  There is a plethora of 1-dimensional advected systems with an absorbing
boundary: the Toom model of anchored interfaces, the directed exclusion process
where in addition to diffusion particles and holes can jump over their right
neighbor, simple diffusion with advection, and Oslo sandpiles. All these models
share a roughness exponent of $\zeta=1/4$, while the dynamic exponent $z$
varies, depending on the observable. We show that for the first three models
$z=1$, $z=2$, and $z=1/2$ are realized, depending on the observable. The Oslo
model is apart with a conjectured dynamic exponent of $z=10/7$. Since the
height in the latter is the gradient of the position of a disordered elastic
string, this shows that $\zeta =5/4$ for a driven elastic string at depinning.
