Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Aircraft Equipment Problem Less Severe; Inflight Event / Encounter Weather / Turbulence
Flight Crew Overcame Equipment Problem; Flight Crew FLC complied w / Automation / Advisory
Aircraft
On climb out to ZZZ both airspeed disagreement cautions came on with +/- 10 knot difference between the Captain and FO (First Officer) airspeed [indicators]. Once at cruise all cautions went away and we continued. Upon descent and on the arrival we again got the 'airspeed disagreement' caution for about 5 minutes then it again disappeared. Continuing on the descent at around 16;000 ft. and in icing conditions the Captain's airspeed went to +/- 50 knots causing the throttles to chase the airspeed. I turned off the autopilot; autothrottles and both flight directors as per the QRH and quickly realized the FO side was working fine. The FO continued the descent.
Climbing out; passing approximately FL280 in IMC conditions; with the CA (Captain) flying; we received an 'IAS DISAGREE' indication. There was a split of approximately 10 KIAS between the CA and FO (First Officer) instruments with a corresponding split in Mach. I; the FO; got out the unreliable airspeed checklist in the QRH to look up the possible indications. After a few moments the indication disappeared and the IAS returned to normal. After beginning a descent the same indications returned and then disappeared as they had before. Passing approximately 16;000 ft. there was a large fluctuation in the CA's airspeed causing a large fluctuation in the autothrottles. The CA disengaged the autopilot and autothrottles. We transferred aircraft control since my indications seemed normal. The CA ran the QRH for unreliable airspeed [and] I flew the approach using the autopilot with the autothrottles disengaged to an uneventful landing.
B737 flight crew reported the Captain's airspeed indicator became unreliable and control was transferred to the First Officer.