[0] <vec:mpikokkos> PetscDALETKFGetLocalizationMatrix(): LETKF localization radius: mean 4.92963, std dev 0.549623
Localization matrix Q created using PetscDALETKFGetLocalizationMatrix
PetscDA Object: 3 MPI processes
  type: letkf
  State size: 160
  Observation size: 40
  Ensemble size: 5
  Assembled: true
  Inflation: 1.
  Square root type: eigen
  Local analysis: Kokkos
  Local observations per vertex: 5
  GPU batch size: 13
  Localization matrix: set
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         : 5
  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 (5 obs per vertex)

Step    0, time  0.000  RMSE_forecast 0.00000  RMSE_analysis 0.00000 [initial]
Step    1, time  0.020  RMSE_forecast 0.00003  RMSE_analysis 0.00003
Step    2, time  0.040  RMSE_forecast 0.00005  RMSE_analysis 0.01441
Step    3, time  0.060  RMSE_forecast 0.01434  RMSE_analysis 0.01434
Step    4, time  0.080  RMSE_forecast 0.01458  RMSE_analysis 0.01186
Step    5, time  0.100  RMSE_forecast 0.01202  RMSE_analysis 0.01202
Step    6, time  0.120  RMSE_forecast 0.01226  RMSE_analysis 0.01138
Step    7, time  0.140  RMSE_forecast 0.01169  RMSE_analysis 0.01169
Step    8, time  0.160  RMSE_forecast 0.01202  RMSE_analysis 0.01176
Step    9, time  0.180  RMSE_forecast 0.01207  RMSE_analysis 0.01207
Step   10, time  0.200  RMSE_forecast 0.01236  RMSE_analysis 0.01280

Statistics (10 steps):
==================================================
  Mean RMSE (forecast) : 0.01014
  Mean RMSE (analysis) : 0.01124
  Observations used    : 5

