The common stability parameters are used by both the implicit SOR solver and the explicit solver.
Threshold water depth for overland flow This is the minimum depth of water on the ground surface before overland flow is calculated. Very shallow depths of water will normally lead to numerical instabilities. The default value is 0.0001 m.
The threshold depth for overland flow should not be confused with the Detention Storage (V1 p. 268). The detention storage is related to the amount of water stored in local depression on the ground surface, which must be filled before water can flow laterally to an adjacent cell.
Threshold gradient for applying low gradient flow reduction In flat areas with ponded water, the head gradient between grid cells will be zero or nearly zero and numerical instabilities will be likely. To dampen these numerical instabilities in areas with low lateral gradients a damping function has been implemented. The damping function essentially increases the resistance to flow between cells. This makes the solution more stable and allows for larger time steps. However, the resulting gradients will be artificially high in the affected cells and the solution will begin to diverge from the Mannings solution. At very low gradients this is normally insignificant, but as the gradient increases the differences can become significant.
The damping function is controlled by a minimum gradient below which the damping function becomes active. Experience suggests that you can get reasonable results with a minimum gradient between 0.0001 and 0.001. The default minimum gradient is 0.0001. Higher values may lead to a divergence from the Mannings solution. Lower values may lead to more accurate solutions, but at the expense of smaller time steps and longer simulation times.
For a detailed discussion of the damping function see the Low gradient damping function (V1 p. 467) or Threshold gradient for overland flow (V1 p. 488).