The data set was produced for the work detailed in ''The response of ice sheets to climate variability'' by K Snow et al (2017, Geophys Research Letters). A coupled ice sheet-ocean model is configured in an idealised setting with an inland-deepening bedrock, forced by far-field hydrographic profiles representative of the Amundsen Sea continental shelf. Similar to observed variability, the thermocline depth in the far-field is moved up and down on various times scales as detailed in the publication, with periods ranging from 2 to ~50 years. Bedrock elevation is provided, and annual melt rate and ice thickness (or sub-annual for short time scales) is provided as well for each forcing period. In addition, similar experiments were carried out with an ice-only model with parameterised forcing. These outputs are provided too.