Find optimal fluxes u and initial CO2 field xo to minimize
subject to the dynamical constraint
where
x are state variables (CO2 concentrations),
h is a vector of measurement operators
z are the observations,
R is the covariance matrix for z,
uo is an a priori
estimate of the fluxes,
Puo is the covariance matrix for uo,
xo is an a priori
estimate of the initial concentrations,
Pxo is the covariance matrix for xo,
Fis the transition matrix (representing the transport model),
and
G distributes the current
fluxes into the bottom layer of the model