1 Introduction

Climate modification by solar geoengineering, or solar radiation management (SRM), is the large‐scale intentional manipulation of radiative forcing (RF) to partially and temporarily reduce anthropogenic climate change (Keith, 2000; National Research Council, 2015). A diverse set of studies have explored climate response to variations in meridional or seasonal patterns of SRM RF. Deliberate tailoring of the RF pattern could improve the ability of SRM to achieve specific climate objectives and might allow the reduction of risks or side effects (Keith & MacMartin, 2015; Kravitz et al., 2016). Using a two‐dimensional (2‐D) chemistry‐transport model (CTM) with an aerosol module, we inject SO 2 or accumulation‐mode particles at different latitudes, altitudes, and seasons, and then explore the ability to achieve a specific meridional RF profile (“controllability”) with linear combinations of these basic scenarios to provide guidance for further experiments with 3‐D high‐resolution dynamical models.

Many studies on the controllability of SRM schemes have focused on modeling with theoretical top‐of‐atmosphere RF adjustments. Using meridional and seasonal alterations of top‐of‐atmosphere RF, MacMartin et al. (2012) showed that regional variations in residual climate change could be reduced, and Kravitz et al. (2016) showed that climate uncertainties could be mitigated through dynamic adjustment of SRM schemes with feedback control. Other studies addressed polar regions, finding, for example, that high‐latitude RF could be effective in preserving the Greenland ice sheet (Caldeira & Wood, 2008). Modeling of polar RF reduction showed enhanced cooling at high latitude compared with effects at lower latitude (MacCracken et al., 2013). Regional dimming experiments near the poles revealed that appropriately designed regional solar radiation reduction was needed to preserve arctic sea ice and control northward heat transport (MacMartin et al., 2012; Tilmes et al., 2014).

Most research on specific SRM implementations has focused on increasing the stratospheric sulfate aerosol burden, in part because it is (arguably) the only SRM method with a strong natural analog that can produce relatively uniform global RF of several Wm−2 using existing technologies (National Research Council, 2015). A few studies have varied SO 2 injections or sulfate loading choosing specific meridional or seasonal variations (Ban‐Weiss & Caldeira, 2010; Haywood et al., 2013; Jackson et al., 2015; Laakso et al., 2017; Niemeier, Schmidt, & Timmreck, 2011; Robock et al., 2008; Tilmes et al., 2017). An early study demonstrated that injection of SO 2 into arctic or equatorial regions resulted in RF changes that extended beyond the regions of injection, causing temperature decrease as well as changes in general circulation pattern and the hydrological cycle (Robock et al., 2008). SO 2 injection above Svalbard with injection amount adjusted annually based on a model predictive control algorithm was shown to preserve the arctic sea ice (Jackson et al., 2015), and SO 2 injection into the stratosphere of either the entire northern or southern hemisphere was shown to cause different impacts on Sahel vegetation (Haywood et al., 2013). Other studies explored global impacts, finding, for example, that specified poleward‐peaked aerosol loading was necessary to achieve a climate more similar to the preindustrial one (Ban‐Weiss & Caldeira, 2010). Exploration of SO 2 injections into various meridional, zonal, and altitudinal bands found that RF efficacy (RF per unit injection rate) could be increased by decreasing injection rate, limiting the zonal and meridional extents of the injection band, and increasing the injection altitude (Heckendorn et al., 2009; Niemeier & Timmreck, 2015), but these studies did not try to achieve specific control of RF spatial profiles consistent with those used in studies described in the preceding paragraph. Recent WACCM studies did address this issue, albeit with injections at a limited number of locations (Kravitz et al., 2017; MacMartin et al., 2017; Tilmes et al., 2017).

The uncertainty in predicting RF for a given SO 2 injection scenario is highlighted by results from the Geoengineering Model Intercomparison Project (GeoMIP). Kashimura et al. (2017) found substantial intermodel disagreement when they examined results from the GeoMIP G4 simulations, which specify a 5 Mt yr−1 SO 2 injection, finding that the globally and temporally averaged forcing varied widely from about −3.6 to −1.6 Wm−2 for the six models studied. Large intermodel disagreement in aerosol optical depth also existed due to differences in model transport and different aerosol size distributions (Pitari et al., 2014). It is possible that intramodel disagreement would be reduced using state‐of‐the‐art 3‐D high‐resolution dynamical models. Such models are, however, computationally expensive, so that it is not practical to simulate the wide range of injection scenarios relevant to assessing the controllability of RF.

The injection of H 2 SO 4 vapor into an aircraft wake was proposed by Pierce et al. (2010) to avoid inefficiently large particles produced by SO 2 injection. Pierce et al. used a plume model to account for the rapid nucleation and coagulation of aerosol particles in an expanding aircraft plume, finding that this method could keep the global aerosol size distribution closer to optimal, reducing the flux of sulfur required for a given RF and producing a more linear response of RF to injection flux. English et al. (2012) modeled injection of H 2 SO 4 evenly mixed over a GCM grid box and found no benefit over SO 2 injection, a result that does not contradict Pierce et al. (2010) because the production of new appropriately sized accumulation‐mode particles depends on the rapid formation of new aerosols in the high‐concentration conditions of an expanding plume. Benduhn et al. (2016) modeled possible stratospheric aircraft injection conditions and confirmed that conditions used by Pierce et al. (2010) could produce a radiatively effective aerosol size distribution. Yet no studies have tested the Pierce et al. H 2 SO 4 scheme in a GCM. For convenience, we will hereafter refer to injection of accumulation‐mode particles that might be produced by injecting H 2 SO 4 into an aircraft wake simply as “accumulation mode sulfate (AM‐H 2 SO 4 )” injection.

The controllability of SRM RF using injections of either SO 2 or AM‐H 2 SO 4 is therefore a vital but inadequately understood link between studies of the climate's response to specified changes in RF and understanding of stratospheric aerosol evolution based on observations and models. Despite the importance of this link, there are no systematic parametric studies of the controllability of RF using sulfate aerosol including in the recent Whole Atmosphere Community Climate Model (WACCM) study (Tilmes et al., 2017). We suspect that this is, in part, because GCMs with comprehensive treatments of aerosols and chemistry are computationally expensive.

We choose to use a 2‐D CTM with treatment of sulfate chemistry and aerosol microphysics. Its computational efficiency allows us to systematically explore the injection parameter space, mapping the model response function in latitudinal, altitudinal, and seasonal dimensions. Our intent is to (a) provide a first systematic estimate of the controllability of RF through SO 2 injections, (b) explore AM‐H 2 SO 4 injection to avoid the approximate 30 day chemical conversion time of SO 2 into H 2 SO 4 to achieve finer temporal and spatial control in RF management, and (c) provide guidance for future modeling efforts using 3‐D high‐resolution dynamical models. Our goal is not to prescribe the “right” answer but to provide guidance to future 3‐D numerical experiments.

The range of desirable RF objectives could include achieving globally uniform RF, balancing hemispherical RF to minimize movement of the Intertropical Convergence Zone (ITCZ) and adjust the precipitation centroid, creating more RF reductions around the polar or tropical regions, and creating peak RF during polar summers to maximize the ice‐albedo response and preserve sea ice with minimal total RF (Kravitz et al., 2016). Our goal is not to address the appropriate goal of RF manipulation, but rather to understand the feasibility and limits to RF control.