The closest a man or woman has gotten to walking on water, is by water skiing barefoot. The difference between a walker and skier, is speed. If someone stepped off a speed boat moving very fast, he may manage a couple of steps. Of course, this would not end well and may result in serious injury. Water is like wet cement to speeding bodies and objects, due to hydrodynamic resistance. It is this property that makes surfing possible.
Water resists deep penetration by speeding objects. A small platform or bare feet, will support a rider with speed. This platform may be in any form that resists deep water penetration. A flat bottom produces the best results. The platform acts as a wing and generates lift . Flotation can be minimized with a power source for speed. Flotation is support my displacement, hydrodynamic lift is support by pressure. Thus a flat short board is the most popular surfboard today.
Movement through water also produces lateral hydrodynamic resistance. This is called wave making resistance. Boats and ships with submerged hulls, push against water or hydrodynamic resistance, constantly. This is like a paddler on a surfboard in an ocean without waves. The paddler will never get his board on a full hydrodynamic plane without a wave. His top speed is restricted like sailboats or large ships. Speed boats differ, as they possess the ability and power to rise above wave making resistance and plane on the surface with hydrodynamic lift. Surfboards are similar to speed boats. Initially both push against hydrodynamic resistance. When a surfboard planes, it rises above the lateral hydrodynamic resistance and is supported by vertical resistance or lift. Like a speed boat the bow rises above the water and the surfboard planes on its aft half.
Vessel move in water through three phases. The first phase is Displacement, the vessel moves by displacing water, forming a bow wake and a trailing wake. The second phase is called Transition. The vessel is just beginning to plane as the bow rises. For a surfboard, it is when it enters a wave just before gravity takes over. The last phase is Planning, the vessel is fully supported by hydrodynamic lift, its bow wave dissipates.
Flight has changed surfing. When surfers land after flight, either in an air drop or aerial maneuver, the surfboard goes from Planning Phase or flight mode to the Displacement Phase. The surfboard skips the Transition Phase. The flat bottom surfboard stalls when it cannot transition. The best bottom design for the Displacement Phase is a semi-displacement shape. A round or vee hull which can cushion landing and displace water are displacement shapes. A semi-displacement hull has a flat planning aft section.
Nose rocker has increased with performance surfing. Nose rocker is the bend in the tip of the surfboard which keeps the from diving under. Vertical surfing has increased the demand for more nose rocker. Rocker underside forms a bow similar to boats. The bow section is vulnerable to high impact and must remain free of the surface. When the bow is flat, it blocks water and attempts to ride on the surface. With high impact, hydrodynamic force on the nose rocker bend can push a surfboard backward and launch the rider.
In the photo below the flat bent bow is generating hydrodynamic lift. The rider is on the verge of losing control.
As rocker increases, so should the bottom roundness or vee. These designs push water out of the board's path and may avoid stalling and catapulting. The rider has a chance to complete his ride.