Date: 201810
Local time of day: 1201-1800
Location: ZZZZ.Airport, FO
Flight conditions: IMC
Weather elements / visibility: Thunderstorm
Aircraft: B737-800
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Initial Approach
ATC / advisory: Center ZZZZ
Reporter organization: Air Carrier
Reporter function: Approach; Pilot Not Flying; Captain
Reporter qualification: Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Human factors: Situational Awareness
Second reporter function: Approach; Pilot Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence
Detector: Automation Aircraft Terrain Warning; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Executed Go Around / Missed Approach; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Requested ATC Assistance / Clarification
Contributing factors: Human Factors; Procedure; Weather
Primary problem: Procedure

Narrative: On star [arrival] for [Runway] XXR RNAV Approach; red storm cells between ZZZZZ and ZZZZZ1. While descending on VNAV PATH cleared by ATC to deviate; [we were] below 4;000 feet [and] got PULL UP red warning on Captain terrain display and PULL UP audio. First Officer had weather radar on his side; he executed Escape Maneuver. At 5;000 feet and HDG 140 with approach; flew to Initial Approach Fix ZZZZZ2 to complete RNAV XXR approach. Normal landing. [We] did not stay on STAR and RNAV course line and deviated around weather in area of terrain. [I suggest to] fly a course deviation away from runway and approach course to the northeast and then south away from weather to the south Initial Approach Fix; where no weather was depicted. Also; ask ATC if another aircraft had flown through storm cells painted on Weather radar and if ride report available. Communication was difficult; the controller not always reporting back a clearance confirmation or question on weather; so [it was] safer to go the long route rather than depend on controller for help.


Second narrative: While flying the STAR to RWY XXR; we were cleared the approach approaching ZZZZZ. Approaching ZZZZZ1 it became clear we were going to have trouble with the weather over and East of ZZZZZ2 as there were several large RED cells. We asked and were cleared to deviate for that weather... but were not given any direction or advice. At a point approximately half way from ZZZZZ1 to ZZZZZ2; we turned direct to ZZZZZ3. It was better for the weather to go direct to ZZZZZ3 and intercept the final there; so we said we were going direct ZZZZZ3. While descending in LNAV and VNAV PATH; with Flaps 5; approximately 180 knots; we got a terrain warning 'PULL UP'. So we executed a Terrain Escape. We climbed to 5;000 [feet] and notified ATC. They told us to maintain 5;000 [feet] and go to ZZZZZ4 for another approach. The next approach and landing were normalSome factors were older model weather radar; lack of ATC involvement/ warning; we could have executed missed approach sooner for the weather; we should have stayed on procedure track until above MSA. Slow down and go into holding if needed... more time to analyze the situation and avoid getting between a rock and a hard spot/ weather. Stay on procedure track until above MSA.


Synopsis: 737-800 Captain reported a Terrain Warning and executing the Escape Maneuver after maneuvering for weather without assistance from ATC.