Spinning up truth for 1000 steps...
[0] <vec:mpikokkos> PetscDALETKFGetLocalizationMatrix(): LETKF localization radius: mean 2.2, std dev 0.
Localization matrix Q created: 40 x 5
PetscDA Object: 3 MPI processes
  type: letkf
  State size: 40
  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: auto
  Localization matrix: set
Lorenz-96 LETKF Example
======================
  State dimension        : 40
  Ensemble size          : 5
  Forcing parameter (F)  : 8.0000
  Time step (dt)         : 0.0500
  Total steps            : 112
  Burn-in steps          : 10
  Spin-up steps          : 1000
  Observation frequency  : 1
  Observation noise std  : 1.000
  Ensemble init std      : 1.000
  Random seed            : 12345
  Localization (obs/vert): 5 

Step    0, time  0.000  RMSE_forecast 0.00000  RMSE_analysis 0.00000  Spread 1.07881 [burn-in]
Step   11, time  0.550  RMSE_forecast 0.28317  RMSE_analysis 0.31059  Spread 0.30573
Step   22, time  1.100  RMSE_forecast 0.29406  RMSE_analysis 0.31443  Spread 0.28839
Step   33, time  1.650  RMSE_forecast 0.57710  RMSE_analysis 0.47151  Spread 0.27668
Step   44, time  2.200  RMSE_forecast 0.40567  RMSE_analysis 0.41562  Spread 0.23945
Step   55, time  2.750  RMSE_forecast 0.32691  RMSE_analysis 0.30162  Spread 0.22197
Step   66, time  3.300  RMSE_forecast 0.34263  RMSE_analysis 0.31166  Spread 0.24455
Step   77, time  3.850  RMSE_forecast 0.40764  RMSE_analysis 0.36689  Spread 0.25965
Step   88, time  4.400  RMSE_forecast 0.32032  RMSE_analysis 0.29974  Spread 0.21059
Step   99, time  4.950  RMSE_forecast 0.43447  RMSE_analysis 0.38503  Spread 0.25953
Step  110, time  5.500  RMSE_forecast 0.47754  RMSE_analysis 0.42261  Spread 0.26530
Step  112, time  5.600  RMSE_forecast 0.41260  RMSE_analysis 0.39809  Spread 0.26215

Statistics (103 forecast steps, 103 analysis steps post-burn-in):
==================================================
  Mean RMSE (forecast) : 0.37408
  Mean RMSE (analysis) : 0.34302
  Observations used    : 112

