Dimensionality of the problem

• Number of observations: M

• Model state dimension: N

• State vector xa and xb: x = (N ´ 1)

• Observation vector: y = (M ´ 1)

• Model equivalent of the observations:

  Hxb = (M ´ 1)
  

• Observation operator H = (M ´N)

• Gain matrix K = (N´M)

• Background error covariances B = ((N´N)

• Observation error covariances R = (M´M)

• Background error in observation space HBHT = (M´M)

@ECMWF 2000

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