Atmospheric Data Assimilation and Quality Control
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Fig.5.2 As Fig. 5.1 for -log(probabilities).
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-A model which represents the "world" with two grid points: x = ( :~ )
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-An instrument which gives one observed value yO midway between the points.
We can interpolate a model estimate y ofthe observed value:
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y = H(x) = -Xl + -x 2
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= Hx = G D(::)
(14)
We need a probability distribution (the background pdf) to describe what we
know about x, before getting the observation. Let us suppose we have a prior estimate Xjb with error variance 0':
(15)