Alessia reached its peak intensity on 27 November with winds of 85 km/h (53 mph) and a barometric pressure of 991 mbar (hPa; 29.26 inHg) and subsequently made its final landfall near Wollogorang.

On 20 November 2013, an area of low pressure, accompanied by persistent deep convection, developed over the southern Indian Ocean, roughly 1,465 km (910 mi) north of RAAF Learmonth in Western Australia.

Environmental conditions favored tropical cyclogenesis, with moderate wind shear, high sea surface temperatures, and prominent outflow that extended into the mid-latitude westerlies.

[2] Owing to increasing organization over the following day, the Joint Typhoon Warning Center (JTWC) issued a Tropical Cyclone Formation Alert for the system late on 21 November.

[3][nb 3] Subsequently, the JTWC began issuing advisories on the system under the identifier Tropical Cyclone 02S on 22 November, estimating it to have attained gale-force winds.

[6][7] The storm, having a maximum diameter of no more than 335 km (208 mi) with gale-force winds covering less than half that distance, maintained a very small central dense overcast as it approached the Kimberley region.

[6] Moving over the Joseph Bonaparte Gulf at the southern end of the Timor Sea early on 24 November, a burst in convection over Alessia's center indicated it was maintaining its intensity as a minimal tropical cyclone.

[11] Continued reorganization of the cyclone's structure took place as it accelerated east toward the Top End region, with defined banding apparent on satellite imagery and a tight circulation center seen on local radar.

[12] Alessia made landfall at 0930 UTC on 24 November near the Daly River mouth, south of Darwin, Northern Territory, before rapidly weakening to a tropical low.

[13] Moving steadily eastward across Top End, Alessia remained weak but its proximity to water allowed significant bursts of convection to develop during this time.

Once offshore, a break in the upper-level ridge previously steering the storm eastward caused a southward shift in the track, bringing it directly over Groote Eylandt for several hours.

[14] Failing to regenerate, Alessia moved eastward before doubling back to the west, passing near the Sir Edward Pellew Group of Islands on 30 November.

[28] Northern Territory Police Commissioner, John McRoberts, urged residents to heed warnings despite the generally non-threatening nature of the storm, "complacency can often be your worst enemy in these types of events.

[33] Effects across the Top End region were similar to Kimberly, some reports of gale-force winds with generally light to moderate rain,[6] peaking at 126 mm (5.0 in) along the Upper Wickham River.

[38] Following Alessia's reorganization over the Gulf of Carpentaria early on 27 November, a cyclone warning was raised for areas between Port Roper, Northern Territory to Karumba, Queensland, including Mornington Island.