Abstract: The exact theoretical expression describing the
probability distribution of nonlinear sea-surface elevations derived
from the second-order narrowband model has a cumbersome form
that requires numerical computations, not well-disposed to theoretical
or practical applications. Here, the same narrowband model is reexamined
to develop a simpler closed-form approximation suitable
for theoretical and practical applications. The salient features of the
approximate form are explored, and its relative validity is verified
with comparisons to other readily available approximations, and
oceanic data.