This has a non-negligible impact on overall efficiency of cooling, cost, air quality, and on acid rain. Note that size distribution affects both the forcing for a given amount of sulfate in the stratosphere, and the lifetime of sulfate and thus the amount of sulfate per unit injection. In WACCM simulations, the latter effect tends to dominate. Aerosol size is uncertain due to uncertain microphysics, particularly from small scale processes which are parameterized in climate models, as well as uncertain small scale dispersion, which influences gas and droplet concentrations thereby changing size and coagulation rates.
Metric
Radiative forcing per unit injection is wrong by a factor of 2 relative to the multi-model mean, due to difference in size distribution
Uncertainty
It is plausible that the multi-model mean could be wrong by a factor of two or more. Note that we don't yet have a well defined inter-model range for consistent scenarios. Further, even if all the models agree, none of the models capture sub-grid-scale processes; if there is inadequate mixing then models could be very wrong (though there is some evidence, e.g. Newman et al. (2001), that the plume mixes out to larger-than-grid-scale within weeks, and evidence from contrail simulations that initial mixing from aircraft wake and vortices will already mix the plume out to ~200 meters)
Decision relevance
The size distribution is a strong control on the forcing (and therefore cooling) efficiency from a given sulfate load, and as a result is a first order control on the required injection magnitude. In principle, one could simply adjust injection rate to compensate and this could be learned early in a deployment ramp-up. This would then affect various impacts which depend on injection magnitude, such as acid rain. The size distribution also controls the ratio of SW forcing to LW absorption, which itself controls the degree of stratospheric heating per unit of cooling. Adjusting the total magnitude of injection therefore does not fully compensate for changes in the size distribution. In the chance that inadequate small-scale mixing results in much larger aerosol sizes than either models predict or from volcanic eruptions, that could lead to SAI being too inefficient, or require some other way of distributing material that doesn't suffer the same limitations. Additionally, if the amount of material needed is not known within a factor of 2, it raises distrust in the modeling.