Hurricane the storm is forecast to strengthen into a rare Category 5 storm as it veers toward the Caribbean island, delivering dangerous flash flooding and rock falls.
The cyclone, which had winds of up to 120 mph as of 06:00 GMT, is presently veering north-west in the Caribbean Sea and is expected to make landfall by midweek, based on data from weather experts.
Alerts of blackouts and disruption to utilities have been released as the hurricane brings up to 30 inches of rain and sea level surges as high as 4m above typical tides. "Take cover without delay," residents have been advised.
This hurricane is the thirteenth cyclone in the ongoing Atlantic season, which normally finishes in November.
A Category 5 cyclone is the most intense classification, with sustained winds of at least 252 km/h.
Although Melissa is expected to weaken to a category four hurricane before reaching Jamaica, experts said there was "very little practical difference in the general consequences" upon reaching the coast, and that the storm will be "equally strong" when it impacts the island.
With storm-force winds and rain already expected long before it crosses Jamaica's central region - including potentially the national capital - alerts emphasize that "safety measures need to be finalized quickly".
"A multi-day period of destructive gusts and torrential rain have begun and will cause severe and deadly rapid water accumulation and numerous mudslides," counseled climate experts.
The nation's leader Andrew Holness said: "I know that there are numerous residents who are worried, who are deeply troubled, and appropriately: concern is justified.
"But the most effective method to address anxiety and any unease and concern is to remain prepared."
Inhabitants are being told to protect their properties with sandbags and timber panels, and to accumulate necessary supplies.
Advisories are also active for regions of Haiti such as the primary urban center, the adjacent nation and eastern Cuba, where Melissa is projected to bring comparable impacts by the middle of next week.
Mudslides currently triggered by the cyclone have already killed two in the country, according to the nation's Civil Protection agency.
This weather system is projected to pass over the island nation by Wednesday before passing across the Antillas Mayores and emerging into the open ocean.
By the time it makes contact with the Caribbean nation, it is anticipated to have weakened to a Category 3 storm.
While it is difficult to link individual weather events to climate change, experts say it is making meteorological events more prevalent and more extreme.
Higher ocean heat produce additional humidity in the air, contributing to the creation of tropical cyclones.
Before the commencement of the current Atlantic hurricane season, meteorological authorities predicted higher-than-average occurrence, citing warmer seas and likely enhanced seasonal rains around African coastal regions - where tropical systems typically originate.
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