Flow in rivers and the coastal ocean is controlled by the frictional force exerted on the water by riverbed or seabed roughness. The frictional force is typically characterized by a drag coefficient Cd, which is estimated from bulk measurements and often assumed constant. Here we demonstrate a relationship between bed roughness and water surface turbulence that can be used to make remote estimates of Cd. We observe that regions with higher bed roughness result in higher turbulent kinetic energy (TKE), which is transported upward by river boils to the water surface. We present a relationship between surface TKE and Cd, and validate this relationship by comparing remotely-sensed estimates of Cd to those from in situ measurements. Thus, our results provide an approach for estimating bottom roughness and Cd based entirely on remotely sensed data, including their spatial variability, which can improve modeling of river discharge and morphodynamics in data-poor regions.