol extinction coefficients.

In summary, a wavelength of 520 nm is not sufficient for the aerosol extinction coefficient retrieval at 5° N. Figure  provides an overview of the retrieval results, i.e. the retrieved aerosol extinction profiles, when the corresponding retrieval for 5° N is performed at 520 nm (same as Fig. a) and at additional larger wavelengths of 1543 nm (b), 1800 nm (c) and 1900 nm (d). Note that the wavelengths of 520 and 1543 nm were chosen as these are two of the wavelengths at which the currently active satellite solar occultation instrument SAGE III/ISS, targets aerosols. 1543 nm is the largest of these wavelengths targeting aerosols .

Figure a–d of clearly show that with increasing wavelength, the retrieved aerosol extinction profile gets closer to the true profile with the best agreement at 1900 nm (especially at the maximum, compared to 1800 nm). The improved retrieval performance reflects the principle that aerosol extinction decreases with increasing wavelength, confirming the generally accepted idea that, in the case of very high emissions, the appropriate approach is to use longer wavelengths for aerosol measurements.

This means that, under the assumptions made here, a wavelength of at least 1900 nm is required for the aerosol extinction profile retrieval at 5° N (AOD≈0.45 at 550 nm). Panel (d) also shows the retrieved profile including the total errors (blue dashed lines), as described in Sect. 2.3.

Corroborating this finding, Fig. b presents a maximum value of the relative residuals between the true (based on the true aerosol extinction profile (MAECHAM5-HAM simulation)) and simulated (based on the retrieved aerosol extinction profile) transmission values of 1.4 % (TH=22 km). The transmission at the minimum still remains on the order of about 10-6–10-5, while the transmission values at the other tangent heights stay within ranges that allow useful measurement information to be retrieved from these heights, leading to the improved retrieval performance. This is also consistently shown in the corresponding line-of-sight (LOS) optical depth (Fig. g).

Although 520 nm is not sufficient for the aerosol extinction profile retrieval at 5° N, a different conclusion can be drawn for 75° S (AOD≈0.35 at 550 nm) (Fig. a) and 75° N (AOD≈0.24 at 550 nm) (Fig. b). The blue dashed lines show the corresponding total errors (compare Sect. 2.3).

In addition, Fig.  shows a comparison of the transmission values at 520 nm (a) and the corresponding relative residuals (b) for 75° N. The comparison for 75° S can be found in the appendix (Fig. ). The relative residuals show the highest value of more than 100 % at TH=12 km, which then decrease to less than 1 % (Fig. b). The pronounced increase in relative residuals at 12 km is primarily related to the very low transmission value at this tangent height (Fig. a) and the corresponding high line-of-sight (LOS) optical depth (Fig. a). Since the residuals are expressed relative to the true transmission, small absolute differences between true and simulated transmission values translate into comparatively large percentage deviations when the transmission approaches its minimum. In addition, this altitude range corresponds to the lower flank of the aerosol extinction profile (Fig. b), where extinction values are still significant but decrease rapidly with decreasing altitude and deviations between retrieved and true aerosol extinction coefficients become more pronounced.

The reduced aerosol loading at these latitudes allows shorter wavelengths to maintain sufficient transmission from the perspective of the solar occultation instrument for the aerosol extinction profile retrieval.

This means that, under the assumptions made here, a wavelength of at least 520 nm is required for the aerosol extinction profile retrieval for 75° S (AOD≈0.35 at 550 nm) and 75° N (AOD≈0.24 at 550 nm).

In contrast, Fig.  illustrates the retrieved vertical profiles of the aerosol extinction coefficients at 45° S (a) and 45° N (b) for 1543 nm, which are in good agreement with the true profiles.

In line with these results, the corresponding transmission values (Fig. a) are in very good agreement, with relative residuals of less than 1 % (Fig. b). The illustration for 45° S can be found in the appendix (Fig. ).

It can therefore be concluded, taking into account the assumptions made here, that with continuous injections of 30 TgSyr-1, a wavelength of at least 1543 nm is required for the aerosol extinction profile retrieval for latitudes of 45° N (AOD≈0.3 at 550 nm) and 45° S (AOD≈0.3 at 550 nm).

The following Fig.  shows the aerosol extinction profile retrieval results for 15° S (panel a) and 15° N (panel b) for a wavelength of 1900 nm. As is the case for 5° N, a wavelength of at least 1900 nm is required for the retrieval of the vertical profiles of the aerosol extinction coefficients at 15° N (AOD≈0.25 at 550 nm) and 15° S (AOD≈0.35 at 550 nm).

The corresponding transmission values from the perspective of a typical satellite solar occultation instrument show the greatest difference at TH=20 km, with 29 % for 15° N (Fig. ). The relative residuals for 15° S are less than 1 % (Fig. ). The higher relative residual (TH=20 km) at 15° N results from differences in the vertical structure of the aerosol extinction profiles. As evident in Fig. , the true profile at 15° N (panel b) exhibits a sharper maximum around 19–20 km and more pronounced curvature changes at 20–21 km compared to the smoother, more monotonic profile at 15° S (panel a).

The results shown above demonstrate that with continuous injections of 30 TgSyr-1, different minimum wavelengths are required for a physically meaningful retrieval result, depending on the latitude. The wavelength-latitude combinations are as follows: 520 nm for 75° N and S, 1543 nm for 45° N and S as well as 1900 nm for 15° N and S and 5° N.

Figure  shows the total errors (in %) for the aerosol extinction profile retrievals for these wavelength-latitude combinations based on the error analysis described above (Sect. 2.3).

The total errors vary depending on wavelength, latitude and altitude. The total errors at the altitude of the injection, here 60 hPa (≈ 19 km), are the following: 6 % (75° N), 16 % (75° S) (Fig. a for 520 nm), as well as ≈ 4 % (45° N and S) (Fig. b for 1543 nm) and ≈ 3 % (15° N and S, 5° N) (panel c for 1900 nm). Note that the large errors at low altitudes are due to the low aerosol extinction coefficients at these altitudes (compare, e.g., Fig. ) and the corresponding low signal. In addition, the high LOS optical depths at low tangent heights (compare Fig. ) also play a role, which likewise leads to a low signal at these altitudes.

Although longer wavelengths prevent the zero transmission problem in regions of high aerosol loadings, they are not optimal under all conditions. Aerosol extinction decreases with increasing wavelength, reducing measurement sensitivity and information content in regions with moderate or low aerosol loading. At latitudes with lower aerosol loading, shorter wavelengths provide higher extinction signal and therefore improved SNRs and retrieval sensitivity. Consequently, an ideal satellite solar occultation instrument for detecting and monitoring large-scale stratospheric aerosol injections should include multiple wavelength channels spanning from the visible (≈ 500 nm) to the near-infrared (≥ 1900 nm), allowing for optimal wavelength selection based on aerosol loading and latitude.

The findings also indicate that the longest wavelength at which SAGE III/ISS targets aerosols, i.e. 1543 nm, is not sufficient for the aerosol extinction profile retrievals for 5° N, 15° N and S, i.e. latitudes near the injection, under the assumptions made here. However, the results demonstrate that encountering the zero transmission problem at a given wavelength does not render solar occultation measurements entirely impossible, rather it indicates that longer wavelengths must be used to obtain meaningful aerosol extinction profiles.

The results presented above reveal a relationship between latitude, AOD, vertical structure, and minimum retrieval wavelength. Thereby, three factors jointly control retrieval feasibility:

First, the AOD determines the overall attenuation of the signal. With high AOD, the extinction of the solar signal is so strong that no meaningful retrieval is possible at the corresponding altitudes. This is accompanied by correspondingly low transmissions from the satellite solar occultation instrument's perspective. The latter two points depend also on the wavelength and latitude.

Second, the vertical profile of the aerosol extinction coefficients, which modulates the retrieval sensitivity. For the latitudes near the Equator, aerosol extinction coefficients peak near 19 km (e.g, Fig. , for 5° N), creating a localized transmission minimum that can fall below detection limits at shorter wavelengths. At higher latitudes, aerosol extinction coefficients peak over a broader altitude range (e.g, Fig. 8 for 45° N and S), reducing peak extinction values and allowing information to be retrieved from a larger altitude range of the vertical profile.

Third, the steady-state nature of continuous injection differs fundamentally from volcanic eruptions, since continuous injections result in a much lower sulfate injection per time compared to a volcanic eruption with the same injected amount.

The injection rate of 30 TgSyr-1 was selected as a deliberately high, upper-end SAI scenario to probe the zero-transmission problem under conditions where radiative forcing effects are most pronounced. This enables an assessment of whether and how zero transmission may emerge in a hypothetical large-scale deployment. While ambitious, injection rates of this magnitude have been discussed in previous SAI modelling studies e.g.,. The injection rate lies at the upper end of proposed scenarios, however, potential upper limits in SAI applications depend on the specific objectives, for instance the targeted radiative forcing.

Furthermore, MAECHAM5-HAM simulation results for an emission rate of 10 TgSyr-1 were examined for the latitude range near the injection. The results show that a minimum wavelength of 1543 nm is already sufficient for 5° N (not shown). The 10 TgSyr-1 injection was selected as a Pinatubo-like reference (the 1991 eruption injected approximately 20 TgSO2), while emphasising that volcanic eruptions represent impulsive rather than continuous injections. This lower rate allows examining whether and to what extent the zero-transmission problem occurs at more moderate injection rates and to determine the minimum wavelength required for the latitude range of the injection, since this latitude range is where aerosol loading is highest (for the month analysed here) and the possible zero-transmission effect is most pronounced, making it the region of greatest concern for this problem.

The relationship between injection rate and wavelength threshold appears monotonic: higher injection rates increase aerosol loading and aerosol optical depth, requiring longer wavelengths to maintain measurable transmission for satellite solar occultation measurements. Comparing the two scenarios, a threefold increase in injection rate (10 to 30 TgSyr-1) corresponds to approximately 23 % increase in the minimum wavelength threshold at 5° N (from 1543 to 1900 nm), suggesting sub-linear scaling. While a complete characterization would require additional intermediate injection scenarios, the results suggest that the zero-transmission problem intensifies with increasing injection rate.

These findings, considering the assumptions made, can have direct implications for solar occultation instrument design. Instruments intended to detect and monitor SAI deployments above a certain size or major volcanic eruptions (or both in the hypothetical case of SAI deployments and a simultaneous volcanic eruption) should incorporate channels extending to at least 1900 nm to ensure coverage for the latitudes with high aerosol loading. The current SAGE III/ISS maximum aerosol wavelength of 1543 nm would be marginally insufficient for retrievals within ≈ ±15° of a 30 TgSyr-1 continuous tropical injection, though adequate for mid-to-high latitudes and lower injection rates (as demonstrated by the 10 TgSyr-1 results at 5° N). Better detector technologies could potentially cover a wider dynamic range with low noise, which could lead to a reduction of the zero transmission problem.

This study has focused on continuous stratospheric aerosol injections under quasi-steady-state conditions without considering natural volcanic perturbations. An important aspect is how coincident volcanic eruptions may amplify or modify the zero transmission problem and associated wavelength requirements. A relatively modest volcanic eruption, such as the 2019 Raikoke eruption, could temporarily increase stratospheric aerosol loading at mid-to-high latitudes. This additional aerosol burden would be superimposed on the background SAI aerosol layer, potentially requiring longer wavelengths than those identified here under pure SAI conditions. The temporal evolution of the combined aerosol load–from the initial volcanic injection through the decay phase–would likely require flexible or adaptive wavelength selection strategies. Even more challenging would be a large tropical volcanic eruption occurring simultaneously with large-scale SAI deployments, which could substantially increase aerosol optical depth in the tropics and potentially reduce transmission even at near-infrared wavelengths such as 1900 nm, particularly at lower tangent heights. A quantitative investigation of combined SAI–volcanic scenarios is beyond the scope of this study and represents an important direction for future work.

The present study provides representative examples illustrating how the minimum wavelength required for a physically meaningful stratospheric aerosol extinction profile retrieval from satellite solar occultation measurements depends on latitude under a continuous tropical injection scenario of 30 TgSyr-1.

While a wavelength of 520 nm is insufficient for the retrieval for 5° N, the opposite can be concluded for 75° N and 75° S. For the latitudes 45° N and 45° S, a wavelength of at least 1543 nm is necessary. In contrast, 1900 nm is sufficient for 15° N and 15° S, as well as 5° N. Consistent with expectations, a longer wavelength is required for the latitude range of and near the injection, in this case at least 1900 nm.

The results also emphasize that encountering the zero transmission problem at shorter wavelengths does not render solar occultation measurements impossible – it requires appropriate wavelength selection based on aerosol loading. Depending on the latitude (see above), the already operating satellite solar occultation instrument SAGE III/ISS could probably also provide aerosol measurements in the relevant altitude range (10–27 km), assuming continuous emissions of 30 TgSyr-1. Specifically, the wavelength channel of 520 nm would be sufficient at high latitudes (75° N and 75° S), while its longest aerosol wavelength channel (1543 nm) would be necessary at mid-latitudes (45° N and 45° S). However, at low latitudes near the injection region (5° N, 15° N, and 15° S), wavelengths longer than SAGE III/ISS's maximum aerosol wavelength of 1543 nm (at least 1900 nm) would be required for physically meaningful aerosol extinction profile retrievals.

The results of this study also confirm the generally accepted idea that, in the case of very high emissions, such as 30 TgSyr-1, which lead to extremely low transmission values (here about 10-14 at 520 nm at a minimum – from the perspective of a typical solar occultation instrument), the appropriate approach is to use longer wavelengths for aerosol measurements. Therefore, the results are also relevant for measurements following major volcanic eruptions.