In a, c, e and f, the red and blue boxes represent 10Be (red) and 26Al (blue) measurements. The vertical dimension of each box represents a distinct segment of core, and vertical lines connect multiple core segments that were amalgamated for each 10Be or 26Al analysis. In most cases amalgamated segments were adjacent to each other, but in some cases (for example, the uppermost two core segments), they were separated by gaps. The width of the boxes shows measurement uncertainty (1σ; see Extended Data Tables 2 and 3) on nuclide concentrations. The thick black lines are nuclide concentrations predicted for each core segment by the best-fitting parameters of each model. b, d, f and h show the exposure history implied by the best-fitting parameters of each model compared to the LR04 oxygen isotope stack from ref. 30. Red bars represent periods of surface exposure and blue bars periods of cover by the ice sheet. a and b show model 2, which is a dynamic steady state model with 100-kyr cycles. This model has one free parameter, which is the fraction of each cycle during which the site is ice-free, and assumes zero surface erosion and 350 g cm−2 cover thickness above the bedrock surface. The best-fitting length of ice-free periods for this model is 8,000 years. All other panels show models with ice-free conditions during some or all middle and late Pleistocene interglaciations, and have two free parameters: the duration of ice-free conditions during interglaciations, and the length of an initial ice-free period in the middle or early Pleistocene. c and d show a model in which the core site is ice-free during all interglacials within the period of 100-kyr-long glacial–interglacial cycles after 1.1 Myr ago, during an (arbitrarily long) series of short interglacials during 41-kyr-long glacial–interglacial cycles before 1.1 Myr ago, and during an initial longer period of exposure in the middle Pleistocene. The best-fitting duration of ice-free conditions during interglacials for this model is 4,200 years. e and f show ice-free conditions during MIS 9, MIS 11 and MIS 13, an (arbitrarily long) period of short ice-free interglaciations during 41-kyr-long cycles before 1.1 Myr ago, and an initial period of continuous exposure in the middle Pleistocene. The best-fitting duration of ice-free conditions during interglacials for this model is 7,400 years. g and h show ice-free conditions during MIS 9, MIS 11 and MIS 13, with (arbitrarily located) occasional ice-free periods in the early and middle Pleistocene. The best-fitting duration of ice-free conditions during interglacials for this model is 18,200 years.