  The shoaling of surface gravity waves has been acknowledged as a mechanism of
rogue wave formation. This problem is generally reduced to water waves passing
over a step, but non-equilibrium physics allows finite slopes to be considered.
Using non-homogeneous spectral analysis of a spatially varying energy density
ratio we describe the dependence of the amplification as a function of the
slope steepness. Increasing the slope increases the amplification of rogue wave
probability, until this amplification saturates at steep slopes. In contrast,
the increase of the down slope of a subsequent de-shoal zone leads to a
monotonic decrease in the rogue wave probability, thus featuring a strong
asymmetry between shoaling and de-shoaling zones. Due to the saturation of the
rogue wave amplification at steep slopes, our model is applicable beyond its
range of validity up to a step, thus elucidating why previous models based on a
step could describe the physics of steep finite slopes. We also explain why the
rogue wave probability increases over a shoal while it is lower in shallower
water.
