B737-800
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Aircraft Equipment Problem Less Severe; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Flight Crew Overcame Equipment Problem; Flight Crew Took Evasive Action
Aircraft; Procedure; Weather
Clean configuration. Airspeed 280 knots. Autopilot on. IMC conditions. Being radar vectored around significant squall line. Anti-ice on. Climbing to cruise altitude and passing altitude about 20;000 feet when my airspeed indicator suddenly went erratic with plus or minus several (at 30 knots greater and less than commanded) indications. Airspeed indicator never reached stick shaker or over-speed warnings limits. Immediately took control of aircraft from autopilot and crosschecked the primary flight display with the Captain and standby indicator. Recommended Captain become pilot flying as his indications were consistent with standby indicator and airspeed indicator was not as erratic as mine (more consistent with turbulent air flying in the 737). After transfer of aircraft control to Captain; I completed the Quick Reference checklist (QRC) and QRH for unreliable airspeed indicator. When double checking the pitot heat was on I notice both Engines Electronic Control (EEC) were in soft alternate mode. During the entire time the aircraft was in IMC the airspeed indicator was erratic and EEC remained in soft alternate. A few minutes later; at level off at cruising altitude (low 20;000s) and out of IMC the airspeed indicator returned to normal along with EEC. Remained clear of clouds and landed uneventfully at ZZZ1. We did not return to ZZZ after [Notifying ATC] because we were more than half way and the squall line was over ZZZ.Unknown as to why airspeed indicator was unreliable and erratic in IMC turbulent air and then returned to normal when clear of clouds. Also did not know why EEC went to soft alternate and then returned to normal.
First Officer reported air data related system failures due to suspected inflight icing conditions which diminished after leaving IMC.