Inversion methods for the
data-rich, fine-scale problem
§Kalman filter: some benefit, but long lifetimes for CO2 limit savings
§Ensemble KF: full covariance matrix replaced by an approximation derived from an ensemble
§Variational data assimilation (4-D Var): an iterative solution replaces the direct matrix inversion; the adjoint model computes gradients efficiently
To get more efficient than the KF, need to dispense with the big covariance matrix -- costs too much to compute and multiply.  Get away with a Ňlow-rankÓ approximation.