Examples in Python from the textbook Probabilistic Forecasting and Bayesian Data Assimilation

In November 2018, I read this textbook from cover to cover and reproduced the examples to gain an understanding of data assimilation.

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Todo:

1. Check mean values for chap5ex17.
2. Complete Chapter 7 example 13
   1. Implement ESRF filter
   2. Fix the implementation of the SIR
   3. Fix ETPF 3d residual calculations
   4. Use a FORTRAN subroutine for the implicit solver
3. Check what is wrong with chapter 8 example 5.
4. Chapter 8 example 9: The matrix PP is introduced to make sure that the mean of the generated ensemble spread does not change (sum over all the ensemble members at a given spatial grid point equals zero). Is this true? Think about it.
5. Might want to implement chap8ex13 and chap8ex21 as a challenge.