The stratospheric aerosol has been of scientific interest since its discovery by Christian Junge and colleagues in 1960 . Aerosol particles have an impact on the radiative balance of the Earth system , and they host important heterogeneous chemical reactions . Therefore, global models require information on stratospheric aerosol records and climatologies.

The strength of heterogeneous chemical reactions scales with the surface area density (SAD) of stratospheric aerosols. The N2O5 hydrolysis on aerosol surfaces (e.g., ) alters the partitioning of active nitrogen NOx to total reactive nitrogen NOy, which affects stratospheric ozone chemistry throughout the aerosol layer, especially under volcanically perturbed conditions . In very cold conditions, such as in the winter polar vortex or in the vicinity of the tropical tropopause, additional heterogeneous reactions may activate chlorine from its reservoir species, leading to enhanced ozone depletion . These chlorine activating reactions occur mainly at the liquid–gas interface and, to a lesser extent, within the liquid bulk phase of these cold binary H2SO4-H2O droplets. Therefore, size information is also required for the corresponding modeling of the heterogeneous reactions in addition to the SAD . Besides these cold H2SO4-H2O droplets, polar winter conditions also favor the formation of polar stratospheric clouds (PSCs), i.e., droplets and solid hydrate particles containing HNO3. However, PSCs are not the subject of this article, and the transition from cold binary H2SO4–H2O particles to large ternary HNO3–H2SO4–H2O droplets and hydrates must be treated individually by each global climate model.

The radiative forcing of the stratospheric aerosol has been addressed by many authors, in particular with respect to volcanic perturbations . Recent major volcanic eruptions – e.g., El Chichón in 1982 and Mount Pinatubo in 1991 – led to a temporary decrease in global mean surface temperature, estimated to reach up to 0.5 K . The moderate volcanic eruptions since 2005 of Augustine, Soufrière Hills, Shiveluch, Kasatochi, Sarychev, and Nabro led to a moderate but persistent increase in the stratospheric aerosol , which may partly explain the early 21st-century “warming hiatus” . Stratospheric aerosol continues to be elevated by volcanic eruptions (Ambae, Ulawun, and Raikoke) in the past few years , including the water-rich Hunga Tonga–Hunga Ha`apai (HTHH) eruption , joined by other not-sulfur-dominated sources: several large wildfire events in British Columbia, Australia, and Colorado . A precise description of the radiative properties of the stratospheric aerosol following such events requires an understanding of the distribution and transformation of particles, i.e., size distribution information, in the fresh volcanic plume (e.g., ). Global size distribution data sets, however, do not exist from direct measurements and need to be retrieved from satellite measured radiative properties. Thus, their quality relies on the retrieval method. This type of data could further inform speculation as to whether artificial stratospheric SO2 injections are a suitable candidate for partially counteracting global warming caused by greenhouse gas emissions (e.g., ).

The operation of global climate models requires knowledge on the radiative forcing by the stratospheric aerosol. This aerosol forcing can be either calculated online, provided that the employed model has microphysics and chemistry modules, or prescribed as external forcing, provided that a sufficiently good observational data set is available. The former requires to model the conversion of aerosol precursor gases (OCS, SO2) via photolysis and oxidation reactions into gaseous H2SO4, which can condense on preexisting aerosol particles or nucleate new ones; calculate size distributions of particles and transport them throughout the stratosphere; and finally calculate by Mie theory the scattering of the incoming solar radiation and absorption of terrestrial radiation. The extensive physico-chemical modeling is computationally intensive but is now used by a number of the global climate models . Yet, the resulting aerosol forcing may differ significantly over different models with interactive aerosols , representing a major source of uncertainty. However, most global circulation models (GCMs) still rely on prescribed chemical and aerosol forcing fields, and even many chemistry–climate models (CCMs) prescribe stratospheric aerosols as a compromise between models' complexity and computational efficiency. Thus, a method of establishing the radiative forcing fields of the stratospheric aerosol for use in global climate models is required. The operation of these models typically requires the space–time-resolved data fields of aerosol extinction coefficients (AECs in text; β in mathematical notation), single-scattering albedos (SSAs; ω), and asymmetry factors (AFs; g) for each wavelength band in each of the models. Establishing these fields, together with SAD and size information, is a major prerequisite for model intercomparison projects (MIPs) .

The starting point for calculating the radiative properties of aerosols is a size distribution that characterizes an aerosol ensemble. A method to derive size distribution parameters from SAGE (Stratospheric Aerosol and Gas Experiment) II multi-wavelength aerosol extinction measurements was originally proposed by and . They used AEC ratios to solve a system of equations for the parameters of a single-mode lognormal (SLN) size distribution. More efforts to retrieve SLN size distributions followed (e.g., , and references therein; ). In quiescent periods, the SLN size distribution approximates the stratospheric aerosol fairly well . However, in volcanically enhanced stratospheric aerosol, additional modes are often present . mention that retrieved SLN size distributions can still produce accurate aerosol properties – even when the aerosol consists of two modes – given that the real distribution is not “extremely bimodal” (i.e., the modes overlap sufficiently well and do not have similar number densities). However, warn of systematic biases caused by SLN size distributions retrieved from occultation measurements. These biases apply to conditions of the stratospheric aerosol, when an SLN size distribution is insufficient to capture the real distribution. While retrieved aerosol SAD for two monodisperse modes with prescribed number densities, most observational products do not provide enough independent information (wavelength channels) to reasonably constrain all parameters of a dual-mode lognormal (DLN) size distribution. This was shown for SAGE data by . In this paper, we focus on a generalized best-fit retrieval approach for SLN size distributions and discuss the limitations of the SLN approximation using comparisons with balloon-borne in situ and lidar measurements.

Dedicated satellite missions to observe the stratospheric aerosol began in 1979 with the SAGE program. Spanning 2 full decades (1984–2005), the SAGE II data are a cornerstone of stratospheric aerosol observations, which has been used extensively. It includes AECs at wavelengths of 1020, 525, 452, and 386 nm, providing information on the size of aerosol particles. However, caution is advised as the uncertainties in these four channels differ considerably, with systematically higher zonal standard deviations in channels at 452 and 386 nm. The latest release of SAGE II data is version 7 , with improved retrieval algorithms compared to earlier versions. In June 2017 the operational period of the Stratospheric Aerosol and Gas Experiment III mounted externally on the International Space Station (SAGE III/ISS; hereafter called SAGE III since we do not discuss SAGE III on the Meteor-3M satellite (SAGE III/M3M) in this article) started providing the SAGE III aerosol extinction on nine different wavelengths, continuing the record of the SAGE instrument family after an interruption of over a decade. In addition to the improved range of the wavelength range further into the near-infrared range (the longest wavelength of SAGE III is 1544 nm as compared to its predecessor SAGE II with 1020 µm), a cloud-cleared version of the SAGE III data has been introduced. The establishment of an official aerosol/cloud categorization algorithm eliminates a time-intensive step in pre-processing that previously had to be done in one of various different ways by the user. The Global Space-based Stratospheric Aerosol Climatology (GloSSAC) incorporates both the SAGE II and SAGE III data sets as well as CLAES-ISAMS (Cryogenic Limb Array Etalon Spectrometer – Improved Stratospheric and Mesospheric Sounder, ), HALOE (Halogen Occultation Experiment, ), OSIRIS, and CALIOP data (described in Sect. S1.3 in the Supplement) to produce a continuous AEC product from 1979 onward (see the Supplement for more information on data sets). Since 2012, the Ozone Mapping and Profiler Suite Limb Profiler (OMPS-LP) on board the Suomi NPP satellite has provided limb scatter measurements. From these data, have retrieved AECs on six wavelengths; however, they report limited accuracy in some of the channels. In the future, the OMPS-LP data might be incorporated into GloSSAC as well, potentially making the composite more robust. Furthermore, the new Climate Data Record of Stratospheric Aerosols (CREST) was published recently , providing a single-wavelength composite of six limb scatter and occultation measurement data sets.

In this paper, we describe and validate the latest version of a generalized method to retrieve SLN size distributions for sulfuric aerosol from the abovementioned AEC data sets and use these to calculate a variety of aerosol optical and mass-related properties. The method is termed REtrieval Method for Aerosol Properties (REMAP). Its strength lies in its flexibility to provide optical properties for any prescribed wavelength band so the output can be tailored to the spectral resolution of any radiation scheme. The REMAP method, previously termed SAGE-4λ and SAGE-3λ, has been used in multiple past and ongoing MIPs (Table ) but has not yet been described in sufficient detail. described the preparation of a Mount Pinatubo forcing data set using this method. However, only a brief description of this specific use case was provided. Here, we first give an overview of all projects, in which REMAP was used including the resulting data sets. We then describe the general methodology in full and give practical information on how to use the code followed by a product validation against measurements.

The predecessors of REMAP were first used to create the aerosol forcing for global models within the IGAC/APARC Chemistry–Climate Model Initiative (CCMI) Phase 1 experiment . To this end, different satellite data sets were selected, screened for cloud contamination, interpolated, and ultimately combined to create a continuous and consistent 50-year record (1960–2011). This record was termed SAGE-4λ because its backbone was the four SAGE II wavelengths (4λ). In addition to SAGE II data, some other satellite AECs, sun photometer data, and information from tropical ground-based lidars for the filling of data gaps under volcanically opaque conditions were combined. For details about the SAGE-4λ record, including gap filling, see Sect. S1. In preparation for Coupled Model Intercomparison Project Phase 6 (CMIP6), constructed the first version of GloSSAC (v1.0), which contained an error in the conversion of CLAES data to SAGE II wavelengths. This was corrected in v1.1 as described by , whereupon we corrected the SAGE-4λ record and made it available to the modeling groups involved in CMIP6 for aerosol forcings. We based this data set on the homogenized single product GloSSAC rather than incorporating different sources as in CCMI-1. Although the CMIP6 forcing data set is primarily based on SAGE II, we no longer used the shortest SAGE II wavelength at 386 nm since its quality was insufficient to improve the result. The data set was therefore designated as SAGE-3λ. describe the CLAES/SAGE II conversion error in their corrigendum and show differences in the aerosol loading and forced temperature and ozone anomalies that arise from using the improved SAGE-3λ data set versus the previous SAGE-4λ. Shortly after we released SAGE-3λ to the modeling community, GloSSAC was further updated with new and improved satellite data sets as GloSSACv2.0, described by . It also extended to the end of 2018 and was subsequently used for the historical hindcast period of the CCMI Phase 2 (CCMI-2022) modeling activity , which required prescribed radiative forcing data sets for stratospheric aerosol. Another set of sensitivity runs within CCMI-2022 simulated a climate intervention scenario and was called senD2-sai. For this experiment, the forcing needed to be derived from a separate model simulation – instead of observations – and spectrally regridded for participating models. Details on this procedure are given in Sect. . Finally, the version of GloSSAC at the time of writing this article (v2.22) includes an aerosol/cloud categorization algorithm and extends to the end of 2023. Finally, we used all available GloSSAC wavelengths with their associated zonal standard deviations (eliminating the quality reduction caused by the shortest SAGE wavelength) for the Hunga Tonga–Hunga Ha`apai Impact Model Observations Comparison (HTHH-MOC) forcings .

Table  shows all data sets produced with REMAP that were distributed to modeling groups along with information about the respective inputs. In summary, REMAP was used to provide data of stratospheric aerosol optical properties to

9 models participating in CCMI-1 in support of ozone and climate assessments (SAGE-4λv2 data set, );

In order to estimate the radiative properties of the aerosol particles, the size distribution is required. It can be retrieved, in a best-fit sense, by comparing the calculated AECs of all size distributions in the allowed parameter space against observations. With the size distribution characterized, the AEC, SSA, and AF of the aerosol ensemble can be calculated using Mie theory . To this end, we assume that the stratospheric aerosol comprises pure aqueous sulfuric acid solution droplets. The sulfuric acid concentration is calculated from the atmospheric relative humidity and temperature using the water vapor pressure of aqueous sulfuric acid . For the relative humidity (RH) and temperature, both model output and reanalysis data can be used. The refractive index as a function of temperature and H2SO4 concentration is then calculated using the parameterization of for visible wavelengths and measurements of for infrared wavelengths. In this way, we take the concentration and temperature dependence of the refractive index into account in both the size distribution retrieval procedure and the final calculation of the optical properties.

Recently, published results of 45 years of ground-based lidar measurements of stratospheric aerosols since 1976 at the station Garmisch-Partenkirchen (47.5° N, 11.0° E, southern Germany). The integrated backscatter coefficients – a quantity required for SSAs – at 694.3 nm can also be calculated using the REMAP method. The agreement between the measured (red symbols and line in Fig. ) and the calculated integrated backscatter coefficients (black line in Fig. ) is very good. It should be noted that here we are comparing the zonal mean value of a 5° latitude band created with REMAP to the more fluctuating values from a single station. REMAP achieves excellent agreement after large volcanic eruptions (e.g., El Chichón in 1982, Mount Pinatubo in 1991, and Raikoke in 2020) but slightly underestimates the sustained volcanic burden in the episode of moderate volcanic eruptions around 2010. The retrieved integrated backscatter is also consistently high-biased in the background state (visible between 1997 and 2004), although other stations also report higher values than Garmisch-Partenkirchen in these years (Thomas Trickl, personal communication, 2024). We can trace this overestimation back to the lowest altitude levels in the stratosphere, where the single-mode lognormal distribution assumption does not hold and aerosol not dominated by sulfur is present, which cannot be correctly interpreted in REMAP. Large deviations in particular accordingly occur during large wildfires without any concurrent volcanic eruption, e.g., during and after the British Columbia wildfires (BC fires in Fig. ) in 2018. In this comparison, even for these poorly captured events, the errors stay well within a factor of 2.

Since 1971, in situ particle measurements using an optical particle counter, OPC , combined with a condensation nuclei counter (CNC) , have been performed on average twice a month at Laramie, Wyoming (41.3° N, 105.5° W, USA). The OPC measures the aerosol number density with radii r≳ 0.15 µm in several size channels. The CNC detects number density condensation nuclei with radii r≳ 10 nm. Uni- or bimodal lognormal aerosol size distributions have been obtained by fitting the measured counts of individual size channels of the OPC and CNC . then calculated the effective radius as the ratio of the third and second moment of the obtained size distributions. Figure a shows mean aerosol effective radius after the Mount Pinatubo eruption (June 1991) between 14 and 30 km height above Laramie. Balloon measurements with 1 standard deviation are shown in blue and the corresponding REMAP values (37.5–42.5° N) in yellow. The momentary state of the stratosphere, measured by the balloons, fluctuates more than the monthly mean values captured by SAGE II, which the retrieval is mostly based on at this time. Regardless, the retrieved values mostly stay well within the measurement uncertainty range.

In Fig. b, measured and retrieved vertical profiles of aerosol SAD after the volcanic eruption of Hunga Tonga–Hunga Ha`apai (January 2022; 20° S, 175° W) are compared. The measured profiles are the result of the Balloon Baseline Stratospheric Aerosol Profiles (B²SAP) campaign and were taken at La Réunion (21° S, 55° E, France) with Portable Optical Particle Spectrometers (POPSs), starting roughly a year after the eruption. The volcanic plume at this time is well mixed zonally and thus visible as elevated SAD between 20 and 25 km in both the balloon and retrieval data even though the longitudes of the eruption site and the balloon launch site are different. Below 15 km, no retrieval data are available because the troposphere is masked out, and thus the orange line is constant at zero. For the profile on 8 Dec 2022, measurements took place during both the ascent and descent of the balloon. The filled patch in light blue is bounded by these two profiles and illustrates the variability that the particle counter records during over slightly over a few hours of flight time. Since balloon campaigns see the momentary state of the atmosphere and the satellite-based retrieval operates on zonal monthly means, some discrepancies are expected to show up on account of short-term variability. Apart from those, both products agree well on the shape and height of the volcanic plume. For the 2 Mar 2023 profile, only the balloon ascent is available, which agrees well with the retrieval. The retrieval peak is roughly 25 % smaller than the OPC peak for this date, which again can be attributed to temporal and zonal averaging. For the 16 Jun 2023 profile, balloon data are scarce and show considerable scattering, and thus no conclusive comparison can be made for this date. More balloon data have been collected at other sites, and we offer an extended comparison, including background conditions, in the Supplement (Sect. S2).

The REMAP method is a useful tool for creating stratospheric aerosol forcings required as input for climate models and converting between different aerosol properties. The retrieval algorithm performs well under typical stratospheric conditions except near the tropopause and in regions with very low signal, typically close to the upper edge of the Junge layer. It has been used for studies on volcanic aerosol in the stratosphere and, more generally, to equip GCMs and CCMs in climate studies. The main limitation of the retrieval is the underlying assumption of a single-mode lognormal size distribution, which is necessary for REMAP to flexibly work on many different data sets with limited wavelength channels. Despite this limitation, REMAP also reproduces the particle size distributions after volcanic eruptions reasonably well. The Mie calculation is based on theoretical understanding and produces optical properties for each wavelength and for each wavelength band. The output parameter space and its resolution can be customized at the cost of computational time.

The backbone of all the stratospheric aerosol data sets created with REMAP for different MIPs are the SAGE II and III AECs at three and six wavelengths, respectively, which have provided the most complete coverage over multiple decades. These data are the basis for deriving important parameterizations that enable retrieval using only two or even one single channel, thus permitting the use of the GloSSAC composite. Between the end of the SAGE II and the beginning of the SAGE III operational period, there is a gap of over 10 years, meaning that no parameterization of similar quality can be established for this time. While OMPS-LP data are available starting in 2012, we have not used them with REMAP because of plans to integrate them into future GloSSAC versions . Also, the limited accuracy of the OMPS (NASA) product reported by raises the question of whether sufficient quality wavelength channels would be available for retrieval. Currently, no other OMPS-LP product suited for use with REMAP exists. Therefore, we suggest using the SAGE III parameterization to bridge the gap, which we also used for the entire GloSSAC period, which is validated here.

The REMAP AECs calculated from the retrieved size distributions agree well with the measured data. This holds in not only the visible and near-infrared spectra (SAGE wavelengths at 525 (532 in SAGE III) nm and 1020 (1022) nm), but also the far-infrared spectrum (HALOE at 3.46 µm and ISAMS at 12.6 µm; see Fig. S3 to this paper for 3.46 µm and Fig. S6 of for 12.6 µm). We also found good agreement with other observational data sets under background and volcanic conditions. We observed major systematic differences only from tropospheric intrusions from wildfires. We conclude that REMAP realistically reproduces the radiative (optical) and physical properties of the stratospheric aerosol, especially in the Junge layer. The main caveat is that the input data must be carefully selected and screened as biases of individual wavelengths and contaminated data points can significantly change the quality of the product. This includes assessing the measurement method and any assumptions made for data taking. Physical, mass-related properties retrieved using REMAP (notably surface area density and mean, median and mode radii) may be subject to larger errors under certain conditions. Even though we show in the Supplement (Sect. S4) that REMAP successfully reproduces AECs of both unimodal and bimodal size distributions, it is conceivable that for a bimodal aerosol, the retrieved size distribution parameters simply accurately recreate the optics but not necessarily all other properties. We suggest that for the satellite-based retrieval of stratospheric aerosol properties, the best way forward is to assimilate all of the available data and encourage the use of REMAP with the latest data releases to produce records and climate model input.