 but was forecast to still be a near major hurricane strength when it passes near or over Jamaica early today, near the Cayman Islands tomorrow, and into Mexico's Yucatan Peninsula on Friday. Center Director Michael Brennan. So we have a hurricane warning in effect for Jamaica. We are expecting a storm surge of five to eight feet above normal tide levels on the coast of Jamaica, especially concerned in the areas around Kingston, those harbors and on the south side of the island.