¡
¡
¡
¡
„0 
„2
„1
„3
x2
x1
x3
x0
Adjoint
Transport
Forward
Transport
Forward
Transport
Measurement
Sampling
Measurement
Sampling
ÒTrueÓ
Fluxes
Estimated
Fluxes
Modeled
Concentrations
ÒTrueÓ
Concentrations
Modeled
Measurements
ÒTrueÓ
Measurements
Assumed
Measurement
Errors
Weighted
Measurement
Residuals
D/(Error)2
Adjoint
Fluxes
= „
Flux
Update
4-D Var Iterative Optimization Procedure
Minimum of cost function J
Figure showing minimization approach with the 4-D Var method.