The Sato/GISS forcing data set (Sato et al., 1993, 2012) provides stratospheric aerosol optical depth at 550 nm (AOD550) and aerosol effective radius (reff) as a function of latitude, height, and time for the period 1850–present. It is based on a mixture of satellite observations, ground-based optical measurements, and volcanological evidence. From 2001–present, the reconstruction is based exclusively on Optical Spectrograph and InfraRed Imager System (OSIRIS) satellite measurements (Bourassa et al., 2008). For eruptions before the satellite era, the spatial structure of the AOD550 is approximated, based on roughly scaled versions of observed eruptions, or global or hemispheric means. Aerosol effective radius is given as an empirical function of AOD550, based on retrievals of AOD and reff following the Pinatubo eruption.

The Ammann et al. (2003) reconstruction provides AOD550 as a function of latitude, height, and time for the period 1890–1999. It is based on estimates of the mass of SO2 injected into the stratosphere, MSO2, from past eruptions. The spatial structure of the AOD550 is produced by a parameterized stratospheric transport routine, representing the growth of AOD, its decay due to cross-tropopause transport, and transport from tropics to high latitudes. Compared to the Sato/GISS reconstruction, this method provides a consistent representation of volcanic forcing for all eruptions; however, it clearly simplifies the volcanic cloud evolutions compared to the observed evolutions of eruptions like Pinatubo.

Building on prior work (Robock, 1981; Robock and Free, 1995), the Gao et al. (2008) reconstruction provides stratospheric sulfate aerosol mass as a function of latitude, height, and time for the period 500–2000, as well as estimates of SO2 injection by individual volcanic events over the same period. SO2 injections are based on ice core records of sulfate flux from Greenland and Antarctica. Using different scaling factors for tropical and extratropical eruptions based on nuclear bomb tests and modeling studies, ice-core-derived sulfate surface deposition rates are scaled to SO2 injections (Gao et al., 2007). Sulfate aerosol mass time series, as a function of latitude and height, were produced using a modified version of the parameterized stratospheric aerosol transport scheme of Grieser and Schönwiese (1999). Conversion of sulfate aerosol mass to radiative properties was left to the implementation of the model, but a linear scaling of aerosol mass to AOD is a commonly used assumption (Schmidt et al., 2011).

The Stenchikov reconstruction provides monthly mean zonal averages of stratospheric aerosol extinction, single scattering albedo, and asymmetry factor as a function of time, pressure, and wavelength, for the period from 1850 to 1999 (Driscoll et al., 2012; Schmidt et al., 2013). This data set was used by the Max Planck Institute Earth System Model and the Geophysical Fluid Dynamics Laboratory's coupled model for historical simulations as part of the Coupled Model Intercomparison Project's fifth phase (CMIP5). It is an extended version of the Pinatubo aerosol data set developed by Stenchikov et al. (1998) on the basis of satellite measurements of aerosol extinction and reff after the Pinatubo eruption. For earlier eruptions, it is based on the Sato/GISS AOD550 and reff reconstruction. Stratospheric background aerosols are ignored, and only sulfate aerosols arising from volcanic eruptions are accounted for.

The Crowley and Unterman (2013; hereafter CU13) reconstruction, as an update to prior work (Crowley, 2000), provides AOD550 and reff in four equal-area latitude bands for the time period 800–2000. It is based on ice core records of sulfate flux from Greenland to Antarctica. Ice core sulfate fluxes are scaled to peak AOD550: for eruptions of Pinatubo magnitude and smaller, this scaling is linear and based on the ratio of satellite-observed SH AOD and the flux of sulfate to Antarctica. For stronger eruptions (like Tambora), CU13 uses nonlinear scaling first introduced by Crowley (2000), setting AOD550 proportional to the two-thirds power of sulfate flux. AOD time series were constructed based on assumptions of linear increase to peak value, a plateau, followed by exponential decay with a 12-month timescale. As in the Sato/GISS reconstruction, effective radius is prescribed as a simple empirical function of AOD.

The aerosol forcing constructed for use in the Chemistry-Climate Model Initiative (CCMI; Eyring and Lamarque, 2013) provides aerosol optical properties EXT, SSA, and ASY as a function of wavelength, latitude, height, and time for the period 1960–present. It also provides internally consistent estimates of aerosol surface area density necessary for stratospheric chemistry simulations. The cornerstone of the CCMI forcing set is the four-wavelength SAGE II extinction data (SAGE_4λ), retrieval version 7, which span the period 1985–2005. During the SAGE II period, the four-wavelength extinction data are used to derive estimates of aerosol effective radius, from which the properties EXT(λ), SSA(λ) and ASY(λ) are derived assuming a single log-normal particle size distribution (Arfeuille et al., 2013). For other time periods, aerosol radiative properties are estimated mainly through single wavelength extinction retrievals from satellite instruments, and the observed correlation between mean aerosol radius and aerosol extinction during the SAGE II period. From 1979 to 1985, the reconstruction is based on single wavelength extinctions measured by the SAM II and SAGE I satellite instruments (Thomason and Peter, 2006). The 1960–1979 pre-satellite period has been constructed from SAGE-II background measurements in the late 1990s, superimposing the volcanic eruptions of Agung (1963) and Fuego (1974). These eruptions were calculated by means of the AER 2-D aerosol model (Arfeuille et al., 2014; Weisenstein et al., 1997), and the results were scaled by means of stellar and solar extinction data (Stothers, 2001). The 2006–2011 period is derived from CALIPSO 532 nm backscatter data. An update to the CCMI reconstruction will be used in the historical simulations (1850–present) within the Coupled Model Intercomparison Project phase 6.

The observational data sets used in the CCMI reconstruction have data gaps, in particular when the atmosphere became opaque directly after volcanic eruptions, which occurred mainly in lower tropical altitudes (below 16 km), and in the high-latitude polar regions due to limited geographical sampling of the satellite instruments (Eyring and Lamarque, 2013). After the eruptions of El Chichón and Pinatubo, data gaps were filled by means of lidar ground station data and interpolation. The remaining data gaps were filled using a linear interpolation approach in altitude and latitude.

The construction of EVA relies extensively on observational constraints. Additionally, when observations cannot adequately constrain EVA parameterizations, EVA is constructed so as to produce reasonable agreement with prior forcing sets. Data sets that were instrumental in the EVA construction include the following:

The estimate of total SO2 injection by Pinatubo of 18 ± 4 Tg (9 ± 2 Tg S) from the total ozone mapping spectrometer (TOMS) instrument (Guo et al., 2004).

Aerosol optical depth at λ=550 nm is simulated by EVA making use of the assumption that it can be a simple function of the stratospheric sulfate mass: AOD550=f(MSO4). Stothers (1984) introduced a simple linear scaling between global sulfate aerosol mass and global mean AOD. Such scalings have a physical foundation (e.g., Charlson et al., 1992) and have long been used to study tropospheric aerosols. A linear relationship between sulfate mass and AOD has been used to convert the sulfate mass estimates of Gao et al. (2007) into radiative properties (Schmidt et al., 2011) and is implicit in the linear scaling of ice core sulfate flux to AOD used by CU13 for eruptions of Pinatubo magnitude and smaller. We apply this same assumption hereafter (up to a threshold M∗; see Sect. 3.6) using a scaling factor A: AOD550=AMSO4,forMSO4<M∗.

Time evolution of sulfate mass is emulated in EVA using a chemical box model framework. Bluth et al. (1997) introduced a simple single-box model of stratospheric aerosol evolution. Changes in stratospheric sulfate aerosol are controlled by injections of SO2 into the box, subsequent conversion of SO2 into sulfate aerosols, and loss of sulfate aerosols to the troposphere. Describing the production and loss of sulfate mass (MSO4, all masses in Tg S) as a function of the SO2 mass (MSO2) and characteristic timescales τprod and τloss, respectively, the time tendency of MSO4 is dMSO4(t)dt=MSO2(t)τprod-MSO4(t)τloss. This equation describing the time evolution of MSO4 can be solved analytically, for example, for a single pulse injection of MSO2 at time t0: MSO4t=MSO2t01-exp⁡-tτprodexp⁡-tτloss.

Equations (2) and (4) can be used to emulate the observed global mean AOD evolution after the Pinatubo eruption. Using the best estimate of a total SO2 injection of 9 Tg S (Guo et al., 2004), the parameters A, τprod, and τloss can be determined based on comparison with the CCMI global mean AOD anomaly time series (Fig. 1). Given the uncertainties in the CCMI AOD in the first months after the Pinatubo eruption due to the gap in the SAGE II observations due to saturation effects (Thomason and Peter, 2006), we have based our fit on the CCMI AOD beginning in July 1992, when SAGE II retrievals of the full tropical stratosphere resumed. Therefore, the fit is not strongly constrained by the peak of global mean AOD in the CCMI reconstruction, but rather by the shape of the AOD decay. Best fit is achieved with values of A=0.0364, τprod=180 days, and τloss=330 days. The resultant value of A is comparable to that suggested by Stothers (1984), whose scaling factor is 0.0267 when converted into units of mass S rather than mass sulfate aerosol, and the stratospheric loss rate (τloss=330 days) is consistent with the decay rate of AOD after Pinatubo noted by other researchers (e.g., Bluth et al., 1997). The best fit production rate, τprod=180 days, is perhaps surprising, given its discrepancy from the observed timescale of SO2 decay, which is around 30–35 days (Bluth et al., 1992; Read et al., 1993). In their single-box aerosol model, Bluth et al. (1997) noted the resulting lag between peak observed AOD and the peak in modeled SO4 mass when using an SO4 production timescale equal to the observed SO2 decay rate, and proposed that the rate of SO4 aerosol increase may be limited by other chemical steps other than the destruction of SO2. We contend that global mean AOD may further depend on the timescale of spatial spreading of the aerosol cloud, since the impact of aerosol contained within a horizontally contained vertical column will be diminished due to shielding effects. Whatever the mechanism responsible, τprod should be interpreted as an effective production timescale, which incorporates not only the chemical conversion of SO2 to SO4 but other processes which damp the rise in AOD. An important caveat of this construction is that the peak loading of the simulated SO4 mass is significantly less than what would result from a complete conversion of SO2 to SO4 prior to any loss. For this reason, the scaling factor A is larger than what would be deduced if the peak SO4 loading is assumed to be equal to the SO2 injection (in Tg S). Finally, we note that since estimates of the mass of SO2 injected by Pinatubo (9 ± 2 Tg S, from Guo et al., 2004) have an uncertainty of about 25 %, the uncertainty in the scaling factor A is at least this large.

The global mean effective radius is computed based on a simple scaling argument. For a given mass of sulfate MSO4, which is distributed equally among N aerosols of radius r, MSO4∼Nr3. If N is constant, then particle radius scales as the one-third power of MSO4. This relationship is similar to that used by CU13, who based reff on the one-third power of AOD550. This follows if r is linearly related to reff, which is the case, for instance, if the aerosol particles are distributed log-normally by size (with a given shape parameter). In EVA, we set

reff=RMSO413, and find a scaling constant R that produces best agreement in terms of the peak global mean reff reached after the Pinatubo eruption in the reff time series of the observation-based reconstructions. Like CU13, we also set a minimum reff of 0.2 µm. With a fit value of R=0.78, the resulting EVA reff time series shows reasonable agreement in peak magnitude compared to the Sato/GISS, CCMI, and CU13 reconstructions with peak values between 0.5 and 0.6 µm (Fig. 1b). Basing reff directly on the sulfate mass in this way does not allow the reproduction of some observed features of the reff evolution apparent in the Sato/GISS reff reconstruction, including the lag of its peak compared to that of AOD550. However, given the simplicity of this approach, and the uncertainties in reff estimates retrieved from satellite sensors, the scaling methodology appears to produce satisfactory results, and even if the Sato/GISS evolution of reff is more realistic, it remains to be demonstrated that this difference has any detectable influence on the climate.

The stratosphere can be separated into regions with distinct dynamical regimes (Plumb, 1996, 2002). One important distinction is that of the relatively undisturbed tropical pipe – where mean residual motion is predominantly upward – from the extratropics, where wave breaking leads to quasi-horizontal mixing, motivating the term “surf zone” (McIntyre and Palmer, 1983). The structure of stratospheric trace-gas species are well reproduced by the so-called “leaky pipe” model of the stratosphere, which differentiates between the different dynamical regimes of the tropics vs. extratropics (Ray et al., 2010). Following these studies, and motivated also by the clear separation of tropical vs. extratropical stratospheric aerosol maxima following the 1991 Pinatubo eruption (Trepte et al., 1994, and Fig. 2), EVA uses a simple three-box representation of the stratosphere, separating it into three regions – equatorial, Northern Hemisphere (NH) extratropical, and Southern Hemisphere (SH) extratropical – and describes the stratospheric aerosol distribution as the superposition of three zonally symmetric, global-scale aerosol plumes.

The aerosol properties of each plume are defined using a static characteristic spatial structure based on extinction from the CCMI reconstruction following the 1991 Pinatubo eruption. To reproduce the observed meridional structure of AOD, we choose for simplicity Gaussian functions, fit as a function of the area-conserving coordinate sin(φ), where φ denotes latitude. The observed evolution of zonal mean AOD550 after Pinatubo (Fig. 2a) shows a clear separation between the three regions, with an initial growth of AOD550 within the equatorial region and later peaks in the NH and SH. We base the structure of the equatorial shape function on the CCMI AOD550 averaged over the first 3 months after Pinatubo, before much transport to the extratropics occurred, and fit a Gaussian function to the central portion of the AOD550 (Fig. 2b). (While the magnitude of AOD550 in the first months is assumed to be highly uncertain during the first months due to saturation effects, we necessarily assume here that the latitudinal structure of the CCMI AOD is reasonably realistic.) Subtracting the Gaussian fit of the equatorial plume from the 4-year mean AOD550 isolates the spatial structure of the remaining extratropical regions (Fig. 2c). We fit the observed extratropical AOD structure with Gaussian functions centered at 45∘ with a width of 14∘. At high latitudes, where the impact of our choice of the sin(φ) coordinate is strongest, the EVA fit shows some disagreement with the CCMI AOD, but much better agreement with the older Sato/GISS reconstruction (not shown). Given that SAGE observations are generally limited to ±60∘ and high-latitude values are extrapolated, and that high-latitude aerosol often resides at heights below 15 km which can be difficult for satellite sensors to retrieve (Ridley et al., 2014), it does not appear warranted to change the sin(φ) fitting procedure adopted at lower latitudes.

The three horizontal shape functions are normalized by their respective global area-weighted mean. In this way, multiplication of a horizontal shape function by the sulfate mass in the region gives, for each latitude, a representation of the local vertically integrated sulfate mass density (kg km-2).

The time evolution of the AOD550 for each region is based on expanding the single-box model of the stratosphere of Sect. 3.2 into a three-box model. In addition to injections of SO2 and loss of sulfate through cross-tropopause transport – as in the global single-box model – sulfate is transported between the three boxes, with time constants τmix and τres defining the rates of two-way mixing and poleward residual circulation, respectively. For example, the rate of change of sulfate mass in the NH region is related not just to SO2-to-SO4 conversion and loss but also to mixing, which is related to the difference of mass between the NH and equatorial plumes, and the transport of mass from the equatorial plume due to the residual mass circulation of the Brewer–Dobson circulation:

dMSO4NHdt=MSO2NHτprod-MSO4NHτloss+MSO4EQ-MSO4NHτmix+MSO4EQτres.

Similar expressions are used for the SH and equatorial regions. In the EVA module code, the differential equations describing the time tendency of SO4 within each region are computed numerically through a forward Euler method: MSO4t+1=MSO4t+ΔMSO4t.

Each eruption is treated as an instantaneous injection of SO2 into one of the three boxes, with the injection region based on the latitude of the volcano, and latitudinal boundaries set to ±25∘ based on satellite-based estimates of the edges of the stratospheric tropical pipe (Neu et al., 2003). In this way, the impact of multiple eruptions occurring with overlapping time periods of impact can be easily handled, as each eruption simply adds to the pre-existing sulfur loading.

The observed AOD550 after Pinatubo shows clear influence of the seasonal cycle of stratospheric transport, with maximum extratropical AOD found in the winter and spring seasons of each hemisphere, qualitatively consistent with the seasonal cycle of the Brewer–Dobson circulation which maximizes in the winter months (Holton et al., 1995). We therefore vary the τmix and τres parameters with calendar month m, using simple sinusoidal relationships, such as τmixNHm=τ‾mix1+Bcos⁡m-1π6,m∈1,2,…,12, where the factor B describes the amplitude of the seasonal variation. Mixing and residual transport in the NH are thus strongest in January and weakest in July, and have an annual average equal to τ‾mix and τ‾res, respectively. Mixing and residual circulation in the SH are phase shifted by 6 months with maximum mixing in July and minimum in January. The mixing and residual transport timescales are equal for both hemispheres, and in the long term, produce relatively even partitioning of sulfate between the NH and SH. A method to reproduce hemispherically asymmetric aerosol evolution is described in Sect. 3.6.

Fitting the parameters B, τmix, and τres was achieved by minimizing the root mean square residuals of the EVA AOD550 with the CCMI AOD550 field for Pinatubo. Owing again to the larger uncertainties in satellite-based aerosol properties in the initial months after Pinatubo due to saturation effects, the fitting procedure ignored the initial 12 months between the latitudes between 20∘ S and 20∘ N. Best fit was achieved with values of τmix=15 months, τres=17 months, and B=0.75, resulting in good agreement with CCMI AOD550 evolution (Fig. 3). The AOD550 evolution of EVA lacks the fine detail of the CCMI data set, but reproduces the general spatiotemporal structure, including the double peak structure in the SH midlatitudes, and the gradual shift from strongest AOD550 in the tropics to the extratropics with time.

In the vertical dimension, observations show that volcanic aerosol extinction values were strongly peaked in the tropics at about 22 km in the first months after the Pinatubo eruption, and thereafter spread somewhat with height, with the peak shifting slightly downwards (Arfeuille et al., 2013). Transport of aerosol from the equatorial region to midlatitudes and high latitudes was episodic in the first year after Pinatubo with contributions from both the lower and upper branches of the Brewer–Dobson circulation (Trepte et al., 1993). Horizontal transport of passive dynamical tracers in the midlatitude stratosphere takes place predominantly along isentropic surfaces, due to large-scale mixing processes resulting from wave activity. Aerosol transport is complicated by additional processes, including gravitational settling and anomalous vertical motions resulting from the heating of the local atmosphere by the absorption of longwave radiation by the aerosols themselves (Rogers et al., 1999). Nonetheless, the variation of peak aerosol extinction in the 4-year post-Pinatubo mean follows isentropic surfaces (derived from ERA-Interim reanalysis data; Dee et al., 2011) reasonably closely in the midlatitudes of the summer hemisphere, with the 430 K potential temperature surface corresponding well with the vertical peak of mean EXT (Fig. 4a). The correspondence between the aerosol loading and isentropic (potential temperature) surfaces breaks down in the high latitudes during winter, where diabatically driven vertical motion within the polar vortex leads to downwelling of air parcels with respect to potential temperature (Manney et al., 1994; Tegtmeier et al., 2008).

To reproduce the variation of the vertical peak of extinction with latitude in the extratropics, we define a vertical “center line” based on climatological potential temperature. While potential temperature does not perfectly follow the observed aerosol peak at high latitudes, by linking the vertical distribution of the aerosol to a temperature-based (rather than mass- or geopotential-based) vertical coordinate, it may be more suitable for application in much warmer or colder climates. Specifically, we define the center line at midlatitudes and high latitudes (φ > 45∘) from the summer 430 K potential-temperature surface for each hemisphere (July for the NH, January for the SH), and the annual mean 430 K potential-temperature surface for -45∘ < φ < 45∘. This empirically defined center line shows reasonable agreement with the observed vertical peak in aerosol extinction in the extratropics (Fig. 4a). In the tropics, the vertical position of the plume is given a vertical offset from the center line.

The vertical shape of extinction in the equatorial region is based on a Gaussian fit of the 4-year Pinatubo mean CCMI extinctions with a vertical width of 2.25 km and a vertical offset of 2.75 km (Fig. 4b). In the extratropics, a Gaussian fit is produced, centered on the defined center line with a width of 2.825 km (Fig. 4c). The vertical shape functions, defined internally on a 1 km vertical grid, are normalized by their vertical sum. Therefore, multiplication of the AOD at each latitude by the normalized vertical shape function produces a profile of aerosol extinction (per kilometer).

The resulting EVA aerosol extinction structure shows good agreement with the 4-year mean CCMI Pinatubo observations (Fig. 5). The use of Gaussian vertical and horizontal shape functions results in fairly good reproduction of the strong extinction gradient at the tropopause.

The spatiotemporal structure of aerosol effective radius is based on the simulated sulfate mass time series for each latitude (i.e., a function of the three-box model and the horizontal shape functions). Effective radius is computed for each latitude and time from Eq. 6, and assumed to be constant with height through the stratosphere. The resulting reff field shows reasonable agreement with observation-based estimates (Fig. 6); however, it appears to produce peak values which are somewhat too large, and peak too early compared to the Sato/GISS reconstruction, as apparent also in the global mean (Fig. 1).

The wavelength-dependent optical properties EXT, SSA, and ASY are computable via Mie scattering theory given knowledge of the extinction at a specific wavelength, and the effective radius of an assumed log-normal size distribution. EVA utilizes look-up tables, computed from Mie theory, assuming a single-mode log-normal size distribution with width parameter σ=1.2, which gives wavelength-dependent EXT scaling ratios (with respect to EXT at 550 nm), ASY, and SSA for varying effective radii, ranging from 0.2 to 1.3 µm, and for 29 wavelengths ranging from 0.2 to 100 µm. Therefore, given the EXT550 and reff at any point in space, EXT(λ), SSA(λ), and ASY(λ) are calculated from the lookup tables through bilinear interpolation. The use of σ=1.2 is roughly consistent with that deduced from observations of the Pinatubo aerosol cloud, with Stenchikov et al. (1998) using σ=1.25 and the CCMI reconstruction using σ=1.2 in gap-filled regions when the SAGE measurements cannot be used to estimate sigma directly (Arfeuille et al., 2013).

Resulting zonal mean AOD at three sample wavelengths are shown in Fig. 7 and compared to the corresponding CCMI values. In general, EVA reproduces the decrease of AOD with increasing wavelength from the visible to the near infrared. SSA and ASY at four wavelengths, at 20 km, are shown in Figs. 8 and 9, and again reproduce reasonably well the variation of magnitude with changing wavelength. Some differences in the spatial structure of SSA are apparent between the EVA and CCMI reconstructions, although it remains to be shown how important such structure is in the overall climate impact of the volcanic forcing.

Satellite observations of aerosol extinction in the years following the 1991 Pinatubo eruption show that the extinction approaches a non-zero minimum value. The assumption that radiative forcing by stratospheric aerosol would decay to zero in the 2000–2010 decade has been shown to lead to non-negligible biases in climate model simulations (Solomon et al., 2011). The background stratospheric aerosol layer is thought to be a result of a combination of factors, including the episodic but ubiquitous influence of relatively minor volcanic eruptions with small stratospheric injections, and the slow and steady influx of aerosols and precursors from the troposphere into the stratosphere (Kremser et al., 2016).

A non-zero background stratospheric aerosol forcing is parameterized within EVA by specifying a constant SO2 injection value, chosen to produce a best fit between the CCMI and EVA global mean AOD time series for the year 2000, where the observed global AOD reached a minimum (Fig. 10). This simple procedure results in a background SO2 injection estimate of 0.2 Tg year-1. For comparison, using the coupled aerosol Solar-Climate Ozone Links chemistry climate model (SOCOL-AER) and CCMI retrievals, Sheng et al. (2015) have inferred a total net sulfur mass flux into the stratosphere of 0.19 Tg year-1.

The structure of the observed aerosol extinction in the meridional height plane during the 2000 minimum is shown in Fig. 11a. Maximum aerosol extinctions in the CCMI data set are in the high-latitude lowermost stratosphere. To best reproduce this structure, the background SO2 injections are split evenly between the two extratropical plumes. The resulting structure of EVA background AOD forcing does not reproduce the lower stratosphere forcing due to the static shape functions of the EVA construction based on the Pinatubo aerosol evolution. Nonetheless, this strategy of background AOD in EVA does somewhat reproduce the meridional structure of the background AOD (Fig. 11c, d).

Some tropical eruptions can lead to relatively even partitioning of aerosol between the NH and SH. For example (discounting the likely small and short-lived impact of the August 1991 Cerro Hudson eruption), the June 1991 eruption of Pinatubo produced NH and SH AOD maxima of similar magnitude (Fig. 3). On the other hand, tropical eruptions like Agung (1963) and El Chichón (1982) are characterized by substantial hemispheric asymmetry in stratospheric aerosol loading. Asymmetries in the radiative forcing, if large enough, may have a detectable climate impact, for instance, through their influence on the latitude of the intertropical convergence zone and subsequent changes in tropical monsoon patterns (Haywood et al., 2013; Oman et al., 2006).

Some degree of hemispheric asymmetry may be expected due to the timing of an eruption with respect to the seasonal cycle of stratospheric transport. One expects tropical eruptions which occur in NH winter (when transport to the NH extratropics is strongest) to produce higher NH aerosol loadings than those in summer. This expectation is reproduced by aerosol general circulation models (Toohey et al., 2011). The seasonal variation of stratospheric transport parameterized within EVA leads to a small degree of hemispheric asymmetry in the resulting AOD patterns depending on season of eruption, with highest asymmetry produced for tropical eruptions in August (AODNH / AODSH = 1.18) and February (AODNH / AODSH = 0.847).

The parameterized seasonal stratospheric transport of EVA qualitatively reproduces the observed SH bias of the AOD from the 18 February 1963 Agung eruption (Fig. 12), albeit with much weaker magnitude. For instance, based on ground-based optical measurements, Stothers (2001) estimated that the SH aerosol loading after Agung was 8 times larger than that of the NH. Furthermore, the hemispheric asymmetry produced by the seasonal stratospheric transport of EVA for El Chichón, for an 4 April eruption date, is much different than the observed strong NH asymmetry (Fig. 12). The degree of hemispheric asymmetry for tropical eruptions may be related to the particular synoptic-scale meteorological conditions at the time and place of the initial SO2 injection, and therefore impossible to reproduce using a climatological transport parameterization.

For these reasons, an anomalous asymmetry factor is included in EVA to allow one to impose an observed asymmetry from data. Hemispheric asymmetry can be specified in the input file, based on direct observational estimates or estimated from the ratio of Greenland to Antarctic ice core sulfate records. When this ratio differs from the asymmetry produced by the seasonal mixing parameterization of EVA, a correction can be applied which attenuates the rate of mixing and transport to one hemisphere for a period of 18 months after the eruption. This correction ensures that the AOD in the midlatitudes and high latitudes shows a hemispheric ratio equal to that of the input value, while retaining the nominal seasonality of stratospheric dynamics.

Hemispheric asymmetry corrections are applied here to the EVA reproductions of the Agung, Fuego, and El Chichón eruptions (Table 1). In order to enhance comparability with the CCMI data set, correction factors for Agung and Fuego are based on the AOD reconstruction of Stothers (2001), and defined as the ratio of the 2-year post-eruption average of hemispheric AOD. This method produces values of 0.19 for Agung and 1.0 for Fuego. For El Chichón, we calculate a correction factor directly from the CCMI AOD550, again as the ratio of the 2-year AOD average for each hemisphere, resulting in a value of 1.5. Applying hemispheric asymmetry corrections in the reconstruction of AOD550 for Agung and El Chichón produces better agreement with the CCMI estimates (Fig. 12). It should be noted here that the CCMI representations for these eruptions are highly uncertain. For Agung, the CCMI data are based on 2-D model results scaled by sparse ground-based measurements, while for El Chichón, it is based on an amalgam of very sparse ground- and airplane-based lidar and satellite observations at only the high latitudes (Thomason and Peter, 2006).

While a simple linear relationship between sulfate mass and AOD (Sect. 3.2) is consistent with available observations, its applicability to eruptions larger than Pinatubo is quite uncertain. Modeling studies imply that for large eruptions, the maximum AOD produced is not a linear function of the injected sulfur (Timmreck et al., 2010). CU13 argued that above some threshold, AOD should scale as the two-thirds power of sulfate aerosol mass rather than linearly. Such a relationship is consistent with the results of an aerosol general circulation model simulating a large range of tropical volcanic eruptions (Metzner et al., 2014). We sketch a simple explanation for this relationship as follows: for a total mass of sulfur (M) distributed among N particles with uniform radius r, the mass of each particle, M/N, is proportional to the volume of each particle (V) and therefore r3: MN∼V∼r3. The AOD is proportional to the total cross-sectional area of the particles: AOD∼Nr2. Combining these equations, AOD can be written as a function of N and M: AOD∼N1/3M2/3. When new particles are formed in proportion to the mass of injected sulfur, N is proportional to M and the AOD scales linearly with M. On the other hand, if injected sulfur mass condenses onto pre-existing particles, N remains constant, and AOD scales with the two-thirds power of M. In EVA, we adopt a threshold-based implementation based on the approach of CU13. We retain this approach for very large eruptions, and scale sulfate to AOD based on two parameters, A1 and A2, such that AOD=A1MSO4,MSO4<M∗A2MSO42/3,MSO4≥M∗, where the threshold M∗ is defined so as to make the relationship continuous: M∗=A2A13.

The two regimes – complete new particle formation from the injected SO2 or complete condensation onto pre-existing particles – obviously represent the two extremes of possible sulfate aerosol evolution, and it seems likely that both processes take place in differing degrees for different eruptions. Other physical parameterizations, for instance, relating N to the logarithm of M are surely possible, and should be explored in future work. The present scheme retains consistency with the reconstruction of CU13, and has the advantage of simplicity, at least for the majority or eruptions for which AOD is a simple linear scaling of sulfate aerosol mass. Scaling considerations for extremely large eruptions should be understood to be a major source of uncertainty in any volcanic forcing reconstruction.

In EVA, the A1 term is based on the peak global mean AOD from the CCMI data set and the best estimate of the 9 Tg S injection from Pinatubo (Sect. 3.2). We choose to define A2 so as to best reproduce the aerosol forcing of CU13 for large eruptions, such as Tambora and Samalas.

Figure 13 shows the relationship between peak global mean AOD and estimated injected SO2 for Pinatubo, Tambora, and Samalas. The linear scaling of CU13, which was based on AOD estimates from Sato/GISS and ice-core-based estimates of SO2 injection, leads to a rather steep curve, which, when extrapolated to the estimated sulfur injection of Tambora, would have produced an estimate of global mean AOD of about 0.7. A much smaller AOD for Tambora (i.e., 0.45) and Samalas was produced by CU13 by incorporating the two-thirds power law, which they applied to eruptions larger than Pinatubo, producing the AOD values shown in Fig. 13.

The linear scaling used in EVA is significantly less steep than that of CU13, a result of the lower peak global mean AOD estimate for Pinatubo from CCMI compared to Sato/GISS, and the larger estimate of SO2 injection from satellite sensors compared to the ice-core-derived estimate of CU13. Extrapolation of the linear scaling of EVA to larger injection magnitudes reproduces the CU13 estimates of AOD and reff for Tambora rather well. A two-thirds power-law relationship is nonetheless implemented in EVA, which applies then to eruptions greater in magnitude than Tambora, and therefore reduces the impact of the Samalas eruption compared to using the linear relationship.

AOD time series produced by EVA using the eruption history of Table 1 are shown in Fig. 14, and compared to the CCMI data set. The magnitude of global mean AOD of the major eruptions is well reproduced by EVA, with slightly larger AOD produced for Pinatubo (as discussed in Sect. 3.2) and slightly lower AOD for Agung compared to the CCMI data, which relies on ground-based optical data to scale the AER model results for Agung and Fuego. A number of relatively minor eruptions before and after the El Chichón eruption (Bluth et al., 1997) – not accounted for in the eruption history used here – likely account for the complex temporal and spatial AOD evolution seen in the CCMI database in the years 1980–1990.

Including the minor eruptions of 2000–2014 in the EVA input file improves the comparison over these years. This time period is examined in more detail in Fig. 15. The EVA global mean AOD tracks the variability shown in the CCMI database (based in this time period on CALIPSO satellite data) rather well. The EVA global mean AOD response to the high-latitude eruptions of Kasatochi (2008) and Sarychev (2009) exceeds that seen in the CCMI data, and appears to persist longer. This is likely a result of the use of a single aerosol loss rate for all eruptions in EVA, based on the observed decay of the aerosol from Pinatubo. It is likely that the processes and related timescales are different for relatively smaller eruptions in the extratropics, but there is presently little understanding of the relationship between eruption strength and resulting aerosol lifetime and there is no consideration of this potential effect in EVA. Nonetheless, we note that the agreement between EVA and CCMI is decent at ∼ 60∘ N, the northernmost limit of the CALIPSO measurements underlying the CCMI data, implying that the stronger apparent disagreement at polar latitudes may be due partly to the gap-filling procedure used in the construction of the CCMI data set. The agreement between EVA and CCMI over this time period is also largely dependent on the accuracy of the stratospheric injection estimates used. The estimates used here, based on MIPAS satellite SO2 measurements, carry an uncertainty on the order of 20 % (Höpfner et al., 2015), with additional (unquantified) uncertainty arising from the separation of the stratospheric component of the total atmospheric injection (Brühl et al., 2015). If desired, agreement between the EVA-based results with the satellite records over the 2004–2014 period could be improved by careful adjustment of the input sulfur injections.

Global mean AOD550 and reff produced by EVA for the 1815 eruption of Tambora are compared to the reconstruction of CU13 in Fig. 16. Using the linear scaling, based on the estimated peak AOD and sulfur injection of Pinatubo, the peak AOD of an estimated 55 Tg SO2 injection by Tambora leads to a smaller global mean AOD in the EVA reconstruction compared to CU13. The EVA AOD peaks at approximately 0.35, while the CU13 reconstruction estimates a global mean AOD peak of ∼ 0.4.

It should be noted that with the Pinatubo-based linear relationship used in EVA, if a nonlinear, two-thirds power-law relationship were implemented with the same threshold used by CU13, i.e., applying to eruptions just greater in magnitude than Pinatubo, then the resulting AOD for Tambora would be significantly smaller than the present EVA estimate.

The aerosol effective radius produced by EVA for Tambora is similar, but slightly larger than the CU13 estimate. This difference comes about because in EVA, reff is scaled according to the SO4 mass, while in CU13, the AOD is used. Since in CU13, the AOD for Tambora is related to the two-thirds power of mass, the muting of the AOD affects also the reff, while in EVA, reff grows linearly with SO4 mass. There are unfortunately no observational estimates of the aerosol size distributions for any eruptions larger in magnitude than Pinatubo (1991), and therefore there is considerable uncertainty regarding the validity of the simple relationships used here and by CU13 for such large eruptions. Simulations of the Tambora eruption with an interactive aerosol model produce similar effective radii as those estimated by EVA (∼ 0.73 µm; Stoffel et al., 2015); future work with such models may help to constrain parameterizations of effective radius.

The zonal mean AOD550 for Tambora from CU13 and from this work are shown in Fig. 17. While the magnitude of peak AOD and its temporal decay are similar in the two reconstructions, the EVA reconstruction provides a more realistic latitudinal distribution of AOD compared to the 4-band structure of CU13. The slight SH bias of the CU13 Tambora AOD550, inferred by CU13 from ice core records, is produced by EVA as a result of the parameterized seasonal transport (Sect. 3.3) with no additional hemispheric correction.