Process-based constraints are not sufficient: evaluating their role in combination with state variable-based constraints on aerosol–cloud radiative forcing

Abstract. Atmospheric aerosols and their interactions with clouds remain one of the largest sources of uncertainty in estimates of effective radiative forcing from aerosol–cloud interactions (ΔF_aci). While perturbed parameter ensembles (PPEs) have been used to explore and constrain this uncertainty using observed state variables, recent work has proposed process-based constraints, such as the slope of the relationship between cloud droplet number concentration (N_d) and liquid water path (L), as potentially more informative indicators. Here we evaluate the effectiveness of the N_d–L slope as a process-based constraint using the UKESM1 model across three climatically distinct marine regions, and compare it with a previously established state variable-based constraint. The slope primarily constrains uncertainty associated with physical atmosphere parameters, while state-based observations constrain aerosol emissions and processes. However, the slope constraint alone produces only small reductions in N_d, L, and ΔF_aci uncertainty. Combining the slope and state-based observations further constrains ΔF_aci beyond the state-based constraint alone (up to an additional 36 % reduction in uncertainty). However, the combined constraint appears to rely on compensating parameter effects, highlighting structural limitations in the model representation of aerosol–cloud interactions. Our results show that process-based constraints provide complementary information to state-variable constraints, but cannot be used in isolation to meaningfully constrain ΔF_aci. Specifically, combining process-based and state-variable constraints reveals structural deficiencies in current climate models, indicating that reducing uncertainty in ΔF_aci ultimately requires improved representation of aerosol–cloud coupling.