The major river channels are sub-aerial delta lobes. These deposited sediments which are now termed Kinderscout Grit.
The paleocurrents deposited sediments during flood events (around where the arrows are situated on the diagram) which formed the Millstone Grits.
After Woodcock & Strachen (2000) and Anderton et al (1979) (see bibliography).
See a detailed diagram of the Palaeography of the Peak District in Lower Carboniferous times on the PDNP geology fact sheets.