  Schramm-Loewner Evolution (SLE) is a stochastic process that helps classify
critical statistical models using one real parameter $\kappa$. Numerical study
of SLE often involves curves that start and end on the real axis. To reduce
numerical errors in studying the critical curves which start from the real axis
and end on it, we have used hydrodynamically normalized SLE($\kappa,\rho$)
which is a stochastic differential equation that is hypothesized to govern such
curves. In this paper we directly verify this hypothesis and numerically apply
this formalism to the domain wall curves of the Abelian Sandpile Model (ASM)
($\kappa=2$) and critical percolation ($\kappa=6$). We observe that this method
is more reliable for analyzing interface loops.
