  A computational strategy based on large deviation theory (LDT) is used to
study the anomalous statistical features of turbulent surface waves propagating
past an abrupt depth change created via a step in the bottom topography. The
dynamics of the outgoing waves past the step are modeled using the truncated
Korteweg-de Vries (TKdV) equation with random initial conditions at the step
drawn from the system's Gibbs invariant measure of the incoming waves. Within
the LDT framework, the probability distributions of the wave height can be
obtained via the solution of a deterministic optimization problem. Detailed
numerical tests show that this approach accurately captures the non-Gaussian
features of the wave height distributions, in particular their asymmetric tails
leading to high skewness. These calculations also give the spatio-temporal
pattern of the anomalous waves most responsible for these non-Gaussian
features. The strategy shows potential for a general class of nonlinear
Hamiltonian systems with highly non-Gaussian statistics.
