  We report imbibition experiments investigating the effect of evaporation on
the interface roughness and mean interface height. We observe a new exponent
characterizing the scaling of the saturated surface width. Further, we argue
that evaporation can be usefully modeled by introducing a gradient in the
strength of the disorder, in analogy with the gradient percolation model of
Sapoval {\it et~al.}. By incorporating this gradient we predict a new critical
exponent and a novel scaling relation for the interface width. Both the
exponent value and the form of the scaling agree with the experimental results.
