Climate model studies of the consequences of solar geoengineering are central to evaluating whether such approaches may help to reduce the harmful impacts of global warming. In this study we compare the sunshade solar geoengineering response of a perturbed parameter ensemble (PPE) of the Hadley Centre Coupled Model version 3 (HadCM3) with a multimodel ensemble (MME) by analyzing the G1 experiment from the Geoengineering Model Intercomparison Project (GeoMIP). The PPE only perturbed a small number of parameters and shares a common structure with the unperturbed HadCM3 model, and so the additional weight the PPE adds to the robustness of the common climate response features in the MME is minor. However, analysis of the PPE indicates some of the factors that drive the spread within the MME. We isolate the role of global mean temperature biases for both ensembles and find that these biases have little effect on the ensemble spread in the hydrological response but do reduce the spread in surface air temperature response, particularly at high latitudes. We investigate the role of the preindustrial climatology and find that biases here are likely a key source of ensemble spread at the zonal and grid cell level. The role of vegetation, and its response to elevated CO2 concentrations through the CO2 physiological effect and changes in plant productivity, is also investigated and proves to have a substantial effect on the terrestrial hydrological response to solar geoengineering and to be a major source of variation within the GeoMIP ensemble.