Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Multiengine
Confusion; Communication Breakdown
ATC Issue All Types; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued New Clearance; Flight Crew Diverted; Flight Crew Executed Go Around / Missed Approach; Flight Crew Requested ATC Assistance / Clarification
Weather; Human Factors
I was pilot monitoring and my captain was pilot flying. We were VMC conditions about to commence the approach into BIH. My captain had pointed out a few minutes prior that he could see MMH visually and it wasn't IMC. ATC cleared us for the RNAV 12 approach and he told me to cancel IFR with Oakland center. I thought that he had BIH in sight so I told Oakland center to cancel our IFR flight plan as he had requested.We began the approach VMC and descended to MDA. We noticed fog over the airport (below us) and then climbed to 13;000 feet (still VMC); and turned north. I contacted Oakland Center and told them we went missed and wanted to proceed to our alternate which was FAT. The controller was really confused and asked who cleared us for the approach and if we were VMC and had the terrain in sight. We had the mountains in sight. After several calls to him; he finally gave us an IFR clearance to proceed to our alternate FAT. Flight landed in FAT and was uneventful. FAT controller gave us phone number to call.
First Officer reported canceling IFR; performed a missed approach and requested a new clearance to their alternate.