Kd vs M

There are two main versions of the excess shear, erodibility equation. The one used in the Parthenaides (1965) (the "dimensonless" form) equation normalizes the excess shear by the critical shear, making the shear term dimensionless. This approach has the intuitive advantage of giving the erodibility coefficient (M) the same units (Mass/Area/Time) as the Erosion rate:

$\begin{array}{l}\displaystyle Erodibility = M \frac{(\tau - \tau_c)}{\tau_c}\end{array}$

However there is an alternate version of the excess shear equation (the "dimensional" form, where erodibility is directly proportional to the simple excess shear.

$\begin{array}{l}\displaystyle Erodibility = K_d \left(\tau - \tau_c \right)\end{array}$

The ratio of erodibility to excess shear (K_d) is also called the "erodibility coefficient", but is not the same value. This expression is more intuitive (erodibility is directly proportional to excess shear), but makes the units of the coefficient less intuitive.

Different disciplines and practitioners tend to favor the different forms of this equation. Make sure you know whether the "Erodibility Coefficient" provided is Kd or M. HEC-RAS includes the option to input either, but setting these equations equal to each other demonstrates a pretty simple conversion between the two coefficients, M is simply the product of Kd and τ_c:

$\begin{array}{l}\displaystyle M\frac{(\tau - \tau_c)}{\tau_c} = K_d(\tau - \tau_c) \vspace{1} M = K_d\tau_c\end{array}$

The 1D sediment calculations in HEC-RAS use the dimensionless (M) form of the excess shear equation, so if users enter Kd, HEC-RAS converts it to M. HEC-RAS converts Kd to M as it writes the data file, so if you open the HDF file the Kd parameters in the interface will not match those written.