MIAMI — Tropical Storm Nicole continued strengthening on Tuesday as Florida’s east coast prepares for a possible tropical storm or Category 1 hurricane later this week. Overnight, the National Hurricane Center nudged its predicted track north toward Melbourne, moving Miami-Dade and Broward out of the cone of uncertainty, but Nicole’s wind field is already nearly the size of the entire state, so its effects will be felt throughout Florida starting as early as Wednesday. Hurricane watches on Florida’s east coast were upgraded to warnings on Tuesday for most of the coast, except Broward and Miami…