Heavy rain has also occurred in Barrow: 0.49 inches yesterday, which is the second highest daily amount ever reported there in the month of June. This continues a pattern of above-normal precipitation in Barrow that has persisted since March of last year; in the nearly 18 months since 2013 began, Barrow has seen nearly twice its normal precipitation. The wettest periods relative to normal were March through September of last year, November and December of last year, and May 2014 through the present. I've plotted the sea level pressure anomaly in each of these periods below; note the strong similarity in terms of the above-normal pressure in the Bering Sea. It appears that this recurring anomaly has helped create a favored path for weather disturbances across the North Slope.
Update: the map below shows the correlation of annual mean sea surface temperature with annual mean sea level pressure at St Paul Island, which is located close to the center of the high pressure zone in the three maps above. This is a negative PDO pattern, and indeed the annual mean PDO index values are correlated at -0.47 with the annual mean pressure at St Paul Island. A negative PDO phase favors high pressure in the Bering Sea, although the correlation is only found in November through April.
The PDO was negative throughout 2013, so this may explain the high pressure in the Bering Sea last year, but it doesn't explain the recent persistence of the pattern, because (a) the PDO is now positive, and (b) the correlation goes away in summer. So I don't have an explanation for the remarkable persistence of the pressure anomaly; and I would suggest that the profound seasonal changes in climate dynamics make it unlikely that a single cause can be identified.