(UPDATE: The person who tweeted the tweet below says the Katena base has one WC135C, and a WC135W flew in on January 7. He speculates they may be deployed to monitor the Chinese nuclear testing later this month.)
The information is unconfirmed.
The WC135 Constant Phoenix is "is a special purpose aircraft derived from the Boeing C-135 and used by the United States Air Force. Its mission is to collect samples from the atmosphere for the purpose of detecting and identifying nuclear explosions." (Wiki)
There's a chatter on Twitter in Japan that one of the WC135W Constant Phoenix flew in on January 7, 2012 and landed on the Kadena US Air Base in Okinawa Prefecture.
This tweet says:
The WC135W (Contact [sic] Phoenix) flew in to Kadena on January 7. The US Air Force owns only 2 WC135W. Was that about this?
By "this", he refers to the site that has the air radiation level measurement around Fukushima I Nuclear Power Plant.
However, on checking the Kadena Air Base website, I find that one WC135 is stationed in Kadena, and operates out of Kadena.
So, I would take the tweet above to mean that the Constant Phoenix came back to the base from a mission to collect atmospheric samples for radiation somewhere. It could be Fukushima, where a spike in radioactive cesium fallout was measured on January 2, it could be North Korea which looks precarious under the new "dear leader", or could be Pakistan, or further afield.
The WC135 Constant Phoenix is "is a special purpose aircraft derived from the Boeing C-135 and used by the United States Air Force. Its mission is to collect samples from the atmosphere for the purpose of detecting and identifying nuclear explosions. It is also informally referred to as the "weather bird" or "the sniffer" by workers on the program."
The WC-135W (tail number 61-2667) is a modified C-135B. The WC-135C (tail number 62-3582) is an extensively modified former EC-135C Looking Glass aircraft. The Constant Phoenix’s modifications are primarily related to the aircraft's on-board atmospheric collection suite, which allows the mission crew to detect radioactive debris "clouds" in real time. The aircraft is equipped with external flow-through devices to collect particulates on filter paper and a compressor system for whole air samples collected in high-pressure holding spheres.
The interior seats 33 people, including the cockpit crew, maintenance personnel, and special equipment operators from the Air Force Technical Applications Center. On operational sorties, the crew is minimized to just pilots, navigator, and special equipment operators, to reduce radiation exposure to mission-essential personnel only.
The Constant Phoenix WC-135 aircraft serves as an aerial collection platform for the Air Force Technical Applications Center (AFTAC) at Patrick AFB, Florida, supporting the detection and identification of debris from nuclear weapons detonations. Two Constant Phoenix aircraft, a WC-135W (AF Serial Number 61-2667) and a WC-135C (AF Serial Number 62-3582) are currently assigned to the 45th Reconnaissance Squadron, 55th Wing at Offutt AFB, Nebraska. This mission was previously conducted by a WC-135W, AF Serial Number 61-2665, which was retired in September 1996. Previously, as many as ten WC-135B weather reconnaissance airplanes flew in support of weather analysis, nuclear detection, and other scientific research.