Spinning up truth for 1000 steps...
PetscDA Object: 1 MPI process
  type: etkf
  State size: 40
  Observation size: 40
  Ensemble size: 5
  Assembled: true
  Inflation: 1.
  Square root type: eigen
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): 7 

Step    0, time  0.000  RMSE_forecast 0.00000  RMSE_analysis 0.00000  Spread 1.21961 [burn-in]
Step   11, time  0.550  RMSE_forecast 0.22601  RMSE_analysis 0.22560  Spread 0.13669
Step   22, time  1.100  RMSE_forecast 0.35594  RMSE_analysis 0.30946  Spread 0.12394
Step   33, time  1.650  RMSE_forecast 0.51756  RMSE_analysis 0.47889  Spread 0.11527
Step   44, time  2.200  RMSE_forecast 0.50767  RMSE_analysis 0.50287  Spread 0.12479
Step   55, time  2.750  RMSE_forecast 1.33733  RMSE_analysis 1.32009  Spread 0.11433
Step   66, time  3.300  RMSE_forecast 2.77948  RMSE_analysis 2.75172  Spread 0.11412
Step   77, time  3.850  RMSE_forecast 3.23808  RMSE_analysis 3.15942  Spread 0.11087
Step   88, time  4.400  RMSE_forecast 3.84820  RMSE_analysis 3.78451  Spread 0.11185
Step   99, time  4.950  RMSE_forecast 4.00994  RMSE_analysis 3.96619  Spread 0.10121
Step  110, time  5.500  RMSE_forecast 4.62201  RMSE_analysis 4.58285  Spread 0.09909
Step  112, time  5.600  RMSE_forecast 4.37918  RMSE_analysis 4.33320  Spread 0.10546

Statistics (103 forecast steps, 103 analysis steps post-burn-in):
==================================================
  Mean RMSE (forecast) : 2.21779
  Mean RMSE (analysis) : 2.18216
  Observations used    : 112

