Two EnKF approaches
¥Serial approach  -  for each observation, update each model variable (tapering the influence of the observation to zero at a specified distance).  Used in NCAR DART.
¥Local approach - update each model variable one at a time, using all observations within a specified radius (increasing R with distance between observation and model variable) - we use this approach since it scales well on massively parallel computers
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So, we have two ways of solving the problem.
Serial approach makes the most sense when you have few obs and a large state vector
Local approach makes more sense when you have lots of obs - then itÕs much easier to parallelize the problem and it scales well on a MP system.  Mathematically, there are differences between the two (the Local approach involves some approximations), but practical experience has shown there is little or no difference in accuracy.