
Symbol  Nomenclature 

 Dimension of state vector 
 Dimension of observation vector 
 Dimension of parameter vector 
 Dimension of control vector 
 Number of observation vectors 
 Time 
 True model state vector 
 Model state vector 
 Vector field of the model 
 Initial condition for model state vector 
 Parameter vector 
 Control vector 
 Observation vector 
 Forward operator relating model state and observations 
 Model counterpart of the observation 
 Observation error vector 
 Covariance of observation error vector 
 Forecast error 
 Systematic component of forecast error 
 Model Jacobian w. R. T. 
 Model Jacobian w. R. T. 
 Sensitivity matrix w. R. T. Parameters 
 Sensitivity matrix w. R. T. Initial condition 
 Jacobian of the forward operator w. R. T. X 
 Sensitivity matrix accounting for 
 Sensitivity matrix accounting for 
 Inner product 
 Objective or cost functions 
 First variations 
 Gradients of cost functions 
 Model state transition matrix (Appendix A) 
 Matrix that determines particular solution (Appendix A) 
