ACR MLG MADE CIRCLING APCH IN WX REPORTED BELOW ARPT MINIMUMS FOR LNDG.

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WX DIVERSION TO AN ON LINE ARPT. I READ AND BRIEFED THE APCH BUT I DID NOT REF THE NOTE. THE CIRCLING MINIMUMS ARE 560 1 1/2 DAYTIME. AT NIGHT THE NOTES SPECIFY HIGHER VIS AND CEILINGS OF 2000'; 4 MI; OR 3000'; 5 MI; DEPENDING ON WHAT'S WORKING. THE PROB AROSE BECAUSE I HAD NOT USED THIS ARPT THAT MUCH. CONTRIBUTING FACTORS WERE EARLY MORNING; LONG NIGHT. I DISCOVERED IT BECAUSE ON THE DOWNWIND THE F/O ASKED ME ABOUT THE REQUIREMENTS. THE CIRCLE WAS COMPLETED SAFELY. ACTUAL WX: 1800 BROKEN; 2500 OVCST; 5 MI. WE UPDATED IT TO 1800 OVCST; 7-800 BROKEN S OF ARPT. HUMAN PERFORMANCE FACTORS: TIRED; AND AS A RESULT MY DEPTH OF ANALYSIS WAS NOT TOO GREAT. WE HAD ALREADY MISSED AT OUR DEST. AT THAT TIME OF THE MORNING A SMALL BOX WITH THE NUMBER '1' JUST DOESN'T STICK OUT. I HAD MADE AN APCH TO THIS ARPT THE PREVIOUS NIGHT. I BELIEVE AFTER CONSIDERABLE THOUGHT THAT I DID NOT THINK ABOUT A CIRCLE UNTIL ON FINAL AND THE FSS GAVE US THE CURRENT WIND. THE WT PENALTY FOR A TAILWIND IS HIGH AND HYDROPLANING IS EASY ON THIS RWY SURFACE. WITH THESE CONCERNS; I CHOSE TO CIRCLE.