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: cholesky
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 0.22423  RMSE_analysis 0.22537  Spread 0.13684
Step   22, time  1.100  RMSE_forecast 0.40737  RMSE_analysis 0.35593  Spread 0.12281
Step   33, time  1.650  RMSE_forecast 0.44021  RMSE_analysis 0.42725  Spread 0.11746
Step   44, time  2.200  RMSE_forecast 0.57957  RMSE_analysis 0.57487  Spread 0.12633
Step   55, time  2.750  RMSE_forecast 1.42650  RMSE_analysis 1.41256  Spread 0.11461
Step   66, time  3.300  RMSE_forecast 2.93639  RMSE_analysis 2.91956  Spread 0.11387
Step   77, time  3.850  RMSE_forecast 2.99173  RMSE_analysis 2.97435  Spread 0.11549
Step   88, time  4.400  RMSE_forecast 5.13715  RMSE_analysis 5.13333  Spread 0.09421
Step   99, time  4.950  RMSE_forecast 4.57854  RMSE_analysis 4.55174  Spread 0.10890
Step  110, time  5.500  RMSE_forecast 5.54694  RMSE_analysis 5.52582  Spread 0.10268
Step  112, time  5.600  RMSE_forecast 4.83874  RMSE_analysis 4.80761  Spread 0.09943

Statistics (103 forecast steps, 103 analysis steps post-burn-in):
==================================================
  Mean RMSE (forecast) : 2.50493
  Mean RMSE (analysis) : 2.48373
  Observations used    : 112

