Bounding Global Aerosol Radiative Forcing of Climate Change

1. Introduction

At steady state and averaged over a suitably long period, the heat content in the Earth system, defined here as the ocean, the atmosphere, the land surface, and the cryosphere, remains constant because incoming radiative fluxes balance their outgoing counterparts. Perturbations to the radiative balance force the state of the system to change. Those perturbations can be natural, for example, due to variations in the astronomical parameters of the Earth, a change in solar radiative output or injections of gases and aerosol particles by volcanic eruptions. Perturbations can also be due to human activities, which change the composition of the atmosphere.

A key objective of Earth system sciences is to understand historical changes in the energy budget of the Earth over the industrial period (Myhre et al., 2017) and how they translate into changes in the state variables of the atmosphere, land, and ocean; to attribute observed temperature change since preindustrial times to specific perturbations (Jones et al., 2016); and to predict the impact of projected emission changes on the climate system. From that understanding climate scientists can derive estimates of the amount of committed warming that can be expected from past emissions (Pincus & Mauritsen, 2017; Schwartz, 2018), estimates of net carbon dioxide emissions that would be consistent with maintaining the increase in global mean surface temperature below agreed targets (Allen et al., 2018), or the efficacy of climate engineering to possibly mitigate against climate changes in the future (Kravitz et al., 2015).

A sustained radiative perturbation imposed on the climate system initially exerts a transient imbalance in the energy budget, which is called a radiative forcing (RF; denoted as $\mathcal{F}$; Figure 1a). The system then responds by eventually reaching a new steady state whereby its heat content once again remains fairly constant. The equilibrium change in global mean surface temperature ΔT _s, in K, is given by

where $\mathcal{F}$ is the global mean RF, in W m⁻², and λ is the climate sensitivity parameter that quantifies the combined effect of feedbacks, in K (W m⁻²)⁻¹ (Ramanathan, 1975). For multiple reasons, including lack of knowledge of λ and the long response time of T _s to RF (Forster, 2016; Knutti et al., 2017; Schwartz, 2012), it has become customary to compare the strengths of different perturbations by their RFs rather than by the changes in T _s that ultimately ensue.

Temperatures in the stratosphere, a region of the atmosphere which is largely uncoupled from the troposphere‐land‐ocean system below, respond on a timescale of months, adjusting the magnitude and in the case of ozone perturbations even the sign of the initial RF (Figure 1b) (Hansen et al., 1997). This adjusted RF is defined by the 5th Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) (Myhre, Shindell, et al., 2013) as the change in net downward radiative flux at the tropopause, holding tropospheric state variables fixed at their unperturbed state but allowing for stratospheric temperatures to adjust to radiative equilibrium. This definition is adopted by this review.

In addition to exerting a RF, changes in atmospheric composition affect other global mean quantities, such as temperature, moisture, surface radiative and heat fluxes, and wind fields, as well as their spatiotemporal patterns. Some of these responses occur on timescales much faster than the adjustment timescales of ocean surface temperatures. These responses are called rapid adjustments and occur independently of surface temperature change (Hansen et al., 2005; Shine et al., 2003). Rapid adjustment mechanisms can augment or offset the initial RF by a sizable fraction, because they involve changes to the radiative properties of the atmosphere, including clouds, and/or the surface, which all contribute substantially to the Earth's energy budget. Consequently, effective radiative forcing (ERF; denoted $\mathcal{E}$; Figure 1c), which is the sum of RF and the associated rapid adjustments, is a better predictor of ΔT _s than RF (Figure 1d). Sherwood et al. (2015) make a pedagogical presentation of the concept of rapid adjustments that was used in IPCC AR5 (Boucher et al., 2013; Myhre, Shindell, et al., 2013). This review also adopts the definition of ERF introduced in the IPCC AR5 (Boucher et al., 2013; Myhre, Shindell, et al., 2013), which is the change in net top‐of‐atmosphere downward radiative flux that includes adjustments of temperatures, water vapor, and clouds throughout the atmosphere, including the stratosphere, but with sea surface temperature maintained fixed. In addition to its influence on global temperature change, ERF is also an efficient predictor of changes in globally averaged precipitation rate (Andrews et al., 2010). Those changes arise from a balance between radiative changes within the atmosphere and changes in the latent and sensible heat fluxes at the surface (Richardson et al., 2016). Accounting for rapid adjustments when quantifying radiative changes is essential to obtain the full response of precipitation.

RF can be induced in multiple ways: changes in atmospheric composition, both in the gaseous and particulate phases, induced by volcanic or anthropogenic emissions; changes in surface albedo; and variations in solar irradiance. An estimated full range of anthropogenic aerosol RF based on an elicitation of 24 experts of −0.3 W m⁻² to −2.1 W m⁻² at the 90% confidence level was presented by Morgan et al. (2006). Individual experts, however, allowed for the possibility of much more negative, but also the possibility even of net positive, RF. A similar degree of uncertainty has been reflected in an evolving series of IPCC assessment reports (Table 1), where best estimates and uncertainty ranges of aerosol RF are also based at least partly on expert judgment. Since RFs are additive within the forcing‐response paradigm, the uncertainty attached to the aerosol ERF translates to the entire anthropogenic ERF (Schwartz & Andreae, 1996). Recognition of this fact has motivated a tremendous effort, now lasting several decades, to better understand how aerosols influence radiation, clouds, and ultimately the large‐scale trajectory of the climate system, involving field measurements, laboratory studies, and modeling from microphysical to global scales (e.g., Ghan & Schwartz, 2007; Kulmala et al., 2011; Seinfeld et al., 2016).

In spring 2018, under the auspices of the World Climate Research Programme's Grand Science Challenge on Clouds, Circulation and Climate Sensitivity, 36 experts gathered at Schloss Ringberg, in the mountains of Southern Germany, to take a fresh and comprehensive look at the present state of understanding of aerosol ERF and identify prospects for progress on some of the most pressing open questions, thereby drawing the outlines for this review. The participants at that workshop expressed a wide range of views regarding the mechanisms and magnitudes of aerosol influences on the Earth's energy budget. This review represents a synthesis of these views and the underlying evidence.

This review is structured as follows. Section 2 reviews the physical mechanisms by which anthropogenic aerosols exert an RF of climate and sets the scope of this review. Section 3 presents a conceptual model of globally averaged aerosol ERF and the different lines of evidence used to quantify the uncertainty bounds in the terms of that conceptual model. Section 4 quantifies changes in aerosol amounts between preindustrial and present‐day conditions. Sections 5 and 6 review current knowledge of aerosol interactions with radiation and clouds, respectively, to propose bounds for their RF, while sections 7 and 8, respectively, do the same for their rapid adjustments. Section 9 reviews the knowledge, and gaps thereof, in aerosol‐cloud interactions in ice clouds. Section 10 reviews estimates of aerosol ERF based on the response of the climate system over the last century. Finally, section 11 brings all lines of evidence together to bound total global aerosol ERF and outlines open questions and research directions that could further contribute to narrow uncertainty or reduce the likelihood of surprises.

2. Mechanisms, Scope, and Terminology

3. Conceptual Model and Lines and Evidence

4. Preindustrial to Present‐Day Change in AOD

While present‐day aerosol properties such as the AOD, ${\tau }_{\mathrm{a}}^{\text{PD}}$, considered here at a wavelength of 0.55 μm, can be measured directly by ground‐based Sun photometers at certain locations or retrieved from satellite observations, the preindustrial (defined here as 1850) value, ${\tau }_{\mathrm{a}}^{\text{PI}}$, is not observable so $\mathrm{\Delta }{\tau }_{\mathrm{a}}={\tau }_{\mathrm{a}}^{\text{PD}}-{\tau }_{\mathrm{a}}^{\text{PI}}$ can only be estimated.

Direct measurements of ${\tau }_{\mathrm{a}}^{\text{PD}}$ come from the ground‐based AErosol RObotic NETwork (AERONET) Sun photometer network (Holben et al., 1998; Smirnov et al., 2009), which provides near‐global but sparsely sampled, cloud‐free hourly ${\tau }_{\mathrm{a}}^{\text{PD}}$ at accuracies better than 0.01 (Eck et al., 1999; Smirnov et al., 2000). With added information of their sky radiances samples, the AERONET Sun photometers also provide information on vertically integrated aerosol size and light absorption. However, continental and often near‐urban locations lead to systematic biases (R. Wang et al., 2018). To supplement these measurements, long‐term satellite remote sensing retrievals are also available, with more than 30 years of passive measurements, including almost two decades of Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol retrievals; and more than a decade of active measurements using the Cloud‐Aerosol Lidar with Orthogonal Polarization (CALIOP). Passive satellites retrieve an AOD from the measured radiance after carefully screening for clouds. Those AOD retrievals are based on radiative transfer calculations that take into account illumination and viewing geometry, extinction by Rayleigh scattering (with attendant assumption on aerosol height), surface reflectance, and aerosol properties (especially angular dependence of scattering and SSA). Levy et al. (2013) evaluate the uncertainty in global mean ${\tau }_{\mathrm{a}}^{\text{PD}}$ from MODIS to about ±0.03, or 15% to 20%. Current satellite lidar retrieval of aerosol extinction requires the ratio of extinction to backscatter that depends on aerosol particle radius, sphericity, and SSA. An aerosol typing algorithm is used to choose from a set of default lidar ratio values, but this is a significant source of retrieval uncertainty. Globally averaged clear‐sky ${\tau }_{\mathrm{a}}^{\text{PD}}$ at 0.55 μm from MODIS/Aqua Collection 6 is, at 0.17, about 30% larger than CALIOP Version 3 at about 0.12 (Winker et al., 2013). The true value is likely somewhere in between, because systematic errors in the MODIS retrieval, mostly driven by errors in surface albedo and cloud artifacts, tend to bias ${\tau }_{\mathrm{a}}^{\text{PD}}$ high, whereas systematic CALIOP errors tend to bias ${\tau }_{\mathrm{a}}^{\text{PD}}$ low (Kittaka et al., 2011). Among the retrieval algorithms applied to measurements by MODIS, the Advanced Along‐Track Scanning Radiometer (AATSR), and the Sea‐Viewing Wide Field‐of‐View Sensor (SeaWIFS), the lowest global mean ${\tau }_{\text{PD}}^{\mathrm{a}}$ of 0.13 is obtained by the DeepBlue algorithm (Hsu et al. 2013) applied to SeaWIFS and the largest, at 0.17, is obtained by both the DarkTarget algorithm (Levy et al. 2013) applied to MODIS/Terra and the Oxford‐RAL Aerosol Cloud algorithm (Thomas et al. 2009) applied to AATSR.

Most GCMs that simulate aerosol distributions routinely calculate τ _a for both present‐day and preindustrial conditions. Figure 4 shows the relationship between Δτ _a and ${\tau }_{\mathrm{a}}^{\text{PD}}$ in all of the CMIP5 (Taylor et al., 2012) models which participated in the sstClimAerosol experiment, the AeroCom Phase II (Myhre, Samset, et al., 2013) models and the density of 1 million emulated simulations of a PPE using the HadGEM3‐UKCA model to sample uncertainties in 26 physical parameters relating to aerosol processes as well as present‐day and preindustrial emissions (Yoshioka et al., 2019). While there is a large spread in the ${\tau }_{\mathrm{a}}^{\text{PD}}$ (shown in the uppermost panel) in the unconstrained PPE, both multimodel ensembles (MMEs) peak between the lower and upper observational estimates. The MMEs simulate a relationship between ${\tau }_{\mathrm{a}}^{\text{PD}}$ and Δτ _a, which one would expect on physical grounds from a residence time argument, allowing the observational constraints on ${\tau }_{\mathrm{a}}^{\text{PD}}$ of 0.13 to 0.17 to be translated into a range for Δτ _a of 0.03 to 0.04. Sampling only those PPE members, which fall within the observational bounds, leads to a constraint on Δτ _a of 0.03 to 0.05. However, one needs to account for the high bias in the default ${\tau }_{\mathrm{a}}^{\text{PD}}$ simulated by the PPE, and a possible high bias in observational estimates, so a range of 0.02 to 0.04 represents a more conservative assessment. By determining the anthropogenic contribution to ${\tau }_{\mathrm{a}}^{\text{PD}}$ in the Monitoring Atmospheric Composition and Climate (MACC) Reanalysis (Benedetti et al., 2009); Bellouin, Quaas, et al. (2013) determine Δτ _a as 0.06. The Max Planck Institute Aerosol Climatology (MAC) (Kinne, 2019; Kinne et al., 2013) combines AERONET climatologies with aerosol properties from AeroCom models (Kinne et al., 2006). They report Δτ _a as 0.03, which is within the range of the GCM estimates. It should, however, be noted that these estimates rely on the same industrial‐era emissions data sets used in many of the GCM simulations. The larger spread in Δτ _a in the PPE is likely due to the fact that it samples uncertainties in these emissions.

Relying on large‐scale models to estimate Δτ _a implies that all preindustrial and present‐day sources and sinks of anthropogenic aerosols are represented in these models. There are several reasons that suggest that this is not the case. Potential underestimates of Δτ _a come from many GCMs neglecting nitrate aerosols (Myhre, Samset, et al., 2013), which are partly anthropogenic, and having difficulties representing anthropogenic contributions to mineral dust aerosols (Evan et al., 2014). Potential overestimates of Δτ _a come from ignoring the possibility that preindustrial fires emitted carbonaceous aerosols at rates similar to present‐day fires (Marlon et al., 2016). In addition, it remains unclear whether biogenic aerosols were more or less prevalent in the preindustrial atmosphere (Ding et al., 2008; Kirkby et al., 2016), and interactions between sulfate aerosol and organic aerosols of biogenic origin may be sizable (Zhu et al., 2019).

Regarding mineral dust aerosols, their anthropogenic component is emitted directly by agriculture and indirectly by soils made more erodible and climate conditions made more erosive by human influence. Estimates of present‐day anthropogenic dust fractions obtained by combining anthropogenic land use data with mineral dust AOD from satellite retrievals range from 8% in North Africa to about 75% in Australia (Ginoux et al., 2012) and China (X. Wang et al., 2018). On a global average, the present‐day anthropogenic mineral dust fraction may be as large as 25% (Ginoux et al., 2010; Huang et al., 2015), translating to an increase in Δτ _a of about 0.007, or 15% to 30% of the range of 0.02 to 0.04 obtained above. However, uncertainties on these estimates are large. A few GCM studies yield a range of 10% to 60% for the global average in the anthropogenic fraction of mineral dust for present‐day (Mahowald & Luo, 2003; Stanelle et al., 2014; Tegen et al., 2004), although their simulated changes in anthropogenic mineral dust aerosol disagree in both sign and magnitude (Webb & Pierre, 2018). This disagreement is at least in part caused by differences in simulated meteorological processes (Fiedler et al., 2016). There are uncertainties on mineral dust distributions in 1850 as well, which depend on how vegetation responds to climate changes (Mahowald, 2007). Considered together the contribution of anthropogenic mineral dust aerosols to ERFari is expected to be smaller than for other anthropogenic aerosols, on the order of −0.1 ± 0.2 W m⁻² (Boucher et al., 2013), owing to compensating contributions of SW scattering and LW absorption. Indeed, Kok et al. (2018) showed that most models underestimate the size of mineral dust aerosols so the compensation between mineral dust SW and LW radiative effects may in fact be stronger than modeled. However, mineral dust aerosols are efficient INPs so anthropogenic mineral dust aerosol potentially alters the radiative properties and life cycle of ice clouds (Gettelman et al., 2012; Kuebbeler et al., 2014; Penner et al., 2018).

Regarding carbonaceous aerosols, emission inventories used by GCMs usually scale fire emissions back to preindustrial levels using historical population changes (e.g., Lamarque et al., 2010), so obtain an increase through the industrial era. Paleoclimate records paint a more complex picture where preindustrial conditions might be more polluted, leading to a smaller Δτ _a. The synthesis of sedimentary charcoal records by Marlon et al. (2016) suggests a sharp increase in biomass burning from 1800 to 1850, a period of high level of biomass burning from 1850 to 1970, a trough around the year 2000, followed by an abrupt increase up to 2010, although data density is highest in North America and Europe, so those trends may not be globally representative. Still, according to Marlon et al. (2016) present‐day (2010) biomass burning appears larger, on a global scale and for the Northern and Southern Hemispheres individually, than preindustrial if the preindustrial reference year is set at 1750. But choosing a reference year of 1850 means that biomass burning levels were similar to present day. In contrast, van Marle et al. (2017) derive, by merging the satellite record with several existing proxies, including the charcoal records, similar biomass burning emissions between 1750 and 1850, and in their reconstruction, global biomass burning emissions increased only slightly over the full time period and peaked during the 1990s after which they decreased gradually. Hamilton et al. (2018) used significantly revised estimates of preindustrial fires in a single global model study and found an effect of only 10% on RFari. But the impact on CCN was larger, reducing the model's RFaci by 35% to 91% depending on the strength of preindustrial fire emissions.

In summary, a range of 0.02 to 0.04 for Δτ _a at 0.55 μm is supported by large‐scale modeling and reanalyses. Combining the range for Δτ _a with the range of 0.13 to 0.17 for ${\tau }_{\mathrm{a}}^{\text{PD}}$ yields a range of 0.14 to 0.29 for $\mathrm{\Delta }{\tau }_{\mathrm{a}}/{\tau }_{\mathrm{a}}^{\text{PD}}$, meaning that human activities are likely to have increased globally averaged τ _a by around 15% to 30% in 2005–2015 compared to the year 1850. The range for Δτ _a may be too narrow if a large contribution by anthropogenic mineral dust or nitrate aerosols has been overlooked by large‐scale models, or too wide if the atmosphere in year 1850 was significantly more polluted by fire emissions than currently thought. Although those differences may not always affect globally averaged ERFari on account of the absorbing properties of the aerosols involved, they could lead to sizable changes in ERFaci.

5. RF of Aerosol‐Radiation Interactions

As stated in section 2.1, efficiency factors for scattering and absorption per unit AOD depend on a wide array of physical and chemical properties of the aerosols. In light of that complexity, the good agreement in clear‐sky sensitivities $S_{\tau }^{\text{clear}}=\partial R_{\text{clear}}/\partial {\tau }_{\mathrm{a}}$ among AeroCom models is remarkable, with Myhre, Samset, et al. (2013) reporting in their Table 3 a value of −23.7 ± 3.1 W m ${}^{-2}{\tau }_{\mathrm{a}}^{-1}$ (neglecting an anomalous outlier because the causes for its very strong clear‐sky RFari are not understood) or, if sensitivities are expressed in terms of planetary albedo, a range for $S_{\tau }^{\text{clear}}$ from 0.06 to 0.08  ${\tau }_{\mathrm{a}}^{-1}$. Clear‐sky RFari against Δτ _a is shown in Figure 5 for two multimodel ensembles and a large single‐model PPE. While there is a large spread in the absolute values of RFari, particularly in the PPE which was designed to explore the full range of parametric uncertainty in HadGEM3 and is unconstrained by observations here, the slope, which is the sensitivity S _τ, is similar between the multimodel and perturbed parameter ensembles.

Uncertainties in the retrieval of τ _abs are much larger than for τ _a and contribute to the spread in $S_{\tau }^{\text{clear}}$ seen in Figure 5. The absorption of seasalt and sulfate aerosols is well constrained, but the absorption of mineral dust and carbonaceous aerosol is poorly characterized. Bond et al. (2013) noted that AeroCom models underestimate τ _abs compared to AERONET so they proposed increasing emissions of absorbing BC aerosols in response. They estimated that the present‐day anthropogenic τ _abs from carbonaceous aerosols is about 0.007 at 0.55 μm. Bellouin, Quaas, et al. (2013) also used AERONET to prescribe aerosol absorption and reached a similar estimate based on a reanalysis of atmospheric composition. But more recent studies challenged the need for scaling of models and the suitability of AERONET constraints, instead improving modeled BC by increasing the model horizontal resolution (X. Wang et al., 2014), reducing BC lifetime (Samset et al., 2014) to reduce overestimations of BC concentrations in remote areas (Kipling et al., 2013), or accounting for AERONET τ _abs sampling errors (X. Wang et al., 2018) and possible high bias compared to in situ airborne absorption coefficients (Andrews et al., 2017). Compared to Kinne (2019), Bond et al. (2013) overestimated anthropogenic τ _abs because they underestimated the contribution of mineral dust aerosol to τ _abs and overestimated the anthropogenic fraction of BC aerosols. The revised calculation by Kinne (2019) therefore motivates a downward revision of τ _abs at 0.55 μm, with a range of 0.0025 to 0.005. Rapid adjustments due to anthropogenic absorption are discussed in section 7.

Extending $S_{\tau }^{\text{clear}}$ to all‐sky conditions requires accounting for masking by clouds above aerosol but also aerosol absorption enhancement when clouds are below the aerosol (Figure 3). According to AeroCom models, those situations only contribute a small forcing on a global average, with a distribution centered around 0 W m⁻² (Schulz et al., 2006). Studies based on CALIOP estimate a positive aerosol radiative effect above clouds (Chand et al., 2009; Kacenelenbogen et al., 2019; Oikawa et al., 2018), resulting from a partial compensation of a positive radiative effect by smoke aerosols with a negative radiative effect from mineral dust aerosols, although the anthropogenic fraction of those aerosols and the resulting cloudy‐sky RFari is unknown. In addition, CALIOP underestimates aerosols at altitudes above 4 km (Watson‐Parris et al., 2018). Although the regional cloudy‐sky radiative effects of ari can be strongly positive (de Graaf et al., 2014; Keil & Haywood, 2003; Peers et al., 2015), a small globally averaged cloudy‐sky RFari is expected because most of anthropogenic aerosols are located in the planetary boundary layer, where their RFari is masked by dense water clouds or partially masked by ice clouds. Indeed, GCMs tend to put too much aerosol mass aloft compared to CALIOP vertical aerosol extinction profiles (Koffi et al., 2016), so even the small cloudy‐sky RFari reported by Schulz et al. (2006) may be an overestimate. Based on the results of Schulz et al. (2006), $S_{\tau }^{\text{cloudy}}$ may be as small as ±0.02 ${\tau }_{\mathrm{a}}^{-1}$. That small efficiency coupled with the regional and seasonal nature of occurrences of anthropogenic aerosols above clouds suggest that all‐sky S _τ is approximately equal to $S_{\tau }^{\text{clear}}$ weighted by an effective clear‐sky fraction, and that cloudy‐sky forcing only adds an uncertainty of ±0.1 W m⁻² (Schulz et al., 2006).

This effective clear‐sky fraction is the complement of the effective cloud fraction for ari, noted c _τ in equation (8). c _τ is the convolution of the cloud fraction $\mathcal{C}$ and cloud optical depth, τ _c, to account for situations where clouds are too thin to completely mask the RFari of aerosols located below them, and Δτ _a, to account for the different distributions of anthropogenic aerosols and low clouds. This gives

where angle brackets denote global‐area‐weighted temporal averaging. Stevens (2015) finds c _τ=0.65, which is close to the mean c _τ of 0.66 obtained by the nine global aerosol‐climate models that participated in Zhang et al. (2016) (Table 3). Those models give a standard deviation for c _τ of 0.06. Because large‐scale models tend to have similar geographical distributions of anthropogenic aerosols, differences primarily stems from different liquid cloud climatologies in AeroCom models. GCMs are known to underrepresent low‐level cloudiness (Nam et al., 2012), so may underestimate c _τ by simulating the wrong spatial patterns of $\mathcal{C}$.

In summary, the RF of ari, $\mathcal{F}\text{ari}$, is computed as in equation 8, $\mathrm{\Delta }{\tau }_{\mathrm{a}}\left[S_{\tau }^{\text{clear}}\left(1-c_{\tau }\right)+S_{\tau }^{\text{cloudy}}{c}_{\tau }\right]$ where the last term represents the contribution of cloudy‐sky ari. The ranges adopted for the terms of this equation are:

• 0.02 to 0.04 for Δτ _a, as obtained by section 4;

• −20 to −27 W m ${}^{-2}{\tau }_{\mathrm{a}}^{-1}$ for $S_{\tau }^{\text{clear}}$, rounding outwards the range simulated by AeroCom models used by Myhre, Samset, et al. (2013). $S_{\tau }^{\text{clear}}$ can also be expressed in terms of planetary albedo by dividing by the globally and annually averaged solar constant of 340 W m⁻²: The range becomes 0.06 to 0.08 ${\tau }_{\mathrm{a}}^{-1}$;

• 0.59 to 0.71 for c _τ, rounding outwards the range simulated by AeroCom models used by Zhang et al. (2016) (Table 3);

• 0.0 ± 0.1 W m⁻² for the product $S_{\tau }^{\text{cloudy}}{c}_{\tau }$, as simulated by AeroCom models (Schulz et al., 2006).

Using the method described in section 2.2 to combine those ranges and compute the first term of equation (8) yields a range for $\mathcal{F}\text{ari}$ of −0.37 to −0.12 W m⁻². The rapid adjustments due to anthropogenic absorption are discussed separately in section 7.

6. RF of Aerosol‐Cloud Interactions in Liquid Clouds

Since liquid clouds and ice clouds behave differently in several aspects, it is useful to distinguish between the two. Clouds with a cloud top temperature warmer than 0 °C are liquid. Clouds colder than this behave in the same way in terms of the mechanisms that determine RFaci if they consist of supercooled liquid water but behave differently when ice becomes present. The three key bulk quantities that describe the properties of a liquid cloud are their LWP, $\mathcal{L}$, their cloud fraction, $\mathcal{C}$, and their droplet number concentration, N _d.

Cloud droplets are formed via adiabatic cooling of air parcels by updrafts that generate supersaturation, and each droplet forms on an aerosol particle that serves as a CCN at the supersaturation determined by the cooling rate. Which aerosols are activated into cloud droplets depends on the size of the particles and their hygroscopicity (Köhler, 1936), as well as on the maximum supersaturation that is reached given the balance between adiabatic cooling due to the updraft that increases supersaturation, and condensation of vapor onto the droplets that reduces it (Twomey, 1959). In consequence, additional aerosol leads to further cloud droplets if they are large enough compared to the preexisting aerosol population. On average, at the scale of an air parcel, an approximately logarithmic scaling between aerosol concentration and N _d is obtained (Twomey, 1959). At the cloud scale, it is therefore sufficient to know the aerosol size distribution and hygroscopicity, as well as the updraft distribution, to predict N _d as well as its sensitivity to the aerosol. A relative change of N _d in response to an aerosol, a, perturbation is thus

The aerosol metric a is left ambiguous here, since in different observations‐based studies, different choices are made. The optimal definition would be the CCN concentration at cloud base, but for many observations (e.g., remote sensing), this quantity is not accessible. The sensitivity ${\beta }_{\ln N-\ln a}$ is often evaluated using linear regressions, with various choices for the aerosol metric a (Feingold et al., 2003; McComiskey et al., 2009). For large updrafts and suitable aerosol, at relatively low background aerosol concentration, such as found for remote marine trade‐wind cumulus, a sensitivity approximately equal to unity is observed with CCN as aerosol metric (Martin et al., 1994; Twohy et al., 2005; Werner et al., 2014). For more general situations, including smaller updraft speeds, higher CCN concentrations, and broader aerosol size distributions, the scaling between aerosol concentration and N _d is substantially lower (e.g., Boucher & Lohmann, 1995; Lu et al., 2009). McFiggans et al. (2006) explore the sensitivity from parcel modeling to obtain values between 0.7 and 0.9. Surface remote sensing statistics yield a range of 0.3 to 0.5 for a coastal site (McComiskey et al., 2009), midlatitude continental sites (Kim et al., 2008; Schmidt et al., 2015) and the Arctic (Garrett et al., 2004). Values can be larger—up to 0.75—when sampling updraft conditions only (Schmidt et al., 2015). Painemal and Zuidema (2013) obtain values as large as 0.8 to 0.9 when combining in situ aerosol observations with aircraft remote sensing for N _d over the Southeast Pacific Ocean.

A wide range of observational evidence from ship tracks, trends in anthropogenic emissions, and degassing volcanic eruptions (Gassó, 2008; Christensen & Stephens, 2011; Yuan, Remer, Pickering, & Yu, et al., 2011; Christensen et al., 2014; McCoy & Hartmann, 2015; Malavelle et al., 2017; Toll et al., 2017; McCoy, Field, et al., 2018; Li et al., 2018) and numerous field studies in different regions (Boucher & Lohmann, 1995; Lowenthal et al., 2004; Rosenfeld et al., 2008; Werner et al., 2014) support the theoretical argument that the impact of additional aerosols in the atmosphere is to increase N _d, and decrease the cloud effective radius as the liquid water is spread among a larger number of droplets (Twomey, 1977). But quantifying those relationships is difficult and depends on cloud regime.

For global coverage, the sensitivity of N _d to aerosol can only be assessed from satellite retrievals (Nakajima et al., 2001; Lohmann and Lesins, 2002; Sekiguchi et al., 2003; Quaas et al., 2006). However, such assessments suffer from a number of problems.

1. Aerosol and cloud quantities usually cannot be retrieved in the same column. It is thus unclear to what extent the aerosol retrieved in clear‐sky pixels is representative of the aerosol relevant for cloud droplet formation (e.g., Gryspeerdt et al., 2015). Even if in general, the horizontal scale of variance of the aerosol is large compared to that of clouds (Anderson, Charlson, Winker, et al., 2003), this assumption may be weak in the proximity of precipitating clouds. In addition, sampling the aerosol radiative properties in close vicinity to clouds leads to errors (Christensen et al., 2017) due to the humidity swelling of the aerosol (Quaas et al., 2010) and misclassification of cloud as aerosols (Zhang et al., 2005).

2. The most straightforward remote sensing aerosol retrieval is the AOD, τ _a. However, τ _a does not scale very well with the relevant CCN concentration at cloud base, because it is a column‐integrated quantity, is affected by humidity, and by aerosols that may not act as CCN (Stier, 2016). Errors in retrieved τ _a are also largest at small values where cloud sensitivity may be largest (Ma et al., 2018). The aerosol index, calculated by multiplying τ _a by a measure of aerosol size, is often suggested as an approximate solution to provide a possibly better indicator of CCN concentrations (Gryspeerdt et al., 2017; Penner et al., 2011; Stier, 2016), but at low aerosol loadings uncertainties in aerosol index are even larger than for τ _a.

3. Cloud droplet number concentration is derived from retrievals in a very indirect way, which relies on cloud top quantities and assumptions to extrapolate down to cloud base where equation (10) applies. Depending in particular on cloud heterogeneity and solar zenith angle, retrievals may be strongly biased (Grosvenor et al., 2018). The retrieved N _d does not directly correspond to the activated droplet concentration near cloud base but is the result of both cloud microphysical processes and cloud entrainment mixing processes. Aggregation to relatively coarse retrieval scales reduces the representativeness of the sensitivity of N _d to the aerosol because important process‐level scales are not captured (McComiskey & Feingold, 2012).

From satellite remote sensing, thus, the sensitivity of N _d to aerosol is often estimated by evaluating equation (10) using τ _a as the aerosol metric. Most of the caveats listed above, except for the increased τ _a when considering retrievals within approximately 15 km of nearby clouds (Christensen et al., 2017), lead to too weak sensitivities when retrieving the N _d—τ _a relationship. Making use of satellite‐based statistics to quantify ${\beta }_{\ln N-\ln {\tau }_{\mathrm{a}}}$ usually yield much smaller values than those derived from airborne measurements (McComiskey & Feingold, 2012; McCoy et al., 2017; Nakajima & Schulz, 2009; Schmidt et al., 2015). The full range for ${\beta }_{\ln N-\ln a}$, using different aerosol quantities for a, compiled by those studies spans 0.14 to 1.00. However, local sensitivities need to be weighted globally to be relevant for the large‐scale forcing. The newest compilation of large‐scale sensitivities by McCoy et al. (2017) obtains (their Figure 3) a range of 0.3 to 0.8. It is difficult to rigorously assign confidence intervals, in particular because the physically meaningful range is bounded. Nevertheless, if one considers the full range of 0.14 to 1.00 from the four studies cited above as the 90% confidence interval, one obtains a ±σ interval of 0.52, which matches the interval obtained by McCoy et al. (2017).

Combining the range of 0.3 to 0.8 for ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$ with the ranges of 0.02 to 0.04 for Δτ _a and 0.13 to 0.17 for τ _a obtained in section 4 yields a range of 0.05 to 0.17 for $\mathrm{\Delta }\ln N_{\mathrm{d}}$, encompassing the estimate of 0.15 obtained by Charlson et al. (1992) and Stevens (2015).

The dependency of cloud reflectance on the bulk cloud properties N _d and $\mathcal{L}$ is based on their relationship with cloud optical depth, τ _c, assuming adiabatic clouds (e.g., Brenguier et al., 2000):

Further, variations in cloud albedo, α _c, are related to variations in τ _c approximately as (Ackerman et al., 2000)

If $d\ln \mathcal{L}$ is set to 0, the RF of the Twomey effect, $\mathcal{F}\text{aci}$, is isolated. According to equation (8), $\mathcal{F}\text{aci}$ is also:

The anthropogenic perturbation of droplet number concentration is estimated from the sensitivity of N to aerosol perturbations, and the relative perturbation in aerosol, $\mathrm{\Delta }\ln N_{\mathrm{d}}={\beta }_{\ln N-\ln a}\mathrm{\Delta }\ln a$. If τ _a is chosen to quantify the aerosol, $\mathrm{\Delta }{N}_{\mathrm{d}}={\beta }_{\ln N-\ln a}\frac{\mathrm{\Delta }{\tau }_{\mathrm{a}}}{{\tau }_{\mathrm{a}}}$, leading to the equation:

For reference, Table 2 summarizes the definitions of the variables used in equation (15).

Since the Twomey effect has little impact on $R_{\text{LW}}^{\uparrow }$, S _N can be redefined for convenience as the sensitivity of the planetary albedo with respect to N _d perturbations:

Inserting equation (13) into equation (16) yields (Twomey, 1977):

The global mean cloud albedo is quantified from the CERES SSF1deg Ed4A (Loeb et al., 2016) at α _c = 0.38 ± 0.02, evaluated as the planetary albedo at 1°×1° grid boxes where the fractional coverage by liquid water clouds is larger than 95%. Propagating the uncertainty in α _c to S _N using equation (17) yields a range for S _N, as defined by equation (16), of 0.077 to 0.080. In equations (6) and (14), c _N is an effective cloud fraction. It is “effective” because it is not just the fractional coverage by liquid water clouds, ${\mathcal{C}}_{\text{liq}}$, as retrieved from satellite data, that would be the relevant quantity at a given location in space and time (e.g., Quaas et al., 2008). Instead, it also takes into account the spatial covariability of the other terms relevant to deriving RFaci. c _N is needed because equation (13) is a global mean equation. In essence, c _N is the spatiotemporally resolved $\mathcal{F}$aci, normalized by the global‐temporal averages of the first four terms on the right‐hand side of equation (13):

where angle brackets denote global‐area‐weighted temporal averaging of two‐dimensional distributions. In other words, it is the fractional coverage of liquid clouds weighted by:

• the sensitivity of cloud albedo to perturbations in N _d, S _N;

• the local sensitivity of N _d to perturbations in aerosol, ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$

• the occurrence of anthropogenic perturbations to the aerosol, $\frac{\mathrm{\Delta }{\tau }_{\mathrm{a}}}{{\tau }_{\mathrm{a}}}$; and

• the incoming solar radiation.

The range in ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$, 0.3 to 0.8, is taken from McCoy et al. (2017) and the range for Δτ _a is that spanned by Bellouin, Quaas, et al. (2013) and Kinne (2019).

The local sensitivity ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$ is calculated using MODIS collection 6 cloud droplet number concentration, sampled following Grosvenor et al. (2018) and the MODIS AOD (Levy et al., 2013). The Δτ _a/τ _a used are from Bellouin, Quaas, et al. (2013). Although the magnitude of ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$ calculated using this method is an underestimate (Penner et al., 2011), c _N only depends on its spatial pattern. To obtain an uncertainty range in c _N, alternative spatial distributions for ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$ are taken from McCoy et al. (2017) and for Δτ _a/τ _a from Kinne (2019), yielding a range for c _N of 0.19 to 0.29. The value of 0.1 used in Stevens (2015) is therefore outside the 68% confidence interval obtained here, but he was likely referring to marine stratocumulus clouds, while the present range encompasses all liquid clouds. Figure 6 illustrates the geographical distribution of c _N as defined in equation (18) but averaging the numerator only in time, not in space. Compared to C _liq, the distribution of c _N emphazises low maritime clouds, and especially stratocumulus decks, which are most sensitive to aerosol perturbations (Alterskjær et al., 2012; Oreopoulos & Platnick, 2008). The tendency of C _N to be larger than C _liq is expected due to spatial correlations between C _liq and β_{ln Nd−ln τa} (Gryspeerdt & Stier, 2012).

In summary, calculating $\mathrm{\Delta }\ln N_{\mathrm{d}}$ as $\mathrm{\Delta }{\tau }_{\mathrm{a}}/{\tau }_{\mathrm{a}}^{\text{PD}}{\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$, where ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}=\partial \ln N_{\mathrm{d}}/\partial \ln {\tau }_{\mathrm{a}}$, yields a range of 0.05 to 0.17, based on the ranges of

• 0.02 to 0.04 for Δτ _a and 0.13 to 0.17 for ${\tau }_{\mathrm{a}}^{\text{PD}}$, following section 4;

• 0.3 to 0.8 for ${\beta }_{\ln N_{\mathrm{d}}-\ln {\tau }_{\mathrm{a}}}$, following McCoy et al. (2017);

Note that McCoy et al. (2017) infer the sensitivity from sulfate mass concentration rather than AOD. Their sensitivity is therefore used here by assuming that the relative perturbation in anthropogenic AOD is proportional to the perturbation in anthropogenic sulfate mass concentration.

The range for $\mathrm{\Delta }\ln N_{\mathrm{d}}$ means that human activities are likely to have increased globally averaged cloud droplet number concentrations by 5 to 17% in 2005–2015 compared to the year 1850. The RF of aci, $\mathcal{F}$aci, is computed following equation (14). The ranges adopted for the terms of this equation are as follows:

• 0.05 to 0.17 for $\mathrm{\Delta }\ln N_{\mathrm{d}}$, as above;

• 0.077 to 0.080 for S _N, based on uncertainties in α _c from CERES. That range converts to a range of −26 to −27 W m⁻² in terms of top‐of‐atmosphere radiation: The conversion is done by multiplying by the global, annual mean incoming solar radiation of 340 W m⁻²;

• the range of 0.19 to 0.29 for c _N.

Using the method described in section 2.2 to combine those ranges and solve equation 15, the range for $\mathcal{F}$aci is −1.10 to −0.33 W m⁻². Rapid adjustments to aci are quantified separately in section 8.

7. Rapid Adjustments to Aerosol‐Radiation Interactions

Both dR/dR _atm and dR _atm/dτ _a of equation (8) have been found to depend on the amount and altitude of absorbing aerosols and the location of those aerosols relative to the clouds by large‐eddy simulations (Johnson et al., 2004), global modeling (Hansen et al., 2005; Penner et al., 2003), and observations (Koren et al., 2004). These findings were summarized into frameworks where the sign of the adjustments depends on the cloud regime and whether aerosols are below, in, or above the clouds (Bond et al., 2013; Koch & Del Genio, 2010), although only a handful of studies were available to illustrate each case. When absorbing aerosol lies within the boundary layer, the RF is positive while when it lies above the boundary layer it is negative. Assessments based on large‐scale modeling, like Boucher et al. (2013), conclude that the rapid adjustments to ari operating via changes in cloud properties exert a negative RF on a global average, of the order of −0.1 W m⁻², suggesting a dominance of absorbing aerosol above clouds. Large eddy simulation (LES) modeling of semidirect effects suggests a positive RF from convective cloud suppression when absorbing aerosol lies within the boundary layer (Feingold et al., 2005) and positive again when absorbing aerosol lies above stratocumulus clouds (Yamaguchi et al., 2015). The latter study showed a delay of the stratocumulus to cumulus transition, complementing observations by Adebiyi et al. (2015). That delay could be associated with a locally large negative RF. But as discussed in section 3.2.1, scaling those results to a global radiative sensitivity is challenging.

In contrast to RFari, a substantial fraction of the rapid adjustments happens in the LW spectrum (Penner et al., 2003). The Precipitation Driver Response Model Intercomparison Project (PDRMIP) (Myhre et al., 2017) focused on rapid adjustments in clouds, but also on the contribution stemming from altered tropospheric temperature and water vapor profiles. Smith et al. (2018) found that rapid adjustments associated with temperature changes in the troposphere and stratosphere and those due to water vapor changes are comparable in magnitude to the rapid adjustments in clouds. Again, most of the rapid adjustments occur in the LW spectrum. The PDRMIP results indicate that the total rapid adjustment represents about half of the strength of the RFari by BC aerosols. Scaling the PDRMIP results to current estimate of global anthropogenic emission of BC (Hoesly et al., 2018) would give a total rapid adjustment due to BC of about −0.2 W m⁻². However, the PDRMIP results are based on global models that may overestimate the lifetime of BC aerosols and their concentrations aloft. A shorter BC lifetime, in better agreement with observations in the middle and upper troposphere, would reduce the magnitude of the rapid adjustment but would also reduce the BC RFari (Hodnebrog et al., 2014).

PDRMIP models find a total rapid adjustment of −1.3 W m⁻² for an instantaneous change in atmospheric absorption of +6.1 W m⁻² (Supplementary Tables 1 and 2 of Myhre et al., 2018), leading to a mean dR/dR _atm=−0.2, with a standard deviation of 0.09. The RF exerted within the atmosphere per unit anthropogenic τ _a is generally small, except over regions and during seasons where the amount of absorbing aerosol is large. On a global, annual average basis, Bellouin, Quaas, et al. (2013) find dR _atm/dτ _a=+41 W m ${}^{-2}{\tau }_{\mathrm{a}}^{-1}$. This is at the higher end of the range obtained by AeroCom models, which span +13 to +47 W m ${}^{-2}{\tau }_{\mathrm{a}}^{-1}$, with a median of +26 W m ${}^{-2}{\tau }_{\mathrm{a}}^{-1}$ and a standard deviation of 9 W m ${}^{-2}{\tau }_{\mathrm{a}}^{-1}$ (Myhre, Samset, et al., 2013).

In summary, rapid adjustments of ari are computed using the second term of equation (8), Δτ _adR/dR _atmdR _atm/dτ _a. The ranges adopted for the terms of this equation are:

• 0.02 to 0.04 for Δτ _a, as obtained by section 4;

• −0.1 to −0.3 for dR/dR _atm based on PDRMIP simulations reported by Myhre et al. (2018)

• 17 to 35 W m ${}^{-2}{\tau }_{\mathrm{a}}^{-1}$ for dR _atm/dτ _a, based on AeroCom simulations reported by Myhre, Samset, et al. (2013).

Using the method described in section 2.2 to combine those ranges yields a range for the rapid adjustments to ari of −0.06 to −0.25 W m⁻². The range for $\mathcal{E}$ari is obtained by adding, with the method described in section 2.2 again, the range for rapid adjustments to the range of −0.12 to −0.37 W m⁻² obtained for $\mathcal{F}ari$ in section 5. Doing so yields a range of −0.23 to −0.58 W m⁻² for $\mathcal{E}ari$. Note that $\mathcal{F}ari$ and its rapid adjustments are correlated, at least in the framework of equation (8), through Δτ _a.

8. Rapid Adjustments to Aerosol‐Cloud Interactions

The change in N _d due to aerosols that drives the Twomey effect may also impact cloud droplet size and so modify cloud processes (Ackerman et al., 2004; Albrecht, 1989). While the RF of the Twomey effect is formulated in terms of a constant $\mathcal{L}$, a change to cloud processes may be able to modify $\mathcal{L}$ and $\mathcal{C}$, possibly generating a significant RF (Albrecht, 1989; Pincus & Baker, 1994). This section concentrates on liquid cloud adjustments. Similar rapid adjustments in response to aerosol perturbations in mixed‐phase and ice clouds may also produce a sizable RF (Lohmann, 2002; Lohmann, 2017; Storelvmo, 2017; Storelvmo et al., 2008) but are covered by section 9 because different processes are involved and the level of scientific inquiry is less advanced. The present section also considers constraints on rapid adjustments in $\mathcal{L}$ and $\mathcal{C}$ separately, following equation (8). This separation allows a better comparison with the observational studies that adopted an approach where a system‐wide variable, the cloud radiative effect, is used to compute ERFaci. Those studies treat “intrinsic” (changes in cloud albedo), and “extrinsic” (changes in $\mathcal{C}$) effects separately (e.g., Chen et al., 2014). Doing so reduces the number of free parameters to just a few (e.g., $\mathcal{C}$, α _c, and τ _a) in which the observational uncertainties are better known than for N _d and $\mathcal{L}$. It also has a closer correspondence to the internal structure of many GCMs, where $\mathcal{L}$ and $\mathcal{C}$ are treated by different parametrizations, even though the liquid cloud adjustments are usually parameterized through modification of the autoconversion rate (e.g. Khairoutdinov and Kogan, 2000), which is the rate at which cloud water becomes rain water. The intrinsic/extrinsic methodology closely agrees with earlier methods (e.g. Quaas et al., 2008), as shown by Amiri‐Farahani et al. (2017) and Christensen et al. (2017).

9. Aerosol Interactions With Ice Clouds

Ice clouds are also affected by aerosol, although the impact of aerosol depends on the aerosol type and the dominant ice nucleation mode. Sulfate aerosols facilitates homogeneous freezing of haze drops in the upper troposphere at cirrus temperatures (lower than about −38 °C). Thus, the increase in sulfate concentrations due to anthropogenic precursor emissions leads to an increase in ice crystal number, N _i. This effect implies cirrus clouds with higher emissivity (less LW radiation emitted to space) and reflectivity (more SW reflected back to space), with RFs of opposite sign. Studies using satellite retrievals of N _i provide some observational evidence for an enhancement from aerosol (Gryspeerdt et al., 2018; Mitchell et al., 2018; Sourdeval et al., 2018) in regions of strong updrafts, although theoretical studies suggest that the overall magnitude of this effect is small because the primary control on the homogeneous nucleation rate is the in‐cloud updraft (DeMott et al., 1997; Jensen et al., 2013, 2016; Kay & Wood, 2008; Krämer et al., 2016; Lohmann & Kärcher, 2002).

Some aerosol types are effective heterogeneous INPs. Mineral dust (particularly feldspars; Atkinson et al., 2013) has been shown to be an effective INP in laboratory studies (Hoose & Möhler, 2012) and is correlated to the occurrence of glaciated clouds (Choi et al., 2010; Tan et al., 2014), so anthropogenic changes to mineral dust aerosols may change INP distributions (see section 4). The internal mixing of dust and soluble aerosol has been shown to suppress the INP activity of dust, such that anthropogenic emissions of liquid aerosol may also impact INP distributions (e.g. Cziczo et al., 2009). The ability of BC to act as an INP depends on its physical characteristics and mixing state, with particles containing macropores being observed to nucleate ice at cirrus temperatures (Mahrt et al., 2018), but there is increasing evidence that it is a poor INP at warmer temperatures (Kanji et al., 2017). In a situation dominated by heterogeneous nucleation, increasing INP would increase N _i. In contrast, in situations dominated by homogeneous nucleation, increasing INP can reduce the available supersaturation below the homogeneous nucleation threshold, reducing N _i (Kärcher & Lohmann, 2003). Similarly, there is some evidence from satellite retrievals for a suppression of homogeneous nucleation and N _i by INP (Chylek et al., 2006; Gryspeerdt et al., 2018; Zhao et al., 2018), but the sparse nature of INP measurements makes these results uncertain. Furthermore, Christensen et al. (2014) found by studying CALIOP lidar observations of over 200 ship tracks in mixed‐phase stratocumulus clouds that increased aerosols enhance the occurrence of ice and decreased total water path in polluted clouds.

The only global estimates of RFaci[ice] and ERFaci[ice] that currently exist are produced using GCMs and mostly focus on cirrus. It is not always possible to separate the instantaneous RF from its rapid adjustments in the literature and it is not clear whether the ERFaci[ice] would scale with the RFaci in a similar fashion to the ERFaci[liq]. Gettelman et al. (2012) found a positive RFaci[ice] of +0.3 W m⁻², or about a 20% offset of RFaci[liquid]. The importance of the fraction of particles acting as INP was highlighted by Penner et al. (2009), who found a negative RFaci[ice] of −0.3 to −0.4 W m⁻² with a lower preindustrial INP population. Similarly, the INP efficiency of BC has a large effect on the simulated N _i and RFari (Penner et al., 2009). The uncertainty in these factors is reflected in the wide range of estimates of ERFaci[ice] (Heyn et al., 2017). In general, aerosol interactions with ice clouds are likely N _i dependent and slightly larger for those states with less homogeneous nucleation and lower ice number concentration in the base state. The uncertainty regarding the balance of homogeneous and heterogeneous nucleation for ice clouds (Gasparini & Lohmann, 2016) and the lack of observations to constrain globally cirrus INP or N _i limit how accurately the aerosol effect on ice clouds can be constrained. On balance, it seems like effects may be small and positive: by increasing ice crystal numbers, cirrus LW increases faster than SW cooling. However, as laboratory measurements have shown that BC is not as efficient an INP as previously thought and does not affect homogeneous nucleation, a large RFaci[ice] is less likely than in the past. Combined with the second order effect of aerosol on homogeneous nucleation, this suggests the resulting RFaci[ice] may be on the order of a small fraction of the total anthropogenic ERFaci, but cannot be bounded yet because of the large uncertainty in the present and preindustrial states of ice cloud nucleation pathways and INP populations.

There is no observational evidence for strong adjustments in mixed‐phase and ice clouds. Christensen et al. (2016) presents some evidence for a modest aerosol radiative warming by deep convective cores without anvil spreading, identified from CloudSat radar observations. The ability of INP to glaciate supercooled liquid clouds in the temperature range of −38 °C to 0 °C is well established theoretically and supported by observed relationships between aerosol and cloud glaciation (Choi et al., 2010; Hu et al., 2010; Kanitz et al., 2011; Tan et al., 2014) at a global scale. An increase in cloud ice through an increase in the number of INPs might be expected to increase precipitation rates (Field & Heymsfield, 2015; Lohmann, 2002), but the resulting impact on cloud water and amount along with the corresponding radiative effect of anthropogenic aerosols is currently not well constrained, with GCM studies suggesting the net overall effect to be small (Hoose et al., 2008; Lohmann, 2002). Models that include explicit treatment of INP sources and cloud microphysics at high resolution suggest a strong link between $\mathcal{L}$ (and reflected SW radiation) and INP driven by changes in precipitation (Vergara‐Temprado, Holden, et al., 2018).

There is some observational evidence of aerosols impacting convective clouds, with many possible mechanisms proposed (Fan et al., 2013; Rosenfeld et al., 2008; Williams et al., 2002). However, interpreting those results based on high‐resolution simulations of deep convective clouds that often last a few hours only may overemphasize the importance of microphysical perturbations that may not matter for longer climate‐relevant systems. While changes in cloud top height have proved difficult to isolate from meteorological covariations (Gryspeerdt, Stier, & Grandey, 2014), studies have found an enhancement of lightning in regions of enhanced aerosol (Yuan, Remer, Pickering, & Yu, 2011; Gryspeerdt, Stier, & Partridge, 2014; Thornton et al., 2017) and increases in cloud top height downwind of volcanoes (Yuan, Remer, & Yu, 2011; Mace & Abernathy, 2016), suggestive of an aerosol impact. The radiative effect of an aerosol impact on convective clouds is unclear. It is possible that an increase in thin anvil cirrus might act as a warming effect (Koren, Remer, et al., 2010), but there are no strong observational constraints on this process and it may be small globally due to the tendency of LW and SW effects to cancel each other (Heyn et al., 2017; Lohmann, 2008) in deep convective clouds. Local circulation changes associated with aerosol gradients could, however, be important. For example, Blossey et al. (2018) found by modeling shipping lanes that the gradient between polluted shipping lane clouds and their cleaner surroundings may strengthens updrafts in the lane.

In summary, there is clear evidence of aerosols influencing the cloud phase but uncertainties remain too large to provide robust assessments. Estimates of the ERFaci[ice] are currently sparse and the uncertainty from cloud microphysics schemes tends to rival potential aerosol effects (White et al., 2017). RFaci[ice] from cirrus would tend to be positive because of anthropogenic aerosols inducing more small ice crystals and higher ice mass through an increase in homogeneous freezing (Gettelman et al., 2012). This response might not occur depending on details of the balance of heterogeneous and homogeneous freezing (Penner et al., 2018; Zhou & Penner, 2014), and the ice nuclei population, but evidence currently supports a positive RFaci[ice] from cirrus of a few tenths of a W m⁻². For shallow mixed‐phase clouds the effect of changes in CCN appears to be smaller than for liquid clouds (Christensen et al., 2014), but there is likely to be a positive RF in response to increases in INP, driven by increases in precipitation (Vergara‐Temprado, Miltenberger, et al., 2018).

The current lack of observational constraints on ice phase processes limits the accuracy with which the ERFaci[ice] can be constrained, so it is not bounded in this review. Observational constraints on the size of anthropogenic perturbation in N _i would allow further progress. In addition, studies providing estimates for sensitivities of ice cloud albedo, ice water path, and ice cloud fraction, as well as cloud top height, to anthropogenic aerosol changes would allow the decomposition of the ice as well as mixed‐phase and LW terms of equation (8) in a way similar to liquid clouds.

10. Inferences Based on Observed Changes in Temperature and Radiation

The temperature of Earth's surface has increased by 1.0 ± 0.2 °C since preindustrial times (Allen et al., 2018), and except for periods lasting less than a few decades, this increase in temperature occurred since 1850 (Hartmann et al., 2013). This increase in temperature is attributed mainly to anthropogenic forcing, primarily the ERFs due to increases in abundance of the greenhouse gases (GHG; positive, warming influence) minus the effective forcings due to increases in abundance of aerosols (negative, cooling influence) (Myhre, Shindell, et al., 2013; Bindoff et al., 2013). Here arguments are presented that the increase in global temperature together with knowledge of the GHG forcing can usefully constrain the aerosol forcing.

Under the assumption that the increase in global temperature is a response to forcing, the continuous increase in Earth's temperature implies that the net average forcing has been positive throughout the period, except for short periods, for example, after volcanic eruptions (Stevens, 2015). Knowledge of greenhouse gas ERF provides a constraint on the magnitude of the total ERF: the total ERF in the year 2011 with respect to year 1750, excluding the aerosol ERF, is estimated as +3.1 ±0.4 W m⁻² (Myhre, Shindell, et al., 2013) (uncertainty converted to ±1σ), implying within the stated assumption that the 2011 aerosol ERF was less negative than −3.5 W m⁻². Rotstayn et al. (2015) analyzed the relationship between the simulated aerosol ERF (2010 vs. 1765) and the simulated change in global mean surface temperature 2000 vs. 1860 in the CMIP5 multimodel ensemble (Fig. 7a). They also cite the average temperature increase over the same period from five observational data sets at 0.6 K. The emergent constraint (Klein & Hall, 2015) constructed by Rotstayn et al. (2015) from surface temperature change suggests values of aerosol ERF around −1.0 W m⁻².

Stevens (2015) proposed that it is possible to draw a tighter constraint on the aerosol ERF by considering an earlier part of the industrial period, when the relative importance of the aerosol ERF would be expected to have been greater due to the assumed sublinearity of the aerosol ERF. He further argued that the constraint is still tighter when assuming that increasing temperatures in the Northern Hemisphere can be linked to a net positive hemispheric ERF. The suggestion, based on a simple model for the hemispheric mean forcing, led to the conclusion that the present global aerosol ERF is unlikely to be more negative than −1.0 W m⁻². However, slightly more comprehensive energy balance models (Booth et al., 2018) and GCMs (Kretzschmar et al., 2017) find that global mean aerosol ERFs as negative as −2 W m⁻² are still consistent with the observed Northern Hemisphere temperature increase. It is plausible that restricting the analysis in the original study by Stevens (2015) to the northern hemispheric energy balance is hampered by the existence of and the uncertainty in the cross‐equatorial energy transports. Requiring instead that each decade during the second half of twentieth century has nonnegative total anthropogenic and natural ERF, taking into account a low efficacy of volcanic forcing (Gregory et al., 2016), shows that it is unlikely that the aerosol forcing is more negative than −1.7 W m⁻². It is noteworthy that the GCMs in the CMIP5 ensemble with the most negative aerosol ERFs exhibit behavior that calls their fidelity into question, such as a much smaller warming than observed for many time periods of the twentieth century (Golaz et al., 2013) or unrealistic pattern in aerosol radiative effects (Stevens & Fiedler, 2017). The globally averaged emission rate of sulfate aerosols has been approximately stable since the mid‐1970s (Hoesly et al., 2018) although the geographical distribution has moved equatorward to different cloud regimes. This allows for a tighter constraint when considering only the more recent past and increasingly tight constraints may be possible in the future if aerosol ERF weakens and CO₂ ERF increasingly dominates the overall anthropogenic ERF (Myhre et al., 2015). It is noteworthy that energy balance calculations with zero aerosol ERF can yield global mean temperature evolutions that are consistent with the instrumental record, albeit requiring low sensitivity. Schwartz (2018) showed that the observed temperature record over the period 1850 to 2011 is consistent with aerosol forcing throughout the IPCC AR5–95% uncertainty range, but requiring low transient sensitivity (1.0 K) for low‐magnitude present aerosol forcing (−0.09 W m⁻²) and high transient sensitivity (2.0 K) for high‐magnitude present aerosol forcing (−1.88 W m⁻²).

A stronger constraint could be obtained if transient climate sensitivity, the ratio of global temperature increase to global mean net forcing, were known to a good accuracy (Schwartz & Andreae, 1996; Knutti et al., 2002; Anderson, Charlson, Schwartz, et al., 2003). Figure 7b displays the hyperbolic inverse relationship between the transient climate response and aerosol ERF shown here for a large ensemble from a simple climate model and from an energy balance model. The ensemble by Smith et al. (2018) has a 16–84% confidence interval for transient climate response of 1.3 to 2.0 K, which translates into a ±1σ confidence interval for aerosol ERF of −1.2 to −0.6 W m⁻². Skeie et al. (2018) obtain a quantitatively similar relationship between aerosol ERF and transient climate response using an energy balance model.

Beyond surface temperature, observations of the radiation budget may be exploited to infer clues about aerosol ERF. Murphy et al. (2009) analyze satellite retrievals of the top‐of‐atmosphere radiation budget. They find a likely range for aerosol ERF of about −0.6 to −1.5 W m⁻². Cherian et al. (2014) explore the observations of surface solar radiation over Europe for the 1980–2005 period, in comparison to GCMs. They relate regional surface solar radiation trends simulated by the GCMs in the CMIP5 multiclimate model ensemble and simulated global mean aerosol ERF. The observed surface solar radiation trend for the 1980–2005 period over Europe, together with the GCM emergent constraint suggested a plausible range of aerosol ERF of −0.9 to −1.5 W m⁻². In turn, Storelvmo et al. (2018) analyzed multiple surface solar radiation measurement stations across the globe with varying record lengths in comparison to the CMIP5 multimodel ensemble. They concluded that all GCMs exhibit much weaker trends in surface solar radiation than the observations they assessed, since the midtwentieth century. However, the simulated temperature trends by the GCMs are consistent with the observed temperature changes. Their result might be indicative of the possibility of a very strong aerosol ERF in the SW spectrum, but does not consider LW components.

In summary, there are two conclusions from the assessment of the climate responses: (i) the fact that surface SW radiation responded to aerosol emission changes as observed, combined with the conclusion by section 4 that anthropogenic aerosols are relatively weakly absorbing on a global average, establishes that the SW component of the aerosol ERF is negative, and (ii) different studies based on observed global temperature changes conclude that an ERF more negative than −1.2 to −2.0 W m⁻², depending on the study, is outside the likely range considered in this assessment. On balance, −1.6 W m⁻² is adopted here for the lower bound of the ±1σ confidence interval.

11. Synthesis and Challenges

Based on the conceptual model of aerosol instantaneous RF and rapid adjustments represented by equation 8, this review has considered several lines of evidence, including modeling and observations at various scales, on the likely strength of aerosol ERF, defined with respect to year 1850. Of all the components of aerosol ERF quantified in this review, and for which different lines of evidence support the existence of an effect, rapid adjustments to aci are most difficult to bound based on current literature, because it is challenging to properly average globally the many possible cloud responses to aerosol perturbations. The dominant uncertainties are, however, the industrial‐era changes in AOD, Δτ _a, and in cloud droplet number concentration, ΔN _d, because they effectively cascade through to each ERF component under the framework of this review and its assumptions. Based on a combination of large‐scale modeling and satellite retrievals, human activities are likely to have increased AOD by 14% to 29% and cloud droplet number concentration by 5‐17% in 2005–2015 compared to the year 1850. Table 4 gives ranges in the 16–84% confidence interval for each term of equation (8). The table also lists the main lines of evidence used in this review to obtain each range. Global modeling and satellite analyses are the main lines of evidence used. Although small‐scale modeling and observation studies should in theory be the most accurate sources for the radiative sensitivities of equation (8), the current lack of a strategy for scaling their results to the global average limits their use.

Evaluating equation (8) using the Monte Carlo approach described in section 2.2 yields a range for total aerosol ERF of −2.2 to −0.6 W m⁻² at the 16% to 84% confidence level. This range is similar to that obtained from a single‐model PPE, constrained by observations, which covers −2.2 to −0.7 W m⁻² (Regayre et al., 2018). In other words, process‐based attempts to quantify aerosol ERF do not constrain the more negative bound. As discussed in section 10, inferences based on observed climate changes provide additional constraints that narrow the distribution by making an aerosol ERF more negative than −1.6 W m⁻² unlikely. The upper bound is not constrained further by those inferences. Consequently, the likely range of aerosol ERF obtained by this review spans −1.6 to −0.6 W m⁻² (±1σ range).

This review estimates all uncertainty ranges at the 16% to 84% confidence level, as discussed in section 2.2. IPCC Assessment Reports make a different choice, reporting at the 5% to 95% confidence level. To facilitate comparisons, Table 5 translates the ranges given by this review to the 5% to 95% confidence level. However, those latter ranges are more dependent on the assumed shapes of the distributions given in Table 4, which are difficult to assess from the literature. Comparing Tables 1 and 5 suggests that working through traceable and arguable lines of evidence, as done in this review, produces uncertainty ranges that are similar to the expert judgment of IPCC AR5, albeit shifted toward more negative ERFs. Accounting for the different preindustrial reference years (1750 for IPCC AR5, 1850 for this review) would shift the present assessed range further, by 0 to −0.2 W m⁻² (Myhre, Shindell, et al., 2013; Lund et al., 2019).

The full probability distribution functions for aerosol ERF and its components are shown in Figure 8. Also shown are the probability distribution functions obtained for total aerosol ERF by the IPCC Fifth Assessment Report (Myhre, Shindell, et al., 2013). The figure illustrates the reduction in the range for ERFari, which is due to a reduction of the likelihood of strong rapid adjustments to ari. The range for ERFaci is much wider in this review than in Myhre, Shindell, et al. (2013), the long tail coming from this review's wider assessment of rapid adjustments of aerosol‐cloud interactions in liquid clouds. Consequently, the range for total aerosol ERF is also much wider. This review, however, decreases the likelihood of an aerosol ERF more positive than −0.4 W m⁻². In addition, recall that total aerosol ERF more negative than −2.0 W m⁻² rely on more speculative aerosol‐driven cloud changes, and are not consistent with observed temperature and surface radiation changes, as discussed in section 10.

There are a number of challenges to overcome to narrow the range of aerosol ERF further. This review has already discussed the challenges associated with the imperfect knowledge of changes in aerosols over the industrial period (Carslaw et al., 2013), which in this review were encapsulated in Δτ _a (section 4), and with aerosol interactions with ice clouds (section 9), which are not yet characterized sufficiently well to allow a global assessment of sensitivities. But other outstanding challenges should be highlighted:

• The lack of resolution of small scales by large‐scale models means that their integration of local processes into a globally averaged number is imperfect. For ari, small scales contribute significantly to spatial variability of relative humidity and unresolved aerosol amount/composition, which together determine hygroscopic growth and the amount of light scattered. Because aerosol growth factors are superlinear, application of a spatially averaged aerosol growth factor could significantly underestimate the average of the local growth factors, particularly at relative humidities above 85% (Haywood et al., 1997; Nemesure et al., 1995; Petersik et al., 2018). For aci, unresolved cloud‐scale vertical motion and turbulent mixing, and coarsely parameterized cloud and precipitation, as well as aerosol sink processes, lead to poor representations of cloud and aerosol fields, their spatiotemporal collocation, and regime‐dependent small‐scale to mesoscale interactions of processes. The emergence of global storm resolving models (Satoh et al., 2018) and the ability to perform global LES for a few days would add substantially to our ability to better quantify these processes.

• The covariability of aerosol, clouds, and meteorological conditions implies scale effects. The fidelity of a modeled ERFaci or ERFari is dependent on the ability of the model not only to generate realistic clouds on average but also to capture their covariability at smaller spatiotemporal scales. As shown by various studies, the composite response does not equal the local responses averaged up to the composite scale. In reality local data typically comprise relatively small aerosol ranges and small albedo, N _d, or effective radius responses. If aci metrics or ERFs are based on aggregation of many such scenes they will tend to bias the relationships by (i) extending the range of conditions beyond the natural local fluctuations and (ii) removing the small‐scale covariability between meteorology and aerosol. The magnitude of these biases is poorly known.

• The frequency of occurrence of aerosol perturbations to planetary albedo in general, and to clouds in particular, has not yet been quantified at the global scale. For example, ship tracks are often cited as evidence that tremendous radiative effects can be generated by anthropogenic aerosol emissions, yet merely 0.002% of the world's commercial ocean‐going fleet are expected to generate a ship track in their wake at any given time (Campmany et al., 2009). So while evidence exists to support large contributions of rapid adjustments to ERFaci, these events seem infrequent. The challenge is that large‐scale attribution of changes in cloud properties to aerosol perturbations is complicated by covariability between meteorological drivers and aerosols, discussed above, and the high degree of natural variability within the cloud deck itself, which can span orders of magnitudes in cloud radiative properties (Wood et al., 2018).

• Models of all scales include a very large number of imprecisely known parameters. In such complex model systems with compensating effects of imperfectly known processes, even tight observational constraint of any model variables can leave open wide ranges of aerosol RFs (Johnson et al., 2018) so understanding why some models do well against multiple constraints is important (Penner, 2019). This model constraint limitation has become known as equifinality (Beven & Freer, 2001).

• Although this review has taken a global perspective in its assessment of aerosol ERF, geographical considerations remain important. For example, it is possible that the radiative sensitivities in equation (8) vary in time when aerosol and/or cloud patterns change in response to changes in emissions and climate. In addition, assuming that aci are saturated in the more polluted regions, then any additional anthropogenic aerosols would need to reach pristine regions in order to exert an ERFaci. More observational evidence is needed to constrain the magnitude with which anthropogenic aerosols affect pristine regions like the Southern Ocean and ocean cloud decks adjacent to continents in the eastern Pacific and eastern Atlantic Oceans.

The lack of evidence to support some of the hypotheses discussed in this review points to the need for improving scientific understanding of aerosol ERF processes and occurrences in the atmosphere. The review has identified a few critical next steps. First, scale effects are increasingly being considered among hierarchies of models and must inform global aerosol model development to ensure a more exhaustive representation of aerosol forcing and rapid adjustment mechanisms. Second, volcanic eruptions and ship tracks have provided important insights into cloud adjustments to aerosol perturbations and may provide opportunities to improve understanding of potential cloud phase shifts and ice cloud responses. Third, the strength of the constraints on aerosol ERF bounds provided by inferences based on observed climate changes is diminished by an incomplete understanding of the uncertainties affecting those methods. “Perfect model” comparisons, where top‐down methods are applied to synthetic data of known equilibrium climate sensitivity and aerosol ERF, would strengthen that important line of evidence. Fourth, statistical methods to thoroughly explore causes of model uncertainty are now being more widely adopted, and are being combined with traditional multimodel ensembles to more rigorously understand the effectiveness of observational constraints. Finally, global large‐eddy simulations hold promise to substantially improve the quantification of aerosol‐cloud interactions.

Glossary

Aerosol

Solid and liquid particulates in suspension in the atmosphere, with the exception of cloud droplets and ice crystals.

Albedo

Ratio of reflected to incident irradiance.

Cloud condensation nuclei

Subset of the aerosol population that serves as sites where water vapor condenses to form cloud droplets.

Effective radiative forcing

The sum of radiative forcing and rapid adjustments (see those terms).

General Circulation Model

Numerical model that solves fluid mechanics equations to simulate the three‐dimensional dynamics of the moist atmosphere. Those models also include parametrizations of radiation, clouds, and, increasingly, aerosols.

Ice nucleating particle

Subset of the aerosol population that facilitate cloud ice crystal formation.

Large eddy simulation

Category of numerical models that solve the fluid dynamics equations by computing the large‐scale motion of turbulent flow.

Liquid water path

Column‐integrated cloud liquid water content, that is, mass of cloud liquid water per unit surface area.

Optical depth

Column‐integrated extinction cross section. Can be defined for any source of extinction in the atmosphere, including aerosols and clouds.

Primary aerosol

Aerosols that are emitted into the atmosphere directly as solid or liquid particulates.

Radiative forcing

Imbalance in the Earth's energy budget caused by human activities or volcanic eruptions, or changes in the output of the Sun or the orbital parameters of the Earth.

Rapid adjustments

Subset of the responses of the atmosphere‐land‐cryosphere system to radiative forcing, which happened independently of the much slower changes in sea surface temperature.

Secondary aerosol

Aerosols formed by atmospheric chemistry from gaseous precursors.

Single scattering albedo

Ratio of scattering efficiency to extinction efficiency, where extinction is the sum of scattering and absorbing. A purely scattering particle has a single‐scattering albedo of 1, and that value decreases with increasing absorption.

Twomey effect

Increase in cloud albedo caused by an increase in cloud condensation nuclei for a fixed water content. Named after the late Sean Twomey, following Twomey (1974).

Acronyms

AeroCom

Aerosol Comparisons between Observations and Models

AERONET

AErosol RObotic NETwork

aci

Aerosol‐cloud interactions

ari

Aerosol‐radiation interactions

AOD

Aerosol optical depth

BC

Black carbon

CALIOP

Cloud‐Aerosol Lidar with Orthogonal Polarization

CCN

Cloud condensation nuclei

CERES

Clouds and the Earth's Radiant Energy System

CF

Cloud fraction

CMIP

Climate Model Intercomparison Project

ERF

Effective radiative forcing

ERFaci

Effective Radiative Forcing of Aerosol‐Cloud Interactions

ERFari

Effective Radiative Forcing of Aerosol‐Radiation Interactions

GCM

General Circulation Model

GHG

Greenhouse gas

IPCC

Intergovernmental Panel on Climate Change

IPCC AR5

5^th Assessment Report of the IPCC

LES

Large eddy simulation

LWP

Liquid water path

MAC

Max Planck Institute Aerosol Climatology

MACC

Monitoring Atmospheric Composition and Climate

MODIS

Moderate Resolution Imaging Spectroradiometer

PDRMIP

Precipitation Driver Response Model Intercomparison Project

PPE

Perturbed parameter ensemble

RF

Radiative forcing

RFaci

Radiative Forcing of Aerosol‐Cloud Interactions

RFari

Radiative Forcing of Aerosol‐Radiation Interactions

Bellouin, N. , Quaas, J. , Gryspeerdt, E. , Kinne, S. , Stier, P. , Watson‐Parris, D. , et al. (2020). Bounding global aerosol radiative forcing of climate change. Reviews of Geophysics, 58, e2019RG000660 10.1029/2019RG000660