  We consider the discretized model of a driven string with an anharmonic
elastic energy, in a two dimensional random potential, as introduced by Rosso
and Krauth. Using finite size scaling, we numerically compute the roughness of
the string in a uniform applied force at the critical depinning threshold. By
considering a string with a net average tilt, we demonstrate that the
anharmonic elastic energy crosses the model over to the quenched KPZ
universality class, in agreement with recent theoretical predictions.
