During an El Ni¿o, an internal coastal Kelvin wave bore propagates poleward along the west coast of North America, leaving behind a steady anomalous coastal jet. A nonlinear, two-layer, f plane, shallow-water model is used to determine the amplitude change of the steady coastal current over an escarpment. As the El Ni¿o-generated warm coastal current passes the Mendocino escarpment off northern California, its amplitude is marginally enhanced. In contrast, for a cold coastal current, the amplitude will be reduced north of the Mendocino escarpment. When the Kelvin wave bore travels over a depth increase, the amplitude change is predicted to be much larger than over a depth decrease (as in the case of the Mendocino escarpment). This model is also applicable to bottom water flowing equatorward along a western boundary. In this case, much larger amplitude changes are found. ¿ 1997 American Geophysical Union