  Sea ice attenuates waves propagating from the open ocean. Here we model the
evolution of energetic unidirectional random waves in the marginal ice zone
with a nonlinear Schr\"{o}dinger equation, with a frequency dependent
dissipative term consistent with current model paradigms and recent field
observations. The preferential dissipation of high frequency components results
in a concurrent downshift of the spectral peak that leads to a less than
exponential energy decay, but at a lower rate compared to a corresponding
linear model. Attenuation and downshift contrast nonlinearity, and nonlinear
wave statistics at the edge tend to Gaussianity farther into the marginal ice
zone.
