Direct numerical simulations of turbulent flows over rough surfaces are conducted to investigate the physics of the transitionally rough regime. Different roughness sizes are analysed within the transitional regime, while keeping the shape of the surface geometry constant. To study the effect of roughness on the flow field, a novel decomposition is used to divide the velocity into two components: a turbulent, geometry-independent contribution, and a geometry-induced contribution, whose intensity is modulated by the overlying turbulence. In the onset of the transitionally rough regime, the turbulent component remains essentially unmodified, and it is anticipated that all the roughness effects can be attributed entirely to the geometry-induced fluctuations. As the roughness size increases further, the turbulent component is also modified, and the fluid-surface interaction becomes more complex.