Originating from a disturbance near the southern tip of Baja California, it soon moved north and developed into a tropical cyclone on September 28.

Heading northward into the Gulf of California, the storm began to weaken later that day due to southwesterly wind shear and land interaction.

Heavy rainfall from Norman was reported in Colima, Jalisco, Nayarit, Sinaloa, Baja California Sur, Durango, and Zacatecas.

While located near Acapulco another burst in convection occurred on September 25, likely due to interaction with the Intertropical Convergence Zone (ITCZ).

By September 27, the system had organized deep convection and was producing tropical storm force winds, but data from scatterometers indicated that it lacked a closed circulation.

[1] Although TWOs issued on September 27 predicted a high probability for development,[4] the chances for tropical cyclogenesis was decreased later that day, due to the system's close proximity to land.

[6] Thus, Tropical Storm Norman developed at 0600 UTC, while located about 115 mi (185 km) southeast of Cabo San Lucas.

[6] However, upon developing into a tropical cyclone at 1200 UTC on September 28, Norman attained its peak intensity with maximum sustained winds of 50 mph (85 km/h).

Later on September 28, the storm entered the Gulf of California and began weakening due to a significant increase in wind shear and interaction with land.

[7] Early on September 29, the storm curved northwestward and was downgraded to a tropical depression due to difficulty in locating the center of circulation and significant disorganization.

[12] Tropical Storm Norman brought extremely heavy rains to Colima, Jalisco, Nayarit, Sinaloa, Baja California Sur, Durango, and Zacatecas.

[15] In Sinaloa, the rains caused by Norman did not represent an important contribution to the 11 dams in the state, with mean water levels rising from 42.5% to 42.6%.

At Camp Mabry in Austin, 1.38 inches (35 mm) of rain fell in a 24‑hour period, breaking a daily precipitation record set in 1985.