In times of warming in polar regions, the prediction of ice sheet discharge is of utmost importance to society, because of its impact on sea level rise. In simulations the flow rate of ice is usually implemented as proportional to the differential stress to the power of the exponent n=3. This exponent influences the softness of the modeled ice, as higher values would produce faster flow under equal stress. We show that the stress exponent, which best fits the observed state of the Greenland Ice Sheet, equals n=4. Our results, which are not dependent on a possible basal sliding component of flow, indicate that most of the interior northern ice sheet is currently frozen to bedrock, except for the large ice streams and marginal ice. Ice in the polar ice sheets flows towards the oceans under its own weight. Knowing how fast the ice flows is of crucial importance to predict future sea level rise. The flow has two components: (1) internal shearing flow of ice and (2) basal motion, which is sliding along the base of ice sheets, especially when the ice melts at this base. To determine the first component we need to know how "soft" the ice is. By considering the flow velocities at the surface of the northern Greenland Ice Sheet and calculating the stresses that cause the flow, we determined that the ice is effectively softer than is usually assumed. Previous studies indicated that the base of the ice is thawed in large parts (up to about 50%) of the Greenland Ice Sheet. Our study shows that that is probably overestimated, because these studies assumed ice to be harder than it actually is. Our new assessment reduces the area with basal motion and thus melting to about 6-13% in the Greenland study area.