Base level of a river is the lowest point to which vertical erosion occurs. It is usually confined to sea level.
A Knickpoint is a sudden change/break in gradient along the long profile of a river. Once a knickpoint is formed the energy of the falling river increases, a process known as rejuvenation.
Knickpoints are accountable for the formation of waterfalls. When a river flows along a knickpoint such as a fault, a waterfall is formed. In addition, if softer rock is overlained by hard rock, erosion will be concentrated along the soft stratum which leaves the river falling over the now hanging hard rock (knickpoint). Waterfalls are typically formed this way.
Knickpoints and Rejuvenation can form as a result of:
Faults
Fault results in up and down throws of land
Isostatic Changes
This involves the rebounding of land once ice that formerly depressed it thawed.
Eustatic Changes
This is the change in sea level. When sea levels drop the base level also drops and the energy of the river increases.
Hard rock underlying soft rock
This causes the river to erode the soft rock leaving the hard rock as a knickpoint.
Grade
A river is in dynamic equilibrium, meaning that the river must change its behavior following any changes along the long profile.