  The topographical scattering of gravity waves is investigated using a
spectral energy balance equation that accounts for first order wave-bottom
Bragg scattering. This model represents the bottom topography and surface waves
with spectra, and evaluates a Bragg scattering source term that is
theoretically valid for small bottom and surface slopes and slowly varying
spectral properties. The robustness of the model is tested for a variety of
topographies uniform along one horizontal dimension including nearly
sinusoidal, linear ramp and step profiles. Results are compared with
reflections computed using an accurate method that applies integral matching
along vertical boundaries of a series of steps. For small bottom amplitudes,
the source term representation yields accurate reflection estimates even for a
localized scatterer. This result is proved for small bottom amplitudes $h$
relative to the mean water depth $H$. Wave reflection by small amplitude bottom
topography thus depends primarily on the bottom elevation variance at the Bragg
resonance scales, and is insensitive to the detailed shape of the bottom
profile. Relative errors in the energy reflection coefficient are found to be
typically $2h/H$.
