Date: 201902
Local time of day: 1201-1800
Location: ZZZ.Airport, US
Flight conditions: IMC
Weather elements / visibility: Icing; Rain; Snow; 1
Light: Daylight
Aircraft: B737 Next Generation Undifferentiated
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
Airspace: Class B ZZZ
ATC / advisory: Tower ZZZ
Reporter organization: Air Carrier
Reporter function: First Officer; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Human factors: Situational Awareness
Second reporter function: Captain; Pilot Not Flying
Anomaly: Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Human Factors; Weather
Primary problem: Weather

Narrative: We had multiple issues getting the Dispatch Release. We continuously updated the weather via ACARS. The weather reported was -FZRAPLSN (Light freezing rain; ice pellets; and snow). We knew that we could not take off without an allowance time for this condition. We finally got [the current] information which showed -FZRAPL. We pushed back; got type I and IV deicing and taxied out. We had an allowance time of 19 minutes so we were pressed for time. ATC gave us taxi instructions to the runway and Tower cleared us for takeoff. Takeoff was uneventful. Two other aircraft took off behind us. Later we learned that just before takeoff ATC changed the weather reported again to the -FZRAPLSN. We were not aware of this at the time. We took off with one minute remaining on the allowance time.


Second narrative: Upon arriving at the gate; I was informed [Company Computer] was down system-wide. While we waited for Dispatch to get a release and weather; for our flight; the weather deteriorated and made for an ugly afternoon. The ATIS had three types of freezing precipitation falling: -FZRAPLSN. (Light freezing rain; ice pellets; and snow) I was discussing our situation with Dispatch and awaiting an email with our release and weather package. According to the Ice Pellet Allowance Time Table Reference Card; we were unable to depart with three types of freezing precipitation. After about an hour and thirty minutes we had received our Dispatch Release and weather package via email; ATIS information came out with two types of precipitation.Light freezing rain and ice pellets. With the new ATIS; I made a call to Dispatch and received the OK to proceed with push back and deicing. We had to complete a manual weight and balance as the Gate Agent had no way to load and send us our final numbers. Once our Deice Crew started the Type 4 deicing process we had 19 minutes to get airborne. After we configured and did our appropriate checklist; we taxied out to [the runway] and departed with 18 minutes on the clock. One minute to spare. I thought we had all our i's dotted and t's crossed. However; on climb out; as I was monitoring the company frequency; I heard a company aircraft say they had to go back to the gate due to three types of precipitation on the ATIS.I requested the latest ATIS over the ACARS. Yankee was now current and it did indeed state freezing rain; ice pellets and snow. The time stamp was during our taxi out. I failed to get an update prior to takeoff. Our flight was not legal for takeoff. Neither Ground nor Tower advised us of the change and I did not think to check the ATIS; as I was focused on taxiing the aircraft safely in the poor weather conditions; remaining vigilant of my surroundings.


Synopsis: B737 NG flight crew reported departing illegally due to weather.