Present-day mass loss from the West Antarctic ice sheet is centred on the Amundsen Sea Embayment (ASE), primarily through ice streams, including Pine Island, Thwaites and Smith glaciers. To understand the differences in response of these ice streams, we ran a perturbed parameter ensemble, using a vertically-integrated ice flow model with adaptive mesh refinement. We generated 71 sets of three physical parameters (basal traction coefficient, ice viscosity stiffening factor and sub-shelf melt rate), which we used to simulate the ASE for 50 years. We also explored the effects of different bed geometries and basal sliding laws. The mean rate of sea-level rise across the ensemble of simulations is comparable with current observed rates for the ASE. We found evidence that grounding line dynamics are sensitive to features in the bed geometry: simulations using BedMap2 geometry resulted in a higher rate of sea-level rise than simulations using a rougher geometry, created using mass conservation. Modelled grounding-line retreat of all the three ice streams was sensitive to viscosity and basal traction, while the melt rate was more important in Pine Island and Smith glaciers, which flow through more confined ice shelves than Thwaites, which has a relatively unconfined shelf.