A319
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (mon) 6
Confusion; Situational Awareness; Workload
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Airspace Structure; Human Factors; Procedure; Weather
Aircraft X departed ZZZ on the ZZZZZ departure towards ZZZZZ1. There had been 2 departures prior to the aircraft that had to deviate below my Minimum IFR Altitude for weather on the departure procedure. Before the Aircraft X departure; the D-Side had called the tower and told them that the other departing traffic had to deviate below the Minimum IFR Altitude; and recommended that Aircraft X wait on the ground; but ended up releasing the Aircraft X aircraft.  Aircraft X checked on and requested a deviation out of 9500 feet. The ZZZ radar had been out of service prior to this departure; but must was returned to service just as Aircraft X was departing at I was able to ID him out of about 8500 feet.I informed the pilot that I could not give a vector until he was out of 11000 or 12000 feet. When the pilot was above the terrain I started to give vectors to the N-NW; trying to keep the pilot in a low Minimum IFR Altitude; but also avoiding the weather. At one point I gave the pilot a 330 heading; which turned him into my 14700 foot Minimum IFR Altitude; when they were at 14100 feet. I realized my mistake and issued a low altitude alert and told the pilot to expedite the climb through 14700 feet. He responded that he was already climbing through 14700 feet. I let the pilot continue to climb above remaining terrain on the 330 heading and then turned him on course. Training was in progress on the d-side during this event. Don't depart aircraft when there is weather in the departure corridor. Give ZZZ Tower a tower radar display so they can have weather depicted to them.
A Center Controller reported they vectored an aircraft below the Minimum IFR Altitude while trying to assist them in avoiding weather.