Roughness length is related to the friction experienced by water (or air) as it flows over a surface. This is the friction parameter preferred by the hydrodynamic modelling team associated with the Mā te haumaru ō te wai project. The modelling team prefers roughness length over Manning's n as it varies less with water depth.

Introduction

The starting assumption is that roughness length is related to some combination of the mean height of any ground cover and the standard deviation of the ground / ground cover in each pixel / grid cell.

The standard deviation and mean height are calculated by filtering the LiDAR points to include the classifications specified in the instruction file (I.e. ground, vegetation and buildings). The standard deviation is simply the standard deviation of the remaining points, while the mean height is defined in relation to the hydrodynamically conditioned DEM again specified in the instruction file.

Equations

zo = min(std/a, height/b)/c

The rational used for this equation is that standard deviation indicates roughness when the height variations of the points is close to the ground, but in instances of a building or forest the roof / canopy standard deviation is not relevant to the ground level roughness. In this case the structure height is used as a proxy instead.

Initial values of a=3, b=6, and c=10 have been used. These will be tuned in future.