The solution: Ensemble Kalman Filtering
1) Perturbed observations and ensembles of data assimilation
Evensen, 1994
Houtekamer and Mitchell, 1998
2) Square root filter, no need for perturbed observations:
Tippett, Anderson, Bishop, Hamill, Whitaker, 2003
Anderson, 2001
Whitaker and Hamill, 2002
Bishop, Etherton and Majumdar, 2001
3) Local Ensemble Kalman Filtering: done in local patches
Ott et al, 2003, MWR under review
Hunt et al, 2003, Tellus: 4DEnKF