A large number of processes are involved in the chain from emissions of aerosol precursor gases and primary particles to impacts on cloud radiative forcing. Those processes are manifest in a number of relationships that can be expressed as factors dlnX/dlnY driving aerosol effects on cloud radiative forcing. These factors include the relationships between cloud condensation nuclei (CCN) concentration and emissions, droplet number and CCN concentration, cloud fraction and droplet number, cloud optical depth and droplet number, and cloud radiative forcing and cloud optical depth. The relationship between cloud optical depth and droplet number can be further decomposed into the sum of two terms involving the relationship of droplet effective radius and cloud liquid water path with droplet number. These relationships can be constrained using observations of recent spatial and temporal variability of these quantities. However, we are most interested in the radiative forcing since the preindustrial era. Because few relevant measurements are available from that era, relationships from recent variability have been assumed to be applicable to the preindustrial to present-day change. Our analysis of Aerosol Comparisons between Observations and Models (AeroCom) model simulations suggests that estimates of relationships from recent variability are poor constraints on relationships from anthropogenic change for some terms, with even the sign of some relationships differing in many regions. Proxies connecting recent spatial/temporal variability to anthropogenic change, or sustained measurements in regions where emissions have changed, are needed to constrain estimates of anthropogenic aerosol impacts on cloud radiative forcing.