This dataset was created from perturbed parameter ensembles (PPEs) using the HadGEM-UKCA atmospheric composition climate model. All data needed to reproduce figures in the Regayre et al. (2020) ACP Letters article "The value of remote marine aerosol measurements for constraining radiative forcing uncertainty" are included. Other output from the PPEs can be obtained by contacting the lead author. The following data are included here: CCN measurement data degraded to match the model-measurement comparison resolution. Unconstrained and constrained CCN0.2 output from the PPE used to make Figure 1. These compressed files contain 48 .dat files. Each .dat file contains the PPE mean, variance and 95% creidble interval data. Files are named consecutively, containing data from 90oS to 90oN at 0oE, then continuing Eastward. When combined, these files provide data for each latitude/longitude pair at the N48 spatial resolution. A zip file of an netcdf file containing 26-dimensional data for parameter values, used to create the sample of 1 million model variants from our statistical emulators of model output. A zip file containing a folder of files made of one million ones and zeros that indicate the retention/rejection criteria from applying our constraint methodology for various constraint combination scenarios, for each model variant. A value of 1 indicates the model variant was retained. Data in these files is in the same order as the unconstrained sample file of parameter values. Compressed files containing global, annual mean RFaci and ERFaci values for the unconstrained set of one million model variants. The compressed netcdf files contain RF (ERF), RFaci (ERFaci) and RFari (ERFari) values.