Attempts to understand how the anthropogenic aerosol affects the climate system have tended to focus on the quantification of its radiative forcing. One way to do this is to characterize the physical properties of the aerosol given knowledge of aerosol and aerosol precursor emissions. Given the aerosol physical properties, optical and cloud active properties can be inferred and used to quantify aerosol radiative forcing. This bottom-up approach has proven to be challenging. One reason is that important aerosol processes remain poorly understood . Another reason is the enormous scale divide between the processes that are understood and those that can be represented with fidelity in a large-scale model. Even processes that are well understood prove difficult to implement consistently e.g.,. From this perspective, it is not surprising that independent efforts adopting bottom-up approaches yield estimates of aerosol radiative forcing that differ widely .

Rather than asking how our understanding of aerosol processes constrains aerosol radiative forcing, a top-down approach asks how the response to a given distribution of aerosol optical and cloud active properties is consistent with the observational record. Present bounds on aerosol radiative forcing are largely a result of such approaches . The goal of the paper is to describe a simple and easy-to-implement aerosol climatology that we have developed to help advance the top-down approach for constraining aerosol radiative forcing.

The idea of using the response of the climate system to a hypothetical (aerosol) forcing as a test of that forcing is at the heart of detection and attribution studies, and presupposes some understanding of the pattern of aerosol forcing and the pattern of the response. For instance, it has been argued that a strong aerosol forcing, which would have been disproportionally concentrated around the source regions in the Northern Hemisphere, is inconsistent with the strong pattern of Northern Hemisphere warming through the first part of the last century . But this argument assumes that warming in the Northern Hemisphere, especially in the Atlantic sector, could not have been as large as the warming observed if the net radiative forcing over the hemisphere, or region, was negative. This need not be the case, as enthalpy may have been imported into the region at a rate that more than offsets the local negative forcing. To test the idea, it would be helpful to see if robust climate responses can be attributed to patterns of aerosol forcing, for which the ability to prescribe the same pattern of forcing across many climate models is a prerequisite.

Given that the 20th century witnessed a large human imprint on the atmospheric aerosol, it seems natural to ask what was different about the climate of the 20th century due to this anthropogenic aerosol. Published studies, usually based on the response of an individual model, hint that aerosol perturbations may be responsible for shifts in patterns of monsoon rainfall , decadal variability in the Atlantic which may have led to a suppression of hurricane activity , diminished sunlight at the surface over Europe and the conspicuous decrease in temperature over the eastern and central United States during the middle of the last century . But these ideas have proven controversial: the response of the intertropical convergence zone (ITCZ) is sensitive to the representation of the cloud processes ; a purportedly strong North Atlantic cooling by the aerosol appears to be inconsistent with the subsurface temperature record , and variations in the surface energy budget are difficult to extract from the noise of natural variability, particularly at high latitudes . Coincident shifts in large-scale modes of natural variability confound attempts to link climate responses to aerosol forcing. For example, the Pacific Decadal Oscillation changed sign in the 1970s, at the same time that aerosol forcing is thought to have maximized over the Atlantic sector . Clearly, a deeper understanding of how the climate system responds to regional heating anomalies would provide a stronger foundation for quantifying the role of aerosol forcing. Toward this end, a simple method for prescribing aerosol-like anomalies in atmospheric composition would be useful.

These thoughts motivated us to develop a simple parameterization of anthropogenic aerosol optical properties and the effect of the anthropogenic aerosol on the radiative properties of clouds for use in climate models. We aimed to develop an analytic description of the anthropogenic aerosol capable of representing its observed spatiotemporal and spectral variability. Similar, albeit even more simplistic, approaches have been attempted in the past , but not for the purpose of studying aerosol changes, and without the benefit of modern observations. Our chosen description would be fit to the present-day observational record, and scaled backward and forward in time to capture past or future changes in aerosol and aerosol precursor emissions. An analytic, albeit empirical, description was desirable to avoid regridding a base climatology for a particular model resolution, and to reduce the input data volume, particularly given the importance and emphasis on the use of higher-resolution simulations in the future. An ability to vary the aerosol properties over time is necessary to represent scenarios of past and possible future effects of anthropogenic activity. In contrast to comprehensive aerosol–chemistry–climate models, we sought an approach that would be computationally lightweight, easy to implement and modify, yet similarly compelling in its ability to represent aerosol radiative forcing. By describing the aerosol in terms of its optical properties and its effect on cloud-droplet population densities, we reduce the chance of introducing discrepancies in forcing that may arise from different choices for how to couple parameterizations of aerosol physical properties to parameterizations of clouds and radiation. It is our hope that the methods we develop will provide a welcome complement to comprehensive aerosol models, spur research into how the climate system responds to forcing and help clarify what degree of detail in the representation of aerosol radiative forcing can lead to a response that is measurable against the noisy background of natural variability.

The organization of the paper is as follows. In Sect. 2, we describe the aerosol distribution component of the parameterization, which is fit to an observational climatology developed for the year 2005. In Sect. 3, we propose an approach for linking anthropogenic aerosol optical depth to changes in cloud active properties. Our representation of the 2005 aerosol distribution and aerosol radiative effects, including induced changes on the scattering cross section and albedo of clouds, is evaluated in Sect. 4 using global simulations with the Max Planck Institute Earth System Model, the MPI-ESM. In Sect. 5, we describe a procedure for scaling the 2005 climatology over the historical period using anthropogenic aerosol and aerosol-precursor emission estimates from different geographic regions, and show how a similar approach can be adopted to projected future emissions. The approach and our main results are summarized in Sect. 6.

Our basic idea is to associate spatial plumes of anthropogenic aerosols with emissions from source regions. The plumes are constructed by fitting to a climatology for the present-day (2005) distribution of anthropogenic aerosol optical depths in the mid-visible (550 nm) range. To capture past changes, the amplitude of these plumes will be scaled with the strength of the anthropogenic emissions within the source region. Major anthropogenic emissions are spatially compact, at least from a planetary perspective. This motivates the adoption of a small number of plumes as basis functions for representing anthropogenic aerosol optical properties and cloud active properties. For simplicity, we consider two plume types: one that is dominated by emissions from industrial emissions, the other from biomass burning. Hereafter, we refer to these as industrial and biomass plumes, respectively, even though each plume really composites over a mixture of source activities. The industrial and biomass plumes are distinguished by the strength of their seasonal cycle, their single-scattering albedo, and their cloud-droplet population density susceptibility to anthropogenic aerosol perturbations.

The plumes are designed to fit the 2005 distribution of mid-visible anthropogenic aerosol optical depth as described by the Max Planck Institute Aerosol Climatology, MAC . MAC provides estimates of monthly mean aerosol optical properties at a spatial resolution of 1∘ of latitude by 1∘ of longitude. Climatological values of aerosol properties are derived from high-quality data by ground-based sun-photometer networks AERONET; merged onto background maps from global models participating in the Aerosol Model Intercomparison Project (AeroCom). The merging is performed for different aerosol properties: aerosol optical depth (AOD) at 440, 550 and 870 nm, absorbing AOD at 550 nm and, in addition, for contributions to these properties by coarse-mode particles or fine-mode aerosol particles. The merged fine-mode AOD (at 550 nm), along with a scaling factor (anthropogenic fraction) based on fine-mode AOD output of comprehensive aerosol–chemistry models, run for present-day and pre-industrial conditions, define the anthropogenic AOD (at 550 nm) map of MAC. An anthropogenic contribution to the coarse mode is assumed negligible. MACv2 (MAC version 2), provides the baseline that the plume concept of MACv2-SP attempts to approximate. MACv2 was adopted because it incorporates a number of improvements compared to version 1, specifically (i) oceanic reference data from the Maritime Aerosol Network – MAN; are now included; (ii) aerosol extensive optical properties are merged; and (iii) on average, a roughly 30 % lower anthropogenic fine-mode AOD fraction is assumed, yielding an anthropogenic AOD more in line with other estimates. Adopting simple plumes as basis functions to represent the anthropogenic aerosol could be adapted to any climatology, but to reflect its origins in MACv2, hereafter we refer to our model as MACv2-SP.

Nine plumes (five industrial and four biomass) appear to adequately capture the spatial distribution of the anthropogenic aerosol of MACv2. The names given to the individual plumes, the location of the plume centers and the type of each plume is summarized in Table  and illustrated in Fig.  relative to the 2005 annual mean of MACv2. The plume centers are placed where the local AOD, as represented by MACv2, maximizes. Even for a perfect climatology this need not coincide with the location where emissions maximize, as the AOD is influenced by deposition and transport. The use of two plumes (north and south central Africa) in close proximity, to define the contribution to anthropogenic AOD over Africa, enables a better representation of different seasonal cycles.

A basic premise in the development of MACv2-SP is that the shape of individual plumes is independent of the strength of the source. This assumption is reasonable as long as effects from changes in the atmospheric circulation remain small relative to uncertainty in the aerosol pattern for a given source. The lack of a clear signal of a feedback on the aerosol forcing from changes in the climate supports this assumption . A climatological approach omits, however, the coupling between synoptic systems and the aerosol. This may be important to the aerosol effect: experience suggests that rainier days are cloudier, but also less aerosol laden at near-surface levels. Hence, prescribing the time mean aerosol may result in a larger radiative forcing than would arise from an aerosol with the same time mean properties, but which was allowed to interact with the circulation, i.e., the bistability hypothesis of . These effects, which are expected to be more pronounced for aerosol–cloud interactions, are accounted for in MACv2-SP by setting the spatial and seasonal pattern of the aerosol based on MACv2, but allowing a degree of freedom in the specification of its amplitude. In MACv2-SP, the eventual amplitude of the forcing, though guided empirically, is in effect a test quantity. The idea to use the flexibility of the parameterization to see what amplitude of forcing produces a response that is difficult to reconcile with the instrumental record (of, say, temperature). Studies using a similar approach e.g., have suggested that this may help provide better bounds on the magnitude of aerosol radiative forcing.

Mathematically, MACv2-SP provides a five-dimensional (three spatial dimensions, time and wavelength) description of the anthropogenic aerosol optical properties. The climatology is built around a description of the volume extinction, ea, at 550 nm. In a second step, described later, the wavelength dependence of the extinction is accounted for, and additional optical properties are specified. Unless an explicit wavelength dependence is specified, all properties are assumed valid at 550 nm.

The total volume extinction of mid-visible radiance by the anthropogenic aerosol, ea, is given as the emission-weighted sum of the extinction from nine different plumes: ea(x,y,z,t)=∑i=19ei(x,y,z,tf(t))Ei(ty(t)).

Here, ei defines the extinction associated with the ith plume for the year 2005, and Ei the emissions scaling. Year-to-year variations are separated from annual variations by describing the time dependence by two separated time variables. The emission scaling depends on ty(t), which denotes an integer year number, ty(t):=⌊t/1y⌋, which can be, for example, 1966 or 2008. The annual cycle depends on the year fraction, tf(t)=t-ty. In principle, tf is a real number defined over the unit interval; in our present implementation, the annual cycle changes discretely over 52 intervals, i.e., roughly on a weekly basis.

The optical path over a layer is defined as the integral of the volume extinction, τ(x,y,t)=∫z1z2e(x,y,z,t)dz

In the event that the path is over the entire atmospheric column, it is referred to as the optical depth. Unless explicitly specified, it is assumed that the interval corresponds to the entire depth of the atmosphere, in which case we speak of the column integral or the anthropogenic aerosol column optical depth.

To derive a relationship between the anthropogenic aerosol and cloud properties, we first explored the relationship between the fine-mode aerosol optical depth, τf, and cloud-droplet population densities, N. The spatial association between estimates of the two quantities is available from satellite observations and from modeling. Three different satellite datasets, described at a spatial (latitude, longitude) resolution of 1∘, are considered. Two datasets are from different processing versions of the MODIS (Moderate Resolution Imaging Spectroradiometer) sensor data, and one is based on the AATSR (Advanced Along Track Scanning Radiometer) sensor data. MODIS, due to its wider swath, offers more samples than AATSR does. A minimum τf of 0.05 was adopted to ensure retrieval reliability. Further details of these data are summarized in Table . Similarly, monthly averaged output from different global aerosol models participating in the AeroCom project was also analyzed. The N values were derived for levels warmer than the melting level from the indirect effect analysis of , and monthly averages of τf were analyzed for both the pre-industrial (1850) and present-day (2005) conditions . Model output was regridded to the spatial resolution (1∘ in latitude by 1∘ in longitude) of the satellite data for subsequent analysis.

The relationships between τf and N in global modeling are quite diverse and, on average, stronger than suggested by observations. In contrast, the satellite retrievals are more consistent, even though spatial (and temporal) coverage is limited to overcast oceanic regions. For this reason, our parameterization is founded on the satellite data; nonetheless, the relationship we derive remains consistent with the modeling given the large model spread.

Values of fine-mode optical depth and cloud-droplet population densities, {τf,N}, retrieved from satellite measurements are presented in Figs.  and . The MODIS collection 6 data are presented for the annual average and for the boreal summer season to allow for comparison with MODIS collection 5.1 (annual) and AATSR (seasonal). Due to quality control requirements, whereby retrievals are avoided in broken cloud scenes, the displayed data locations represent only a subset of the actually available data for τf and N.

Overall, the retrievals suggest that there is a relationship between τf and N. For instance, regions of elevated τf over the eastern-boundary currents in the Atlantic, near the Indian subcontinent, west of Japan and between Japan and the Asian mainland (Fig. ) also correspond to elevated values of N (Fig. ). The presence of an apparent relationship is consistent with previous work. , for instance, related local observations of total AOD to measurements of cloud condensation nuclei (CCN) and then, in a second step, related values of CCN to N. Some early studies of aerosol radiative forcing also adopted a similar approach e.g.,. The correspondence between τf and N is not perfect. For example, elevated values of N over the Californian stratocumulus regions (Fig. ) do not show a commensurately pronounced retrieval of τf (Fig. ) – although even here variability in the background contribution to fine-mode aerosol may mask relationships. In addition, although the retrievals of τf from the different satellite platforms are broadly consistent, estimates of N are much more variable and show systematic differences across the various products. Retrievals of N based on MODIS collection 5.1 yield much larger estimates than those based on collection 6.0 (e.g., Table ).

The covariation between τf and N is quantified through a consideration of all of the available data, as shown in Fig. . To construct this figure, retrieved values of N are binned as a function of τf drawn from clear-sky retrievals in the same geographic region. Shown are retrievals from satellite data (upper panel) and model output (lower panel). Values of τf>0.25 were excluded due to insufficient samples. The data of the joint histograms are statistically analyzed in 20 τf bins. Along the median values in each histogram, logarithmic fits of the form N∝ln⁡(τf) have been constructed and are displayed in Fig. . Despite considerable scatter, the relationship between N and τf is a systematic one: across almost all of the τf bins, N increases with τf, and this increase becomes smaller for larger τf. This is true for both the model output and the retrievals, although the relationship is somewhat stronger in the latter, and a bit less regular. A logarithmic function captures this behavior and is consistent with understanding that an increase in τf is expected to be associated with a smaller increase in N the larger N (or τf) was to begin with. One reason for such behavior is that with more available cloud condensation nuclei, peak supersaturations reduce, leading to a smaller activated fraction . Although the exact form of any purported relationship between τf and N can be debated, this analysis shows that a logarithmic relationship reasonably represents the data.

This logarithmic relationship forms the basis for representing the Twomey effect in MACv2-SP. The functional form proposed based on the analysis of the satellite data, Fig. , gives N=aNln⁡bN(τa+τbg)+1, where {aN,bN,τbg} are parameters. For the fit to MODIS C6, aN=16 and bN=1000. The value of τbg scales a spatial pattern of the background fine-mode aerosol that is the same as for τa, but is not something that can be derived from the data. It is a tuning parameter. Physically, we associate τbg with a background contribution to the AOD, as even in a pristine atmosphere cloud condensation nuclei are produced from purely natural processes and assumed to be distributed with the meteorology similar to τa. Based on Eq. , N(x,y,t)N1850(x,y,tf)=ln⁡bN(τa+τbg)+1ln⁡bNτbg+1.

By prescribing the MACv2-SP Twomey effect in the form of the ratio N/N1850, it does not interfere with the background (1850) droplet population, N1850, that was used to tune the host model, and it ensures that, all else being equal, the proportional change in N due to the anthropogenic aerosol will be insensitive to N1850. The strength of the Twomey effect in MACv2-SP thus depends largely on the specification of τbg.

In MACv2-SP, τbg is calculated identically to τa except that there is no emission weighting and the background plume amplitudes (the τi in Eq. ) are chosen to represent the contribution of the pre-1850 aerosol to N1850. These were chosen to be prescribed factors for industrial versus biomass regions with values that gave what are believed to be reasonable, globally and annually averaged droplet concentrations for the present day. A globally uniform background fine-mode AOD of 0.02 is also included on top of the pre-industrial (1850) source contribution so as to represent the effect of distributed sources such as sea salt, or DMS (dimethyl sulfide) emissions, on the background (1850) cloud-droplet population density. Because it describes the background, τbg is not emission weighted, but adopts values that are fixed in time. In Eq. (), the possibility of maintaining an annual cycle in the prescription of N1850 is indicated by the dependence on tf, even if in the present implementation of MACv2-SP such an effect is not implemented. Because τbg is specified as part of MACv2-SP, it will not necessarily be consistent with the N1850 of the models. But given that the purpose is simply to specify a consistent value of N/N1850 for all of the models, this is only a formal inconsistency in how one interprets Eq. (). Its ultimate consequence is that it inhibits models with a cleaner background state from having a larger Twomey effect for the same aerosol perturbation.

Equation () is consistent with the data and with understanding, but it is admittedly crude. One could imagine a variety of other relationships fitting the data equally well. Precisely for this reason, we favor a very simple form, as it makes the underlying assumptions transparent and easy to change. Toward this end, in a companion paper, examine in some detail how the effective radiative forcing depends on the form of Eq. () and its parameters. Consistent with what was found by , it is shown that the strength of the background, τbg, has the greatest impact on the radiative forcing from aerosol–cloud interactions, and it does so by effectively controlling how far from the plume center aerosol perturbations are allowed to influence cloud properties. If aerosol perturbations are allowed to extend further over the remote oceans, affecting larger regions with a darker surface, a greater (more negative) global mean radiative forcing arises.

The year-to-year variations are specified as a time series, Ei(ty), with ty denoting the year following a Gregorian calendar. Physically, it can be thought of as the column anthropogenic aerosol optical depth of the ith plume, at the plume center, normalized by its value in a reference year. Ei(ty)=τi(ty)/τi(tref) By definition, Ei(ty) is unity at ty=tref. In the present implementation, tref=2005.

Different approaches to the annual scaling have been considered. One approach is to scale values of τi by its ratio in any given year to its ratio in 2005 as calculated by aerosol–climate models. This approach helps account for the variety of processes that likely control AOD and can also be readily extended to the future. This connection to the more comprehensive modeling is attractive, but makes it difficult to change and lacks the transparency we desire. Instead, Ei(ty) is related to estimates of the past or projections of future emissions. If Eik(ty) denotes the annual emissions of component k for plume i, then Ei(ty)=∑kwkEik(ty)-Eik(1850)∑kwkEik(2005)-Eik(1850),fort≥1850, where wk denotes the weighting of the kth constituent emission contribution to the plume amplitude, for instance, SO2. Equation () ensures that Ei(1850)=0 and Ei(2005)=1. This prescription has been chosen with application to CMIP6 in mind, as it allows τa to be added to the background used by models in their control run, which is traditionally taken as 1850. Hence, the application of the MACv2-SP does not require models to rerun their control simulations. If one is interested in using this method for periods prior to 1850, or for scenarios where Eik(ty)<Eik(1850), the implied negative perturbation may exceed the background, which would require the approach to be revisited. Defining Ek(ty) as the global emissions of constituent k, the global weighting, E(ty), is defined analogously to Eq. ().

Both SO2 and NH3 emissions are allowed to contribute to Ei(ty). For these emissions, we use estimates from the Community Emissions Data System (CEDS; see http://www.globalchange.umd.edu/ceds/ceds-cmip6-data/). The CEDS is a data-driven, open-source framework developed to provide historical emission estimates of aerosol and precursor compounds. These emission data are being released for use as historical forcing input data for CMIP6. So as to capture all emissions, each country in the CEDS is associated with one of our nine plumes, as described by Table . The Ei(ty) are provided as an 11-year averaged value centered on the whole year, e.g., 1910 or 1950. As an example, Ei(t1950) is calculated using the emission data from 1945 through 1955 inclusive. Yearly values are then interpolated from these decadal values. Yearly values could easily be provided, but specifying the data in terms of decadal averages makes the climatology easier to change. Because the CEDS only includes emissions through 2014, the last decadal value in 2010 is an average over the 10-year period between 2005 and 2014.

Determining the Ei by SO2 emissions alone is not the same as assuming that only SO2 contributes to the anthropogenic aerosol, but rather that other anthropogenic aerosol and precursor compound emissions scale with the emission of SO2, an important but subtle distinction. Scaling anthropogenic aerosol forcing by SO2 emissions alone appears to reasonably capture the behavior of CMIP5 models . Nonetheless, there is some evidence that aerosol forcing may have begun to decouple from SO2 emissions with the onset of more stringent air quality controls in some countries beginning in the late 1970s and will increasingly do so in the future . To allow for this possibility, we add a second component which scales like the NH3 emissions. The relative weight of these two components is chosen so that the optical depth of the plume associated with the NH3 component is one-third of that from SO2 in the year 2005 (Table ). This ratio of one-third was chosen to match the ratio between present-day sulfate and ammonia forcing in the AeroCom II models .

As intended, the addition of an NH3 component to the temporal scaling moderates the effect of air quality regulations since the late 1970s. This is shown in Fig. . The blue dashed curve in the upper panel describes the relative contribution of aerosol precursors which scale like SO2. A value of 0.5, as is, for instance, evident around 1950, means that these precursors contributed to a global anthropogenic AOD relative to 1850 that is 50 % of what it was in 2005. The green dashed curve shows the same for components that scale with NH3 emissions, and together the blue and green curves sum to E(ty), as shown by the black curve. Absolute values of the equivalent SO2 emissions plus 0.55 times NH3 emissions (each measured in Tg), and the relative contribution of absorbing aerosol emissions, are tabulated for different time periods for the different plumes in Table .

Other factors, which do not correlate with regional NH3 and SO2 emissions, may also influence the amplitude of anthropogenic aerosol plumes. However, a direct link to emissions is simple, transparent and appears to capture the main features seen in more complex models. This is evident both in terms of the temporal trend in the global signal and in shifts of regional patterns, e.g., the very large regional shifts in aerosol loading over the last 40 years. Prior to the 1990s, emissions from North America and Europe dominated contributions to the anthropogenic aerosol. Thereafter, Asian sources became more important. This is shown in the lower panel of Fig. , where the relative contributions to E from a particular plume, Ei, or a group of plumes, is plotted. It shows, for instance, that according to MACv2-SP, in the year 2010, south and east Asia were responsible for 60 % of the total anthropogenic aerosol. Before 1970 emissions in the Atlantic sector were responsible for the vast majority of emissions. Changes in emissions over Europe rather than North America appear to be more important for the rapid rise of emissions, from about half their present-day values in 1950 to their local maximum around 1980. Because European emissions are more centered over the continent, one would expect this rise to be somewhat less effective than it would have been had it been associated with North American sources. The emissions history also suggests that the overwhelming amount of emissions have and continue to be dominated by Northern Hemisphere sources.

In the present implementation, the single-scattering albedo of the individual plumes does not vary with time. A different balance of emissions of absorbing versus scattering aerosols can be evaluated by comparing estimates of historical black carbon emissions to the emission factors used to scale the amplitudes of the MACv2-SP plumes. This ratio is plotted in Fig.  and suggests that the ratio was more or less constant over the first half of the last century, and began to decrease after around 1980 as efforts were made to limit SO2 emissions. A more absorbing anthropogenic aerosol would, all else being equal, lead to less radiative forcing per unit optical depth. The effects on the regional scale can be large, as is demonstrated by comparing the change in the ratio of black carbon to equivalent SO2 emissions over the historical record (e.g., Table ). Based on the CEDS data, the amount of black carbon emissions per unit equivalent SO2 emissions was about twice as large over Europe in 1950 as it was in 2005. This apparent brightening of the aerosol prior to about 1970 suggests that aerosol forcing in the period before extensive efforts to reduce SO2 emissions in the 1970s would have contributed to the radiative efficiency of the aerosol increasing with time, decreasing again after 1980. For the present, such effects are not included in MACv2-SP, which does not consider aerosol composition changes for biomass and industrial plumes over time. In light of the arguments of , experiments to judge the magnitude of such changes are warranted.

An empirically based analytic parameterization of anthropogenic (post-1850) aerosol optical properties and their associated Twomey effect, MACv2-SP, has been developed for use in climate modeling studies. MACv2-SP is empirical in that it is fit to the gridded MACv2 climatology, and thereby is directly constrained by understanding and measurements of the spatial distribution of the present-day anthropogenic aerosol. An analytic description was motivated by a desire to ease implementation and input data requirements, thereby helping ensure that the climatology could be consistently implemented across a range of models, including very-high-resolution models, and also varied easily. By describing the aerosol in terms of the post-1850 anthropogenic perturbation, MACv2-SP avoids the problem of perturbing the control climate of models in which it is implemented. By proposing a plausible representation of the anthropogenic aerosol that can be consistently implemented in many climate models, robust and consistent responses to aerosol forcing may emerge and these could provide a stronger top-down constraint on the magnitude of that forcing.

It is demonstrated that a plume-based model, which we call MACv2-SP, with relatively few degrees of freedom adequately captures the more complex MACv2 grid-point climatology. A total of nine plumes, describing the patterns of aerosol optical properties attributable to major emission regions, were sufficient to capture spatial variations in the anthropogenic aerosol. Each plume is in turn constructed from two independent features designed to capture differences in the near- and far-field aerosol response to sources and differences in meteorology that shape the plumes. Account was also taken of the annual cycle, the vertical distribution and the spectral dependence of aerosol optical properties. Perturbations to cloud active properties associated with the anthropogenic aerosol were scaled by fine-mode aerosol optical depth, using relationships derived from observational data and more comprehensive modeling. Despite its vastly reduced number of degrees of freedom, MACv2-SP is capable of reproducing the spatial distribution and amplitude of the anthropogenic AOD in MACv2, fitting the observations better (RMSE of 0.19 versus an AeroCom median RMSE of 0.63) than what is presently possible using process-based models. Other features, such as total AOD and the ratio of Northern Hemisphere to Southern Hemisphere loading, are also well captured by MACv2-SP.

MACv2-SP represents temporal variations in the anthropogenic aerosol by scaling the strength of its plumes in the year 2005 by estimates of historic (or possibly projections of future) emissions. In deriving the temporal scaling, both nitrate-like and sulfate-like aerosol precursors are accounted for. By “nitrate-like” or “sulfate-like” we mean that the temporal scaling of the precursors is like ammonia or like sulfur dioxide, but could in reality be attributable to a broader range of anthropogenic aerosol sources. These scaling factors are derived by associating national emission inventories with the nine plumes and provide a simple way of linking knowledge of aerosol emissions to plausible patterns of radiative forcing.

The approach underlying MACv2-SP is based on a single or guiding assumption: the difference between the climate response by a model using a fully interactive description of the aerosol, as compared to a climatological description of aerosol properties tuned to give the same radiative forcing, is small as compared to uncertainties arising from other sources, e.g., cloud parameterizations. This assumption, though common to any climatology, emphasizes that MACv2-SP is meant to be a reference aerosol-forcing climatology, not a reference aerosol climatology. Serving this purpose requires sufficient degrees of freedom to match both the radiative forcing arising from aerosol–cloud interactions and aerosol–radiation interactions, at the surface and the top of the atmosphere, and also describe the large-scale pattern of regional forcing. As a reference forcing climatology, MACv2-SP should not be interpreted in terms of its nominal physical parameters, but rather in terms of the radiative forcing it produces.

In constructing MACv2-SP, we have made a number of simplifications or secondary assumptions. We call these “secondary” because they are easy to modify without altering the basic approach. Nonetheless, because these simplifications reflect our beliefs as to what features of the anthropogenic aerosol are unimportant to the climate response, they are itemized here in the hope that they might help guide and focus future research. These are S1:

that MACv2 adequately describes the spatial distribution of the anthropogenic aerosol;

The climatology is constructed in a manner that makes it easy to relax and test many of these assumptions. For instance, the parameterization of the Twomey effect is easy to modify; likewise, the assumption that the single-scattering albedo of industrial plumes have not changed over the historical period can be relaxed. Although focusing on the simplifications itemized above encourages the thought that the climatological approach is too simple, it may well be that it is already more detailed than is really necessary for most purposes. For instance, there is scant evidence that many of the features which we endeavor to incorporate, such as the seasonal cycle, details of the plume shape or even such a large number of plumes, are important for the climate response. For this reason, future work should also explore the effect of simplifying MACv2-SP, as it may well turn out that even a substantially simpler implementation can capture the main response of the climate system to forcing.

MACv2-SP is implemented into the Earth system model of the Max Planck Institute for Meteorology (the MPI-ESM1.2), and an ensemble of simulations is used to estimate instantaneous and effective radiative forcing. Both forcing estimates for clear-sky and all-sky conditions are calculated. The all-sky effective radiative forcing is estimated from the simulations to be -0.5 W m-2. Clouds, by masking aerosol–radiation interactions, diminish the forcing, something that is partially offset by accounting for aerosol–cloud interactions. As a result, the net effect of clouds on aerosol radiative forcing is small but slightly positive, as the clear-sky effective radiative forcing (-0.67 W m-2) is more negative than the all-sky radiative forcing (-0.50 W m-2). Because cloud masking effects are not independent of the aerosol–cloud interactions, the effect of clouds, which are small here, can be inflated if the two effects are considered independently, as is usually the case. An instantaneous radiative forcing (all-sky) of -0.6 W m-2 is associated with the MPI-ESM1.2 implementation of MACv2-SP, as estimated from a double call to radiation. Adjustments, defined as the difference between the effective and instantaneous radiative forcing thus also act to weaken the overall forcing by about 20 %.

Though an effort has been made to characterize different measures of the radiative forcing associated with the MPI-ESM1.2 implementation of MACv2-SP, these numbers are intended more as a characterization of MACv2-SP and less as a new estimate of aerosol forcing. Although developed to mimic MACv2 and the synthesis of past AeroCom studies, MACv2 has been formulated so that it should be easy to adjust parameters to match other estimates of forcing, for instance, to allow for more potent aerosol–cloud interactions. The real purpose behind the development of MACv2-SP is to enable its use across a range of models in the hope that robust model responses emerge in a way that identifies additional constraints on the magnitude of the forcing, for instance, through detection and attribution approaches centered around the pattern of the response. Such an effort would be aided if MACv2-SP is adopted for use by other models.

The MACv2-SP climatology, including algorithms and input data used to generate the climatology, is provided as an electronic supplement to this paper. Primary data and scripts used in the analysis and other supplementary information that may be useful in reproducing the author's work are archived by the Max Planck Institute for Meteorology and can be obtained by contacting publications@mpimet.mpg.de.