The amplitude ratio between surface and bedrock topography has been predicted to depend strongly on the ratio of deformational velocity to mean basal sliding velocity. Observations made prior to and during a surge of Tungnaárjökull, Vatnajökull ice cap, Iceland, allow this prediction to be tested. During the surge, the ratio of internal deformational velocity and basal sliding (slip ratio) changed from about unity to a few hundred. The amplitude ratio changed from about 0.1 to about 0.7. This increase in amplitude ratio is in good overall agreement with predictions based on an analytical perturbation analysis for a linearly viscous medium which includes the effects of horizontal deviatoric stresses on glacier flow. An increase in amplitude ratio of this magnitude is not predicted by a similarly linearized analysis that employs the commonly used shallow-ice approximation. The strong increase in transfer amplitude observed in the surge of Tungnaárjökull is a clear illustration of the effects of horizontal stress transmission on glacier flow reported here for the first time.