The transition from Traditional Alphanumeric Codes (TACs; TEMP, SYNOP etc) to BUFR (Binary Universal Form for the Representation of meteorological data) has been going on for at least a decade. The WMO codes page and its links have a lot of information about the codes and the migration (not always up-to-date, and the "migration complete" label for November 2010 in the migration matrix was an aspiration rather than accomplished fact; there is also a new WMO Codes Registry which is still being populated). BUFR is a Table-Driven Code Form (TDCF; the other main WMO one being CREX). Such a migration involves many people in many countries and once the reports have been prepared and transmitted via the GTS (Global Telecommunication System) then the task of processing them and using them in Numerical Weather Prediction (NWP) can begin. These Wiki pages are intended to help with this task by sharing information between different centres. One important aspect is data validation, or identifying bugs and features of the BUFR reports and where necessary providing feedback to the data producers and getting errors resolved.
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For surface stations the basic content of TAC and BUFR reports is much the same (there may be higher precision for some variables in BUFR, and there is provision for more frequent reporting) - the main advantage of BUFR is the provision of extra meta-data (such as height of temperature and wind measurement and instruments used). For land stations there is explicit inclusion of position information (which has both pros and cons, see Meta-data page). Note that there are several different BUFR templates for "SYNOP" data (and that values can be set to missing) so particular meta-data items may not be available for all stations. The work on marine BUFR templates and reports is at an earlier stage than that for land stations. (Note that METAR code will be replaced by an XML based code: ICAO Meteorological Exchange Model - IWXXM. This is outside the scope of these pages.) For radiosondes there are more major changes to report structure - all levels (either up to 100 hPa or up to balloon burst) should be reported together (not as separate "Parts" for standard and significant levels). For some stations there is also a move to reporting of high resolution data (eg every two seconds during the flight) which can result in 5000 or more levels compared to 200 or so for TEMP code (all parts combined). For some stations/templates there are more meta-data and also position/time information for each level which should facilitate more accurate treatment of radiosonde drift.
A poster on the status in early June 2014 and ECMWF plans is available at UEF2014 presentations (pdf, ~10MB).
On 11 November 2014 ECMWF made a change to its global 4D-Var system to process the new BUFR reports operationally. Many are being monitored without being assimilated for now. Those assimilated initially are a) land surface reports from UK, Ireland and Netherlands, b) high resolution reports from 16 European stations plus some ASAP ships, c) WIGOS AMDAR reports. For these stations BUFR is used in preference to TAC, but if the BUFR report is missing then the TAC report will be used. Some other ECMWF systems (surface, MACC and ERA-Interim analyses) are not yet using the BUFR reports. In the coming months more BUFR surface and high-resolution radiosonde reports will be assimilated, there are no plans to assimilate reformatted TEMP reports because of the problems described in Structure.