xi
5.7.1
Individual Quality Control ....................................................... 89
5.7.2
Simultaneous Quality Control .................................................. 89
5.7.3
Variational Analysis with non-Gaussian Errors ....................... 92
5.7.4
Comparison .............................................................................. 94
5.8
Monitoring ................................................................................ 96
6
Sequential Data Assimilation for Nonlinear Dynamics: The
Ensemble Kalman Filter ........................................................ 97
GEIR EVENSEN
6.1
Introduction .............................................................................. 97
6.2
Extended Kalman filter ............................................................ 98
6.3
Ensemble Kalman Filter ......................................................... 100
6.3.1
Representation of error statistics ............................................ 101
6.3.2
Prediction of error statistics ................................................... 102
6.3.3
An analysis scheme ................................................................ 103
6.3.4
Summary ................................................................................ 105
6.4
An example ofthe analysis scheme ....................................... 106
6.5
A highly nonlinear case: the Lorenz equations ...................... 108
6.5.1
Model Equations .................................................................... 108
6.5.2
Discussion of cases ................................................................ 109
6.6
An ensemble Kalman filter for an OGCM: Preliminary results 112
6.7
Summary ................................................................................ 116
7
Assimilation of Satellite Altimetry in Ocean Models ........ 117
KEITH HAINES
7.1
Introduction ............................................................................ 117
7.2
Physical relationships between sea level and hydrography ... 117
7.3
Convergence in twin-experiment assimilation experiments .. 122
7.4
Assimilation ofTOPEX data into the OCCAM model .......... 124
7.5
Future development priorities ................................................ 128
7.6
Conclusions ............................................................................ 129
8
Ensembles, Forecasts and Predictability ............................ 131
ANTONIO NAVARRA
8.1
Introduction ............................................................................ 131
8.2
Sensitivity to initial conditions ............................................... 133
8.3
The traditional paradigm ........................................................ 135
8.4
Finite time instabilities ........................................................... 137
8.5
Ensembles .............................................................................. 139
8.6
Forecasting with ensembles ................................................... 144
8.7
Conclusions ............................................................................ 147