Localization matrix Q created: 80x40, no localization/global (all weights = 1.0)
PetscDA Object: 1 MPI process
  type: etkf
  State size: 160
  Observation size: 40
  Ensemble size: 10
  Assembled: true
  Inflation: 1.
  Square root type: cholesky
Shallow Water [L]ETKF Example
============================
  Test case             : Dam-break
  Flux scheme           : Rusanov (1st order)
  State dimension       : 160 (80 grid points x 2 DOF)
  Observation dimension : 40
  Ensemble size         : 10
  Domain length (L)     : 80.0000
  Gravitational const   : 9.8100
  Time step (dt)        : 0.0200
  Total steps           : 10
  Observation frequency : 2
  Observation noise std : 0.030
  Random seed           : 12345
  Localization          : None/Global (7 obs per vertex)

Step    0, time  0.000  RMSE_forecast 0.00000  RMSE_analysis 0.00000 [initial]
Step    1, time  0.020  RMSE_forecast 0.00002  RMSE_analysis 0.00002
Step    2, time  0.040  RMSE_forecast 0.00004  RMSE_analysis 0.01665
Step    3, time  0.060  RMSE_forecast 0.01664  RMSE_analysis 0.01664
Step    4, time  0.080  RMSE_forecast 0.01682  RMSE_analysis 0.01212
Step    5, time  0.100  RMSE_forecast 0.01233  RMSE_analysis 0.01233
Step    6, time  0.120  RMSE_forecast 0.01255  RMSE_analysis 0.00716
Step    7, time  0.140  RMSE_forecast 0.00729  RMSE_analysis 0.00729
Step    8, time  0.160  RMSE_forecast 0.00740  RMSE_analysis 0.00696
Step    9, time  0.180  RMSE_forecast 0.00701  RMSE_analysis 0.00701
Step   10, time  0.200  RMSE_forecast 0.00703  RMSE_analysis 0.00799

Statistics (10 steps):
==================================================
  Mean RMSE (forecast) : 0.00871
  Mean RMSE (analysis) : 0.00942
  Observations used    : 5

